Vaned Diffuser Inlet Flow Conditions for A High Pressure Ratio Centrifugal Compressor

Transcription

1 Copyright 1978 by ASME $3.00 PER COPY $1.50 TO ASME MEMBERS 1.004;.., w, v. vc..av, IO JI nnncv n, no J..v,wuv..a. raa.wu.vn wnei. cv 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 Technical Division, and the author(s). 78-GT-50 Vaned Diffuser Inlet Flow Conditions for A High Pressure Ratio Centrifugal Compressor G. VERDONK von Karman Institute, Chausee de Waterloo, Rhode-St-Genese, Belgium This paper contains a theoretical and experimental investigation of the flow in the vaneless and semi-vaneless space of a transonic radial compressor diffuser, especially for working points corresponding to the mass flow below choking values, in the efficient operating regimes. A type-dependent finite difference calculation has been developed for the inviscid flow. This method has been combined with a shock-boundary layer-interaction theory, which allows a more realistic calculation of the velocity distribution, taking into account the boundary layer variation along the sidewalls. In parallel with this analytical study, several diffuser geometries were also performance tested. A special data-reduction program allowed calculation of the throat blockage and the velocity distribution throughout the diffuser based on static and total pressure measurements. Schlieren pictures were also taken in order to have a better insight in the real flow phenomena at the diffuser entrance. From this experimental data, a detailed comparison with the analytical study was made. This combined theoretical and experimental study made it possible to show the influence of the geometrical parameters of the vaneless and semi-vaneless space on the velocity distribution, and on the throat blockage. Together with the data available in literature for channel diffusers, it allows a better prediction of the overall performances of diffuser systems. Contributed by the Gas Turbine Division of The American Society of Mechanical Engineers for presentation at the Gas Turbine Conference & Products Show, London, England, April 9-13, Manuscript received at ASME Headquarters December 14, Copies will be available until January 1, THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS, UNITED ENGINEERING CENTER, 345 EAST 47th STREET, NEW YORK, N.Y

2 Vaned Diffuser Inlet Flow Conditions for A High Pressure Ratio Centrifugal Compressor G. VERDONK NOMENCLATURE b = diffuser depth B = diffuser throat blockage factor C pi = static pressure coefficient from rotor outlet to diffuser throat C pch = static pressure coefficient from diffuser throat to diffuser outlet C ptot = static pressure coefficient from rotor outlet to diffuser exit D = diameter m = mass flow rate p = pressure R = radius T = temperature U = tangential velocity V = absolute velocity L = length of divergent channel N = number of vanes w = diffuser width a = absolute flow angle (from radial direction) ass = vane setting angle (angle of the tangent at the suction side LE) IL= slip factor (u4 /U4 ) Subscripts 3 rotor inlet (mass flow average) 4 rotor outlet; diffuser inlet 5 diffuser throat 6 diffuser outlet o total s static t diffuser throat u tangential component INTRODUCTION From detailed pressure measurements throughout channel diffusers, an analytical flow model has been established (1-3). 1 This analyti- 1 Underlined numbers in parentheses desigcal flow model is characterized by (Fig. 1) a "zone of rapid adjustment" in front of the throat, where the isobaric lines change from a direction almost parallel to the flow to a direction perpendicular to it. Further, in the divergent channel, the flow is almost one-dimensional. On the basis of this flow model, the vaned diffuser has been subdivided into two flow regions, which can be investigated separately: the study of the vaneless and semi-vaneless space up to the throat on one side, and the study of the divergent channel on the other side. It has been demonstrated (1-5) that the one-dimensional diffuser data established by Rundstadler (4) gives an accurate representation of the performances of the divergent channel of a compressor diffuser. However, for a correct prediction, the inlet conditions of the channel (blockage and Mach number in the throat) have to be known. These conditions are dependent on the diffusion of the flow in the vaneless and semivaneless space (called "inlet region"). This research program was carried out to make a systematic experimental study of three parameters defining the geometry of the inlet region in order to evaluate their influence on the diffuser and overall compressor characteristics. These parameters are: the diffuser throat dimensions, the diffuser vane setting angle, and the suction side shape of the vane. In addition, a theoretical method has been developed, which enables calculation of the Mach number distribution in the vaneless and semi-vaneless space and of the throat blockage, especially for working points corresponding to the mass flow below choking value. TEST FACILITY AND INSTRUMENTATION A high pressure ratio centrifugal compressor was operated with different vane-island, nate References at end of paper. 7

