Original Article

Determination of the isentropic turbineefficiency due to adiabatic measurementsand the validation of the conditions via anew criterion

R Zimmermann, R Baar and C Biet

Abstract

The determination of the isentropic turbine efficiency under adiabatic and SAE boundary conditions is studied in this

paper. The study is structured into two parts. The first part describes the possibility of measuring the isentropic turbine

efficiency directly. Normally this is not possible in measurements conducted following the SAE J922 guidelines.

Therefore, the experiments have been carried out under adiabatic conditions, and combined with improved measuring

equipment. The results were compared with adiabatic computational fluid dynamics simulations of this turbocharger. In

the second part, a new criterion is defined in order to evaluate the quality of the adiabatic measurements and compare

them with standard measurements. The investigation has been carried out with multiple turbochargers ranging from very

small to medium passenger car size turbochargers. In the end, a possible application for the criterion is given.

Keywords

Turbocharger, turbine, experimental

Date received: 6 April 2016; accepted: 16 August 2016

Introduction

The testing procedure for turbochargers according toSAE J922 recommends a turbine entry temperature of873K.1 This represents a good average value referringto actual operation temperatures of turbochargers, ifapplied to an engine. On the downside, it leads toseveral problems during the testing procedure. Dueto the high turbine inlet temperature, the results aresuperposed by the influence of heat transfer. Thiseffect has the biggest impact on low turbochargerspeeds. The heat transfer causes difficulties to identifythe aerodynamic behavior of the turbocharger at thetest bench. Especially, the isentropic turbine efficiencycannot be obtained under those conditions.

There are mainly two reasons. First, the alreadymentioned heat transfer, which influences the actualvalue of the turbine outlet temperature. And secondthe complex flow field downstream the turbine wheel,where there is a turbulent flow field with high spatialtemperature gradients. They cover a width of 50K incomputational fluid dynamics (CFD) simulations.4

There are a number of possibilities to look intothis. One option is to determine the heat flows thatoccur during the process. Approaches using thismethod are shown for example by Bohn et al.2 andLuckmann et al.3 In addition to the heat transfer

information, the friction power has to be determinedas well. With operating models for friction and heattransfer, the isentropic efficiency can be calculatedfrom the measurement values.

The approach is to minimize the heat flows duringthe actual measurement in order to achieve almostadiabatic conditions. Approaches that follow thisidea are investigated by Baar et al.4 and Baines et al.5

Adiabatic conditions and setup

SAE J922 and J1826 are today’s standard to recordturbocharger characteristic maps.6 The agreement onthis standard, including the recommended turbineinlet temperature of a constant 873K, resembles thereal-world application to a proper degree. It allowsthe comparison between different turbocharger testbenches. But on the downside, the isentropic turbine

Institute for Land and Sea Transport, Technical University of Berlin,

Germany

Corresponding author:

R Zimmermann, Institute for Land and Sea Transport, Technical

University of Berlin, Carnotstr. 1A 10587 Berlin, Germany.

Email: rainer.zimmermann@tu-berlin.de

Proc IMechE Part C:

J Mechanical Engineering Science

0(0) 1–10

! IMechE 2016

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DOI: 10.1177/0954406216670683

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efficiency (equation (1)) cannot be obtained using thismeasurement setup.

�Tis ¼T3 � T4

T3 � T4isð1Þ

The first reason is the occurrence of heat flowwithin the turbocharger and the heat flow towardsthe environment. This can be reduced by properinsulation up to a certain point, but, the issue stillremains. Due to the significant heat loss, betweenthe measurement planes of turbine inlet and turbineoutlet, the measured T4 drops low and this increasesthe isentropic turbine efficiency up to implausiblevalues high above 1. This effect occurs at almostevery turbocharger speed.

