93-GT-405 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St., New York, N.Y. 10017 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. Papers are available from ASME for 15 months after the meeting. Printed in U.S.A. Copyright © 1993 by ASME TRANSONIC COMPRESSOR ROTOR CASCADE WITH BOUNDARY-LAYER SEPARATION: EXPERIMENTAL AND THEORETICAL RESULTS R. Fuchs, W. Steinert, and H. Starken Deutsche Forschungsanstalt fur Luft- and Raumfahrt e.V. Institut fur Antriebstechnik Koln, Germany ABSTRACT u A transonic compressor rotor cascade designed for an inlet x 13 Mach number of 1.09 and 14 degrees of flow turning has been redesigned for higher loading by an increased pitch-to-chord ratio. Test results, showing the influence of inlet Mach number and flow angle on cascade performance are presented and compared to data of the basic design. Loss-levels of both, the original and the redesigned higher loaded blade were identical at design condition, but the new design achieved even lower losses at lower inlet Mach numbers. The computational design and analysis has been performed by a fast inviscid time-dependent code coupled to a viscous direct/inverse integral boundary-layer code. Good agreement was achieved between measured and predicted surface Mach number distributions as well as exit-flow angles. A boundary-layer visualization method has been used to detect laminar separation bubbles and turbulent separation regions. Quantitative results of measured bubble positions are presented and compared to calculated results. NOMENCLATURE velocity coordinate in chordwise direction flow angle with reference to circumferential direction (3 5stagger angle with reference to circumferential direction flow turning (3, — 13 O boundary layer displacement thickness SZboundary layer momentum thickness S, boundary layer energy loss thickness w total pressure loss coefficient _ (Pu — piz)/(Pu — p^) or relaxation factor SUBSCRIPTS 1 inlet plane far upstream 2 i in tr outlet plane far downstream inviscid instability transition v Viscous AVDR, Q axial-velocity-density-ratio between inlet and outlet of cascade 1c H,, H 32 M M„ n p blade chord length shape factor b,/S z shape factor 8 ; /62 Mach number isentropic Mach number = f(p/p„) iteration number static pressure Pi total pressure Re Reynolds number s/c pitch to chord ratio INTRODUCTION The increase of compressor stage pressure ratios in modern turbofan-engines leads to supersonic relative inlet Mach numbers. By increasing the inlet Mach number the average Mach number ahead of the shock waves grows even more and the shock losses are increasing too. That means boundary layer separation can occur near design or even at design conditions. For these highly loaded flow conditions computational methods are required, which can predict accurate surface Mach Presented at the International Gas Turbine and Aeroengine Congress and Exposition Cincinnati, Ohio — May 24-27, 1993 Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms number distributions, boundary layer behaviour and performance parameters like losses and turning. Especially in design procedures the codes should work as fast and cheap as possible, because many calculations are required to optimize the cascade geometries for design and off-design flow conditions. In the investigations described here an Inviscid-Viscous Interaction (IVI) approach is validated for application in design systems. A transonic compressor rotor cascade, whose MCA-blades had been designed in the past by mainly empirical methods, was redesigned using this method for a new prescribed blade Mach number distribution and increased pitch/chord ratio. Both cascades had been tested in the same wind tunnel of DLR Cologne. The test results of the redesigned cascade are presented and compared to the reference cascade and to computational results. IVI-Systems are commonly used in cascade computational analysis. For subsonic flows see for instance Janssens and Hirsch (1983), for transonic/supercritical applications Barnett and al. (1990) and for transonic/supersonic applications Calvert (1982). The method used here is a time-dependent inviscid code coupled to a direct or inverse integral boundary layer code for handling unseparated or separated