performance prediction of cross-flow fans using...

International Journal of Rotating Machinery 20052 112ndash116ccopy 2005 Jae-Won Kim et al

Performance Prediction of Cross-Flow FansUsing Mean Streamline Analysis

Jae-Won KimDepartment of Mechanical Engineering Sunmoon University Asan City Chung Nam 336-804 KoreaEmail jwksunmoonackr

Eun Young AhnDivision of Information amp Communication Engineering Cheonan University Cheonan Chung Nam 330-704 KoreaEmail ahnyoungcheonanackr

Hyoung Woo OhDepartment of Mechanical Engineering Chungju National University Chungju Chungbuk 380-702 KoreaEmail hw ohchungjuackr

Received 22 February 2004

This paper presents the mean streamline analysis using the empirical loss correlations for performance prediction of cross-flowfans Comparison of overall performance predictions with test data of a cross-flow fan system with a simplified vortex wall scrollcasing and with the published experimental characteristics for a cross-flow fan has been carried out to demonstrate the accuracyof the proposed method Predicted performance curves by the present mean streamline analysis agree well with experimentaldata for two different cross-flow fans over the normal operating conditions The prediction method presented herein can be usedefficiently as a tool for the preliminary design and performance analysis of general-purpose cross-flow fans

Keywords and phrases cross-flow fan mean streamline analysis loss correlation performance prediction

1 INTRODUCTION

The cross-flow fans are not so widely used in industrial ap-plications as axial-flow or centrifugal fans due to their lowefficiency However their silent operations are particularlysuitable in domestic applications such as air-conditioner andair-curtain systems The cross-flow fan has a drum-type im-peller with multiple forward-curved blades and can generatehigh discharge flow rate by simply increasing the longitudi-nal axial length of impeller Figure 1a represents the overallgeometry of cross-flow fan running in the market Figure 1bshows the two-stage traverse of inflowsoutflows and the sup-plementary structure such as vortex wall (straight line in thisfigure) and rear guide As shown in Figure 1b the flows passbetween the blades on one side of the impeller through theinternal space of the runner and then through the blade pas-sages for a second time to discharge on the other side of theimpeller

This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution andreproduction in any medium provided the original work is properly cited

There have been a number of previous works for variouskinds of performance characteristics of cross-flow fans in theopen literature (Tanaka [1] Tsurusaki et al [2] Lazzaretto etal [3] Matsuki et al [4]) Experimental investigations to ver-ify the validity of similarity laws have been made by Tanakaand Murata [5 6] They presented the most detailed analy-sis on similarity operation for cross-flow fans It was foundthat performance curves for cross-flow fans are affected byflow viscosity for the blade Reynolds numbers lower than10 000 to 15 000 Moreover they observed that the impellerdimensions also influence fan performance curves A largerimpeller diameter results in an approximately proportionalincrease in the maximum flow coefficient

Other studies in the literature (Murata and Nishihara[7 8] Porter and Markland [9] Martegani et al [10]) havedemonstrated that fan performance curves are strongly af-fected by the vortex shape and dimension which are in-fluenced by the shape and dimension of the casing wallsfor a given impeller These findings suggest further stud-ies of the effects on fan performance of Reynolds numberand fan dimensions under varied casing geometrical charac-teristics Although the computational fluid dynamics (CFD)

Prediction of Fan Performance 113

(a)

Inflow

Outflow

1i

1o

+ω

2i

2o

(b)

Figure 1 Overall geometry and flow configuration of a cross-flowfan

procedures have substantially progressed in the analysis ofturbomachinery over the past several decades owing to theirexpensive and time-consuming resource in calculating theunsteady three-dimensional rotating flow field through aturbomachine the mean streamline performance analysisusing empirical loss correlations has continued to play a keyrole in the most accurate and practical application of predict-ing the performance of turbomachinery

The present study is aimed at finding proper loss correla-tions for more precise performance prediction of cross-flowfans The predictions using the empirical loss models sug-gested here are compared with experimental data obtainedfrom this study and also with the published data in the openliterature (Porter and Markland [9])

