THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS Three Perk Avenue, New YoriL N.Y. 100164990 99-GT-103 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 It the paper Is published In an ASME Journal. Authorization to photocopy ' for Internal or personal use is granted to libraries and other users registered with the Copyright Clearance Center (CCC) provided $3/article is paid to CCC, 222 Rosewood Dr., Danvers, MA 01923. Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department. Copyright 01999 by ASME All Rights Reserved Printed In U.SA. NUMERICAL INVESTIGATIONS ON THE OPTIMUM DESIGN OF RETURN CHANNELS OF MULTI-STAGE CENTRIFUGAL COMPRESSORS 1111111111110)111111111 L. J. Lenke and H. Simon Institute of Turbomachinery University of Duisburg 47048 Duisburg Germany ABSTRACT Numerical simulations of the flow within return channels for the aerodynamic design are presented. The investigated return channels are typical to join the exit from one stage of a centrifugal machine to the inlet of the next stage and cover the range of high flow coefficients. Due to the strongly three-dimensional flow structure with high streamline curvature and secondary flows on hub and shroud of the return channel vanes, a modified explicit algebraic Reynolds stress model will be used. Starting with a comparison between measurements and numerical results to demonstrate the performance of the turbulence model in the prediction of losses, exit flow angle and separation behavior, further numerical investigations with different variations of the geometry of the channel will be considered. 3-D turbulent calculations at the design point and part load range show the influence of the design especially of the crossover bend onto the flow structure. INTRODUCTION The development of modern industrial centrifugal compressors demands extensive optimization of all flowconducting components with regard to maximum efficiencies and to accuracy of design calculation. This is particularly true for the return passages especially with regard to the lower efficiencies of multistage centrifugal compressors compared to single-stage compressors. The flow in return passages is characterized by repeated deflection downstream of the diffusor coupled with further deceleration and the interaction of the flow with the next impeller blade. The return channel vanes serve to ensure uniform and generally swirlfree flow to the next stage with minimum flow losses for the design point and for the part load range. The literature offers little information relative to specific return system design and performance prediction models for this component. Most published experimental and theoretical investigations are directed toward developing a better understanding of these complex flows (e.g. Nykorowytsch (1983), Aungier (1988), Lenke and Simon (1998), Rautaheimo and Ojala (1998)). Aungier (1993) presented a computerized interactive design system for the performance analysis of vaneless diffusers, crossover bends and return channels. From the wide range of applications in which centrifugal compressors are used, a return channel with large flow coefficients is investigated in this paper. The three-dimensional phenomena and viscous effects such as secondary flow and wakes have appreciable effect on the fluid dynamic and performance of centrifugal compressors. Especially the deceleration of the flow introduces large separations and recirculations which will decrease the efficiency. With the progress in high performance computers as well as CFD, major advances have been made in predicting three-dimensional turbulent flows. There are already a large number of linear two-equation turbulence models but a basic flaw of these kind of models, namely their failure to correctly predict the amount of separation in adverse pressure gradient flows, is still unresolved. However, for the prediction of large flow separations and recirculations these turbulence models have to be abandoned in favor of higher order turbulence models which will increase strongly the numerical effort. Recently, the non-linear two-equation models which are applied within the context of the standard two-equation models extend the range of applicability of the two-equation Presented at the International Gas Turbine & Aeroengine Congress & Exhibition Indianapolis, Indiana June 7-June 10, 1999
