Transaction B: Mechanical EngineeringVol. 16, No. 4, pp. 281{290c Sharif University of Technology, August 2009

Modeling of Twin-Entry Radial TurbinePerformance Characteristics Based

on Experimental Investigation UnderFull and Partial Admission Conditions

A. Hajilouy1;�, M. Rad1 and M.R. Shahhosseini1

Abstract. In this paper, the performance of a turbocharger twin-entry radial in ow turbine isinvestigated analytically and experimentally under steady state, full and partial admission conditions. Inthis modeling, the mass ow rate, pressure ratio and e�ciency of the turbine are assumed unknown. Theturbine geometry and the inlet total pressure and temperature are known, hence, the turbine performancecharacteristics can be obtained. In the turbocharger laboratory, performance characteristics of the turbineare determined, measuring the main parameters for various operating conditions. Comparing the modeland experimental results shows good agreement. Also, considering the e�ect of test parameters onperformance uncertainty, it shows that the pressure ratio has more in uence. Finally, the uncertainty ofe�ciency decreases as the pressure ratio increases.

Keywords: Radial in ow turbine; Full and partial admission conditions; Modeling; Turbocharger.

INTRODUCTION

Radial in ow turbines are widely used in diesel andCNG engine turbochargers, increasing power and e�-ciency and decreasing SFC in engines [1]. This paperfocuses on twin-entry radial turbine applications wherethe inlet ows are not the same. This is the case forturbochargers of multi-cylinder engines. Usually, inthese turbochargers, twin-entry radial turbines give theadvantage of using the exhaust pulse energy of gases. Inthese applications, turbines often work under o�-designconditions. Therefore, turbine performance charac-teristics under such conditions are important [1,2].There are a few published studies of twin-entry radialturbines under full and partial admission conditions;almost all of them are experimental [3-5]. Pischiger andWunsche [2] studied the interaction between the inletgas ows from the twin-entry turbines under steadyconditions. They showed that unequal inlet conditionshave a signi�cant e�ect on the ow pattern and tur-bine performance. Furthermore, they considered the

1. Department of Mechanical Engineering, Sharif University ofTechnology, Tehran, P.O. Box 11155-8639, Iran.

*. Corresponding author. E-mail: hajilouy@sharif.edu

Received 24 February 2007; received in revised form 14 August2007; accepted 10 February 2008

isentropic ow area through each entry, and showedthat this area depends on the pressure ratio betweenentries and the overall mean expansion ratio. Theperformance characteristics of a twin entry turbinewere prepared experimentally by Dale and Watson [5],showing that the best e�ciency is not under full admis-sion conditions. Then, Capabianco and Gambarotta [6]showed experimentally the e�ect of each entry of thevolute on full and partial admission conditions. Bainesand Yeo [7] performed ow laser measurements in aturbine rotor inlet and exit under full and partialadmission conditions. They suggested that the changesin performance under partial admission considerationsare linked to a spanwise variation in the rotor incidenceangle and velocity components at the rotor inlet.

The major modeling activities and performancepredictions of a radial in ow gas turbine were focusedon single entry turbines [8-12]. Chen and Winterbonemodeled a single entry radial turbine [9]. Heribernikand Dobovisek [10] presented a model for predictingsingle and twin-entry turbine performances based onideal relations. Gassemi et al. [12] presented a modelfor predicting single and twin entry turbine perfor-mances. They modi�ed the one-dimensional perfor-mance prediction method of a single-entry turbine toanalyze the twin-entry turbine performance.

282 A. Hajilouy, M. Rad and M.R. Shahhosseini

This research is based on experimental results.Due to the non-ideal measurement conditions, whichwere typically encountered during the test, the uncer-tainty of the test data is considered. A number ofresearch �ndings and standard codes have discussedgas turbine testing errors and uncertainties [14]. Thetest codes of PTC10 [15], PTC 19.1 [16] discuss in-struments, thermodynamic calculations and laboratorypreparations. Dale and Watson [5] discussed theuncertainty of a radial in ow gas turbine and showedthe variation of uncertainty with the speed ratio.Meanwhile, Yong and Penz [17] and Arcoumanis [18]presented a turbocharger test facility, test design andtest procedure.