3 Fig. 1 Constant static pressure contours Fig. 2 Compressor rig instrumentation planes

4 Table 1 Wheel no prerotatlon 20 radial ended blades Diffuser series: D-3 D-5 D N b 5/w 5 (A w5 /w 5 (AR) L / w a SS a PS Finally, an orifice (mass flow-measurement) and a throttle valve in the return section of the loop. Fig. 3 Schlieren optical system channel-type diffusers in a closed test loop with Freon 12 gas. The operation conditions were varied from choke to surge at different speeds (80, 90, and 100 percent of the design speed2 ). The instrumentation is shown in Fig. 2 and consists of: Total pressure and total temperature probes in the settling chamber (plan 0) Static pressure holes, a total pressure probe (movable in radial direction) and also three thermocouples at the inlet of the rotor (plan I) Static pressure holes along the shroud of the rotor from inlet to outlet 48 static pressure holes in the back plate of the diffuser throughout one diffuser channel, plus a total pressure tube in the leading edge of one of the diffuser vanes Static pressure holes and thermocouples in the collector (Plan II) and in the volute (plan III) 2 20,500 rpm for an inlet temperature of 20 C and a mixture of 90 percent Freon and 10 percent air. A Schlieren system was also employed as shown in Fig. 3. It comprises a prism, P 2, directing the light beam to an off-axis spherical mirror (MS), a plane mirror (MP), and a reflecting plate in the diffuser channel. This is made possible since the light beam falls at a very small angle ("0.2 deg) on this plate. The reflected beam is received by a second prism (P 1 ) which directs the light beam to the camera. Table 1 gives the geometry of the rotor and of the different diffuser types, which were tested. The main differences between the diffusers are shown in Figs. 4(a), 4(b), 4(c) and may be summarized as: D-3/D-101: influence of throat geometry, Fig. 4(a) D-5/D-101: influence of the diffuser vane setting angle, Fig. 4(b) D-105/D-101: influence of the suction side of the vane, Fig. 4(c) DATA REDUCTION The data reduction techniques for the various diffuser performance parameters are described in detail as follows. Rotor Exit Total Pressure In order to calculate the Mach number 4

5 Table 2 P 4 Vm G m C2] L l^tdfl y4 ^ TomJ U`J V u4v Vrn6J Cer ]] _ T54 p '54 J ' Table 3 P. )mss- ( PO calc. yc^) Fig. 4(a) Diffuser throat geometries ( P. ) meas. 80 /, 90 /. 100 /. D-5 80/ /1 08 D / / / / / / / /9-4 G 90/ /6-2 0 D /5 008 D / / / / / / / was, therefore, made using the Euler equation in the following manner: Fig. 4(b) Diffuser setting angle changes c 0 TC = U4Vu4 - U3 u3 (1) It was assumed that the process in the diffuser was adiabatic, which means that the total temperature at the diffuser outlet (which was measured) was the same as at the outlet of the rotor. However, the temperature increase between inlet and outlet of the rotor was not only due to the work achieved by the rotor, but also due to the disk friction, which is given by ( 6 ) as: U4 x D2 x C M x 2 (AT o ) D.F. cp x 7r x D4 x b 4 x V n4 (2) where C M is an empirical friction coefficient, which is CM 4.5 x 1O Fig. 4(c) Diffuser suction surface variations distribution in the inlet region of the diffuser and the blockage in the throat, the total pressure at the rotor outlet has to be known. As previously mentioned, the total pressure was measured by means of a tube, located in the leading edge of one of the diffuser vanes. However, the flow was very unsteady in this region, so the question arose whether or not to rely upon the measured value of P. An independent check The calculation procedure for (A T0)D.F, is iterative: initially, assume a density of P 4. Together with the mass flow, calculate V n4 by means of the continuity equation. Knowing Vm4 and with equation (2), calculate ( A To)D.F. From this latter value and (A To)meas.1 deduce ( A To ) work This allows the calculation of µ and Vu4. From V4 compute T s (energy equation). Finally, from the measured static pressure at the rotor outlet (p s4 ) and T s obtain a value of p 4, which has to be compared to the initial one. Table 2 indicates the calculation procedure. 5