channel width impeller tip diameter turbulent kinetic energy static pressure total pressure impeller tip speed volume flow rate at stage inlet nondimensional wall distance flow angle with tangential direction blade angle with tangential direction dissipation rate of turbulence energy flow coefficient PS SS Subscripts 3 4 6 static pressure recovery coefficient total pressure loss coefficient = (Pis - pie)/(pts - Ps) pressure side suction side wall inlet plane of 180 -bend outlet plane of 180 -bend outlet plane of return channel Table 1: Nomenclature models. In this paper an explicit algebraic Reynolds stress model in conjunction with k and e equations is used to predict the turbulent flow through a return channel investigated by Rothstein and Simon (1983). A selection of different incidence parameters are compared with measurements to illustrate the performance of the calculations and the influence of design variations. THE NUMERICAL SCHEME In this investigation the code developed by Reichert (1995) with a finite volume formulation of the full Navier- Stokes equations is used picking up elements from Roe's and Other's scheme (Reichert and Simon, 1994). Furthermore, only steady state solutions are considered. For high convergence rates, an implicit, Newton-Raphson-like iterative method is used to solve first the averaged conservation equations and then the modeled transport equations but with different CFL numbers for each set of equations. Furthermore, the local time step size is calculated using a CFL number, which is a function of the local change of the density (details are described in Lenke and Simon, 1997b). For the simulation of turbulent flows non linear eddyviscosity models are an increasingly popular approach, motivated principally by the desire to combine the physical realism offered by second-moment closure with the simplicity and numerical robustness of linear eddy-viscosity models. Gatski and Speziale (1993) derived an explicit algebraic stress equation for three-dimensional turbulent flows which must be solved in conjunction with two transport equations. In the present study the algebraic stress equation is solved with the standard k-equation and an c-equation which is extended by an additional production range time scale and a cross-diffusion term to improve the separation behavior of the turbulence model (details are described in Lenke and Simon, 1997a and 1998). Boundary Conditions At the inlet boundary the averaged total pressure and total density were specified. Furthermore, the distributions of the radial velocity component and the flow angle were taken from the measurements (Rothstein and Simon 1983) with increasing values of the velocity and flow angle towards the inner contour. At the outlet, a variation of a constant static pressure near the hub was used to establish a radial pressure distribution and the correct mass flow. All solid surfaces were modeled as rigid, non-slip and adiabatic. The other flow quantities were extrapolated from the interior. At the inlet no values about the measured turbulent kinetic energy are available so that k and c were extrapolated from the interior which leads to an averaged turbulence intensity of nearly 1%. NUMERICAL RESULTS The calculations to be presented have been done for the flow through a return channel with a large flow coefficient = V/u2di = 0.12. Two different return channel vanes are investigated with a design blade angle behind the 180 -bend of,ff4 = 30 and 134 = 40 0 (Fig. 1). The geometry of the channel and the computational H-grid are shown in Fig. 1. The grid is a single block grid with 45 x 45 x 188 grid points and y4 < 1. Only near the leading edge y 4 has maximum values of 5 in a very small region. The geometry of the channel for both return channel vanes is characterized by a constant channel width between point 3 and 4 with an increasing cross-sectional area up to point 5 and a decreasing cross-sectional area up to point 6. This acceleration of the flow and the straight contour of the vane near the trailing edge lead to a nearly swirlfree exit flow. Due to the large flow coefficient the channel width at the exit is very large and it remains only a short flow path between the vanes. For all presented geometries three different calculations with different inlet flow angles and corresponding mass flow rates have been done. But 2
Figure 1: Return system geometry and grid topology (45 x 45 x 188 grid points). only for the first return channel passage with two different vanes measurements taken from Rothstein and Simon (1983) were available. Comparison with Experimental Data (300 Vane) The ratio of passage width to mean streamline radius of curvature (characterized by 263/(b3 + = 1.08) is very high. This leads to smaller multi-stage compressors but also to higher losses over the bend. The high streamline curvature within the return channel causes strong secondary flows and the calculated Mach number distribution in Fig. 2 shows a very inhomogeneous flow between hub and shroud. At the inlet the Mach number increases towards the inner contour, which is already attributable to the effect of the subsequent 180 bend. At the outer contour the meridional velocity distribution in Fig. 3 indicates a large separation, but Fig. 3 shows also a homogeneous distribution of the tangential component of the velocity in a wide range of the crossover bend. Downstream the 180 bend Fig. 3 indicates a second separation at the inner contour thus between the vanes the flow is moved towards