The heat flow can be minimized by applying adia-batic conditions. Therefore, the adiabatic conditionssuggested by Baines et al.5 were used for the initialinvestigations. The approach is set atop of twocolumns. The first aims to minimize heat transferwithin the turbocharger by setting all dominant tem-peratures to equal values at every operation point.The key temperatures for the turbocharger are thecompressor outlet temperature, which best representsthe compressor housing temperature, and the turbineentry temperature, which dominates the turbine sideand the oil inlet temperature that governs the bearinghousing. During the experiment, those temperatureswere adjusted at every operation point to equal valuesto fulfil the second equation. The turbocharger testbench offers the possibility to control the turbineinlet temperature, as well as the oil inlet temperature.Therefore, the governing temperature is the compres-sor outlet temperature, which is depending on the

actual operation point of the turbocharger andcannot be controlled. All other temperatures are setto match this value. In fulfilment of the secondequation, the temperature difference that drivesevery heat transfer becomes zero and, thereby, theheat transfer diminishes according to equation (3).

T2 ¼ T3 ¼ TOil,mean ð2Þ

_Qi ¼ �i � Ai � Ti � Tj

� �ð3Þ

The second column is a thick insulation tominimize the external heat flow to the environment.To verify the functionality of the setup, additionaltemperature probes have been installed at the surfacesof turbine housing, bearing housing, and compressorhousing. All in all, eight probes have been installed.Three of them are mounted on the turbine housing,another three on the compressor housing. Theremaining two are installed on the bearing housing.The employed probes are small PT100 resistancethermometers, which have a sufficient temperaturerange for the experiment and provide a high reso-lution as well as a high precision. The setup for theadiabatic measurement is shown in Figure 1. Thecomplete setup is insulated within the measurementplanes that correspond to the system boundaries.

After taking care of the heat flow, only one obs-tacle of measuring the isentropic turbine efficiencyremains—the unknown flow structure of the fluiddownstream the turbine wheel. Due to the expansionof the hot gas and the rotation of the impeller, theflow field downstream shows a complex pattern oftemperature gradients as well as a high swirl compo-nent. This makes it practically impossible to

Figure 1. Turbocharger setup at the test bench including insulation.

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determine the right turbine exit temperature with thestandard three or more thermocouple approach.

It is necessary to employ some additionalequipment into the setup to obtain a reliable valuefor the turbine outlet temperature. There is a trade-off. It is possible to measure the temperature as closeas possible behind the turbine. This minimizes theheat loss problem, but the measurement equipmenthas to be able to deliver a reliable result despite ofthe complex flow field. A successful approach hasbeen presented in the 20147 where a new sensordevice, capable of measuring the mean value of a com-plete tube cross section, has been introduced.4,7

To improve the reliability of the standard tempera-ture sensors, a mixing device has been installed inthe measurement pipe following the turbine outlet.The effect of this device has been topic of an intenseCFD investigation as well as an experimental valid-ation, which is also published by Baar et al.4 and themain results as well as a schematic drawing of themixing device are displayed in Figure 2. The CFDresults show how efficiently this mixing device reducesthe temperature gradient in the flow field and enablesa valid temperature measurement at its exit. Startingfrom a difference of 10K across the flow field withoutthe device, the remaining temperature differencedecreases down to 1K with the mixer. The experimen-tal validation displayed similar results, which are pre-sented in detail in Baar et al.4 The device is installed inthe measurement tube at a distance of 40 cm behindthe turbine and homogenizes the flow field. On thedownside, the mixer generates a small pressure loss.The pressure loss value ranges from 10 mbar at smallflow rates to 120 mbar at max mass flow rate.4 Tocompensate the pressure loss in the calculations, anadditional pressure sensor has been installed in frontof the mixing device.

One last aspect that has to be mentioned is that dueto the temperature change across each speed line, thespeed parameter (equation (4)) differs from operationpoint to operation point. The usual range observed dur-ing experiments is a change of about 100 r=min=

ffiffiffiffiKp

perspeed parameter line. Finally, due to the change of oiltemperature, the friction situation changes from oper-ation point to operation point as well.

