99-GT-452 - Conference Proceedings
Transcription
99-GT-452 - Conference Proceedings
THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS Three Park Avenue, New York. N.Y. 10016-5990 99-GT-452 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 lithe 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 1999 by ASME All Rights Reserved Printed in USA STRUCTURE AND PROPAGATION OF ROTATING STALL IN A SINGLE- AND A MULTI-STAGE AXIAL COMPRESSOR 11110111119,111 11111111 H. M. Saxer-Felici, A. P. Saxer, F. Ginter, A. Inderbitzin, G. Gyarmathy Turbomachinery Laboratory Institute of Energy Technology Swiss Federal Institute of Technology (ETHZ) 8092 Zurich, Switzerland ABSTRACT The structure and propagation of rotating stall cells in a single- and a two-stage subsonic axial compressor is addressed in this paper using computational and experimental analysis. Unsteady solutions of the 2o inviscid compressible (Euler) equations of motion are presented for one operating point in the fully-developed rotating stall regime for both a single- and a two-stage compressor. The inviscid assumption is verified by comparing the single-stage 2-D inviscid/compressible solution with an equivalent 2-D viscous (Navier-Stokes) result for incompressible flow. The structure of the rotating stall cell is analyzed and compared for the single- and two-stage cases. The numerical solutions are validated against experimental data consisting of flow visualization and unsteady row-by-row static pressure measurements obtained in a four-stage water model of a subsonic compressor. The CFD solutions supply a link between the observed experimental features and provide additional information on the structure of the stall flow. Based on this study, supporting assumptions regarding the driving mechanisms for the propagation of fully-developed rotating stall cells and their structure are postulated. In methodical respect the results suggest that the inviscid model is able to reproduce the essentials of the flow physics associated with the propagation of fully-developed, fullspan rotating stall in a subsonic axial compressor. p0 70 TRS U2 ww a, R ACp stagnation pressure stagnation temperature rotor period rotating stall period time rotor speed at Euler radius axial & tangential relative velocity components absolute and relative flow angles (from axial) blockage factors from unsteady pressure trace Eq.( I) & from instantaneous cell width Eq. (2) static density pressure coefficient = (p 13)/( I -p l U22 ) flow coefficient at Euler radius = ux /U2 stage static-to-static pressure coefficient 2 = (h3 — h 1 )/ Cl; (air), = (p3 — p l )/(p U2 ) (water) — Subscripts 1,11. 12, 2. 22, 23, 3 axial stations, see Fig. 1 Superscripts time-averaged value I. INTRODUCTION NOMENCLATURE Abbreviations CFD IGV RS tot computational fluid dynamics inlet guide vanes rotating stall frame of reference Symbols F. R front, rear boundaries of stall cell It static enthalpy static pressure For decades, the operational stability of compression systems has been a major concern of industrial and aeroengine gas turbine designers, see for example the early work of Emmons etal. (1955). In this respect, rotating stall (RS) is a key flow phenomenon limiting the operational stability of compressors. In order to better predict its occurrence, and ultimately to control it, further research is required. RS is identified by large scale flow distortions propagating around the compressor annulus at a fraction of the rotor speed. It often precedes surge, a phenomenon involving mass flow pulsations within the whole compression system. RS, as well as surge, detrimentally affects the performance and sometimes the structural integrity of the machine. Presented at the International Gas Turbine & Aeroengine Congress & Exhibition Indianapolis, Indiana — June 7-June 10, 1999 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms Ranging from stall inception, see for example (Gamier et al., 1993), (Tryfonidis et al., 1995), (Camp & Day, 1997). to operation in deep stall with or without surge (Day et at, 1978), (Das & Jiang, 1984), (Breugelmans et al., 1985), (Mathioudalcis & Breugelrnans, 1988), the studies describing and analyzing the unstable behaviour of compressors are mainly based on experimental work. From these observations a number of theoretical linear and non-linear models (Greitzer, 1976a,b), (Moore & Greitzer, 1986), (Demargne & Longley, 1997) have been developed and applied to study the dynamics of the whole compression system with a view to ultimately control RS and surge (Paduano at al., 1993), (Gysling & Greiner, 1994). An other approach is to use CFD to focus on the phenomenological understanding of the structure of rotating stall from a fluid dynamics point of view (Outa et at, 1994), (Nishizawa & Takata, 1994), (Saxer-Felici et al., 1998a). Some approaches combine CFD with semi-empirical models (Hendricks eta]., 1996), (Longley, 1997). A comprehensive review of compressor stability models is given by 1,ongley (1993). The present work concerns the fluid dynamic behaviour of fullydeveloped, full-span RS in high hub-to-tip ratio axial compressors using computational analysis and experimental data. The configuration presented here is relevant for repeating stages as found in the rear part of modern land-based compressors. The base flow is not far from being 2-D in such low aspect ratio bladings. The present objective is to study the structure of fully-developed rotating stall and the mechanisms for its propagation in a single- and two-stage axial compressor using two numerical methods and experimental results. This is somewhat unusual as the classical CFD research approach is to focus on RS inception (He, 1997), (Gong et at, 1998), (Hoying et al., 1998). The first numerical method, MULTI2 (Saxer, 1992), uses the Euler equations to solve the inviscid compressible flow while the second, FENFLOSS (Ruprecht, 1989), (Ginter, 1997), solves the incompressible Navier-Stokes equations with a mixing-length turbulence model. Both numerical techniques are based on the 2-D unsteady equations of fluid motion. The 2-D assumption is motivated by experimental observations, see for example (Day et al., 1978), which point out the essentially axial-tangential nature of full-span RS in low aspect ratio bladings. Also the experiments of (Das & Jiang, 1984) with a high hub/ tip ratio blading indicate that 3-D effects are markedly reduced as the axial gaps are reduced. The use of the Euler equations for propagating rotating stall cells is prompted by previous experimental and theoretical studies (Cumpsty & Greitzer. 