Interface Effects Between a Moving Supersonic Blade Cascade and a Downstream Diffuser Cascade

73-GT-23 $3.00 PER COPY $1.00 TO ASME MEMBERS The Society shall not be responsible for statements or opinions advanced in papers or in 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 or Proceedings. Released for general publication upon presentation. Full credit should be given to ASME, the Professional Division, and the author Is). Copyright 1973 by ASME Interface Effects Between a Moving Supersonic Blade Cascade and a Downstream Diffuser Cascade JEA FABRI Mem. ASME JEA REBOUX FRACIS HIRSIGER Office ational d'etudes, et de Recherches Aerospatiales, ChAtillon, France Theoretical and experimental research conducted on a rotating supersonic blade cascade shows that absolute and relative velocities at rotor outlet are functions of the rotating cascade and the downstream diffuser cascade geometry, independently of the inlet mass flow rate. The radial maldistribution of the flow that results from this property of supersonic blade cascades is analyzed. Contributed by the Gas Turbine Division of The American Society of Mechanical Engineers for presentation at the Gas Turbine Conference and Products Show, Washington, D.C., April 8-12, 1973. Manuscript received at ASME Headquarters December 19, 1972. Copies will be available until February 1, 1974. THE AMERICA SOCIETY OF MECHAICAL EGIEERS, UITED EGIEERIG CETER, 345 EAST 47th STREET, EW YORK,.Y. 10017

Interlace Effects Between a Moving Supersonic Blade Cascade and a Downstream Diffuser Cascade JEA FABRI JEA REBOUX FRACIS HIRSIGER ITRODUCTIO Experimental investigations on supersonic axial flow compressors have shown in many cases a radial maldistribution of the flow at the rotor outlet (1-4). 1 The deficiency in'axial velocity near the outer casing is characteristic of a flow separation at blade tip, the greater part. of the flow being concentrated near the hub. Since most of the supersonic compressors described in the literature are of the shock-inthe-rotor type, such a flow separation may be due to high pressure gradients that the outer casing boundary layer cannot support. However, this does not seem to be the only explanation of the dead flow bubble near the outer casing, and the aim of the present paper is to give a simple theoretical model showing that the radial maldistribution of the flow can also be explained by the result of matching the flow coming out of the rotor, and controlled by the rotor geometry, with the inlet conditions of the downstream stator, controlled by the stator geometry. If such an assumption is verified by the experiments, it would be possible to find some way to correct this flow maldistribution and to improve the performance of supersonic compressors. VELOCITY DISTRIBUTIO DOWSTREAM OF A SUBSOIC ROTOR In order to emphasize the difference in behavior of a subsonic and a supersonic rotor, the well-known operation of a subsonic rotor will be recalled. In axes moving with the rotor, the direction of the velocity at each radius depends essentially on the blade channel geometry and is only slightly a function of Mach number and incidence angle. For a given speed of rotation and upstream mass flow rate, the conditions downstream of the Underlined numbers in parentheses designate References at end of paper. rotor are quite easily obtained by means of a step-by-step method. The local efficiency, i.e., the efficiency of each individual blade section, is function of blade geometry, Mach number, angle of attack, and diffusion factor As long as the mass flow exceeds the stall limit, a mathematical solution of the fluid dynamic equations can be obtained that corresponds to the wholly filled downstream channel. It is characteristic, for subsonic rotor operation, that changing the setting of the downstream stator blades does not change the rotor outlet velocity. distribution. It will be shown that, due to the rotor-stator interface matching conditions, this is not true anymore for supersonic rotors (2). VELOCITY DISTRIBUTIO DOWSTREAM OF A ROTOR OF SHOCK-I-ROTOR TYPE For a shock-in-rotor type supersonic compressor, outlet velocity is subsonic in reference axes moving with the rotor. The relative outlet angle is fixed by blade channel geometry, as in the subsonic case. The main difference between the operation of subsonic and supersonic compressors comes from the fact that absolute velocity at the rotor-stator interface is then either transonic or supersonic, due to the high speed of rotation. Since transonic. and supersonic blade cascade operation is controlled by unique incidence condition (8,9), there necessarily exists a matching condition between rotor outlet and stator inlet in supersonic compressors. The theoretical and experimental investigation of transonic and supersonic blade cascade operation shows that the inlet flow angle depends, in a wide range of Mach number, on blade geometry only. Thus in the rotor-stator interface relative velocity, W2, and absolute velocity, C 2, at radius, 1