flow cases. The inviscid/viscous coupling is modelled by the solid displacement surface method in an iterative manner. In the case of separated flows a semi invers iteration method with a velocity coupling model on the limiting streamlines is used. CASCADE DESIGN The geometry of the reference cascade L030-4 was also Selected by the AGARD working group 18 (Schreiber and Starken, 1984, 1990) as a test case. It is the 45%: blade height section out of a DFVLR transonic compressor rotor (Dunker and Hungenberg, 1980, Dunker, 1990). The cascade geometry was deduced from the MCA-type rotor blade by projecting the coordinates from the meridional stream surface upon a cylindrical stream surface which crosses the blade centerline. The blade section was designed for a supersonic inlet Mach number of M 1 =1.09, with a normal shock wave ahead of the cascade entrance, subsonic deceleration in the cascade passage and a turning angle of 0=12.5 degrees. In the cascade tests the turning angle was 0=13.5 degrees. Calvert (1983) presented a comparison of DLR test results and calculations performed by his IVI-code (Calvert, 1982). The redesigned cascade, designated here as DLR-TSG89-5. was designed using the direct 1V1 method which is described later in this paper and which was used also for test verlfications. The design goal was to find out the loading limits of an MCA-type blade in a transonic cascade at identical inlet conditions, stream-tube contraction (AVDR) and flow turning. The pitch chord ratio was increased up to s/c=0.7 for the new design instead of 0.62 of the basic one. The blade contour was changed step by step until the velocity distribution was considered to be favourable. Figure I provides plots of both cascades and the design data. The blade coordinates can be found in the appendix. Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms MCA L030-4 s/c=0.62 DLR TSG 89-5 s/c=0.70 TSG 89-5 L030-4 s/c 6 M, MT f2 0 AVDR 0.62 138.51° 1.09 148.66° 0.71 136.17 12.49' / 1 3.5° EXP. 1.212 0.70 138.0° 1.09 148.5° 0.71 134.5` 14.O 1.2 Figure 1. Geometry and design data of (L030-4) cascade and redesigned cascade (TSG89-5) CASCADE WIND TUNNEL The DLR transonic cascade wind tunnel is it continuously running facility operating in a closed loop. For operation in the transonic and supersonic range, the upper wall of the test Section (Figure 2) is slotted and connected to a suction system. SLOTTED UPPER ENOWALL WITH SUCTION SIDEWALL BOUNDARY LAYER SUCTION FLOW 1/ PROBE TAILBOARD WITH THROTTLE / PROBE N / TRANSONIC TAILBOARO Figure 2. Test Section of the DLR transonic cascade wind tunnel The suction system is also used to reduce the upstream side wall boundary layer through protruding slots and to vary the axial velocity density ratio via slotted side walls. A special throttle device in the downstream area of the blade row I necessary, because at some flow conditions at supersonic inlet velocities the back pressure can be varied independently of the upstream flow conditions. Also for operation in the transonic regime the tailboard throttle system is necessary to control and adjust the upstream flow conditions. The throttle system is combined with two tailboards hinged to the trailing edges of , the outermost blades. The bottom tailboard consists of a closed box with a slotted surface in which the back pressure is transferred upstream. The cascade span is 168mm and 7 blades are mounted between plexiglas windows in rotatable sidewalls of 2m in diameter. Periodicity is checked by sidewall pressure taps 24.5mm or half a pitch upstream and downstream of cascade inlet- and outlet plane. The inlet Mach number is determined by the inlet total pressure of the settling chamber and the upstream sidewall static pressures. Because at supersonic velocity probes would disturb the inlet flow field, the inlet flow angle 13, is determined by a method presented by Steinert et al. (1991). This method is based on blade to blade calculations performed at different inlet flow conditions of the cascade test range. These calculations lead to it correlation between M. (3, and M,,. where M„ is the local isentropic Mach number determined at it fixed position in the front part of ttte suction side. 