1982), (Longley, 1993), (Gyarmathy, 1996), (Gong et al., 1998), which clearly indicate the crucial impact of fluid inertia for stall cell propagation. Furthermore, as shown in external (Rizzi & Eriksson, 1984) and internal (Felici, 1992) aerodynamics, the Euler equations allow the generation and capture of strong vortical flows as encountered during rotating stall operation. The two numerical methods are applied to a single- and a two-stage axial compressor bearing similarity (File et al., 1997) with any of the repeating stages of the four-stage water model of a subsonic axial compressor (Hof et at, 1996). Because of the limitations linked to the choice of the CFD models applied (no 3-D effects, number of stages) and the differences between CFD and experimental setups, only the general mechanism of RS cell propagation and cell structure is discussed, while overlooking detailed flow features which are much smaller than, say, the size of the blade pitch. Reference is made throughout the paper to previous experimental work on other relevant configurations to point out the validity of the current CFD approach as well as the existing discrepancies. This step is required in order to apply the present inviscid CFD method for the control of RS in a future phase. Due to the limited computational resources available, a full-annulus, 3D unsteady, viscous multi-stage simulation is here not possible. Instead, different contributions to the RS phenomenon are pointed out by a stepwise removal of different levels of simplifications (for example inviscid vs. viscous, single-stage vs. two-stage). The paper is organized as follows. Both the inviscid/compressible and viscous/incompressible numerical schemes are briefly described, together with the in-house experimental setup. CFD and experimental global data such as performance map and blockage are discussed first Then, detailed unsteady solutions for the single-stage compressor are presented by cross-comparing the inviscid/compressible and the viscous/incompressible solutions with in-house experimental data. This supports the validity of the inviscid assumption and provides the basis to discuss the structure of the rotating stall cell. The time-variations of the flow parameters in the two-stage compressor are then shown and discussed together with CFD and experimental flow visualization in the absolute and RS cell-based frame of reference. Finally a summary of the essential results and the conclusions are drawn regarding the flow physics associated with full-span. fully-developed RS in low subsonic axial compressors. II. NUMERICAL PROCEDURES As described hereafter, the time-marching solvers MULT12 (Saxer, 1992) and FENFLOSS (Ruprecht, 1989), (Ginter, 1997) differ both in the physical assumptions for the flow to be solved, as well as in their basic numerical schemes and grid structures. 11.1 Inviscid flow solver (MULT121 A multi-block grid generator MELLIP (Saxer-Felici, 1996) and an unstructured flow solver MULTI2 (Saxer, 1992) are used. MELLIP solves the Poisson equations in the blade-to-blade plane. An iterative successive line over-relaxation technique is applied on blocks of C and H grid types with moving block boundaries, resulting in an overall unstructured smooth grid. The source terms are calibrated to control spacing and orthogonality at the blade surfaces. MULTI2 solves the time-dependent Euler equations for compressible flow with an explicit, finite-volume, node-based Ni-Lax-Wendroff type algorithm (Ni, 1981) extended to 3-D unstructured meshes and hexahedral cells (Saxer, 1992). MULTI2 can solve the time-dependent as well as the steady-state interaction in multistage configurations. In this study, the 3-13 solver is used in 2-D mode with three 2-D meshes piled up to form a two-cell-height 3-D control volume. A combined second- and fourth-difference numerical smoothing consistent with the second-order accuracy (both in space and time) of the discretization scheme is added to prevent high frequency oscillations and to capture shock waves. In the present subsonic cases, the second-difference smoothing is turned off. 11.2 Viscous flow solver (FENFLOSS) The commercial grid generator ICEM (ICEM, 1997) and the 2-D flow solver FENFLOSS (Ruprecht, 1989), (Ginter, 1997) are used. The finite-element code FENFLOSS solves the Navier-Stokes equations for incompressible flows based on a Petrov-Galerkin formulation on a 2 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms multi-block grid with 4-node elements. The momentum equations are solved by a segregated solution algorithm with a preconditioned conjugated gradient algorithm for non-symmetrical sparse matrices and a modified Uzawa pressure correction algorithm. Time-dependent flows are simulated by a fully-implicit three-level time discretisation of second-order accuracy and the rotor/stator interaction is obtained by overlapping grids over one grid element (Ginter, 1997). Since no interpolation is required at the interface, the balance equations are satisfied. An algebraic mixing-length turbulence model is used in the solver. This code has been applied to several flow problems in hydraulic turbomachinexy (Ruprecht et al., 1994), (Gentner et al., 1998). and stator, and solidity are retained from the experimental model. The geometry used in the simulation corresponds to a cut at the (RMS) Euler radius of any of the repeating stages of the four-stage water model described in Chapter III and in (Saxer-Felici et al., 1998a). The domain used in the inviscid two-stage calculation is shown in Figure 1 with the location of the rotor inlet (station 1), a station ahead of the first rotor (station 11), the rotor/stator interface of stage 1 (station 12), the exit of stage 1 = inlet stage 2 (station 2), the rotor/stator interface of stage 2 (station 22), a section downstream of stator 2 (station 23) and finally the exit boundary (station 3). Both the inviscid and viscous procedures use block-structured grids which are shown in a blow-up of the near-blade region. In both the inviscid and viscous procedures the grids are attached to the local blade row and the governing equations are solved relative to this coordinate system. Hence, for the grid region attached to the moving rotor blades the equations are solved in the relative frame of reference (for example in the regions limited by the sections Ito 12 and 2 to 22 in Fig. 1a). In the regions attached to a stator the grid is stationary and absolute flow variables are used (regions 12 to 2 and 22 to 3). In comparison to the inviscid grid (Fig. 1W), the viscous mesh presents JI.3 Computational domains Whereas inviscid solutions have been obtained on a single- and two-stage compressor, the viscous procedure is applied only on the single-stage configuration. In order to reduce CPU time, the circumferential domain is reduced to 15 blades (30 blades are used in the test rig compressor), see also Section IV.3. Axial spacing between rotor stations I 11 12 2 22 23 stage 1 3 stage 2 a) ostationary numerical probe stations II 12 2 23 22 Figure 1: a) Two-stage computational grid on 15 channels for inviscid calculation, b) blow-up of near-blade region for inviscid calculation (twostage, 59085 nodes/mesh plane), c) blow-up of near-blade region for viscous calculation (single-stage, 124853 nodes/mesh plane). Location of stationary numerical probes is indicated. 