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Transient Conjugate Heat Transfer Analysis of a TurbineStage using CFD

Fazal Rehman*

Honeywell Turbo Technologies, Torrance, CA, 90505

Radial turbine stage in a turbocharger is subjected in the field to a time varying turbineinlet temperature. Accurate fatigue life calculation of the turbine wheel and the turbinehousing requires an accurate prediction of the metal temperature distribution that isvarying in time. Conjugate Heat Transfer analysis of a radial turbine stage was performedusing Computational Fluid Dynamics (CFD) to achieve the goal of accurately predictingmetal temperature distribution. The flow model consisted of a radial turbine wheel and thehousing with both the fluid and metal zones modeled, and non-conformal interfaces betweensolid-fluid zones. The wheel fluid and metal part were modeled using hexahedral cells, whilethe housing fluid and metal parts were meshed using tetrahedral cells. A mixing plane wascreated between the rotating wheel fluid zone and the non-rotating housing fluid zone.

Temperature distribution was measured in the rotating radial turbine wheel usingtelemetry instrumentation, as well as in the stationary housing structure. Experimentalmeasurements were conducted in a gas stand for several time varying turbine inlettemperature ramps as well as for constant turbine inlet temperature. A constant turbineinlet temperature case was selected for simulation and the CFD predicted metaltemperatures for the wheel and the housing were compared with experimentally measuredtemperatures. Once calibration of the CFD model was done, a time varying turbine inlettemperature case was simulated. CFD predictions of the time varying temperaturedistribution in the turbine wheel and turbine housing matched well with the experimentaldata.

NomenclatureC = degree CelsiusCFD = Computational Fluid DynamicsDO = discrete ordinatee = turbulence dissipationF = degree FahrenheitFEA = finite element analysisHgG = mercury gageH2OG = water gageICE = internal combustion enginek = turbulence kinetic energyK = degree Kelvinkrpm = thousand revolutions per minuteMPa = mega-pascalPa = pascalPISO = pressure-velocity with splitting operatorT = temperatureTC = thermocouple

* Principal Engineer, Honeywell Turbo Technologies, 3201 W. Lomita Blvd., Torrance, CA 90505

9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference5 - 8 June 2006, San Francisco, California

AIAA 2006-3264

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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I. IntroductionTurbocharger in its basic configuration comprises of a gas turbine and a compressor mounted on the same shaft.

Exhaust gases from an Internal Combustion Engine drive the gas turbine and the power is used to compress ambientair supplied to the ICE. This increase in mass of air supplied to ICE at a higher pressure results in an increase in thepower output of the engine. An additional benefit of turbochargers is the reduction in emissions of the exhaust to theatmosphere. Reduction in vehicle exhaust gas emissions to ultra-low levels has driven increasingly higher exhausttemperatures and understanding the effects of these higher operating temperatures is essential for optimumturbocharger design.

Turbine wheels in an automotive exhaust turbocharger are subjected to a duty cycle in which speed is varied aswell as the turbine inlet gas temperature which results in a complex time varying temperature distribution in theturbine wheel and housing. These temperature distributions in the turbine wheel and stationary housing structureproduce stresses which are in addition to those generated by other types of loadings. During its life time a turbinewheel has to sustain vibratory, thermal and centrifugal stresses in a corrosive environment. Three main failuremechanisms that are associated with turbine thermo-mechanical fatigue are mechanical fatigue, creep and oxidation.All of the durability analyses depend upon accurate metal temperature prediction in a transient duty cycle whereturbine wheel speed and gas inlet temperature are varying.

In order to calculate temperature distribution in the wheel and the housing it was decided to use ComputationalFluid Dynamics (CFD) and run conjugate heat transfer analysis of the radial turbine stage. Several scientists andengineers have applied conjugate heat transfer to determine temperature distribution in turbine blades and vanes.Heidmann et al. (1) have found that conjugate heat transfer gives a temperature distribution that is different from theone obtained by applying adiabatic wall solution. Takahashi et al. (2) analyzed a turbine wheel using conjugate heattransfer.

In this study, in addition to modeling fluid flow through the turbine stage, turbine wheel rotor and the stationaryhousing structure was also modeled. Structured mesh was generated in the fluid part and metallic part of the rotor. ANavier-Stokes finite volume CFD solver Fluent was selected for solving the conjugate heat transfer model and itprovided temperature distribution in the gas flow, turbine wheel metal and the stationary housing structure. Resultsof temperature prediction were verified with experimental temperature measurements on the wheel and thestationary housing. Using the transient temperature distribution, thermal stress calculations can be performed atdiscrete time points in the transient cycle. Problem areas can be identified from the stress contours and a fatigue lifeprediction can be performed. Starting design can be modified by further simulations and the final optimized designis prototyped and built for qualification by testing.

