research article mathematical model for elliptic torus of
TRANSCRIPT
Research ArticleMathematical Model for Elliptic Torus ofAutomotive Torque Converter and Fundamental Analysis ofIts Effect on Performance
Chunbao Liu Changsuo Liu and Wenxing Ma
School of Mechanical Science and Engineering Jilin University Changchun 13002 China
Correspondence should be addressed to Wenxing Ma mawxjlueducn
Received 15 January 2015 Accepted 21 April 2015
Academic Editor Kacem Chehdi
Copyright copy 2015 Chunbao Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Passenger car torque converters have been designed with an increasingly flatter profile in recent years for the purpose of achievinga weight saving and more compact size However a flatter design tends to result in the reduced hydrodynamic performance Toimprove its performance a new flat torus of elliptic type method concentrating on the solution to flat TC was put forward and fourtorque converters of different flatness ratios were designed to judge the superiority of the flat torus design method The internalflow characteristics were numerically investigated using CFD codes and resulted in good agreement with experimental data Theresults indicate that the main cause of this performance degradation can be attributed to deterioration of the velocity fields of thepump and a case of flatness ratio 08 illustrates the reason that the performance designed by the flat torus design method basedon the elliptic shape is more excellent than that of the traditional one Furthermore this study proposed a structure of removal ofinner ring to improve the performance of torque converter
1 Introduction
Internal combustion engine vehicles that employ automatictransmissions typically include a torque converter (TC)positioned between the engine and the transmission of thevehicle A torque converter is a fluid coupling device typicallyincluding an impeller at the input coupled to an output shaftof the engine and a turbine at the output coupled to theinput shaft of the transmission The smooth transmission oftorque is provided and torque amplification at the low speedsis accomplished with the device A pump a turbine and astator are all parts of a torque converter The working fluidin the closed system is light oil and the pump which in manyways acts as a centrifugal pump energizing the fluid while theturbine extracts the energy from the fluid
Most passenger cars with small and medium displace-ment engines have adopted a front-wheel-drive layout inrecent years and the gears of gearbox and output torque ofpassenger cars equippedwithAT are continuously increasingThese components togetherwith locking clutch and torsionalvibration damper need more space [1 2] TCs accordingly
have been designed with an increasingly narrower profilefor the purpose of achieving a smaller axial size which alsotranslates into weight savingThe TC structure is bound to beflat and the performance needs constant improvement suchas Exedy flat torque converters [3] whose maximum widthof circle is shortened to 30 but whose torque is increased to106
Several numerical and experiment attempts have beenmade to elucidate the flow characteristics inside TC passagesEjiri and Kubo [4] investigated the hydraulic performanceof a torque converter using a five-hole Pitot tube Resultsindicated that the pump is a major source of loss at the mostfrequently utilized speed ratio range Flow visualization anda three-dimensional flow analysis were used to investigatethe cause of the losses in the pump Marathe and Lakshmi-narayana [5] also obtained average and unsteady pressureand velocity data upstream and downstream of a torqueconverter pump using the high frequency response five-holeprobe Separation zones were found near the core at the0800 speed ratio and at the shell at the 0065 speed ratioThe complexity of the flow in TC has led to the increasing
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 851816 13 pageshttpdxdoiorg1011552015851816
2 Mathematical Problems in Engineering
T
W
P L1L2
S D
D0
(a) Torus
0
M
SC
h
L
Z
R
H
120579
01a
b
E
(b) Intermediate flow line
Figure 1 Dimensions in torus cross section
reliance on computational fluid dynamics (CFD) as a designtool for improving efficiency A three-dimensional transientincompressible viscous Navier-Stokes code was employedby Dong et al [6] to predict the performance of TC andnumerical solution was found to be consistently within 5of the experimental data Kim et al [7] made a performanceestimation model for a TC using correlation between theinternal flow field and energy loss coefficient Jung et al [8]performed a comparative study to investigate the effects ofdifferent methods for handling the relative motion of partsand improved the accuracy
The analysis of flow characteristic of a TC is quite complexdue to several conditions First the flow field changes largelyover the typical operating range for example incidence flowangles to all of the component blades change drastically [9]Second the flow is also turned to the transverse direction ina short distance in both the pump and turbine namely flowenters these components in the axial direction and turned tothe radial direction and then rapidly turned into the reverseaxial direction leading to further separation [10ndash13] The TCpump is therefore a complexmixed-flow variety of hydraulicturbomachine with a variety of forces acting on the fluidparticles [14 15]
Only a few analytical studies have focused on the influ-ence of flatness ratio of TC on hydrodynamic performanceEjiri and Kubo [16] manufactured and tested four TCs ofdifferent flatness ratios to evaluate the change in their overallperformance However the design method they adopted isstill a traditional torus design method which is suitable tovarious types of TCs that is the shell is firstly determinedaccording to the flow section area and then the averagepoint method is adopted to achieve the inner and middlestreamlines However the inherent defects exist such as thepoor stability of the flow area along the axial flow linethe inconsistent change in curvature and the roughness of
the flow line Furthermore the traditional defined flatnessratio always loses the details of characteristics on the wholecircle
In the present work a new design method of elliptictype has addressed the above shortcomings the performancecharacteristics of TC of flatness ratio 08 were numericallyinvestigated through the CFD approaches It has demon-strated the superiority of newmethod and also illustrated theinternal flow mechanism of performance improvement
This study is organized as follows In Section 2 a newdesign method of elliptic type concentrating on the solutionto flat TC is proposed Then the performance characteristicsof TC are investigated using CFD codes and experiment inSection 3 respectively The overall performance of differentflatness ratio and the superiority of the new method areanalyzed and discussed in Section 4 Furthermore Section 5presents a structure in which inner ring is removed Finallythe specific conclusions of this paper are given in Section 6
2 New Design Method of Flat TorqueConverter Torus
21 Parameters of the Intermediate Line Parameter In the newmethod the intermediate flow line in circle is defined as theellipse type in theROZcoordinate system the torus of TCandintermediate flow line are shown in Figure 1 the ratio of theshort axis 119886 to the long axis 119887 is defined as the flatness rationamely FR = 119886119887 while the flatness ratio was previouslydefined as the ratio of maximum width 119882 and maximumeffective circle diameter 119863
The elliptic equation of the intermediate flow line is de-fined as
1198852
1198862
+
(119877 minus ℎ)2
1198872
= 1 (1)
Mathematical Problems in Engineering 3
where 119885 = 119886 cos 120579 and 119877 = 119887 sin 120579 + ℎ (120579 is the centrifugalangle for the ellipse) 119872 is a point on the oval curve with theangle 120579 SMC line is perpendicular to the oval curve on point119872 and the coordinate of 3 points is 119878 (119885
119878 119877119878)119872 (119885
119872 119877119872
)and 119862 (119885
119862 119877119862) respectively [17 18] The normal equation is
119877119878minus 119877119872
1198862(119877119872
minus ℎ)
=
119885119878minus 119885119872
1198872119885119872
(2)
The effective diameter119863 the smallest wheel diameter1198630
and the width of the torus 119882 are known Thus the effectivetotal area of torque converter is
119865119863
=
1205871198632
4
(3)
The current cross section area 119865119872is as follows
119865119872
= 119896119865119863 (4)
where 119896 is the empirical coefficient between 0166 and 027and statistics suggest that the best value is 023 [19] Theintermediate streamlines divide current cross section madeup of the outer circle and the inner circle equally Thus point119872 would divide 119865
119872equally [20] and the equations could be
expressed as120587
cos (1205872 minus 120579)
(1198772
119878minus 1198772
119872) =
119865119872
2
120587
cos (1205872 minus 120579)
(1198772
119872minus 1198772
119862) =
119865119872
2
(5)
At themoment 119878 and119862 are a point on the outer and innercircles respectively with a certain step Δ120579 When 120579 startsfrom 0 to 2120587 the tracks of 119878 and point119862would form the outerand inner circles respectively Δ120579 becomes smaller and thedesign accuracy increases When 120579 starts from 0 and 120587 thepoint 119877
119878= ℎ the boundary of the outer circle would reach
the maximum the absolute value of 119885119878is equal to the half of
width 119882 Then the expression of 119886 is as follows
119886 =
119882 minus 1198651198982120587ℎ
2
(6)
When 120579 reaches 1205872 119877119878
= 1198632 then the expression of 119877119867is
as follows
119877119867
=radic
(
119863
2
)
2
minus
119865119898
2120587
(7)
When 120579 reaches 31205872 119877119878= 11986302 and the expression of 119877
119871is
119877119871
=radic
(
1198630
2
)
2
+
119865119898
2120587
(8)
As shown in Figure 1 the length of axial 119887 is
119887 =
119877119867
minus 119877119871
2
(9)
The center coordinate of the oval is (0 ℎ) and the expressionof ℎ is
ℎ =
119877119867
+ 119877119871
2
(10)
Table 1 Parameters of YH245 of different flatness ratios
Typea b c d
Width (119861mm) 69 635 58 525Traditional flatness ratio (119890) 028 026 024 021New flatness ratio (FR) 09 08 07 06
22 Parameters of the Outer and Inner Circles A series ofcoordinates of points 119878 and119862 which form the outer and innercircles respectively could be obtained from the parametersof the intermediate flow line the coordinatersquos expression 119877
119878
of the outer circle is
119877119878=
radic1198772
119872plusmn
119865119898
2120587radic1 + 11988741198852
1198721198864(119877119872
minus ℎ)2
(11)
According to (2) the expression of 119885119878is as follows
119885119878= 119885119872
+
(119877119878minus 119877119872
) 1198872119885119872
1198862(119877119872
minus ℎ)
(12)
When 120579 exceeds 120587 values of this formula would becomenegative otherwise they would become positive Similarlythe coordinatersquos expression 119877
119862of the inner circle can be
obtained as follows
119877119862
=radic
1198772
119872plusmn
119865119898
2120587radic1 + 11988741198852
1198721198864(119877119872
minus ℎ)2
(13)
When 120579 exceeds 120587 values of this formula would become pos-itive otherwise they would become negativeThe expressionof 119885119862is follows
119885119862
= 119885119872
minus
(119877119872
minus 119877119862) 1198872119885119872
1198862(119877119872
minus ℎ)
(14)
The torus design of elliptic typemethod could ensure thatthe design flow line and element line are perpendicular toeach other while avoiding a crowd of corrections the flowline designed is smooth and the curvature is continuousParameters of YH245 of different flatness ratios are displayedin Table 1 and 4 tori of different flatness ratio are shown inFigure 2
