Experimental Analysis Data on the Transonic Flow Past a Plane Turbine Cascade

Transcription

1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 90-GT E. 47 St., New York, N.Y 1T7 The Society shall not be responsible for statements or opinions advascedin papers or in disnussion at meeti^,ys 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 horn ASME for fb teen n1nnths after the meeting. Printed in USA. Copyright 1990 by ASME Experimental Analysis Data on the Transonic Flow Past a Plane Turbine Cascade M. S TASTNY 9KODA Concern Enterprise Power Machinery Plant Plzen, Czechoslovakia P. SAFARIK* *Institute of Thermomechanics Czechoslovak Academy of Sciences Praha, Czechoslovakia ABSTRACT The paper presents results from aerodynamic tests on a transonic rotor turbine profile cascade, including interferograms of the flow field and aerodynamic data measured downstream from the cascade. The dimensions and aerodynamic data on the cascade are given in detail. Analysis following the experimental data collection was aimed at investigating the sensitivity of transonic flow in the vicinity of the throat and related conditions leading to the compression effect. Further, the development of the flow structure and the cascade parameters over a wide range of exit Mach numbers, as well as incidence angles are shown. The experimental data are compared with results of calculations based on mathematical models. NOMENCLATURE b 1[mm] _ 2 chord e Im kg s ] stagnation internal energy per unit volume H 12 boundary layer form parameter i 1.] incidence angle, i = M Mach number o -1[mm] _ 2 width of the cascade throat p [m kg s pressure Re Reynold number s [mm] circumference of the flow profile t [mri pitch u,v [m s ] velocity components along the x and y axes x,y [mm] coordinates of the profile a [o] or along the profile flow angle C. W2 ae [o] [m] stagger angle impulse thickness of the boundary layer Poisson constant (for air at= 1.4) [%] energy loss coefficient = 100(1 az^12;s ).Z relative velocity (the ratio of the given and critical velocities [kg m 3] density S2 AVDR - axial velocity density ratio SUBSCRIPTS 1 inlet 2 exit is isentropic flow max maximum t derivative in time x,y derivative in the coordinates x, y INTRODUCTION The results of aerodynamic research tests on profile cascades at transonic flow velocities are invaluable for improvements on -new machine designs and verification on the routine test methods. Higher efficiency and operational reliability of new turbines and compressors are attainable largely due to such experimental research programs. Of the many problems related to the aerodynamic research on a transonic profile cascade, the following areas deserve special attention: the design and verification of new experimental methods, development of numerical model methods and expanding the theoretical understanding of the flow mechanisms. The research on turbine profile cascades in the High-speed laboratory of the Institute of Thermomechanics has been carried on for over 25 years in close cooperation with the ^KODA Concern Enterprise in Plzen. Transonic profile cascades are tested using dry air in *Presented at the Gas Turbine and Aeroengine Congress and Exposition June 11-14, 1990 Brussels, Belgium

