Numerical Analysis into the Effects of theUnsteady Flow in an Automotive Hydrodynamic

Torque ConverterPablo De la Fuente, Horst Stoff, Werner Volgmann and Marek Wozniak

Abstract—In this paper the characteristics of a three dimen-sional, incompressible, turbulent, unsteady flow within a one-stage two-phase automotive hydrodynamic torque converter wasnumerically simulated and analyzed. For the investigation thefinite volume method has been employed.

The commercial 3D Navier-Stokes Software CFX of ANSYSInc. was used to investigate the flow inside a torque converter.The software solves the incompressible Reynolds-Averaged-Navier-Stokes (RANS) equations on the entire flow domainusing the k-ε turbulence model. To compare the simulation withexperimental results, the nondimensional characteristics wereused. The flow field is determined by the blade position of bothrotors, which have different rotating velocities. Discrepanciesbetween the steady and unsteady simulations were found anddiscussed. The unsteady flow at the pump exit and turbine inletwill be analized through instantaneous flow fields in a period.

Index Terms—hydrodynamic torque converter, CFD, un-steady flow, fluid flow simulation.

I. INTRODUCTION

THE fluid in a hydrodynamic torque converter (H.T.C.)is responsable for the torque conversion and power

transfer from the engine to the transmission and influencesthe propulsion efficiency. H.T.C. are commonly used invehicle power transmission systems such as cars, buses andlocomotives. Its typical configuration consists of a pump,driven by the engine that transmits the generated angu-lar momentum, a turbine that transmits the torque to thetransmission and a stator, which makes possible the torqueconversion through the redirection of the flow to the pump.

Some advantages are the capacity to provide torque am-plification during the start-up conditions, a soft start fromstandstill and the capacity for damping transmission throughthe absorbtion of torsional vibrations introduced from theengine. One disadvantage is the higher fuel consumptionand lower efficiency compared with the gear transmission.So it is necessary to optimize its operating work throughunderstanding the flow behaviour. The internal flow withinH.T.C. is three-dimensional, turbulent, viscous, complex,highly unsteady and difficult to analize because of theoperating conditions that consist of three elements rotatingat different velocities.

The two principal unsteady problems concern the ex-ternally forced unsteadiness like the blade-row interaction,

Manuscript received March 04, 2011; revised March 28, 2011. This workwas supported by DAAD (Deutscher Akademischer Austauschdienst).

P. D., H. S. and W. V. are with the Department of Fluid-Energy Machines,Ruhr-University Bochum, Germany (email: pablo.delafuente@rub.de,horst.stoff@rub.de, werner.volgmann@rub.de).

M. W. ist with the Technical University of Lodz, Poland (email:marek.woziak.1@p.lodz.pl).

where the geometry of the flow changes with the rotation ofthe row and the self-excited unsteadiness like the turbulentmotion. Due to the proximity of the components there is amutual interaction that causes periodically unsteady forces,which are caused due to blade/wake interaction, potentialflow interaction and 3D flow effects. Most turbomachineryflows are inherently und strongly unsteady in nature. In manycases a steady flow is assumed for convenience. However,when it becomes necessary to invoke more realistic unsteadyanalysis this assumption shows disadvantages.

Unsteady flow phanomena like blade row interactionshould be investigated through truely unsteady calculation[1]. In addition, the transition between rotating and sta-tionary motion can cause unsteady loading on the blades.The complexity of the flow field is directly influenced bygeometric considerations like the spacing between blades. Inthe last years CFD tools make possible to reduce the costand save time for the flow analysis and have been used topredict the flow in turbomachinery because of its property todeliver fast predictions of instantaneous flow field states bynumerical calculation. CFD tools use the computer resourcesto calculate the flow by complex mathematical models.

In a number of papers the performance of H.T.C. have beenstudied with CFD tools [2]–[4] and have been demonstratedhow complex the flow is inside the machine. Measurementshave been discussed in [5], [6]. Schulz [4] used a finitevolume method in calculating three-dimensional, incom-pressible, turbulent flow. Steady and unsteady calculations tosimulate the pump/turbine interactions were performed. Theircalculations showed that unsteady rotor-stator interaction wasnegligible, but needed to be accounted for the unsteadyinteraction between the pump and the turbine. They came tothe conclusion that viscous effects were not fully reproduced.Roecken [7] investigated the flow in a H.T.C. and unsteadypressure curves were measured between the two rotors andwere compared with calculations obtained from a finitevolume procedure. The comparison of torques showed agood agreement so that the authors came to the conclusionthat experimental analysis could be described by numericalcalculations.

