Effect of Temperature Nonuniformity on Heat Transfer

Imran Qureshi1 Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK e-mail: [email protected]

Andy D. Smith Rolls-Royce PLC, Turbine Sub-Systems, Moor Lane, Derby DE24 8BJ, UK

Kam S. Chana QinetiQ Limited, Cody Technology Park, Farnborough GU14 0LX, UK

Thomas Povey Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK

Effect of Temperature Nonuniformity on Heat Transfer in an Unshrouded Transonic HP Turbine: An Experimental and Computational Investigation Detailed experimental measurements have been performed to understand the effects of turbine inlet temperature distortion (hot-streaks) on the heat transfer and aerodynamic characteristics of a full-scale unshrouded high pressure turbine stage at flow conditions that are representative of those found in a modern gas turbine engine. To investigate hot-streak migration, the experimental measurements are complemented by threedimensional steady and unsteady CFD simulations of the turbine stage. This paper presents the time-averaged measurements and computational predictions of rotor blade surface and rotor casing heat transfer. Experimental measurements obtained with and without inlet temperature distortion are compared. Time-mean experimental measurements of rotor casing static pressure are also presented. CFD simulations have been conducted using the Rolls-Royce code HYDRA and are compared with the experimental results. The test turbine was the unshrouded MT1 turbine, installed in the Turbine Test Facility (previously called Isentropic Light Piston Facility) at QinetiQ, Farnborough, UK. This is a short duration transonic facility, which simulates engine-representative M, Re, Tu, N / 冑T, and Tg / Tw to the turbine inlet. The facility has recently been upgraded to incorporate an advanced second-generation temperature distortion generator, capable of simulating well-defined, aggressive temperature distortion both in the radial and circumferential directions, at the turbine inlet. 关DOI: 10.1115/1.4002987兴 Keywords: hot-streak, OTDF, RTDF, HP turbine, heat transfer, aerothermodynamics, HP rotor, rotor casing

1

Introduction

The mainstream gas temperature at the inlet of the high pressure turbine of modern gas turbine engine is around 1600° C, considerably higher than the melting point of the metal. To enable turbine blades to survive in such a harsh environment, internal and external blade cooling and thermal barrier coatings are employed. The use of cooling techniques allows higher turbine operating temperature but the HP compressor air requirement reduces overall turbine performance: The combusting mass flow is reduced, and the introduction of cooling flow into the hot gas path causes aerodynamic loss. Blade cooling optimization is therefore a key to achieving high overall turbine performance. Over the past few decades, significant improvements have been made in the overall blade cooling design. This is the result of design experience and understanding gained from experimental and predictive heat transfer data for the HP turbine stage. Understanding of the complex flow processes in the tip and casing region in particular is still relatively limited because of the scarcity of experimental data taken in facilities at engine-representative conditions. Very few experimental studies have been reported in the open literature that concern HP rotor and casing heat transfer data taken in rotating transonic high pressure turbine test facilities. There are even fewer studies that also consider the effect of nonuniform inlet temperature profiles in this environment. It is well known, however, that 1 Corresponding author. Contributed by the International Gas Turbine Institute of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 1, 2010; final manuscript received July 4, 2010; published online May 25, 2011. Editor: David Wisler.

Journal of Turbomachinery

the rotor flow is grossly affected by, for example, incidenceinduced temperature segregation, buoyancy, relative total pressure induced secondary flow patterns, over tip leakage flow, and wall shear. The study of these phenomena demands a fully scaled turbine experiment with a realistic inlet temperature field. This paper presents blade surface and rotor casing heat transfer data from a full-scale rotating transonic turbine test facility with an enginerepresentative nonuniform inlet temperature profile. 1.1 Rotor Casing Heat Transfer. The flow-field on the rotor casing is complex and highly unsteady because of the close proximity of the rotor blades, which are moving through the potential field of the nozzle guide vanes. In modern military engines operating at high turbine entry temperatures, active cooling of the rotor casing is now a requirement. Thus, better understanding of casing heat transfer will enable the performance penalty associated with this cooling flow to be reduced. The significant majority of published literature on rotor blade tip secondary flows, tip leakage flow, and tip gap studies comes from linear cascade experiments. Bunker 关1兴 provided a comprehensive review of the past research on turbine blade tip flows. Low speed studies have provided valuable insight into some of the fundamentals of blade tip flow but more recent comparisons of turbine blade tip heat transfer in low and high speed flows 共Wheeler et al. 关2兴兲 highlight significant differences in the heat transfer characteristics. This necessitates testing at high speed under engine-representative conditions for accurate heat transfer predictions in tip region. A good representative flow in the tip region can be achieved in a transonic rotation environment in which the boundary layers and wall shear