This paper describes a method of prediction ofthe performance of a twin-entry radial in ow turbineunder steady, full and partial admission conditions.This model is based on one-dimensional performanceprediction. Loss coe�cients due to friction, clearance,blade loading and exit kinetic energy, which were al-ready developed for a single entry turbine, are modi�edfor a twin-entry turbine. Furthermore, additional lossesare considered due to partial admission conditions. Theresults of the model are evaluated with experimentalresults. Finally, an analytic method is described todetermine turbocharger turbine measurement uncer-tainties. By introducing experimental errors to theuncertainty equation, the e�ciency uncertainties of theturbine are obtained.

MODELING

The steady state performance prediction model devel-oped in this investigation is based on the solution ofan adiabatic, steady state, one-dimensional ow in atwin-entry radial in ow turbine. In one-dimensionalmodeling, due to the three-dimensionality and com-plexity of the ow pattern within the turbine, a goodunderstanding of the ow behavior is necessary toestimate accurate loss coe�cients. In this method,the mean ow parameters are obtained along a meanstreamline on key stations (inlet and exit of eachsection), using continuity, momentum, energy and stateequations and the second law of thermodynamics. Inthis study, the turbine ow passage is divided into�ve components including inlet passage, volute casing,interspace, incidence and rotor which are shown inFigure 1, and the ow is modeled in each section withimposing loss equations. This model is implied for aturbine with the main geometrical dimensions as shownin Table 1.

Inlet Passage

The program input consists of turbine geometry, inlettotal pressure and temperature and rotor speed, by

Figure 1. Twin-entry radial in ow gas turbine and mainmodeling stations.

Table 1. The turbine geometry.

Volute inlet area (A0) 0.0022 (m2)

Rotor inlet mean diameter (D3) 0.0736 (m)

Rotor inlet blade height (b3) 0.0088 (m)

Exducer hub diameter (D5h) 0.0233 (m)

Exducer shroud diameter (D5s) 0.0576 (m)

Number of blades (Z) 11

assuming a range of the critical velocity ratio (C=Ccr)for each inlet (shroud side and hub side).Therefore,for this modeling, the critical velocity at each side isdetermined by [9]:

Ccr =

s2 RT00

+ 1: (1)

Static density at the inlet is determined by:

�0

�00=

"1� � 1

+ 1

�CCcr

�2#1= �1

: (2)

Thus, the mass ow rate at the inlet of a turbine foreach side is determined. The Mach number at station 1,Figure 1, (M1) for each side is computed from thefollowing equation, derived in [3]:

_mpRT00= A1P00

=�0�1 cos(�1)M1

�1+

�12

M21

� +12(1� )

;(3)

where:

� = e(��s=R): (4)

The inlet duct is short and direct. Therefore, itsloss coe�cient, �0�1, and exit ow angle, �1, areassumed one and zero, respectively. Having solvedEquation 3, the ow properties in station 1, Figure 1,are determined.

Modeling of Twin-Entry Radial Turbine Performance 283

Volute Casing

The turbine spiral volute exit ow parameters shouldbe determined. In station 2, Figure 1, for each entrythe following equation is computed iteratively:

_mpRT01= A2P01

=�1�2 cos(�2)M2

�1+

� 12

M22

� +12(1� )

:(5)

The ow angle, �2, and the ow entropy gain, �1�2, areobtained from a method presented by Balje [20]. Then,the iteration loop is repeated until the desired accuracyis obtained and exit Mach number and properties aredetermined.

Interspace

In the interspace area (stations 2 and 3, Figure 1), theinteraction of the hub and the shroud side ows aretaken into consideration (Figure 2). For determiningthe ow properties at the exit of this region, governingequations for each side are solved. The loss coe�cientin this region is due to the friction of the hub andshroud streams and the wake of the divider. Themethod used to calculate the wake loss is given in [21].