6 D A.-e 80-9 LIEE _i 15 1c fi acceptable, since the pressure loss over the shock is negligible for the range of Mach numbers which are present in the inlet region. Overall Uncertainty of the Compressor Diffuser Performance Results Using the average of the differences between the measured and calculated total pressure values of Table 3 as uncertainty estimate for the total pressure at the rotor outlet, and with the following ratios for the other primary measurement uncertainties (5), o p5 p 5 ^ p 6 p6 = = A p05 = p0 5 A5 5 = Fig. 5 Mach number variation D percent rpm From the value of (A To)meas, corrected for disk friction the total pressure can be calculated. Table 3 indicates that the measured and calculated total pressures show a good correspondence. The Diffuser Static Pressure Coefficient The static pressure coefficient is given by: C = (ps) o - (ps)i p (po)i (ps)i It is possible to identify three recovery zones: 1 The C of the divergent channel (from throat to diffuser outlet): CpCH 2 The C of the inlet region (from rotor exit to throat): C pi 3 The C of the diffuser (from rotor exit to diffuser outlet): Cptot The measured total pressure at the diffuser vane leading edge (P 0 ) i was used for C pi and CpCH as well as for Cptot, and it was assumed that the flow was isentropic from the rotor exit to the throat. This approximation may be considered Q m m = A T T0 5 This yields the uncertainty in the derived quantities: a m5 M = A Cp CH = CpCH A B5 B = Diffuser Test Results A general discussion of the results obtained for the D-101 diffuser will be presented first followed by a comparative study between the results obtained for the different diffusers. Mach Number Variation Figs. 5 and 6 give the variation of the Mach number through the inlet region of the D- 101 diffuser, for 80 and 100 percent rpm. In Fig. 5, the flow is almost sonic over the first part of the suction surface. There is a gradual acceleration in front of the throat, 6

7 D-101 _r 100/ %RPM h ^ 100/6 '6._. o100/8 EEl FIG 7 C 15 M k eel 51 x/c Fig. 6 Mach number variation D percent rpm followed by a local deceleration to M = 1, with a subsequent reacceleration to peak supersonic conditions. This indicates that, for this speed line, the diffuser is the choking element. In Fig. 5, it can also clearly be seen that the shock is moving forward with increasing back pressure. For the working points, 80/9 and 80/12, located in the mass flow range of the compressor, the shock has moved well in front of the throat. The Mach number in the throat is subsonic and the flow undergoes a subsonic diffusion in the divergent channel. From the Mach number variation of the 90 percent speedline, the diffuser is also found to be choked at the high flow rates. For 100 percent rpm, on the contrary, the Mach number in the throat is supersonic (point 100/3 and 100/6), which indicates a "started regime." Detailed investigation of the rotor (5) has shown that for this speedline, the rotor is choked. The variation for the operating point 100/ 8, located in the mass flow range of the compressor, shows that the throat Mach number is subsonic. The Mach number in front of the shock is M = 1.30, which is the limit for the shock Fig. 7 Channel static pressure recoveries boundary-layer interaction without separation (^). Static Pressure Coefficient In Fig. 7, the values of C pi, CpCH, and Cptot are drawn as a function of the mass flow. In Fig. 7(a), it is seen that C pi does not change as long as the working points are located on the vertical part of the overall compressor characteristic curve (no change of mass flow). For these working points, the shock system is located in the divergent channel. The flow in front of the throat is not influenced by a change in back pressure. Once the strong shock is in front of the throat, C pi will increase. When the mass flow diminishes, the Mach number in the throat decreases, while the Mach number at the rotor exit remains almost constant, so that the diffusion in the inlet region becomes more important. Consider the variation of C pch, Fig. 7(b). In choking conditions, there is a strong increase in C pch because of the increase in back pressure. As soon as the mass flow decreases, C pch decreases 7