II. Geometry of the simulation domainGeometry of the radial turbine stage consisting of the

turbine wheel (blue color), turbine housing (red color) andcenter housing (yellow color) as shown in Figure 1 wascreated using CATIA. Necessary simplifications to thegeometry were made while maintaining most features ofthe original geometry. The water cooled center housingwhich houses the bearings and the shaft was oversimplified and modeled as a cylindrical cavity filled withwater. This provides the necessary boundary condition tothe turbine housing and back face of the turbine wheel,while not increasing the model size as well as simplifyingthe meshing process. Turbine wheel shaft was alsosimplified and the seal groves were not modeled. Hot airsupply pipe was attached to the inlet of the turbinehousing, and the exhaust pipe was attached to the outlet ofthe turbine housing.

Figure 1. Radial Turbine Stage Geometry

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III. MeshingFor modeling the rotating fluid domain between the

blades hexahedral cells were used and the surface meshalong the wheel passages was stream wise aligned. Thefluid mesh was refined until the non-dimensionalparameter yplus is less than one everywhere in the flowdomain. The solid part of rotating wheel as shown inFigure 2 was meshed using hexahedral elements and itwas not as refined as the fluid mesh between the blades.The number of rotor fluid elements was 1,958,651whereas the number of rotor solid elements was 555,264.This required the use of non-conformal interface betweenthe boundary of rotor solid zone and rotor fluid zone atthe blade wall. A mixing plane was created between therotating wheel fluid region and the non-rotating voluteregion and solution results indicate that mass and energywas conserved across the mixing plane.

Figure 2. Turbine Wheel MeshVolute fluid zone was meshed using tetrahedral cells

with prism layers along the wall surfaces in order to havebetter resolution for boundary layers. The turbine housingsolid part was meshed using 641,489 tetrahedral elementsas shown in Figure 3, whereas the total number of cells inthe turbine housing fluid zone was 275,370. A non-conformal interface was placed between the fluid zoneand solid zone of the turbine housing. Hexahedral cellswere used for meshing the inlet supply region and theoutlet exhaust region. A non-conformal interface wasplaced between the inlet supply region and the turbineinlet as well as between the outlet exhaust region and theturbine outlet. The center housing solid part was meshedusing 422,372 tetrahedral elements. The total number ofcells in the model was 4.3 million.

Figure 3. Turbine Housing Mesh

IV. Model SetupCFD code Fluent was utilized in segregated mode to first simulate the steady state test case. Realizable k-e

turbulence model along with standard wall functions was used that includes viscous heating effects. The energyequation was enabled to model conjugate heat transfer throughout the solution domain. DO (discrete ordinate)radiation model was used to model radiation heat transfer between the back disk of the turbine wheel and the face ofcenter housing facing the back disk of the turbine wheel. Second order upwind discretization was used for all theequations and PISO (pressure-implicit with splitting of operators) scheme was utilized for Pressure-Velocitycoupling. Hot air was modeled as perfect gas with temperature dependent properties and the solid part of the modelwas assigned appropriate metal properties that are variable with temperature. In order to stabilize the calculation,initially the secondary gradient calculation of the energy equation is disabled. After stable solutions are obtained, thesecondary gradient calculation of the energy equation is enabled and the alternate formulation for wall temperaturesis used in order to maintain the stability. CFD simulation results are compared with experimental results in sectionVII for the steady state case.

Due to 4.3 million cell size of the model, a quasi-steady state approach was developed for the turbine inlettemperature ramp up and ramp down simulations. It was estimated that the residence time of air flow through theturbo charger is small and hence the flow field was quasi-static. Only the energy equation for solid zones needed tobe adjusted, so steady state solver was used with appropriate modifications of the energy equation in solid zones. Anunsteady term of the energy equation was added as a source term to the steady state energy equation of the solid

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SignalConditioner

InductionPower Coil

StationaryAntenna

RotatingAntenna

TransmitterModule

Thermocouples

zones and the implicit scheme was used to solve this transient test case. CFD predictions for the transient test caseare compared with experimental measurements in section VIII.