3 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms EXPERIMENTAL SETUP A not quite usual test rig to study RS in an axial compressor is in operation at the Turbomachinery Laboratory of the ETHZ. It builds upon previous experimental work on a single-stage centrifugal air compressor (Hunziker & Gyarmathy, 1993) and its water-driven model designed using the principle of hydrodynamic analogy (File et al., 1997). discontinuities in the metrical properties at the block interfaces and a faster coarsening of the grid within the inlet and exit regions. Whereas the trailing edge is cut in the viscous computation, the inviscid grid includes a wedged trailing edge. Also, the two grid densities differ largely in the blade-to-blade region. However, these differences do not significantly influence the RS flow structures under investigation, see Chapter IV. 11.4 Boundary conditions Damnation Axial Compressor Inviscid flow solver MULTI2. As described in Saxer & Giles (1993) non-reflecting boundary conditions are used. Long inlet and exit farfields (as compared to the actual setup of a test rig stage) are adopted and steady-state non-reflecting boundary conditions are applied based on circumferentially averaged quantities at the inlet and the exit. In this respect, any uncertainty in modelling the unsteadiness reaching the farfield boundaries should be minimized, despite the large perturbation produced by the RS cell. At the rotor inlet, the average entropy (or stagnation pressure), the stagnation temperature, and the tangential flow angle are set in the absolute frame of reference with pi? = I bar, To = 300K, a = -31.3 °. This is in contrast to calculations performed in the stable branch of the characteristic, where in standard practice the rothalpy and relative flow angles are set at the rotor inlet. In the rotating stall regime, when setting the absolute inlet flow angle (corresponding to the metal angle of the upstream existing IGV's trailing edge, see Chapter III and Fig. 2), the relative flow angle and the flow coefficient are free to adjust to the local flow conditions. The circumferentially averaged conditions allow local flow adjustments due to potential effects. At the exit, the average static pressure is prescribed in order to reach the desired throughflow coefficient Fr0.25 in the RS regime. At the rotor/stator interfaces an unsteady numerically non-reflecting procedure based on the local characteristic variables ensures a physically consistent boundary condition even in the presence of the strong backflow characteristic of the RS regime (Saxer, 1992). A no mass flux condition is enforced at the pseudo hub and tip walls as well as on the stator and rotor blades, A periodic condition is applied between the circumferential upper and lower boundaries of the multiple blade passage domain. In this low Mach number application, the rotor speed U2= 164.08 m/s is derived by matching the non-dimensionalized velocity triangle from the design values at iti=0.39 together with an inlet axial Mach number of 0.18 (ratio of specific heats x=1.4). This value of Mach is chosen sufficiently low to mimic incompressible flow and high enough to ensure a reasonable convergence of the flow solver.The instantaneous error in the continuity equation applied on the computational domain is lower than 1% of the inlet mass flow. Viscous flow solver FENFLOSS. The rotor-relative inlet velocity vector is imposed with w, = 0.537 m/s, w = 1.821 m/s. For incompressible flow calculation, the pressure level is arbitrary, and for convenience is set to p3 = 0 bar at the stator exit. The rotational speed U2 = 2.142 in/s is as in the experiment. With these, the flow coefficient is set to (N—y=0.25 and the rotor-relative inlet flow angle to [3 1 =13 1 = 73.6°. A no slip condition is assumed at the blade surfaces. 210 time-steps are used for one rotor revolution (14 time-steps/pitch). 12 iterations are applied for each time-step of the implicit algorithm with data exchange at the interface at each iteration. Throttle Valve 111 II If Flow Straightener a) Venturi Tube IN N., Dimensions In [mm] position tO 9 8 6 5 4 3 2 c) IGV's 0 Pitot Tube Figure 2: a) Schematic of closed-loop water model rig, b) 4-stage axial compressor with plexiglas casing, c) indication of pressure measurement locations. 4 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms between the computed cases, the RS cell shown in Fig 7a) is represented at an instantaneous and slightly larger flow coefficient of 9=0.27. In addition, the experimental correlations by Day et al. (1978) show that the blockage increases with the number of stages. Between stage I and 2, within the RS cell, the flow in the absolute frame of reference is nearly tangential in the direction of rotation with a velocity up to twice the rotor speed. This high-speed tangential motion produces trailing edge flow separation and vortex roll-up in stator I, blocking the stator passages as seen in the middle of Fig. 8a). Flow visualization near the trailing edge of the last stator. A blowup of the stator flowtield represented by trajectories of numerical bubbles set in three channels (representing the middle portion of the RS cell) is displayed in Figure 9 for the inviscid/compressible single- and two-stage solutions together with photographs taken near the stator trailing edge of stage 4 in the test rig. The time-lag At corresponds to the passage of 113 of the RS cell. The video camera shutter time is 4 ms corresponding to a streak length of 0.22 blade pitch for particles travelling at 1.12=2.1 m/s. To produce a similar effect in the CFD solution, the position of three ghost bubbles are shown in addition to the current bubble position corresponding to a streak length of 0.21 blade pitch for particles travelling at C/ 2=164.08 m/s. Almost identical flow features are found in the two CFI) solutions. As mentioned above, the suction pulse at the cell front drives exit-domain fluid back into the stator passages, producing