Assessment of the Self-Recirculating Casing Treatment Concept to Axial Compressors

Transcription

1 AIAA Assessment of the Self-Recirculating Casing Treatment Concept to Axial Compressors Vishwas Iyengar * and Lakshmi N. Sankar Georgia Institute of Technology, Atlanta, Georgia and Saeid Niazi Sukra Helitek, Inc., Ames, IA, Performance characteristics of a transonic axial flow compressor called NASA Rotor 67 have been analyzed using a three-dimensional time accurate Navier-Stokes analysis. The operating range is limited at low-mass flow rates due to the occurrence of 3-D stall which grows with time causing surge. This study investigates the use of a passive technique called Self-Recirculating Casing Treatment that has been proposed at the U.S. Army Research Lab to alleviate the stall phenomenon and restore stable operation for previously unstable conditions. It is demonstrated that the stable operating range can be extended by delaying the initiation of surge. P 0 T 0 P P V P m c m t K κ a P γ Nomenclature = total pressure = total temperature = plenum pressure = plenum volume = exit mass flow rate = plenum throttle mass flow rate = plenum chamber constant = recirculation loss factor = speed of sound in the plenum chamber = Ratio of specific heats I. Introduction IGH-speed, high pressure ratio axial compression systems are widely used in many aerodynamic applications. H These devices often have a limited mass flow rate range over which stable operation occurs. At low-mass flow rates fluid dynamic instabilities develop causing a deterioration of the system operations. Two specific types of instabilities rotating stall and surge- have been observed in practice. Rotating stall is essentially a 2-D unsteady local phenomenon where the flow is no longer periodic from blade to blade. The stalled regions rotate about the shaft axis and jump from blade to blade. This can lead to blade vibrations and fatigue. * Graduate Research Assistant, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA , Student Member AIAA. Regents Professor and Associate Chair (Academic), School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA , Associate Fellow AIAA. Aerospace Engineer, Sukra Helitek, Inc., 3146 Greenwood Rd., Ames, IA , AHS Member. Copyright 2005 by Vishwas Iyengar, Lakshmi N. Sankar and Saeid Niazi. Published by the American Institute of Aeronautics, Inc. or the American Society of Mechanical Engineers with permission. 1

2 Surge is a self excited cyclic phenomenon affecting the whole compression system. It is accompanied by low frequency fluctuations in pressure and mass flow rate. A complete reversal of flow is also possible. Surge is classified into four different types based on the severity of flow and pressure fluctuations: Mild surge, Classic surge, Modified surge, Deep surge. Throughout the aero-propulsion history, much work has been done on broadening the compressor operating range. Various control strategies have been proposed to alleviate rotating stall and surge. Much of the pioneering work on the control and alleviation of rotating stall and surge was done using carefully conducted experiments and through phenomenological models of stall and surge. With the growth of Computational Fluid Dynamics (CFD) as a valuable analysis tool, it has now become possible to simulate and understand the physics behind rotating stall and surge. Three dimensional codes capable of analyzing unsteady turbomachinery flow with single and multiple blade passages have been developed by several researchers 1-5. Most of these studies have been limited to modeling steady flow phenomena in axial and centrifugal compressors, near or at, design conditions. There have also been limited attempts to model active and passive control methodologies which can alleviate the stall/surge phenomena. It has been found that the adverse flow conditions in the tip clearance can region cause surge/stall phenomena and reduce the pressure rise, flow range, and efficiency of the turbomachinery. Blockage development in a transonic axial compressor rotor was studied by Suder 6, and the impact of shocks on blockage was investigated. Chima 7 studied the tip clearance effects on a transonic compressor rotor. The interaction of the tip vortex, the passage shock, and the casing boundary layer were studied using the computations. End wall and casing treatments for a NASA Rotor 67 configuration have been investigated by Crook et al 8. The present authors have developed a 3-D unsteady flow solver, GT-TURBO3D (Georgia Tech-Turbomachinery 3D), that is capable of modeling multi-stage axial and centrifugal compressors. Ref. 9 and 10 report results from the application of this solver to a NASA low-speed centrifugal compressor. Niazi et al 11 performed numerical simulation of rotating stall and surge alleviation for an axial compressor (Rotor 67). Active control methods such as bleeding and injection were studied, with the objective of extending the stable operating range of compressors. Open and closed loop bleeding was investigated by Niazi 11-12, while leading edge steady and pulsed jet concepts were studied by Stein 13. These authors reported an increased operating range with the employment of active control techniques. Active Control techniques are adaptive, flexible, and effective. They have two drawbacks. Since the air is being bled, there is a loss of high pressure air which reduces the total pressure rise across the compressor, and the efficiency. Secondly, it is necessary to have a properly designed active controller and actuator, which may involve moving parts. Passive control concepts (e.g. casing treatment) are limited in extending the compressor operating range, but do avoid these drawbacks. One passive control concept called self-recirculating casing treatment model was recently proposed by Hathaway 14 and has already been applied by him to a multiple passage NASA Rotor 67 configuration. In this approach, high pressure air is bled from a port downstream of the rotor, and injected upstream of the blade leading edge, as shown in figure 1. Hathaway was able to extend the possible stable operating range of the compressor with little or no loss in the overall compressor efficiency. II. Research Objectives The objective of the present research is to understand and independently verify Hathaway s self-recirculating casing treatment concept by applying to a single stage of the NASA Rotor 67 rotor configuration. This is done through an examination of the flow features when the rotor undergoes 3-D stall. The self-recirculation control is subsequently initiated, and the resulting beneficial effects on the flow features are documented. These qualitative studies are augmented by an extraction of relevant quantitative information (performance map of the compressor) at on- and off-design conditions, and comparison with available experimental data. III. Configuration The NASA Rotor 67 configuration was selected for this computational investigation. There is a large body of experimental and computed data available for controlled and baseline configurations. The design pressure ratio for the Rotor 67 configuration is 1.63, at a mass flow rate of kg/sec. The rotor has 22 blades with a design rotational speed of rpm. The tip leading edge speed is 429 m/sec with a tip relative mach number A nominal H-H type grid with 125 cells in the streamwise direction, 63 and 41 in radial and circumferential directions, respectively was generated using GRIDGEN package. The clearance gap was spanned by six cells in the radial direction. The body fitted H-grid used in this study is shown in figure 2. 2