3 Numerical Calculation Methods andExperiment of Flat TC
31 Governing Equation We utilized large eddy simulationas it is very efficient at dealing with turbulence flow InLES an implication theory of self-similarity states that largeflow eddies depend on geometry whereas smaller ones aremore universalThis feature allows explicitly solving for largeeddies during calculation and implicitly accounting for smalleddies by using a subgrid-scale model [21] The governingequations used in the LES model were obtained by filtering
4 Mathematical Problems in Engineering
(a) 09 (b) 08 (c) 07 (d) 06
Figure 2 Tori of different flatness ratios
the time-dependent incompressible Navier-Stokes equationsas follows
120597 (120588119906119894)
120597119909119894
= 0
120597 (120588119906119894)
120597119905
+
120597 (120588119906119894119906119895)
120597119909119895
= minus
120597119901
120597119909119894
+
120597
120597119909119895
(120583
120597119906119894
120597119909119895
) +
120597120591119894119895
120597119909119895
(15)
where 119906119895 119901 and 120588 represent the filtered mean velocity
filtered pressure and density respectively the subgrid-scaleReynolds stress is
120591119894119895
= minus2V119879119878119894119895
+
1
3
120591119896119896
120575119894119895 (16)
where the rate of strain tensor 119878119894119895is
119878119894119895
=
1
2
sdot [(
120597119906119894
120597119909119895
) + (
120597119906119895
120597119909119894
)] (17)
119906119905is the subgrid-scale turbulent viscosity and was modeled
by employing the Smagorinsky model as follows
120583119905= 120588119871119904radic2119878119894119895119878119894119895 (18)
119871119904is the mixing length for subgrid-scale and is defined as
119871119904= min (119896120575 119862
11990411988113
) (19)
where 119896 is the von Karman constant and is considered asbeing 041 119862
119904is the Smagorinsky constant and is considered
as being 01
32 Computational Setup ANSYS FLUENT software wasemployed to solve the incompressible Navier-Stokes equa-tions without heat transfer [22 23] During calculation
Table 2 CFD model description
Analysis type Transient stateTurbulence model LESPressure-velocity coupling SIMPLETransient formulation Second-order implicitPump status Fixed at 2000 rpmTurbine status Varied from 0 rpm to 2000 rpmStator status Stationary
the pump and the turbine rotate along the gird interfaceaccording to a certain time step size (00005 s) The solutionwas assumed to have convergedwhen the rate of change in themass flow rate in two consecutive circulatory iterations andall normalized residuals in mass and momentum conserva-tion equations were less than 10minus4 for the differences of resultsin these criteria not obvious [24] the total time step is 200The rotational speed of pump is the same with experimentMesh interfaces were arranged on the intersecting surfacesof different impellers The properties of CFD model aresummarized in Table 2
The complex geometry of hydrodynamic elements wasaccurately represented and the computational meshes wereappropriately distributed with ANSYS ICEM computationalfluid dynamics (CFD) software to generate the structuredhexahedral grid of the entire TC Mesh-point clustering wasperformed near the boundary layer and cell deformity waschecked with the software Figure 3 describes the generationprocess of the structured grid of entire passage A meshsensitivity test in the LES model was performed to minimizethe effect of number error The number of grids is 325178715445 1378562 and 1765797 respectively
33 Experiment on Flat TC The experiment on performancecharacteristics of TC was carried out through the test
Mathematical Problems in Engineering 5
(a) (d)(c)
(b)
Figure 3 Generation process of the structured grid of entire passage (a) entire passage (b) single passage (c) single structured grid modeland (d) entire passage of the structured hexahedral
1 2 3 54
7 689
3
v v
Figure 4 Schematic diagram of test platform for hydraulic torque converter 1 drive 2 coupling 3 sensor 4 torque converter 5 loadingdevice 6 industrial control computer 7 signal converting card 8 hydraulic station 9 control cabinet
platform shown in Figure 4 by Zhejiang Torque ConverterTechnology Co Ltd in November 2011 The performanceof a TC is defined by several operating parameters that aredescribed as follows
119878119877 (Speed Ratio) Consider
SR =
119873turbine119873pump
(20)
119879119877 (Torque Ratio between the Pump and the Turbine) Con-sider
TR =
119879turbine119879pump
(21)
119862119865 (Capacity Factor) Consider
CF =
119879pump times 106
119873pump2
(22)
6 Mathematical Problems in Engineering
0123456789
0 01 019 029 039 048 06 069 074 081 0888
03 million07 million
13 million17 million
15171921232527293133
0 01 02 03 04 05 06 07 08 09
Experiment03 million07 million
13 million17 million
SR SR
Capa
city
fact
or (C
F)
Abso
lute
erro
r of C
F (
)
(a) CF and CF absolute error
1111213141516171819
0 01 02 03 04 05 06 07 08 090
05
1
15
2
25
3
0 01 019 029 039 048 06 069 074 081 088SRSR
Torq
ue ra
tio (T
R)
Abso
lute
erro
r of T
R (
)
Experiment03 million07 million
13 million17 million
03 million07 million
13 million17 million
(b) TR and TR absolute error
Figure 5 Results of CFD analysis of different mesh densities
120578 (Efficiency) Consider
120578 =
119873turbine times 119879turbine119873pump times 119879pump
= SR times TR (23)
where 119873 is the rotating speed (rpm) and 119879 is the torqueof each component To compare prediction accuracy underdifferent grid densities the absolute error of prediction isdefined as follows
119864119905=
10038161003816100381610038161003816119868TM minus 119868Exp
10038161003816100381610038161003816
119868Exptimes 100 (24)
where 119868 represents the capacity coefficient torque ratioefficiency and other physical quantities and the subscriptsTM and Exp denote the simulation and test data respectively
Figure 5 illustrates that the simulated resultsmoved closerto the experimental data with increasing element numbersOnly subtle changes were observed when element numbersincreased from 13 million to 17 million After an evaluation
of computation amount and accuracy 13 million was used insubsequent CFD simulations
4 Analysis and Discussion
41 Performance Comparison of Different Flatness Ratio Themeasured overall performance of test torque converters issummarized in Figure 6 in terms of the efficiency capacityfactor and volume flow rate under SR = 081 conditionwherevehicles are operated most frequently in driving
Overall efficiency begins to decrease from FR = 09 toFR = 06 in Figure 6(a) It decreases by no more than 10point from FR = 09 to FR = 08 but dramatically decreasesfrom FR = 08 to FR = 06 Figure 6(b) shows the computedtorque capacity coefficient and circulatory flow rate Thecapacity factor and volume flow rate begin to decrease fromFR = 08 to FR = 06 The tendency of the torquecapacity coincides relatively well with that of the volumeflow rate Figure 6 indicates a significant deterioration in itsperformance potential along with the narrower profile
Mathematical Problems in Engineering 7
75
77
79
81
83
85
87
89
05 06 07 08 09 1Flatness ratio
Ove
rall
effici
ency
()
(a) Overall efficiency
20
21
22
23
24
25
26
005
0055
006
0065
007
05 06 07 08 09 1Flatness ratio
Capa
city
fact
or (C
F)
CF
Q
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) Capacity factor and volume flow rate
Figure 6 Overall performance under SR = 081
Flatness ratio
90
92
94
96
98
05 06 07 08 09 1
PumpTurbineStator
Effici
ency
()
Figure 7 Element efficiency under SR = 081
In order to further investigate the factors influencingperformance deterioration the efficiency of elements will bethen discussed
The individual efficiencies of the pump turbine andstator (120578
119901 120578119879 and 120578
119878 resp) and the overall efficiency 120578TC are
defined by the following expressions
120578119901
=
(1199011199012
minus 1199011199011
)
1205881199081(1199031199012
1198811199012
minus 1199031199011
1198811199011
)
120578119879
=
1205881199082(11990311990521198811199052
minus 11990311990511198811199051)
(1199011199051
minus 1199011199052)
120578119878= 1 minus
(1199011199051
minus 1199011199052)
(1199011199012
minus 1199011199011
)
(25)
where subscripts 1 and 2 refer to the inlet and outlet ofelement respectively
Figure 7 displays the efficiency of elements under SR =
081 compared with Figure 6(a) the main cause of decline
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
FR = 08FR = 09
FR = 07FR = 06
Roth
alpy
(m2
s2)
Figure 8 Rothalpy change on the pressure surface of pump underSR = 081
in the overall efficiency is attributed to the pump lossHere Rothalpy is introduced to quantitatively evaluate thehydraulic loss For viscous flow the difference of parametersbetween two points on a streamline represents hydraulic lossRothalpy is defined as follows
119877 =
119875
120588
+
1
2
1205962minus
1
2
1205832 (26)
where 119875 is the pressure 120588 is the density 120596 is the relativevelocity and 120583 is the circumferential velocity
Figure 8 displays the Rothalpy change from the inlet tothe outlet on the pressure surface of the pump blades underSR = 081The leading edge corresponds to about ldquo0ndash01rdquo andthe trailing edge corresponds to about ldquo09ndash1rdquoThedecrease inRothalpy from FR = 09 to FR = 06 undoubtedly coincideswell with the pump efficiency in Figure 7
42 Performance Comparison of Two Methods Figure 9(b)shows two kinds of torus the transitional one is extractedfrom cross-sectional views of FR = 08 in Figure 9(a)
8 Mathematical Problems in Engineering
Lock-up clutch
Turbine
Pump
Stator
(a) Torus cross-sectional views
New torus methodTraditional method
Core
Shell
Inlet
Mid-chord
Outlet
(b) Two tori
Figure 9 Comparison of torus on different method
SR
09
11
13
15
17
19
21
00 01 02 03 04 05 06 07 08 09
New torus methodTraditional method
TR
(a) Torque ratio
30
40
50
60
70
80
90
02 03 04 05 06 07 08 09SR
Effici
ency
()
New torus methodTraditional method
(b) Efficiency
20
25
30
35
40
45
50
0 01 02 03 04 05 06 07 08 09
CF
SR
New torus methodTraditional method
(c) Capacity factor
Figure 10 Comparison of performance curves between two methods
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Decision SciencesAdvances in
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
2 Mathematical Problems in Engineering
T
W
P L1L2
S D
D0
(a) Torus
0
M
SC
h
L
Z
R
H
120579
01a
b
E
(b) Intermediate flow line
Figure 1 Dimensions in torus cross section
reliance on computational fluid dynamics (CFD) as a designtool for improving efficiency A three-dimensional transientincompressible viscous Navier-Stokes code was employedby Dong et al [6] to predict the performance of TC andnumerical solution was found to be consistently within 5of the experimental data Kim et al [7] made a performanceestimation model for a TC using correlation between theinternal flow field and energy loss coefficient Jung et al [8]performed a comparative study to investigate the effects ofdifferent methods for handling the relative motion of partsand improved the accuracy
The analysis of flow characteristic of a TC is quite complexdue to several conditions First the flow field changes largelyover the typical operating range for example incidence flowangles to all of the component blades change drastically [9]Second the flow is also turned to the transverse direction ina short distance in both the pump and turbine namely flowenters these components in the axial direction and turned tothe radial direction and then rapidly turned into the reverseaxial direction leading to further separation [10ndash13] The TCpump is therefore a complexmixed-flow variety of hydraulicturbomachine with a variety of forces acting on the fluidparticles [14 15]