Relative velocity w2 Absolute velocity 2 Rotor velocity r, are given by equation (1) (Fig. 1): r ch 2 2,,0,77 (.1;2, a first-order approximation can be obtained. By substituting the value of C 2 taken from equation (2) and the value of T 2 from equation (3) into equation (4), a differential equation is obtained for p 2 where only the radial variation of angles fl 2 and a 2 appears Co 14 /27;14 c! z _ 7:e df- re/ cog, (/1,54.1/?)./. e, To obtain the pressure distribution from equation (5), the value of p 2 must be known at some given radius. Let us assume that efficiency, Ili, is known at the blade root section, r = ri, then Fig. 1 Velocity triangles at rotor-stator interface e-112-12- (4) (5) h/2 ei5da -(-0 K2, GO /2 - tfiz t/z (1) Tai e.o.c.,aice,,,) -' ( 7-2 ) / (6) 162 and a 2 are the corresponding flow angles measured from the axial direction, fi' 2, defined by rotor blade channel geometry and a 2, by stator blade cascade unique incidence. The relative and absolute velocities at radius, r, can then be determined as functions of rotor angular speed, w, and of angles, /3 2 and a 2, independently from the rotor inlet mass flow Co ;2.- Asir 7:?2 Lct/fri (2) and (/'z) (7) e.02--p. 7)7, 2,4 A. r- (4, or,,,,e4,,,,/7)!4) 74,-/,_.P4.,,, (Xario.ft,A4 A 2 / 1 From pressure distribution (7) and velocity distribution (2), the radial distribution of efficiency can also be derived /)fril al -4-6e) 612-66rIA Such a result seems paradoxical, but it is very naturally derived from the foregoing assumptions based on well-known theoretical and experimental results. Furthermore, total temperature, T ee, and static temperature, T2, at rotor outlet will also be functions of radius and angles, f2 and a 2, only wq2 T.,/ -1- q,(47 C4o,e2 t'am A) (3) 6014 1 in of 1,4 2 7:2-7;1 + (4" tla-a *24 (1C" a:2 i1 421/411/ 4]E 9 To 4 (8) This means that in a supersonic compressor of the shock-in-rotor type where relative outlet velocity is subsonic and absolute velocity is either transonic or supersonic, the flow configuration in the blade channels and the position of the shock waves are such as to give, at the rotor outlet section, the efficiency distribution required by the radial equilibrium condition. If the efficiency is known at the blade root radius, it can be calculated at The computation of the pressure distribution all the other radii. at the rotor outlet still requires a complete three- In a similar way, the fraction of the annulus dimensional analysis of the flow field. However, area filled by the flow (10) can be determined: by means of the simplified radial equilibrium It corresponds to the area necessary to satisfy equation the mass flow conservation equation 2

Pressure taps "41 Lim maw..17 E Rotor E in II stator (a) Test section of supersonic moving cascade (b) General view of test facility Fig. 2 Supersonic moving cascade test facility e)y-, -2rr y 6t.o where ml is the inlet mass flow rate and r *, the limiting radius of the outer casing separation bubble. Usually r * is smaller than outer radius, r o' but if the calculations show that when in equation (9) the upper limit equals r and the value of inlet mass flow rate, 1111), is sill not attained, a mass flow blockage due to the stator appears that may give flow instabilities. All these calculations were based on the experimental results showing that the non-flow bubble appears near the outer casing wall. This may correspond to boundary-layer separation due to high adverse pressure gradients. Since the relative flow is supersonic, an oblique shock wave always preceeds this separated flow, and the streamline deflection given by this shock wave is related to upstream Mach number and pressure ratio through the shock wave. The unknown efficiency used in equation (6) must, therefore, be chosen in such a way as to give the same radial extent of the separation bubble by using the mass flow conservation equation (9) or the shock wave deflection equation. EXPERIMETAL IVESTIGATIO O ITERFACE EFFECTS BETWEE A MOVIG SUPERSOIC BLADE CASCADE AD A DOWSTREAM DIFFUSER CASCADE The experimental study of the rotor-stator interface was performed on a rotating supersonic cascade (Fig. 2). This test facility uses a low speed of sound, Freon-114, gas, and requires only (9) a small power (about 30 kw). The main characteristics of the rotating cascade are given in Table 1. The experiments described here were performed at low supersonic speeds in order to be sure to obtain supersonic peripheral velocity and subsonic relative exit velocity. Two different stator blade cascades were used: 1 Stator I was thin bladed in a cylindrical channel; 2 Stator II was thick bladed in a convergingdiverging channel. Fig. 3 gives the main geometrical characteristics of the rotor blades and of the two stator cascades investigated. The moving cascade will be characterized by its peripheral Mach number, M *, and the Mach number, m * -1, of the in-coming flow. 2 The variation of this parameter is plotted in Fig. 4. Results of traverses between rotor and stator Table 1 Characteristics of the Rotating Supersonic Cacade Outer diameter 465 mm Inner diameter 445 mm Blade shape double circular Blade chord 6o mm umber of blades 26 Speed of rotation 5500 to 8000 rpm Peripheral Mach number _1 to 1.43 2 The Mach numbers used in the present analysis are velocities divided by the critical velocity of sound corresponding to the absolute inlet conditions. 3