3 Mass flow rate and total pressure ratio through the compressor were monitored as a convergence criterion. The entire flow field was saved at selected time levels for diagnostic purposes. In general, calculations needed to be carried out for 1½ to 3 compressor rotor revolutions before steady convergence, or limit cycle oscillations, could be attained. IV. Boundary Conditions The following boundary conditions were used in this study. The present analysis is capable of more general situations (e.g. multi-stage rotor-stator configurations, non-uniform inflow and outflow). These situations are not relevant to the present study, and are not discussed here. Inflow Boundary: The total pressure P 0 and the stagnation temperature are assumed to be known at the inflow boundary. The tangential components of velocity at the flow boundary conditions are set to zero, assuming no swirl. 2a The Riemann invariant v n was extrapolated from the interior, where a is the local speed of sound and v n γ 1 is the velocity component normal to the inlet. Outflow Boundary: The analysis can operate in one of two modes prescription of static pressure at the exit, or a prescription of the mass flow rate through the system. In this study, the desired mass flow rate was specified. It is assumed that the outflow downstream of the rotor exhausts into a plenum chamber with a constant volume V P. From conservation of mass and isentropic gas law it can be shown that the pressure in the plenum P P varies as: dp dt p 2 p a = ( mc mt) (1) V p In the above expression m c represents the computed mass flow rate at the downstream plane, and m t is the desired or target mass flow rate (assumed to leave the plenum through a throttle valve). A first order discretization of equation (1) gives: n 1 p c t n P + = P + K( m m ) (2) p The constant K in equation (2) is dependent on the plenum chamber volume, and the time step chosen. For the purpose of this study K is chosen as The three components of velocity and the total temperature T 0 are extrapolated from the interior. Density is subsequently found from the equation of state. Periodicity: Only one blade passage is modeled in this study as the simulation of the entire flow requires significant computational resources. It is assumed that the flow through the blade passage (when viewed in a rotating coordinate system) is identical from one passage to the next, and periodic boundary condition is applied. The flow properties at the block boundaries are computed by averaging the properties on either side of the boundary at the periodic boundaries. Zonal Boundaries: The flow field is divided into patched zones where neighboring zones share grid lines on their boundaries. At the zonal boundaries the flow properties are computed by averaging the properties on the neighboring points. Solid Walls: A no-slip boundary condition is used at the solid walls. The flow velocity at the grid points on the compressor blades and the shaft were set equal to Ω r, while the velocity on the walls of the inlet and diffuser were set to zero. Density, pressure and temperature values at all the solid surfaces were extrapolated from the interior. 3