a separation at the trailing edge. The suction side due to a trailing edge separation. This vortex grows and decays in size as the cell passes by and is finally expelled at the cell rear due to the pressure pulse seen in Fig. 6b). The evolution of this vortical feature is explained in more detail below when comparing flow visualization in the single- and the two-stage case with in-house experimental data. Whereas these global flow structures agree well between the two computed solutions, the size of the recirculation bubble upstream of the rotor is larger in the inviscid solution than in the viscous one. In the stator channels, identical flow features are found in the two CFD solutions, though the magnitude and size of the trailing edge vortex may differ. IV.4 Two-staae inviscid solution Rotating stall cell structure. Instantaneous streamlines drawn in the absolute and in the cell-based frame of reference are depicted in Figure 8 for the two-stage in viscid/compressible computation at =O.25. One point to notice first is that the flow features located upstream of the first rotor and behind the last stator are very similar to the single-stage cases as described above. The blockage and the axial extent, though, as inferred from the limiting streamlines in the cell-based frame of reference, are larger than in the single-stage inviscid/compressible case (compare Fig. 8a) with 6a) & Fig. 8b) with 7a)). This is consistent with the observation that although the mean operating points are the same stagnation point at stagnation point tagnation point a) single-stage b) two-stage c) experiment Figure 9: Trajectories of tracer particles in the last stator, shown in the absolute frame of reference at two instants separated by a time lag ha corresponding to the passage of the third of the RS cell (At = XTR513). a) single-stage computation, b) two-stage computation, c) experiment. In the experiment the streak length is 0.22 blade pitch for particles travelling at U2=2,I m/s and 0.21 blade pitch in the CFD solutions for particles travelling at C12=164.08 m/s. 9 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms The experimental stage average data obtained in the four-stage axial compressor water model is also marked in Fig. 3 for design conditions and at iT=0.24 & c=0.26. As expected, the viscous and experimental values are close for design conditions, while the inviscid computation produces a much larger stage pressure rise due to the absence of the viscous effects influencing the work of the stage. Interestingly, within RS operation the experimental mean pressure rise per stage lies in between the two single-stage computed solutions for both 11:=024 and .(1)=0.26. The magnitude of the difference between the two CFD solutions is of the order of the difference between the first and fourth stage in the experiment (individual experimental stage pressure rises are not shown here). This seems to indicate that within fully-developed fullspan RS inviscid mechanisms generating the circumferential blockage are of importance. The stage average pressure coefficient for the two-stage inviscid computation is also indicated in Fig. 3. As expected for a repeating stage machine, the average values closely match the ones computed for the single-stage, both in the stable and RS regimes. At the computed RS operating point, the first stage is producing most of the pressure rise, a phenomenon also observed in the in-house experiment. Figure 4: Computed and measured blockage factors as a function of the flow coefficient. IV.2 Circumferential blockage IV.3 Siogle-stage solutions As observed in the experiment, all CFD solutions produce a single RS cell. The measured and computed flow blockages are shown in Figure 4 as a function of the flow coefficient. As expected and similarly described by Day et al. (1978), the experimental blockage A defined by Unsteady static pressure traces. In Figures 5a) & 5b), the inviscid and viscous computed traces of static pressure coefficient are shown for 6 rotor revolutions for 9=0.25 and for a stationary numerical probe located in the middle of a blade passage at the rotor/stator interface. In Figure 5c), the measured casing wall pressure trace taken at the rotor/ stator interface of stage 4 (pos. 8 in Fig. 2c)) is displayed for(70.24. It also shows the passage of a single RS cell. Both computed results show the passage of a time-periodic fullydeveloped single rotating stall cell with sharp static pressure gradients corresponding to the cell width and weaker gradients within the sound flow regions. The RS frequency is larger in the inviscid solution than in the viscous case (64% of the rotor speed compared to 55%), but the amplitudes of the static pressure fluctuations are comparable. The blockage coefficient marked in Fig. 5 is obtained from the pressure traces according to the definition given by Eq. (1). In both computations bumps appear in the pressure traces and therefore variations occur in the blockage. As discussed in (Saxer-Felici et al., 1998a) and (Saxer etal., 1999), the shape of the rotating stall cell varies periodically from compact (low blockage) to diffused (large blockage) for a given mean flow coefficient. In the inviscid computation, the blockage varies from 32% to 47%. In the incompressible viscous flow computation shown in Fig. 513) the volume flow is kept constant through the setting of the boundary conditions, but the solution still exhibits a variation in RS cell blockage (20% to 41%) due to the presence of fluctuations in the head rise. Note the smoothness of this pressure trace compared to the experimental and inviscid cases. Compared to the CFD solutions (shown at the Euler radius), the amplitude of the measured pressure traces is smaller (by a factor 2 approximately, which corresponds, as expected to the ratio of experimental to numerical blade count per row). This is consistent with the momentum exchange theory discussed below. The shapes of the traces are in good agreement between the CFD and the experimental data. The measured RS cell travels at 54% of the rotor speed, nearly matching the computed value in the viscous/incompressible case. The _ time between suction peak and next pressure peak time between two suction peaks interface of stage 2 (station 22), in agreement with the experimental data taken at the rotor/stator interface of stage 4 (pos. 8 in Fig. 2c)). Overall, the comparison suggests that the computed blockage and its variation with tp are consistent with experimental results. 