8 NCH F. 8.8 D 'I. RPM Mt Fig. 8 Throat blockage and Mach number versus channel recovery, 80 percent rpm too. Due to the higher diffusion in the inlet region (C pi ), the blockage in front of the throat increases. Rundstadler ( 4 ) shows this factor has a detrimental effect on C pch, so that CpCH decreases. The resulting effect of C p i and CpCH is Cptot In Fig. 7(c), it is observed that for choking conditions, Cptot increases because CpCH increases while Cpi remains constant. For working points located in the mass flow range of the compressor, C pch decreases and C pi increases. The superposed effect is a decrease in Cptot Note that for D-101, a positive sloped characteristic is obtained without going immediately into surge. Blockage Factor CpCH is drawn versus the blockage factor, B, in Fig. 8. The variation of C PCH shows a vertical part where the blockage remains constant while C pch increases. This is due to the fact that, as long as the shock is located in the divergent channel, the diffusion in front of the throat remains unchanged and so does the blockage in the throat. When the shock has moved in front of the throat, the shock boundary layer interaction and the diffusion behind the shock cause a strong increase in blockage (and a decrease in CpCH). Overall Performance The overall compressor characteristic curves of D-101 diffuser are shown in Fig. 9. From one speed line to another, the mass flow increase can be shown to be proportional to the square of the tangential velocity. This rule is valid as long as the diffuser is choked. This is the case for the 80 and 90 percent rpm. The different change in mass flow increase for the 100 percent rpm line is due to the fact that, at that speed, the rotor is choked. This confirms what has been found previously from the Mach number distribution. The variation of the adiabatic efficiency and of the total pressure ratio as a function of the mass flow is analogous with what has been found before for Cptot' For the D -3, D-5, and D-105 diffusers, the same data reduction was performed. From this study, it appears that for all the D-3 overall compressor characteristics, 8

9 100!. RPM Fig. 9 Overall compressor performance D-101 Table 4 02 Fig. 10 Throat blockage and Mach number versus channel recovery, 100 percent rpm 100% RPM M4 a 4 D D Table 5 M4a 4 «SS D-5 (100/2) D-101 (100/3) the diffuser was the choking element (even for 100 percent rpm). For D-5 and D-105, however, the diffuser was the choking element only for 80 and 90 percent rpm. For 100 percent rpm, the rotor was the choking element. In the following section, the results obtained with these diffusers will be compared with the D-101 characteristics. COMPARATIVE STUDIES OF DIFFUSER CHARACTERISTICS The comparative influence of the three dif- fuser types on static pressure recovery and throat blockage is presented as follows: Influence of the Throat Dimensions (D-3/D-101) Table 1 shows that an increase of the throat section changes the geometry of the divergent channel. Further, as for all overall characteristics of D-3, the diffuser was the choking element, a change in throat section also lead to a change in choking mass flow. As a consequence, the rotor outlet conditions changed as indicated in Table 4. Summarizing these findings, when the diffuser is the choking element, a change in throat section will involve a change in inlet flow conditions as well as a change in diffuser geometry, and a comparison of the diffuser characteristics between D-3 and D-101 becomes difficult. Influence of the Vane Setting Angle (D -5/D-101) Consider first the influence of vane set- 9

10 D-101 / L 1_1 90 /. RPM D _- D- 105 C Plot M, { B, ( D D-105 D-101 D-105 A M, op.2 ia 00 / IE 6, 0 8 Fig / 90 / m (kg/s ) Overall static pressure recovery versus flow i (. I Table 6.,c D-5 «4 ass D-101 a4 "Ss 80/ / / / / / ting angle (relative to the radial direction) on the blockage in the throat. Two working points with identical diffuser inlet conditions were selected and are shown in Table 5. It is seen in Table 5 that the diffusion of the flow from rotor outlet to throat is more important in D-101 than in D -5. Comparing the velocity distributions, the flow undergoes a stronger deceleration along the first half of the vane suction side in D-101 than in D -5, because of the higher negative incidence. This causes the higher blockage in the throat (shown in Fig. 10). As the flow is supersonic in the throat, this results in a lower throat Mach number. It, therefore, is concluded that an increase in vane setting angle leads to an increase in throat blockage. In Fig. 11, the variation of Cptot for the D-5 and D-101 are superposed. Cptot of D-5 is increasing with decreasing mass flow, while Cptot of D-101 is decreasing with decreasing mass flow. Similar results were obtained by Reeves (8). The flow angles at the rotor exit are tabulated versus the vane setting angle in Table 6. The tabulated.0e 0e Fig. 12 Throat blockage and Mach number versus channel recovery, 90 percent rpm data indicates that for D-5 the flow was approaching the vane leading edge under zero incidence, resulting in a slightly negative sloped characteristic, while for D-101, the flow had a high negative incidence, thus producing a positive sloped characteristic. Influence of the Suction Surface Shape (D-101/ D-105) In Fig. 12, the variation of the static pressure coefficient of D -101 and D -105 are plotted versus throat blockage and Mach number. In this graph, it is seen that the shape of the suction surface has no influence on the blockage. The Mach number distribution along the suction surface revealed that the maximum in the velocity distribution has moved upstream, but the overall diffusion from diffuser inlet to throat remained the same. Overall static pressure recovery Cptot for D-105 at 90 percent rpm is also shown in Fig. 11, indicating similar values to D-101 are obtained. C'CH 10