the outer contour. But Fig. 4 shows, that negative meridional velocities are limited to the range of the leading edge. With larger inlet angle (as = 42 ) the rise in the meridional component increases the streamline curvature due to the shorter flow path. But in this case the meridional velocity distributions show smaller separations within the 180 bend which decrease the loss behavior of the 180 0 bend. These separations have no significant influence on the averaged flow angles within the 180 bend, which increase only up to 1-2. The effect of separation downstream of the 180 bend can be detected in the corresponding wall surface pressure distributions in Fig. 5b. The high surface pressure at suction side indicates the decelerated flow near hub while the low pressure distribution indicates the acceleration near shroud. At pressure side the pressure distributions between hub and shroud are similar. Moreover, the pressure distributions show clearly the discontinuity of the curvature in the pressure side contour at the transition into the straight section. At mid span the comparison between measured and calculated pressure distributions in Fig. 5 show, that the simulation is able to calculate the pressure distributions 3
-:-.. ---- ------:- - suction side Figure 2: Mach number distribution within the channel at design point (a:3 = 29 ). Figure 4: Velocity vectors at 4% of span near hub. Mach number distributions Figure 3: Projections of the velocity vectors in two planes within the 180 bend. 4
b) 2.0 2.0 20 Pw P9 Pe3 P3 0 Citk. 03 = 42 03 = 16-1.0 1.0 0 0.5 0 0.5 1.0 16% of span (near to hub) - - 84% of span (near to shroud) rs,o Exp Data (pressure, suction surface) (Rothstein and Simon (1983)) Prediction -2.0 0 0.5 Figure 5: Surface pressure distributions at mid span: a) Low flow 03 = 16, b) design point a3 = 29 and c) High flow 03 = 42. qualitatively. But due to the large differences between hub and shroud, the differences at mid span can be caused by relatively small errors in the calculation of the velocity distribution within the crossover bend. With small inlet flow angle (03 = 16 ) the calculated Mach number distribution at mid span indicates a large separation at suction side beginning at 25% of chord length, which is displayed too in Fig. 5a by the linear pressure distribution at suction side. This separation is caused by the incidence flow angle at the leading edge. In combination with the separation downstream of the 180 bend the separation point moves upstream close to the leading edge near hub. The measurements show a linear pressure distribution beginning near the leading edge which indicates that the simulation underpredicts the separation at the inner contour of the 180 0 bend. The development of pressure side separation near the leading edge with large inlet flow angle can be detected in Fig. 5c, which effects the rise in the losses too. Losses and Exit Flow Angles Fig. 6 shows the loss coefficient, the pressure recovery coefficient and the mean exit flow angle as a function of the inlet flow angle. The measurements of both return channels (30 and 40 return channel vane) display a loss minimum at approximately the design point, but the largest values for the pressure recovery are obtained at smaller flow angles. With regard to the loss minima, both return channels are equivalent, but the loss curve of the 40 vane is flatter. This distribution is strongly attributable to the lower incidence angles in the range of large inlet flow angles but also to the lower load caused by the smaller diffusion. The averaged exit flow angles are nearly constant over the operating range and display a prewhirl to the next stage less than 5. Only in the range of very small flow angles a rise of the exit flow angle occurs into the negative prewhirl region. The simulation is not able to calculate the same level of losses especially the calculated losses of the 40 vane are too high. But the calculated loss and pressure recovery distributions agree qualitatively with the measurements. The calculated exit angles are within the band of less than 5 5
0 8 (36 4 --.-. ID 2 di, ' e A as 13V- rei c: Exp. Data 30 vane 30 vane - 40 vane.0 90 A36 a6-1.0-2.0 loo 90 o a --c'"---.. ----,... -----, a... re c ii ---.. A --- m 0 80 100 30 a3 30 vane - 40 0 vane o o Exp. Data 30 vane A e Exp. Data 40 vane Figure 6: Calculated loss coefficients, recovery coefficients and exit flow angles compared with measurements (Rothstein and Simon (1983)). prewhirl too. Fig. 6 shows only the averaged exit flow angles. The exit flow angle distributions between hub and shroud in Fig. 7 show great deviations from the averaged values with a flatter distribution with the 40 vane. These exit flow angle distributions are caused by the secondary flow from pressure to suction side near hub and shroud illustrated in Fig. 4 and 8. Crossover Bend Design The above presented return channel was characterized by a large