0.15 _ 9 (I) varies linearly with the flow coefficient in the RS regime. It ranges from —30% at RS inception to 85% where full annulus stall is developed. Consistent with experimental observations, no RS operation with a blockage below —30% can be sustained in the computations, i.e. the flow solution jumps back to the stable branch of the characteristic. For the single-stage computational solutions two values of blockage are given. This is required since in the inviscid computation, the blockage varies periodically with tp for a given mean operating point (Saxer-Felici et al., I998b). This corresponds to a surge-like mechanism (±-10% of the inlet mass flow) superimposed upon the rotating stall phenomenon, see dashed fine in Fig. 4. Hence, the following definition for the blockage is used instead of Eq. (1) and applied to two instantaneous operating points at times corresponding to a local high and a local low flow coefficient, while ja0.25. — circumf dist. between suction peak and next pressure peak ( 2) periphery The analysis presented in Saxer-Felici et al. (1998b) indicates that computed blockage values follow this correlation for different grid sizes. For the viscous solution, the two values of blockage indicated for ri=0.25 correspond to the extreme values inferred from Fig. 5b) (discussed below), i.e. corresponding to a high and low head rise, see also (Saxer, 1999). Both pulsations encountered in the inviscid and viscous solutions lead to a change in the cell shape and are discussed in the next Section. In the two-stage computation, the mass flow pulsation is reduced, hence the variation of blockage with tp is smaller than in the single-stage computation. A mean blockage value of 40% is computed at the rotor/stator 6 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms 0.25 The opposite occurs at the rear of the cell (R). In this theory, the magnitude of the pressure pulses at the front and rear boundaries of the RS cell is inversely proportional to the width of the cell boundary zone, i.e. of the circumferential extent of the pressure spike. By allowing only 15 channels in the computation instead of 30 in the experiment, the extent of this zone is reduced by approximately a factor 2 for a given blockage. Overlooking the local blade-to-blade effects, the shape and magnitude of the static pressure tracts at the rotor/stator interface agree well between the two CFD solutions. Both exhibit a severe change in static pressure at the cell rear and front boundaries, although the gradient is steeper at the rear than at the front, a phenomenon which is consistent with experimental observations (Cumpsty & Greitzer 1982), (Das & hang, 1984). The front (F) and rear (R) boundaries of the inviscid RS cell are marked in Fig. 6 using the modified blockage coefficient X, based on the static pressure trace defined by Eq. (2) for a given time occurrence. For the viscous RS cell, the front and rear boundaries are defined by the occurrence of the same flow features in the streamline field as in the inviscid calculation. see Fig. 6c). Hence, by inspection of the velocity field the inviscid and viscous blockages agree well, although a strict application of Eq. (2) (based on static pressure) to the viscous/ incompressible solution would result in a lower blockage than in the inviscid solution. For the flow coefficient profiles, the characteristic behaviour is identical in both cases. Note that a good approximation for the blockage can also be obtained by considering the width of the RS cell as the peripheral distance formed by the bisection of the mean flow coefficient with the local throughflow. Rotating stall cell structure. The cell structure is shown in Figure 7 by instantaneous streamlines drawn in the RS cell frame of reference for the single-stage cases: a) inviscid/compressible computation and b) viscous/incompressible computation. Clearly the two CFD solutions exhibit a strikingly similar RS cell structure, which is discussed first. In the RS cell frame of reference, the incoming flow presents a tangential component opposed to the rotor speed and the cell appears steady apart from the local effects of the blade passing and the low-frequency change in cell shape due to the periodic variation of blockage with p (SaxerFelici et at, 1998a). In this frame of reference the cell is characterized by a large recirculation bubble upstream of the rotor, a broad lowvelocity region with large scale vortex shedding downstream of the stator, and tangential counter-current flows within the rotor and stator rows. The large recirculation bubble ahead of the rotor comprises two opposing vortices dividing the incoming flow in two streams to the front and the rear of the RS cell. The upstream vortex is undisturbed, while the other one is disrupted by the sequence of rotor blades crossing it. In the sound flow outside the RS cell the axial velocity is larger and the incidence angle on the rotor blade is lower than at the inlet boundary, making the stage operate at a higher flow coefficient than at the average _ p. This can be viewed as the presence of a cylindrical body formed by two counter-rotating vortices placed in a potential flow field. Downstream of the stalled stator blades, near the trailing edge, the suction pulse formed at the front of the cell (see Figs. 6a) and 6c)), tends to drive downstream fluid back into the stator channels. Part of this fluid is transported ahead of the stator and then tangentially in the direction of rotation, and finally washed out in a stator passage closer to the front of the RS cell. Another part of this fluid rolls up into a vortex near the experimental blockage for stage 4 varies between 34% to 40%, and lies in the range of the obtained CFD values. I.5 1.0 a) inviscid a Cp 0.5 0.0 -0.5 -1.0 4.5 0 4 2 yr(Rotor Revs.) 1.5 1.0 0.5 b) viscous aCp 0.0 -0.5 4.0 -1.5 0.6 04 0.2 c) experiment wd MN= oCp 0.0 11111111111a1 MUM a cm= -0.2 -0.6 0 2 tif (Rater 4 6 ) Figure 5: Computed static pressure coefficient at Tp0.2.5 for singlestage computations at a stationary probe located along the rotor/ stator interface for a) inviscid computation and b) viscous computation. c) Measured value for cifl.24 between rotor and stator at pos. 8 shown in Fig. 2. Circumferential variations of pressure and throughflow. A comparison between the inviscid/compressible and viscous/ incompressible solutions for the single-stage axial compressor is given below. More details can be found in a parallel study in (Saxer et al., 1999). In Figures 6a) and 6c), the instantaneous streamlines are drawn in an absolute frame of reference showing the RS cell captured by the two CFD methods. The solutions outline identical basic flow features, though the axial extent of the RS cell in the viscous solution seems smaller. Also shown are the static pressure coefficient and flow coefficient profiles along the rotor/stator interface for both CFD solutions (Fig. 6b)). This type of pressure and axial velocity profile agrees well with idealized 1-D inviscid models (Cumpsty & Greitzer, 1982), (Gyarmathy, 1996), which consider momentum exchange between sound and stalled flow. At the cell front (F), a pressure low accelerates the stagnant fluid in the rotor channels leaving the cell and decelerates the sound flow in the stator channels as these enter the cell. 7 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms ACp \ .