2 a wind tunnel of the atmospheric type, with a vacuum tank operated discontinuosly, using highly sophisticated measuring technique including a traversing probe behind the profile cascades and optical (interferometric and schlieren) devices. This paper presents results from an extensive experimental research program on a rotor blade from the transonic turbine stage. The profile cascade denoted KOOA-ETALON SE1050, chosen as suitable for investigation and verification of the test methods, was derived from a section drawn through the rotor blades of a ^KOOA turbine. Experiments were carried out for Mach numbers M ranging from 0.5 to 1.5 and incidences angt^^ s i ranging from to Experimental results are compared with characteristics derived by computational methods mentioned briefly in one of the following paragraphs. were used to investigate this ohenompnon. The cascade was designed for the inlet flow angle 8 of 70.7, exit Mach number ^.,, = 1.208, and for wet stream. Fluctuations itt s loading of the last stage in real operating conditions of the turbine result in variations of the flow parameters at the cascade inlet. The changes in the incidence angle i due to different Mach number M can be calculated on condition that the outl^t angle from the nozzle blade cascade varies only by the supersonic deviation [L 2]. The resulting relationship shown in Fig.2 is compared with a choked characteristic measured in a wind tunnel. For less than the nominal load the incidence angles i are negative, for aerodynamic overload, positive.the wind tunnel used for experiments excluded the possibility of reaching the desired inlet Mach numbers M 1 in the overload model conditions. PROFILE TURBINE CASCADE SE1050 The profile cascade SE1050 was designed for the last stage of a KODA steam turbine 40 with the blade length 1085 mm and a nominal speed of 3000 rpm. The last stage is operated i[ 0 1 at transonic flow velocities [L 1]. 20 The SE1050 profile is a section view of 0 a rotor blade at the distance 320 mm from the root. The rear part of the suction side is straight. The trailing edge at the pressure side is designed to suppress the inner shock wave. The cascade arrangement is shown in Fig.l, where the profile coordinates are given in the 0-20 o experiments - 40 performance conditions 1L X W Mlmax 0.5 M1 Fig.2 Inlet parameters i,m 1 of the cascade SE1050 profile casca4& EXPERIMENTAL RESULTS Fig.l Schematic presentation of the SE1050 profile cascade One of the rear -on -s why the SE1050 profile had been chosen for detailed investigation was that a local decrease in the flow velocity had been detected near the beginning of the straight part of the suction side of the profile; both aerodynamic annlvsis and computational methods The profile cascade SE1050 was tested in the aerodynamic wind tunnel of blowdown type. The cascade composed from 8 blades of 160 mm length was placed in test section without tail boards. The ratio of upstream length to tunnel width is 25. Optical and aerodynamic measuring methods were used (the schlieren and interferometric methods, the latter with setting at the infinite width of the fringe, and traversing probe method). The periodicity was checked in middle three channels only (see Fig.4,6,7).

3 . The experimental conditions are listed below: Incidence angle i E. ] Fig Inlet Mach number M Outlet isentropic Mach number M2is Reynolds number relating to the profile chord and outlet isentropic Mach number, Reis Energy loss coefficient, c 1%J Outlet angle [ ] Table 1 The regions of stagnation pressure and temperature during all measurements were Pa and K. The primary characteristic derived from experiments was the velocity function M 1 = M 1 (M, i) shown in Fig.3. This characteristic yih. as, in turn, the maximum inlet velocity function M = M (i), see Fig.2, providing information Bn ndi co ions under which aerodynamic choking of the cascade occurs. 1.0 M, 0.5 if ]= x^ '._ i,-f 1 +ii Fig.4 The interferometric picture of flow in the SE1050 cascade (i =0, M2is =1.189,--- sonic line) A c OJ 0.1 M2;f c v n c_-v a o d o : 0 as M:^s C suction side x/b pressure side Fig.3 The relationship between the inlet parameters i, M and exit Mach number M measured on these1050 cascade in 2is a wind tunnel The interferogram in Fig.4 shows the flow field in the cascade for i = 0 0, i.e. (approximately) the nominal operating mode. A set of interferograms yielded the relative velocity distribution along the profile.2.= 2 (x/b,m2is' 13). The relative velocity distribution is shown for the nominal inlet flow angle in Fig. 5. Values of A were taken from interferograms and checked by two static pressure orifices. Fig.5 Distribution of the relative velocity along the profile SE1050 for various Mach numbers M 2is (i =,0 0 ) The interferograms in Figs.6 and 7 show the flow fields in the cascade for extreme values of the incidence angle. Figure 6 (i = -67 ) relates to a very small load on the machine, Fig.7 to overload operating conditions with a positive incidence angle (1 = 30 ). The traversing probe method makes it possible to derive, using integral balancing of the mass, momentum and energy of the flow, the referential conditions at the outlet of the cascade and determine the basic flow characteristics: the outlet flow angle and the energy loss coefficient, as functions of the isentropic Mach 3

4 number and incidence angle 13 2 = 02 (M 2is, i). seefig.8, and = ^' (M2is, i), see Fig.9 I 3 {ti Fig.8 The relationships between the exit flow angle Gi l and Mach number M 2the incidence angle i, for the SE1050 cascade Fig.6 The interferometric picture of flow in the 5E1050 cascade (i = -67 0, M2is = 0.905) 25 (%J II MVA is Mt , Fig.7 The interferometric picture o; flow in the SE1050 cascade (i = 30 2is = ) M 4 n if'] 50 Fig.9 The relationship between the energy loss coefficient and the incidence angle i and Mach number M2is, for the SE1050 cascade