Only a few analytical studies have focused on the influ-ence of flatness ratio of TC on hydrodynamic performanceEjiri and Kubo [16] manufactured and tested four TCs ofdifferent flatness ratios to evaluate the change in their overallperformance However the design method they adopted isstill a traditional torus design method which is suitable tovarious types of TCs that is the shell is firstly determinedaccording to the flow section area and then the averagepoint method is adopted to achieve the inner and middlestreamlines However the inherent defects exist such as thepoor stability of the flow area along the axial flow linethe inconsistent change in curvature and the roughness of
the flow line Furthermore the traditional defined flatnessratio always loses the details of characteristics on the wholecircle
In the present work a new design method of elliptictype has addressed the above shortcomings the performancecharacteristics of TC of flatness ratio 08 were numericallyinvestigated through the CFD approaches It has demon-strated the superiority of newmethod and also illustrated theinternal flow mechanism of performance improvement
This study is organized as follows In Section 2 a newdesign method of elliptic type concentrating on the solutionto flat TC is proposed Then the performance characteristicsof TC are investigated using CFD codes and experiment inSection 3 respectively The overall performance of differentflatness ratio and the superiority of the new method areanalyzed and discussed in Section 4 Furthermore Section 5presents a structure in which inner ring is removed Finallythe specific conclusions of this paper are given in Section 6
2 New Design Method of Flat TorqueConverter Torus
21 Parameters of the Intermediate Line Parameter In the newmethod the intermediate flow line in circle is defined as theellipse type in theROZcoordinate system the torus of TCandintermediate flow line are shown in Figure 1 the ratio of theshort axis 119886 to the long axis 119887 is defined as the flatness rationamely FR = 119886119887 while the flatness ratio was previouslydefined as the ratio of maximum width 119882 and maximumeffective circle diameter 119863
The elliptic equation of the intermediate flow line is de-fined as
1198852
1198862
+
(119877 minus ℎ)2
1198872
= 1 (1)
Mathematical Problems in Engineering 3
where 119885 = 119886 cos 120579 and 119877 = 119887 sin 120579 + ℎ (120579 is the centrifugalangle for the ellipse) 119872 is a point on the oval curve with theangle 120579 SMC line is perpendicular to the oval curve on point119872 and the coordinate of 3 points is 119878 (119885
119878 119877119878)119872 (119885
119872 119877119872
)and 119862 (119885
119862 119877119862) respectively [17 18] The normal equation is
119877119878minus 119877119872
1198862(119877119872
minus ℎ)
=
119885119878minus 119885119872
1198872119885119872
(2)
The effective diameter119863 the smallest wheel diameter1198630
and the width of the torus 119882 are known Thus the effectivetotal area of torque converter is
119865119863
=
1205871198632
4
(3)
The current cross section area 119865119872is as follows
119865119872
= 119896119865119863 (4)
where 119896 is the empirical coefficient between 0166 and 027and statistics suggest that the best value is 023 [19] Theintermediate streamlines divide current cross section madeup of the outer circle and the inner circle equally Thus point119872 would divide 119865
119872equally [20] and the equations could be
expressed as120587
cos (1205872 minus 120579)
(1198772
119878minus 1198772
119872) =
119865119872
2
120587
cos (1205872 minus 120579)
(1198772
119872minus 1198772
119862) =
119865119872
2
(5)
At themoment 119878 and119862 are a point on the outer and innercircles respectively with a certain step Δ120579 When 120579 startsfrom 0 to 2120587 the tracks of 119878 and point119862would form the outerand inner circles respectively Δ120579 becomes smaller and thedesign accuracy increases When 120579 starts from 0 and 120587 thepoint 119877
119878= ℎ the boundary of the outer circle would reach
the maximum the absolute value of 119885119878is equal to the half of
width 119882 Then the expression of 119886 is as follows
119886 =
119882 minus 1198651198982120587ℎ
2
(6)
When 120579 reaches 1205872 119877119878
= 1198632 then the expression of 119877119867is
as follows
119877119867
=radic
(
119863
2
)
2
minus
119865119898
2120587
(7)
When 120579 reaches 31205872 119877119878= 11986302 and the expression of 119877
119871is
119877119871
=radic
(
1198630
2
)
2
+
119865119898
2120587
(8)
As shown in Figure 1 the length of axial 119887 is
119887 =
119877119867
minus 119877119871
2
(9)
The center coordinate of the oval is (0 ℎ) and the expressionof ℎ is
ℎ =
119877119867
+ 119877119871
2
(10)
Table 1 Parameters of YH245 of different flatness ratios
Typea b c d
Width (119861mm) 69 635 58 525Traditional flatness ratio (119890) 028 026 024 021New flatness ratio (FR) 09 08 07 06
22 Parameters of the Outer and Inner Circles A series ofcoordinates of points 119878 and119862 which form the outer and innercircles respectively could be obtained from the parametersof the intermediate flow line the coordinatersquos expression 119877
119878
of the outer circle is
119877119878=
radic1198772
119872plusmn
119865119898
2120587radic1 + 11988741198852
1198721198864(119877119872
minus ℎ)2
(11)
According to (2) the expression of 119885119878is as follows
119885119878= 119885119872
+
(119877119878minus 119877119872
) 1198872119885119872
1198862(119877119872
minus ℎ)
(12)
When 120579 exceeds 120587 values of this formula would becomenegative otherwise they would become positive Similarlythe coordinatersquos expression 119877
119862of the inner circle can be
obtained as follows
119877119862
=radic
1198772
119872plusmn
119865119898
2120587radic1 + 11988741198852
1198721198864(119877119872
minus ℎ)2
(13)
When 120579 exceeds 120587 values of this formula would become pos-itive otherwise they would become negativeThe expressionof 119885119862is follows
119885119862
= 119885119872
minus
(119877119872
minus 119877119862) 1198872119885119872
1198862(119877119872
minus ℎ)
(14)
The torus design of elliptic typemethod could ensure thatthe design flow line and element line are perpendicular toeach other while avoiding a crowd of corrections the flowline designed is smooth and the curvature is continuousParameters of YH245 of different flatness ratios are displayedin Table 1 and 4 tori of different flatness ratio are shown inFigure 2
3 Numerical Calculation Methods andExperiment of Flat TC
31 Governing Equation We utilized large eddy simulationas it is very efficient at dealing with turbulence flow InLES an implication theory of self-similarity states that largeflow eddies depend on geometry whereas smaller ones aremore universalThis feature allows explicitly solving for largeeddies during calculation and implicitly accounting for smalleddies by using a subgrid-scale model [21] The governingequations used in the LES model were obtained by filtering
4 Mathematical Problems in Engineering
(a) 09 (b) 08 (c) 07 (d) 06
Figure 2 Tori of different flatness ratios
the time-dependent incompressible Navier-Stokes equationsas follows
120597 (120588119906119894)
120597119909119894
= 0
120597 (120588119906119894)
120597119905
+
120597 (120588119906119894119906119895)
120597119909119895
= minus
120597119901
120597119909119894
+
120597
120597119909119895
(120583
120597119906119894
120597119909119895
) +
120597120591119894119895
120597119909119895
(15)
where 119906119895 119901 and 120588 represent the filtered mean velocity
filtered pressure and density respectively the subgrid-scaleReynolds stress is
120591119894119895
= minus2V119879119878119894119895
+
1
3
120591119896119896
120575119894119895 (16)
where the rate of strain tensor 119878119894119895is
119878119894119895
=
1
2
sdot [(
120597119906119894
120597119909119895
) + (
120597119906119895
120597119909119894
)] (17)
119906119905is the subgrid-scale turbulent viscosity and was modeled
by employing the Smagorinsky model as follows
120583119905= 120588119871119904radic2119878119894119895119878119894119895 (18)
119871119904is the mixing length for subgrid-scale and is defined as
119871119904= min (119896120575 119862
11990411988113
) (19)
where 119896 is the von Karman constant and is considered asbeing 041 119862
119904is the Smagorinsky constant and is considered
as being 01
32 Computational Setup ANSYS FLUENT software wasemployed to solve the incompressible Navier-Stokes equa-tions without heat transfer [22 23] During calculation
Table 2 CFD model description
Analysis type Transient stateTurbulence model LESPressure-velocity coupling SIMPLETransient formulation Second-order implicitPump status Fixed at 2000 rpmTurbine status Varied from 0 rpm to 2000 rpmStator status Stationary
the pump and the turbine rotate along the gird interfaceaccording to a certain time step size (00005 s) The solutionwas assumed to have convergedwhen the rate of change in themass flow rate in two consecutive circulatory iterations andall normalized residuals in mass and momentum conserva-tion equations were less than 10minus4 for the differences of resultsin these criteria not obvious [24] the total time step is 200The rotational speed of pump is the same with experimentMesh interfaces were arranged on the intersecting surfacesof different impellers The properties of CFD model aresummarized in Table 2
The complex geometry of hydrodynamic elements wasaccurately represented and the computational meshes wereappropriately distributed with ANSYS ICEM computationalfluid dynamics (CFD) software to generate the structuredhexahedral grid of the entire TC Mesh-point clustering wasperformed near the boundary layer and cell deformity waschecked with the software Figure 3 describes the generationprocess of the structured grid of entire passage A meshsensitivity test in the LES model was performed to minimizethe effect of number error The number of grids is 325178715445 1378562 and 1765797 respectively
33 Experiment on Flat TC The experiment on performancecharacteristics of TC was carried out through the test
Mathematical Problems in Engineering 5
(a) (d)(c)
(b)
Figure 3 Generation process of the structured grid of entire passage (a) entire passage (b) single passage (c) single structured grid modeland (d) entire passage of the structured hexahedral
1 2 3 54
7 689
3
v v
Figure 4 Schematic diagram of test platform for hydraulic torque converter 1 drive 2 coupling 3 sensor 4 torque converter 5 loadingdevice 6 industrial control computer 7 signal converting card 8 hydraulic station 9 control cabinet
platform shown in Figure 4 by Zhejiang Torque ConverterTechnology Co Ltd in November 2011 The performanceof a TC is defined by several operating parameters that aredescribed as follows
119878119877 (Speed Ratio) Consider
SR =
119873turbine119873pump
(20)
119879119877 (Torque Ratio between the Pump and the Turbine) Con-sider
TR =
119879turbine119879pump
(21)
119862119865 (Capacity Factor) Consider
CF =
119879pump times 106
119873pump2
(22)
6 Mathematical Problems in Engineering
0123456789
0 01 019 029 039 048 06 069 074 081 0888
03 million07 million
13 million17 million
15171921232527293133
0 01 02 03 04 05 06 07 08 09
Experiment03 million07 million
13 million17 million
SR SR
Capa
city
fact
or (C
F)
Abso
lute
erro
r of C
F (
)
(a) CF and CF absolute error
1111213141516171819
0 01 02 03 04 05 06 07 08 090
05
1
15
2
25
3
0 01 019 029 039 048 06 069 074 081 088SRSR
Torq
ue ra
tio (T
R)
Abso
lute
erro
r of T
R (
)
Experiment03 million07 million
13 million17 million
03 million07 million
13 million17 million
(b) TR and TR absolute error
Figure 5 Results of CFD analysis of different mesh densities
120578 (Efficiency) Consider
120578 =
119873turbine times 119879turbine119873pump times 119879pump
= SR times TR (23)
where 119873 is the rotating speed (rpm) and 119879 is the torqueof each component To compare prediction accuracy underdifferent grid densities the absolute error of prediction isdefined as follows
119864119905=
