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Saeid NiaziAdvisor:Lakshmi N. Sankar
School of Aerospace EngineeringGeorgia 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 Numerical Simulation of Rotating Stall and Surge AlleviationStall and Surge Alleviation
in Axial Compressors in Axial Compressors
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OverviewOverview 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
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Objectives and MotivationObjectives and Motivation
• Use CFD to explore and understand compressor
stall and surge
• Develop and test control strategies (bleed valve)
for axial compressors
Cho
ke
Lim
it
Flow Rate
To
tal P
ress
ure
Ris
e
Lines of ConstantRotational Speed
Lines of ConstantEfficiency
Surg
e L
imit
Desired Extension of Operating Range
Safety Margin
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1
2
1
2
1
2
Blade 1 sees a high
Blade 1 stalls. Blade 1 recovers.Blase 2 stalls.
t=0 t= 0+ t=0++
What is Rotating Stall?What is Rotating Stall?
• Rotating stall is a 2-D unsteady local phenomenon.
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Rotating Stall (Continued)Rotating Stall (Continued)Types of Rotating StallTypes of Rotating Stall
Full-span
Part-spanFrom one to nine stall cells have been reported.
Stall cells affect the shape of performance map (e.g. Abrupt stall, Progressive stall).
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What is Surge?What is Surge? Mild Surge Deep Surge
Time
Flow Rate
Period of Deep Surge Cycle
Flow Reversal
Pressure Rise
Flow Rate
MeanOperating Point
Limit CycleOscillations
Pressure Rise
Flow Rate
PeakPerformance
Time
Flow Rate
Period ofMild Surge Cycle
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• 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 ? How to Control Stall ?
Guide Vanes
MovablePlenum Walls
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How to Control Stall? (Continued)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)
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Mathematical FormulationMathematical Formulation
t
qdV Eˆ i Fˆ j G ˆ k n dS Rˆ i Sˆ j T ˆ k
n dS
Reynolds Averaged Navier-Stokes Equations in FiniteVolume 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’sscheme is used in the present simulation.
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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)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.
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Mathematical Formulation (Continued)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.
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Boundary ConditionsBoundary Conditions
Inlet:p0,T0,v,w specified;Riemann-Invariant extrapolated from Interior.
Exit:.mt 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.
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)mm(V
a
dt
dptc
p
2pp
Conservation of mass:
Outflow Boundary ConditionsOutflow Boundary Conditions
mc
.
Outflow Boundary
Plenum Chamberu(x,y,z) = 0 •pp(x,y,z) = CT.•isentropic
mt
.
ap, Vp
All other quantities extrapolated from Interior.
tcPlenum
mmdt
dV
2Plenum
Plenum
ap
Isentropic state in plenum:
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Axial Compressor (NASA Rotor 67)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
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Literature Survey on NASA Rotor 67Literature 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)
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Axial Compressor (NASA Rotor 67)Axial Compressor (NASA Rotor 67)
4 BlocksBaseline Grid:66X32X21180,000 Cells
Meridional Plane
Plane Normal to Streamwise
Hub
LE TE
Fine Grid:131X63X411,400,000 Cells
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1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1
To
tal
Pre
ssu
re R
atio
CFD without Control
CFD with Open-Loop Control
CFD with Closed-Loop Control
Experiment
Chokedm
m.
.
Stable ControlledConditions
A
BC
DE
Peak Efficiency
Onset Of Stall
Stalled, Unstable
Performance MapPerformance MapPeak Efficiency, Operating Point APeak 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.
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Adiabatic EfficiencyAdiabatic EfficiencyChoke m
m
1
1
01
02
1
01
02
TT
pp
ad
0.84
0.86
0.88
0.9
0.92
0.94
0.88 0.9 0.92 0.94 0.96 0.98 1
Eff
icie
ncy
Experiment
CFD
Peak Efficiency
Near Stall Radial distributions of total stagnation pressure and temperature were mass averaged across the annulus
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Axial Velocity Profile at the InletAxial Velocity Profile at the Inlet (Peak Efficiency, Operating Point A)(Peak Efficiency, Operating Point A)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.00 0.20 0.40 0.60 0.80 1.00
Fraction of Span from Hub to casing
U/V
ST
D
CFD-Baseline Grid
CFD-Fine Grid
Laser Measurment
• Good agreement between the measurement and the predictions was observed.
• Grids have enough resolutions to capture the boundary layer profiles.
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30% Span
70% Span
Static Pressure Contours Static Pressure Contours (Peak Efficiency, Operating Point A)(Peak Efficiency, Operating Point A)
Blade to blade periodic flow exists at peak efficiency condition.
Near the tip shock becomes stronger.
S
P
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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.
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Shock-Boundary Layer InteractionShock-Boundary Layer Interaction (Peak Efficiency, Operating Point A) (Peak Efficiency, Operating Point A)
LE
TE
Shock
Near Suction Side
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LE
TE
Shock
Velocity Profile at Mid-PassageVelocity Profile at Mid-Passage ( (Peak efficiency, Operating Point A)Peak efficiency, Operating Point A)
•Flow is well aligned.•Very small regions of separation observed in the tip clearance gap (Enlarged view).