2 MEAN STREAMLINE ANALYSIS

The prediction method based on the mean streamline anal-ysis using empirical loss correlations has been developed forperformance evaluation of cross-flow fan and its predictivecapabilities validated by comparing with experimental dataobtained from the fan test rigs

The measurement system (wind tunnel) that pertains tothe ASHRAE (American Society of Heating Refrigeratingand Air-Conditioning Engineers) Standard (1985) has beenutilized for the estimation of performance characteristics

U1i

β1i

W1i

α1i

V1i

U1o

β1o

W1o

α1o

V1o

(a)

U2i

β2i

W2i

α2i

V2i

U2o

β2o

W2o

α2o

V2o

(b)

Figure 2 Velocity triangles of a cross-flow fan

3 EMPIRICAL LOSS CORRELATIONS

Mean streamline analysis adopted for performance pre-diction of cross-flow fans in the present study is a one-dimensional analysis that the flow is considered to be uni-formly distributed over the cross-section of flow passagewhere only the overall characteristics of the component per-formance are modeled not with particular emphasis on un-derstanding internal flow phenomena but with taking com-ponent losses into consideration

In order to apply this prediction method to cross-flowfans the velocity triangles (for the averaged velocity com-ponents) at the inlet and outlet parts have to be first de-termined The averaged velocity can calculate the merid-ional velocity components over the impeller flow passageand the tangential velocity components evaluated from themeridional velocity and the impeller rotational speed Whilethe no-slip tangential flow condition has been employed forcomputing the tangential velocity components the impellerexit flow condition that is the tangential velocity componentat the position 2o can be estimated by using the concept of aslip factor Figure 2 shows the typical inlet and outlet velocitytriangles (Figure 2a and Figure 2b respectively) of a cross-flow fan

Even though the flow between the impeller blades is as-sumed to be under ideal frictionless conditions the relativeeddies in the impeller blade passage can make the impellerexit relative flow angle differ from the impeller exit blade an-gle A measure of deviation can be calculated using the con-cept of a slip factor The present study applies the slip factorformulation of Stodola (Eck [12]) without any modification(see (1)) to calculate the tangential absolute velocity compo-nent at the impeller outlet Figure 3 shows the impeller exit

114 International Journal of Rotating Machinery

Vslip

V2oid

W2o

V2o

β2o

β2ob

W2oid

U2o

Figure 3 Modified velocity triangle with slip velocity at the im-peller exit

velocity triangle considering the slip velocity (Vslip)

Vslip = π U2o sinβ2ob

Z (1)

Euler input work of cross-flow fans can then be calculated asfollows

HEuler =[U2oVu2o +U1iVu1i

]

g (2)

where the plus sign is due to the opposite direction ofU1i andVu1i However in most cases the performance calculation ofcross-flow fans can be achieved with acceptable accuracy un-der the condition of no inlet prewhirl (Vu1i

sim=0)The pressure rise performance of cross-flow fans can be

evaluated by the following equations

∆po = ρg[HEuler minus

sum∆HL

] (3)

∆ps = ∆po minus 12ρV

2 (4)

wheresum∆HL represents the sum of all internal total pressure

head losses in cross-flow fan The present study adopts therecommended loss models for centrifugal pumps (Oh andChung [13]) to predict the performance curves of cross-flowfans The dynamic pressure velocity in this study is an aver-age velocity based on the area of a large plenum chamber onwhich the static pressure taps are fitted

Total internal aerodynamic losses consist of losses in theimpeller and those in the scroll casing Many investigatorshave studied losses generated within the turbomachinerycomponent Their specific effects and contributions to theentropy increase in turbomachines are given in the literature(Whitfield and Baines [14] Denton [15]) The representativedistributions of specific loss mechanisms in turbomachinesare given in [16] by Thanapandi and Prasad The loss mecha-nisms in the impeller are assumed to be made up of incidenceand skin friction losses and the scroll casing loss includes ex-pansion enlargement and skin friction losses

Incidence loss ∆Hinc

The direction of the relative flow no longer coincides withthe blade angle as the flow rate is varied As a result of anyvariation of incidence at the leading edges of the blades a losscalled an incidence loss arises and can be modeled as follows