The H.T.C. used in this paper was designed by ZF SachsAG and its geometry was published in [8]. The one-stagetwo-phase W240 H.T.C. has an outer diameter of 240 [mm].The pump contains Zp =31, turbine Zt =29 and statorZs =11 blades respectively. The operating fluid is AutomaticTransmission Fluid ATF LT 71141 whose densitiy is ρ =802[ kg/m3] and the viscosity is ν =0,00653 [ Pa s] at 95[ ◦C] [9]. All calculations were performed at a constanttemperature of the fluid.

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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II. BASIC EQUATIONS AND TURBULENCE MODELLING

It is recognised that Navier-Stokes simulations can provideuseful information to understand of unsteady effects in turbo-machinery [10]. In H.T.C. the unsteady flow is governed bythe RANS Reynolds-Averaged-Navier-Stokes transient equa-tions for an incompressible flow by the turbulent viscosityhypothesis. The calculations were all done with the standardk− ε turbulence model [11]. The continuity and momentumequations for an incompressible flow are respectively:

∂Uj∂xj

= 0 (1)

∂Ui∂t

+Uj∂Ui∂xj

= −1

ρ

∂P

∂xi+

∂

∂xj

[ν

(∂Ui∂xj

+∂Uj∂xi

)− ui′uj ′

]− ρ(2εijkωjuk + ωiωjxj − ωjωjxi) (2)

Where t is the time, U(u, v, w) the velocity vector of theflow, P the pressure, ρ the density and ν the kinematicviscosity of the fluid. In the eddy-viscosity turbulence modelthe Reynolds stresses ui′uj ′ are assumed to be proportionalto the mean velocity gradients with the constant turbulentviscosity. These equations are time-averaged over a periodT. The values of the turbulent kinetic energy k and turbulentenergy dissipation ε are obtained by solution of the conser-vation equations (3) and (4):

∂k

∂t+ Uj

∂k

∂xj=

∂

∂xj

[(ν +

νtσk

)∂k

∂xj

]+ Pk − ε (3)

∂ε

∂t+ Uj

∂ε

∂xj=

∂

∂xj

[(ν +

νtσε

)∂ε

∂xj

]+ c1ε

ε

kPk − c2ε

ε2

k(4)

Where c1ε, c2ε, σε and σk are constants. Pk is the turbulenceproduction due to viscous forces. To obtain a numericalsolution these partial differential equations must be firstdiscretised on a grid that covers the flow domain.

III. SIMULATION OF THE INTERNAL FLOW

It will be assumed that the flow is three-dimensional,incompressible, viscous and turbulent. The pump speed staysconstant nP = 2000 min−1 and the turbine speed changesdepending on the speed ratio. The Reynolds number isRe =

ωP · d2P, externalν = 1481802[−]. At the interfaces a frozen

rotor and a transient rotor-stator model were used for a steadyand unsteady simulation respectively. The advection termsof the flow will be solved with the advection scheme optionHigh Resolution with Second Order Differencing. The H.T.C.works like a closed circuit because the working fluid is notsubjected to external forces except the forces applied by thecomponents. By the calculation the flow will adjust itself by aclosed loop algorithm depending on the boundary conditionsat inlet and outlet according to the speed ratio ν. A convergedsteady simulation with blades at standstill was used as initialvalue for the unsteady case. For the unsteady simulation atime step ∆t is needed, in which the relative position ofthe rotors will be updated. The unsteady simulation wasperformed for six different operating points between 0.01 and0.8, which are characterized by the speed ratio (ν = nt

np).

For the unsteady simulation at design point ν=0.7, whichcorresponds to the highest value of the efficiency, the timestep was calculated by using (5). This time step size has been

Fig. 1. Three-dimensional Computational Analysis Model

Fig. 2. Computational Mesh at Center Planes (Mid Section)Turbine (right)- Stator (center) - Pump (right)

chosen in order to resolve the unsteadiness in the pump-turbine interaction area with 33 time steps. This time stepcoincides with the Courant Number 4.6.

