1. School of Aerospace Engineering MITE Saeid Niazi Advisor:Lakshmi N. Sankar School of Aerospace Engineering Georgia Institute of Technology http://www.ae.gatech.edu/~lsankar/MURI Supported by the U.S. Army Research Office Under the Multidisciplinary University Research Initiative (MURI) on Intelligent Turbine Engines Numerical Simulation of Rotating Stall and Surge Alleviation in Axial Compressors

2. School of Aerospace Engineering MITE Overview l Objectives and Motivation l Surge and Rotating Stall l Mathematical Formulation l NASA Axial Rotor 67 Results: Peak Efficiency Conditions Onset of Stall Conditions Stall Condition l NASA Axial Rotor37 Results l Bleeding Control Methodology: Active Control I (Open-Loop) Active Control II (Closed-Loop) l Conclusions l Recommendations

3. School of Aerospace Engineering MITE Objectives and Motivation Use CFD to explore and understand compressor stall and surge Develop and test control strategies (bleed valve) for axial compressors Choke Limit Flow Rate Total Pressure Rise Lines of Constant Rotational Speed Lines of Constant Efficiency Surge Limit Desired Extension of Operating Range Safety Margin

4. School of Aerospace Engineering MITE 1 2 1 2 1 2 Blade 1 sees a high  Blade 1 stalls. Blade 1 recovers. Blase 2 stalls. t=0t= 0 + t=0 ++ What is Rotating Stall? Rotating stall is a 2-D unsteady local phenomenon.

5. School of Aerospace Engineering MITE Rotating Stall (Continued) Types of Rotating Stall Full-span Part-span From one to nine stall cells have been reported. Stall cells affect the shape of performance map (e.g. Abrupt stall, Progressive stall).

6. School of Aerospace Engineering MITE What is Surge? Mild SurgeDeep Surge Time Flow Rate Period of Deep Surge Cycle Flow Reversal Pressure Rise Flow Rate Mean Operating Point Limit Cycle Oscillations Pressure Rise Flow Rate Peak Performance Time Flow Rate Period of Mild Surge Cycle

7. School of Aerospace Engineering MITE Movable plenum wall Gysling, Greitzer, Epstein (MIT) Guide vanes Dussourd (Ingersoll-Rand Research Inc.) Casing Treatments Bailery and Voit (NASA Glenn Research Center) How to Control Stall ? Guide Vanes Movable Plenum Walls

8. School of Aerospace Engineering MITE How to Control Stall? (Continued) Air Injection Air-injection Murray, Yeung (Cal Tech) Fleeter, Lawless (Purdue) Weigl, Paduano, Bright (MIT & NASA Glenn ) Alex Stein (Ph. D Dissertation, Ga Tech) Bleed Valves Diffuser bleed valves Pinsley, Greitzer, Epstein (MIT) Prasad, Numeier, Haddad (GT)

9. School of Aerospace Engineering MITE Mathematical Formulation    t q  dV  E ˆ i  F ˆ j  G ˆ k     ndS  R ˆ i  S ˆ j  T ˆ k     ndS Reynolds Averaged Navier-Stokes Equations in Finite Volume Representation: where, q is the state vector. E, F, and G are the inviscid fluxes, and R, S, and T are the viscous fluxes. A cell-vertex finite volume formulation using Roe’s scheme is used in the present simulation.

10. School of Aerospace Engineering MITE i-1 i i+1 i+2 Cell face i+1/2 Stencil for q left Stencil for q right Left Right * * Mathematical Formulation (Continued) Four point and six point stencils are used to compute the inviscid flux terms at the cell faces, For Example for four point stencil: This makes the scheme third or fifth-order accurate in space.

11. School of Aerospace Engineering MITE Mathematical Formulation (Continued) The viscous fluxes are computed to second order spatial accuracy. A three-factor ADI scheme with second- order artificial damping on the LHS is used to advance the solution in time. The scheme is first or second order accurate in time. The Spalart-Allmaras turbulence model is used in the present simulations.

12. School of Aerospace Engineering MITE Boundary Conditions Inlet: p 0,T 0,v,w specified; Riemann- Invariant extrapolated from Interior. Exit:. m t specified; all other quantities extrapolated from Interior. Solid Walls: no-slip velocity conditions;  p/  n=  n = 0 Zonal Boundaries: Properties are averaged on either side of the boundary. Periodic Boundaries: Properties are averaged on either side of the boundary.