10038161003816100381610038161003816119868TM minus 119868Exp
10038161003816100381610038161003816
119868Exptimes 100 (24)
where 119868 represents the capacity coefficient torque ratioefficiency and other physical quantities and the subscriptsTM and Exp denote the simulation and test data respectively
Figure 5 illustrates that the simulated resultsmoved closerto the experimental data with increasing element numbersOnly subtle changes were observed when element numbersincreased from 13 million to 17 million After an evaluation
of computation amount and accuracy 13 million was used insubsequent CFD simulations
4 Analysis and Discussion
41 Performance Comparison of Different Flatness Ratio Themeasured overall performance of test torque converters issummarized in Figure 6 in terms of the efficiency capacityfactor and volume flow rate under SR = 081 conditionwherevehicles are operated most frequently in driving
Overall efficiency begins to decrease from FR = 09 toFR = 06 in Figure 6(a) It decreases by no more than 10point from FR = 09 to FR = 08 but dramatically decreasesfrom FR = 08 to FR = 06 Figure 6(b) shows the computedtorque capacity coefficient and circulatory flow rate Thecapacity factor and volume flow rate begin to decrease fromFR = 08 to FR = 06 The tendency of the torquecapacity coincides relatively well with that of the volumeflow rate Figure 6 indicates a significant deterioration in itsperformance potential along with the narrower profile
Mathematical Problems in Engineering 7
75
77
79
81
83
85
87
89
05 06 07 08 09 1Flatness ratio
Ove
rall
effici
ency
()
(a) Overall efficiency
20
21
22
23
24
25
26
005
0055
006
0065
007
05 06 07 08 09 1Flatness ratio
Capa
city
fact
or (C
F)
CF
Q
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) Capacity factor and volume flow rate
Figure 6 Overall performance under SR = 081
Flatness ratio
90
92
94
96
98
05 06 07 08 09 1
PumpTurbineStator
Effici
ency
()
Figure 7 Element efficiency under SR = 081
In order to further investigate the factors influencingperformance deterioration the efficiency of elements will bethen discussed
The individual efficiencies of the pump turbine andstator (120578
119901 120578119879 and 120578
119878 resp) and the overall efficiency 120578TC are
defined by the following expressions
120578119901
=
(1199011199012
minus 1199011199011
)
1205881199081(1199031199012
1198811199012
minus 1199031199011
1198811199011
)
120578119879
=
1205881199082(11990311990521198811199052
minus 11990311990511198811199051)
(1199011199051
minus 1199011199052)
120578119878= 1 minus
(1199011199051
minus 1199011199052)
(1199011199012
minus 1199011199011
)
(25)
where subscripts 1 and 2 refer to the inlet and outlet ofelement respectively
Figure 7 displays the efficiency of elements under SR =
081 compared with Figure 6(a) the main cause of decline
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
FR = 08FR = 09
FR = 07FR = 06
Roth
alpy
(m2
s2)
Figure 8 Rothalpy change on the pressure surface of pump underSR = 081
in the overall efficiency is attributed to the pump lossHere Rothalpy is introduced to quantitatively evaluate thehydraulic loss For viscous flow the difference of parametersbetween two points on a streamline represents hydraulic lossRothalpy is defined as follows
119877 =
119875
120588
+
1
2
1205962minus
1
2
1205832 (26)
where 119875 is the pressure 120588 is the density 120596 is the relativevelocity and 120583 is the circumferential velocity
Figure 8 displays the Rothalpy change from the inlet tothe outlet on the pressure surface of the pump blades underSR = 081The leading edge corresponds to about ldquo0ndash01rdquo andthe trailing edge corresponds to about ldquo09ndash1rdquoThedecrease inRothalpy from FR = 09 to FR = 06 undoubtedly coincideswell with the pump efficiency in Figure 7
42 Performance Comparison of Two Methods Figure 9(b)shows two kinds of torus the transitional one is extractedfrom cross-sectional views of FR = 08 in Figure 9(a)
8 Mathematical Problems in Engineering
Lock-up clutch
Turbine
Pump
Stator
(a) Torus cross-sectional views
New torus methodTraditional method
Core
Shell
Inlet
Mid-chord
Outlet
(b) Two tori
Figure 9 Comparison of torus on different method
SR
09
11
13
15
17
19
21
00 01 02 03 04 05 06 07 08 09
New torus methodTraditional method
TR
(a) Torque ratio
30
40
50
60
70
80
90
02 03 04 05 06 07 08 09SR
Effici
ency
()
New torus methodTraditional method
(b) Efficiency
20
25
30
35
40
45
50
0 01 02 03 04 05 06 07 08 09
CF
SR
New torus methodTraditional method
(c) Capacity factor
Figure 10 Comparison of performance curves between two methods
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
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OptimizationJournal of
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International Journal of
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Operations ResearchAdvances in
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
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Algebra
Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
where 119885 = 119886 cos 120579 and 119877 = 119887 sin 120579 + ℎ (120579 is the centrifugalangle for the ellipse) 119872 is a point on the oval curve with theangle 120579 SMC line is perpendicular to the oval curve on point119872 and the coordinate of 3 points is 119878 (119885
119878 119877119878)119872 (119885
119872 119877119872
)and 119862 (119885
119862 119877119862) respectively [17 18] The normal equation is
119877119878minus 119877119872
1198862(119877119872
minus ℎ)
=
119885119878minus 119885119872
1198872119885119872
(2)
The effective diameter119863 the smallest wheel diameter1198630
and the width of the torus 119882 are known Thus the effectivetotal area of torque converter is
119865119863
=
1205871198632
4
(3)
The current cross section area 119865119872is as follows
119865119872
= 119896119865119863 (4)
where 119896 is the empirical coefficient between 0166 and 027and statistics suggest that the best value is 023 [19] Theintermediate streamlines divide current cross section madeup of the outer circle and the inner circle equally Thus point119872 would divide 119865
119872equally [20] and the equations could be
expressed as120587
cos (1205872 minus 120579)
(1198772
119878minus 1198772
119872) =
119865119872
2
120587
cos (1205872 minus 120579)
(1198772
119872minus 1198772
119862) =
119865119872
2
(5)
At themoment 119878 and119862 are a point on the outer and innercircles respectively with a certain step Δ120579 When 120579 startsfrom 0 to 2120587 the tracks of 119878 and point119862would form the outerand inner circles respectively Δ120579 becomes smaller and thedesign accuracy increases When 120579 starts from 0 and 120587 thepoint 119877
119878= ℎ the boundary of the outer circle would reach
the maximum the absolute value of 119885119878is equal to the half of
width 119882 Then the expression of 119886 is as follows
119886 =
119882 minus 1198651198982120587ℎ
2
(6)
When 120579 reaches 1205872 119877119878
= 1198632 then the expression of 119877119867is
as follows
119877119867
=radic
(
119863
2
)
2
minus
119865119898
2120587
(7)
When 120579 reaches 31205872 119877119878= 11986302 and the expression of 119877
119871is
119877119871
=radic
(
1198630
2
)
2
+
119865119898
2120587
(8)
As shown in Figure 1 the length of axial 119887 is
119887 =
119877119867
minus 119877119871
2
(9)
The center coordinate of the oval is (0 ℎ) and the expressionof ℎ is
ℎ =
119877119867
+ 119877119871
2
(10)
Table 1 Parameters of YH245 of different flatness ratios
Typea b c d
Width (119861mm) 69 635 58 525Traditional flatness ratio (119890) 028 026 024 021New flatness ratio (FR) 09 08 07 06
22 Parameters of the Outer and Inner Circles A series ofcoordinates of points 119878 and119862 which form the outer and innercircles respectively could be obtained from the parametersof the intermediate flow line the coordinatersquos expression 119877
119878
of the outer circle is
119877119878=
radic1198772
119872plusmn
119865119898
2120587radic1 + 11988741198852
1198721198864(119877119872
minus ℎ)2
(11)
According to (2) the expression of 119885119878is as follows
119885119878= 119885119872
+
(119877119878minus 119877119872
) 1198872119885119872
1198862(119877119872
minus ℎ)
(12)
When 120579 exceeds 120587 values of this formula would becomenegative otherwise they would become positive Similarlythe coordinatersquos expression 119877
119862of the inner circle can be
obtained as follows
119877119862
=radic
1198772
119872plusmn
119865119898
2120587radic1 + 11988741198852
1198721198864(119877119872
minus ℎ)2
(13)
When 120579 exceeds 120587 values of this formula would become pos-itive otherwise they would become negativeThe expressionof 119885119862is follows
119885119862
= 119885119872
minus
(119877119872
minus 119877119862) 1198872119885119872
1198862(119877119872
minus ℎ)
(14)
The torus design of elliptic typemethod could ensure thatthe design flow line and element line are perpendicular toeach other while avoiding a crowd of corrections the flowline designed is smooth and the curvature is continuousParameters of YH245 of different flatness ratios are displayedin Table 1 and 4 tori of different flatness ratio are shown inFigure 2
3 Numerical Calculation Methods andExperiment of Flat TC
31 Governing Equation We utilized large eddy simulationas it is very efficient at dealing with turbulence flow InLES an implication theory of self-similarity states that largeflow eddies depend on geometry whereas smaller ones aremore universalThis feature allows explicitly solving for largeeddies during calculation and implicitly accounting for smalleddies by using a subgrid-scale model [21] The governingequations used in the LES model were obtained by filtering
4 Mathematical Problems in Engineering
(a) 09 (b) 08 (c) 07 (d) 06
Figure 2 Tori of different flatness ratios
the time-dependent incompressible Navier-Stokes equationsas follows
120597 (120588119906119894)
120597119909119894
= 0
120597 (120588119906119894)
120597119905
+
120597 (120588119906119894119906119895)
120597119909119895
= minus
120597119901
120597119909119894
+
120597
120597119909119895
(120583
120597119906119894
120597119909119895
) +
120597120591119894119895
120597119909119895
(15)
where 119906119895 119901 and 120588 represent the filtered mean velocity
filtered pressure and density respectively the subgrid-scaleReynolds stress is
120591119894119895
= minus2V119879119878119894119895
+
1
3
120591119896119896
120575119894119895 (16)
where the rate of strain tensor 119878119894119895is
119878119894119895
=
1
2
sdot [(
120597119906119894
120597119909119895
) + (
120597119906119895
120597119909119894
)] (17)
119906119905is the subgrid-scale turbulent viscosity and was modeled
by employing the Smagorinsky model as follows
120583119905= 120588119871119904radic2119878119894119895119878119894119895 (18)
119871119904is the mixing length for subgrid-scale and is defined as
119871119904= min (119896120575 119862
11990411988113
) (19)
where 119896 is the von Karman constant and is considered asbeing 041 119862
119904is the Smagorinsky constant and is considered
as being 01
32 Computational Setup ANSYS FLUENT software wasemployed to solve the incompressible Navier-Stokes equa-tions without heat transfer [22 23] During calculation
Table 2 CFD model description
Analysis type Transient stateTurbulence model LESPressure-velocity coupling SIMPLETransient formulation Second-order implicitPump status Fixed at 2000 rpmTurbine status Varied from 0 rpm to 2000 rpmStator status Stationary
the pump and the turbine rotate along the gird interfaceaccording to a certain time step size (00005 s) The solutionwas assumed to have convergedwhen the rate of change in themass flow rate in two consecutive circulatory iterations andall normalized residuals in mass and momentum conserva-tion equations were less than 10minus4 for the differences of resultsin these criteria not obvious [24] the total time step is 200The rotational speed of pump is the same with experimentMesh interfaces were arranged on the intersecting surfacesof different impellers The properties of CFD model aresummarized in Table 2
