22 Assessment+of+Heat+Transfer+Effects+on+the+Performance+of+a+Radial+Turbine+Using+Large+Eddy+Simulation

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Assessment of heat transfer effects on theperformance of a radial turbine using large

eddy simulation

F. Hellstrom1,2

L. Fuchs2

SAAB Automobile Powertrain, Sweden1

Department of Mechanics/CICERO, the Royal Institute of Technology, Sweden2

ABSTRACT

One way to reduce fuel consumption and emissions is to downsize the engine incombination with turbo-charging. The turbine works under highly unsteady flowconditions, since the exhaust flow is pulsatile, turbulent and with a varying strengthof the axial and secondary flow components. The heat transfer from the fluid to theturbine housing will be different for a pulsatile flow compared to a non-pulsatileflow. Therefore, the effects of heat transfer at the walls on the turbine performanceworking under pulsatile flow conditions are assessed and quantified by performing anumerical study with Large Eddy Simulation. Two cases are considered, one casewith adiabatic walls and one case with heat transfer at the walls. The results showthat the difference in the obtained shaft power is small. Even the differences in thetime mean efficiency is small, it only differs with 2 percent units, even though theheat transferred to surroundings is as large as approximately 60 percent of thedelivered shaft power.

NOMENCLATUR

ui Velocity components (m/s) x i Spatial coordinates (m) p Pressure (Pa) P shaft Shaft power (W) ρ Density (kg/m3) Enthalpy change (W)

T Temperature (K) C p Specific heat (J/kg K) h Specific enthalpy (J/kg) η Efficiency qi Heat flux (W/m2) γ Ratio of specific

Mass flow (kg/s) R Gas constant (287 J/kg K)

t Time (s) Pr Prandtl numberFriction velocity Velocity normalized by the

friction velocity

1 INTRODUCTION

The last decade, downsizing has become more popular and this is due to theadvantages of the smaller turbocharged engine with lower fuel consumption and aless negative impact on the environment. A key component for downsizing is the

turbocharger. Due to the design of the internal combustion engine, the turbineworks under pulsatile flow conditions. The effects of pulsatile flow on the turbine



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performance have been investigated with both experimental and numericalmethods. For turbines operating under pulsatile flow conditions, the mean efficiencyis lower as compared to non-pulsatile flow conditions for the same mass flow andpressure ratio. The instantaneous performance can be higher or lower, see forexample the different studies performed by Capobianco, M. and Marelli, S. (1),Szymko et al. and (2), and Chen et al. (3). It has to be emphasized that it may be

difficult to compute the efficiency in an accurate way, due to the phase shiftbetween pressure and mass flow and the time it takes for the energy to propagatefrom the measuring point to the turbine wheel, as has been showed by for exampleby Hellstrom and Fuchs, (4) and (5). It is equally difficult to measure the timedependent shaft power which, for example makes direct model validationproblematic.

Heat losses will of course affect the performance of the turbine. The heat transfer orheat losses from the turbine can be divided into two major categories, the internalheat losses and external heat losses. The internal heat losses is the heat that isgoing into the bearing house, and then transferred to the oil, cooling water andsome amount of the heat will go into the compressor. The external losses are the

heat that is transferred to the surroundings due to convection and thermal radiationfrom the turbine house. Baines et al. (6) assessed in an experimental work the heattransfer in turbochargers (working under non-pulsatile flow conditions) with theobjective to develop a 1-D heat transfer model. They concluded that the internallosses are much greater than the external heat losses and that the heat losses arestrongly dependent on the turbine inlet temperature and the Reynolds number.Romagnoli and Martinez-Botas (9) conducted experiments on a turbochargermounted on an IC-engine, with the objective to assess the heat transfer processesin a turbocharger and to develop a simplified 1-D heat transfer model. Themeasurements show that the radiated heat from the engine strongly affects thetemperature distribution at the turbocharger casing, and this must be taken intoaccount when using heat transfer models for turbochargers mounted on engines.Other investigations on heat transfer effects on the turbocharger performance, see

for example the work carried out by Shaaban and Seume (7) and Bohn et al. (8)more focus on how the heat transfer from the turbine affect the performance of thecompressor.

It may be expected that the heat transfer will be affected by the pulsatile flow,since the pulsations will affect the boundary layer. Both increase and decrease of the heat transfer in pulsating flow in pipes has been reported in the literature fordifferent pulsation frequencies, amplitudes and mean Reynolds numbers. Therefore,the effects of heat transfer at the walls on the turbine performance working underpulsatile flow conditions are assessed and quantified by performing a numericalstudy with Large Eddy Simulation. The performance and the flow field are alsocompared to result from LES computation where the walls are treated as being

adiabatic. The considered turbine is a vane less radial turbine with nine blades witha size of the turbine is typical for a turbocharger mounted on a 2.0 liters IC engineof a passenger car.