V. Operating Conditions in Test CellSteady state tests and transient cycle tests were conducted on a turbocharger in a gas stand with the capability to

provide hot air at different mass flow rates and temperature. For the steady state test, hot air at a static pressure of37.6 inch of HgG (1.27 MPa_guage) and a total temperature of 1195F was supplied to the turbine at a mass flow rateof 135.8 lbm/min. The turbine gas exhaust pressure was about the same as atmospheric pressure and the exhausttotal temperature was recorded as 912F with the turbine rotating at 63.9 krpm. The center housing was providedwith cooling water at 200F and oil at a temperature of 190F was supplied to the bearings. The ambient temperaturein the test cell was 90F and ambient air motion was negligible in the test cell.

For the transient testing, the hot air supply temperature to the turbine was varied in a cyclic manner from amaximum value of 1425F to a minimum value of 350F over a cycle time of 500 second. The speed varied in-phasewith turbine gas inlet temperature from a maximum of 50 krpm to a minimum of 38 krpm and the mass flow ratevaried from 103 lbm/min and 78 lbm/min.

VI. Temperature Measurement on Housing and WheelTemperature was measured on the stationary and

moving parts using thermocouples installed on theturbine housing, center housing and turbine wheel. Theturbine housing and center housing are stationary partsand a conventional system was sufficient to readtemperature from the various thermocouples installed.The turbine housing had ten thermocouples installed onthe outside as shown in Figure 4, with fivethermocouples (TC 1 through 5) installed on the sideattached to the center housing and five thermocouples(TC 6 through 10) at the biggest diameter. Thethermocouple measurements on the housing for thesteady state case were utilized for calibrating theboundary conditions for the conjugate heat transfer CFDruns. A listing of these measurements for the steady statecase is provided in Table 1, along with the CFDpredictions. The center housing was similarlyinstrumented with thermocouples and the measurementswere utilized for setting up boundary conditions.

Figure 4. Turbine Housing with installed ThermocouplesOne of the methods for measuring and transmitting temperature data from a rotating wheel is to use a telemetry

system. Telemetry system accepts the thermocouple signal in the form of voltage and transmits it from the movingcomponents to the stationary data acquisition system. The telemetry system consists of a transmitter, a receiver, apower supply, stationary antenna, rotating antenna and signal conditioner.

Figure 5. Block Diagram of a Telemetry System

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1

7

14

3

10

6

12

5

114

2

9

13

Temperature is sensed by thermocouplesinstalled on the rotating turbine wheel andtransferred to a transmitter module mounted in acavity machined in the compressor nose. Thetransmitter is mounted in the compressor nosesince temperature is the lowest at this locationand suits well for the electronics. The transmitterconverts the temperature to a frequencymodulated electronic signal which is transmittedto the adjacent stationary antenna. The signal isthen conditioned in a receiver and data can bedisplayed in engineering units. The transmitter iscapable of operating at speeds in excess of 100krpm. A section of the transmitter installationsetup is shown in Figure 6.

Legend for figure6:1. Compressor Housing2. Compressor Wheel3. Stationary Antenna4. Transmitter Cartridge5. Rotating Coil Support6. Stationary Coil Support7. Connector Pin8. Insulation Bushing9. Insulation Button10. Insulation Spacer11. Support Ring12. Support Strut13. Transmitter14. Rotating Antenna

Figure 6. Section View of the installed Telemetry System

Thermocouple locations (TC1, TC4, TC5,TC6) on the turbine wheel are illustrated inFigure 7.

• TC1 located on the blade inducer• TC4 located on the blade exducer• TC5 located on the wheel nose• TC6 located on the wheel back disk

A listing of these measurements for the steadystate case is provided in Table 2, along with theCFD predictions. Temperature measurements forthe transient test case provided in Figure 11b areutilized for the CFD model validation.

Figure 7. Turbine Rotor Section with Thermocouple Locations

VII. Steady State CFD Simulation ResultsThe steady state flow case was modeled first to validate the flow model, boundary conditions, material properties

and other assumptions. Test cell measurements indicated that hot air enters the radial turbine stage at a totaltemperature of 1195F and exits at 912F, and this was used to validate the conjugate heat transfer CFD simulation as

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shown in Figure 8. Overall mass is balanced across theturbine stage and the results also satisfy energyconservation. The main area of concern was the mixingplane between the non-rotating volute fluid and therotating rotor fluid. There is a 0.32% energy imbalanceacross the mixing-plane and the mass imbalance acrossthe mixing plane was negligible, thus validating theusage of the mixing plane model for the graduallyvarying turbine inlet temperature case.