'fhe correlation yields (3,, it M, and M„ are measured during: the test. The downstream flow values of static pressure p, total pressure p,2 and flow angle distribution 132 are measured by moving a combined probe over more than one blade pitch at cascade midspan position. To measure the isentropic Mach number distribution in one blade passage the third and fourth blade were equipped with 13 pressure taps each at mid-span. For boundary layer visualization on the profile surfaces an ink tracing method was used. Coloured ink was introduced into the boundary layer through one or more pressure taps. By this method boundary layer separation can be detected. The extension of the separation region, which means length of the laminar separation bubble or the turbulent separation region, was determined in additional tests, introducing ink in it stepw ise manner tap by tap downstream of the incipient separation locus. VISCOUS ANALYSIS The computational method used here is an inviscid-viscous interaction technique for calculation of the blade-to blade (S I ) flow field. The inviscid part is based on the time-dependent Euler code of Denton (1982), which includes transonic flows with shocks and shock losses. The stream tube thickness (AVDR) was varied linearly between cascade leading and trailing edge plane in all calculated examples presented. The viscous part contains both it direct and inverse mode integral boundary layer code. The direct version of this code is based on the method of Walz (1969). which uses a two parameter formulation that are it velocity profile form factor and a momentum thickness parameter. ]'his method was improved and inverted by Thiede et al. (1082). Transition and Separation. Exponential functions of the shape factor I -I, , are used in the transition criteria of the Thiede method and can be found in the appendix. Laminar separation is set at a shape factor I I,, < 1.515. The calculation is continued with attached turbulent boundary layer and assuming zero laminar separation bubble length. Turbulent separation is set at it shape factor H,. < 1545 or M > 1.32. Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms IVI procedure. On the front part of the blades, as long as the boundary layers are attached, the inviscid calculation determines the velocity distribution and the direct mode of the boundary layer code calculates the new blade shape by adding the resulting displacement thickness at each mesh point. As soon as boundary layer separation is expected, caused by shock boundary layer interaction or rapid deceleration, the direct mode should become unstable. Then the code switches to the inverse mode and the velocity distribution is calculated by an estimated displacement thickness distribution down to the cascade trailing edge. Both the inviscid and viscous velocities have to be cotnbined by an inviscid-viscous coupling procedure which is introduced after every inviscid-viscous iteration loop. In the method used here, the matching procedure of Carter (1979) was applied, in which the two resulting velocities at each surface net point from the inviscid and the inverse viscous calculation arc coupled by the relation (51,+ 1[1 i-(i)(u v /u, --- 1 )] where 5, is the displacement thickness, added to the profile shape, n is the iteration number. w is a relaxation factor, u, is the local viscous and u, the inviscid velocity. Mixing procedure. The final mixing calculation is performed using the flow properties of the trailing edge plane and solving the conservation equations for mass, momentum and energy (see Weber et al., 1987). Thereby the trailing edge Flow values taken from the inviscid and viscous calculation are changed to constant exit flow properties M2, (3,, p, 2 and the loss coefficient w The total pressure distribution in the trailing edge plane estimated by the inviscid calculation includes both numerical losses and physical shock losses. Looking at the complex shock structure in the Schlreren pictures Figure 10 and Figure 13 it seems impossible to separate the shock losses from the numerical losses. However due to the lack of a shock boundary interference loss model in the boundary layer calculation so far, the calculated boundary layer losses are too low and therefore an overprediction