But since for this investigation the goal is to focuson the isentropic efficiency, this aspect does not affectthe results.

nTCred¼

nTCffiffiffiffiffiffiT3

p ð4Þ

Experimental results

With all requirements meeting, the experiments werecarried out at the turbocharger test bench of theTechnical University of Berlin. An electric heatingsystem with a maximum power output of 24 kW hasbeen used to control the turbine inlet temperatureduring the adiabatic measurements. During the cam-paign one parameter had to be changed. The surfacetemperature probes delivered values, which showedthat the match of the oil inlet temperature onto thecompressor outlet temperature, led to mismatchingbearing housing temperatures. Due to the heat fromthe friction power, the bearing was warmer than thehousings of turbine and compressor. To rematch thesurface temperatures, the mean oil temperatures wasset equal to the compressor outlet. Figure 3 shows thefinal results for the fluid temperatures. The tempera-tures are displayed above the corrected compressormass flow to transfer information into a knownchart. The corrected compressor mass flow is

Figure 2. Scheme of mixing device and CFD results of the influence towards the distribution of turbine outlet temperature.

Zimmermann et al. 3

calculated by using the equation recommended inSAE J922. The results underline that throughout thecomplete test the adiabatic conditions have been keptwell. As mentioned before, additional temperatureprobes have been installed in the housing to ensureequal surface temperatures.

These results are shown in Figure 4. Compared tothe fluid temperatures, the overall values are afew Kelvin lower. The difference is negligible at60 k r/min, but increases with higher compressor tem-peratures to about 5K at 100 k r/min at the surge line.The wall temperatures fit quite well with each other.Figure 5 shows the values for the overall differences inhousing temperatures throughout the complete meas-urement campaign. Displayed are the minimal, themean, and the maximal values for all probes foreach operating point. The figure illustrates that themaximal difference between the hottest and the cold-est point reaches 6.5K in the worst operating point.

This indicates that despite themassive insulation therestill remains a minor heat transfer into the environmentas well as aminor internal heat transfer. Nevertheless, allthe surface temperatures are in the same range, indicatingthat the approach overall does work well.

After considering the temperatures and surveyingthe functionality of the approach the more interestingobjective, the determination of the isentropic turbineefficiency, can be pursued. The diagram in Figure 6shows the different turbine efficiencies. To calculatethe isentropic turbine efficiency equation (1) isemployed. The effective efficiency (equation (6)) is cal-culated in accordance with the SAE standard.

�Cis ¼T2 � T1

T2is � T1ð5Þ

�T ¼ �Tis � �Tm ¼1

�Cis�

_mC

_mT��hCis�hTis

ð6Þ

The first thing that is apparent is the rise of theeffective efficiency for the SAE measurement for thesmall turbocharger speed at 60 k r/min. This can beexplained by the impact of heat transfer from the tur-bine towards the compressor. Thereby, the compres-sor outlet temperature rises and decreases themeasured isentropic compressor efficiency calculatedby the use of equation (5) decreases. This change leadsto the rise of the effective turbine efficiency in equa-tion (6), where the isentropic compressor efficiency isused in the denominator. This is a measurement errorresulting from the assumption that the turbochargercan be treated as an adiabatic system. During themeasurement under adiabatic conditions, this trendis not present, simply because there is no significantheat transfer into the compressor. Above the effectiveefficiency are the results for the isentropic efficiency.These values look plausible; they are about10% points higher than the effective values. This iswhere the values are estimated to be, because theydo not include friction. Furthermore, the course ofthe values for all turbocharger speeds indicates thatthe measurement must have been very close to theadiabatic level.

If there still had been a significant heat transfer onthe turbine side, the isentropic turbine efficiencyvalues were supposed to be much higher. Very assur-ing was the final comparison of the measured datawith the adiabatic CFD simulation. The results ofthe simulation are almost exactly at the same levelas the measurement results, and underline theapproach.

Figure 3. Mean values of fluid temperatures under adiabatic conditions for turbocharger speeds between from 60 k r/min to

100 k r/min.