-50
-30
-10
10
30
50
-40 -30 -20 -10 0 10 20 30 40
% Mass Flow rate Fluctuations
% P
ress
ure
Flu
ctua
tion
s
Fluctuations are very small (2%).
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LE
TE
Clearance Gap
Enlarged View of Velocity Profile in Enlarged View of Velocity Profile in the Clearance Gapthe Clearance Gap
(Peak efficiency, Operating Point A)(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.
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Performance MapPerformance MapOnset of Stall, Operating Point BOnset 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.
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1
To
tal
Pre
ssu
re R
atio
CFD without Control
CFD with Open-Loop Control
CFD with Closed-Loop Control
Experiment
Chokedm
m.
.
Stable ControlledConditions
A
BC
DE
Peak Efficiency
Onset Of Stall
Stalled, Unstable
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IIIIIIIV
LE
TE
I
II
III
IV
Location of the Probes to Calculate the Location of the Probes to Calculate the Pressure and Velocity FluctuationsPressure 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.
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Mass Flow and Total Pressure Fluctuations Mass Flow and Total Pressure Fluctuations (Onset of the Stall, Operating Point B)(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.
-50
-30
-10
10
30
50
-40 -30 -20 -10 0 10 20 30 40
% PressureFluctuations
% Mass Flow Rate Fluctuations
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Pressure Fluctuations at the ProbesPressure Fluctuations at the Probes(Onset of the Stall, Operating Point B)(Onset of the Stall, Operating Point B)
0.45
0.55
0.65
0.75
0.85
0.95
0 5 10 15
Rotor Revolution, t/2
P
P
-0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15
Rotor Revolution, t/2
P
PP
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.
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Performance MapPerformance MapStalled, Operating Point CStalled, Operating Point C
The computational averaged mass flow rate at point C is 29.4 kg/s.
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1
To
tal
Pre
ssu
re R
atio
CFD without Control
CFD with Open-Loop Control
CFD with Closed-Loop Control
Experiment
Chokedm
m.
.
Stable ControlledConditions
A
BC
DE
Peak Efficiency
Onset Of Stall
Stalled, Unstable
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Mass Flow and Total Pressure Fluctuations Mass Flow and Total Pressure Fluctuations (Stalled, Operating Point C)(Stalled, Operating Point C)
% Pressure
-50
-30
-10
10
30
50
-40 -30 -20 -10 0 10 20 30 40
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.
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Velocity ProfileVelocity Profile (Stalled, Operating Point C)(Stalled, Operating Point C)
f=84.0 Hz= 1/70 of blade passing frequency
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0.45
0.55
0.65
0.75
0.85
0.95
0 5 10 15 20 25
Rotor Revolution, t/2
P
P
Probes Average Pressure Fluctuations Probes Average Pressure Fluctuations (Stalled, Operating Point C)(Stalled, Operating Point C)
Compressor experiences very large pressure fluctuations at the inlet upstream of the compressor face.
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Probes Average Axial Velocity Fluctuations Probes Average Axial Velocity Fluctuations (Stalled, Operating Point C)(Stalled, Operating Point C)
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 5 10 15 20 25Rotor Revolution, t/2
a
U
Precursor Level Stall Level Recovery Level
Three Different levels in axial velocity and pressure fluctuations were observed.
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Deviations of Axial Velocities from Their Deviations of Axial Velocities from Their Mean Values at the ProbesMean Values at the Probes
(Stalled, Operating Point C)(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).
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25
Rotor Revolution, t/2
a
UU
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NASA Rotor 67 ResultsNASA Rotor 67 Results (Rotating Stall) (Rotating Stall)
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NASA Rotor 67 ResultsNASA Rotor 67 Results (Rotating Stall) (Rotating Stall)
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Axial Compressor (NASA Rotor37)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
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Axial Compressor (NASA Rotor37)Axial Compressor (NASA Rotor37)
4 BlocksBaseline Grid:119X71X411,385,000 Cells
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1.2
1.25
1.3
1.35
1.4
1.45
1.5
11 12 13 14 15 16
To
tal
Pre
ssu
re r
atio
Experiments
CFD
A
B
C
Corrected Mass Flow Rate
Performance Map at 70% Design SpeedPerformance Map at 70% Design Speed(NASA Rotor37)(NASA Rotor37)
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Mass Flow and Total Pressure Fluctuations Mass Flow and Total Pressure Fluctuations (At points A, B, and C, NASA Rotor37)(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.
-50
-30
-10
10
30
50
-40 -20 0 20 40
-50
-30
-10
10
30
50
-40 -20 0 20 40
-50
-30
-10
10
30
50
-40 -20 0 20 40
% of Total Pressure
Fluctuations
% Mass Flow Rate Fluctuations
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One Tip Chord
Stall Active Control I Stall Active Control I Open-LoopOpen-Loop
(NASA Rotor67)(NASA Rotor67)
A fraction of mass flow rate is removed at a constant rate in an azimuthally uniform rate.