\ b ' \--' \ • viscous - ) single-stage abs. ) single-stage abs. los , Figure 6: a) Instantaneous streamlines in absolute frame of reference from inviscid computation, b) momentary profiles of static pressure and flow coefficients along the rotor/stator interface, c) instantaneous streamlines in absolute frame of reference from viscous computation. viscous inviscid ) single-stage cell lot ) single-stage cell fox. Figure 7: Instantaneous streamlines in RS cell frame of reference for a) single - stage inviscid and b) single - stage viscous computations. inviscid inviscid a) two-stage abs. fox. b) two-stage cell for. Figure 8: Instantaneous streamlines in a) absolute frame of reference and b) cell frame of reference for two-stage inviscid computations. 8 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms between the computed cases, the RS cell shown in Fig 7a) is represented at an instantaneous and slightly larger flow coefficient of 9=0.27. In addition, the experimental correlations by Day et al. (1978) show that the blockage increases with the number of stages. Between stage I and 2, within the RS cell, the flow in the absolute frame of reference is nearly tangential in the direction of rotation with a velocity up to twice the rotor speed. This high-speed tangential motion produces trailing edge flow separation and vortex roll-up in stator I, blocking the stator passages as seen in the middle of Fig. 8a). Flow visualization near the trailing edge of the last stator. A blowup of the stator flowtield represented by trajectories of numerical bubbles set in three channels (representing the middle portion of the RS cell) is displayed in Figure 9 for the inviscid/compressible single- and two-stage solutions together with photographs taken near the stator trailing edge of stage 4 in the test rig. The time-lag At corresponds to the passage of 113 of the RS cell. The video camera shutter time is 4 ms corresponding to a streak length of 0.22 blade pitch for particles travelling at 1.12=2.1 m/s. To produce a similar effect in the CFD solution, the position of three ghost bubbles are shown in addition to the current bubble position corresponding to a streak length of 0.21 blade pitch for particles travelling at C/ 2=164.08 m/s. Almost identical flow features are found in the two CFI) solutions. As mentioned above, the suction pulse at the cell front drives exit-domain fluid back into the stator passages, producing a separation at the trailing edge. The suction side due to a trailing edge separation. This vortex grows and decays in size as the cell passes by and is finally expelled at the cell rear due to the pressure pulse seen in Fig. 6b). The evolution of this vortical feature is explained in more detail below when comparing flow visualization in the single- and the two-stage case with in-house experimental data. Whereas these global flow structures agree well between the two computed solutions, the size of the recirculation bubble upstream of the rotor is larger in the inviscid solution than in the viscous one. In the stator channels, identical flow features are found in the two CFD solutions, though the magnitude and size of the trailing edge vortex may differ. IV.4 Two-staae inviscid solution Rotating stall cell structure. Instantaneous streamlines drawn in the absolute and in the cell-based frame of reference are depicted in Figure 8 for the two-stage in viscid/compressible computation at =O.25. One point to notice first is that the flow features located upstream of the first rotor and behind the last stator are very similar to the single-stage cases as described above. The blockage and the axial extent, though, as inferred from the limiting streamlines in the cell-based frame of reference, are larger than in the single-stage inviscid/compressible case (compare Fig. 8a) with 6a) & Fig. 8b) with 7a)). This is consistent with the observation that although the mean operating points are the same stagnation point at stagnation point tagnation point a) single-stage b) two-stage c) experiment Figure 9: Trajectories of tracer particles in the last stator, shown in the absolute frame of reference at two instants separated by a time lag ha corresponding to the passage of the third of the RS cell (At = XTR513). a) single-stage computation, b) two-stage computation, c) experiment. In the experiment the streak length is 0.22 blade pitch for particles travelling at U2=2,I m/s and 0.21 blade pitch in the CFD solutions for particles travelling at C12=164.08 m/s. 9 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms separated flow rolls-up into a vortex near the suction side (solid box). As the RS cell moves through the stator, this vortex grows, lifts up from the suction surface and moves towards the pressure side. Simultaneously, the stagnation point on the pressure surface moves towards the trailing edge and the flow behind the stator becomes more tangential (solid box at a later time). As the RS cell is leaving this portion of the stator, the positive pressure pulse at the cell rear drives sound flow coming from the rotor into the stator channel and confines the vortex near the trailing edge on the pressure surface, until it is washed out in the exit region. The location of the stator trailing edge vortex, its motion, the location of the stagnation point and the direction of the flow behind the stator are consistent with the experiment (Fig. 9c)). Unsteady static pressure traces. The computed inviscid/compressible, normalized static pressure traces for the two-stage axial compressor are shown for 6 rotor revolutions and five axial stations at(T0.25 in Figure I Oa). These represent the unsteady pressure fluctuations recorded by spatially stationary numerical probes, which are located as indicated in the figure at axial stations II, 12, 2, 22 and 23 (see also Fig. I). It has to be mentioned that the mean pressure rise per stage is only 0.5, which is not apparent in Fig. 10a) due to the normalization. This means that the pressure fluctuations associated with RS are quite intense in