13. School of Aerospace Engineering MITE Conservation of mass: Outflow Boundary Conditions mcmc. Outflow Boundary Plenum Chamber u(x,y,z) = 0 p p (x,y,z) = CT. isentropic mtmt. a p, V p All other quantities extrapolated from Interior. Isentropic state in plenum:

14. School of Aerospace Engineering MITE Axial Compressor (NASA Rotor 67) 22 Full Blades Inlet Tip Diameter 0.514 m Exit Tip Diameter 0.485 m Tip Clearance 0.61 mm Design Conditions: –Mass Flow Rate 33.25 kg/sec –Rotational Speed 16043 RPM (267.4 Hz) –Rotor Tip Speed 429 m/sec –Inlet Tip Relative Mach Number 1.38 –Total Pressure Ratio 1.63 –Adiabatic Efficiency 0.93 514 mm

15. School of Aerospace Engineering MITE Literature Survey on NASA Rotor 67 Computation of the stable part of the design speed operating line: NASA Glenn Research Center (Chima, Wood, Adamczyk, Reid, and Hah) MIT (Greitzer, and Tan) U.S. Army Propulsion Laboratory (Pierzga) Alison Gas Turbine Division (Crook) University of Florence, Italy (Arnone ) Honda R&D Co., Japan (Arima) Effects of tip clearance gap: NASA Glenn Research Center (Chima and Adamczyk) MIT (Greitzer) Shock boundary layer interaction and wake development: NASA Glenn Research Center (Hah and Reid). End-wall and casing treatment: NASA Glenn Research Center (Adamczyk) MIT (Greitzer)

16. School of Aerospace Engineering MITE Axial Compressor (NASA Rotor 67) 4 Blocks Baseline Grid: 66X32X21 180,000 Cells Meridional Plane Plane Normal to Streamwise Hub LE TE Fine Grid: 131X63X41 1,400,000 Cells

17. School of Aerospace Engineering MITE Stable Controlled Conditions A B C D E Peak Efficiency Onset Of Stall Stalled, Unstable Performance Map Peak Efficiency, Operating Point A Measured mass flow rate at Peak Efficiency: 34.61 kg/s. CFD mass flow rate at Peak Efficiency: 34.23 kg/s. Fine grid studies gave nearly identical results.

18. School of Aerospace Engineering MITE Adiabatic Efficiency Peak Efficiency Near Stall Radial distributions of total stagnation pressure and temperature were mass averaged across the annulus

19. School of Aerospace Engineering MITE Axial Velocity Profile at the Inlet (Peak Efficiency, Operating Point A) Good agreement between the measurement and the predictions was observed. Grids have enough resolutions to capture the boundary layer profiles.

20. School of Aerospace Engineering MITE 30% Span 70% Span Static Pressure Contours (Peak Efficiency, Operating Point A) Blade to blade periodic flow exists at peak efficiency condition. Near the tip shock becomes stronger.  S P

21. School of Aerospace Engineering MITE Measured Computed Relative Mach Contours at %30 Span (Peak Efficiency, Operating Point A) Small regions of supersonic flow on suction sides near the blade leading edge were observed.

22. School of Aerospace Engineering MITE Shock-Boundary Layer Interaction (Peak Efficiency, Operating Point A) LE TE Shock Near Suction Side

23. School of Aerospace Engineering MITE LE TE Shock Velocity Profile at Mid-Passage ( Peak efficiency, Operating Point A) Flow is well aligned. Very small regions of separation observed in the tip clearance gap (Enlarged view). % Mass Flow rate Fluctuations % Pressure Fluctuations Fluctuations are very small (2%).

24. School of Aerospace Engineering MITE LE TE Clearance Gap Enlarged View of Velocity Profile in the Clearance Gap (Peak efficiency, Operating Point A) The reversed flow in the gap and the leading edge vorticity are growing as the compressor goes to the off-design conditions.

25. School of Aerospace Engineering MITE Performance Map Onset of Stall, Operating Point B Measured mass flow rate at onset of stall: 32.1 kg/s. CFD prediction mass flow rate: 31.6 kg/s. Stable Controlled Conditions A B C D E Peak Efficiency Onset Of Stall Stalled, Unstable

26. School of Aerospace Engineering MITE I IIIII IV LE TE  I II III IV Location of the Probes to Calculate the Pressure and Velocity Fluctuations The “numerical”probes are located at 30% chord upstream of the rotor and 90% span and are fixed. Similar to non intrusive measured at selected locations.

27. School of Aerospace Engineering MITE Mass Flow and Total Pressure Fluctuations (Onset of the Stall, Operating Point B) Compared to the mass flow rate and pressure fluctuations at peak efficiency, point A, the fluctuations increased by a factor of 15.

28. School of Aerospace Engineering MITE Pressure Fluctuations at the Probes (Onset of the Stall, Operating Point B) Rotor Revolution,  t/2  All the Probes show same amount of deviation from their mean value and very close to zero, indicating the flow is periodic from blade to blade and no evidence of stalled cells.