11 D- 3--_D ^ c 760 Hg T Fig. 13 Influence of diffuser throat dimensions on compressor characteristic Fig. 14- Influence of diffuser setting angle on compressor characteristic From these results, it appears that the shape of the suction side has little influence on the diffuser characteristics. COMPARISON OF THE OVERALL COMPRESSOR CHARACTERIS- TICS The effects of the test diffuser geometry variations on the overall compressor characteristics are discussed in detail in the following. Influence of the Throat Dimensions (D-3/D-101) The overall compressor characteristics of D-3 and D-101 diffusers are plotted in Fig. 13 from which it is observed that the influence of the throat section on the mass flow range of the compressor is very important. The increase in mass flow range with increasing throat dimensions is related to the fact that the characteristics of the rotor and the diffuser must match. If the throat section of the diffuser is too small, the surge line of the rotor (or of the diffuser) is reached when the diffuser gets out of choking conditions. This was the case of all the D-3 characteristics. By increasing the throat section, the choking line of the diffuser was moved to the right, so that both characteristics were matching (D-101). The large reduction in compressor efficiency and pressure ratio at 100 percent rpm with the D-101 diffuser was a consequence of rotor choking. Influence of the Vane Setting Angle The influence of the vane setting angle on the overall compressor characteristics is shown in Fig. 14. The choking mass flow for 80 and 90 percent rpm increased from D-101 to D-5 diffusers while the choking mass flow for 100 percent rpm remained unchanged. As mentioned previously, the blockage in the throat is smaller for D-5 than D-101 (see Fig. 10). As for 80 and 90 percent rpm the diffuser was the choking element, this decrease in blockage lead to an increase in choking mass flow. For 100 percent rpm, however, 11

12 so Fig. 16 Curvilinear orthogonal grid system 1.8 i.4 Fig. 15 Influence of suction surface on compressor characteristic the rotor was the choking element. As both compressors incorporated the same rotor, there was no difference in choking mass flow, in spite of a change in the throat blockage. From Fig. 14, it is observed that the vane setting angle also significantly influenced the compressor mass flow range. For 100 percent rpm, the mass flow range for D-101 was 8.1 percent, while for D-5 diffuser, it was only 1 percent. Influence of the Suction Surface Shape (D-101/ D-105) The characteristic curves of D-101 and D- 105 diffusers are plotted for the 90 percent rpm speed line in Fig. 15. The same mass flow range, adiabatic efficiency, and pressure ratio are obtained for D-105 as for D-101 diffusers. These results show that the suction surface shape has little effect on the overall compressor performances. Theoretical calculations confirming these test results are discussed as follows. THEORETICAL STUDIES The numerical method employed for diffuser flow analysis was a combination of a transonic flow calculation for the inviscid flow (from blade to blade) and shock boundary-layer interaction theory, which allowed the calculation of the boundary layer variation along the side walls of the diffuser. The calculation of the inviscid flow was made by a type dependent finite difference calculation (L, 9). This is a Murman-Cole type calculation using the curvilinear orthogonal grid system shown in Fig. 16. The calculation started from a fictitious inlet radius where the mass flow per passage was defined. Uniform inlet conditions along the rotor exit radius were imposed. This meant that the local influence of the diffuser vane L.E. on the flow leaving the impeller was neglected, and that a rapid mixing of the rotor outlet flow took place. Periodicity conditions required the same velocity components at both sides of the grid system between the diffuser inlet and the blade L.E. Uniform flow conditions were imposed at the outlet. A centered difference scheme was used in subsonic points; a forward difference scheme was used in supersonic points. This 2-D potential flow calculation method was extended to a quasi-3-d flow calculation by adding a correction term for the variation of passage height (due to the variation of the 12