4 Self-Recirculating Casing Treatment Boundary Conditions: The self-recirculating casing treatment model is shown in figure 1. The bleed port is located on the casing downstream of the blade, and the injection port is located upstream of the blade casing. In the present work, these were modeled as slots that run azimuthally along the casing from one blade to the next. The bleed port areas were controlled by changing the width of the slots.. Conservation of mass requires both bleed ( m ) and injection ( m 1 2 ) mass flow rates to be the same. Conservation of energy requires that the total temperature of the bled fluid be the same as that reintroduced at the injection port. Thus, we require: m& = m& T01 = T02 (3) We also assumed that there was a total pressure loss in the duct connecting the bleed ports and the injection ports. Thus, p0,2 = ( 1 k) p0, 1 (4) In this study κ was set to 0.2, assuming a 20% loss. Hathaway has used a similar model in Ref. 13. Bleed Boundary: The bleed/injection port locations, the bleed/injection port cross sectional areas, and static pressure at the bleed port are all user specified inputs. These were arbitrarily chosen in this study, and no attempt has been made to optimize these quantities. The pressure at the bleed port was set to 0.9 P, ensuring an adequate pressure drop between the flow immediately behind the compressor and the bleed port. This parameter may be varied to increase or decrease the amount of bleed mass flow rate. A more effective way of changing the flow rate is to change the bleed port width, and hence the port cross-sectional area. This was done in the present work. The density and two tangential components of velocity are extrapolated from the interior. The bleed port area is sized large enough to ensure that the flow will not choke. The normal velocity V n at the bleed port was also extrapolated, and we subsequently computed the bleed mass flow rate m& = ρa where A 1 is the bleed port cross-sectional area v n Injection Boundary: At the injection boundary, since m & 1 = m& 2, the total mass flow rate is known. T 02 and P 02 are also known as discussed earlier. The static pressure is extrapolated from the interior of the compressor flow field to the injection port as the jet is subsonic. The isentropic relations (Equation 7 below) were used estimate T 2. The density is subsequently found from the equation of state (Equation 8 below).. P P γ 1 T = γ T (7) P= ρrt (8). m = ρ Av n2 (9) 2 2 vn vt CT p 02 = CT p (10) The normal component of velocity is found from (Eq.9). The other components of velocity (tangential to the port) were chosen from a combination of yaw angle (zero here), and T 02 (Eq.10). V. Results Before applying the present analysis to off-design conditions, a careful validation of the flow solver was done at the design mass flow rate (33.25 kg/sec). The code validation studies and agrid convergence studies are documented in the Ph D dissertation of Niazi 11, found at and are not reproduced here for brevity. 4