29. School of Aerospace Engineering MITE Performance Map Stalled, Operating Point C The computational averaged mass flow rate at point C is 29.4 kg/s. Stable Controlled Conditions A B C D E Peak Efficiency Onset Of Stall Stalled, Unstable

30. School of Aerospace Engineering MITE Mass Flow and Total Pressure Fluctuations (Stalled, Operating Point C) % Pressure -50 -30 -10 10 30 50 -40-30-20-10010203040 Fluctuations % Mass Flow Rate Fluctuations Compared to the mass flow rate and pressure fluctuations at peak efficiency, point A, the fluctuations increased by a factor of 50.

31. School of Aerospace Engineering MITE Velocity Profile (Stalled, Operating Point C) f=84.0 Hz= 1/70 of blade passing frequency

32. School of Aerospace Engineering MITE Rotor Revolution,  t/2  Probes Average Pressure Fluctuations (Stalled, Operating Point C) Compressor experiences very large pressure fluctuations at the inlet upstream of the compressor face.

33. School of Aerospace Engineering MITE Probes Average Axial Velocity Fluctuations (Stalled, Operating Point C) Rotor Revolution,  t/2  Precursor LevelStall LevelRecovery Level Three Different levels in axial velocity and pressure fluctuations were observed.

34. School of Aerospace Engineering MITE Deviations of Axial Velocities from Their Mean Values at the Probes (Stalled, Operating Point C) Frequency Hz Power Spectral Density Flow is not symmetric from one flow passage to the next. Frequency of stalled cells is 100 Hz (38% of the rotor frequency). Rotor Revolution,  t/2 

35. School of Aerospace Engineering MITE NASA Rotor 67 Results (Rotating Stall) 

36. School of Aerospace Engineering MITE NASA Rotor 67 Results (Rotating Stall)

37. School of Aerospace Engineering MITE Axial Compressor (NASA Rotor37) 36 Full Blades Tip Clearance 0.36 mm Design Conditions: –Mass Flow Rate 20.2 kg/sec –Rotational Speed 17188 RPM (286.5 Hz) –Rotor Tip Speed 454.19 m/sec –Inlet Tip Relative Mach Number 1.48 –Total Pressure Ratio 2.106

38. School of Aerospace Engineering MITE Axial Compressor (NASA Rotor37) 4 Blocks Baseline Grid: 119X71X41 1,385,000 Cells

39. School of Aerospace Engineering MITE A B C Corrected Mass Flow Rate Performance Map at 70% Design Speed (NASA Rotor37)

40. School of Aerospace Engineering MITE Mass Flow and Total Pressure Fluctuations (At points A, B, and C, NASA Rotor37) The amplitudes of mass flow and total pressure ratio fluctuations grow as the mass flow rate through the compressor decreases. % of Total Pressure Fluctuations % Mass Flow Rate Fluctuations

41. School of Aerospace Engineering MITE One Tip Chord Stall Active Control I Open-Loop (NASA Rotor67) A fraction of mass flow rate is removed at a constant rate in an azimuthally uniform rate. Pressure, density and tangential velocities are extrapolated from interior. U n = m b /(  A b ).

42. School of Aerospace Engineering MITE Performance Map Open-Loop Active Control, Operating Point D Open-loop control was applied to the unstable operating condition at point C. 3.2% of the mean mass flow rate was removed from the compressor. Stable Controlled Conditions A B C D E Peak Efficiency Onset Of Stall Stalled, Unstable

43. School of Aerospace Engineering MITE Mass Flow and Total Pressure Fluctuations (Operating Points C and D) % Mass Flow Rate Fluctuations % Total Pressure Fluctuations Without Control, Point C With Open-Loop Control, Point D 3.2% bleed air reduces the total pressure fluctuations by 75%.

44. School of Aerospace Engineering MITE Velocity Profile Controlled Operating Point D 3.2% Bleeding nearly eliminates reversed flow near LE.

45. School of Aerospace Engineering MITE Axial Velocity Near LE Open-Loop Control, Operating Point D % From Hub After 1.5 Rev. After 0.5 Rev. Bleed Valve.

46. School of Aerospace Engineering MITE Axial Velocity Fluctuations at the Probes (Open-Loop Control, Operating Point D) All the Probes are identical, indicating that no stalled cells exist in the flow. 3.2% bleeding eliminates the reversed flow at upstream of the compressor face. Rotor Revolution,  t/2 

47. School of Aerospace Engineering MITE Bleeding Effectiveness (Open-Loop Control) Open-loop control and operating point F have the same throttle position.