ratio of passage width to mean streamline radius of curvature (263/(63 + bz ) = 1.08) within the crossover bend. Aungier (1993) mentioned that values less than 0.4 should be preferred. Fig. 9 shows the Mach number distribution within the return channel with 263/(63+10 = 0.74 and the 30 return channel vane. The reduced streamline curvature to A SS 50 shroud 0.5 hub Figure 7: Exit flow angle distributions between hub and shroud. shroud (plane 5 in Fig. 2) fl 11)11, Immtir,,,, No I 0 / r 1 /II III I 1 I, If "././.../..K1/1//iih In,,,,,,,,,, F.... I F,,,,,, I III/ hi/ t11.1 ///Y/ ----------.ifffil ///,,,,,,,,,, PS //n th. I t 'left e t Hit I.,ehtteN \ \,, t ".. hub - plane 6 in Fig. 2 Figure 8: Secondary flow near trailing edge and exit of 90 bend (03 =30 ). improves the separation behavior within the 180 bend. Especially the separation at the inner contour decreases with lower Mach number level at the inlet of the vanes. Between the vanes the highest Mach numbers are now near mid span with an increasing wake region at suction side. On this account the low streamline curvature has nearly no influence on losses at design point. But at part load range the losses decrease more. The recovery coefficient and the averaged exit flow angle distribution are not influenced significantly. But the homogeneous flow at the inlet of the vanes reduces the secondary flow from pressure to suction side (Fig. 10) which causes a smoother velocity distribution at the exit. The exit flow angle varies between 70 at mid span and 110 near hub and shroud. The comparison of the measurements in Fig. 6 shows that 6
(36..... -.. --Cr.-.--.-' 0 A36 -- at -20 100 90 - - - -... - _.... -. 793/(93 + 6,0 = 0.74 293/(93 + ti, ) = 1.08 _ an 10 30 a3 Figure 9: Mach number distribution within the channel with modified crossover bend at design point (30 0 vane) and loss coefficient, recovery coefficient and exit flow angle. Figure 10: Velocity vectors at 4% of span near hub (th = 30. 263/(63 + bz ) = 0.74). Figure 11: Modified crossover bend with 40 return channel vane. 7
.8.4 -. -..._ :7:4...0 A36 --...`z.c.. a6 2.0 100 so - - - - - -. - BD 100 30 400 vane 64/1,3 = 0.71 40 vane b4/63 = 1 30 vane 64/63 = 1 a3 Figure 13: Modified vane design with 30 vane construction angle at the inlet. number level on the separation behavior decreases but these additional losses continue to be dominant compared to the loss distribution of the 30 vane. The influence of this modification onto the recovery coefficient and exit flow angle is very small. Figure 12: Loss coefficient, recovery coefficient and exit flow angle for modified crossover bend (64/63 = 0.71, 263/(63 + bz ) = 0.74). higher design inlet angles of the return channel vanes flatten the loss distribution. To move the loss minimum of these vanes to lower inlet flow angles Fig. 11 shows a modified crossover bend design with a reduced channel width at the exit of the 180 0 bend (64163 = 0.71, 263/(63 + 64 = 0.74). The acceleration within the 180 bend increases the flow angle by nearly 10. In combination with the 40 vane the design flow angle at the inlet of the 180 0 bend remains at 30. Another advantage results from the reduced length of flow path due to the smaller deflection of the flow by the vanes. With this modification Fig. 12 shows that the minimum of the loss distribution moves to smaller inlet flow angles compared to the 40 vane within the original return passage. The reduced streamline curvature of the 180 0 bend decreases the losses over the whole operating range. The separations at the outer and inner contour of the 180 bend decrease but therefore the Mach number downstream of the 180 bend increases. With small inlet flow angle this higher Mach number level increases the separation at suction side. The flow separates at the leading edge of the vane over the whole channel width which effects a rise in the losses (Fig. 12). With larger flow angle the effect of the higher Mach Return Channel Vane Design Return channel vane design should typically feature front loaded vanes to minimize discharge flow deviation. Fig. 13 shows a modified vane design which is based on the assumption to move the deceleration and deflection of the flow closer to the inlet. These return channel vanes have a vane construction angle of th = 30 at the inlet and the same return system design with 64/63 = 1 and 263/(63 + 64 = 0.74. At design point and with high flow (a3 = 42 ) the short flow path reduces the losses (Fig. 14). Furthermore, the reduced curvature of the pressure side avoids separations at pressure side which leads to a flatter loss distribution in the range of larger flow angles. But these improvements will be equalized by the high losses with small flow angles due to the increased deflection of the flow near leading edge (Fig. 14). Another influence of the vane design is shown by the averaged exit flow angle with small flow angle (Fig. 14). The higher exit flow angle results mainly by the increasing exit flow angle near mid span due to the quick deflection of the flow near the leading edge and the reduced curvature of the pressure side. Moreover, the secondary flow from pressure to suction side near hub decreases. At design point both return channel vanes shown in Fig. 13 have little effect on losses and averaged exit flow angles. Only the increased streamline radius of curvature within the crossover bend decreases secondary flow and improves 8
