Rodrick V. Chima

Glenn Research Center, Cleveland, Ohio

A Three-Dimensional Unsteady CFD Model

of Compressor Stability

NASA/TM—2006-214117

February 2006

GT2006–90040
The NASA STI Program Office . . . in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space

science. The NASA Scientific and Technical

Information (STI) Program Office plays a key part

in helping NASA maintain this important role.

The NASA STI Program Office is operated by

Langley Research Center, the Lead Center for

NASA’s scientific and technical information. The

NASA STI Program Office provides access to the

NASA STI Database, the largest collection of

aeronautical and space science STI in the world.

The Program Office is also NASA’s institutional

mechanism for disseminating the results of its

research and development activities. These results

are published by NASA in the NASA STI Report

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant

phase of research that present the results of

NASA programs and include extensive data

or theoretical analysis. Includes compilations

of significant scientific and technical data and

information deemed to be of continuing

reference value. NASA’s counterpart of peerreviewed formal professional papers but

has less stringent limitations on manuscript

length and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies

that contain minimal annotation. Does not

contain extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by

NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions,

often concerned with subjects having

substantial public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific

and technical material pertinent to NASA’s

mission.

Specialized services that complement the STI

Program Office’s diverse offerings include

creating custom thesauri, building customized

databases, organizing and publishing research

results . . . even providing videos.

For more information about the NASA STI

Program Office, see the following:

• Access the NASA STI Program Home Page

at http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA Access

Help Desk at 301–621–0134

• Telephone the NASA Access Help Desk at

301–621–0390

• Write to:

 NASA Access Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076
Rodrick V. Chima

Glenn Research Center, Cleveland, Ohio

A Three-Dimensional Unsteady CFD Model

of Compressor Stability

NASA/TM—2006-214117

February 2006

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for

Turbo Expo 2006

sponsored by the American Society of Mechanical Engineers

Barcelona, Spain, May 8–11, 2006

GT2006–90040
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics

Program at the NASA Glenn Research Center.
ABSTRACT

A three-dimensional unsteady CFD code called CSTALL has been

developed and used to investigate compressor stability. The code

solved the Euler equations through the entire annulus and all blade

rows. Blade row turning, losses, and deviation were modeled using

body force terms which required input data at stations between blade

rows. The input data was calculated using a separate Navier-Stokes

turbomachinery analysis code run at one operating point near stall,

and was scaled to other operating points using overall characteristic

maps. No information about the stalled characteristic was used.

CSTALL was run in a 2-D throughflow mode for very fast calculations of operating maps and estimation of stall points. Calculated pressure ratio characteristics for NASA stage 35 agreed well with

experimental data, and results with inlet radial distortion showed the

expected loss of range. CSTALL was also run in a 3-D mode to investigate inlet circumferential distortion. Calculated operating maps for

stage 35 with 120 degree distortion screens showed a loss in range and

pressure rise. Unsteady calculations showed rotating stall with two

part-span stall cells. The paper describes the body force formulation in

detail, examines the computed results, and concludes with observations about the code.

NOMENCLATURE

b blockage

inviscid fluxes

e total energy

F body force for turning

f body force for loss

h, p, T, s enthalpy, pressure, temperature, entropy

Centrifugal, Coriolis, and blockage source terms

m meridional directional

corrected mass flow

q vector of conserved variables

t time

V velocity

cylindrical coordinates

cylindrical velocity components

relative flow, blade, and deviation angles

difference

streamwise grid direction

density

throughflow time scale

body force vector

body force scaling function

turning function for deviation

blade row angular velocity

loss coefficient

Subscripts

0 stagnation state

1,2 upstream, downstream

LE, TE leading edge, trailing edge

turning, entropy, deviation, reference point

grid exit, downstream of throttle

Superscripts

relative velocity

ss steady state

INTRODUCTION

Compressor stall and surge can have catastrophic consequences in

aircraft, yet prediction of these phenomena remains as one of the

major unsolved problems in turbomachinery. Many models of stall

that give some insight into the phenomena have been developed but

few models are capable of predicting stall onset, except perhaps for

full computational fluid dynamic (CFD) analysis of the entire compressor which is beyond the scope of this paper. Existing models

range from analytic models of rotating stall or compression system

stability to 2-D or 3-D CFD models of compression systems. All models require input of some information about compressor performance,

E, G, H

K

m ̇

c

x, , θ r

u v w , ,

β χ δ, ,

∆

ξ

ρ

τ

Φ

φ

φturn

Ω

ω

t s, , , δ ref

ex ∞,

V′

A THREE-DIMENSIONAL UNSTEADY CFD MODEL OF COMPRESSOR STABILITY 

Rodrick V. Chima 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

NASA/TM—2006-214117 1
usually equivalent to axisymmetric pressure rise and loss characteristics for the machine over its entire operating range, including stall.

This information can be difficult to obtain accurately. This paper

describes a 3-D unsteady CFD model of compressor stability that uses

a new method for obtaining information about compressor performance directly from steady CFD calculations performed separately.

First some existing models and their input requirements will be

described.