5 A. Off-Design Analysis (without recirculation control) One way to assess the performance of a compression system is by mapping the the total pressure ratio as a function of the mass flow rate through the compressor. In experiments, such a performance map is usually obtained by changing the mass flow rate using a throttle valve in the plenum chamber. Calculations were done at various prescribed mass flow rates, in order to obtain the complete performance map for the Rotor 67 configuration. 15 different operating points ranging from design to off-design conditions were investigated. Figure 3 shows the computed and measured performance map. The total pressure ratios at full speed (100% RPM) are plotted against mass flow rate normalized by choked mass flow rate. Stable operating range was found to occur is between kg/sec (approximately 8% below the choked mass flow rate) and kg/sec. As the mass flow rate was decreased, the system first entered into a limit cycle oscillation. It was found that the amplitude of the associated temporal variations in the total pressure ratio increased as the target mass flow rate was decreased. Range bars are shown in figure 3 at the off-design operating points below the stable range to give an indication of the amplitude of these oscillations. An examination of the flow field, to be discussed below, indicated the onset and progressive growth of 3-D reversed flow within the blade passage. The details of the flow were studied at three points, A, B and C, indicated on the performance map. Point A corresponds to the peak efficiency condition while points B and C correspond to off design mass flow rates of 31.8 kg/sec and 31.5 kg/sec, respectively. Velocity vector plots in the meridional plane along with temporal history of the mass flow rate and of the total pressure ratio were used to investigate the onset of stall/surge regime. Many researchers 6-8, 14 have reported that aerodynamic blockage at the casing (or end-wall) rapidly grows as the compressor approaches the state of stall. Leading-edge vortex and tip-clearance vortex can lead to end-wall blockage. The generation of the leading edge vortex at Point B is clearly seen in figure 4, which shows a top view of the path of particles originating at the leading edge. It has been postulated that this vortex acts as an obstruction that extends across the passage and produces a wake-like structure along its entire length. The associated low momentum flow at the leading edge can aggravate the aerodynamic blockages at the blade/end-wall. As pointed by Chima 7, the flow in the vicinity of the blade is strongly affected by the roll-up of the leading edge tip vortex. In our flow visualization studies of point C it was found that the temporal growth of these vortices can result in large regions of reversed flow in the vicinity of the blade tip. Because it was difficult to assess the flow features solely from plots of the particles in the tip vortex region, the velocity field in the mid-pitch plane was monitored to get an understanding of the flow physics. Figure 4 shows the velocity vector plots in the meridional plane at mid blade pitch for point B. Limit cycle, nearly-periodic growth and shrinkage of the recirculating region was observed for point B. It appears that the low momentum boundary layer fluid adjacent to the end-wall interacts with the leading edge vortex and triggers a reversal of flow near the leading edge. Point B is a stable condition, in that the separated flow vectors, mass flow rate, and the total pressure ratio exhibit limit cycle oscillations that hover around nominal time averaged values. These oscillations do not grow unbounded with time, and are thus stable. Point C, shown in figure 5, on the other hand is an unstable operating condition. It is seen that the separated flow region first appears around ¼ cycles of blade rotation, and rapidly grows with time. If left unchecked, this will lead to an uncontrolled temporal and spatial growth of the reversed flow and surge. Another way to investigate the stability of the compressor is by monitoring the fluctuations in the compressor mass flow rate and total pressure ratio. The mass-flow rate and total pressure ratio variation at points A, B and C are shown in figure 7. These plots show the fluctuation of the compressor mass flow rate from the time-average mean value against the total pressure ratio fluctuation from its time-averaged mean value. Under stable operation these fluctuations should steadily approach the origin or exhibit small limit cycle closed trajectories around the origin. At off design conditions these fluctuations would spiral out as high amplitude fluctuations. At the peak efficiency operating condition A, figure 7a shows that the variation between the compressor mass flow rate and total pressure is minimal, indicating that this is a stable operating point. At Point B, figure 7b shows an increased variation between the total pressure ratio and the mass-flow compared to the figure 7a, suggesting the onset of unstable operation. At the operating point C (figure 7c), somewhat larger amplitude fluctuations in both mass flow rate and total pressure ratio were observed compared to figure 7b. From the above diagnosis it is clear that the compressor experiences large amplitude instabilities at off-design conditions. As a result of these instabilities, highly complex three dimensional unsteady flows occur near the blade. The authors suspect that at operating point C, the compressor is in a state of modified surge, which is a combination of rotating stall and surge. 5