2 NUMERICAL METHOD AND COMPUTED CASES

2.1 Governing equations and numerical methodThe governing equations that describe the conservation of mass, momentum andenergy for a fluid are the Navier-Stokes equations complemented with the equationof state.



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(1)

(2)

(3)

(4)

where τij is the stress tensor, defined as:

(5)

In this study, the governing equations are solved numerically. Since the flow ispulsatile with separations, the Large Eddy Simulation (LES) turbulence modelingapproach is used. In LES, the large scale of the flow is resolved, while the smallerscales have to be modeled. This also means that the resolved field is 3-dimensionaland time resolved. The modeling of the unresolved scales is done by a so-calledsubgrid scale model. Many of available subgrid scale models are to diffusive, as forexample the Smagorinsky model, for this kind of flow. Therefore, an implicit LESapproach is used, which implies that no subgrid scale model at all is used. Instead,the numerical dissipation will dissipate the energy of the smallest scales. A formal

second order TVD scheme is used for the convection terms, and a first order implicitEuler scheme has been used for the temporal discretization. As long as the timestep is small, with a Courant number smaller than unity, the accuracy of thesolution will be determined by the spatial schemes. The issue of near wall treatmentof heat-transfer, in general and in particular in the LES framework, is not resolved.Different methods have been proposed but the applicability of these are notgeneral. In this study, we have used a model that assumes that the heat-transfercoefficient is proportional to the wall friction velocity.

(6)

where Pr is the turbulent Prandtl number and Pcorr is correction factor based on theturbulent and laminar Prandtl number. This model is based on statistical data, andone can argue if it is valid for pulsatile flow or not.

The wheel is modeled by the sliding mesh technique, which implies that the part of the mesh that describes the wheel is rotating in relative to the stationary turbinehouse. At the interface between the moving and stationary part, the moving meshis made to slide past the stationary part. At this sliding interface, the connectivityfor cells on either side of the interface changes at each time step. With thistechnique, the effects of blade passage at the tongue will be captured.



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2.2 Computed cases and boundary conditionsThe used geometry in this study is a nine bladed nozzle-less radial turbine, with asize that is typical for a turbocharger mounted on a 2.0 liter IC engine of apassenger car, and in Figure 1 the used geometry is depicted. The leading edge tipradius of the wheel is 22.10 mm and the trailing edge tip radius is 18.75 mm. Thewaste-gate valve is closed for both cases.

The total number of cells for the mesh used are 1 401 143, with approximately850 000 cells in the wheel region and approximately 550 000 is located in thevolute and the diffuser. In the wheel, only hexahedron cells are used, while in therest of the domain a grid with dominantly hexahedron cells are used. The gapbetween the blade tips and shroud are resolved by 4 cells in the radial direction.The near-walls regions have better resolution than the regions in the “core-region”,but one should note that it is difficult to define the number of grid points in the “boundary layer”, since the thickness of that layer varies in the domain, due towakes and separation regions. In order to assess the adequacy of the resolution,energy spectra for the velocity fluctuations was studied and it was found to havethe characteristics -5/3 slope (over a range that varies from almost one order of

magnitude and larger), indicating that the resolution is such that it is in the inertialsubrange. Also, by estimating the missing part of the spectrum, we have found thatthe resolved spectrum contains well over 95% of the total turbulent kinetic energy.

Figure 1. Applied inlet conditions to the turbine (left figure) and wall temperaturesfor the non-adiabatic case (right figure).

At the inlet to the turbine, time varying mass flow rate and a temperature tracesare applied, which are is depicted in Figure 1. From the specified mass flow rate,the axial velocity component is computed at each boundary face at the inlet with

the face area and the density. The density is computed with the specifiedtemperature and the pressure is obtained from the solution. All secondary flowcomponents are assumed to be zero. The turbulent fluctuations are also neglected.For a real case, the flow is highly unsteady, with both secondary flow componentsand non-uniform axial velocity distribution, due to the pulsatile flow and thegeometrical shape of the manifold upstream. Since the objective is to compare theeffects of heat transfer, the “simplified” inlet boundary condition is used. At theoutlet, a non-reflecting boundary condition is applied. The rotational speed is set to97 897 rpm, which together with the mass flow and temperature trace that areapplied at the inlet, corresponds to an engine operational point of 1500 rpm for a 4-cylinders otto engine with wide open throttle. All walls are modeled as beingsmooth, which is not the case for the real geometry, but since this a comparative

study, it can be used. One case is modeled with adiabatic walls while the other caseis modeled with a fixed wall temperature. For the case with fixed wall temperatures,the applied temperature at the wall of the volute is 823 °K and the temperature of