∆t =1

(ωp − ωt)· 1

Zp· 1

33= 9.75 · 10−5[s] (5)

One complete turn of the pump coincides with 309 ∆t.At ν=0.7 after 900 time steps and the reach of three sameperiods the results were considered periodic. The time ofthe steady computation was approximately 597 minutes.By the unsteady calculation the time necessary to reachthree same periods was about 6000 minutes (700 ∆t) with7 loops for every time step. The calculations have beenmade on an Intel Core i3 using four processors in parallel.Starting from a converged steady-state solution, a convergedunsteady solution can be obtained in a matter of five days.As conclusion, an unsteady simulation consumes ten timesmore CPU time compared to the steady method.

A. Calculating mesh

The flow will be discretized in a finite volume mesh tocarry out the numerical simulations. The virtual model ofthe H.T.C. involves the geometry and the circulating three-dimensional flow. The development of the CAD Model,shown in the Fig. 1 and the study of the quality of themesh were presented and developed in the previous work[12], [13]. The mesh convergence study showed that beyond400000 points the results are almost the same proving thegrid independence of the solution. The mesh was createdfor one passage of each element (P1T1L1) and copied forthe comparison model (P3T3L1), which contains 3 pump,3 turbine pitches and 1 stator pitch. With the periodicityoption and repeated boundary conditions the full H.T.C. wasmodelled in order to reduce time and computer memory.

The Fig. 2 shows the mesh used for calculations. Thenumber of elements for every pitch are 80580, 200925 und345222 for the pump, turbine and stator respectively andthe total number of mesh elements for the calculations is626727. In order to avoid errors and exacerbated computerrequirements in the unsteady simulation because of theunequal pitch between components, it means the connectionof dissimilar meshes, the P3T3L1 model presented in Fig. 3will be used and compared for validation with the results

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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Fig. 3. Numerical Grid of the P3T3L1 Model

TABLE IOVERLAPPING RELATION AT THE INTERFACES

Pitch ratio W240(P1T1L1) W240(P3T3L1)

P/T 0,935 0,935T/L 0,379 1,138L/P 2,818 0,939

of the model P1T1L1. The total number of elements ofthe P3T3L1 model is 1189737 elements. Both models areidentical in each pitch computational grid but different in thenumber of computed pitches used in each component. For anoptimum analysis the net pitch change across the interfacesmust be close to unity [14]. The table I shows the pitch ratiovalues, which correspond to the fractional change areas ofthe two connected components.

The table I shows clearly that the model P3T3L1 results ina pitch ratio close to the ideal value. The results and compar-ison of both models through their characteristic lines will bepresented in the next step, where the torque conversion andthe torque coefficient will be compared with measurements.

B. Performance characteristics

In this chapter the calculated performances of the H.T.C.will be compared with measurements. For this purpose,the torques will be calculated for validation. The non-dimensional characteristics of the H.T.C. consist of twocurves determining torque conversion µ and torque coeffi-cient λ as a function of rotational frequencies (ωP , ωT ) andtorque (MP , MT ) of the pump and turbine:

ν =ntnp

; µ =

∣∣∣∣MT

MP

∣∣∣∣ ; λ =MP

ρ ·ω2P · d5P,external

(6)

To cover one blade pitch of the pump and turbine theperiod was calculated by ν=0.7. The period of the pump andturbine are TP=10∆t and TT=15∆t respectively. Then theperiod of the unsteady solution is 60∆t, which correspondsto the time after which the pump and turbine blades are in thesame relative position again. After performing the steady andunsteady analysis of the H.T.C. the evaluation of the qualityof the CFD simulation will be studied by comparing thenumerical and experimental characteristics [8] concerning λand µ at speed ratios 0.01-0.8. To obtain the time-averagedtorque for the unsteady condition at each operating pointthe data of one period are averaged. The 1D calculationshave been made with the fluid friction factors 0.2 and shockloss coefficient 1.0 for the losses. The efficiency will not beplotted because it provides no new information (η = µ · ν).