The friction and the wake losses are calculatedseparately. Friction loss and ow angle are obtainedusing a simple numerical method to solve continuity,momentum, energy and gas state equations simultane-ously. The wake loss is obtained by considering theaverage condition in the inlet and the simultaneoussolving of the governing equations [21]; half of thewake loss is considered for each entry. Then, thesetwo losses are added together for each entry. Therefore,�2�3;friction and �2�3;wake are de�ned, and the followingtotal ow entropy gain correlation for each entry is usedto calculate the losses in the interspace area:

Figure 2. Hub and shroud velocity.

�2�3 = �2�3;friction:p�2�3;wake: (6)

In section 3, Figure 1, for each entry Equation 6 issolved iteratively:

_mpRT02= A3P02

= �2�3 cos(�3)M3

�1+

� 12

M23

� +12(1� )

:(7)

Incidence

Incidence loss at the rotor inlet is the main cause of ane�ciency drop under o�-design conditions. In practice,the best e�ciency occurs at an optimum incidenceangle. Therefore, any deviation from the optimumincidence angle causes extra losses. In this modeling,the incidence area (stations 3 and 4, Figure 1) is ahypothetical region and the incidence loss is part ofthe rotor loss, but for the reason of modeling strategyit is modeled separately. The objective of the incidencemodel is to drive an entropy increase due to theincidence angle. Several models have been introducedto calculate the incidence losses. In this study, aNASA extended model is used, which is based on theassumption that the kinetic energy associated with thechange in relative tangential velocity is converted intothe internal energy of the working uid [9]. This regionis assumed as a moving passage and Equation 8 is usedfor computing the relative Mach number at this section:

_mpRT 003= P 003A4

=�3�4M 04�

1+ � 1

2M 024

��( +1)=2( �1)

:(8)

The incident loss, �3�4, is calculated by [10]:

If j�3 � �3optj > �=4 then :

�h00inc = h003 � h004s =12

[W3 sin (j�3 � �3optj)]2 :(9)

And if j�3 � �3optj < �=4, then:

�h00inc =12W 2

3 (0:5 + j�3 � �3optj � �=4) : (10)

So:

�3�4 =�

1� �h00inccpT 003

� �1

: (11)

Also, the optimum ow angle is calculated by [3]:

�3opt = arctan� �1:98ZB(1� 1:98=ZB)

tan(�3)�: (12)

284 A. Hajilouy, M. Rad and M.R. Shahhosseini

Rotor

The complex three-dimensional ow pattern in therotor raises the di�culties in the rotor modeling andcauses major turbine losses in the rotor. The followingequations are used for ow modeling at the single-entry turbine rotor, which combines the equations ofcontinuity, energy and entropy [3]:

_mpRT 004= A5P 004

= cos(�5):�:M 05�1 +

( � 1)2

M025

��( +1)=2( �1)

�1� U2

4 � U25

2cpT 004

�( +1)=2( �1)

; (13)

where:

� =�

1� � 1 RT 00e

U2t �q

� =( �1)

; (14)

�q =h00e � h00es

U2t

=�h00esU2t

: (15)

Equation 13 is modi�ed for the twin-entry turbinerotor, considering the e�ect of partial admission con-ditions. Therefore, the following non-dimensionalequation is used for modeling the twin-entry rotor owarea (stations 4 and 5, Figure 1) [13]:

_mpR= A5

0@qT 004;s

P 004;s

1AMrs

:

0@qT 004;h

P 004;h

1AMrh

=

�4�5: cos(�5)M 05�

1 +( � 1)

2M 025

�� ( +1)2( �1)

8<: 1� U24 � U2

52CpT 004;s

!Mrs

:

1� U2

4 � U25

2CpT 004;h

!Mrh9=;

( +1)2( �1)

;(16)

where Mrs = _m_ms+ _mh and Mrh = _mh

_ms+ _mh .In Equation 16, the e�ect of shroud and hub side

ow losses can be considered. For this reason, thefollowing model is suggested [13]:

�4�5 =

(�1� � 1

RT 005U2t �qs

�Mrs

�1� � 1

RT 005U2t �qh

�Mrh) �1

: (17)

Also, the single-entry rotor loss coe�cient is modi�edto obtain losses in the twin-entry rotor as follows.

a) Friction Loss

This loss is computed in the same way as obtained ina curved duct [11,22]:

�qfr = fcLHDH

:�W 2

2U2t; (18)