6 Off design Analysis with Self-Recirculating Casing Treatment Control Following the above study of the anatomy of the flow field in the vicinity of stall and surge, we applied Hathaway s self-recirculating casing treatment concept to NASA Rotor 67, at two mass flow rates. Condition D corresponds to kg/sec, while condition E corresponds to a mass flow rate of kg/sec. These mass flow rates are well below those of points B and C. The bleed port width was adjusted so that 0.75% of the total mass flow rate is bled at Port 1 downstream of the rotor (and reinjected upstream at Port 2). Figures 8 and 9 shows the time history of the flow field near the tip at mid blade pitch at the new stable operating points D and E, respectively. The development of the leading edge vortex can be noticed after half a revolution, but it can be observed that unlike the uncontrolled case the region of reversed does not increase in size. Even after one and a half rotor cycle the reversed flow region is highly localized and does not affect the flow at the trailing edge. The region of separated flow at the trailing edge has been completely eliminated. An overall comparison between Figures 8-9 and Figure 6 shows that the self-recirculating casing treatment has been effective in restoring attached flow over much of the tip section. Path of particles originating at the leading edge for point E is shown in figure 10. Although the overall path of the vortex has not been significantly altered, it can be observed that the leading edge vortex does not move as much in-board on the blade as previously observed in Figure 3 for condition C. The performance map of the rotor equipped with self-recirculation control is shown in Figure 11. It is seen the previously unstable points B and C have been replaced with two stable point D and E, and the useful operation of the compression system has been extended to kg/sec (89.8% of choked mass flow rate). In other words, with the use of the self-recirculation control concept, the compressor can be usefully operated between kg/sec and kg/sec. It may be recalled that the stable operating range without control was between kg/sec and kg/sec. Thus, due to the application of the self-recirculation control, the stable operating range has been extended by 26.5%. This is a considerable extension in range that will benefit modern transonic compressors that tend to have a very limited range of stable operation. In order to understand more about how and why the self-recirculation mechanism works, the flow field in figure 8 and 9 are revisited. By bleeding approximately 0.75% of the mean flow downstream of the blade, the previously existent trailing edge blockage is relaxed and the region of reversed flow is alleviated. The hypothesis behind bleeding is that at lower mass flow rates, the working fluid does not have adequate momentum to overcome the adverse pressure gradient and viscous forces. As a consequence of bleeding, the flow has been accelerated by removing some of the highly pressurized flow downstream of the compressor. All of the bled mass is injected upstream of the blade to fill the mass deficit associated with the leading edge tip vortex. The low momentum flow at leading edge is energized and the region of reversed flow has shrunk in size. As discussed earlier, the leading edge tip vortex does not propagate inboard over the blade and this allows the rotor blade to operate in an efficient manner. Figure 12 and 13 shows the fluctuations between total pressure ratio and mass flow rate with and without control for operating points D and E respectively. It is evident from the plot that the fluctuations have shrunk considerably with control compared to the case without any control. The time history of the mass flow rate deviation from the average compressor mass flow for points D and E are shown in figures 14 and 15 respectively. It was found that the oscillations from the average value have been damped out with the use of control. These findings further substantiate that the compression system operates in a stable manner and that the initiation of the modified surge has been successfully delayed. VI. Conclusions and Recommendations An in-house flow solver GTTURBO3D has been previously validated as a tool for modeling and understanding the unsteady flow often associated with axial flow compressors. In this study, this tool was used to conduct an independent assessment of the self-recirculating casing treatment concept proposed by Hathaway. A diagnosis of the flow field was carried out for the NASA Rotor 67 configuration for off-design flow conditions. It was found that at low operating mass flow rates, the compressor experiences considerable instability due to highly complex separated flow in the tip region. This unsteady flow in the rotor tip region was studied and its association with compressor entering a state of modified surge was identified. Hathaway s Self-recirculating casing treatment was found to be very effective. It was shown that control concept can potentially alleviate the instabilities at lower mass flow rates and hence increase the stable operating range of the compressor. This was traced to the removal of low momentum fluid downstream of the blade trailing edge, and the energizing effects of the flow injection on the leading edge vortex flow field in the tip region. 6

7 The stable operating range was increased from the kg/sec to kg/sec range without any control to kg/sec and kg/sec range with the application of the control concept. This corresponds to a 26.5% extension. This study represents only a first step in independently assessing and understanding this powerful passive control concept. Many of the variables (slot area, slot location, injection area, injection angle, bleed port pressure, etc) have been selected by trail and error, and have not been optimized. By careful optimization of these independent variables, it should be possible to further improve the performance of Rotor 67 and similar rotors. Acknowledgements This work was carried out under the University Research Engineering Technology Institute (URETI) Program on Aeropropulsion and Power Technology, Task The program is sponsored by National Aeronautics and Space Administration (NASA) and the Department of Defense. The authors would like to thank Joseph Gillman for his participation in this study. References [1] Chima, R. V., and Yokota, J. W., Numerical Analysis of Three-Dimensional Viscous Internal Flow, AIAA Journal, Vol. 28, No. 5, 1990, pp [2] Hall, E. J., Aerodynamic Modeling of Multistage Compressor Flow Fields - Part 1: Analysis of Rotor/Stator/Rotor Aerodynamic Interaction, ASME paper 97-GT-344, [3] Dawes, W. N., A Numerical Study of the 3D Flowfield in a Transonic Compressor Rotor With a Modeling of the Tip Clearance Flow, AGARD Conference Proceedings n 401, Neuilly sur Seine, Fr. [4] Hah, C., and Wennerstrom, A. J., Three-Dimensional Flowfields Inside a Transonic Compressor With Swept Blades, Journal of Turbomachinery, Vol. 113, [5] Hathaway, M. D., and Wood, J. R., Application of a Multi-Block CFD Code to Investigate the Impact of Geometry Modeling on Centrifugal Compressor Flow Field Predictions, Transactions of the ASME, Vol. 19, Oct 1997, pp [6] Suder K.L., Blockage Development in a Transonic, Axial Compressor Rotor, Turbo-Expo 97, Orlando, Florida. [7] Chima, R.V., Calculation of Tip Clearance Effects in a Transonic Compressor Rotor, NASA TM , May [8] Crook, A.J., Greitzer, E.M., Tan, C.S., and Adamczyk, J.J., Numerical Simulation of Compressor Endwall and Casing Treatment Flow Phenomena, Journal of Turbomachinery, Vol. 115, July 1993, pp [9] Niazi, S., Stein, A., and Sankar, L.N., Development and Application of a CFD solver to the Simulation of Centrifugal Compressors, AIAA paper , [10] Stein, A., Niazi, S., and Sankar, L.N., Computational Analysis of Stall and Separation Control in Centrifugal Compressors, AIAA paper , July [11] Niazi, S., Numerical Simulation of Rotating Stall and Surge Alleviation in Axial Compressors, Ph.D. Dissertation, Georgia Institute of Technology, Aerospace Engineering, July [12] Niazi, S., Stein, A., and Sankar, L.N., Computational Analysis of Stall Control Using Bleed Valve in a High-Speed Compressor, AIAA Paper [13] Stein, A., Computational Analysis of Stall and Separation Control in Centrifugal Compressors, Ph.D. Dissertation, Georgia Institute of Technology, Aerospace Engineering, May [14] Hathaway, M.D., Self-Recirculating Casing Treatment Concept for Enhanced Compressor Performance, Turbo-Expo 2002, Amsterdam, Holland. 7