Pampreen [1] gives an excellent review of several analytic models

of compressor stall. Early models predict the propagation velocity of

stall cells. Later system stability models predict the behavior of a duct/

compressor/plenum/throttle system. These models usually assume

that the axisymmetric static pressure rise characteristic of the compressor is known at all flow conditions, including stall.

Takata and Nagano [2] developed a nonlinear analysis of rotating

stall that modeled incompressible flow through a 2-D isolated blade

row with infinitesimal pitch but finite chord. The static pressure loss

and exit flow angle were assumed to be known functions of the incidence angle, and changes in loss were assumed to lag in time behind

changes in incidence. The numerical results predicted stall inception,

stall cell growth, and stall cell propagation velocity. Several authors

have extended these ideas to 2-D compressible flows using modern

CFD methods. Longley [3] presented an unsteady 2-D model of compressor stability and tested the model for a hypothetical four-stage

compressor. Demargne and Longley [4] applied the model to four real

compressors. Lindau and Owen [5] applied a similar model to NASA

compressor stage 35. Both models used measured blade row characteristics extended over a large flow range as input, and used time-lag

equations to update the body-force terms gradually.

Inviscid axisymmetric throughflow models have long been used to

model steady flows in turbomachinery. These models represent the

axisymmetric average flow on a meridional surface. Since the equations are averaged tangentially they cannot predict turning, and since

they are inviscid they cannot predict losses. Body force terms are

added to model these effects. Marble [6] derived a formulation for

body forces required to produce given changes in swirl and

entropy along a streamline. Stewart [7] described an iterative formulation for body forces required to turn the flow to a given angle, and

used that formulation in an axisymmetric model of a full engine. Both

of these formulations were used in the present work and are described

later.

By incorporating axisymmetric throughflow codes or ideas in

unsteady CFD codes, several authors have developed codes for modeling circumferential distortion and stall. Throughflow codes usually

incorporate extensive correlations for blade row turning and loss, and

thus provide rough predictions of blade row performance at all operating points. The codes often require additional calibration for each new

case. Escuret and Garnier [8] developed two unsteady codes for compressor instability. The first was a 2-D throughflow analysis that modeled stall and surge. The second was a 3-D stall model. Both codes

were coupled to a SNECMA throughflow code to provide the blade

row characteristics, and both used time-lag models to update the

body-force terms. Hale, et al. [9] merged the HT0300 throughflow

code and the 3-D NPARC code (now called WIND) to produce his

TEACC code. That code was used to predict the effects of circumferential distortion on steady performance of an isolated rotor. Hale, et al.

[10] used the same code to predict the performance of a 3-stage military fan coupled to an F-16 forebody and inlet.

Gong et al. [11] described a 3-D computational model for compressor instability. The model was applied to the GE low-speed (incompressible) research compressor and was used to simulate both modal

and spike stall inception. Gong’s dissertation [12] extended the model

to compressible flows and used it to show the steady response of

NASA stage 35 to inlet distortion. In this work the body forces were

modeled using two constant force coefficients similar to lift and drag

coefficients. Hsiao, et al. [13] incorporated the compressible model in

the WIND Navier-Stokes code and used the code to analyze a nacelle/

fan/exit guide vane/nozzle configuration. Here the body forces were

interpolated directly from 3-D Navier-Stokes solutions of the rotor

and guide vane onto the entire throughflow grid, so the model was

limited to one operating point.

In the present work a new CFD code called CSTALL was developed to investigate compressor stability. The code was used to solve

the unsteady 3-D Euler equations through a compressor using a finitedifference scheme. The computational grid shown in Fig. 1 resolved

the blade planform but was evenly spaced in the circumferential direction. The equations were treated as axisymmetric in blade passages

(shown in color.) Marble’s formulation for turning and loss forces was

used for steady calculations, and Stewart’s formulation for turning to a

specified angle was used for unsteady calculations. Body force input

data was calculated using a Navier-Stokes turbomachinery analysis

code run at one operating point near stall, and was scaled to other

operating points using normalized characteristic maps. No information about the stalled characteristic was used. The input data was easy

to obtain and allowed the inviscid axisymmetric throughflow code to

represent the blade rows with the same accuracy as the underlying

Navier-Stokes calculations. CSTALL was used in a 2-D throughflow

mode for fast calculations of operating maps and estimation of stall

points, in a 3-D mode for calculations of circumferential distortion,

rvθ( )

Figure 1 — Meridional grid used for NASA stage 35.

NASA/TM—2006-214117 2
and in a 3-D unsteady mode to investigate rotating stall in a compressor stage.

GOVERNING EQUATIONS

The governing equations are the Euler equations written in cylindrical coordinates in a stationary frame of reference.

(1)

where

(2)

(3)

The energy e is given by and the pressure p is

given by , where .

is the total body force per unit mass and will be discussed in

detail later. is a source term that includes the centrifugal and Coriolis forces, and derivatives of the blockage b, which is the fraction of

the annulus open to the flow. To account for blade thickness, b can be

modeled as . To account for endwall blockage, b can

be varied by some function of axial distance.