�W 2 =12�(MrsW4s +MrhW4h)2 +W 2

5�; (19)

fc = f(1 + 0:75Re0:25pDH=2rc); (20)

where:

1pf

= 0:2 ln�ReDH

pf�� 1:19: (21)

b) Blade Loading Loss

The following equation is used to calculate the bladeloading loss [23]:

�qbl =C2�3Dt

ZLRU2t: (22)

LR is calculated using the equation given by Whit�eldand Baines [3].

c) Clearance Loss

The clearance loss is calculated from the followingequation [3]:

�qcl = 0:4(eCl=bt)(C�3=Ut)2; (23)

where:

eCl = 0:008=(2bt=Dt): (24)

d) Exit Loss

The exit loss is considered with the assumption thatthe kinetic energy associated with rotor exit velocity,at the outlet of the rotor, is dissipated:

�qexit = 0:5C2

5U2t: (25)

Modeling of Twin-Entry Radial Turbine Performance 285

Finally, the non-dimensional energy loss in the rotor�qtotal is determined:

�qtotal = �qfr + �qbl + �qcl + �qexit; (26)

�R = e(��s=R) =�

1� � 1 RT 005

U2t �qtotal

� =( �1)

:(27)

e) Rotor Mixing Loss

Rotor mixing loss is considered only in the twin-entryradial turbine, as a result of the di�erence in the mass ows of the shroud and hub entries. As shown inFigure 3, the entropy increase for this process can beobtained by solving the governing equation within thecontrol volume, encompassing the mixing process at therotor inlet for revealing the downstream ow propertiesand the entropy gain. Therefore, the entropy gainassociated with the mixing process between hub andshroud side ows is obtained from:

�smR

=

� 1ln�Ty�T3

�� ln

�Py�P3

�; (28)

�R�mixing = e(��sm=R): (29)

Finally, the rotor loss coe�cient is obtained:

�rotor = �4�5 = �R:�R�mixing: (30)

SOLUTION PROCEDURE

The analysis consists of a section by section solutionof ow conditions through the turbine along the meanstreamline. In this procedure, the turbine geomety isspeci�ed. Meanwhile, at a �xed rotor speed, speedvelocity ratios for both entries are given. With thisratio, the mass ow for each entry is speci�ed. Underthese conditions, ow equations for each section are

Figure 3. Hub and shroud mixing station.

solved up to the end. The iteration loop is repeateduntil the desired accuracy is reached. By solving the ow equations, the Mach number, loss coe�cent andexit properties for each area are determined. Thus, atthe end of each area, exit conditions, which are inletconditions of the next area, are determined. In thisprocedure, ow at each side is considered separatelyup to passage 4-5. In passage 4-5, just one ow isconsidered. At the end of the procedure, the massparameter, pressure ratio and total-static e�ciencyare calculated and this procedure is repeated for thenext velocity ratio up to the end of the (C=Ccr)range. Indeed, in this program, the stator is chockedwhen (C=Ccr)3 = 1 and the rotor is chocked when(W=Wcr)5 = 1, which are the maximum ows perunit area, and the program is terminated at theseconditions.

TURBOCHARGER LABORATORY

The turbocharger test rig has been designed, estab-lished and equipped to investigate di�erent automotiveturbochargers under a variety of operational condi-tions, based on the ow simulation of a turbochargerusing compressed air. The main speci�cations of thetest, which can be carried out in the rig, are as follows:

1. Steady ow tests using a compressor to absorb andmeasure the power of the turbine;

2. Full and partial admission measurements on atwin-entry turbine using a twin-inlet test system.The arrangement of the test rig facility is shownschematically in Figure 4.