To obtain the torque on each component, the force on theblade surface was integrated, so that with the radius to therotating X-axis the torque can be calculated. The comparison

ν [ - ]

µ[

-]

0 0.2 0.4 0.6 0.81.0

1.5

2.0

2.5

3.0 Experimental1DSteady P1T1L1Steady P3T3L1Unsteady P3T3L1

Fig. 4. Torque Conversion µ

ν [ - ]

λ[

-]

0 0.2 0.4 0.6 0.8

2.0E-03

2.5E-03

3.0E-03

Experimental1DSteady P1T1L1Steady P3T3L1Unsteady P3T3L1

Fig. 5. Torque Coefficient λ

is showed in the Figs. 4 and 5. The torque coefficient has aslightly larger discrepance than the torque conversion results.However, the torque conversion and the torque coefficientare in accordance well with experimental data. Concerningµ, the torque calculations demonstrate that the time-averagetorques given by the unsteady calculation are higher and havea better agreement with the measurements than those fromthe steady calculation (µ). As it can be seen the presentedcalculated three-dimensional characteristics are representingthe behaviour of the experimental results. As far as λ isconcerned, the results from the steady simulation show abetter agreement with the experimental data. Despite thedeviation of the pitch ratio of the P1T1L1 model from theideal value, however this agree with the measurement aswell as the P3T3L1 model. The data show explicitly that theincrease of λ is due to the unsteady flow. At small operatingpoints the λ deviation increases because the unsteady pumptorques are higher. This confirms the trend in the simulationand will be used to study the internal flow effects in theH.T.C..

The Fig. 6 shows the convergence history for the steadyand unsteady calculations at ν=0.7 for the maximum residu-als of the momentum. Convergence properties are influencedby the quality of the 3D mesh. It is also necessary thatthe solution be extended for long enough time to etablish

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

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Timestep0 500 100010-6

10-5

10-4

10-3

10-2

10-1

100

101

MAX P-MassMAX U-MomMAX V-MomMAX W-Mom

Fig. 6. Convergence History at Design Point ν=0.7

TABLE IISTEADY AND TIME-AVERAGED UNSTEADY TORQUES AT ν=0.7

Method MP [Nm] MT [Nm] µ

Steady 78.18 93.10 1.1908Unsteady 78.21 93.36 1.1937Experimental – – 1.16

periodic flow behaviour. For example at ν=0.8 about 500iterations were needed for the convergence of the steadysimulation and 400 iterations were required to etablish threesame periods (T = 40 ∆t) under the maximum residual below10−3. The table II shows that the calculated torques at ν=0.7have very small differences and the torque conversion µagree well with the experimental value. We can see that theunsteady µ is only 2.9% higher than the experimental dataand the steady µ about 2.7%. The differences between theglobal value µ in both calculations are very small.

The Fig. 7 shows the oscillation of the torques at ν=0.7.The steady simulation does not account for transient effectssuch as acceleration or inertia, because of that the steadysimulation is not able to resolve the torque oscillationsas shown by the plot. The time-averaged unsteady torquesare higher than the steady torques because of the unsteadyflow. This can result due to the unsteadiness depending onthe relative position of the blade that causes the torqueoscillation. The blade motion is sustained by extraction ofenergy from the uniform flow during each blade passage withthe corresponding frequency.

It should be noted that these torque fluctuations are theoscillation from the time-averaged values used for validation.The pump torque fluctuations in Fig. 8 vary by up to ±6%around the time-averaged value whereas the turbine torqueeven reaches ±9%. So we can come to the conclusion thatdue to the unsteadiness the pump and the turbine torques havea periodically behaviour. The forced response problem is dueto the potential flow interaction between fixed and rotatingcomponents, as well as periodic shocks on downstreamblading. These effects play a very important role on themachine life, it means structural fatigue and potential failure.

Time step

[Nm

]

600 800 1000 1200

60

80

100

120MP

MT

Fig. 7. Time Evolution of Torques ν=0.7

Timestep

∆M[

%]

600 800 1000 1200

-10

0

10

MP

MT

Fig. 8. Variation in Percent

IV. RESULTS AND DISCUSSION

A. Comparison between steady and unsteady simulation

The localization of the unsteady effects was done bycomparison between the steady and unsteady state. The com-parison in the chapter III-B of the nondimensional charac-teristics showed differences between the steady and unsteadycalculations. However, the steady simulation means that theresults only analyze the flow at a certain relative positionin comparison with the unsteady calculation reproducing thevariation in the flow as the position blade changes and takeaccount the time-dependent effects. In this part of the workthe steady and unsteady flow field will be compared for onerelative position in order to locate the present unsteadiness.For this purpose, the Fig. 9 shows the meridional velocitydifference ∆Cm between steady and unsteady simulation.