5 DISCUSSION AND ANALYSIS OF THE EXPERIMENTAL RESULTS The relationship between the inlet Mach number M 1 and outlet isentropic Mach number M shown in Fig.3 has a maximum relating to tf aerodynamic choking mode. Certain irregularities in shape of these characteristics for extreme values of the incidence angle (i >_ 20 0 ) can be attributed to the complexity of the choking mechanism in combination with the extensive flow separation on the hand, and the marginal 3D flow effects in the measurement zone. The maximum inlet Mach numbers measured at the nominal incidence angle are slightly lower than that resulting from 1D analysis (M lmax = 0.405). M1max 0 [ 2 + (f-1)mimax 12(21-1) t $III L ac+1 1 (1) The outlet angle 132 determined by the traversing probe method is shown in Fig.8. The well known tendency for increasing the exit flow angles at supersonic deviation can also be expressed analytically using the following equation resulting from the equation of continuity for isentropic flow: _ o Sin (32k t (2) (ae-1) 11:15 ] 2W ^2 M2i5 z+1 ^2k (3) The experimental results indicate that above tendency is less pronounced in the region of extreme positive incidence angles (i = 20 ). It has also been found that the extreme positive incidence angles at subsonic velocities do not result in opposite deviation of outlet flow angles as with other cascades [L 3]. A possible explanation to this may be the small value of the pitch-chord ratio of the 5E1050 cascade. The energy loss vs. incidence angle characteristic in Fig.9 came out as expexted. However, or extreme incidence angles (i<-50 or i > 20 ) the loss coefficient tends to decrease with growing Mach numbers. This can be attributed to the substantial and approximately constant energy loss due to flow separation on the leading edge of ths profile. The critical Mach number for i = 0 is M2iscrit (see Fig.5). The energy loss related to the nominal operating mode ( f = 4.6%) is acceptable so that the cascade SE1O50 is considered to be well suited for the given transonic operation. The inlet flow velocities correspond with the desired operating conditions very well, see Fig.2. The same is true of the exit flow angle, where the measured value is very close to the estimate used in calculations. From the measured characteristics it follows that the minimum energy loss (f n = 3.3%) can be expected at subsonic veloci^les and the incidence angle of -20. It should be noted, however, that the pitch-chord ratio (t/b = 0.551) of the SE1050 cascade, resulting from the overall turbine stage design, was much smaller than what is taken to be general optimum value. A noticable increase in energy loss occurs in the regions of extreme incidence angles (i<-40 and i>10 ). The analysis of flow in the cascade zone itself is based on optically measured data. The channels between the profiles are regions of flow acceleration, as shownin the interferogram in Fig.4. The acceleration on the pressure side is monotonic. Near the throat the velocity of sound is reached; the sonic line can be identified at the coordinate x/b = 0.40 on the suction side. Further expansion into supersonic velocities leads to decrease and subsequent increase of the flow velocity on the suction side. Intensive supersonic expansion is terminated by an inner exit shock wave, reflected from the neighbouring profile. After the interaction of the shock wave and boundary layer the supersonic expansion is showed down, to become again more intensive before the trailing edge. The phenomenon of local supersonic compression accompanying the transonic expansion was analysed. It can be shown that the compression effect is directly related to the curvature of the suction side at the coordinate x/b = 0.5. The explanation is readily available in the schematic diagram in Fig.10. Expansion waves of the first form reflect from the sonic line as compression waves of the second form and, on reaching the profile surface, slow down the expansion. In the region between the second neutral characteristic the compression waves are not eliminated and reflect from the surface as compression waves, which all results in decreasing the flow velocity. sonic line A / / 2n neutral characteristic st neutral characteristic Fig.10 A schematic picture of the local supersonic compression