Pressure, densityand tangential velocities areextrapolated from interior.
Un = mb/(Ab)
.
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Performance MapPerformance MapOpen-Loop Active Control, Operating Point DOpen-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.
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1
To
tal
Pre
ssu
re R
atio
CFD without Control
CFD with Open-Loop Control
CFD with Closed-Loop Control
Experiment
Chokedm
m.
.
Stable ControlledConditions
A
BC
DE
Peak Efficiency
Onset Of Stall
Stalled, Unstable
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Mass Flow and Total Pressure Fluctuations Mass Flow and Total Pressure Fluctuations (Operating Points C and D)(Operating Points C and D)
-50
-30
-10
10
30
50
-40 -20 0 20 40
-50
-30
-10
10
30
50
-40 -20 0 20 40
% 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%.
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Velocity ProfileVelocity ProfileControlled Operating Point DControlled Operating Point D
3.2% Bleeding nearly eliminates reversed flow near LE.
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Axial Velocity Near LEAxial Velocity Near LE Open-Loop Control, Operating Point DOpen-Loop Control, Operating Point D
% F
rom
Hub
After 1.5 Rev.
After 0.5 Rev.
Bleed Valve.
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Axial Velocity Fluctuations at the ProbesAxial Velocity Fluctuations at the Probes(Open-Loop Control, Operating Point D)(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.
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 1 2 3 4 5
Rotor Revolution, t/2
a
U
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5
a
UU
Rotor Revolution, t/2
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Bleeding Effectiveness Bleeding Effectiveness (Open-Loop Control)(Open-Loop Control)
Open-loop control and operating point F have the same throttle position. 0.6
0.7
0.8
0.9
1
1.1
1.2
28 29 30 31 32 33 34 35
CFD without Control
CFD with Open-Loop Control
Throttle Characteristic
sec)/(.
kgmp
refP
PA
BC
D
FPlenumChamber
cm tmPm
bm
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Stall Active Control IIStall Active Control IIClosed-LoopClosed-Loop
(NASA Rotor67)(NASA Rotor67)
Pressure Sensors
Controller Unit
Bleed Valve
Pressure, densityand tangential velocities areextrapolated from interior.
The bleed valve is activated whenever the pressure sensors in the upstream of the compressor face exceed a user permitted range.
pAKm bbb .
b
bn
pku
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0.45
0.55
0.65
0.75
0.85
0.95
0 5 10 15 20 25
Rotor Revolution, t/2
P
P
Permitted Upper Limit
Permitted Lower Limit
Closed-Loop Stall ControlClosed-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.
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Performance MapPerformance Map(Closed-Loop Control, Operating Point E)(Closed-Loop Control, Operating Point E)
Closed-loop control was applied to the unstable operating condition at
point C.
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1
To
tal
Pre
ssu
re R
atio
CFD without Control
CFD with Open-Loop Control
CFD with Closed-Loop Control
Experiment
Chokedm
m.
.
Stable ControlledConditions
A
BC
DE
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.
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Axial Velocity Fluctuations at the ProbesAxial Velocity Fluctuations at the Probes(Closed-Loop Control, Operating Point E)(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.
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 1 2 3 4 5
Rotor Revolution, t/2
a
U
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5
a
UU
Rotor Revolution, t/2
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Bleeding Effectiveness Bleeding Effectiveness (Closed-Loop Control)(Closed-Loop Control)
Closed-loop control and stall operating condition, point G, have the same throttle position.
0.6
0.7
0.8
0.9
1
1.1
1.2
28 29 30 31 32 33 34 35
CFD without Control
CFD with Close-Loop Control
Throttle Characteristic
A
BC
E
G
sec)/(.
kgmp
refP
P
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ConclusionsConclusions• 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.
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• 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)Conclusions (Continued)
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• 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, Kt is the throttle characteristic, and At is the throttle area.
RecommendationsRecommendations
)(2
tcp
pp mmV
a
dt
dp
PAKm ttt .
mc
.
Throttle flow rate
Plenum Chamberu(x,y,z) = 0 •pp(x,y,z) = CT.•isentropic mt
.
ap, Vp
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Recommendations (Continued)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.
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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
y
U
*
t eueC
C = 0.0168 = Clauser Constant
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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
21
2
221
12
221
~~~~1~~
1~
Ufd
fc
fccSfcDt
Dtt
bwwbtb
TimeRate ofChange
Production Diffusion Destruction (in BL) Transition(Trip Fct)
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Eigenmode Analysis (GTSYS3D)Eigenmode Analysis (GTSYS3D)• Calculates eigenvalues/-vectors of the compression
system matrix
• Based on small perturbation Euler model:q = q0 + q
• The resulting form is:d/dt(q) = Aq
where: - q is the state vector of small perturbations- A is the system matrix of size
5N1N2N3 x 5N1N2N3
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How to Control Surge (Active Control)How to Control Surge (Active Control)
Controller Unit
Bleed Air
PressureSensorsAir
Injection