In the three parts in the Fig. 9 differences were found.As it can be seen, the flow fields between the stator-pumpand turbine-stator to be almost identical but a comparisonof the pump-turbine interaction area shows clearly higherdiscrepancies between both calculations in the blade wakeregion. The unsteady effects can clearly be seen along thepressure surface of the pump and the suction surface of theturbine. This interaction is the reason for faster mixing, herethe wake region is smaller in the steady than in the unsteady

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

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(a) Turbine (left)-Pump (right)

(b) Turbine (up)-Stator (down) (c) Stator (down)-Pump (up)

Fig. 9. Meridional Velocity Difference ∆Cm between the Steady andUnsteady Flow Field at the Midspan Plane

simulation. It means that in the steady simulation the wakesat the interface will be transported downstream and findthe turbine blades causing the upstream moving against thedownstream flow from the pump exit. The highest differencesat the turbine inlet occur in the area of the stagnation point. Inthe turbine passage the unsteady effects are small. However,in the suction side of the pump inlet and in the rotor-rotorinteraction area these become significant.

At the turbine inlet the deviation increases due to theblade/row interaction. One physical effect that can be re-sponsible for this is a shock wave forming at the trailingedge which interacts with the vortex shedding process behindthe blade. This phenomenon can be supported by observinga steady-state calculation that should not show this. In theunsteady simulation the flow must accelerate around thetrailing edge much more than in the steady calculation inorder to fill the wake. From this comparison, it is clear thatthe unsteady effects over the turbine suction surface are notequivalent to the effects on the pressure side of the blade.At the turbine inlet can be seen, that the mixing process ofunsteady flow leaving the pump blade is strongly affected bythe position of the pump that causes downstream conditions.

We can come to the conclusion that the wakes of thedownstream flow by the steady simulation will be clearlypredicted larger than by the unsteady calculation. Moreinformation about the interaction area between the rotorscan be obtained by the plotting of the meridional velocityfluctuation for relative positions of the pump and turbine.

B. Unsteady Simulation

The flow inside the H.T.C. is periodic in time (T=60∆t).First of all, it is known that the effects of these interactionsdepend on the number of blades (ZP = 31 and ZT = 29).In this part of the paper the pump/turbine interface will bestudied by analizing of the unsteady instantaneous meridionalvelocity (Cm) for four different relative pump/turbine posi-tions of a period T at the pump exit and turbine inlet. Theimportant problem here is how the flow information passes

(a) T

(b) T+T4

(c) T+T2

(d) T+ 3T4

Fig. 10. Cm Contour Plot for One Period T at Turbine Inlet and PumpBlade Relative position (represented by black lines)

between two rotating blade rows. In Fig. 10 the unsteady Cmdistribution is shown in an axially constant contour plot at theturbine inlet located downstream of the pump. The objectivehere is to show the velocity distribution in the relative frameof reference of the turbine inlet for distinct relative positionsof the pump. The contours show clearly three low velocityregions, which represent exactly the relative pump bladeposition in front of the turbine inlet. These low velocityareas are due the dcownstream effect of the wakes fromthe pump and the stagnation regions of the turbine. Herethe superposition of the pump and turbine blade wakes takeplace. This interaction between the downstream pump wakesand the upstream turbine wakes seem to be the principalcause of the unsteady disturbances, which are directly relatedwith pressure and torque oscillations (Fig. 7).

Because of the small axial gap, the pump causes andownstream unsteady effect on the turbine inlet flow asshown in the Fig. 10. The unsteady flow of the turbine inletflow field can clearly be seen. The pump has a significantdownstream influence on the turbine inlet flow because thepump exit flow will be forced into the turbine inlet passagesdepending on the relative position between pump and turbine.The low velocity region (wake) between two large velocityareas coincides with the pump blade position and its suctionside. This location is affected by the position of the pumpblades. No significant influences of the pump blade positionscould be seen in the low velocity area under the high velocity

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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(a) T

(b) T+T4

(c) T+T2

(d) T+ 3T4

Fig. 11. Cm Contour Plot for One Period T at Pump Exit and TurbineBlades Relative Position (black lines)

region in the passage.The Fig. 11 shows the pump exit plane and the relative

turbine blade positions for a cycle. A slightly periodicallyinfluence on the pump exit due to the aerodynamic bladerow interactions can be observed. The position of the turbineblades causes only slightly unsteady effects and velocitydecrease at the pump exit. The influence of the turbinewill be reduced in direction of the pump pressure side.Due to the aerodynamic interactions of the blade rows thevelocity distributions change considerably in time. For thisreason unsteady blade forces and torques are generated. Theprincipal cause of wake interaction is the downstream rowthat is directly influenced by the pitch ratio, the differentrotating speeds, axial gap between components (proximity)and complex geometry. The main consequences of the growthof unsteadiness are the increase of the losses and on the otherhand the increased loading of the blades with fluctuatingforces, causing that the blades can be excited to vibrate.