of the losses is avoided. This was the case in many transonic and supercritical cascade calculations we performed. Convergence and computer time. To start the IVI solution procedure, 300 time steps of the inviscid Euler code are used before running the boundary layer calculation for the first time. Every next viscous update is performed after 100 Euler time steps until convergence is reached. Convergence is assumed if the change in meridional velocity per cycle at every mesh point is less than 0.005% of an average velocity for the whole flow and if the relative change of displacement thickness S, is less than 4C/. These criteria lead to total time step numbers between 1700 (design) and 2100 (off design) with it I9x70 calculating grid and require 2 to 3 minutes on it small mainframe computer Amdahl 580-58/60. Comparable solutions of a Navier-Stokes code at our Institute require I to 2 hours on it work station of similar speed. The recalculation of the inviscid mesh after every viscous update in the presented solid displacement u - face method is not it costly approach, because a mesh update of 1330 points requires very little CPU time. CASCADE PERFORMANCE • M,= 1.15 ° M,= 1.09 ❑ M,= 1.02 o M,= 0.92 AVDR=1.20 To make cascade analysis useful for compressor designers, the main performance values as total pressure loss and flow turning have to be presented over the entire operating range of inlet Mach number and inlet flow angle. .20 .18 .16 Influence Of Inlet Mach Number On Total Pressure Losses The measured variation of the total pressure loss coefficient with inlet Mach number at design inlet flow angle and design AVDR are presented in Figure 3 for the redesigned cascade DLR-TSG99-5 and the reference cascade L030-4 and compared to calculated results for the first one. .14 U ,- .12 Q) o .10 V W .08 0 0, =148.5* AVDR=1.2 ❑ Reference L030-4 0 Redesign TSG 89-5 .06 o Predict. TSG 89-5 .04 0.16 3 .02 .00 144 0.12 inlet angle a) 0.0E Figure 4. Tested loss versus inlet angle at different inlet Mach numbers 0.01 The pressure loss coefficients of both cascades measured at design inlet Mach number and design AVDR are presented in Figure 5 and compared to calculations for the redesign. V ti 0 156 a, Li 0 -J ❑ Reference L030-4 Redesign TSG 89-5 M,= 1.09 AVDR =1 .20 0 0.8 0.9 1.0 1.1 0 o Predict. TSG 89-5 1.2 .20 Inlet Mach number M, .18 Figure 3. Tested and predicted loss versus inlet Mach number 3 .16 c At it constant inlet flow angle the losses increase continuously with increasing inlet Mach number. This behaviour is mainly caused by increasing shock strength in front of the cascade which is resulting in higher shock losses and higher shock/boundary layer interference losses. Compared to the original design, the new cascade TSG89-5 offers lower losses at subsonic and low supersonic inlet velocities, whereas at design inlet Mach number both loss-levels are of the same magnitude. The calculation shows good agreement at subsonic and sonic inlet velocities but lower losses at design conditions. U w 0 o .14 .12 to a .08 .06 0 n .04 .02 A .00 ,i 144 146 Influence Of Inlet Flow Angle On Total Pressure Losses And Flow Turning Total pressure loss. The measured loss characteristics of the new cascade DLR-TSG89-5 are schown in Figure 4 for inlet flow angle variations and different inlet Mitch numbers. This figure clearly shows the characteristic narrowing of the operating range of it transonic cascade with increasing inlet Mach number. The inlet flow angle range decreases from 9.5 degrees at M, = 0.£i2 to 3.5 degrees at M, = 1.15. At the design Mach number M, = 1.09 the operating range is of the order of 5 degrees of incidence. U 148 r 150 152 inlet angle p 154 156 1 Figure 5. Tested and predicted loss parameter versus inlet angle The test results of the two cascades are almost identical, but the predicted loss values are unsatisfactory. The minimum total pressure losses of 8% can be found at design and at slightly positive incidences. 4 Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms 1.6 Flow turning. The variation of the flow turning with inlet flow angle at design inlet Mach number and design AVDR are presented in Figure 6 . ° ° Experim. 