comparison to design flow pressure differences. The traces indicate the passage of a time-periodic fully developed single RS cell travelling at 62% of the rotor speed. The comparison between the traces at the rotor/stator interfaces in stage I and 2 (stations 12 and 22) indicates that a more clearly defined RS pattern is computed in stage 2. In the unstalled portion of the flow, the circumferential pressure gradient is more uniform in stage 2 (station 22) than in stage 1 (station 12). This is consistent with our experimental observations, which show the measured casing wall pressure traces between the rotor and stator of stages 2 and 4 (pos. 2 & 8 in Fig. 2c)) for Tc=0.26 in Figures I la) & c), respectively. Considering the flow inbetween stages, i.e. station 2 in Fig. 10a), notice that the 14% blockage value is somewhat misleading. Indeed the circumferential extent of the RS cell is almost constant throughout the two stages, as deduced from the inspection of the cell structure in Fig. 8b). Notice the plateau in the circumferential pressure distribution outside the RS cell, which contrasts with the pressure gradient found at the rotor/stator interfaces of stage 1 & 2 (stations 12 and 22, respectively). This plateau is qualitatively observed in the experiments (Fig. 11b), i.e. between stage 3 and 4 in the water model (pos. 7 in Fig. 2c)). Ahead of the first rotor in Fig. 10a) (station 11), the drop in static pressure corresponds to the passage of a vortex trapped in a large recirculation bubble forming the RS cell, as explained above. Overlooking the local blade passing effects, a fairly smooth pressure gradient within the sound flow between the peaks is computed. This suggests that the RS cell acts as an obstruction like a cylindrical solid body placed in a potential flow producing a potential field deflecting the incoming flow, as postulated above. Behind the last stator (station 23), the amplitude of the fluctuations due to the passage of the RS cell is about 1/3 of the one encountered within the stages. This behaviour is consistent with the experimental observations of (Das & Jiang, 1984). In our measurements (see Fig. 1 I d)) taken at the stator exit of stage 4 (pos. 9 in Fig. 2c)), the trace shows a similar behaviour with the CFD one shown in Fig. 10a) at station 23. Unsteady flow coefficient Similarly to the unsteady pressure, timetraces of the local flow coefficient are plotted in Figure 10b) for the axial stations 11, 12. 2, 22 and 23. The passage of the RS cell is associated with regions of low throughflow and strong backflow within its center. In the sound flow region, the flow coefficient is increasing from inlet to exit. Interestingly, the mean throughflow in the sound flow region = 0.46) corresponds to the value obtained for operation in the stable branch of the characteristic at the same pressure rise (see Fig. 3), as originally con-elated from experimental data by Day et al. in 1978. Unsteady tangential flow angle. The evolution of the absolute tangential flow angle during RS is plotted in Figure 10c). As already inferred from Fig. 8 the passage of the RS cell is marked by an abrupt change of flow direction. Three different patterns are seen within the two-stage machine. Ahead of the first rotor (station 11), the angle within the sound flow region evolves smoothly from the value set by the inlet guide vane (i.e. inlet boundary conditions) to almost tangential conditions as the RS cell approaches the numerical probe. Within the RS cell near the cell front, the flow is nearly tangential in the direction of the rotor rotation, as experimentally observed by Das & Jiang (see Figs. 6 & 12 in Das & Jiang, 1984) and Mathioudakis & Breugelmans (see Fig. 8 in Mathioudakis & Breugelmans, 1988). At the rotor/stator interfaces of stage I and 2 (stations 12 and 22. respectively), the flow changes abruptly from tangential in the direction of rotor rotation to the opposite direction during the passage of the RS cell. This produces strong vortical flow, as seen in Fig. 8. The third pattern is identified between stage I and 2 and downstream of stator 2 (stations 2 and 23, respectively). In the sound flow region, the tangential angle closely matches the value obtained in the unstalled branch of the characteristic obtained at a throughflow above the design value (since c s„no fl ow > o• Within the RS cell the flow is almost tangential. The small bump observed bserved during stall downstream of stator 2 (station 23) is an indication of the vortex shedding mentioned in Section IV.3. Absolute velocity. The time-variation of the absolute velocity normalized by the rotor speed U2 is plotted in Figure 10d). Within the RS cell the above mentioned nearly tangential velocities ahead of rotor I and 2 are much larger than the velocity in the sound flow. At the rotor/ stator interfaces 12 and 22, the opposite is computed with fluid of low velocity found ahead of stators. This behaviour is confirmed by the measurements of Das & hang (1984) at midspan. The 2-D assumption is supported by cross-analysis with experimental data obtained in other subsonic compressors, for example (Das & Jiang, 1984), which indicate that 3-D effects strongly diminish as the axial gap between blade rows decreases for this type of high hub/tip ratio blading. This is pointed out as the axial gap in the geometry under investigation is even smaller than the smallest axial gap studied in (Das & Jiang, 1984), (i.e. 0.29 chord length compared to 0.4, and 0.7 hub/tip ratio compared to 0.82 in this study). On the other hand these same experiments (midspan values at a normalized axial gap of 0.4) confirm most of the key flow features defining the structure of the RS cell computed in this study. 10 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms _ 11 \-7C, \:° b) 1.1 0.8 d) 2.4 c) 1.0 0.6 90 0.5 0.4 60 0.0 0.2 -0.5 0.0 • 1.0 2 1.5 1.5 0.8 1.0 0.6 0.5 0.4 0.0 0.2 •03 0.0 -1.0 .2 4 -1.5 1.5 RS eel 0.8 1.0 0.6 0.5 0. 00 0.2 .0.5 0.0 60 a2 &sip= -30.3° a2 1 16 0.8 2 0.4 0.0 0.8 2.4 TV T44.40.621 1.5 1 .0 aCp22 C22IU' 0.6 0.5 0.4 0.0 0.2 1.6 30 0.0 4.54 Some 60 90 • 1.5 1.5 0.8 I 02 0.6 ,14,. 0.0 I 4 2 30 .2 i 2.4 90 30 0.2 i 00 60 0.4 . 0.8 -30 2 -1.0 so 1.4 6 0 VT (Rotor Revs.) 4 90 6 0 VT (Rotor Revs.) 00 6 0 2 t/T (Rotor Revs.) 2 4 6 VT(Rotor Revs.) Figure 10: Variation of flow parameters in time at different axial positions during RS operation for the two-stage computation at T:=0.25. Top: first rotor inlet, bottom: last stator outlet. a) Static pressure coefficient, b) flow coefficient, c) absolute flow angle, d) ratio of absolute velocity to rotor speed. Values are recorded by stationary probes placed at different axial positions. 