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are representative of the engine and in which the unsteady processes are correctly modeled 共rotor tip and casing flows interacting with vane wakes兲. Some of the earliest data obtained in a full-scale transient test facility was reported by Guenette et al. 关3兴 who performed the time-averaged and time-resolved heat transfer and static pressure measurements on a high pressure turbine rotor casing. The heat transfer measurements were performed at seven locations along one axial row on the casing. It was found that time-averaged heat flux drops by a factor of 4 or 5 along the blade chord, which was identified to be due to the rotor enthalpy extraction and the changes in the heat transfer coefficient. The measurements did not allow these effects to be separated. Metzger et al. 关4兴 also reported high heat transfer rates observed on the rotor casing tested under engine-representative flow conditions. In their later analysis, they identified that the clearance gap and blade tip are exposed to full mainstream gas temperature, indicating that the source of the measured high heat transfer rates is likely to be high leakage flow temperatures rather than convective heat transfer coefficients. In their study, Polanka et al. 关5兴 found the turbine tip and shroud heat transfer rates with levels as high as the stagnation region on the airfoil. In none of these studies was it possible to evaluate the driving gas temperature, and therefore, it was not possible to reduce the measured heat transfer rates to Nusselt number. A comprehensive investigation of the heat transfer and static pressure on the rotor casing of a high pressure axial turbine under enginerepresentative conditions has been reported by Thorpe et al. 关6兴. The researchers were able to evaluate adiabatic wall temperature and thus the true Nusselt number. Both casing heat transfer rate and adiabatic wall temperature were found to vary strongly in axial direction, whereas the drop in Nusselt number was found to be gradual-based upon which they suggested that measured heat transfer rates are primarily associated with changes in flow recovery temperature observed along the axial chord rather than changes in heat transfer coefficient. None of the above studies investigate the effects of a nonuniform temperature field at the turbine inlet. Chana et al. 关7兴 developed an inlet temperature distortion generator. They reported rotor tip and rotor casing heat transfer measurements with and without inlet temperature distortion 共Chana and Jones 关8兴兲. A reduction of casing heat load was found with inlet temperature nonuniformity as compared with the uniform temperature case. For the current investigation, a second-generation enhanced inlet temperature distortion generator 共Povey and Qureshi 关9兴兲 was developed, which is capable of simulating aggressive radial and circumferential temperature profiles representative of an extreme cycle of a modern gas turbine combustor. The effect of this profile on the rotor casing aerodynamic and heat transfer characteristics is described in this paper. 1.2 Rotor Surface Heat Transfer. Although a significant number of experimental rotor surface heat transfer studies from full-scale rotating turbine rigs have now been reported in open literature, most have been performed with a uniform inlet temperature field, for example, Didier et al. 关10兴, Haldeman and Dunn 关11兴, Allan et al. 关12兴, and Haldeman et al. 关13兴 among others. Studies conducted with engine-representative inlet temperature are scarce. In the increasingly demanding design environment of the HP turbine, it is now relevant to model such effects for improved heat transfer predictions. Butler et al. 关14兴 investigated the redistribution of an inlet temperature distortion through a high pressure turbine stage in a low speed rotating test facility. A hot-streak, seeded with CO2, was introduced at the inlet, and the migration of hot gas was deduced from the measured CO2 concentration through the stage. Results indicated that the rotor flow-field was significantly affected by the introduction of upstream temperature distortion, with the hot gas migrating to the pressure side and cold gas to the suction side. This segregation of hot and cold gases was also demonstrated, both theoretically and experimentally, by Kerrebrock and Mikola011005-2 / Vol. 134, JANUARY 2012

Fig. 1 Schematic of QinetiQ turbine test facility

jczak 关15兴. In addition, a significant increase in rotor secondary flow was observed, the result of greater nonuniformity of total pressure in the rotor relative frame. Shang et al. 关16兴 studied the effects of inlet temperature distortion on rotor blade surface heat transfer in a transonic turbine and also performed computational analysis of the influence of hot-streaks on the blade heat load 共Shang and Epstein 关17兴兲. A significant increase in the rotor pressure surface heat flux was observed with inlet temperature distortion. Hot gas was found to move radially toward hub under the influence of buoyancy. There have also been numerous computational studies of the effects of hot-streak migration through the HP stage, for example, Boyle and Giel 关18兴, Gundey-Burlet and Dorney 关19兴, Dorney and Sondak 关20兴, Prasad and Hendricks 关21兴, He et al. 关22兴, Ong and Miller 关23兴, An et al. 关24兴. The intent of this paper is to present experimental heat transfer results on rotor surface along with a computational study performed to get an insight toward the effect of hot streak migration.

2

Experimental Facility

The Turbine Test Facility 共TTF兲 at QinetiQ UK is a short duration light piston driven facility with a full-sized high pressure turbine test stage. The main components of the facility––共i兲 the high pressure reservoir, 共ii兲 the pump-tube that contains a lightweight piston, 共iii兲 a fast acting plug valve, 共iv兲 the turbine stage 共working section兲, and 共v兲 the turbobrake––are highlighted in the schematic of the test facility shown in Fig. 1. The operating principles of this type of facility were first described by Jones et al. 关25兴. Prior to an experimental run, the plug valve is closed, the working section and exhaust tank are evacuated, and the turbine disk is spun to the design speed using an air motor. Air from the high pressure reservoir is injected into the piston tube behind the light piston. The piston moves down the piston tube, with a very small pressure difference across it, compressing and heating the working gas 共air兲 in front of it 共approximately兲 isentropically. When the desired working section pressure is achieved, the fastacting plug valve is opened and the working gas flows out of the piston tube into a large annulus. Here, the gas settles and enters the working section through a contraction at the inlet of turbine stage, which simulates the exit of a combustor. The test run ends when the piston reaches the end of the piston tube. Steady conditions are achieved for approximately 500 ms, during which the experimental data is acquired, with all the nondimensional parameters matched to that of a modern gas turbine engine. The intrastage hub platform leakage flow is minimized by the use of a labyrinth seal. During the steady part of the run, the net leakage is zero, as during the start up process, the hub plenum becomes pressurized to the mean external platform static pressure. The turbobrake 关26兴 ensures approximately constant speed of turbine during the run. The TTF has been used to test both a single HP turbine stage 关27兴 and a 1.5 stage turbine 关28兴. The operating conditions for TTF tests are listed in Table 1. The test turbine 共MT1兲 stage has 32 NGVs and 60 rotor blades with a tip clearance gap of 1.2%. Transactions of the ASME


Table 1 Turbine stage operating conditions for TTF Parameter 共unit兲 p01 共bar兲 T01 共K兲 Tg / Tw M hub 2 M casing 2 ␻ 共rpm兲 p02rel 共bar兲

3

Nominal value

Allowable run-to-run variations 共%兲

4.6 444 1.50 1.054 0.912 9500 2.697

⫾1 ⫾2 ⫾2 ⫾1 ⫾1 ⫾1 ⫾1

Temperature Distortion Generator

For this study, the TTF has been upgraded with an enhanced overall temperature distortion function 共EOTDF兲 generator, which simulates the temperature profile measured in a modern gas turbine engine at the most extreme point in the cycle. To allow comparisons with CFD simulations, a hot-streak to vane count of 1:1 was chosen. The design of the EOTDF simulator, which is a novel development on an earlier simulator in the same facility, is discussed by Povey and Qureshi 关9兴 and is put in the context of a recent review of temperature distortion simulators by the same authors 关29兴. The comparison of the temperature profile at the inlet of the turbine stage with and without inlet temperature distortion is presented in Fig. 2. The measurements have been performed over 2 NGV pitches in the circumferential direction at the locations 共dots兲 shown in the figure. Figure 2共a兲 is the uniform temperature profile 共design inlet temperature of 444 K兲. Figure 2共b兲 is the EOTDF profile with a mass mean temperature of 444 K. The maximum temperature was 525 K at the center of the hot-streak, and the minimum temperature was 310 K near the outer endwall. The max-to-min temperature ratio was approximately 1.70. The max-to-mean temperature ratio was approximately 1.18. The profile is characteristic of modern combustors in that it is aggressive in the radial nonuniformity but relatively weak in the circumferential nonuniformity. The EOTDF system allows the clocking of hot-streak with respect to vanes. For the current investigations, the hot-streaks were

Fig. 2 Turbine inlet total temperature profile with „a… uniform inlet conditions and „b… with inlet EOTDF


Fig. 3 Comparison of circumferentially averaged inlet temperature with and without EOTDF

aligned with the vane leading edge. Figure 3 compares the radial profiles for the two cases 共open circles represent EOTDF兲. An inlet total pressure survey was also conducted over 2 NGV pitches, with and without EOTDF. Figure 4 shows the measured total pressure profiles. Both profiles were nominally uniform, with a mean value of around 4.6 bars. The maximum variation from the mean was 0.65% 共uniform兲 and 0.74% 共EOTDF兲. The significance of the inlet pressure profile in determining secondary flow development is now well understood. Excellent uniformity of inlet pressure in both the uniform and EOTDF cases allowed the isolated effect of hot-streaks on the HP stage to be considered in these experiments. The additional effect of nonuniformity in total pressure can also be achieved with the present injection system but a uniform total pressure field was desired for the current investigation. The circumferentially averaged radial total pressure profiles for the uniform and EOTDF cases are presented in Fig. 5 共open circles represent EOTDF兲. The two profiles are very similar in form with variations of less than 0.5% from a flat profile.

Fig. 4 Turbine inlet total pressure profile with „a… uniform inlet conditions and „b… with inlet EOTDF

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Fig. 5 Comparison of circumferentially averaged inlet pressure with and without EOTDF

4

Experimental Instrumentation and Data Reduction

4.1 Rotor Casing Heat Transfer Measurements. Thin-film platinum resistance heat transfer gauges were used to measure heat flux on the rotor casing. The gauges were deposited on Kapton™ 共polyamide兲 bonded to a Perspex casing cassette. A set of four Perspex casing cassettes was used 共approximately 20 gauges per cassette兲, providing a composite map of about 80 measurement points. The measurements covered approximately 2 NGV pitches in the circumferential direction and the rotor axial chord in the axial direction. Heat transfer electrical analog 共HTA兲 circuits 关30兴 were used to directly measure the heat flux data during a test. Using the measured heat flux data, the temperature signal was reconstructed for each gauge, as described in Oldfield et al. 关31兴. During a run, the heat flux drops with time as the surface temperature rises. The surface temperature rises by up to 60° C, allowing a regression of heat flux against surface temperature to obtain local adiabatic wall temperature 关31兴. The adiabatic wall temperature was used to reduce the heat flux data to Nusselt number, based upon the rotor true chord, using the relation given in Eq. 共1兲. Nu =

q˙C 共Taw − Tw兲k

共1兲

The thermal conductivity of air 共k兲 was evaluated at mean inlet total temperature. The regression to achieve Taw was relatively stable for a run with uniform inlet temperature, as shown by the sample plots in Fig. 6 for one gauge. However, for runs with temperature distortion, the regression was unstable and this technique could not reliably be used––a known problem with heat flux data in the presence of inlet temperature distortion. There are two particular reasons. The mixing of hot and cold gas streams causes unsteadiness in local driving temperature at a relatively low frequency. This causes large excursions from the expected regression line. Also, the EOTDF profile reduced the temperature in the near wall region to close to the wall temperature. Thus, the temperature rise during the run was relatively smaller, causing more uncertainty in the regression. For this reason, regressions to Nu were not possible for EOTDF using the heat transfer data obtained. During a test, hot and cold streams are introduced in a controlled manner and are allowed to partially mix to form the desired temperature profile. It is known by direct measurement that these gases are introduced in a steady manner. Measurements at the inlet plane to the NGV show that the initial mixing process has moderate unsteadiness however. Here, it is thought that the tem011005-4 / Vol. 134, JANUARY 2012

Fig. 6 „a… Heat flux measured using gauge model point 5152 during test run-3891. „b… Temperature reconstructed from measured heat flux. „c… Heat flux plotted against reconstructed temperature to obtain Taw by extrapolation. „d… Nusselt number obtained using the evaluated Taw.

perature gradients act as a marker for the unsteadiness naturally present in the inlet flow. Good average temperatures can be obtained at a point using a single run 共500 ms兲, allowing the profiles presented in Fig. 2 to be obtained with an excellent degree of repeatability. Deeper into the turbine, increased mixing 共the result of turbulence, secondary flows, etc.兲, and––in the rotor passage–– decreased gas/wall temperature difference make measurements of Nusselt number intrinsically difficult in a short duration facility when temperature variations are present in the inlet stream. It is difficult to see how this problem will easily be overcome with enhanced radial temperature profiles. 4.2 Rotor Casing Pressure Measurements. Time-averaged static pressure was also measured on the rotor casing. A Perspex cassette with 57 flush mounted pneumatic tappings was used. The tappings were fitted in rows at an angle of 52 deg to the axial, approximately following the stagger angle of the rotor blade. The tappings covered over 1 NGV pitch circumferentially, and the rotor axial chord axially. 4.3 Rotor Surface Heat Transfer Measurements. Heat transfer measurements were obtained on the rotor surface at 10%, 50%, and 90% spans using platinum resistance thin film gauges with two-layered substrate, an insulating layer of Kapton™ on a 共thermally兲 semi-infinite layer of metal. The theory for the use of multilayered gauges is given in Doorly and Oldfield 关32兴. To minimize the effects of slip-ring noise, the signals were highfrequency boosted using an in-shaft pre-amplifier. The natural temperature signal was recovered by deboosting the signal in post-processing. The heat flux was evaluated from the measured surface temperature by using fast Fourier transform technique 关33兴. The overall temperature rise on the rotor surface during the steady part of the run is too small to allow the use of regression technique 共described in Sec. 4.1兲 to obtain the local adiabatic wall temperature; the reason for which is the low gas to wall temperature ratio in the rotor relative frame. Hence, the heat flux data was reduced to Nusselt number using the rotor relative inlet total temperature, using Eq. 共2兲. The rotor relative inlet total temperature has been computed numerically using the design angles and velocity triangles at each span. NuT02rel =

q˙C 共T02rel − Tw兲kT02rel

共2兲

Transactions of the ASME


Table 2 Measurement precision and absolute uncertainty Precision

Absolute uncertainty

Variable

Uniform

EOTDF

Uniform

EOTDF

T0 Tw q˙ Nu

⫾1 K ⫾1.5 K 1.5% 2.4%

⫾3 K ⫾1.5 K 1.5% ––

⫾4 K ⫾2.4 K 5.6% 7.6%

⫾6 K ⫾2.4 K 5.6% ––

4.4 Measurements Uncertainty. A detailed treatment of the uncertainty related to the heat transfer measurements in the transient turbine experiment environment is provided by Povey 关34兴. The precision and absolute uncertainties obtained for uniform inlet and EOTDF measurements are presented in Table 2.

5

Numerical Simulations

Three-dimensional computational simulations were conducted with and without EOTDF, using the Rolls-Royce in-house CFD solver HYDRA. The measured temperature profiles at NGV inlet 共Fig. 2兲 were used for CFD computations for both cases. A structured computational grid comprising 1 NGV and 2 rotor blades representing 32 vanes and 64 rotor blades 共actual vane/blade count is 32/60兲 was developed using Rolls-Royce in-house tool parametric design rapid meshing 共PADRAM兲, with about 3 million mesh cells. To compensate for the change in numbers, the rotor airfoils were skewed to reproduce the capacity of the original geometry. Both steady and unsteady solutions were obtained. Nonlinear unsteady calculations were performed using implicit dual time-stepping. The results from unsteady solutions were time-averaged for comparison with steady solutions. The Spalart– Allmaras turbulence model was implemented with wall functions. For each case, two heat flux predictions were obtained at different isothermal wall temperatures, Tw1 and Tw2. The heat transfer coefficient was then evaluated using Eq. 共5兲. Adiabatic wall temperature was obtained by substituting heat transfer coefficient in either Eq. 共3兲 or Eq. 共4兲. q˙1 = h共Taw − Tw1兲

共3兲

q˙2 = h共Taw − Tw2兲

共4兲

h=

6

共q˙1 − q˙2兲共Tw2 − Tw1兲

Fig. 7 Rotor casing heat transfer measurements with uniform inlet conditions: „a… measurement points and interpolation grid, „b… area plot of Nusselt number, and „c… area plot of computed adiabatic wall temperature

vane wakes 共in the circumferential direction兲. Measurements obtained with inlet EOTDF are presented in Fig. 8. Figure 8共a兲 shows the measurement points where the heat flux and wall temperature data were acquired. The inherent problem of conducting regressions for turbine experiments with nonuniform inlet temperature has been discussed. In order to allow the data to be presented in a pseudo-non-dimensional form 共but not exactly as it requires independent evaluation of heat transfer coefficient and Taw兲, the assumption was made that the Nusselt number distribution was the same for EOTDF as for uniform inlet temperature. There is evidence in support of this assumption in the previous studies; for example, Metzger et al. 关4兴 and Thorpe et al. 关6兴 found that the reduction of heat flux observed with axial distance was mainly due to the changes in the driving gas temperature and not the heat transfer coefficient. Using the Nu measured with uniform inlet, local adiabatic wall temperature with EOTDF was evaluated. The following relation was used: q˙共t兲 = hEOTDF关Taw共t兲 − Tw共t兲兴

共6兲

共5兲

Results and Discussion––Rotor Casing

6.1 Experimental Rotor Casing Heat Transfer Results. Time-averaged heat transfer measurements performed on the rotor casing with uniform inlet temperature are presented in Fig. 7. The data were acquired as part of an earlier program, using the same instrumentation as used for the current program 共Chana and Jones 关8兴兲. Figure 7共a兲 shows the measurement points and also the triangular grid used for interpolation. Using the technique described earlier, the measured heat flux and wall temperature data was used to evaluate adiabatic wall temperature at each gauge location. Figure 7共c兲 shows the area plot of the adiabatic wall temperature. The Taw drops from approximately 410 K at rotor inlet to 330 K at the rotor exit. This drop is because of the work extraction process though the rotor passage. The evaluated driving gas temperature was used to reduce the heat flux data to Nusselt number. Figure 7共b兲 presents the plot of Nu that has been time-averaged over a period of around 250 ms 共about 2375 blade passing兲 during the steady part of the run. The variation in Nu is observed in axial as well as circumferential direction, with peak values just downstream of rotor inlet 共in the axial direction兲, and inline with the Journal of Turbomachinery

Fig. 8 Rotor casing heat transfer measurements with EOTDF: „a… measurement points and interpolation grid, „b… Nusselt number, assumed to be the same as with uniform inlet conditions, and „c… adiabatic wall temperature

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Fig. 9 Circumferentially averaged Nusselt number „exp…; assumed the same for uniform and EOTDF

where hEOTDF = huniform Figure 8共c兲 shows the area plot of computed Taw with EOTDF, time-averaged over the steady period of the run. A considerable reduction in Taw is observed with EOTDF, which is particularly pronounced over the early part of the rotor chord, although the effect persists throughout the rotor passage. This reduction is expected because of the pronounced inlet radial temperature profile with EOTDF; note that inlet temperature near the casing endwall for EOTDF was approximately 310 K 共cf. 444 K for uniform inlet temperature兲. By taking a circumferential average of the results, these trends are more readily compared, as shown in the plots below. Figure 9 presents the circumferential average of Nu, which is assumed to be the same for uniform and EOTDF cases. The maximum variation in Nu is around 40% as we move along the axial direction. Figure 10 shows the significant reduction 共about 50%兲 in the rotor casing heat load caused by the introduction of EOTDF. 6.2 Computational Rotor Casing Heat Transfer Results. Numerical solutions were obtained for uniform inlet temperature and for inlet EOTDF. For each case, two heat flux solutions were obtained at different wall temperatures to compute heat transfer coefficient. The time-averaged Nu and Taw, from instantaneous unsteady solutions 共10 time steps兲, are presented in Fig. 11 共uniform inlet temperature兲 and Fig. 12 共EOTDF兲. The area plots cover about 1 NGV pitch in the circumferential direction and rotor inlet to exit in the axial direction. The overall trends are quite similar for both the cases. A small circumferential variation is seen downstream of the NGV wakes. The variation in Nu is small; however, Taw varies significantly in the axial direction. The comparison of the two cases shows a pronounced reduction in the casing heat load with EOTDF 共as also seen in the experimental results兲, whereas the distribution of Nu has very little difference. The results support the assumption made for ex-

Fig. 10 Comparison of circumferentially averaged Taw„exp…; with and with out EOTDF

011005-6 / Vol. 134, JANUARY 2012

Fig. 11 Rotor casing heat transfer CFD predictions with uniform inlet temperature: „a… computed Nusselt number from predicted heat flux and „b… predicted adiabatic wall temperature

perimental data to compute Taw with EOTDF. Using the circumferential average of the results, the difference in Nu and Taw for the two cases is presented in Fig. 13 and Fig. 14 below. The difference in the predicted Nusselt number for uniform inlet temperature and EOTDF was small in comparison to the variation in Taw. The experimental Nusselt number for uniform inlet temperature is also plotted for comparison in Fig. 13. The

Fig. 12 Rotor casing heat transfer CFD predictions with inlet EOTDF: „a… computed Nusselt number from predicted heat flux and „b… predicted adiabatic wall temperature

Fig. 13 Rotor casing circumferentially averaged Nusselt number



Fig. 14 Rotor casing circumferentially averaged adiabatic wall temperature „CFD…

agreement between the measured and predicted Nu is generally good, especially from 20% to 75% of the rotor axial chord. However, CFD overpredicts the values toward the leading and trailing edges. Similarly, the predicted Taw for EOTDF is much lower than that observed in the experiments, which signifies that CFD underpredicts the mixing that results from the migration of hot-streak through the rotor passage. The maximum variation in the CFD predicted heat transfer coefficient is about 8% in the axial direction between the uniform and EOTDF cases. The surface plots for the predicted instantaneous heat transfer coefficient for the two cases are shown in Figs. 15共a兲 and 15共b兲 for comparison. The increase in the heat transfer coefficient, observed for EOTDF, can be a result of the changes in secondary flow arising as a result of the migration effect 共discussed later兲 that develops in the flow with EOTDF. A comparison of the surface flow pattern on the pressure-surface 共PS兲 of the rotor that highlights the migration of flow toward the tip for EOTDF is presented in Fig. 16. However, an in-depth analysis of the flow in the tip gap region is required to explain the changes resulting from the secondary flow activity. 6.3 Casing Pressure Results. The results obtained from the time-averaged static pressure measurements on the rotor casing

Fig. 17 Rotor casing measured static pressure with uniform inlet and with inlet EOTDF

are presented in Fig. 17. Measurements obtained with and without inlet EOTDF are presented for comparison. The dots indicate the points where the measurements were obtained. In the circumferential direction for both cases, high pressures are observed inline with the gap between NGVs and the lower values are observed at the predicted wake lines. The potential field effect of the NGVs reduces with axial distance. The casing static pressure drops from a value of about 2.8 bars at the rotor inlet to a value of about 1.4 bars at the rotor exit. The results are generally similar for the two cases with a mean difference of less than 2% of the reading. The time-averaged static pressure results on the rotor casing, obtained from unsteady numerical predictions, are presented in Fig. 18. The results show a similar trend as seen in the experimental results. The predicted results compare very well with measurements. The mean percentage difference between CFD predictions and experimental results is about 0.5% for uniform case and 3.5% for EOTDF.

7

Results and Discussion––Rotor Surface

7.1 Experimental Rotor Surface Heat Transfer Results. Rotor surface heat transfer measurements were conducted at 10%, 50%, and 90% spans for uniform inlet temperature and for inlet EOTDF. For inlet EOTDF, two rotor blades at each of 10%, 50%, and 90% spans were instrumented with thin-film gauges to increase the measurement density. These are represented as EOTDF共b1兲 and EOTDF共b2兲 in the relevant plots. Approximately six gauges were used on each PS at a given span location. Suctionsurface 共SS兲 instrumentation was similar. The processed heat flux data for inlet EOTDF is presented in Figs. 19–21, respectively, for each span and compared with the heat flux data obtained from a previous program with uniform

Fig. 15 Surface plots for predicted casing heat transfer coefficient: „a… uniform and „b… EOTDF

Fig. 16 Comparison of predicted surface flow pattern for uniform inlet and EOTDF


Fig. 18 Rotor casing predicted static pressure with uniform inlet and with inlet EOTDF

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Fig. 19 Rotor surface measured heat flux at 10% span

inlet conditions. No data were available for comparison on the PS at midspan for uniform inlet temperature and could only be obtained for EOTDF共b2兲 on this surface. The EOTDF heat flux at 50% span is considerably higher as compared with the uniform case, which is expected of the upstream radial temperature profile with high temperature gas around midspan. However, the trends observed at 10% and 90% spans are not as expected of inlet EOTDF radial profile that has low temperatures near the endwalls. The EOTDF heat flux on PS for both 10% and 90% spans is higher than the corresponding SS. In addition, the heat flux on PS becomes higher than that of uniform case as we move toward the trailing edge. For a meaningful comparison, the measured heat flux data was reduced to heat transfer coefficient and Taw. For the uniform inlet case, the heat transfer coefficient was obtained by using rotor relative inlet total temperature 共T02rel兲, as explained in Sec. 4.3, to compute the driving gas temperature, i.e., assuming that the variation in local Taw along the surface is small. This assumption is assessed later from the CFD predictions for the rotor surface adiabatic wall temperature for the uniform case. The results are shown in Fig. 22. The difficulty in evaluating the heat transfer coefficient for the cases with inlet temperature distortion has already been discussed. Hence, to evaluate variations in Taw with EOTDF, it was assumed

Fig. 22 Rotor surface heat transfer coefficient at 10%, 50%, and 90% spans „uniform…

that the heat transfer coefficient was the same for the two cases. Although this assumes similarity of flow-field, which is not strictly accurate, experience suggests that the effect of the change in heat transfer coefficient on heat flux is typically less significant than the change in driving gas temperature. There is support for this assumption from the CFD predictions, which will be presented later. The Taw evaluated based upon this assumption is presented in Figs. 23–25, respectively, for each span. Significant variation is observed especially toward the tip and the hub. The comparative results obtained from CFD predictions are presented below, which is followed by the discussion on the observed trends. 7.2 Computational Rotor Surface Heat Transfer Results. Heat flux predictions on the rotor surface, obtained from steady and unsteady CFD solutions, were used to compute the heat transfer coefficient at 10%, 50%, and 90% spans. The results obtained are compared in Figs. 26–28, respectively, for uniform inlet and EOTDF cases. The difference between steady 共st兲 and time-averaged unsteady 共un兲 solutions is generally small, suggesting––perhaps surprising––that the dominating physical processes are primarily steady in nature. The predicted heat transfer coefficient for the two cases are quite similar at each span, which indicates that the dif-