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Definition of the new criterion

The measurement campaign under adiabatic condi-tions led to reasonable isentropic turbine efficiencies.But there is still missing a criterion to determine, if thegiven measurement fulfils adiabatic conditions to asufficient level or not. There exist already someapproaches to define an adiabatic criterion e.g. the�-criterion developed by IAV Berlin,8 but to developa simple criterion, without detailed knowledge of theconstruction of the turbocharger, to determinewhether a measurement is adiabatic or not, it isimportant to decide for a measured variable that

can be used, to compare different measurement con-ditions with one other. In order to achieve this, at firstit is necessary to look into the measurement signals,which are given by the turbocharger test bench. Theprimary objective is to find a base solely pillowedupon signals that are reliable. In this case, reliablemeans those quantities must not be affected by theheat transfer that innately occurs in every operatingturbocharger. This leads to the quantities on thesystem inlet boundaries. Because on both systementries there is no heat transfer that influences themeasurement values. Any prior heat transfer mayhappen, but is not affecting any equation regarding

Figure 4. Mean values of surface temperatures under adiabatic conditions for turbocharger speeds between 60 k r/min and

100 k r/min.

Figure 5. Comparison of overall housing temperatures.

Zimmermann et al. 5

the observed system. To compare properties of theturbocharger turbine under different conditions, usu-ally the reduced turbocharger speed and otherreduced quantities are employed. This decision isbased upon the equivalent theorem of Mach.9 Butobserving the compressor side on different turbinetemperatures and taking reduced turbochargerspeeds into account is difficult, because the powerconsumption of the compressor is strictly related tothe real, the physical turbocharger speed. Therefore, apower-based observation seems more effective thanthe observation of reduced quantities.

In order to pursuit the idea of a power-basedapproach, first of all a reliable x-coordinate isneeded. The measured, or calculated, variable is theisentropic compressor power. The big advantage is theprior demanded independency from all occurring heattransfers. The isentropic compressor power, as shownin equation (7), uses the compressor inlet temperatureas the only temperature and this is the most reliabletemperature available at the system boundaries of aturbocharger. Since it is only dependent on the ambi-ent temperature

PCis ¼ _mc � cpC � T1 � ���1�

Ctt� 1

� �ð7Þ

The next reason for choosing it is based on thefundamental character of the compressor. Neitherits isentropic compressor power nor its true isentropiccompressor efficiency is affected by the state of thefluid. Both features are also completely independentfrom any heat transfer. The measured isentropic com-pressor efficiency, however, is affected by theoccurring heat transfer from the turbine and the hous-ing into the compressor, and the heat transfer fromthe compressor into the environment. But this is only

a measurement error, because the temperaturesemployed to calculate the isentropic efficiency areaffected by the heat transfer. As afore said, the trueisentropic compressor efficiency remains unaffected.This is a minor simplification, since in reality the airinside the compressor heats by a few Kelvin. But thishas only influence onto the specific heat capacity. Theheat capacity is temperature dependent. But the high-est difference of compressor outlet temperaturebetween adiabatic and hot measurements foundduring the experiments is about 20K. This risechanges the heat capacity only by about then 0.1%.

At one certain compressor operating point withone dedicated mass flow rate, a defined speed, andpressure ratio, the compressor will always need thesame amount of power. This is valid regardless ofthe state of the turbine side. Due to this, always thesame turbine shaft power is needed. This provides abasis to compare turbocharger measurements underdifferent thermal conditions with each other.

To determine whether the measurement is suffi-ciently adiabatic on the turbine side, the totalenthalpy flow over the turbine can be observed. Asmentioned before the identical compressor operatingpoint needs always exactly the same amount of tur-bine shaft power. In other publications it is alreadymentioned that the measured turbine power can bedivided into two parts (equation (8)). One part is theaerodynamic power PT, which goes into the turbineshaft, and the rest is energy, which is transferred in theform of heat transfer _QT into the environment oradjacent turbocharger components. Concluding this,the total turbine power is used as axis of ordinates forthis criterion.

� _HT ¼ _mT � cpT � T3 � T4ð Þ ¼ _QT þ PT ð8Þ

Figure 6. Characteristic turbocharger maps for adiabatic conditions and at 600�C for 60 k r/min to 120 k r/min.