∆Hinc = W2ui

2g (5)

Skin friction loss ∆Hsf

The skin friction loss is defined as the total pressure loss dueto shear forces exerted on the fluid within the impeller chan-nels This loss is modeled using pipe flow correlations as

∆Hsf = 2CfLbDhyd

W2

g (6)

Expansion loss ∆Hexp

This loss is due to sudden expansion of flows from impellerexit to scroll casing which can be estimated as the followingequation

∆Hexp = 075(Vu2o minusVth)2 +V 2

m2o

2g (7)

Enlargement loss ∆Henl

Enlargement loss from scroll casing throat to fan discharge isusually expressed as

∆Henl = (Vth minusVexit)2

2g (8)

Skin friction loss in scroll casing ∆Hvsf

The skin friction loss in scroll casing is also taken to be equiv-alent to skin friction loss experienced by a fully developedflow in a pipe This loss is modified using experimental co-efficient ξ (taken as 035 in this study) as follows

∆Hvsf = ξ C fSsc

Ath

V 2th

2g ξ = 02minus 05 (9)

4 EXPERIMENTAL APPARATUS

A test setup was designed and built following the ASHRAEStandard (1985) The overall layout of the experimental ap-paratus is shown in Figure 4 With such arrangement the fa-cility could be used to measure the fan performance curvesBasic experimental measurements including fan static pres-sure discharge flow rate and impeller rotational speed aretaken in the present study Wall static pressures in a plenumchamber are averaged in a manifold with four duct taps Thebulk total pressure delivered total head is derived from thestatic pressure measurements and the assumption of uniformvelocity at the measuring station The fan discharge flowrate is calculated from the pressure difference across nozzles


Cro

ss-fl

owfa

n

Static pressure tap

Driving motor

Ou

tflow Blower

(a)

Static pressure taps

Inflow

Drivingmotor

(b)

Figure 4 Schematic diagram of test setup

in a settling chamber A discharging blower with a butter-fly valve in the fan tester achieves airflow regulation Theperformance measurements are made at constant speeds of1 015 rpm through 1 450 rpm (with a step of 145 rpm) by adirect current electric motor Uncertainties are evaluated forflow rate and pressure rise Flow variables for flow rate andpressure rise utilize electric signals from pressure transducerswhose accuracy is equal to plusmn01 percent The overall uncer-tainty level of flow rate is in the range ofplusmn004658 percent toplusmn010691 percent because of the flow rate coefficient for thepresent venturi meter in the fan tester

5 RESULTS AND DISCUSSION

Performance predictions by the proposed method hereinare compared with the test results of two cross-flow fansFigure 5 shows a comparison of predictions (denoted bylines) and test data (represented by symbols) for the staticpressure rise characteristic curves of the prototype whose im-peller is composed of 34-circular arc forward-curved bladeswith outer diameter 95 mm and longitudinal axial length848 mm It is found that the agreement between calculationsbased on the mean streamline using the empirical loss corre-lations and experimental results is quite well over the normaloperating flow regions at higher rotational speeds

Although the present mean streamline (one-dimensional) analysis has proved to be inadequate inthe low flow rate region where the flow is strongly unsteadyunstable and three-dimensional the overall predictivecapability provides an indirect confirmation of the accuracyof the employed loss correlations in the normal operatingconditions The calculated distributions of specific losses

5

4

3

2

1

0

Stat

icpr

essu

reri

se(m

mH

2O

)

0 5 10 15 20 25 30 35

Volume flow rate (m3min)

1 450 rpm (experiment)1 305 rpm (experiment)1 160 rpm (experiment)

1 015 rpm (experiment)Prediction

Figure 5 Comparison of predicted and experimental static pres-sure rise performances for a cross-flow fan

6

5

4

3

2

1

0

minus1

Hea

dlo

ss(m

)

0 5 10 15 20 25 30 35


Discharge loss (1 450 rpm)Scroll casing loss (1 450 rpm)

Incidence loss (1 450 rpm)Skin friction loss (1 450 rpm)