1.4 24 22 20 ❑ M,= 1.09 ❑ Reference L030-4 AVDR= 1 .20 0 Redesign TSG 89-5 o Predict. TSG 89-5 C 1.0 PS t U 0 16 00 0 Q O 0 .0 0 U 14 Q0 12 C 10 .6 Test Caic. 1.087 1.088 148.4° 148.4° 0.692 0.694 14.4° 13.4° 1.20 1.20 0.081 0.057 1.463 1.462 M .4 M2 p 8 AVDR 2 6 4 0 2 0 144 SS 1.2 m 18 0) - calcur. L 146 148 150 154 152 inlet angle 156 .2 .8 .6 .4 x/chord 1.0 Figure 7. 'rested and predicted Mach number distribution, 0° incidence p 1 Figure 6. Tested and predicted flow turning versus inlet angle 1.6 At design inlet flow angle both, the design flow turning of 0=13.5° of the cascade 1..03(1-4 and O=14° of the cascade TS089-5 are well verified test results. The numerically h, dieted results of the Flow turning of the redesigned cascade shows similar agreement to the experimental data. To analyze the total pressure loss development shown in Figure 5 in more detail, in the following chapters the profile Mach number distributions at three characteristic inlet flow angles are presented. The flow angles selected are the design angle p 1 =148.5°, the positive incidence (3,=151.6° and the lowest negative incidence (3,=146.5° (incidence =-2°), when the blade passage gets choked, which is called unique incidence at supersonic inlet velocity. Additionally at corresponding inlet flow angles boundary layer visualization test results and calculations will be presented. 1.4 ❑ v Experim. - ❑❑ ❑ caic. Ss 1.2 E C 1.0 U 0 V ° U °- 0 .6 C a) °' °° P, M2 AVDR w P2 /P, .2 .0 L v ❑ ❑ v v ° PS M .4 .0 °° v v v e PROFILE MACH NUMBER DISTRIBUTION .2 Cale. Test 1.084 1.084 151.6° 151.6° 0.623 0.661 17.2° 15.7° 1.23 1.23 0.098 0.117 1.529 1.466 .4 .6 .8 1.0 x/chord Design. A comparison between the tested and calculated surface Mach number distributions is shown in Figure 7 for the design values M,=1.09, (3 1 = ] 48.5° and AVDR ( ))=].20. There is an excellent agreement to be seen for both Mach number distributions on suction and pressure side. Slight differences at the front part of the pressure surface can be explained by the course computational mesh in the leading edge region. The mesh size used in all cases was 70 points in axial direction with 37 points along the blade surfaces and 19 points in circumferential direction to realize calculation times as short as possible. Near Stall. The comparison of the measured and predicted Mach number distributions at (3 1 =151.6 ° at 3 degrees positve incidence near stall is shown in Figure 8. Certain differences between measured and predicted distributions can be seen on the front part of the pressure side and Figure 8. Tested and predicted Mach number distribution, +3 incidence 0 the rear part of the suction side. Also the calculated turning angle is 1.5 degree too low. These differences may be caused by the highly 3-D character of the flow at this positive incidence, which was also observed in the flow pattern of boundary layer ink injection tests. Although the ink tests showed no separation in the mean section, in fact it should be a separated flow case. Because no shock boundary layer interaction model was applied in the calculation no separation was predicted there. This should also explain the differences of the deviation angles in test and calculation. Flow visualhi Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms .0 ization by stroboscopic Schlieren video pictures showed also a remarkebly unsteady flow- and shock behaviour, which alltogether may lead to these different results. Choking. The comparison of the measured and predicted Mach number distributions at R 1 =146.7° (unique incidence, choked passage) is shown in Figure 9. 1.6 ❑ v Experim. Calc. 1.4 1.2 N ❑ LS ° LS TS -c c ❑ ° pO E CL O o v v ' 1.0 0 0 SS Experimental separation Exp. .6 4 lam. sep. bubble Calc. Test M1.085 1.083 146.8° 146.7° 0.714 0.721 02 11.2° 11.7 1.13 1.12 AVDR 0.090 0.125 P 2 /P '1.425 1.383 M 0 .2 Figure 10. Schlieren picture at unique incidence Clow condition, -2° incidence PS B.L. Prediction: L lam. sep. T turb. sep H test uncertainty .6 .4 x/chord .8 1.0 Figtne 9. Tested and predicted Mach number distribution, _ -2° incidence , tested and predicted boundary layer phenomena indicated There is as in the design flow case an excellent agreement of predicted and tested Mach number distributions on both profile surfaces. The