6 This phenomenon can also be solved numerically using existing methods for modelling of the transonic flow. Sensitivity and accuracy of numerical methods should be verified by comparison with experimental results. For example methods based on Euler equations lead to solutions demonstrating the existence of supersonic compression in connection with transonic expansion. As follows from analysis of entropy production in boundary layer, continuous increase in velocity along the profile surface is advantageous. Extreme values of the incidence angles cause flow separation on the leading edge of the blade. Separation ocrd urs ou^side the incidence angle range of -30 to 10. Interferogram in Fig.6 shows a complex transonic flow field for a small-load mode of operation. The origi- / nally subsonic flow on the inlet side of the /1.2 cascade is accelerated in the flow channel and reaches supersonic velocities. The potential flow region is further bounded by a local separated flow on the pressure side of the profile, 77 / / which can be attributed to the extreme value of / the incidence angle (-67 W//. 1,3 ), and by the boundary 0.8 layer on the suction side of the profile. Apart 5 - from that, another local transonic region is noticeable on the suction side near the trailing edge, and a relatively wide wake i(0] 50 Flow separation on the suction side of the profile due to the cascade overload is demonstrated in Fig.7. The separation is quite extensive (but not reaching beyond the cascade Fig.11 The relationships between AVDR and the zone) and causes substantial increase in energy incidence angle i and Mach number M2is loss. Disturbances from the wake may travel for the SE1050 cascade along the separated flow region and influence the flow field in the channel between the profiles. COMPARING EXPERIMENTAL RESULTS WITH MODEL The authors of this paper support the concept published in fl 4] by Kiock and collabora- CALCULATIONS tors that axial velocity density ratio (AVDR) should be known to give credibility to experimental results. AVDR is a complex parameter providing information on the effect of the data processing methods and measuring techniques. AVDR can be determined by traverse measurements using the following relationship e+1 H^1+ ^21 M2 sin M ( + ee-1 1 \ 2(K-1) sin Pi Poi 1 \ 2 2) (4) Extensive measurements made it possible to establish the AVOR values for various incidence angles and exit isentropic Mach numbers. The results are presented in Fig.11. It is obvious that AVDRs measured differ significantly from unity, characteristic of a plane flow. S2 = i 0.9 Ma 1. \ 1 / The results from the wind tunnel measurements on the SE1050 profile cascade have been used to verify 2D model calculations (S2 = 1) of the flow field in a plane turbine cascade. For example, for the flow modes with a local supersonic region, weak shock waves and the exit Mach numbers up to M = 0.906, the experimental results were compared with numerical solutions of 2D velocity field (9.= 1), derived by the method of full potential equations by Fort and Kozel [L 5). The calculated velocity field is almost the same as that derived by interferometric measurements excepting minor differences in the areas of the leading edge and of high flow velocities. A 2D-model (St = 1) based on Euler equations (5) was used for deriving the velocity distribution in the transonic region near the nominal operating mode: where W x y = t + x t w-col llu,4vell F -cot 1I Qv,Vu z+p,4uv, (e+p)ull G = cot II 4u, 4uv, Qv2+ p (e + p) v Il p =(ae-1)ie-4 2 (u2+v2)] (5)

7 Hoi:ejsi and Rais in [L 6]solved equations (5) using the time-marching and finite volume cell-centered methods. Shared H-type grid with 1024 cells and difference scheme of Runge-Kutta type with a non-linear artifitial viscosity term were used for the numerical solution by PC. The calculated distribution of the a=const curves for the SE1050 profile cascade is shown in Fig.12 6 for ths following parameters: 13 1 = 70.7 (i = 0 ), M 2is = ( a 2is = = 1.150) and 2e= 1.4. The result of calculation is in good agreement with the interferogram in Fig.4, including the shape of the sonic line and the supersonic compression area in the cascade throat (which is slightly smaller). Excepting the reflected inner shock wave, the calculation method gives realistic estimates on the Xi Q4 o.< calculation (L calculation ILGI experiment o.c -1 suction aide pressure side x/b Fig.12 The calculated distribution of the relative velocity isolines in the SE1050 cascade (i=0, M2is= 1.189) onic line inner shock wave outer shock wave a= 1.15 Fig.13 Distribution of the relative vel8city along the cascade profile (i = 0 M 2is = 1.189) To study the effect of viscosity on the flow behaviour in the cascade placed in the wind tunnel, the profile boundary layers was calculated using a threecomponent model and integral equations for the boundary layers [L 8] [L 9], [L 10]. The exper6mental data on the SE 1050 cascade for i = 0, M = and Re = were taken as p3'rameters needed for calculation. The results are presented in Fig.14, where the momentum thickness of the boundary layer d and the form parameter H are shown. The laminar boundary layer on t^i3 suction side of the profile loses stability in the region of supersonic compression, which leads to natural transition to turbulence. The loss of stability occurs on the pressure side as well, but not to give transition to turbulence ib.10 2 positions of the exit shock waves. The exit inner shock wave angle is practically the same as -^ H 1.2 that derived by experiment. Certain deficiency of the numerical I I a method is obvious near the leading edge of profile, especially at the pressure side. A compa- 0.1 C3 rison of experimentally and analytically derived a.-distributions along the profile is pre- II _CE sented in Fig.13. Significant differences are m I^ CO noticeable in the supersonic region ( a > 1) at a 2 ^ b the suction side and near the leading edge on the pressure side. Fig.13 also includes results of Kozel and Nguyen van Nhac, Vavfincova IL 7] based on similar computational techniques with exceptions of Mac Cormack difference scheme and FAS-multigrid method applications. With regard to the fact that, on the one transition U.3 XIS t suction side pressure side loss of stability hand, the viscosity of the fluid was taken to Fig.14 Calculated distribution of the boundary be negligible in numerical models and, on the layer parameters 62, H 12 along the other hand, the flow in the comparison experi- profile (derived from the velocity ment was not a purely plane one (SZ= 0.9), good distribution measured u on the SE1050 agreement was found between the experimental cascade for i = 0 and M 2is = 1.189) and computational results. 1.2