Figure 6 Loss distributions in a cross-flow fan over the normaloperating condition

concerned in this analysis program are presented in Figure 6(eg operating condition for 1 450 rpm) The overall distri-butions of losses indicate that the scroll casing and dischargelosses are major losses over the operating flow regioncomparing to the impeller losses As a reference in Figure 6the discharge loss as an additional loss in the present study isdefined as the total pressure loss which is attributable to fluidmomentum loss through sudden area change from the scrollcasing discharge to the large plenum chamber with the staticpressure taps fitted and can be expressed as a reduction inthe scroll casing discharge dynamic pressure with expansionloss coefficient (Streeter [17])


3

25

2

15

1

05

0

ψs

andψo

0 02 04 06 08 1

φ

70

60

50

40

30

20

10

0

ηo(

)

ψo

ηo

ψs

Prediction

Figure 7 Comparison of calculated and measured performancesfor a cross-flow fan (Porter and Markland [9]) symbols representexperimental data 2 250 rpm

As shown in Figure 5 the characteristic curve of cross-flow fans shows a dip at low flow rates that is the pressurehead first decreases with increasing flow rate to form a localminimum and then increases to reach a local maximum Theeccentric vortex motion inside a rotating fan in this low ca-pacity range causes this wavy variation The eccentric vortexmotion reduces flow rates as an obstacle in a cross-flow fan(Lazzaretto et al [3] Murata and Nishihara [7 8] Porter andMarkland [9] Eck [12]) These phenomena lead to the no-ticeable discrepancy between calculations based on the meanstreamline analysis and measured data under the conditionof low flow rate and rotational speed

The prediction procedures based on the same numeri-cal scheme have also been tested against Porter and Mark-landrsquos work [9] for analysis validation of the present methodA comparison between the calculated and experimentalcharacteristic curves is illustrated in Figure 7 Although thepresent analysis method using the empirical loss models sug-gested in this paper is quite simple it can be seen from theresults in Figure 7 that the overall agreement of the predic-tion performance with the experimental data is fairly goodover the operating range

6 CONCLUDING REMARKS

The mean streamline analysis procedure has been utilizedfor prediction of the performance characteristics of cross-flow fans The set of loss correlations suggested by this studyis found to predict the performance curves of cross-flowfans with acceptable accuracy Although the present analysismethod could not properly handle the low flow character-istics peculiar to cross-flow fans in the low flow region thepredictions agree very satisfactorily with the measured per-formance curves over the normal operating conditions Thepredictive procedure developed throughout this study can be

used efficiently as a conceptual design tool in the prelimi-nary design phase of cross-flow fans and also assist the un-derstanding of the operational characteristics of cross-flowfans

ACKNOWLEDGMENT

This work was supported by the Regional Research Centerfor Advanced Climate Control Technology in Korea

REFERENCES

[1] S Tanaka ldquoScale effects in cross-flow fanrdquo JSME InternationalJournal Series B vol 59 pp 1153ndash1160 1993

[2] H Tsurusaki Y Tsujimoto Y Yoshida and K Kitagawa ldquoVi-sualization measurement and numerical analysis of internalflow in cross-flow fanrdquo ASME Journal of Fluids Engineeringvol 119 pp 633ndash646 1997

[3] A Lazzaretto A Macor A D Martegani and V MartinaldquoExperimental optimization of the casing of a cross flow fan(in Italian)rdquo in Proceeding of 52 Convegno Nazionale ATISGEditoriali-Padova Cernobbio Italy September 1997

[4] K Matsuki Y Shinobu and A Takushima ldquoExperimentalstudy of internal flow of a room air conditioner incorporatinga cross-flow fanrdquo ASHRAE Transactions vol 94 pp 364ndash4501988

[5] S Tanaka and S I Murata ldquoScale effect in cross-flow fans (ef-fects of fan dimension on performance curves)rdquo Bull JSMESeries B vol 37 no 4 pp 844ndash852 1994

[6] S Tanaka and S I Murata ldquoScale effect in cross-flow fans (ef-fects of fan dimension on flow details and the universal rep-resentation on performances)rdquo Bull JSME Series B vol 38no 3 pp 388ndash397 1995