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the wall of the diffuser is set to 726 °K. Those temperatures are frommeasurements on an equivalent engine at approximately the same operation point.The turbine wheel wall is assumed to be adiabatic, since it is gas in the regionbetween the wheel and back plate, but this cavity is not modeled in this study. Thespecified wall temperatures with the computed heat transfer coefficient will of course determine the heat transfer at the non-adiabatic walls. A more accurate

method is to use a conjugate heat transfer model, where the walls are modeled aswell. But still, it is a question how to specify the boundary conditions at the outsideof the turbine wall. In reality, the boundary condition at the turbine wall depends onthe under-hood configuration.

3 RESULTS AND DISCUSSION

3.1 ResultsThe first results to be compared are the global figures, such as mass flow averagedtemperature and pressure at inlet and the outlet, shaft power etc. In the second

sub-section, the details of the flow field will be assessed.

3.1.1 Turbine performance and global dataIn Figure 2, the shaft power is plotted for the two cases, and as can be seen, thedeviations between the two cases are small. The time mean shaft power for onepulse differs with approximately 1% (which is less than the numerical uncertainty),as reported in Table 1.

Figure 2. The time resolved shaft power during one pulse for the two differentcases, (left figure) and the heat transfer from volute and diffuser to the surroundingair during one pulse (right figure).

Even though the shaft power is almost equal, heat is transferred to thesurroundings for the case with non-adiabatic walls. In Figure 2, the heat losses forthe volute and diffuser are plotted, respectively. The maximum heat loss occurswhen the mass flow rate reaches its maximum value. At this instant, thetemperature of the pulsating gas also reaches its maximum value. The volute hasthe largest maximum instantaneous heat transfer rate of the two considered parts,but the time mean value of the heat transfer for one pulse does not differssignificantly; the time mean value for volute is 1.10 kW and for the diffuser 1.08kW. This shows the same trend as reported in available literature; see for exampleBaines et al. (6). The time mean shaft power during one pulse is 3.66 kW for thecase with heat transfer and 3.71 kW for the case with adiabatic walls. This givesthat time mean heat losses are as large as 59% of the delivered shaft power for

this case. This is due to that the shaft power is very low during the majority of thepulse, while the heat transfer is not.



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An obvious figure to compare for these two cases is the efficiency, if the flow wasnon-pulsatile. In this study, where the geometry is the same for the two cases, themass flow rate and the inlet temperature, a time mean efficiency can be computedand it is defined as:

(7)

The defined efficiency is the heat efficiency if one uses the same the nomenclatureas Hagelstein et al. (10) and Shaaban and Seume (7). The shaft power and theisentropic power for the different case are integrated over one pulse, and the timemean efficiency for the case with heat transfer is 61 % and for the case withadiabatic walls it is 63 %, respectively.

Table 1. Time mean value of global parameters

Case with

heat transfer

Case with

adiabatic walls

Ratio

(Xht/Xadiabatic)Shaft power (kW) 3.66 3.71 99 %

Efficiency (as definedin (7))

61 % 63 % 97 %

Heat transfer fromvolute walls (kW)

1.10 0 -

Heat transfer fromdiffuser walls (kW)

1.08 0 -

Static pressure at theinlet (kPa)

178 179 99 %

Static pressure at theoutlet (kPa)

130 131 99 %

Temperature at theoutlet (K)

969 1013 96 %

The pressure ratio over the turbine is also almost equal for the cases, but the casewith adiabatic walls has a slightly higher pressure level in the whole turbine. This isdue to the higher temperature at the outlet and the used boundary conditions,which does not set the pressure at the outlet to a fixed value. The temperature atthe outlet is the global parameters that show the largest deviation (except from butthe heat transfer from the walls). The time mean value for the temperature is 969°K and 1013 °K for the case with heat transfer and the case without, respectively.By using the time mean total temperature difference and the time mean mass flowfor the two cases, the enthalpy differences can be computed.

(8)

For the considered cases the enthalpy difference is 2.1 kW, which is the same asthe differences between shaft power and heat losses.