supersonic velocities on the front part of the pressure side indicate clearly that the maximum possible mass flow is reached. The Schlieren picture in Figure 10 illustrates this flow condition by showing the two shock system of the oblique leading edge shock of the incoming flow and the normal passage shock close downstream of the minimum cross section of the blade passage. Opening the throttle moves the passage shock further downstream without influencing the inlet flow anymore. Thereby the passage shock losses increase due to higher average Mach numbers ahead of the shock in the diverging passage. In Figure 5 this behaviour is documented in the vertical left branch of the loss parameter curve at maximum negative incidence. BOUNDARY LAYER RESULTS The validation of the boundary layer calculation has been performed at design and off-design inlet flow angles. The choking flow angle was chosen for representation of the offdesign flow case because of the better 2D flow character at this incidence in contrast to the stall flow case as it was described in the last chapter. The inlet turbulence level of Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms 2.5% was derived from laser measurements and the inlet Reynolds number varied from 1.1 * 1(> 6 to 1.3* 10 6 for the tests and was set 1.1*106 for all calculations. Choking. In Figure 9 the tested and predicted laminar and turbulent separation regions are also shown. The results of the ink injection tests indicate a laminar separation bubble on the pressure side, extending over the whole shock induced deceleration region from 25%. to 50% of chord. The uncertainty is one pressure tap distance, which can be seen in Figure 9 and Figure 12 as the distance between two symbols, which varies from 5% to 9% of chord length. The incipient laminar separation is very well predicted by the calculation, but because there is no separation bubble length model implemented in the boundary layer code until now, the extension of the bubble could not be predicted. The laminar separation point is interpreted as transition point and the calculation is continued with reattached turbulent boundary layer. On the suction side the ink test indicated a separation starting at the beginning of the shock induced deceleration without reattachment. The boundary layer calculations showed good agreement in predicting the laminar separation. But as on the pressure side, downstream of the laminar separation point the calculation is continued with an unseparated turbulent boundary layer leading to turbulent separation at 82c/ of chord length. These deticiences of the boundary layer code in predicting laminar separation bubbles as well as complete laminar separation due to shock wave interaction should give the explanation for the differences in total pressure loss results in Figure 5. The distributions of the displacement thickness 8, and the shape factors H, 2 and H_, 2 on the suction and pressure side of the profile are shown in Figure 11. The kink in all curves of Figure 11 indicates the laminar separation or laminar turbulent transition. The 8, curves (Figure I l top) shows the rapid increase of the boundary layer displacement thickness behind the shock and in the shock deceleration region on both surfaces. On the pressure side the 1l 32 distribution (Figure 11 bottom) shows a minimum at 50%. of chord, indicating that the shock deceleration area is not large enough to reach the turbulent separation criteria of H 3 ,= 1.545. The axial distance from the beginning of the Suction Side 1.6 Pressure Side ❑ 1.4 .020 .VLV Y .015 .015 1.2 .010 .010 E C 1.0 E .005 .005 U C t U .0 a .000 .0 .2 .4 .6 .8 1.0 000.0 .2 .4 .6 .8 1.0 N 4 4 3 .2 .4 .6 .8 1.0 Colc. -M 1.115 f, 147.7° M z0.719 12.8° 0 AVDR 1 .20 0.062 P 2 /P, 1.489 B.L. Test Prediction: 1.110 148.0 ° © lam. sep. 0.700 13.8 °test 1 .21 uncertainty 0.097 1.480 .2 .4 .6 .8 1.0 x/chord t Figure 12. Tested and predicted Mach number distribution, = incidence, increased inlet Mach number M,=1.11 and tested and predicted boundary layer phenomena I.. 3 1 PSF a^ LS .0 2 .0 7/ 1 LS SS 7 m a 0 s / ❑ CL .6 0 5 0 U a Colo. U 6 a Experimental v Experim. lam. sep. bubble 1.8 I- 0 21 1.7 U 1.6 N a - 1 r exper. lam. - bubble 1 1.4 x/chord