[7] S I Murata and K Nishihara ldquoAn experimental study of crossflowmdash1st report effects of housing geometry on the fan per-formancerdquo Bull JSME vol 19 no 129 pp 461ndash471 1976

[8] S I Murata and K Nishihara ldquoAn experimental study of crossflowmdash2nd report movements of eccentric vortex inside im-pellerrdquo Bull JSME vol 19 no 129 pp 472ndash491 1976

[9] A M Porter and E Markland ldquoA study of the cross flow fanrdquoJournal Mechanical Engineering Science vol 12 no 6 pp 421ndash431 1970

[10] A D Martegani G Navarro A Macor et al ldquoExperimentaland numerical analyses of a cross flow fan (in Italian)rdquo in Pro-ceeding of 54 Congresso Nazionale ATI vol 2 pp 1409ndash1423SGEditoriali-Padova Lrsquoaquila Italy September 1999

[11] ASHRAE Standard Laboratory Methods of Testing Fans forRating American Society of Heating Refrigerating and Air-Conditioning Engineers Atlanta Ga USA 1985

[12] B Eck Fans Pergamon Press New York NY USA 1973[13] H W Oh and M K Chung ldquoOptimum values of design vari-

ables versus specific speed for centrifugal pumpsrdquo Proceedingsof the I MECH E Part A Journal of Power and Energy vol 213no 3 pp 219ndash226 1999

[14] A Whitfield and N C Baines Design of Radial Turboma-chines Longman Scientific and Technical Essex UK 1990

[15] J D Denton ldquoLoss mechanisms in turbomachinesrdquo ASMEJournal of Turbomachinery vol 115 no 4 pp 621ndash656 1993

[16] P Thanapandi and R Prasad ldquoPerformance prediction andloss analysis of low specific speed submersible pumpsrdquo Pro-ceedings of the I MECH E Part A Journal of Power and Energyvol 204 no A4 pp 243ndash252 1990

[17] V L Streeter Handbook of Fluid Dynamics McGraw-HillNew York NY USA 1961

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Navigation and Observation



DistributedSensor Networks



(a)

Inflow

Outflow

1i

1o

+ω

2i

2o

(b)

Figure 1 Overall geometry and flow configuration of a cross-flowfan

procedures have substantially progressed in the analysis ofturbomachinery over the past several decades owing to theirexpensive and time-consuming resource in calculating theunsteady three-dimensional rotating flow field through aturbomachine the mean streamline performance analysisusing empirical loss correlations has continued to play a keyrole in the most accurate and practical application of predict-ing the performance of turbomachinery

The present study is aimed at finding proper loss correla-tions for more precise performance prediction of cross-flowfans The predictions using the empirical loss models sug-gested here are compared with experimental data obtainedfrom this study and also with the published data in the openliterature (Porter and Markland [9])

2 MEAN STREAMLINE ANALYSIS

The prediction method based on the mean streamline anal-ysis using empirical loss correlations has been developed forperformance evaluation of cross-flow fan and its predictivecapabilities validated by comparing with experimental dataobtained from the fan test rigs

The measurement system (wind tunnel) that pertains tothe ASHRAE (American Society of Heating Refrigeratingand Air-Conditioning Engineers) Standard (1985) has beenutilized for the estimation of performance characteristics

U1i

β1i

W1i

α1i

V1i

U1o

β1o

W1o

α1o

V1o

(a)

U2i

β2i

W2i

α2i

V2i

U2o

β2o

W2o

α2o

V2o

(b)

Figure 2 Velocity triangles of a cross-flow fan

3 EMPIRICAL LOSS CORRELATIONS

Mean streamline analysis adopted for performance pre-diction of cross-flow fans in the present study is a one-dimensional analysis that the flow is considered to be uni-formly distributed over the cross-section of flow passagewhere only the overall characteristics of the component per-formance are modeled not with particular emphasis on un-derstanding internal flow phenomena but with taking com-ponent losses into consideration