8 Figure 1. Hathaway s Self-Recirculating Casing Treatment Model Figure 2. Computational Grid for the Rotor 67 Configuration Figure 3. Computed and Measured Performance Map of the Rotor 67 Compressor Point A corresponds to the peak efficiency condition. Points B and C correspond to mass flow rates of 31.8 kg/sec and 31.5 kg/sec, respectively. 8

9 Figure 4. Top View of the Particle Traces at the Blade Tip for Point B (31.8 kg/sec mass flow rate). (a) After 1/4 cycle (b) After ½ cycle (a) After 3/4 cycle (b) After One full cycle (a) After 1 1/4 cycle (b) After 1 /2 cycles Figure 5: Time history of flow field at operating point B at the mid pitch plane. Periodic formation and mild growth of flow reversal is seen. This is the first unstable operating point. 9

10 Tip LE TE a). After ¼ cycle b). After ½ cycle c). After ¾ cycle d). After 1 cycle e). After 1¼ cycle f). After 1 ½ cycle Figure 6: Time history of flow field at operating point C at the mid pitch plane. The formation and steady growth of flow reversal is seen. Flow reversal starts at the streamwise location approximately near the leading edge and rapidly grows. 10

11 a). b). c). Figure 7: Total pressure ratio and mass fluctuations at a). Point A (34.96 kg/sec), b) Point B (31.80 kg/sec), c). Point C (31.50 kg/sec) 11

12 Injection Tip Bleed LE a). After ¼ cycle TE b). After ½ cycle c). After ¾ cycle d). After 1 cycle e). After 1¼ cycle f). After 1 ½ cycle Figure 8: Time history of flow field at operating point D with control concept at the mid pitch plane. The region of separated flow is minimal compared to figure 4, and does not grow with time indicating that a steady state has been established. 12

13 a). After ¼ cycle b). After ½ cycle c). After ¾ cycle d). After 1 cycle e). After 1¼ cycle f). After 1 ½ cycle Figure 9: Time history of flow field at operating point E with control concept at the mid pitch plane. The region of separated flow is minimal compared to figure 4, and does not grow with time indicating that a steady state has been established. 13

14 Tip Tip Leading edge Trailing edge Leading edge Trailing edge Root Root a). b). Figure 10: Top view of particle traces at the leading edge with recirculation control at Point E, a). Controlled case, b) Figure 3 is reproduced here for one to one comparison. Figure 11: Performance map with self-recirculation control applied to Rotor 67 configuration. Figure 12: Pressure and mass flow fluctuations with and without recirculation control, corresponding to a mass flow rate of kg/sec (Point D). Figure 13: Pressure and mass flow fluctuations with and Figure 14: Time history of the mass flow rate deviation without recirculation control, corresponding to a mass flow 14 from averaged compressor mass flow rate with and without rate of kg/sec (Point E). American Institute of Aeronautics control, and Astronautics corresponding to a mass flow rate of kg/sec (Point D).

15 Figure 15: Time history of the mass flow rate deviation from averaged compressor mass flow rate with and without control, corresponding to a mass flow rate of kg/sec (Point E). 15