13 measured x calculated D5 with dockage variation BO/. RPM M rotor =1 07 M rotor = 1.08 a rotor = a rotor nn I B_._. = 6.2/, D /. RPM A measured calculated with blockage variation Mentor =115 M,tor =1.15 Vrotor =78.9' D(rotor B._. = 6.2 % 1E B , Fig. 17 Throat blockage and Mach number variation Fig. 18 Throat blockage and Mach number variation D-5 80 percent rpm D percent rpm boundary-layer thickness over the shock). From an analysis of the Schlieren pictures as well as from the literature survey ( 1, 4 ), it can be postulated that the boundary-layer thickness along the suction surface of the vane is negligible relative to the boundary layer along the sidewalls because of the presence of a secondary flow in the inlet region of the diffuser. This secondary flow effect carries the boundary layer away from the suction side to the sidewalls. This is the reason why the boundary-layer thickening along the sidewalls was mainly responsible for the blockage in the throat. The variation of the boundary-layer thickness over the shock was calculated every 20 iterations as a function of the local shock strength by means of a discontinuity analysis (1). This was also an iterative procedure where the local velocity was calculated as a function of the existing blockage and where the change in blockage was regularly readapted to the calculated shock strength. Comparison of the Theoretical and Experimental Results The measured Mach number distributions along a central streamline are compared to the one obtained by the 2-D and quasi -3 -D calculation in Fig. 17. The diffuser inlet blockage is 6.2 percent and the calculated throat blockage is 14 percent which shows a good agreement with the experimental results. The measured Mach number distribution for the working point 90/3 of the D-105 diffuser is compared with the calculated distribution in Fig. 18. As can be observed, the Mach number distribution based on static pressure measurements indicates the presence of one shock. However, on the Schlieren picture, Fig. 19, two shocks can be seen. The positioning of the second shock (in the direction of the flow) corresponds to the one indicated by the static pressure measurements; the first shock is located more upstream. The calculated Mach number distribution shows two shocks, whose positions correspond to the measured shock positions (based on the Schlieren picture). Good agreement with the measured blockage factor in the throat was also obtained. The influence of the blockage factor at the inlet of the diffuser is shown in Fig. 20. Three cases were studied: the first one was the reference case for which the blockage was zero; 13

14 1 a Brota 0 / Mrota = = 0 /. krota _._ab,aa4 / Mrota = 115 B 5 = 8.82 / <rota` '.& r4t 8 /. Mmta = 1.14 B5 =14.6/ rota= KEEL xex x ( Tot.8.7 l `1 \\ T* 15 Fig, 19 Schlieren photograph..j 10 D n tnc Fig. 20 Influence of blockage at diffuser inlet on throat blockage o SCHML : 3/1 Fig. 21 Diffuser vane inlet regions for the other two cases, the blockage at the inlet It is observed from Fig. 20 that the blockage at were 4 and 8 percent. The corresponding inlet the diffuser inlet has a tremendous influence on conditions were: blockage in the throat. B4 M a4 In summary, good agreement was obtained be- 0% tween the experimental velocity distribution and o the quasi-3-d calculations. The blockage in the 115, % ,1 throat was a strong function of the blockage at 14