81) b) ACp pos. 2 2 VT (Rotor Revs.) 6 ACp pos. 7 C) d) ACp pos. 8 0 6 0 VT (Ro(or Revs.) VT (Rotor Revs.) 2 aCp pos. 9 4 6 VT (Rotor Revs.) Figure 11: Variation of static pressure in time at different axial positions (see Fig. 2c)) during RS operation for the experiment at j= O.26. II Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms V. SUMMARY AND DISCUSSION VI. CONCLUSIONS Rotating stall is analyzed in a single- and two-stage subsonic axial compressor using two numerical methods for unsteady flows and experimental data. One method (MULT12) is based on the Euler equations for an inviscid/compressible fluid, while FENFLOSS solves the Navier-Stokes equations for incompressible flow. With solutions presented for one operating point in the RS regime at 64% of design flow, the two methods are able to consistently reproduce the periodic propagation of a fully-developed single rotating stall cell in more than qualitative agreement with the experimental observations. When comparing the inviscid/compressible with the viscous/ incompressible solution in the single-stage configuration, the global structure of the RS cell and the essentials of its dynamic behaviour are found to be remarkably similar, although no "optimization" (grids, parameters) of the two methods has been attempted here. For example, a noteworthy common feature is the formation of a moving recirculation bubble ahead of the rotor (i.e. in the inlet region) comprising two counter-rotating vortices dividing the incoming flow in two streams suggesting that the stagnant fluid contained in the RS cell acts as an obstruction like a cylindrical solid body placed in an otherwise potential flow. The major differences between the inviscid and viscous cases concern essentially the strength of recirculation areas and, to a lesser extent, the RS speed of propagation. This suggests that the speed of propagation of the RS cell could be finked not only to the row-to-row momentum exchange mechanism but also to the strength of the large recirculation bubble upstream of the rotor. The use of numerical techniques involving different physical assumptions (inviscid vs. viscous, compressible vs. incompressible) to generate RS suggests that the inception mechanism does not appear to influence the final structure of the fully-developed rotating stall pattern. A two-stage MULTI2 solution is presented for the same operating point in the RS regime. Ahead of the first rotor and behind the last stator the flow features are similar to the single-stage solutions. Both at the first and second stage rotor/stator interfaces a momentum exchange mechanism takes place between the blade rows entering and leaving the stalled cell, i.e. at the RS cell front and rear boundaries. This phenomenon is also identified in the single-stage CFD solutions and confirmed experimentally by analysis of the circumferential static pressure traces. It is also consistent with 1-D idealized models (Cumpsty & Greitzer, 1982), (Gyannathy. 1996). In the interspace between stage I and stage 2 a tangential flow in the direction of rotation is produced with a velocity much larger than the rotor speed. This generates trailing edge separation and vortex roll-up blocking the stator passages of the first stage. Downstream of the last stator, tangential flow, vortex roll-up and vortex shedding is computed in both the single- and two-stage cases. Both CFD solutions of the single-stage and two-stage cases are compared with experimental data obtained in a water model of a fourstage subsonic axial compressor of equivalent geometry. The static pressure traces and the flow visualization compares well with the CFD solutions. The major difference lies in the amplitude of the pressure spikes, which scales like the ratio of experimental to CFD blade count number per row. The 2-D assumption in the computations is supported by comparisons with in-house experimental data on key flow features as well as by other experimental studies with a similar hub/tip ratio, for example (Das & Jiang. 1984), where 3-D effects are shown to be small for the short axial gaps modelled in this study. A numerical study of the structure and propagation of fullydeveloped, full-span rotating stall is presented for a single- and twostage subsonic 2-D axial compressor. The conclusions derived from the analysis of the CFD results (inviscid/compressible and viscous/ incompressible) and the experimental data obtained in a 4-stage water model can be summarized as follows. • A strong recirculation bubble comparable in size to the circumferential width of the RS cell lies ahead of the first rotor. High speed flow occurs between this recirculation zone and the first rotor. This feature is common to both the single- and the two-stage solution. • The momentum exchange between blade rows at the rotor/stator interface applies in both the single- and the two-stage machine. This confirms the essentially inertial nature of the driving mechanism for the propagation and structure of full-span, fully-developed RS. • A different RS flow structure is found at the stator/rotor interface (in between stages) compared to the one observed within stages at the rotor/stator interface. In this respect, the blockage value based on unsteady static pressure traces seems to be a poor indicator of the cell width, when applied in between stages. • In the two-stage solution, the flow in the interspace between stage 1 and stage 2 is characterized by a large tangential velocity (up to twice the rotor speed) within the RS cell producing a multiple flow separation and corresponding blockage of the first stage stator passages. • Using CFD flow visualization in both the absolute and cell-based frames of reference offers a more complete picture of the structure of RS. This provides the missing link between the features observed in the in-house and other experiments. REFERENCES Breugelmans, F. A. E., Mathioudalcis, K. Casalini, F., 1985: "Rotating Stall Cells in a Low-Speed Axial Flow Compressor", AIAA Journal of Aircraft, Vol. 22, No. 3, pp. 175-181, March. Camp T. R. and Day I. 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Gyarmathy G., I 998b: "Numerical and Experimental Study of Rotating Stall in an Axial Compressor Stage". AIAA Paper 98-3298, Presented at the 34th AIAA/ASME/SADASEE Joint Propulsion Conference & Exhibit, July 13-15, 1998, Cleveland. OH. Tryfonidis M., Etchevers 0., Paduano J. D., Epstein A. H., Hendricks G. J., 1995: "Pre-Stall Behavior of Several High-Speed Compressors", ASME Journal of Turbomachinery, Vol. 117, No. I, pp. 62-80. 13 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms