HEAT TRANSFER IN A ROTATING RADIAL CHANNEL WITH SWIRLING INTERNAL FLOW

Transcription

1 m THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St., New York, N.Y GT-214 The Society shall not be responsible for statements or opinions advanced in papers or discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy for internal or personal use is granted to libraries and other users registered with the Copyright Clearance Center (CCC) provided $3/article or $4/page is paid to CCC, 222 Rosewood Dr., Danvers, MA Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department. Copyright CC 1998 by ASME All Rights Reserved Printed in U.S.A. HEAT TRANSFER IN A ROTATING RADIAL CHANNEL WITH SWIRLING INTERNAL FLOW B. Glezer and H. K. Moon Solar Turbines Incorporated San Diego, California J. Kerrebrock, J. Bons, and G. Guenette Massachusetts Institute of Technology Cambridge, Massachusetts ABSTRACT This paper presents experimental results for heat transfer in swirling internal flow, obtained in two ways. A test rig simulated a rotating blade's leading edge internal passage with heated walls and screw-shaped cooling swirl generated by flow introduced through discrete tangential slots. Spatially resolved variations of the surface heat transfer coefficients were measured in the rotating rig using an IR radiometer. A blade tested in the actual engine environment had similar geometry of the leading edge cooling passage. The blade surface temperatures were mapped in the engine with thermal paints and compared with a traditional convective cooling configuration. The data from the rotating rig and engine measurements are also compared with non-rotating heat transfer results obtained in the hot cascade using a traversing pyrometer at a realistic wall-tocoolant temperature ratio. The results are presented for realistic rotational numbers, ranging from 0 to 0.023, and for representative Reynolds number of 20,000 based on the channel diameter. The effect of Coriolis forces is evident with the change of direction of the rotation. A slight negative influence of the crossflow, which increased toward the outer radius of the channel, was recorded in the rig test results. The results presented will assist in better understanding of the screwshaped swirl cooling technique, providing the next step toward the application of this highly-effective internal cooling method for the leading edges of turbine blades. NOMENCLATURE d Swirl Tube Diameter (mm) J Electric Current (amp) k Thermal Conductivity (W/(m K)) L Swirl Tube Length (mm) m Total Mass Flow (Kg/s) r Radial Distance from Swirl Tube Axis (mm) R Electric Resistance (Ohm) T Temperature ( K) u Mass Averaged Radial Velocity (m/s) v Tangential Velocity (m/s) x Axial Distance (mm) Cr Skin-Friction Coefficient dr Density Ratio Nu Nusselt Number Re Reynolds Number Ro Rotation Number 'r Torque (N m) p Absolute Viscosity (Pa s) w Angular Speed (rad/s) it Swirl Tube Rotation Speed (rad./s) Subscripts c coolant g gas j jet I local m metal p plenum w wall av average in inlet ps pressure side ss suction side INTRODUCTION Cooling of the turbine blade leading edges remains a critical issue for advanced gas turbine engines. A screw-shaped swirl cooling technique introduced for the blade leading edges (Glezer et al, 1996, 1997), promises improved cooling performance in comparison to conventional internal cooling methods. Subsequently, a significant effort has been undertaken to understand its complicated flow phenomena and heat transfer. When applied to a blade leading edge, the swirling motion in the leading edge passage is induced by jets which are tangential to the concave inner surface of the passage, resulting in significant augmentation of the internal heat transfer Presented at the International Gas Turbine & Aeroengine Congress & Exhibition Stockholm, Sweden June 2-5, 1998

2 along the leading edge with crossflow playing an insignificant role in the overall process. An important factor for the heat transfer augmentation is the generation of GSrtlier vortices along the entire concave surface of the passage, as was recorded in a recent flow visualization study performed by Ligrani et al., Additional details of the pressure distribution and heat transfer measurements in a swirl chamber closely simulating the flow and wall-tocoolant temperature (or density) ratio in the swirl cooled blade are presented in a parallel study performed by Ligrani et al., The complexity of the fluid mechanics of this blade cooling technique is comparable to that of internal blade leading edge jet impingement, which has been studied for the last 20 years. A well-known disadvantage of a row of jets impinging normally to the wall of the confining channel is that a crossflow significantly reduces its cooling effectiveness (Kercher, Tabakoff, 1970). To overcome this negative effect, discharge of the spent air through film holes is required. As a result, this cooling system is no longer truely internal, producing negative consequences that include penalties in cost, thermodynamic efficiency and durability. However, traditionally at high operating temperatures corresponding to TRIT (Turbine Rotor Inlet Temperature) above 2150 F, this combination of impingement and film cooling of the blade leading edge has been used due to the limitations of presently available internal cooling techniques. The screw-shaped swirl cooling technique has the potential to expand the limit of internal cooling to match external blade heat loads for TRIT up to 2300 F, which are typical for many of the first stages of industrial turbines as well as for many of the second stages of aircraft turbines. A number of previous studies were focused on effects of rotation on nonswirling flows and heat transfer in smooth channels, passages with ribs and passages with confined jets (Morris, 1981; Epstein, et al, 1984; Harasgama & Morris, 1988; Bunker & Metzer, 1990; Wagner et al, 1991; Moms & Salemi, 1992; Prakash & Zerkle, 1992; Parsons et al., 1996). These studies showed that the rotation induces Coriolis and radial centrifugal buoyancy forces which can significantly affect flow and heat transfer phenomena in the rotating blade passages. Because the flow field is coupled with the temperature field, causing density-difference-driven buoyancy forces, one might expect quite complicated heat transfer phenomena, particularly in the case of a distinctly three-dimensional swirling flow. The authors of this paper are not aware of any data which have been generated prior to this work for the effects of rotation on the heat transfer in radial channels with swirling flow, particularly when significant temperature differences exist between the wall of the channel and the swirling flow. This paper presents and compares experimental results from three separate studies: Heat transfer measurements in a rotating cylindrical channel with discrete rectangular jets positioned along the channel tangentially to its inner surface, Hot annular cascade heat transfer measurements in a screw-swirl cooled turbine blade without rotation, Temperature/heat transfer mapping of the screw-swirl cooled blade in the actual engine environment with rotation. HEAT TRANSFER MEASUREMENTS IN THE ROTATING RIG The measurements were conducted in the MIT rotating heat transfer facility originally designed and used in impingement cooling studies (Kreatsoulas, 1983). Experimental ADaaratus and Methodology The rig is shown in Figure 1. The test section, simulating a blade leading edge, was attached to an arm which rotates in a vacuum chamber to 1. Vacuum Chanter/Protective Casing 10. Outlet Flow 2. Rotting Arm 11. Motor 3. Test Section and Mkrors Outline 12. Instrumentation Slip Ring 4. Balance WeIght 13. Housing 5. Shaft 14. IA Detector 6. Power Slip Ring 15. Imaging System 7. Heat Exchangers 16. Seals 8. Onboard Instrumentation Box 17. Optical Encoder 9. Inlet Flow 1 e. Power Wkes fl2040wm FIG. 1 - ROTATING RIG SCHEMATIC eliminate external heat transfer to the test section. The screw-swirl cooled blade leading edge was modeled by a radially positioned cylindrical thinwalled Nichrome tube test section connected to a parallel cylindrical coolant supply plenum by a series of tangential injection tubes, as shown schematically in Figure 2. PORT ORCTALIBRATION F THERMOCOUPLE Cu POWER STUD Cu POWER STRAP T o ^Y VIEW A-A E INI.r TUBE 45' q H I 10 mm $ A A 90 IMAGING \ TUB VIEW ^ 135 F ui R DIRECTION INLET OF ROTATION THERMOCOUPLE FIG. 2 - SCHEMATIC OF SWIRL TUBE TEST SECTION Both the supply plenum and swirl chamber were made of 0.25 mm thick Nichrome, heated resistively by current driven by a potential applied between its inner and outer electrically conductive support flanges. Because the Nichrome test section has a very low temperature coefficient of resistivity, the heating rate is very near constant over the surface of the swirl tube. It is important to notice for the purpose of later discussion that similarly to the actual engine blade the coolant supply plenum is dead ended while the swirl chamber, simulating a leading edge, is a through flow channel with a 90 turning outlet. The shaft carrying the rotating arm and test section is driven by a 7.5 HP, RPM variable-speed motor. The shaft speed is measured by an optical encoder mounted in the rear end of the shaft. Data acquisition is triggered by the index pulses of the encoder. The rotor assembly includes 2

3 two sections of slip rings, one supplying electrical potential to the test section and another transferring signals from the rotating instrumentation to readout devices. Bulk fluid temperatures at the inlet and outlet of the test section are measured using type K thermocouples, coupled to Omega Miniature Temperature Transmitters which are current drivers that produce a current proportional to the temperature measured. Surface temperature measurements are obtained by the combination of an infrared detector and an imaging system. The infrared detector is a liquidnitrogen-cooled Electro-Optical Systems HgCdTe infrared detector with an internal high/low gain preamplifier. The detector is mounted on a non-rotating horizontal stage which is driven by a stepper motor and a Warner electric linear actuator. The horizontal stage is itself mounted on a vertical stage, also driven by a stepper motor. Each motor is connected to an indexer which in turn communicates with a computer. Linear potentiometers attached to the two stages give their position with respect to some reference and allow them to be positioned to a desired location. The two degrees of freedom available to the stages are updown and forward-backward which allow for radial positioning of the IR detector and focusing respectively. The imaging system consists of primary and secondary mirrors which, together with the flat minors behind the model, allow viewing of all surfaces of the swirl tube, focusing the radiation from the surface of the model to the IR detector with 1 mm spatial resolution. The data reported here is from only the front surface of the swirl tube. This system was calibrated by heating the swirl tube without flow but filled with a thermally conducting body supplied with three thermocouples. Since the primary heat loss was (during calibration) by conduction through the ends of the test section to the supporting structure, the temperature distribution was parabolic along with the radial direction and at any given radius the test section was nearly isothermal. This enabled the construction of a relationship between local test section temperature and detector signal, which accounted for variations in emissivity of the test section and for peculiarities of the imaging optics. Given this test section configuration, there were the following parametric variations available: Reynolds number, varied by changing the mass flow and/or pressure. The Reynolds number is defined in terms of the total mass flow and swirl tube diameter: Re 4m ndµ where m is the mass flow and d is the swirl tube diameter. Density ratio, varied by changing heating current, and defined by: T - T. dr 1n Tn where T f is the coolant inlet temperature and T. is the wall temperature. Direction of rotation, placing the injection tubes on either the leading or trailing side of the simulated leading edge. The designation forward rotation here means the injection is at the trailing side. Rotation number varied by the speed of rotation, and defined as: Ro = Qd U where u is the mass-averaged radial velocity in the swirl tube based on the inlet density and 0 is the angular velocity. In most of the data to be discussed, the Reynolds number was set at a representative value of about 20,000, the density ratio at about 0.2 and the flow was outward. The rotation number was set in the range from a representative value of about 0.02 or to a very low value (in the order of.002) that minimized the effects of rotation. With the measured temperature distribution, the determination of the local Nusselt number proceeds as follows. First, the Nusselt number is defined in terms of the local convective heat flux and the difference between local wall temperature and an estimate of the local coolant temperature: d(gresistive q adiative) Nu a k(tw-tfuid) Tf-id = Tinier + (T.- Tinlet)( X I L) The local radiative heat loss was estimated from the measured temperature and the inlet and exit temperatures were determined by thermocouples at the respective locations. Discussion of Rotating Rig Results The primary results of the investigation are illustrated by Figures 3A, B and C which display Nu maps of the swirl tube surface for very slow rotation, nominal reverse rotation and nominal forward rotation, respectively. (Here forward rotation is defined as that where the injection is on the trailing side of the tube, reverse when it is on the leading side.) The vertical coordinate is radial distance on the test article. The horizontal coordinate represents a frontal 90 view of the test section with the right edge of the images corresponding to a radial plane 45 downstream of the injection slots with the tangential flow moving from right to left. For all these cases the Reynolds number, density ratio and electric heating values were kept approximately the same. Figure 3A shows that for very slow rotation, an average at each radial location of the jets Nu is nearly constant over the surface of the swirl tube except near the bottom, where the swirling flow is not well developed due to opposing viscous forces and also near the top, where some effects of the crossflow become noticeable. Some decay in the local heat transfer from the right to the left along the circumference of the tube appears to be typical for each jet location. This is primarily associated with a gradual rise of the coolant temperature near the wall, while the local air bulk reference temperature remains the same and also with jet momentum reduction. Rotation of the test section had a very significant effect on the results. When the test section rotates from the left to right (jet are positioned at the leading edge of the tube), two effects can be noticed (Fig. 3B). The decay of the heat transfer in the circumferential direction observed earlier, becomes more pronounced for most of the surface. The effect of Coriolis forces, opposing the tangential momentum of the flow produced by the jets, and inertial forces of rotation redistributing the flow along the tube radius are the primary sources of this degradation. Another important observation for this case is of an increase of the circumferential average heat transfer coefficient toward the tip of the test 3

4 100 NU SURFACE MAP FRONT 90 ONLY CASE 3A 90 3A 3B 3C ' ROT = 0.002R <-- < <-- 90 RE = AMPS = 145 IMAGING DR = VIEW Numean = 150 <-- < < <-- <-- t CASE 3B 45 i E 60 U) 150 ROT = 0.023R m <-- < RE = CO 50 AMPS 145 IMAGING DR= VIEW 145 Numean = w U <-- <-- <-- =, 135 R o 40?LY< 140 DIRECTION OF ROTATION CASE 3C r'r < < < ROT = 0.023F 0 RE = <-- <-- <-- AMPS = 145 IMAGING 125 DR = VIEW 10 Numean = ' F <-- i <-- < 120 Jet Locations : Jet Locations Jet Locations DIRECTION 0 OF ROTATION 135' ' 45 DISTANCE AROUND PERIMETER FIG. 3-THE EFFECT OF ROTATION ON A SCREW-SHAPED COOLING SWIRL 9aw-oa3csa.b section, beyond the level observed in the stationary case (Fig. 3A). This suggests a dominating role of the increasing flow discharged through the jets, which are located near the outer radius. Such an increase in the flow in the rotating case is induced by the inertial pumping, which results in an increase toward the tip of the tube of the difference in static pressure between the dead ended supply tube and through flow swirl tube. The tendency for the cooling air from the jets to be transported outward by buoyant forces also might enhance heat transfer toward the tip of the swirl tube. However, a realatively low ratio T f T C = 1.14 did not allow to observe it clearly. A significant improvement in the heat transfer can be seen in the case 3C with rotation from the right to the left (jets are positioned at the trailing edge of the tube). In this case one can also observe a radial redistribution of the heat transfer due to inertial forces. However, the entire range of the heat transfer is improved by approximately 9% (including correction for a slight difference in the Reynolds number). This gives a clear indication of the positive effect of the Coriolis force acting in the same direction as the tangential momentum of the jets. This brings an average heat transfer coefficient over the entire frontal view of the test section to the level of the stationary case with total compensation of the negative impact of the rotation. ACTUAL BLADE HARDWARE TESTING Blade Cooling Design and Test Procedure This part presents a validation of the results described in the previous section using existing turbine blades from a medium-sized Solar engine. Implementation of screw-shaped swirl cooling of the leading edge was restricted to redesign of the internal casting core without changes to the external blade geometry. It was recognized than preservation of the external blade shape, particularly when radius of the leading edge of the blade was small, could result in compromising the effectiveness of the swirl cooling technique. This factor should be taken into consideration when a screwshaped swirl cooling is compared to other internal cooling techniques. However, an important objective of the test was to demonstrate the effect of rotation on the heat transfer in the actual engine environment. Figure 4 shows schematically the modification of the standard blade to implement the leading edge cooling with discrete tangential jets generating the screw-shaped swirl in the leading edge passage and directing the flow of the spent air through the blade tip passage. 4

5 STANDARD MODIFIED arrxa FIG. 4- BLADE MODIFICATION FOR DEMONSTRATION TEST Cascade Tests The first phase of the test was performed in the stationary annular hot cascade rig (Fig. 5) previously described by Glezer, et al, The hot cascade rig satisfies similarity between engine and the rig for all critical nondimensional parameters except these associated with rotation, including Re, Ma, Tw/Tg and Tw/Tc. The test section includes five blades (Fig. 6) positioned downstream of a turbulence-generating grid. Realistic turbulence intensity in order of 12-15% was established based on the measurements performed with a heat flux probe described by Zhang and Glezer, The flow rates for the mainstream gas and coolant were determined with turbometers providing accuracy within 1%. Tw/Tc ratio was set at 1.6. COMPRESSED INFRARED AIR COOLINGM- PYROMETER FLOW -- METER AIR OBSERVATION METERT \ FUEL AIR HEATER TEST SECTION EXHAUST GAS TO STACK INSTRUMENTED HIGH SPEED DJ1TA AIRFOIL PROCESSING PYROMETER ^ SYSTEM COMBUSTOR // `^" AIR RIG CONTROL THERMOCOUPLE PRINTER 9771O#OOSM FIG. 5 -TURBINE AIRFOIL COOLING CASCADE TEST RIG Temperature mapping of the cooled blade was performed with a custom-designed wide temperature range pyrometer (shown schematically in Fig. 5) which was described in detail by Moon, et al, The pyrometer was attached to a numerically-controlled traversing device providing a spatial resolution of the blade surface temperatures 0.2 mm in the radial direction and 0.01 degree in the rotational mode. A central test blade was instrumented with two thermocouples buried FIG. 6 - HOT CASCADE TEST SECTION - LEADING EDGE VIEW flush into the blade wall to provide a reference temperature for emissivity correction. To minimize thermal radiation error from the neighboring slave blades in the cascade, they were also cooled to the same level as the test blade. Mainstream pressure, velocity and temperatures were verified prior to the test with the flow traversing device in both radial and circumferential directions. Engine Tests The temperature mapping of the same swirl cooled blade in the engine was performed using thermal paints to produce a temperature-time-dependent irreversible color map of the blades. (A unique automatic color recognition technique developed at Solar, provided temperature map of the thermallypainted part after the test, with exact reference to the actual geometry of the test article.) The swirl-cooled blades tested in the engine were accompanied by a thermally painted set of uncooled blades to verify the radial gas temperature profile as it is seen by the tested blades in the engine. The blade cooling air inlet temperature, which is used in the definition of cooling effectiveness, was calculated from the engine compressor discharge air temperature. Comparison of Actual Blade Test Results Figure 7 presents non-dimensional blade leading edge stagnation line temperature distribution obtained in the hot cascade. A very small variation of the mainstream gas temperature in the cascade and correspondingly small variation of the surface metal temperature produce an almost constant Tm/Tg ratio. The engine test results), even with rotation, do not show noticeable difference. Figure 8 compares these results, in terms of local cooling effectiveness, based on fixed inlet temperature of the cooling air. Very minor (under 5%) difference in the cooling effectiveness between stationary and rotating tests can be detected, as it was observed in the rotating MIT rig. Figure 9 superimposes the test results, obtained in the study presented here, on the Nu = f(re) plot for optimized geometry published earlier by Glezer, et al., Results from MIT rig tests which are focused primarily of a relative effect of rotation, are not superimposed here. The hot cascade and engine test data are all positioned below the level which was reported for the optimized cases. This suggests the importance of an optimized swirl passage geometry, which was compromised in the standard blades available for the test. Proper radial location and sizes of the tangential slots combined with optimized external and internal geometry of the leading edge of the

