Saeid Niazi Advisor:Lakshmi N. Sankar School of Aerospace Engineering

1. Numerical Simulation of Rotating Stall and Surge Alleviation in Axial Compressors 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

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

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

4. t=0 t= 0+ t=0++ 2 2 2 1 1 1 Blade 1 sees a high a. Blade 1 recovers. Blase 2 stalls. Blade 1 stalls. What is Rotating Stall? • Rotating stall is a 2-D unsteady local phenomenon.

5. Rotating Stall (Continued)Types of Rotating Stall 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). Full-span

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

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

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

9.        ˆ ˆ ˆ ˆ ˆ ˆ    q dV  E i  F j  G k  n dS  R i  S j  T k  n dS  t  Mathematical Formulation 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. Stencil for q right Stencil for q left Right Left * * * * i-1 i i+1 i+2 Cell face i+1/2 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. 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. Periodic Boundaries: Properties are averaged on either side of the boundary. Exit: . mt specified; all other quantities extrapolated from Interior. Inlet: p0,T0,v,w specified; Riemann-Invariant extrapolated from Interior. Zonal Boundaries: Properties are averaged on either side of the boundary. Solid Walls: no-slip velocity conditions; dp/dn=dr/dn = 0 Boundary Conditions

13. Plenum • Chamber • u(x,y,z) = 0 • pp(x,y,z) = CT. • isentropic . mt ap, Vp Outflow Boundary . mc Outflow Boundary Conditions Conservation of mass: Isentropic state in plenum: All other quantities extrapolated from Interior.

14. 514 mm 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

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

17. Stalled, Unstable B C E D Onset Of Stall A Stable Controlled Conditions Peak Efficiency Performance MapPeak 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. Adiabatic Efficiency Peak Efficiency Radial distributions of total stagnation pressure and temperature were mass averaged across the annulus Near Stall

19. 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. Static Pressure Contours (Peak Efficiency, Operating Point A) Blade to blade periodic flow exists at peak efficiency condition. P 30% Span Near the tip shock becomes stronger. W S 70% Span

21. 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. Computed Measured

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

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

24. LE Clearance Gap TE 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. Stalled, Unstable B C E D Onset Of Stall A Stable Controlled Conditions Peak Efficiency Performance MapOnset 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.

26. I II III IV TE LE I III II IV W 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. 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. Pressure Fluctuations at the Probes(Onset of the Stall, Operating Point B) Rotor Revolution, Wt/2p Rotor Revolution, Wt/2p 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. Stalled, Unstable B C E D Onset Of Stall A Stable Controlled Conditions Peak Efficiency Performance MapStalled, Operating Point C The computational averaged mass flow rate at point C is 29.4 kg/s.

30. 50 30 Fluctuations 10 -40 -30 -20 -10 0 10 20 30 40 -10 -30 -50 % Mass Flow Rate Fluctuations Mass Flow and Total Pressure Fluctuations (Stalled, Operating Point C) Compared to the mass flow rate and pressure fluctuations at peak efficiency, point A, the fluctuations increased by a factor of 50. % Pressure

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

32. Probes Average Pressure Fluctuations (Stalled, Operating Point C) Compressor experiences very large pressure fluctuations at the inlet upstream of the compressor face. Rotor Revolution, Wt/2p

33. Probes Average Axial Velocity Fluctuations (Stalled, Operating Point C) Precursor Level Stall Level Recovery Level Three Different levels in axial velocity and pressure fluctuations were observed. Rotor Revolution, Wt/2p

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

35. NASA Rotor 67 Results (Rotating Stall) W

36. NASA Rotor 67 Results (Rotating Stall)

37. 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. Axial Compressor (NASA Rotor37) 4 Blocks Baseline Grid: 119X71X41 1,385,000 Cells

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

40. % of Total Pressure Fluctuations % Mass Flow Rate Fluctuations 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.

41. Pressure, density and tangential velocities are extrapolated from interior. Un = mb/(rAb) 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.

42. Stalled, Unstable B C E D Onset Of Stall A Stable Controlled Conditions Peak Efficiency Performance MapOpen-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.

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

44. Velocity ProfileControlled Operating Point D 3.2% Bleeding nearly eliminates reversed flow near LE.

45. Axial Velocity Near LEOpen-Loop Control, Operating Point D After 1.5 Rev. % From Hub After 0.5 Rev. Bleed Valve.

46. Rotor Revolution, Wt/2p Rotor Revolution, Wt/2p 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.

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

48. Controller Unit Pressure Sensors Bleed Valve Stall Active Control II Closed-Loop (NASA Rotor67) 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. 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. Permitted Upper Limit Permitted Lower Limit Rotor Revolution, Wt/2p

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