A comparison was made between temperaturemeasured on the outside of the turbine housing usingthermocouples and predictions made using conjugateheat transfer CFD as shown in Figure 9. CFD resultsare in agreement with measurements as shown in Table 1.

Figure 8. Contours of gas total temperature (F).

Table 1. Comparison of temperature measured andpredicted on the turbine housing.

Figure 9. Contours of temperature (F) in the housing.

Temperatures measured using telemetry on therotating wheel were compared with conjugate heattransfer CFD predictions in Table 2 and the results weremixed. Predictions were very close to experimentalmeasurements for TC(6) located in the lower back-diskof the turbine wheel and fairly close for TC(1) located inthe turbine wheel inducer. However the predictions werenot as close to measurements for TC(4) and TC(5) whichare located on the blade exducer and turbine wheel noserespectively.

Table 2. Comparison of temperature measured andpredicted on the turbine wheel.

Figure 10. Contours of temperature (F) in the wheel

TC# Measured(F) Predicted(F)1 970.5 971.82 1003.9 1013.53 1031.2 1023.54 1032.3 1031.45 1043.0 1043.16 1178.7 1161.37 1177.1 1153.38 1176.7 1157.49 1170.2 1153.5

10 1166.6 1145.7

TC# Measured(F) Predicted(F)1 1000 10244 972 8685 951 8636 831 838

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VIII. Transient Case CFD Simulation ResultsAfter validation of the steady state test case it was decided to simulate a transient duty cycle in which turbine

speed and turbine gas inlet temperature is varied in phase. Turbine gas inlet temperature varied from 1425F to 350 Fand speed varied from 50 krpm to 38 krpm over a cycle time of 500 sec as shown in Figure 11a. CFD code Fluentwas able to convert the transient boundary condition data into piece-wise polynomial functions of time used insimulation of the transient duty cycle. Due to the large size of the model, a quasi-steady state approach wasdeveloped for the turbine inlet temperature ramp up and ramp down simulations.

Conjugate heat transfer CFD simulation results of temperature at the thermocouple locations on the turbinewheel are presented in Figure 11a with corresponding measured temperatures in Figure 11b. Simulated results arecompared with experimental data and they follow the same trend. During heating part of the cycle, turbine bladeinducer attains the highest temperature and wheel back disk the lowest temperature. Blade exducer temperature islower than the blade inducer temperature but higher than that of the back disk. During cooling part of the cycle, thetemperature distribution reverses with blade inducer attaining the lowest temperature and wheel back disk thehighest temperature. Contour plots of temperature in the turbine wheel at various times in the transient duty cycleare presented in figures 12 thru 19. Transient CFD simulation results for TC1 located at the inducer and TC6 locatedat the wheel lower back disk are close; however there is some difference between measured temperature andsimulation results for TC4 located at the exducer and TC5 located at the wheel nose.

Conjugate Heat Transfer Simulation of Transient Cycle

0

200

400

600

800

1000

1200

1400

1600

0 100 200 300 400 500 600

Time(sec)

Sp

eed

(Hz)

and

Tem

per

atu

re(F

)

TC1TC4TC5TC6SpeedTinlet

Figure 11a. Time history of turbine inlet temperature and predicted temperatures in turbine wheel.

Measured Temperature during Transient Cycle

0200400600800

1000120014001600

0 100 200 300 400 500 600

Time(sec)

Tem

per

atu

re(F

)

TC1

TC4

TC5

TC6

Figure 11b. Time history of measured temperatures in turbine wheel.

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Figure 12. Temperature(K) contour at time 70 sec

Figure 13. Temperature(K) contour at time 150 sec

Figure 14. Temperature(K) contour at time 190 sec

Figure 15. Temperature(K) contour at time 250 sec

Figure 16. Temperature(K) contour at time 270 sec

Figure 17. Temperature(K) contour at time 310 sec

Figure 18. Temperature(K) contour at time 410 sec

Figure 19. Temperature(K) contour at time 470 sec

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References1Heidmann, J. D., Kassab, A. J., Divo, E. A., Rodriguez, F., and Steinthorsson, E., “Conjugate Heat Transfer on a Realistic

Film-Cooled Turbine Vane,” ASME Paper GT2003-38553.2Takahashi, T., Watanabe, K., “Thermal Conjugate Analysis of a First Stage Blade in a Gas Turbine,” ASME Paper GT2000-

251.