6 ,^ -o---o 1000 o ASME (96-GT-181) DEMO Blade Test p 0.eo ~ Engine Hot Cascade I Hot Cascade Engine tom' BLADE HEIGHT, % 9rtzowo FIG. 7- LOCAL GAS TO METAL TEMPERATURE RATIOS te F7' ' Engine Hot Cascade BLADE HEIGHT, % S7 4-OOIM FIG. 8-COOLING EFFFECTIVENESS COMPARISON blade are needed to achieve the best cooling performance of the screw-shaped swirl cooling technique. CONCLUSIONS The study reported here, of the effect of rotation on the heat transfer in the screw-shaped swirl cooling technique, has assisted in better understanding of this complicated flow phenomena. Coriolis forces play an important role in enhancing the internal heat transfer when their direction coincides with a tangential velocity vector of the swirling flow. The opposite is true for the reverse rotation resulting in Coriolis forces opposing the swirling flow. Centrifugal and coolant density ratio driven buoyancy forces do not appear to produce a significant effect on the overall average heat transfer, but lead to redistribution of the local heat transfer along the passage Reo, (000) VM FIG. 9 - EFFECT OF ROTATION ON HEAT TRANSFER OF SCREW-SHAPED SWIRL COOLING Direct comparison of the Tw/Tc ratio effect on the heat transfer in the rotating rig (Tw/Tc = 1.14) and in the engine test (Tw/Tc = 1.6) did not produce any measurable difference in the heat transfer values. Optimization of the internal passage geometry in relation to location and size of the tangential slots is very important in achieving the best performance of the screw-shaped swirl for the internal blade leading edge cooling. BIBLIOGRAPHY Bunker, R. S., and Metzger, D. E., 1990, "Local Heat Transfer in Internally Cooled Turbine Airfoil Leading Edge Regions: Part I- Impingement Cooling Without Film Coolant Extraction," ASME Journal of Turbomachinery, Vol. 112, No. 3, pp Epstein, A. H., Kerrebrock, J. L., Koo, J. J., and Preiser, U. Z., 1985, "Rotational Effects On Impingement Cooling," Symposium on Transport Phenomena in Rotating Machinery, Honolulu, HI. Glezer, B., Moon, H. K., Zhang, L., and Camci, G., 1994, "Application of a Heat Flux/Calorimeter-Based Method to Assess the Effect of Turbulence on Turbine Airfoil Heat Transfer," ASME 94-GT-95. Glezer, B., Moon H. K., and O'Connell, T., 1996, "A Novel Technique for the Internal Blade Cooling," ASME Paper 96-GT-181 Glezer, B., Lin, T., and Moon H. K., 1997, "An Improved Turbine Cooling System," U. S. Patent No Harasgama, S. P., and Morris, W. D., 1988, "AThe Influence of Rotation on the Heat Transfer Characteristics of Circular, Triangular, and Square-Sectioned Coolant Passages of Gas Turbine Rotor Blades," Transactions of the ASME, Journal of Turbomachinery, Vol. 110, pp Ligrani, P. M., Hedlund, C. R., Moon, H. K., and Glezer, B, 1998, "A Heat Transfer and Flow Phenomena in a Swirl Chamber for Turbine Blade Internal Cooling," ASME 43rd International Gas Turbine and Aeroengine Congress and Exposition, Stockholm, Sweden, submitted. Ligrani, P. M., Hedlund, C. R., Thambu, R., Babinchak, B. T., Moon, H. K., and Glezer, B, 1997, "Flow Phenomena in Swirl Chambers," ASME Paper 97-GT-530. Kercher, D. M., and Tabakoff, W., 1970, "Heat Transfer by a Square Array of Round Air Jets Impinging Perpendicular to a Flat Surface Including L

7 the Effect of Spent Air," ASME Journal of Engineering for Power, Vol. 92., No. 1, pp Kreatsoulas, J. C., 1983, "An Experimental study of Impingement Cooling in Rotating Turbine Blades," MIT Gas Turbine Laboratory Report 178, Cambridge, MA. Moon, H. K., Glezer, B., Mink, B. and Marvin, W., 1995, "Development of a Wide Range Temperature Pyrometer for Gas Turbine Application," ASME Paper 95-GT-126. Moms, W.D., 1981, "Heat Transfer and Fluid Flow in Rotating Coolant Channels," Research Studies Press. Morris, W.D. and Salemi, R., 1992, "An Attempt to Uncouple the Effect of Coriolis and Buoyancy Forces Experimentally on Heat Transfer in Smooth Circular Tubes that Rotate in the Orthogonal Mode", Transactions of the ASME Journal of Turbomachinery, Vol. 114, pp Prakash, C. and Zerkle, R., 1992, "Prediction of Turbulent Flow and Heat Transfer in a Radially Rotating Duct", Transactions of the ASME Journal of Turbomachinery, Vol. 114, pp Parsons, J. A., Han, J. C. and Lee, C. P., "Rotation Effect on Jet Impingement Heat Transfer in Smooth Rectangular Channels with Four Heated Walls and Radially Outward Cross Flow," ASME Paper No. 96-GT Wagner, J. H., Johnson, B. V. and Hajek, T. J., 1991, "Heat Transfer in Rotating Passages with Smooth Walls and Radial Outward Flow," Transaction's of the ASME Journal of Turbomachinery, Vol. 113, pp , Zhang, L. and Glezer, B., 1995, "Indirect Turbulence Measurement in Gas Turbine Stages Using Heat Flux Probe," ASME Paper 95-GT