The complex geometry of hydrodynamic elements wasaccurately represented and the computational meshes wereappropriately distributed with ANSYS ICEM computationalfluid dynamics (CFD) software to generate the structuredhexahedral grid of the entire TC Mesh-point clustering wasperformed near the boundary layer and cell deformity waschecked with the software Figure 3 describes the generationprocess of the structured grid of entire passage A meshsensitivity test in the LES model was performed to minimizethe effect of number error The number of grids is 325178715445 1378562 and 1765797 respectively
33 Experiment on Flat TC The experiment on performancecharacteristics of TC was carried out through the test
Mathematical Problems in Engineering 5
(a) (d)(c)
(b)
Figure 3 Generation process of the structured grid of entire passage (a) entire passage (b) single passage (c) single structured grid modeland (d) entire passage of the structured hexahedral
1 2 3 54
7 689
3
v v
Figure 4 Schematic diagram of test platform for hydraulic torque converter 1 drive 2 coupling 3 sensor 4 torque converter 5 loadingdevice 6 industrial control computer 7 signal converting card 8 hydraulic station 9 control cabinet
platform shown in Figure 4 by Zhejiang Torque ConverterTechnology Co Ltd in November 2011 The performanceof a TC is defined by several operating parameters that aredescribed as follows
119878119877 (Speed Ratio) Consider
SR =
119873turbine119873pump
(20)
119879119877 (Torque Ratio between the Pump and the Turbine) Con-sider
TR =
119879turbine119879pump
(21)
119862119865 (Capacity Factor) Consider
CF =
119879pump times 106
119873pump2
(22)
6 Mathematical Problems in Engineering
0123456789
0 01 019 029 039 048 06 069 074 081 0888
03 million07 million
13 million17 million
15171921232527293133
0 01 02 03 04 05 06 07 08 09
Experiment03 million07 million
13 million17 million
SR SR
Capa
city
fact
or (C
F)
Abso
lute
erro
r of C
F (
)
(a) CF and CF absolute error
1111213141516171819
0 01 02 03 04 05 06 07 08 090
05
1
15
2
25
3
0 01 019 029 039 048 06 069 074 081 088SRSR
Torq
ue ra
tio (T
R)
Abso
lute
erro
r of T
R (
)
Experiment03 million07 million
13 million17 million
03 million07 million
13 million17 million
(b) TR and TR absolute error
Figure 5 Results of CFD analysis of different mesh densities
120578 (Efficiency) Consider
120578 =
119873turbine times 119879turbine119873pump times 119879pump
= SR times TR (23)
where 119873 is the rotating speed (rpm) and 119879 is the torqueof each component To compare prediction accuracy underdifferent grid densities the absolute error of prediction isdefined as follows
119864119905=
10038161003816100381610038161003816119868TM minus 119868Exp
10038161003816100381610038161003816
119868Exptimes 100 (24)
where 119868 represents the capacity coefficient torque ratioefficiency and other physical quantities and the subscriptsTM and Exp denote the simulation and test data respectively
Figure 5 illustrates that the simulated resultsmoved closerto the experimental data with increasing element numbersOnly subtle changes were observed when element numbersincreased from 13 million to 17 million After an evaluation
of computation amount and accuracy 13 million was used insubsequent CFD simulations
4 Analysis and Discussion
41 Performance Comparison of Different Flatness Ratio Themeasured overall performance of test torque converters issummarized in Figure 6 in terms of the efficiency capacityfactor and volume flow rate under SR = 081 conditionwherevehicles are operated most frequently in driving
Overall efficiency begins to decrease from FR = 09 toFR = 06 in Figure 6(a) It decreases by no more than 10point from FR = 09 to FR = 08 but dramatically decreasesfrom FR = 08 to FR = 06 Figure 6(b) shows the computedtorque capacity coefficient and circulatory flow rate Thecapacity factor and volume flow rate begin to decrease fromFR = 08 to FR = 06 The tendency of the torquecapacity coincides relatively well with that of the volumeflow rate Figure 6 indicates a significant deterioration in itsperformance potential along with the narrower profile
Mathematical Problems in Engineering 7
75
77
79
81
83
85
87
89
05 06 07 08 09 1Flatness ratio
Ove
rall
effici
ency
()
(a) Overall efficiency
20
21
22
23
24
25
26
005
0055
006
0065
007
05 06 07 08 09 1Flatness ratio
Capa
city
fact
or (C
F)
CF
Q
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) Capacity factor and volume flow rate
Figure 6 Overall performance under SR = 081
Flatness ratio
90
92
94
96
98
05 06 07 08 09 1
PumpTurbineStator
Effici
ency
()
Figure 7 Element efficiency under SR = 081
In order to further investigate the factors influencingperformance deterioration the efficiency of elements will bethen discussed
The individual efficiencies of the pump turbine andstator (120578
119901 120578119879 and 120578
119878 resp) and the overall efficiency 120578TC are
defined by the following expressions
120578119901
=
(1199011199012
minus 1199011199011
)
1205881199081(1199031199012
1198811199012
minus 1199031199011
1198811199011
)
120578119879
=
1205881199082(11990311990521198811199052
minus 11990311990511198811199051)
(1199011199051
minus 1199011199052)
120578119878= 1 minus
(1199011199051
minus 1199011199052)
(1199011199012
minus 1199011199011
)
(25)
where subscripts 1 and 2 refer to the inlet and outlet ofelement respectively
Figure 7 displays the efficiency of elements under SR =
081 compared with Figure 6(a) the main cause of decline
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
FR = 08FR = 09
FR = 07FR = 06
Roth
alpy
(m2
s2)
Figure 8 Rothalpy change on the pressure surface of pump underSR = 081
in the overall efficiency is attributed to the pump lossHere Rothalpy is introduced to quantitatively evaluate thehydraulic loss For viscous flow the difference of parametersbetween two points on a streamline represents hydraulic lossRothalpy is defined as follows
119877 =
119875
120588
+
1
2
1205962minus
1
2
1205832 (26)
where 119875 is the pressure 120588 is the density 120596 is the relativevelocity and 120583 is the circumferential velocity
Figure 8 displays the Rothalpy change from the inlet tothe outlet on the pressure surface of the pump blades underSR = 081The leading edge corresponds to about ldquo0ndash01rdquo andthe trailing edge corresponds to about ldquo09ndash1rdquoThedecrease inRothalpy from FR = 09 to FR = 06 undoubtedly coincideswell with the pump efficiency in Figure 7
42 Performance Comparison of Two Methods Figure 9(b)shows two kinds of torus the transitional one is extractedfrom cross-sectional views of FR = 08 in Figure 9(a)
8 Mathematical Problems in Engineering
Lock-up clutch
Turbine
Pump
Stator
(a) Torus cross-sectional views
New torus methodTraditional method
Core
Shell
Inlet
Mid-chord
Outlet
(b) Two tori
Figure 9 Comparison of torus on different method
SR
09
11
13
15
17
19
21
00 01 02 03 04 05 06 07 08 09
New torus methodTraditional method
TR
(a) Torque ratio
30
40
50
60
70
80
90
02 03 04 05 06 07 08 09SR
Effici
ency
()
New torus methodTraditional method
(b) Efficiency
20
25
30
35
40
45
50
0 01 02 03 04 05 06 07 08 09
CF
SR
New torus methodTraditional method
(c) Capacity factor
Figure 10 Comparison of performance curves between two methods
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
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Differential EquationsInternational Journal of
Volume 2014
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Algebra
Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
(a) 09 (b) 08 (c) 07 (d) 06
Figure 2 Tori of different flatness ratios
the time-dependent incompressible Navier-Stokes equationsas follows
120597 (120588119906119894)
120597119909119894
= 0
120597 (120588119906119894)
120597119905
+
120597 (120588119906119894119906119895)
120597119909119895
= minus
120597119901
120597119909119894
+
120597
120597119909119895
(120583
120597119906119894
120597119909119895
) +
120597120591119894119895
120597119909119895
(15)
where 119906119895 119901 and 120588 represent the filtered mean velocity
filtered pressure and density respectively the subgrid-scaleReynolds stress is
120591119894119895
= minus2V119879119878119894119895
+
1
3
120591119896119896
120575119894119895 (16)
where the rate of strain tensor 119878119894119895is
119878119894119895
=
1
2
sdot [(
120597119906119894
120597119909119895
) + (
120597119906119895
120597119909119894
)] (17)
119906119905is the subgrid-scale turbulent viscosity and was modeled
by employing the Smagorinsky model as follows
120583119905= 120588119871119904radic2119878119894119895119878119894119895 (18)
119871119904is the mixing length for subgrid-scale and is defined as
119871119904= min (119896120575 119862
11990411988113
) (19)
where 119896 is the von Karman constant and is considered asbeing 041 119862
119904is the Smagorinsky constant and is considered
as being 01
32 Computational Setup ANSYS FLUENT software wasemployed to solve the incompressible Navier-Stokes equa-tions without heat transfer [22 23] During calculation
Table 2 CFD model description
Analysis type Transient stateTurbulence model LESPressure-velocity coupling SIMPLETransient formulation Second-order implicitPump status Fixed at 2000 rpmTurbine status Varied from 0 rpm to 2000 rpmStator status Stationary
the pump and the turbine rotate along the gird interfaceaccording to a certain time step size (00005 s) The solutionwas assumed to have convergedwhen the rate of change in themass flow rate in two consecutive circulatory iterations andall normalized residuals in mass and momentum conserva-tion equations were less than 10minus4 for the differences of resultsin these criteria not obvious [24] the total time step is 200The rotational speed of pump is the same with experimentMesh interfaces were arranged on the intersecting surfacesof different impellers The properties of CFD model aresummarized in Table 2
The complex geometry of hydrodynamic elements wasaccurately represented and the computational meshes wereappropriately distributed with ANSYS ICEM computationalfluid dynamics (CFD) software to generate the structuredhexahedral grid of the entire TC Mesh-point clustering wasperformed near the boundary layer and cell deformity waschecked with the software Figure 3 describes the generationprocess of the structured grid of entire passage A meshsensitivity test in the LES model was performed to minimizethe effect of number error The number of grids is 325178715445 1378562 and 1765797 respectively
33 Experiment on Flat TC The experiment on performancecharacteristics of TC was carried out through the test
Mathematical Problems in Engineering 5
(a) (d)(c)
(b)
Figure 3 Generation process of the structured grid of entire passage (a) entire passage (b) single passage (c) single structured grid modeland (d) entire passage of the structured hexahedral
1 2 3 54
7 689
3
v v
Figure 4 Schematic diagram of test platform for hydraulic torque converter 1 drive 2 coupling 3 sensor 4 torque converter 5 loadingdevice 6 industrial control computer 7 signal converting card 8 hydraulic station 9 control cabinet
platform shown in Figure 4 by Zhejiang Torque ConverterTechnology Co Ltd in November 2011 The performanceof a TC is defined by several operating parameters that aredescribed as follows
119878119877 (Speed Ratio) Consider
SR =
119873turbine119873pump
(20)
119879119877 (Torque Ratio between the Pump and the Turbine) Con-sider
TR =
119879turbine119879pump
(21)
119862119865 (Capacity Factor) Consider
CF =
119879pump times 106
119873pump2
(22)
6 Mathematical Problems in Engineering
0123456789
0 01 019 029 039 048 06 069 074 081 0888
03 million07 million
13 million17 million
15171921232527293133