.8 (36.4 -... --......4- - as.0 - A36-1.0 2.0 100 - - - modified 30 vane -- vane modified vane 263/(63 + eh) = 0.74 - - 30 0 vane 263/(63 + b.) = 0.74 - - - 30 vane 263/(b3 + b.) = 1.08 800 10 --::::::::"--'-------- Figure 14: Loss coefficient, recovery coefficient and exit flow angle for modified vane design (64/63 = 1 and 263/(63 + 61 ) = 0.74). a3 in both cases the exit flow behavior (Fig. 15). CONCLUSIONS An explicit algebraic Reynolds stress model including an additional cross-diffusion production range time scale term in the e-equation has been used for the simulation of the flow through different return channels. Predicted distributions of loss coefficients show the qualitative agreement with experimental data so that the presented CFD model is well suited to aerodynamic design activity. Starting with an existing return system with a large ratio of passage width to mean streamline radius of curvature within the crossover bend and high flow coefficient the reduction of this ratio shows improvements of the return system performance in the part load range. The losses depend on the separations within the crossover bend and care has to be taken to avoid small streamline radius of curvature. Furthermore, a homogeneous flow distribution between hub and shroud at the inlet of the vanes reduces secondary flow within the channel and causes a smoother flow angle dis- Figure 15: Exit flow angle distributions between hub and shroud. tribution between hub and shroud at the exit of the return channel. However, in the case with very small ratio of passage width to mean streamline radius of curvature (e.g. low flow coefficient return channel with 263/(63 + b.) = 0.29, Lenke and Simon (1998)) the frictional losses are more dominant and increase the losses over the bend. The modification of the return channel vanes (increasing inlet blade angle or reduced curvature at pressure side) show little improvements in the range of high mass flow rates. But further investigations are necessary to achieve similar improvements in the part load range near surge. The presented numerical simulations have shown their superior capacities if used as an optimization tool in the design of turbomachinery components so that CFI) has become a most effective tool to reduce the extent of expensive measurements. ACKNOWLEDGEMENTS The authors would like to thank Mannesmann DEMAG DELAVAL Turbomachinery for providing the return channel geometry and experimental data. 9
REFERENCES Aungier, R. H., 1988, "A Performance Analysis For The Vaneiess Components Of Centrifugal Compressors", Flows in Non-Rotating Turbomachinery Components, ASME FED Vol. 69, pp. 35-43. Aungier, R. H., 1993, "Aerodynamic Design and Analysis of Vaneless Diffusers and Return Channels," International Gas Turbine and Aeroengine Congress, Cincinnati, ASME- Paper 93-GT-101. Gatski, T. ft., Speziale, C. G., 1993, "On Explicit Algebraic Stress Models for Complex Turbulent Flows," Journal of Fluid Mechanics, Vol. 254, pp. 59-78. Lenke, L..1., Simon, H., 1997a, "An Improved Algebraic Reynolds Stress Model for Predicting Separated Flows," Proceedings of the 7th International Symposium on Computational Fluid Dynamics, 15-19 September, Beijing, China. Lenke, L. J., Simon, H., 1997b, "Viscous Flow Field Computations for a Transonic Axial-Flow Compressor Blade Using Different Turbulence Models," International Gas Turbine and Aeroengine Congress, Orlando, ASME-Paper 97- GT-207. Lenke, L. J., Simon, H., 1998, "Numerical Simulation of the Flow through the Return Channel of Multi-Stage Centrifugal Compressors," International Gas Turbine and Aeroengine Congress, Orlando, ASME-Paper 98-GT-255. Nykorowytsch, P., 1983, "Return Passages of Multi-Stage Turbomachinery," ASME FED Vol. 3. Rautaheimo, P., Ojala, J., 1998, "Description of the Numerical Methodology for the ERCOFTAC Test Case F3," ERCOFTAC Seminar and Workshop on Turbomachinery Flow Prediction VI, 5.-8. Januar, Aussois, France. Reichert, A. W., Simon, H., 1994, "Numerical Investigations to the Optimum Design of Radial Inflow Turbine Guide Vanes," International Gas Turbine and Aeroengine Congress, den Haag, ASME-Paper 94-GT-61. Reichert, A. W., 1995, "Striimungssimulationen zur optimierten Gestaltung von Turbomaschinenkomponenten," Ph.D. Thesis, University of Duisburg. Rothstein, E., Simon, H., 1983, "On the Development of Return Passages of Multi-Stage Centrifugal Compressors," ASME-Spring-Conf., Houston, FED-Vol. 3, G 00225 10