Fig. 23

Comparison of rotor surface Taw at 10% span


Fig. 24

Comparison of rotor surface Taw at 50% span

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Fig. 29 Predicted rotor surface adiabatic wall temperature distribution; uniform Fig. 25 Comparison of rotor surface Taw at 90% span

Fig. 27 Comparison of rotor surface heat transfer coefficient CFD predictions at 50%

wrapped surface of rotor blade for each case. For uniform inlet temperature, the distribution of Taw is quite uniform. A variation of up to 3% 共of the inlet value兲 is observed as we move from LE to TE. Thus, the assumption to use T02rel as local Taw is reasonably accurate 共for the uniform case兲. On the SS, the temperature is generally lower than the PS because of lower recovery temperatures. The integrated value of Taw at a span on SS is about 2% lower than PS. This difference also constitutes the temperature segregation effect caused by the relatively colder wake impinging on the SS of the blade. A very clear signature of the tip leakage vortex is observed on the SS at about 90% span, indicating the leakage flow at much higher temperature than the mainstream flow. Unlike uniform inlet, there is pronounced variation in local Taw along the surface for inlet EOTDF, as shown in Fig. 30. Thus, the assumption of constant T02rel at a given span height is poor for the cases with inlet temperature distortion. The distribution of Taw for EOTDF shows clear evidence of hot gas segregation toward the PS of the vane. This segregation effect is well known in situations with pronounced hot-streaks. The mechanism is a change in incidence angle in rotor relative frame that directs hot gas toward the pressure side at the midspan and cold gas toward the SS at the hub and casing. In addition, secondary flows are generated by the density 共thermal variation兲 and pressure gradients introduced by the hot-streak that cause the migration 共spread兲 of midspan hot gas toward the endwalls on PS of the blade. The comparison of the adiabatic wall temperature predictions with the experimental results is presented in Fig. 31–33, respectively, for each span; both steady and time-averaged unsteady CFD results are plotted. In general, the Taw predictions from CFD are in excellent agreement with the experimental results. The predicted segregation of flow 共at each span兲 and migration of flow 共at 90% and 10% PS兲 follows the trend observed in the measurements. The only significant discrepancy between prediction and experiment is at 10% span on the SS. Here, the predicted adiabatic wall temperature with inlet EOTDF is significantly lower than that inferred from the experiment. The experimental value is, in fact, similar to the situation with uniform inlet temperature. There is evidence in favor of the experimental observa-


Fig. 30 Predicted rotor surface adiabatic wall temperature distribution; EOTDF

ference observed in heat flux predictions between uniform inlet temperature and EOTDF are primarily due to the changes in the local driving gas temperature 共earlier this was used as an assumption to draw comparisons of experimental results兲. The slight variations observed are caused by the changes in flow pattern–– resulting from the variation of rotor relative inlet total temperature and pressure for the two cases, which will be discussed later. Figure 29 presents the predicted values of Taw on the un-



JANUARY 2012, Vol. 134 / 011005-9


Fig. 31 Comparison of experimental and predicted rotor surface Taw at 10% span

tion: 共1兲 An overall increase in temperature toward the hub has been reported in previous hot-streak studies. Shang and Epstein 关17兴 observed the migration of hot-streak toward the hub under the influence of buoyancy. He et al. 关22兴 showed the migration of hot flow from the PS hub toward SS hub under the combined influence of rotor hub passage vortex and the cross-passage movement due to the upstream NGV wake. 共2兲 A total temperature survey performed in a plane downstream of rotor exit with inlet EOTDF 共conducted as part of turbine efficiency measurement–– not presented here兲 shows that hot-streak migrates toward the hub as it passes through the rotor passage. These observations suggest that the difference of results on this surface is likely a discrepancy in CFD toward predicting the accurate influence of these phenomena in the SS hub corner. The small difference between the steady and time-averaged unsteady predictions indicates that in this case, the EOTDF profile is dominated by a radial distribution, and this appears to be primarily a steady effect 共caused by radial rather than circumferential nonuniformity兲. The impact of the radial nonuniformity of inlet EOTDF is explored using the CFD results. Figure 34 shows the computational prediction of the migration of the EOTDF profile through the vane

Fig. 34 Hot-streak migration through vane passage; total temperature „K… plots


Fig. 35 Comparison of „a… isentropic Mach number at NGV exit. „b… Total temperature „absolute frame… at NGV exit.


Fig. 36 „a… Comparison of vane exit total temperature at midheight. „b… Total temperature „rotor relative… at NGV exit.