In order to apply this prediction method to cross-flowfans the velocity triangles (for the averaged velocity com-ponents) at the inlet and outlet parts have to be first de-termined The averaged velocity can calculate the merid-ional velocity components over the impeller flow passageand the tangential velocity components evaluated from themeridional velocity and the impeller rotational speed Whilethe no-slip tangential flow condition has been employed forcomputing the tangential velocity components the impellerexit flow condition that is the tangential velocity componentat the position 2o can be estimated by using the concept of aslip factor Figure 2 shows the typical inlet and outlet velocitytriangles (Figure 2a and Figure 2b respectively) of a cross-flow fan

Even though the flow between the impeller blades is as-sumed to be under ideal frictionless conditions the relativeeddies in the impeller blade passage can make the impellerexit relative flow angle differ from the impeller exit blade an-gle A measure of deviation can be calculated using the con-cept of a slip factor The present study applies the slip factorformulation of Stodola (Eck [12]) without any modification(see (1)) to calculate the tangential absolute velocity compo-nent at the impeller outlet Figure 3 shows the impeller exit


Vslip

V2oid

W2o

V2o

β2o

β2ob

W2oid

U2o




Z (1)



]

g (2)





sum∆HL

] (3)


2 (4)






∆Hinc = W2ui

2g (5)



∆Hsf = 2CfLbDhyd

W2

g (6)




m2o

2g (7)




2g (8)



∆Hvsf = ξ C fSsc

Ath

V 2th

2g ξ = 02minus 05 (9)




Cro

ss-fl

owfa

n

Static pressure tap

Driving motor

Ou

tflow Blower

(a)


Inflow

Drivingmotor

(b)






5

4

3

2

1

0

Stat

icpr

essu

reri

se(m

mH

2O

)

0 5 10 15 20 25 30 35





6

5

4

3

2

1

0

minus1

Hea

dlo

ss(m

)

0 5 10 15 20 25 30 35







3

25

2

15

1

05

0

ψs

andψo

0 02 04 06 08 1

φ

70

60

50

40

30

20

10

0

ηo(

)

ψo

ηo

ψs

Prediction







ACKNOWLEDGMENT


REFERENCES




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Vslip

V2oid

W2o

V2o

β2o

β2ob

W2oid

U2o




Z (1)



]

g (2)





sum∆HL

] (3)


2 (4)






∆Hinc = W2ui

2g (5)



∆Hsf = 2CfLbDhyd

W2

g (6)




m2o

2g (7)




2g (8)



∆Hvsf = ξ C fSsc

Ath

V 2th

2g ξ = 02minus 05 (9)




Cro

ss-fl

owfa

n

Static pressure tap

Driving motor

Ou

tflow Blower

(a)


Inflow

Drivingmotor

(b)






5

4

3

2

1

0

Stat

icpr

essu

reri

se(m

mH

2O

)

0 5 10 15 20 25 30 35





6

5

4

3

2

1

0

minus1

Hea

dlo

ss(m

)

0 5 10 15 20 25 30 35







3

25

2

15

1

05

0

ψs

andψo

0 02 04 06 08 1

φ

70

60

50

40

30

20

10

0

ηo(

)

ψo

ηo

ψs

Prediction







ACKNOWLEDGMENT


REFERENCES




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Cro

ss-fl

owfa

n

Static pressure tap

Driving motor

Ou

tflow Blower

(a)


Inflow

Drivingmotor

(b)






5

4

3

2

1

0

Stat

icpr

essu

reri

se(m

mH

2O

)

0 5 10 15 20 25 30 35





6

5

4

3

2

1

0

minus1

Hea

dlo

ss(m

)

0 5 10 15 20 25 30 35







3

25

2

15

1

05

0

ψs

andψo

0 02 04 06 08 1

φ

70

60

50

40

30

20

10

0

ηo(

)

ψo

ηo

ψs

Prediction







ACKNOWLEDGMENT


REFERENCES




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3

25

2

15

1

05

0

ψs

andψo

0 02 04 06 08 1

φ

70

60

50

40

30

20

10

0

ηo(

)

ψo

ηo

ψs

Prediction







ACKNOWLEDGMENT


REFERENCES




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









performance prediction of cross-flow fans using...

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