x/chord Fiore 11. Displacement thickness and shape factors. = -2n incidence laminar separation at x/c=O.25 and the minimum at x/c=O.50 corresponds very µell to the test results of the bubble length in Figure 9. The identical effect is to be seen in the H i , distribution, but the H:, relative minimum is more intensive than the H I , relative maximum. This may be a simple method to predict laminar separation bubble length, but it has to be I I confirmed by future tests. Increased inlet Mach number. Because of the minimum loss level at design inlet conditions there should he no complete Figure 13. Schlieren picture at increased inlet Mach number M,=1.1 1, _ -0.5° incidence turbulent ,,;paration on the suction side (Figure 5). But the question should he answered, if an increased inlet Mach number would prevent the laminar separation from reattachment. Therefore a test was made with an inlet Mach number of M 1 =1.11 and (3 1 =1421.0 °. The surface Mach number distributions are presented in Figure 12 and the Schlieren picture in Figure 13 demonstrates the shock system of the same flow of chord length. The predicted laminar separation point on the suction side is found slightly further downstream. Again the bubble length is not predicted as explained before. '_No pressure side boundary layer tests have been performed and therefore no comparisons of tested and predicted boundary layer separation results are possible. The development of displacement thickness 6, and shape factors 11 1 , and FI„ on suction and pressure side is shown in Figure 14. It can be observed that the shock induced diffusion on the case. Again at this increased Mach number a very good agreement of the predicted and tested Mach number distribution is apparent. The ink injection test on the suction side of the profile showed a laminar separation bubble starting at the beginning of the deceleration at 5W,-,, and reattachment at 65 1%: suction surface does not cause the Ii,, value to fall below the turbulent separation criteria of i1=1.545. Again the axial distance from the start of laminar separation at x/1=0.50 and the described minimum point at x/1=0.65 correspond very 7 Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms 0 U, N face Mach number distributions and overall flow turning. But the boundary layer analysis clarified the incomplete handling of the shock boundary layer interaction and separation bubble structure which resulted in differences in overall loss performance. A method for predicting laminar separation bubble length has been suggested. Pressure Side Suction Side .020 .020 .015 .015 .010 .010 .005 .005 U -c C N E N u 0 a .000 0 .0 .2 .4 .6 .8 I 1.0 ACKNOWLEDGMENTS .0 .2 .4 .6 .8 This work was partially supported by Arbeitsgemeinschaft I-lochtemperatur-Gasturbine AG Turbo, German Bundesministerium fur Forschung and Technologie and German Bundesministerium der Verteidigung. The authors gratefully acknowledge the permission for publishing the results. i 1.0 6 6T- 0 U O REFERENCES U 0 0 r Barnett, M., Hobbs, D.E. and Edwards, D.E., 1990, "lnviscid-Viscous Interaction Analysis of Compressor Cascade Performance", ASME-Paper 90-GT-15 Calvert, W.J., 1982, "An inviscid-viscous interaction treatment to predict the blade-to-blade performance of axial compressors with leading edge normal shock waves", ASME-Paper 92-GT-135 Calvert, W.J., 1983, "Application of an inviscid-viscous interaction method to transonic compressor cascades", Viscous Ejkcts in Turbomachines, AGARD-CP-351, pp2/1-2/13 Carter, J.E., 1979, "A New Boundary-Layer Inviscid Interaction Technique for Separated Flow", AIAA-Paper 79-1450 Denton, J.D., 1982, "An Improved Time Marching Method for Turbomachinery Flow Calculation", ASME-Paper 82-G1'239 Dunker, R.J. and Hungenberg, H.G., 1980, "Transonic Axial Compressor Using Laser Anemometry and Unsteady Pressure Measurements", A/AA Journal, Vol.18, No.8 , August 1980 Dunker, R.J. 1990, "Test-Case E/CO-4 Single Compressor Stage", Test Cases For Computation Of Internal Flows in Aero Engine Components, AGARD-AR-275, pp.245-285 Janssens, P. and Hirsch, C., 1983, "A Viscid Inviscid Interaction Procedure for Two Dimensional Cascades", Viscous Effects in Turhomac•hines, AGARD-CP-351, pp.3/I-3/17 Schreiber, H.A. and