0 01 02 03 04 05 06 07 08 09
Experiment03 million07 million
13 million17 million
SR SR
Capa
city
fact
or (C
F)
Abso
lute
erro
r of C
F (
)
(a) CF and CF absolute error
1111213141516171819
0 01 02 03 04 05 06 07 08 090
05
1
15
2
25
3
0 01 019 029 039 048 06 069 074 081 088SRSR
Torq
ue ra
tio (T
R)
Abso
lute
erro
r of T
R (
)
Experiment03 million07 million
13 million17 million
03 million07 million
13 million17 million
(b) TR and TR absolute error
Figure 5 Results of CFD analysis of different mesh densities
120578 (Efficiency) Consider
120578 =
119873turbine times 119879turbine119873pump times 119879pump
= SR times TR (23)
where 119873 is the rotating speed (rpm) and 119879 is the torqueof each component To compare prediction accuracy underdifferent grid densities the absolute error of prediction isdefined as follows
119864119905=
10038161003816100381610038161003816119868TM minus 119868Exp
10038161003816100381610038161003816
119868Exptimes 100 (24)
where 119868 represents the capacity coefficient torque ratioefficiency and other physical quantities and the subscriptsTM and Exp denote the simulation and test data respectively
Figure 5 illustrates that the simulated resultsmoved closerto the experimental data with increasing element numbersOnly subtle changes were observed when element numbersincreased from 13 million to 17 million After an evaluation
of computation amount and accuracy 13 million was used insubsequent CFD simulations
4 Analysis and Discussion
41 Performance Comparison of Different Flatness Ratio Themeasured overall performance of test torque converters issummarized in Figure 6 in terms of the efficiency capacityfactor and volume flow rate under SR = 081 conditionwherevehicles are operated most frequently in driving
Overall efficiency begins to decrease from FR = 09 toFR = 06 in Figure 6(a) It decreases by no more than 10point from FR = 09 to FR = 08 but dramatically decreasesfrom FR = 08 to FR = 06 Figure 6(b) shows the computedtorque capacity coefficient and circulatory flow rate Thecapacity factor and volume flow rate begin to decrease fromFR = 08 to FR = 06 The tendency of the torquecapacity coincides relatively well with that of the volumeflow rate Figure 6 indicates a significant deterioration in itsperformance potential along with the narrower profile
Mathematical Problems in Engineering 7
75
77
79
81
83
85
87
89
05 06 07 08 09 1Flatness ratio
Ove
rall
effici
ency
()
(a) Overall efficiency
20
21
22
23
24
25
26
005
0055
006
0065
007
05 06 07 08 09 1Flatness ratio
Capa
city
fact
or (C
F)
CF
Q
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) Capacity factor and volume flow rate
Figure 6 Overall performance under SR = 081
Flatness ratio
90
92
94
96
98
05 06 07 08 09 1
PumpTurbineStator
Effici
ency
()
Figure 7 Element efficiency under SR = 081
In order to further investigate the factors influencingperformance deterioration the efficiency of elements will bethen discussed
The individual efficiencies of the pump turbine andstator (120578
119901 120578119879 and 120578
119878 resp) and the overall efficiency 120578TC are
defined by the following expressions
120578119901
=
(1199011199012
minus 1199011199011
)
1205881199081(1199031199012
1198811199012
minus 1199031199011
1198811199011
)
120578119879
=
1205881199082(11990311990521198811199052
minus 11990311990511198811199051)
(1199011199051
minus 1199011199052)
120578119878= 1 minus
(1199011199051
minus 1199011199052)
(1199011199012
minus 1199011199011
)
(25)
where subscripts 1 and 2 refer to the inlet and outlet ofelement respectively
Figure 7 displays the efficiency of elements under SR =
081 compared with Figure 6(a) the main cause of decline
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
FR = 08FR = 09
FR = 07FR = 06
Roth
alpy
(m2
s2)
Figure 8 Rothalpy change on the pressure surface of pump underSR = 081
in the overall efficiency is attributed to the pump lossHere Rothalpy is introduced to quantitatively evaluate thehydraulic loss For viscous flow the difference of parametersbetween two points on a streamline represents hydraulic lossRothalpy is defined as follows
119877 =
119875
120588
+
1
2
1205962minus
1
2
1205832 (26)
where 119875 is the pressure 120588 is the density 120596 is the relativevelocity and 120583 is the circumferential velocity
Figure 8 displays the Rothalpy change from the inlet tothe outlet on the pressure surface of the pump blades underSR = 081The leading edge corresponds to about ldquo0ndash01rdquo andthe trailing edge corresponds to about ldquo09ndash1rdquoThedecrease inRothalpy from FR = 09 to FR = 06 undoubtedly coincideswell with the pump efficiency in Figure 7
42 Performance Comparison of Two Methods Figure 9(b)shows two kinds of torus the transitional one is extractedfrom cross-sectional views of FR = 08 in Figure 9(a)
8 Mathematical Problems in Engineering
Lock-up clutch
Turbine
Pump
Stator
(a) Torus cross-sectional views
New torus methodTraditional method
Core
Shell
Inlet
Mid-chord
Outlet
(b) Two tori
Figure 9 Comparison of torus on different method
SR
09
11
13
15
17
19
21
00 01 02 03 04 05 06 07 08 09
New torus methodTraditional method
TR
(a) Torque ratio
30
40
50
60
70
80
90
02 03 04 05 06 07 08 09SR
Effici
ency
()
New torus methodTraditional method
(b) Efficiency
20
25
30
35
40
45
50
0 01 02 03 04 05 06 07 08 09
CF
SR
New torus methodTraditional method
(c) Capacity factor
Figure 10 Comparison of performance curves between two methods
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
(a) (d)(c)
(b)
Figure 3 Generation process of the structured grid of entire passage (a) entire passage (b) single passage (c) single structured grid modeland (d) entire passage of the structured hexahedral
1 2 3 54
7 689
3
v v
Figure 4 Schematic diagram of test platform for hydraulic torque converter 1 drive 2 coupling 3 sensor 4 torque converter 5 loadingdevice 6 industrial control computer 7 signal converting card 8 hydraulic station 9 control cabinet
platform shown in Figure 4 by Zhejiang Torque ConverterTechnology Co Ltd in November 2011 The performanceof a TC is defined by several operating parameters that aredescribed as follows
119878119877 (Speed Ratio) Consider
SR =
119873turbine119873pump
(20)
119879119877 (Torque Ratio between the Pump and the Turbine) Con-sider
TR =
119879turbine119879pump
(21)
119862119865 (Capacity Factor) Consider
CF =
119879pump times 106
119873pump2
(22)
6 Mathematical Problems in Engineering
0123456789
0 01 019 029 039 048 06 069 074 081 0888
03 million07 million
13 million17 million
15171921232527293133
0 01 02 03 04 05 06 07 08 09
Experiment03 million07 million
13 million17 million
SR SR
Capa
city
fact
or (C
F)
Abso
lute
erro
r of C
F (
)
(a) CF and CF absolute error
1111213141516171819
0 01 02 03 04 05 06 07 08 090
05
1
15
2
25
3
0 01 019 029 039 048 06 069 074 081 088SRSR
Torq
ue ra
tio (T
R)
Abso
lute
erro
r of T
R (
)
Experiment03 million07 million
13 million17 million
03 million07 million
13 million17 million
(b) TR and TR absolute error
Figure 5 Results of CFD analysis of different mesh densities
120578 (Efficiency) Consider
120578 =
119873turbine times 119879turbine119873pump times 119879pump
= SR times TR (23)
where 119873 is the rotating speed (rpm) and 119879 is the torqueof each component To compare prediction accuracy underdifferent grid densities the absolute error of prediction isdefined as follows
119864119905=
10038161003816100381610038161003816119868TM minus 119868Exp
10038161003816100381610038161003816
119868Exptimes 100 (24)
where 119868 represents the capacity coefficient torque ratioefficiency and other physical quantities and the subscriptsTM and Exp denote the simulation and test data respectively
Figure 5 illustrates that the simulated resultsmoved closerto the experimental data with increasing element numbersOnly subtle changes were observed when element numbersincreased from 13 million to 17 million After an evaluation
of computation amount and accuracy 13 million was used insubsequent CFD simulations
4 Analysis and Discussion
41 Performance Comparison of Different Flatness Ratio Themeasured overall performance of test torque converters issummarized in Figure 6 in terms of the efficiency capacityfactor and volume flow rate under SR = 081 conditionwherevehicles are operated most frequently in driving
Overall efficiency begins to decrease from FR = 09 toFR = 06 in Figure 6(a) It decreases by no more than 10point from FR = 09 to FR = 08 but dramatically decreasesfrom FR = 08 to FR = 06 Figure 6(b) shows the computedtorque capacity coefficient and circulatory flow rate Thecapacity factor and volume flow rate begin to decrease fromFR = 08 to FR = 06 The tendency of the torquecapacity coincides relatively well with that of the volumeflow rate Figure 6 indicates a significant deterioration in itsperformance potential along with the narrower profile
Mathematical Problems in Engineering 7
75
77
79
81
83
85
87
89
05 06 07 08 09 1Flatness ratio
Ove
rall
effici
ency
()
(a) Overall efficiency
20
21
22
23
24
25
26
005
0055
006
0065
007
05 06 07 08 09 1Flatness ratio
Capa
city
fact
or (C
F)
CF
Q
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) Capacity factor and volume flow rate
Figure 6 Overall performance under SR = 081
Flatness ratio
90
92
94
96
98
05 06 07 08 09 1
PumpTurbineStator
Effici
ency
()
Figure 7 Element efficiency under SR = 081
In order to further investigate the factors influencingperformance deterioration the efficiency of elements will bethen discussed
The individual efficiencies of the pump turbine andstator (120578
119901 120578119879 and 120578
119878 resp) and the overall efficiency 120578TC are
defined by the following expressions
120578119901
=
(1199011199012
minus 1199011199011
)
1205881199081(1199031199012
1198811199012
minus 1199031199011
1198811199011
)
120578119879
=
1205881199082(11990311990521198811199052
minus 11990311990511198811199051)
(1199011199051
minus 1199011199052)
120578119878= 1 minus
(1199011199051
minus 1199011199052)
(1199011199012
minus 1199011199011
)
(25)
where subscripts 1 and 2 refer to the inlet and outlet ofelement respectively
Figure 7 displays the efficiency of elements under SR =
081 compared with Figure 6(a) the main cause of decline
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
FR = 08FR = 09
FR = 07FR = 06
Roth
alpy
(m2
s2)
Figure 8 Rothalpy change on the pressure surface of pump underSR = 081
in the overall efficiency is attributed to the pump lossHere Rothalpy is introduced to quantitatively evaluate thehydraulic loss For viscous flow the difference of parametersbetween two points on a streamline represents hydraulic lossRothalpy is defined as follows
119877 =
119875
120588
+
1
2
1205962minus
1
2
1205832 (26)
where 119875 is the pressure 120588 is the density 120596 is the relativevelocity and 120583 is the circumferential velocity
Figure 8 displays the Rothalpy change from the inlet tothe outlet on the pressure surface of the pump blades underSR = 081The leading edge corresponds to about ldquo0ndash01rdquo andthe trailing edge corresponds to about ldquo09ndash1rdquoThedecrease inRothalpy from FR = 09 to FR = 06 undoubtedly coincideswell with the pump efficiency in Figure 7
42 Performance Comparison of Two Methods Figure 9(b)shows two kinds of torus the transitional one is extractedfrom cross-sectional views of FR = 08 in Figure 9(a)
8 Mathematical Problems in Engineering
Lock-up clutch
Turbine
Pump
Stator
(a) Torus cross-sectional views
New torus methodTraditional method
Core
Shell
Inlet
Mid-chord
Outlet
(b) Two tori
Figure 9 Comparison of torus on different method
SR
09
11
13
15
17
19
21
00 01 02 03 04 05 06 07 08 09
New torus methodTraditional method
TR
(a) Torque ratio
30
40
50
60
70
80
90
02 03 04 05 06 07 08 09SR
Effici
ency
()
New torus methodTraditional method
(b) Efficiency
20
25
30
35
40
45
50
0 01 02 03 04 05 06 07 08 09
CF
SR
New torus methodTraditional method
(c) Capacity factor