8 CONCLUSION The extensive experimental research proggram on the 5E1050 profile cascade yielded information on the structure and parameters of the flow field. Special attention was given to extreme 0 operating modes where the flow separation on the leading edge of the profiles astny M.: Calculation of aerodynamic properties of turbine cascades of profiles at results in significant increase of energy loss. subsonic velocities. Strojnicky casopis No.3, The effect of transonic compression and the (1985), p conditions under which it may occur were studied. The basic aerodynamic characteristics APPENDIX of the profile cascade were used to specify recommended operational parameters and pref.err Appendix: Coordinates of the profile SE1050 ed operating modes for the cascade. The numerical solutions presented in the paper were in good agreement with the experimental data. Detailed profile coordinates ( altogether 1000 points) are available for anyone who might be interested in cross- -checking a calculation method. ACKNOWLEDGEMENT The authors wish to express their sincere gratitude for the support the received from the managements of both the Institute of Thermomechanics of the Czechoslovak Academy of Sciences and the Power Machinery plant of the SKODA Concern Enterprise, and the assistance from many collaborators in these institutions. REFERENCES 1 Sfastny M., Afatik P.: Profile Cascades of the Last Steam Turbine Stage. Proc. from the IV International Techno-Scientific Conf. "Steam Turbines of Large Output - Design and Operation", Elblag - Gdansk, Poland, (1988), p Safarik P., Sfastny M.: Off-design performance of the last stage rotor blading of steam turhine of large output. Strojnicky casopis No.5 (1987), p (in Czech). 3 Dvorak R., Safarfk P.: An Experimental Study of High Speed Flow in Turbine Cascades at Extreme Incidences. Proc. from the Conf. "Steam turbines of large output", Karlovy Vary, (1984). 4 Kiock R., Lehthaus F., Baines N.C., Sieverding C.H. The transonic flow through a plane turbine cascade as measured in four European wind tunnels. ASME paper No. 85-IGT- -44 (1985). 5 Fort J., Kozel K.: Numeric solution of inviscid two-dimensional transonic flow through a cascade. ASME paper, No.86-GT-19, (1986). 6 Horejsi I., Rais M.: On two methods of solution of fluid flow in cascades. Proc. from the conference "Large steam turbines", Karlovy Vary, Czechoslovakia, (1989). 7 Kozel K., Vavrincova M., Nguyen van Nhac: Numerical solution of the Euler equations for transonic flows in a 3D channel and through a 2D cascade. Int. conference on applied mechanics, Beijing, China, (1989). 8 Curle N.: The Laminar Boundary Layer Equations, Oxford University press (1962). 9 Green J.E., Weeks D.J., Brooman W.F.: Prediction of Turbulent Boundary Layers and Wakes Compressible Flow by a Lag-Entraiment Method. Rep. and Mem. No.3791, (1973) : l,13912? 2.P , A , , , , , , ) n , ,c , ? ,4P ,f , n.( , ,, ,26106P e ' 7, ( , , , ,68905? r , , ',791'54 0.( , , ,