Three screw compressors are employed to producehigh pressure air, adjustable up to a 13 bar gauge witha mass ow rate of 0.4 kg per sec. The main compressedair supply line is a 3-inch diameter pipe. The mass owrate is adjusted using an electro-pneumatic valve. Inorder to measure the steady ow air mass ow rate,in turbine side three and in the compressor side, oneori�ce plate calibrated to BS 1042 is used [19]. Thecompressed air can be heated up to 200 degrees Celsiususing an electrical heater unit. This is to preventthe condensation of any water vapor at the turbineblades, where there is a high temperature drop dueto the air expansion. The heater unit consists of 32elements, each 2 kW in power, suitable for various mass ow rates and di�erent temperature rise conditions. Aturbocharger compressor absorbs the turbine outputpower, acting as a dynamometer, and controls therotational speed of the turbocharger. The compressoroutlet air passes through an additional throttle valveand is exhausted to the atmosphere out of the labora-tory by a two-inch exit duct. Also, the mass ow ratesto the two-entry can be controlled independently. A

286 A. Hajilouy, M. Rad and M.R. Shahhosseini

Figure 4. Schematic of turbocharger test rig and measuring stations.

full admission condition to the turbine occurs when thecontrol valves of each entry are fully opened. A partialadmission ow condition is achieved by varying the owin each entry. The full admission performance of atwin-entry turbine for 30000, 40000, 50000 and 60000rpm is shown in Figures 5 and 6. The operation rangeis limited by the surge point of the loading compressor.Figure 5 shows the mass ow curves and Figure 6 showsthe total-static e�ciency curves versus the pressureratio. The maximum di�erence between experimentaland theoretical results under full admission conditionsis 2% for mass parameter and 1.5% for e�ciency.

FULL AND PARTIAL ADMISSIONRESULTS

In the literature, Zanghaneh et al. [24] for a single-entry turbine, and Baines and Yeo [7] for a twin-entry turbine with full and partial admission conditionsshowed that the ow at the rotor inlet tends to pass

Figure 5. Experimental and theoretical results of mass ow characteristics under full admission.

through the shroud side, and the best e�ciency isobtained when there is more ow in the shroud side.As shown in experimental results (Figure 7), the beste�ciency occurs when Ms=Mh = 1:15. Therefore, inthis case, losses are the lowest. Figure 8 shows that in

Modeling of Twin-Entry Radial Turbine Performance 287

this condition, the mass ow parameter is higher thanthe full admission condition with the same pressureratio due to lower losses. Figure 9 shows the e�ciencyprediction of the turbine under �ve di�erent partialadmission conditions that are compared with exper-imental results at 50000 rpm, having the maximum

Figure 6. Experimental and theoretical results ofe�ciency characteristics under full admission.

Figure 7. Measured e�ciency under full and partialadmission at 50000 rpm.

Figure 8. Measured mass parameter under full andpartial admission at 50000 rpm.

Figure 9. Experimental and modeling e�ciency resultsunder partial admission at 50000 rpm.

288 A. Hajilouy, M. Rad and M.R. Shahhosseini

deviation of calculated results from experimental datafor a shroud side closed condition (Case a). This canbe due to the less accurate estimate of the mixing lossat the inlet of the rotor.

TURBINE TEST UNCERTAINTIES

After calibrating the instruments, making sure of cor-rect installation and conforming to standard codes, thesources of measurement errors encountered during testmeasurements should be determined. Measurementsare always subject to error, i.e. the di�erence betweenthe true and measured values. Since the true valueis unknown, the error in measurement cannot bedetermined exactly. Therefore, only the error band canbe estimated. Thus, uncertainty is introduced, whichis an estimate of the interval about the measurementvalue that is expected to encompass the true value.

The total measurement error consists of twocomponents: (1) Systematic error or bias or �xederror; (2) Random error. Accurate measurementrequires minimization of both systematic and randomerrors [16].

For uncertainty analysis, a procedure is intro-duced that consists of �ve basic steps, as explained indetail in [25].

Data Reduction Equations

The total to static e�ciency equation of a turbine is asfollows:

�ts =1� T0out

T0in

1� hPoutP0in

i �1 : (31)

Therefore, the parameters that are measured duringa test for this case are: the turbine inlet and outlettemperatures and pressures.

