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

School of Aerospace Engineering

MITE

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


MITE

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


MITE

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


MITE

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.


MITE

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).


MITE

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


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 ? How to Control Stall ?

Guide Vanes

MovablePlenum Walls


MITE

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)


MITE

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.


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)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.


MITE

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.


MITE

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.


MITE

)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:


MITE

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


MITE

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)


MITE

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


MITE

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.


MITE

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


MITE

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.


MITE

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


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.


MITE

Shock-Boundary Layer InteractionShock-Boundary Layer Interaction (Peak Efficiency, Operating Point A) (Peak Efficiency, Operating Point A)

LE

TE

Shock

Near Suction Side


MITE

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%).


MITE

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.


MITE

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



Experiment

Chokedm

m.

.


A

BC

DE

Peak Efficiency

Onset Of Stall

Stalled, Unstable


MITE

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.


MITE

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


MITE

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


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.


MITE

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



Experiment

Chokedm

m.

.


A

BC

DE

Peak Efficiency

Onset Of Stall

Stalled, Unstable


MITE

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


Compared to the mass flow rate and pressure fluctuations at peak efficiency, point A, the fluctuations increased by a factor of 50.


MITE

Velocity ProfileVelocity Profile (Stalled, Operating Point C)(Stalled, Operating Point C)

f=84.0 Hz= 1/70 of blade passing frequency


MITE

0.45

0.55

0.65

0.75

0.85

0.95

0 5 10 15 20 25


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.


MITE

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.


MITE

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


a

UU


MITE

NASA Rotor 67 ResultsNASA Rotor 67 Results (Rotating Stall) (Rotating Stall)


MITE

NASA Rotor 67 ResultsNASA Rotor 67 Results (Rotating Stall) (Rotating Stall)


MITE

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


MITE

Axial Compressor (NASA Rotor37)Axial Compressor (NASA Rotor37)

4 BlocksBaseline Grid:119X71X411,385,000 Cells


MITE

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)


MITE

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



MITE

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)

.


MITE

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



Experiment

Chokedm

m.

.


A

BC

DE

Peak Efficiency

Onset Of Stall

Stalled, Unstable


MITE

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


% Total Pressure

Fluctuations

Without Control, Point C

With Open-Loop Control, Point D

3.2% bleed air reduces the total pressure fluctuations by 75%.


MITE

Velocity ProfileVelocity ProfileControlled Operating Point DControlled Operating Point D

3.2% Bleeding nearly eliminates reversed flow near LE.


MITE

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.


MITE

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


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



MITE

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


Throttle Characteristic

sec)/(.

kgmp

refP

PA

BC

D

FPlenumChamber

cm tmPm

bm


MITE

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


MITE

0.45

0.55

0.65

0.75

0.85

0.95

0 5 10 15 20 25


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.


MITE

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



Experiment

Chokedm

m.

.


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.


MITE

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


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



MITE

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


MITE

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.


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)Conclusions (Continued)


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, 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


MITE

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.


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

y

U

*

t eueC

C = 0.0168 = Clauser Constant


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

21

2

221

12

221

~~~~1~~

1~

Ufd

fc

fccSfcDt

Dtt

bwwbtb

TimeRate ofChange

Production Diffusion Destruction (in BL) Transition(Trip Fct)


MITE

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


MITE

How to Control Surge (Active Control)How to Control Surge (Active Control)

Controller Unit

Bleed Air

PressureSensorsAir

Injection

Documents

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