1...'..---- / 0 A ---- o -- -- a --E-- S3 30. 0, Rotor Stotorl Stator II Fig. 3 Geometry of rotor and stator 1,5 Statorl A 60 45 2 e A Stator II design inlet Stator-II o Fig. 4 Inlet Mach number function of rotor Mach number 50 40 Stator I design inlet 30 20 10 0 HUB TIP Stator 7n* II I 1,80 l o 1 o 1,17 o 1,43 Fig. 5 Absolute flow angle at rotor stator interface o 1,17 are plotted in Figs. 5 and 6. Absolute angle a 1,43 (Fig. 5) depends on the stator geometry and is Fig. 6 Relative flow angle at rotor outlet seemingly independent from the speed of rotation for a given stator. It does not depend either from the axial velocity downstream of the rotor. The outlet angle, 162, in relative reference frames has not the constant value one would expect 4 Stator 111 I 1,80 A it should have. Such discrepancy is usual in most compressor experimentation, and the phenomenon is even emphasized by the blade boundary separations

due to boundary-layer shock wave interactions inside the blade channels (Fig. 6). The limiting radius, r *, corresponding to the area occupied by the flow downstream of the rotor, is shown in Fig. 6; it corresponds to the limit above which axial velocity is rapidly decreasing, indicating thus the existence of a separated flow region. In order to show the physical meaning of this phenomenon, Fig. 7 shows the approximate shape of the streamlines in a meridian plane of the test cascade, indicating namely the radial and longitudinal extent of the dead flow bubble. COCLUSIO The theoretical and experimental investigation of the rotor-stator interface in a rotating supersonic cascade followed by a diffuser cascade shows the basic difference between the velocity distributions at the outlet of a supersonic rotor and at the outlet of a conventional rotor. The classical assumption, that the fluid fills completely the whole area downstream of the rotor, and that the mass flow conservation condition constitutes the main equation for the determination of velocity distribution downstream of the rotor, is not valid for supersonic compressors. Analysis of the interface matching conditions between relative flow coming out of the rotor and absolute flow entering the stator shows that the radial distributions of velocity and temperature are functions of radius, speed of rotation, rotor geometry, and also stator geometry. The radial distributions of pressure and efficiency, and the area filled by the flow downstream of the rotor, depend also on the in-coming mass flow and on the shock wave boundary-layer interaction at the outer casing wall. REFERECES 1 Serovy, G. K., "Recent Progress in Aerodynamic Design of Axial Flow Compressors in the United States, Journal of Engineering for Power, Transactions of ASME, July 1966. 2 Otsuka, S., et al., "An Experiment on A Rotor 76.1,00 Fig. 7 Streamlines and dead flow bubble in a supersonic moving cascade Supersonic Axial Flow Compressor," Tokyo Joint International Gas Turbine Conference and Product Show, JSME, Vol. 4, Oct. 1971. 3 Chauvin, J., "Research on the Concept of Blunt Trailing Edge Blades," Von Karman Institute for Fluid Mechanics, S.R., Vol. 1, 1965. 4 Charron, F., Janssens, G., and Paulon, J., "Banc d'essais de Compresseur Supersonique OERA," Aeronautique et Astronautique, Paris (to be published). 5 Le Bot, Y., Paulon, J., and Belaygue, P., "Theoretical and Experimental Determination of Pressure Losses in A Single Stage Axial Flow Compressor," Journal of Engineering for Power, Vol. 92, A, o. 4, Oct. 1970. 6 Tipton, D. L., Improved Techniques for Compressor Loss Calculation, in AGARD, "Advanced Components for Turbojet Engines," CP34, 1968. 7 Hirsinger, F., "Détermination de la Position des Ondes de Choc dans une Grille dlaubes Supersonique par la Condition dlinterface," La Recherche Aerospatiale (to be published). 8 - Chauvin, J., Breugelmans, F., and Janigro, A., "Supersonic Compressors," Von Karman Institute for Fluid Mechanics, CR 7, 1967. 9 Fabri, J., Mass Flow Limitation in Supersonic Compressors, in AGARD "Advanced Compressors," LS 39-70, 1970. 10 Paulon J., and Reboux, J., "Data Validity Criteria for Supersonic Axial Compressors," ASME Paper o. 72-GT-100. 5