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passage colored by total temperature 共note that the vanes are made transparent in Figs. 34共c兲 and 34共d兲 for clarity兲. The hot-streak, which is geometrically aligned with the vane leading edge, divides into two parts at the vane leading edge. There is some redistribution of the profile as it moves through the passage. At the exit of the vane, the temperature profile is broadly similar to that at inlet but the hot-spot is split by a cold vane wake. Figure 35共a兲 compares the circumferentially averaged radial profile for vane exit Mach number for the two cases. The vane exit Mach number is 共about兲 similar for uniform inlet and for EOTDF. However, the flow with EOTDF inherits the upstream nonuniformities in temperature, as shown in Fig. 35共b兲 for the same plane. Figure 36共a兲 compares the total temperature at midheight at vane exit for the two cases to highlight the extent of the circumferential nonuniformities in temperature caused by the wake 共and the low temperature gas between the neighboring hot-streaks in the case of EOTDF兲. The comparison shows that the flow-field



Fig. 37 „a… Comparison of predicted rotor relative inlet whirl angle. „b… Difference in rotor relative inlet whirl angle.

entering the rotor for EOTDF is dominated by the radial nonuniformities in temperature than the circumferential, which translates into the rotor relative frame as shown in Fig. 36共b兲. The difference in temperature in the rotor relative frame results into a change in tangential flow velocity with inlet EOTDF, which causes a change in flow incidence angle. The comparison of the predicted whirl angle at rotor inlet and the difference in whirl angle for the two cases is presented in Fig. 37. Inlet EOTDF causes positive incidence at midspan and negative incidence at the hub and casing. It is noteworthy that the effect of negative jet produced by the colder wake is to reduce the effect of hot-streak around the midspan region and also to enhance the effect of EOTDF cold flow near the tip and hub regions. As a result, the difference caused in the whirl angle is maximum near the tip. In addition, the nonuniformities in the rotor relative total pressure are generated. Figure 38 compares the rotor relative inlet total pressure for the two cases and also plots the percentage difference between them. An increase of 1% is observed for EOTDF at the midspan hot-streak region, and a decrease of 1% is observed near the casing as well as the hub. The result is a pair of counterrotating vortices driving the midspan hot fluid toward the endwalls. It is the combined effect of the nonuniformities generated in the whirl and the pressure field in the relative frame that lead to segregation and migration effects 共even in the steady flow environment兲.

8

Conclusion

Detailed experimental and numerical investigations of the effects of a pronounced inlet temperature distortion 共EOTDF兲 on rotor and casing heat transfer have been performed in a transonic turbine stage in a short duration engine test facility at scaled engine conditions. Experiments have been performed with and without temperature distortion and are compared with steady and unsteady stage CFD solutions.

Fig. 38 „a… Comparison of rotor relative inlet total pressure. „b… Percent difference of rotor relative inlet total pressure between uniform and EOTDF.


The heat transfer results on the rotor and casing have been presented in the form of adiabatic wall temperature and the heat transfer coefficient. The effect of a predominantly radial temperature profile is a considerable reduction of time-averaged heat load on the rotor casing, roughly consistent with the change in adiabatic wall temperature expected at the wall. The effect is reduced deeper into the rotor passage because of additional mixing in the rotor. CFD predictions suggest that the change in heat transfer coefficient with the introduction of inlet EOTDF is small. The reduction in heat flux on the rotor casing is primarily caused by the change in driving gas temperature. The redistribution of the temperature profile in the rotor passage and the impact on the heat transfer characteristics of the rotor have been considered. Significant changes in heat flux 共more than doubled or more than halved兲 result by the introduction of inlet EOTDF. These changes result primarily from changes in local adiabatic wall temperature and––less significantly––changes in heat transfer coefficient. The latter effect is more significant at 10% and 90% spans but is of order 10%. The distribution of Taw on the PS and SS was predicted numerically and was in good agreement with experimental measurements over most of the surface. Significant differences between uniform inlet temperature and inlet EOTDF arise as the result of redistribution of the hot and cold gases in the rotor. This effect results from incidence-induced segregation of flow and pressure-induced migration of flow, causing hot gas to migrate toward the PS at midspan and spread on this surface and cold gas to migrate toward the SS. This is primarily a steady effect caused by the radial temperature profile.

Acknowledgment The authors would like to acknowledge the financial support provided by the European Commission for the TATEF II project in which this research formed a part. The experiments were performed at QinetiQ, Farnborough, UK. The significant contribution of QinetiQ staff during testing is acknowledged.

Nomenclature Roman and Greek M ⫽ Mach number Tg ⫽ gas temperature, K Tw ⫽ wall temperature, K N / 冑T ⫽ 共pseudo兲 nondimensional speed T ⫽ temperature, K p ⫽ pressure, bar ␻ ⫽ turbine speed 共rpm兲 q˙ ⫽ heat flux, kW/ m2 Taw ⫽ adiabatic wall temperature, K k ⫽ thermal conductivity h ⫽ heat transfer coefficient C ⫽ rotor true chord, mm Subscripts, Superscripts, Abbreviations 0 ⫽ total 共absolute兲 1 ⫽ NGV inlet plane 2 ⫽ NGV exit plane rel ⫽ rotor relative CFD ⫽ computational fluid dynamics exp ⫽ experimental Re ⫽ Reynolds number Tu ⫽ turbulence intensity EOTDF ⫽ enhanced overall temperature distortion function TTF ⫽ turbine test facility HP ⫽ high pressure NGV ⫽ nozzle guide vane Nu ⫽ Nusselt number JANUARY 2012, Vol. 134 / 011005-11


PS, SS LE, TE st un b1 b2

⫽ ⫽ ⫽ ⫽ ⫽ ⫽

pressure side and suction side, respectively leading edge and trailing edge, respectively CFD steady results CFD time-averaged unsteady results instrumented rotor blade 1 instrumented rotor blade 2

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