V. CONCLUSION

The present paper shows the flow investigation of a torqueconverter. Comparing unsteady with steady calculations the

particularities can be localized and quantified. To simulate aflow field having high frequency oscillations due to phenom-ena such as blade/wake interactions, very fine grids and smalltime steps as well as high computer resources are required.The computational resources time for unsteady flow are tentimes higher than those for a steady.

Measurements verify the calculated global values obtainedby CFD calculations. The results (Fig. 5) indicate thatdifferences between steady and unsteady simulation occursignificantly at low operating points. The torque conversiondiffers less than 4% over the operating area.

The results showed a 3D unsteady behaviour in thepump/turbine interaction area between incoming wakes andturbine passage structure. The wake area shows a wake struc-ture in the region at turbine inlet. The significant changes invelocity are induced by the relative position of the rotors. Atthe interaction region there is a superposition of the bladewakes (blade cutting), that causes an increase of the Cm.

The turbine blade position have a little influence on thepump exit flow field, whereas the turbine inlet flow shows asignificant periodic dependence on the relative pump bladepositions. The change in velocity are induced by the relativemotion of the rotors. It was noted that the rotor wakesat turbine inlet are stronger than those at pump exit. Atthe speed ratio ν=0.7 the downstream flow into the turbinepassage is uniform and more forced against the blades thanfor lower speed ratios because of rotating velocity differencebetween pump and turbine. Because of that it is expectedthat more unsteadiness at lower speed ratios appear (Fig. 5).

REFERENCES

[1] A. Ruprecht. Unsteady Flow Analysis in Hydraulic Turbomachinery.Technical report, Institute of Fluid mechanics and hydraulic MachineryUniversity of Stuttgart, Germany, May 2001. Invited lecture, AppliedIndustrial Fluid Dynamics, Aalborg.

[2] J. Schweitzer and J. Gandham. Computational fluid dynamics intorque converters: validation and application. International Journalof Rotating Machinery, 9:411–418, 2003.

[3] J. Park and K. Cho. Numerical flow analysis of torque converterusing interrow mixing model. JSME International Journal, 41:847–854, 1998.

[4] H. Schulz; R. Greim and W. Volgmann. Calculation of three dimen-sional viscous flow in hydrodynamic torque converter. ASME Journalof Turbomachinery, 118:578–589, 1996.

[5] Y. Kunisaki et al. A study on internal flow field of automotive torqueconverter: three dimensional flow analysis around a stator cascade ofautomotive torque converter by using PIV and CT techniques. JSAE,22:559–564, 2001.

[6] A. Habsieger and R. Flack. Flow characteristics at the pump-turbineinterface of a torque converter at extreme speed ratios. InternationalJournal of Rotating Machinery, 9:419–426, 2003.

[7] T. Roecken; C. Achtelik and R. Greim. Stroemungsuntersuchungin hydrodyamischen Wandlern: Zusammenspiel von Messung undRechnung. Forsch Ingenieurwes, 63:293–307, 1997.

[8] H. Foerster. Automatische Fahrzeuggetriebe: Grundlagen, Bauformen,Eigenschaften, Besonderheiten. Springer-Verlag Berlin et al., 1990.

[9] Esso A.G. Bereich S.: Datenblatt ATF LT 71141. 1. MoorburgerBogen 12, 1995. 21079 Hamburg.

[10] M. Giles. Calculation of unsteady wake/rotor interaction. J. Propul.Power, 4:356–362, 1988.

[11] B. Launder and D. Spalding. The numerical computation of turbulentflows. Computer Methods in Applied Mechanics and Engineering,3:269–289, 1974.

[12] M. Wollnik; W. Volgmann and H. Stoff. Importance of the navier-stokes sorces on the flow in a hydrodynamic torque converter. WSEASTransactions on Fluid mechanics, 5:363–369, 2006.

[13] M. Wollnik. Auswirkungen des Schaufelkanalverlaufs auf die Anteilehydrodynamischer Kraftuebertragung in Trilok-Drehmomentwandlern.PhD thesis, Ruhr-University-Bochum, 2008.

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Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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