15 rd B5 = 16.6 /. Mrota = 1.15 A B 5 = 16.1 /. arota o---- D- 103 B5 = 15.1% Brot /. Fig. 23 Diffuser passage shapes ^o DI-A BS= 7.c / Mto,= 1.12 ^.--.«Di-B B5= 9.8 % biota= 79.3 brota= 5% DV -C 85=11.5 / I Fig. 22 Mach number variations D-101/D-105/D the inlet of the diffuser. With a Bi = 6.2 percent good agreement was obtained for all test cases. In a general way, the value of Bi should be determined from the rotor discharge flow conditions. Influence of the Suction Surface of the Vane The calculation method allowed substantiation of the influence of the suction side of the vane. Fig. 21 shows comparative suction surface contours indicating the suction side is more concave than the D-101 and D-105. In Fig. 22, it is seen that the shock is moving forward as the shape of the vane becomes more concave. This confirmed the trend, which had already been experimentally determined. On the other hand, the blockage factor, B t, was not influenced by the suction side shape, as was also confirmed by the experiments. Since the blockage in the throat does not change and since this parameter was apparently the main factor influencing the C p of the diffuser, it was concluded that the shape of the vane is not an important consideration in the diffuser stage. Influence of the Throat Dimensions In Fig. 23, three diffusers are drawn with Fig. 24 Mach number distribution before throat different throat dimensions. Each of these three diffuser geometries were analyzed for same diffuser inlet conditions where the rotor was the choking element. In this instance, a change in diffuser geometry does not produce a change in choking mass flow and thus in rotor outlet conditions. The velocity distributions and the blockage in the throat are plotted in Fig. 24, indicating that the bigger the throat section, the lower the Mach number was in the throat. In order to obtain such a lower throat Mach number, the flow accelerates in front of the throat so as to produce a higher shock strength. This result is in agreement with the experimental results of xc 15

16 I Welliver and Acurio (1). This increasing shock strength causes a higher blockage in the throat. The blockage factor and the Mach number in the throat permit calculation of the static pressure coefficient of the divergent channel. Taking into account the change in diffuser geometry and with the channel performance characteristics of Rundstadler ( 4), the following results were obtained. Di -A Di-B Di-C CpCH Alternatively, the static pressure coefficien of the inlet region, C pi, is increasing. Di-A Di-B Di-C M M This yields a total pressure coefficient, Cptot: Di-A Di-B Di-C Cptot From this analysis, it is concluded that with a bigger throat dimension, an increase in the static pressure coefficient of the diffuser may be expected. This statement is valid as long as the shock boundary-layer interaction in front of the throat occurs without separation. CONCLUSIONS This combined theoretical and experimental study has made it possible to correlate the influence of three geometrical factors of the inlet region of the diffuser on the velocity distribution and on the blockage in the throat. Together with the data of Rundstadler for channel diffusers, it permits an improved prediction of the overall performances of the vaned diffusers (of the channel type) for high pressure ratio single-stage centrifugal compressors. ACKNOWLEDGMENT The financial support of the von Karman Institute and of the Institute for Scientific Research in Industry and Agriculture are gratefully acknowledged. REFERENCES 1 Welliver, A., and Acurio, J., "Element Design and Development of Small Centrifugal Compressors," USAAVLABS Technical Report 67-30, Fort Eustis, Va., Aug Dean, R. C., Wright, D. D., and Rundstadler, P. W., "Fluid Mechanics of High Pressure Ratio Centrifugal Compressor Data," USAAVLABS Technical Report 69-76, Fort Eustis, Va., Feb Verdonk, G., "Experimental Investigation of the Flow in Diffusers for Advanced Centrifugal Compressors," V.K.I. PR 73-10, June Rundstadler, P. W., "Pressure Recovery Performances of Straight Channel, Single Plane Divergence Diffusers at High Mach Numbers," CREARE T.N. No. 88, Verdonk, G., "Theoretische en Experimentele Studie van de Transsone Stroming in Schoepen-Diffusoren voor Radiale Compressoren," Ph.D. thesis, University of Ghent, Vavra, M. H., Problems of Fluid Mechanics in Radial Turbomachinery, V.K.I. C.N. 55, Panaras, A., Calculation of a Boundary Layer Interacting with a Normal Shock by a Discontinuity Analysis, V.K.I. T.N. 121, Oct Reeves, G. B., "Estimation of Centrifugal Compressor Stability with Diffuser Loss- Range Systems," 1976 Gas Turbine and Fluids Engineering Divisions Conference, New Orleans, La., Roustan, M., and Van Den Braembussche, R., "Application d 1 une M4thode de Relaxation a l'etude d 1 une Grille d'aubes Trans-Sonique," V.K.I. PR ,