6 Proc IMechE Part C: J Mechanical Engineering Science 0(0)

The idea behind this is quite simple. In Figure 7,the plots of total turbine enthalpy drop over the isen-tropic compressor power are shown for a small auto-motive turbo charger. Additionally, the figure alsoshows the connection between the measurementpoints at maximum isentropic compressor power ateach speed line as interpolated straight line (solid).This approach follows the idea that the point of max-imum compressor power is part of all compressorcharacteristic maps. Furthermore, contrarily to theresistance line, or the choke line it is rarely affectedby the test bench setup. If assumed that all the turbinepower is used to be converted into compressor power,as soon as the required compressor power reacheszero, the turbine power has to be down to zero as well.

As mentioned before, the chosen comparison pointitself is not important, it is only important, to use thesame point for all speed lines. Investigations on usingdifferent compressor operation points will be dis-cussed later. The interpolated line cuts the x-coordi-nate almost at zero, missing zero by 0.165 kW.

This indicates an almost adiabatic measurement. Itis also remarkable, how well all the points of max-imum compressor power fit into the straight line. Toillustrate the impact of heat transfer in this criterion,the adiabatic measurements are compared to thestandard measurements under SAE conditions. Theresults are listed and described in the followingsection.

Application onto multiple turbochargers

During recent experiments, multiple turbochargershave been tested under the adiabatic conditionsdefined in equation (2). All the turbochargers havebeen tested at the same test bench with equal adjacentgeometry, equal instrumentation, and equal

insulation. These facts ensure good comparisonbetween the single measurement campaigns. Theresults for those investigations are shown inFigure 8. The red lines represent the hot gas measure-ments at a turbine entry temperature of 873K accord-ing to the SAE J922. The black lines represent theadiabatic measurement recorded under the adiabaticdefinition introduced above. The solid lines show theconnection between the points of maximum isentropiccompressor power and the extrapolation towards zeroisentropic compressor power. The remaining offsetfrom the x-axis of the charts can be regarded asheat loss at zero compressor power. The adiabaticmeasurements show almost no remaining heat lossat zero compressor power. This can be observed forall four investigated turbochargers. The slopes of allfour straights appear to be the same; in fact, they onlydiffer by about 5%.

In the same manner, as for all adiabatic measure-ments the turbine power at zero isentropic compressordecreases to zero. It can be observed that for the SAEconditioned measurements, a certain amount of tur-bine power remains at zero isentropic compressorpower. This can be interpreted as minimal heat trans-fer into the environment during the measurement andis a clear sign that the measurement does not fulfiladiabatic conditions. The remaining heat transferpower differs from 2 to 3 kW. The exact values andtheir comparison to the adiabatic measurements areshown in Figure 9. This figure underlines the hugedifference in heat transfer and, thereby, the resultingincrease in turbine power, or heat energy, needed toresult in the same amount of power on the turbineshaft.

To solidify the approach, deeper investigationshave been performed on those turbochargers, whereadditional measurement data had been available.

Figure 7. Isentropic compressor power and turbine enthalpy flow under adiabatic conditions.

Zimmermann et al. 7

The first variation discussed is a variation of turbineentry temperature. For two of the four turbochargers(TC1 and TC3), additional characteristic maps at dif-ferent turbine entry temperatures had been recorded.For TC1, the additional turbine temperature was473K, and for TC3 the additional temperature was1173K. The charts of those additional maps havebeen added to the prior shown charts. Both variationsare presented in Figure 10. For the smaller turbochar-ger TC1 the temperature being lower than 873K butstill higher than temperature needed for adiabatic

conditions, the reference line can be found in betweenboth lines and closer to the adiabatic line. Thismatches with our approach, since the turbine inlettemperature is closer to the adiabatic turbine inletconditions. For TC3, the highest turbine entry tem-perature also induces the highest heat losses and,therefore, the highest straight line. For both tempera-ture variations the criterion fits. This variation stressesthat the established criterion works on a wide range ofturbine entry temperatures and that it can also beapplied to a wide range of turbochargers.