3.2 Details of the flow field

To be able to understand the results presented in the previous section, the flowfields for the two cases have to be assessed. Since no significantly differencesbetween the two considered cases could be noted during the pulse, two timeinstants are chosen, one at high mass flow (at the peak of the inlet mass flow rate)and one at a mass flow rate at the inlet of approximately 0.05 kg/sec during the

declining phase. Since a method where the wheel is actually rotating is used, asmall difference in the wheel position occurs in some of the plots, which depends on



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that they are not from the exact same time step. The velocity field in the volutedoes not differ in a significantly way between the two cases. In Figure 3, the Machnumber and in-plane relative velocity components are plotted for the non-adiabaticcase at an instant with high mass flow rate at the inlet. In these figures, one cansee the effect of tongue, which creates a wake, which then disturbs the flow intothe blade passage that just has passed the tongue. In the area with smallest cross

section the highest Mach number occurs, and for these two cases it is slightly aboveunity at high mass flow rates. When the blades have passed the tongue, a tipvortex starts to roll up. The extent and rotation direction of the leading edge tipvortex changes during the pulse.

Figure 3. Snapshot of the Mach number and velocity field at high mass flow ratefor the case with non-adiabatic walls. Left figure: Mach number. Right figure: In-plane relative velocity components. The cutting plane intersects the leading edge of the wheel in between the hub and shroud.

The temperature distribution for the same instant and cutting plane is showed inFigure 4. The effects of the heat transfer at the walls can be seen in the rightfigure, where a thin thermal boundary layer is located at the walls. One can alsosee that the wall has cooled down the gas, especially in the volute. The further thegas is convected in the volute, the more heat is transferred to the walls andsurroundings. As also can be seen, the temperature in the wheel is much higher forthe case with adiabatic walls. When comparing Figure 3 and Figure 4, one can seea correlation between the location of the vortices and the regions of lowrespectively high temperatures (depending on the case).



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Figure 4. Snapshot of the temperature at high mass flow rate. Left figure: Withadiabatic walls. Right figure: With non-adiabatic walls. The cutting plane intersectsthe leading edge of the wheel in between the hub and shroud.

Figure 5. Snapshot of the velocity and temperature at low mass flow rate for thenon-adiabatic case. Left figure: In-plane velocity components. Right figure: Temperature distribution.

For the adiabatic case, the hot gas at the walls in the volute is convected throughthe turbine, with only a small contribution to the shaft power output. At the inletregion of the wheel, gas with higher temperature is trapped in the tip vortex cores,but further downstream in the wheel, the high temperature gas regions are mixeddue to the different vortices that are created in the wheel, and then convected outof the wheel. Since strongest vortices are located in the upper half of the bladepassages, the highest temperature occurs at the shroud side.



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Figure 6. Snapshot of the temperature and velocity at high mass flow rate for thenon-adiabatic case. Left figure: In-plane velocity components. Right figure: Temperature distribution.

But for the case with heat transfer, the gas near the wall in the volute is cooleddown, and gas with low temperature is convected into the region between theblades by the tip vortices. Also, at the hub and shroud side of the inlet region to thewheel, cold gas from the thermal boundary layer is convected into to the wheel.Since this gas has a lower temperature than the gas in the core region, the gas incore region will be cooled when it is mixed with the gas in the tip vortices and therecirculation zone created at the shroud side if the inlet region to wheel.

In the diffuser, the deviation of the temperature is larger between the two cases,

which also can be seen in Table 1, where the time averaged outlet temperature issignificantly higher for the adiabatic case. This is due to the mixing of regions withgas from the bulk flow and gas from the thermal boundary layer in the wheel andthe heat losses at the walls. The rate of heat transfer from the diffuser becomeslarger when the mass flow rate is low compared to the heat transfer from thevolute. This is due to the vortices that are created in the diffuser downstream of thewheel. These vortices are created due to the rotating jet like flow that comes out of the turbine wheel, and are located in the region between the high velocity from thewheel and the diffuser wall, as depicted in Figure 5 and Figure 6. The vortexstructure closest to the wall is the strongest. At low mass flow rates, hot gas frominstants at high mass flow rate and high temperature is trapped in these vortices.For the case with non-adiabatic walls, the gas trapped in these vortices is cooled by

the wall, as also is depicted in Figure 5. Since the gas that is trapped in this vortexhas a higher temperature than the gas in volute, the heat transfer from the diffuserwill be higher at instants with low mass flow rate compared to the heat transferfrom the volute. At instants at high mass flow rates, gas with lower temperature istrapped in the vortex cores, as depicted in Figure 6. The gas with lowertemperature in the vortex has its origin from instants with lower temperature at theinlet. This then implies that the heat transfer from the diffuser will be relative lowercompared to instants at a low mass flow rate at the inlet. More details of the fieldfor these two cases can be found in Hellstrom and Fuchs (11).