Sensitivity Coe�cients

Sensitivity coe�cients play an important role in eval-uating instrument errors, also helping to identify pa-rameters which have the most signi�cant e�ect onuncertainty. The sensitivity coe�cient is the ratio of

the change in the result to a unit change in parameters.The relative sensitivity of y to Xi is given by:

Sr �Xi =�@y@ �Xi

�� �Xi

y

�: (32)

Substituting Equation 31 into Equation 32 gives therelative sensitivity of e�ciency to a unit change in eachparameter of Equation 31. As shown in Table 2, thesensitivity of e�ciency to the input and output tem-perature is more than the input and output pressure.Therefore, temperature has a stronger in uence one�ciency. Meanwhile, as the pressure ratio increases,sensitivity to the pressure and temperature decreases.

Uncertainty of Results

For an uncertainty analysis, it is assumed that all mea-surement parameters are independent and have Gaus-sian normal distributions around their mean valueswith a statistical bound of a 95% con�dence interval.So, total uncertainty, U95, for a given function, X, isdetermined as:

Bry = t95

" jXi=1

�Sr �Xi

�r �Xi2

�2#1=2

; (33)

�ry =

" jXi=1

(Sr �Xi�r �Xi)2

#1=2

; (34)

Ur95 = t95

s�Bry

2

�2

+ (�ry)2: (35)

In these equations, t95 is determined by student-tdistribution.

The total uncertainty of the turbine e�ciencyversus pressure ratio for four test speeds is shown inFigure 10. As the pressure ratio increases, the e�ciencyuncertainty decreases in the range of the experimentalpressure ratio. In the range of the experimental pres-sure ratio, high uncertainty in the low pressure ratioshows a higher sensitivity of uncertainty to the lowspeed condition in the turbine. This result is expectedand can be explained as follows: The larger the pressureor temperature inlet-outlet di�erential, the smaller therelative in uence of individual measurement errors ontotal performance uncertainties.

Table 2. Mean relative sensitivity of e�ciency in constant speed at 50000 rpm.

Pressure Ratio Exit Pressure (%) Inlet Pressure (%) Exit Temperature (%) Inlet Temperature (%)

1.372 2.98 -2.98 -15.36 15.36

1.387 2.91 -2.91 -14.86 14.86

1.398 2.84 -2.84 -14.47 14.47

1.412 2.75 -2.75 -13.83 13.83

1.425 2.69 -2.69 -13.50 13.50

Modeling of Twin-Entry Radial Turbine Performance 289

Figure 10. Total e�ciency uncertainty versus turbinepressure ratio.

CONCLUSION

In this paper, a one-dimensional ow model for theperformance prediction of a twin-entry radial in owgas turbine under partial and full admission conditionsis presented. A steady ow model, based on losscorrelation, is used to predict the turbine performance.Results of this model are compared with experimentaldata and they are in reasonable agreement. Themain limitation in experimental data is due to thecompressor surge. The di�erence between experimentaland theoretical results under full admission conditionsis 2% for mass parameter and 1.5% for e�ciency. How-ever, under partial admission conditions, the maximumdi�erence between results reaches to 5% for a shroudside closed case and this deviation can be due to a lessaccurate estimate of mixing loss and equally dividedinterspace loss. Also, the total uncertainty of theturbine e�ciency is obtained and results show that itdecreases as the pressure ratio increases. Also, the highuncertainty in the low pressure ratio illustrates turbinesensitivity to the low speed condition.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the valuable sup-port and funding of the Energy Conversion Center atSharif University of Technology, as well as the Ministryof Industry of I.R. IRAN.

NOMENCLATURE

A areab blade heightD diametere clearance between rotor blades and

shroudf skin friction coe�cient for smooth wallfc skin friction coe�cient for curved pipe

L lengthM mass ow rate, Mach numberMrh hub side entry mass ow rate to total

mass ow rateMrs shroud side entry mass ow rate to

total mass ow rateP pressureRe Reynolds numberT temperatureC ow velocityU blade velocityZ rotor blade number� relative angle of ow� e�ciency� loss coe�cients entropy, sensitivity coe�cientU(y) uncertainty�P mass average pressure�T mass average temperature

Subscripts and Superscripts

0 turbine entry, stagnation property1 volute casing entry2 interspace entry3 rotor entry4 inlet to rotor5 rotor exitBL blade loadingCl clearancey passage exit (downstream of rotor

inlet)h hub sides shroud sidets total to staticR rotorfr frictionH hydraulicm mixing0 relative condition

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