Figure 8. Adiabatic criterion for adiabatic conditions and for hot conditions applied on four different turbochargers.

Figure 9. Heat transfer at zero isentropic compressor power for all investigated turbochargers.

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Conclusions

In its first part, this publication delivers the possibilityto directly measure the isentropic turbine efficiency.The employed setup gives a direct and unhinderedway to investigate the aerodynamic properties of agiven turbocharger. The comparison with the numer-ical investigations shows that the results are plausible.

In the second part, the new criterion has beenintroduced and the functionality of the criterion hasbeen shown for multiple turbochargers and with mul-tiple turbine entry temperatures. The approach iscompletely power based and, therefore, offers theopportunity to easily compare turbine measurementsunder different boundary conditions. The approachreduces the turbocharger into a black box model.

Outlook

Indeed the criterion offers a lot more. It is a purepower-based approach and will therefore work at allturbine temperatures, as already shown. The next ideacan be to use this criterion to recalculate simple hotgas measurements and, thereby, to obtain the isen-tropic turbine efficiency without having to do adia-batic measurements at all. A possible approachwould use the characteristic line drawn by the connec-tion of the maximum isentropic compressor poweroperation points. It is possible to completely solveequation (8) by knowing the total enthalpy dropand the adiabatic need power and transform it intothe following form (example for 873K)

� _HT873 ¼ _mT � cpT � T3 � T4ð Þ ¼ _QT þ PTadiab ð9Þ

� _HT873 � PT adiab ¼ _QT ð10Þ

Now with _QT available, a quasi-adiabatic tempera-ture can be determined, which would occur, if themeasurement at 873K would have been adiabatic.This temperature is called TQ0 and is indicated as aheat transfer free turbine temperature. With this tem-perature, it should be possible to determine the

isentropic turbine efficiency directly from hot gasmeasurements (equation (11)). This shall be thetopic in our upcoming research works.

�Tis ¼TQ0 � T4

T3 � T4isð11Þ

Furthermore, the slopes which are all about thesame will be taken into consideration to find thereason behind this property.

Finally, if the information about the heat lossesfrom the turbine under given boundary conditionscan be determined from the data, this might be usedto parameterize turbocharger heat transfer modelssuch as the lumped capacity heat transfer modeldescribed in the work of Burke et al. This will alsobe a part of future work, because this is a uniquepossibility to set up a process that can be used toestimate the heat transfer of a given turbocharger,without the gigantic effort normally needed togather all the information for the heat transfermodels.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest withrespect to the research, authorship, and/or publication ofthis article.

Funding

The author(s) received no financial support for the research,

authorship, and/or publication of this article.

References

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2. Bohn D, Wolf M, Moritz N, et al. FVV Vorhaben 755Abschlussbericht: Modellierung des Warmeflusses imund am System Turbolader; FVV Heft R717, 2002.

3. Luckmann D and Uhlmann T. FVV Vorhaben 1038

Abschlussprasentation: Erweiterte Turbinenkennfeld-messung Abschlussprasentation FVV-Forschungsvorhaben Nr. 1038 Dortmund, 2012.

Figure 10. Turbine inlet temperature variation for two turbochargers (TC1 left with additional 473 K and TC3 right with additional

1173 K).

Zimmermann et al. 9

4. Baar R, Biet C, Boxberger V, et al. Moglichkeiten derdirekten Bestimmung des isentropen Turbinenwir-kungsgrads, Aufladetechnische Konferenz Dresden,

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8. Binder M, Bottcher L andGrigoriadis P.Advanced turbo-charger model for 1D ICE. Warrendale, PA: SAE, 2013.

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Appendix

Notation

A surface

cp isobaric heat capacityh specific enthalpyH enthalpy_m mass flown turbocharger speedP power_Q heat flowT temperature

� heat transfer coefficient� efficiency� isentropic exponent� pressure ratio

Subscript

C compressoris isentropicm mechanicQ0 heat flow freered reduceds statict totalT turbineTC turbocharger1 compressor inlet2 compressor outlet3 turbine inlet4 turbine outlet

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