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4 SUMMARY AND CONCLUSIONS

The effects of heat transfer on the performance of a radial turbine working underpulsatile flow conditions are asses by using CFD with the Large Eddy Simulationapproach. Two cases where considered, one with adiabatic walls and one with heattransfer at the walls.

The results show that the heat transfer only has a small influence on the turbineshaft power. The difference in delivered shaft power is very small, the time meanshaft power over one pulse differs with 1 %. The time mean efficiency is affected,which is slightly lower for the case with heat losses at the wall. One could expectthat the difference in efficiency should be larger, since the time mean heat transferis as high as 59 % of the time mean shaft power. In and downstream of the wheel,the temperature differences for two cases are significant, and that is due to the

vortex structures created at the inlet of the wheel mixes the cold gas from theboundary layer into the core region for the non-adiabatic case.

The small effect of the heat losses on the turbine performance shows that themodeled turbine cannot utilizes all available energy, since heat losses that are

almost as high as 59% of the shaft power, does not affect the shaft power in asignificantly way.

ACKNOWLEDGMENT

The work was sponsored by the Swedish Emission Research Program, EMFO andSAAB Automobile Powertrain, Sweden. Thanks are also due to the computer centersat KTH (PDC) and LiU (NSC) for the provided computer resources required carryingout this work.

© Authors 2010

REFERENCE LIST

(1) Capobianco, M. and Marelli, S., 2006. “Turbocharger turbine performanceunder steady and unsteady flow: test bed analysis and correlation criteria”.ImechE Conference Transactions, 8th International Conference onTurbochargers and Turbocharging

(2) Szymko, S., Martinez-Botas, R.F. and Pullen, K.R., 2005. “Experimentalevaluation of turbocharger turbine performance under pulsating flowconditions.” GT2005-68878, ASME Turbo Expo 2005: Power for Land, Sea

and Air, Reno-Tahoe, Nevada, USA

(3) Chen, L. Zhuge, W. Zhang, .Y, Yazhuo, .L and Zhang, S., 2008. “Investigation of flow structure in a turbocharger turbine under pulsatingflow conditions.” SAE 2008-01-1691, 2008 SAE, International Powertrains,Fuels and Lubricants Congress, Shanghai, China

(4) Hellstrom, F., and Fuchs, L., 2009. “Numerical computation of the pulsatileflow in a turbocharger with realistic inflow conditions from an exhaustmanifold”. GT2009-59619, ASME Turbo Expo 2009: Power for Land, Sea andAir Orlando, USA

(5) Hellstrom, F., and Fuchs, L., 2008. “Numerical computations of pulsatile flowin a turbo-charger”. AIAA-2008-073, 46th AIAA Aerospace Sciences Meetingand Exhibit, Reno, 7-10 January 2008.



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(6) Baines, N., Wygant, K.D., Dris, A., 2009, “The analysis of heat transfer inautomotive turbocharger”, GT2009-59353, ASME Turbo Expo 2009: Powerfor Land, Sea and Air Orlando, USA

(7) Shaaban, S. and Seume, J.R., 2006, ”Analysis of turbochager non-adiabaticperformance”, ImechE Conference Transactions, Turbocharging and

turbochargers C647/, pp 119-130

(8) Bohn, D., Heuer, T. and Kusterer, K., 2005, ”Conjugate flow and heattransfer investigation of a turbo charger”, J. of Engineering of Gas Turbinesand Power, pp 663-669

(9) Romagnoli, A. and Martinez-Botas, R., 2009, “Heat transfer on aturbocharger under constant load points”, GT2009-59618, ASME Turbo Expo2009: Power for Land, Sea and Air Orlando, USA

(10) Hagelstein, D., Beyer, B., Seume, J. and Rautenberg, M., 2002, ”Heuristicalview of on the non-adiabatic coupling system of combustion engine and

turbocharger”, ImechE Conference Transactions, Turbocharging andturbochargers C602/015/2002., pp 349-360,

(11) Hellstrom, F., and Fuchs, L., 2010. “ Heat transfer effects on theperformance of a radial turbine working under pulsatile flow conditions.” AIAA-2010-903, 48th AIAA Aerospace Sciences Meeting Including the New

Horizons Forum and Aerospace Exposition 4 - 7 January 2010, Orlando,Florida

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22 Assessment+of+Heat+Transfer+Effects+on+the+Performance+of+a+Radial+Turbine+Using+Large+Eddy+Simulation