Starken, H., 1984, "Experimental Cascade Analysis of a Transonic Compressor Rotor Blade Section", ASME Journal cif Engineering for Gas Turbines and Power, Vol.106, April 1984, pp.288-294 Schreiber, H.A. and Starken, H., 1990, "Test-Case E/CA-4 Low Supersonic Compressor Cascade MCA", Test Cases For Computation Of internal Flows in Aero Engine Components, AGARD-AR-275, pp.81-94 Steinert, W., Fuchs, R. and Starken, H., 1991, "Inlet Flow Angle Determination of Transonic Compressor Cascades•", ASME Journal of Turboniachinery, Vol.114, No.3 Thiede, P., Dargel, G. and Elsholz, E., 1982, "Viscid-Inviscid Interaction Analysis on Airfoils with an Inverse Boundary Layer Approach", Recent Contributions to Fluid Mechanics, W.Haase, ed., Verlag Springer, Berlin Walz, A., 1969, Boundary Layers of Flow and Temperature, MIT Press, Cambridge MA. In .0 .2 .4 .6 .8 1.0 .0 .4 .6 .8 1.0 1.9 i! I 0 0 .2 1.8 1.7 1' e a o 1. U, 1. 1.4 1.6 exper. lam. 1.5 bubble .0 .2 .4 .6 x/chord .8 1.0 1.4 . 6 8 1. x/chord Figure 14. Displacement thickness and shape factors, _ -0.5° incidence well to the test results of the bubble length in Figure 12. This result confirms the method of predicting laminar separation bubble length by measuring the axial distance beween "laminar kink" and relative minimum of the calculated H 32 distribution. But additional tests are needed to confirm this method. CONCLUSIONS It has been demonstrated, that a fast quasi-3-d inviscid-viscous interaction code (IVI) is an extremly helpful and economic tool in a design process, developing cascade blades for a definite blade pressure distribution and the corresponding flow turning. Applying such a tool it was possible to redesign the midsection cascade L030-4 of it DLR transonic rotor for higher loading. The pitch/chord ratio was increased keeping the same loss level and incidence range at design condition with lower losses at subdesign inlet Mach numbers. Such a design, realized in a compressor stage, would help to reduce the number of blades and th,j,lore costs and weight. The comparison of prediction and test results at design and off design conditions showed good agreement for blade sur8 Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms Weber, A., Faders, M., Starken, H. and Jawtusch. V., 1987, "Theoretical and Experimental Analysis of a Compressor Cascade at Supercritical Flow Conditions", ASME-Paper 87- Coordinates Of The Tested 13 lade GT-256 APPLNDIX Transition Criteria AReo,.rr = Re6,.u.0 - Rea,,m log ^ 0 Re 6 , ,11 = 4.556 - 76.87(1.670-1{ 3 ,) x.54. log 1 ARe^, rru log 10 ARe^ .1ru = 1.6435 - 24.2(1.515 -II) for 1.515_<FI-,<- 1.56 )27 5 = 3.312 - 967.5(1.515 - H) 2715 for 1.56 5 ft 21 .625 Cascade Geometry Blade chord c = 70mm pitch/chord ratio s/c = 0.70 Stagger angle (3, = 138.0` Downloaded From: http://asmedl.org/ on 03/09/2015 Terms of Use: http://asme.org/terms Pressure Side Suction Side XP/C' YP/C XS/C YS/C 0.000000 0.001079 0.000000 0.001079 0.003475 -0.003988 0.0021.50 0.003624 0.012482 -0.004814 0.015514 0.005994 0.040001 -0.006858 0.052144 0.01 1841 0.068217 -0.008297 0.088304 0.017280 0.097066 -0.009185 0.124012 0.022326 0.126483 -0.009580 0.159279 0.026988 0.156403 -0.009537 0.194118 0.031279 0.186763 -0.009112 0.228536 0.035204 0.217497 -0.008362 0.262540 0.038768 0.248542 -0.007341 0.296130 0.041973 0.279832 -0.006107 0.329304 0.044816 0.31 1304 -0.004715 0.362052 0.047288 0.394359 0.049378 0.342893 -0.00322 2 0.374534 -0.001683 0.426200 0.051063 0.406164 -0.000154 0.457541 0.052312 0.437718 0.001309 0.488333 0.053085 0.469130 0.002649 0.518511 0.053323 0.547986 0.052951 0.500359 0.003829 0.576659 0.051881 0.531395 0.004842 0.604631 0.050202 0.562236 0.005685 0.632100 0.048086 0.592878 0.006356 0.659201 0.045650 0.623318 0.00685 0.686027 0.042976 0.653553 0.007167 0.712646 0.040120 0.683579 0.007303 0.713394 0.007254 0.739104 0.037125 0.765439 0.034024 0.742993 0.007018 0.772374 0.006592 0.791679 0.030839 0.801534 0.005974 0.817844 0.027589 0.830468 0.005160 0.843952 0.024290 0.859174 0.004147 0.870016 0.020952 0.887648 0.002933 0.896048 0.017587 0.922056 0.014201 0.915887 0.001514 0.948046 0.010799 0.943887 -0.000112 0.971647 -0.001947 0.974026 0.007388 1.000000 0.003972 0.999163 -0.003995

© Copyright 2018