48. School of Aerospace Engineering MITE Stall Active Control II Closed-Loop (NASA Rotor67) Pressure Sensors Controller Unit Bleed Valve Pressure, density and tangential velocities are extrapolated from interior. The bleed valve is activated whenever the pressure sensors in the upstream of the compressor face exceed a user permitted range.

49. School of Aerospace Engineering MITE Rotor Revolution,  t/2  Permitted Upper Limit Permitted Lower Limit Closed-Loop Stall Control The bleed valve was not activated during first two lower amplitude levels, recovery and precursor levels. It is activated only during the stall level.

50. School of Aerospace Engineering MITE Performance Map (Closed-Loop Control, Operating Point E) Closed-loop control was applied to the unstable operating condition at point C. Stable Controlled Conditions A B C D E Peak Efficiency Onset Of Stall Stalled, Unstable Under closed- loop control, on an average, 1.8% of the mean flow was removed through the bleed valves.

51. School of Aerospace Engineering MITE Axial Velocity Fluctuations at the Probes (Closed-Loop Control, Operating Point E) All the Probes show nearly the same amount of deviation, very close to zero, indicating that no stalled cells exist in the flow. Closed-loop control eliminates the reversed flow at upstream of the compressor face. Rotor Revolution,  t/2 

52. School of Aerospace Engineering MITE Bleeding Effectiveness (Closed-Loop Control) Closed-loop control and stall operating condition, point G, have the same throttle position.

53. School of Aerospace Engineering MITE Conclusions A three-dimensional unsteady Navier-Stokes analysis capable of modeling multistage turbomachinery components has been developed for modeling and understanding surge and rotating stall. The flow solver were applied to two axial compressors: NASA Rotor67, and NASA Rotor37 configurations. Results were obtained in both the stable and the unstable branches of performance maps. Many important phenomena such as shock boundary layer interaction, shock locations and tip leakage flow were accurately captured. Results compare well with available experimental results. For the axial compressor Rotor67, reversed flow over the casing is strong under off-design conditions.

54. School of Aerospace Engineering MITE For both configurations, the fluctuations of mass flow rate and total pressure ratio grow as the mass flow rate through the compressors decreased. Results revealed that instabilities for NASA Rotor67 begins as a mild surge. The mild surge is followed by a modified surge. (Combined surge and rotating stall). The angular velocity of the stalled cells is 38% of the rotor RPM. Stall and surge in NASA Rotor67 could be eliminated using either an open-loop control with preset amount of bleeding, or variable amounts of bleeding based on a closed-loop control law. Smaller amounts of compressed air need to be removed with closed-loop control (1.8%), compared to open-loop control (3.2%). Conclusions (Continued)

55. School of Aerospace Engineering MITE In this study, it was assumed that the nominal mass flow rate through the throttle valve is constant. The work should be extended to the situation where the mass flow rate through the throttle valve fluctuates. This will permit coupling with downstream components. The suggested outlet boundary condition to calculate the backpressure is: Here, K t is the throttle characteristic, and A t is the throttle area. Recommendations mcmc. Throttle flow rate Plenum Chamber u(x,y,z) = 0 p p (x,y,z) = CT. isentropic mtmt. a p, V p

56. School of Aerospace Engineering MITE Recommendations (Continued) Other types of control devices, such as inlet guide vanes, casing treatment, should be investigated. Recently, an air injection control methodology has been computationally studied by Alex Stein at CFD Lab at Georgia Tech. Experimental evidence also exists indicating that air injection may reduce the amounts of the bleeding. This work should be extended to a systematic study of these concepts.

57. School of Aerospace Engineering MITE Why Spalart-Allmaras Model ? Code Previously had an Algebraic Eddy Viscosity Model (by Baldwin & Lomax) Works O.K. for Attached and Mildly Separated Flows (Airfoils with Mild  ) ** UU y U **  t  e u e   C C = 0.0168 = Clauser Constant

58. School of Aerospace Engineering MITE Spalart-Allmaras Model Well Behaved Compared to K-  -Models Eddy Viscosity t Seldom Negative No Special Treatment (e.g. Wall Functions) Near Wall  t can be Comparable to  t for Mean Flow Time Rate of Change ProductionDiffusionDestruction (in BL)Transition (Trip Fct)

59. School of Aerospace Engineering MITE Eigenmode Analysis (GTSYS3D) Calculates eigenvalues/-vectors of the compression system matrix Based on small perturbation Euler model: q = q 0 +  q The resulting form is: d/dt(  q) = A  q where:-  q is the state vector of small perturbations - A is the system matrix of size 5N 1 N 2 N 3 x 5N 1 N 2 N 3

60. School of Aerospace Engineering MITE How to Control Surge (Active Control) Controller Unit Bleed Air Pressure Sensors Air Injection