Figure 10 Comparison of performance curves between two methods
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
0123456789
0 01 019 029 039 048 06 069 074 081 0888
03 million07 million
13 million17 million
15171921232527293133
0 01 02 03 04 05 06 07 08 09
Experiment03 million07 million
13 million17 million
SR SR
Capa
city
fact
or (C
F)
Abso
lute
erro
r of C
F (
)
(a) CF and CF absolute error
1111213141516171819
0 01 02 03 04 05 06 07 08 090
05
1
15
2
25
3
0 01 019 029 039 048 06 069 074 081 088SRSR
Torq
ue ra
tio (T
R)
Abso
lute
erro
r of T
R (
)
Experiment03 million07 million
13 million17 million
03 million07 million
13 million17 million
(b) TR and TR absolute error
Figure 5 Results of CFD analysis of different mesh densities
120578 (Efficiency) Consider
120578 =
119873turbine times 119879turbine119873pump times 119879pump
= SR times TR (23)
where 119873 is the rotating speed (rpm) and 119879 is the torqueof each component To compare prediction accuracy underdifferent grid densities the absolute error of prediction isdefined as follows
119864119905=
10038161003816100381610038161003816119868TM minus 119868Exp
10038161003816100381610038161003816
119868Exptimes 100 (24)
where 119868 represents the capacity coefficient torque ratioefficiency and other physical quantities and the subscriptsTM and Exp denote the simulation and test data respectively
Figure 5 illustrates that the simulated resultsmoved closerto the experimental data with increasing element numbersOnly subtle changes were observed when element numbersincreased from 13 million to 17 million After an evaluation
of computation amount and accuracy 13 million was used insubsequent CFD simulations
4 Analysis and Discussion
41 Performance Comparison of Different Flatness Ratio Themeasured overall performance of test torque converters issummarized in Figure 6 in terms of the efficiency capacityfactor and volume flow rate under SR = 081 conditionwherevehicles are operated most frequently in driving
Overall efficiency begins to decrease from FR = 09 toFR = 06 in Figure 6(a) It decreases by no more than 10point from FR = 09 to FR = 08 but dramatically decreasesfrom FR = 08 to FR = 06 Figure 6(b) shows the computedtorque capacity coefficient and circulatory flow rate Thecapacity factor and volume flow rate begin to decrease fromFR = 08 to FR = 06 The tendency of the torquecapacity coincides relatively well with that of the volumeflow rate Figure 6 indicates a significant deterioration in itsperformance potential along with the narrower profile
Mathematical Problems in Engineering 7
75
77
79
81
83
85
87
89
05 06 07 08 09 1Flatness ratio
Ove
rall
effici
ency
()
(a) Overall efficiency
20
21
22
23
24
25
26
005
0055
006
0065
007
05 06 07 08 09 1Flatness ratio
Capa
city
fact
or (C
F)
CF
Q
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) Capacity factor and volume flow rate
Figure 6 Overall performance under SR = 081
Flatness ratio
90
92
94
96
98
05 06 07 08 09 1
PumpTurbineStator
Effici
ency
()
Figure 7 Element efficiency under SR = 081
In order to further investigate the factors influencingperformance deterioration the efficiency of elements will bethen discussed
The individual efficiencies of the pump turbine andstator (120578
119901 120578119879 and 120578
119878 resp) and the overall efficiency 120578TC are
defined by the following expressions
120578119901
=
(1199011199012
minus 1199011199011
)
1205881199081(1199031199012
1198811199012
minus 1199031199011
1198811199011
)
120578119879
=
1205881199082(11990311990521198811199052
minus 11990311990511198811199051)
(1199011199051
minus 1199011199052)
120578119878= 1 minus
(1199011199051
minus 1199011199052)
(1199011199012
minus 1199011199011
)
(25)
where subscripts 1 and 2 refer to the inlet and outlet ofelement respectively
Figure 7 displays the efficiency of elements under SR =
081 compared with Figure 6(a) the main cause of decline
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
FR = 08FR = 09
FR = 07FR = 06
Roth
alpy
(m2
s2)
Figure 8 Rothalpy change on the pressure surface of pump underSR = 081
in the overall efficiency is attributed to the pump lossHere Rothalpy is introduced to quantitatively evaluate thehydraulic loss For viscous flow the difference of parametersbetween two points on a streamline represents hydraulic lossRothalpy is defined as follows
119877 =
119875
120588
+
1
2
1205962minus
1
2
1205832 (26)
where 119875 is the pressure 120588 is the density 120596 is the relativevelocity and 120583 is the circumferential velocity
Figure 8 displays the Rothalpy change from the inlet tothe outlet on the pressure surface of the pump blades underSR = 081The leading edge corresponds to about ldquo0ndash01rdquo andthe trailing edge corresponds to about ldquo09ndash1rdquoThedecrease inRothalpy from FR = 09 to FR = 06 undoubtedly coincideswell with the pump efficiency in Figure 7
42 Performance Comparison of Two Methods Figure 9(b)shows two kinds of torus the transitional one is extractedfrom cross-sectional views of FR = 08 in Figure 9(a)
8 Mathematical Problems in Engineering
Lock-up clutch
Turbine
Pump
Stator
(a) Torus cross-sectional views
New torus methodTraditional method
Core
Shell
Inlet
Mid-chord
Outlet
(b) Two tori
Figure 9 Comparison of torus on different method
SR
09
11
13
15
17
19
21
00 01 02 03 04 05 06 07 08 09
New torus methodTraditional method
TR
(a) Torque ratio
30
40
50
60
70
80
90
02 03 04 05 06 07 08 09SR
Effici
ency
()
New torus methodTraditional method
(b) Efficiency
20
25
30
35
40
45
50
0 01 02 03 04 05 06 07 08 09
CF
SR
New torus methodTraditional method
(c) Capacity factor
Figure 10 Comparison of performance curves between two methods
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
75
77
79
81
83
85
87
89
05 06 07 08 09 1Flatness ratio
Ove
rall
effici
ency
()
(a) Overall efficiency
20
21
22
23
24
25
26
005
0055
006
0065
007
05 06 07 08 09 1Flatness ratio
Capa
city
fact
or (C
F)
CF
Q
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) Capacity factor and volume flow rate
Figure 6 Overall performance under SR = 081
Flatness ratio
90
92
94
96
98
05 06 07 08 09 1
PumpTurbineStator
Effici
ency
()
Figure 7 Element efficiency under SR = 081
In order to further investigate the factors influencingperformance deterioration the efficiency of elements will bethen discussed
The individual efficiencies of the pump turbine andstator (120578
119901 120578119879 and 120578
119878 resp) and the overall efficiency 120578TC are
defined by the following expressions
120578119901
=
(1199011199012
minus 1199011199011
)
1205881199081(1199031199012
1198811199012
minus 1199031199011
1198811199011
)
120578119879
=
1205881199082(11990311990521198811199052
minus 11990311990511198811199051)
(1199011199051
minus 1199011199052)
120578119878= 1 minus
(1199011199051
minus 1199011199052)
(1199011199012
minus 1199011199011
)
(25)
where subscripts 1 and 2 refer to the inlet and outlet ofelement respectively
Figure 7 displays the efficiency of elements under SR =
081 compared with Figure 6(a) the main cause of decline
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
FR = 08FR = 09
FR = 07FR = 06
Roth
alpy
(m2
s2)
Figure 8 Rothalpy change on the pressure surface of pump underSR = 081
in the overall efficiency is attributed to the pump lossHere Rothalpy is introduced to quantitatively evaluate thehydraulic loss For viscous flow the difference of parametersbetween two points on a streamline represents hydraulic lossRothalpy is defined as follows
119877 =
119875
120588
+
1
2
1205962minus
1
2
1205832 (26)
where 119875 is the pressure 120588 is the density 120596 is the relativevelocity and 120583 is the circumferential velocity
Figure 8 displays the Rothalpy change from the inlet tothe outlet on the pressure surface of the pump blades underSR = 081The leading edge corresponds to about ldquo0ndash01rdquo andthe trailing edge corresponds to about ldquo09ndash1rdquoThedecrease inRothalpy from FR = 09 to FR = 06 undoubtedly coincideswell with the pump efficiency in Figure 7
42 Performance Comparison of Two Methods Figure 9(b)shows two kinds of torus the transitional one is extractedfrom cross-sectional views of FR = 08 in Figure 9(a)
8 Mathematical Problems in Engineering
Lock-up clutch
Turbine
Pump
Stator
(a) Torus cross-sectional views
New torus methodTraditional method
Core
Shell
Inlet
Mid-chord
Outlet
(b) Two tori
Figure 9 Comparison of torus on different method
SR
09
11
13
15
17
19
21
00 01 02 03 04 05 06 07 08 09
New torus methodTraditional method
TR
(a) Torque ratio
30
40
50
60
70
80
90
02 03 04 05 06 07 08 09SR
Effici
ency
()
New torus methodTraditional method
(b) Efficiency
20
25
30
35
40
45
50
0 01 02 03 04 05 06 07 08 09
CF
SR
New torus methodTraditional method
(c) Capacity factor
Figure 10 Comparison of performance curves between two methods
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Mathematical Problems in Engineering
Lock-up clutch
Turbine
Pump
Stator
(a) Torus cross-sectional views
New torus methodTraditional method
Core
Shell
Inlet
Mid-chord
Outlet
(b) Two tori
Figure 9 Comparison of torus on different method
SR
09
11
13
15
17
19
21
00 01 02 03 04 05 06 07 08 09
New torus methodTraditional method
TR
(a) Torque ratio
30
40
50
60
70
80
90
02 03 04 05 06 07 08 09SR
Effici
ency
()
New torus methodTraditional method
(b) Efficiency
20
25
30
35
40
45
50
0 01 02 03 04 05 06 07 08 09
CF
SR
New torus methodTraditional method
(c) Capacity factor
Figure 10 Comparison of performance curves between two methods
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 9
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1
Traditional methodNew torus method
Nondimensional distance
Roth
alpy
(m2
s2)
(a) SR = 00
Traditional methodNew torus method
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Roth
alpy
(m2
s2)
(b) SR = 04
3000
3100
3200
3300
3400
3500
3600
0 01 02 03 04 05 06 07 08 09 1Nondimensional distance
Traditional methodNew torus method
Roth
alpy
(m2
s2)
(c) SR = 08
Figure 11 Rothalpy distribution on the pressure surface of pump
The performance characteristics of the torque converters areinvestigated by numerical analysis using CFD codes Theresults are shown in Figure 10 stall torque ratio is increasedfrom 188 to 212 the highest efficiency on SR = 081
is improved from 856 to 8707 while capacity factordecreases by 12 compared to the traditional method whichmeans more energy could be transferred to pump fromthe engine In summary the performance of the flat torqueconverter designed by adopting the flat torus design methodbased on the elliptic type is more excellent than that of thetraditional design method due to the superior geometry Asthe correlation between overall and pump efficiency is quiteremarkable in Figure 8 the subsequent discussion will focuson the pump flow and loss
Figure 11 displays the Rothalpy distribution from inlet tooutlet of pump inTCbased on twomethodsThedifference inRothalpy from inlet to outlet decreases gradually along withSR compared with the traditional one Rothalpy distributionin new torus method is gentler and the difference of which isrelatively less
The results illustrate not only the superior geometry ofthe newmethod but also the region where large loss occurred
with a flatter design Shock loss owing to the incidence flowangle to the blades changing drastically is attributed to theflow deterioration in the leading edge [25] which accountsfor about 20 of hydraulic loss inside pump experimentresults for the velocity field in a torque converter pumphad been carried out by Flack and Brun [26] who hadconcluded that the strong jetwake characteristics includingbackflows and circulatory secondary flows were the mainfactors contributing to Rothalpy loss inmain flow region (01ndash09) complex flow including the free streamflow blades wakeflow core-suction corner separation and mixing flow in exitregion of pump found by Dong et al [27] was considered togenerate the loss in the trailing edge
Figure 12 displays the distribution of Rothalpy from theshell to core for the chord plane of pump where ldquo0rdquo refers tothe shell surface and ldquo1rdquo refers to the core surface
Type ldquoardquo means TC on new method and the other meanstraditional one The Rothalpy difference of any curve onabscissa axes represents the hydraulic loss from shell to corewhich would be gradually decreased with the increase of SRThe loss on core surface (the region closing to 1) is mainlyfocused on the first part of passage where is located on
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Mathematical Problems in Engineering
0010203040506070809
1
3100 3200 3300 3400 3500
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
(a) SR = 00
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
Non
dim
ensio
nal d
istan
ce
0010203040506070809
1
3100 3200 3300 3400 3500
Rothalpy (m2s2)
(b) SR = 04
0010203040506070809
1
3200 3300 3400 3500 3600
Non
dim
ensio
nal d
istan
ce
Rothalpy (m2s2)
Outlet (type a)Midchord (type a)Inlet (type a)
Outlet (type b)Midchord (type b)Inlet (type b)
(c) SR = 08
Figure 12 Rothalpy distribution on chord plane of pump
the region between inlet and mid-chord By contrast the losson the shell surface (the region closing to 0) exhibits an evendistribution on inlet midchord and outlet In addition theRothaply changes of type a is more smooth and continuouswhich suggests the internal flow status of pump on newmethod is superior to the traditional one
5 Influence of Removal of Inner Ring
In order to further expand the existing space reduce thetorque converter axial size andmaintain overall performanceof TC in this paper three kinds of flatness ratio of TC (060055 and 050)without inner ring based on new torusmethodwere designed as shown in Figure 13
Figure 14 shows volume flow rate and capacity factor of4 types of TC on two conditions comparison on the sameflat ratio (FR = 060) demonstrates the function of innerring in regulating the volume flow rate and capacity factor
After removing the inner ring high-speed working mediumflowing from the pump in the radial plane would impactturbine blade more widely which makes the turbine obtainmore power Furthermore volume flow rate and capacityfactor have lost approximately 15 of their value whenflatness ratio decreased from 06 to 05 on stall condition(SR = 0) while on condition of SR = 08 the difference in 3types becomes less distinct from each other
Figure 15 displays the highest efficiency and stall torqueratio on SR = 08 of the prototype FR = 06 and 3 kinds oftorque converters without the inner ring a similar pattern inwhich the highest efficiency and stall torque ratio decreasealong with a flatter profile in TC without the inner ring is stillvalid At the same time the comparison between (a) and (b)indicates that the effect of removal of inner ring on improvingthe performance of existing torque converters is remarkableThe highest efficiency increased by 25 percentage points stalltorque ratio is improved from 179 to 218 and comparison
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 11
(a) FR = 06 (inner ring) (b) FR = 06 (c) FR = 055 (d) FR = 05
Figure 13 Four types of torus of different flatness ratio
4547495153555759616365
0085
01
0115
013
0145
045 05 055 06 065
Capa
city
fact
or (C
F)
Flatness ratio
CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(a) SR = 0
20
25
30
35
40
45
0055
006
0065
007
0075
045 05 055 06 065Flatness ratio
Capa
city
fact
or (C
F) CF
Q
(a)
(c)
(d)
(b)
Volu
me fl
ow ra
te (Q
) (m
3 s)
(b) SR = 08
Figure 14 Volume flow rate and capacity factor of 4 types of TC
805
81
815
82
825
83
835
84
17
18
19
2
21
22
23
0475 05 0525 055 0575 06 0625
Stall torque ratioHighest efficiency
Flatness ratio
(a) (c)
(d)
(b)
Stal
l tor
que r
atio
(TR 0
)
TR0
Hig
hest
effici
ency
(120578)
()
120578
Figure 15 Highest efficiency and stall torque ratio of differentflatness rate
between (a) and (d) indicates that it is possible to achievemore space and more efficiency and larger stall torque ratioat the same time if the inner ring is removed
6 Conclusion
In this paper a flat torus of elliptic typemethod concentratingon the solution to flat TC is put forward to improve theperformance The internal flow characteristics of TC arenumerically investigated using CFD codes and resulted ina good agreement with experimental data Four torqueconverters of different flatness ratios are designed to judge thesuperiority of newmethod Rothalpy is used to quantitativelyevaluate the hydraulic loss and predict the region wherelarge loss occurred with a flatter design The calculationsindicate that the performance of the passenger car flat torqueconverter deteriorates with the decreasing flatness ratio
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
12 Mathematical Problems in Engineering
Furthermore this paper also proposes a structure of removalof inner ring to improve the performance of TC the specificconclusions are as follows
(1) The results indicate that themain cause of this perfor-mance degradation can be attributed to deteriorationof the velocity fields of the pump
(2) The performance of the flat torque converter designedby adopting the flat torus designmethod based on theelliptic shape ismore excellent the internal flow statusof pump on newmethod is superior to the traditionalone
(3) Removal of the inner ring is a feasible way to improvethe efficiency while satisfying space requirements
The stator applied in this paper is straight up and downcalled the cylindrical shape In future studies other shape-likecones and arc would be checked out to see whether or not theshock loss on leading edge of the pump could be lightened up
Nomenclature
CF Capacity factorFR Flatness ratio119862119904 Smagorinsky coefficient
119896 Turbulent kinetic energy (m2s2)119873 Rotating speed (rpm)119875 Fluid pressure (pa)119876 Volume flow rate (m3s)119903 Radius (m)SR Speed ratio119879 Torque (nsdotm)TR Torque ratio between pump and turbine119906119894 Time-averaged velocity (ms)
119883119894 Coordinate (m)
Greek Letters
120578 Efficiency120576 Turbulent dissipation rate (m2s3)120583 Circumferential velocity (ms)120583119905 Turbulence viscosity coefficient
120588 Density (kgm)119906119879 Eddy viscosity coefficient
] Turbulent viscosity (m2s)120596 Relative velocity (ms)
Subscripts
119875 Pump119878 Stator119879 TurbineTC Torque converter
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National High-Tech RampDProgram of China (2014AA041502)
References
[1] T Ochi H Takeuchi H Kimura and K Watanabe ldquoDevelop-ment of a super-flat torque converter for the new toyota FWD6-speed automatic transaxlerdquo SAE Technical Paper 2006-01-01492006
[2] T Kietlinski and M Fingerman ldquo248mm elliptical torqueconverter from daimlerchrysler corporationrdquo SAE TechnicalPaper 2007-01-0241 2007
[3] K Saitou ldquoBlade structure for torque converter and process ofproducing the samerdquo US Patent 8128370 2012
[4] E Ejiri and M Kubo ldquoPerformance analysis of automotivetorque converter elementsrdquo Journal of Fluids Engineering vol121 no 2 pp 266ndash275 1999
[5] B V Marathe and B Lakshminarayana ldquoExperimental investi-gation of steady and unsteady flow field upstream and down-stream of an automotive torque converter pumprdquo InternationalJournal of Rotating Machinery vol 5 no 2 pp 99ndash116 1999
[6] Y Dong V Korivi P Attibele and Y Yuan ldquoTorque converterCFD engineering part I torque ratio and K factor improvementthrough stator modificationsrdquo SAE Technical Paper 2002-01-0883 2002
[7] B S Kim S B Ha W S Lim and S W Cha ldquoPerformanceestimation model of a torque converter part I correlationbetween the internal flow field and energy loss coefficientrdquoInternational Journal of Automotive Technology vol 9 no 2 pp141ndash148 2008
[8] J H Jung S Kang and N Hur ldquoA numerical study of a torqueconverter with various methods for the accuracy improvementof performance predictionrdquo Progress in Computational FluidDynamics vol 11 no 3-4 pp 261ndash268 2011
[9] C Liu A Untaroiu H G Wood Q Yan and W WeildquoParametric analysis and optimization of inlet deflection anglein torque convertersrdquo Journal of Fluids Engineering vol 137 no3 Article ID 031101 2015
[10] Y Dong and B Lakshminarayana ldquoRotating probe measure-ments of the pump passage flow field in an automotive torqueconverterrdquoTransactions of the ASME Journal of Fluids Engineer-ing vol 123 no 1 pp 81ndash91 2001
[11] J Schweitzer and J Gandham ldquoComputational fluid dynamicsin torque converters validation and applicationrdquo The Interna-tional Journal of Rotating Machinery vol 9 no 6 pp 411ndash4182003
[12] W D Claudel R D Flack and A Yermakov ldquoAverage velocitymeasurements in six automotive torque converters Part IPumpmeasurementsrdquo Tribology Transactions vol 44 no 4 pp511ndash522 2001
[13] C Lee W Jang J M Lee and W S Lim ldquoThree dimensionalflow field simulation to estimate performance of a torqueconverterrdquo SAE Technical Paper 2000-01-1146 2000
[14] H S Su G L Yang L Q Zhang and W B Cao ldquoNumericalanalysis on the external characteristic of torque converter basedon UDFrdquo Applied Mechanics and Materials vol 318 pp 44ndash492013
[15] R Flack ldquoExperimental flowfields in an automotive torque con-vertermdashan invited summary and review paperrdquo InternationalJournal of Vehicle Design vol 38 no 2-3 pp 240ndash258 2005
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 13
[16] E Ejiri and M Kubo ldquoInfluence of the flatness ratio of anautomotive torque converter on hydrodynamic performancerdquoJournal of Fluids Engineering vol 121 no 3 pp 614ndash620 1999
[17] S Liu and L Quan ldquoMathematical model of hydrodynamictorque converter and analytic description of streamlinerdquo Chi-nese Journal ofMechanical Engineering (English Edition) vol 22no 1 pp 70ndash77 2009
[18] A Kesy and A Kadziela ldquoApplication of statistical formulas tohydrodynamic torque converter modellingrdquo Archives of Civil ampMechanical Engineering vol 9 no 4 pp 33ndash48 2009
[19] V J Janacek ldquoThe design of a single-stage three-element torqueconverterrdquo SAE Technical Paper 610576 1961
[20] S P Liu and Q Long ldquoMinimum curvature design of three-element centripetal-turbine hydrodynamic torque convertersrdquoJournal of China Ordnance vol 5 no 2 pp 119ndash125 2009
[21] E Lenormand P Sagaut L T Phuoc and P Comte ldquoSubgrid-scale models for large-eddy simulations of compressible wallbounded flowsrdquo AIAA Journal vol 38 no 8 pp 1340ndash13502000
[22] Y Lei C Wang Z Liu and X Li ldquoAnalysis of the full flow fieldof Torque Converterrdquo Advanced Materials Research vol 468-471 pp 674ndash677 2012
[23] W Wei and Q D Yan ldquoStudy on hydrodynamic torque con-verter parameter integrated optimization design system basedon tri-dimensional flow field theoryrdquo SAE Technical Paper2008-01-1525 2008
[24] G Bois A C Bayeul C Leclerc B Meredith and Y LebouvierldquoNumerical torque converter performance predictions valida-tion and application to a rapid one dimensional approachrdquo inProceedings of the ASME Fluids Engineering Division SummerMeeting Paper no FEDSM2005-77039 pp 1095ndash1102 ASMEHouston Tex USA June 2005
[25] S O Kraus R Flack A Habsieger G T Gillies and K Dul-lenkopf ldquoPeriodic velocity measurements in a wide and largeradius ratio automotive torque converter at the pumpturbineinterfacerdquo Journal of Fluids Engineering vol 127 no 2 pp 308ndash316 2005
[26] R Flack and K Brun ldquoFundamental analysis of the secondaryflows and jet-wake in a torque converter pumpmdashpart I modeland flow in a rotating passagerdquo Journal of Fluids Engineeringvol 127 no 1 pp 66ndash74 2005
[27] Y Dong B Lakshminarayana and D Maddock ldquoSteady andunsteady flow field at pump and turbine exits of a torqueconverterrdquo Journal of Fluids Engineering vol 120 no 3 pp 538ndash548 1998
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of