Axisymmetric Equations in Blade Passages

The full 3-D Euler equations (1 – 3) are solved in the annular ducts

outside of blade passages. Within blade passages there should be no

communication with neighboring passages, but the uniform computational grid used here does not resolve the solid blade shapes. Instead it

is assumed that blades are infinitely thin and that the flow is axisymmetric on each meridional grid surface. The blockage term

described above is used to account for variation of the throughflow

velocity due to finite blade thickness.

Stator passages are modeled as axisymmetric in the absolute frame

of reference and the θ-derivatives can be dropped immediately:

 in stator passages. (4)

Rotor passages are modeled as axisymmetric in the relative frame

of reference. Equations (1 - 2) are transformed to the relative frame,

all θ-derivatives are set to zero, then the equations are transformed

back to the absolute frame. The result is that

 in rotor passages, (5)

where is the blade row rotational speed.

BODY FORCES

Ducts are modeled using the 3-D Euler equations with all body

forces . Blade passages are modeled using the axisymmetric

Euler equations which give no information about turning or loss. That

information is specified using the body force term . The formulation used for is based on the formulation developed by Marble [6]

and outlined below.

The body force array used in (1) may be written as

 in blade passages. (6)

The term used in the energy equation represents the work done

by a rotor.

The total force vector can be written as , where is

a turning (or lift) force normal to the relative velocity ,

(7)

and is a loss (or drag) force parallel but opposed to

(8)

where is the relative tangential velocity component.

The components of these forces can be found by starting with the

steady, axisymmetric Euler equations in non-conservative form. The

equations can be written along a meridional streamline using the

following transformations:

(9)

The momentum equations become simply

(10)

(x, θ, r)

∂t

∂q

∂x

∂E 1

r

--

∂θ

∂G

∂r

∂H

+ + + = K + Φ

q br

ρ

ρu

ρv

ρw

e

= K

0

rp∂xb

–bρvw

b ρv

2

( + p) rp∂r+ b

0

=

E br

ρu

ρu

2 + p

ρuv

ρuw

u(e + p)

= G br

ρv

ρuv

ρv

2 + p

ρvw

v(e + p)

= H br

ρw

ρuw

ρvw

ρw2 + p

w(e + p)

=

e ρ CvT

1

2

--V

2

+

 

  =

p (γ – 1) e

1

2

--ρV

2 –

 

  = V

2 u2 v2 w2 = + +

Φ

K

b θsθp–

N

2π

= -----

b

1

r

--

∂θ

∂G

= 0

1

r

--

∂θ

∂G

Ω

∂θ

∂ q →

Ω

Φ = 0

Φ

Φ

Φ br 0 Φx Φθ Φr

rΩΦθ, , , ,

T

=

rΩΦθ

Φ Φ = F + f F

V′

F ⋅ V′ = 0

uFxv′Fθ wFr+ + = 0

f V′

f || V′

f

x

f

θ

f

r

( , , ) – f

(u, v′, w)

V′

= ---------------------

v′ = v – rΩ

m

dm2 dx

2 dr2 = +

vm

2 u2 w2 = +

vm∂mu∂x w∂r= +

x: ρvm∂mu ∂x+ p Φx=

θ: ρvm∂m(rv) rΦθ=

r: ρvm∂mw ∂r+ p

ρv

2

r

-------- Φr= +

NASA/TM—2006-214117 3
The -momentum equation immediately gives the total tangential

force,

. (11)

showing that the change of angular momentum along a streamline is

proportional to the total applied tangential force.

Loss forces are derived from the canonical equation of state,

. This equation is applied along a streamline and

the pressure gradient is eliminated using the momentum equations,

giving:

(12)

where is the total enthalpy. Equation (7) can be used to eliminate

three terms on the right hand side, leaving

(13)

In the absence of losses the right side of (13) equals zero since the

entropy gradient and the loss forces are both zero. The terms

remaining on the left side of (13) give:

(14)

Equations (11) and (14) can be combined to give the differential form

of the Euler turbine equation:

(15)

which will be used later.

Equation (14) says that the rate of increase of total enthalpy along a

streamline equals the rate at which torque does work on the system.

This is a general application of the first law of thermodynamics and is

true whether losses are present or not. Thus it follows that the entropy

variation along a streamline can found from the right side of (13):

(16)

Solving for the magnitude of the loss force ,

(17)

At this point , , , and are all known. The

meridional turning force is found using equation (7,) then

are found by assuming that is tangent to the streamwise grid lines which follow the hub and casing.

(18)

Body Force Required to Turn to a Specified Angle

It is often desirable to specify the relative flow angle

within the blade row, where is the blade angle and is the deviation. There does not seem to be a way to specify the turning force

explicitly in terms of ; however, an iterative scheme similar to a

scheme described by Stewart [7] can be used. The angles are shown in

Fig. 2 and the relative velocity is shown misaligned with the

desired flow angle . A turning force is defined to be proportional

to the difference between the desired and actual tangential velocity

components,

(19)

When the flow turns to the desired angle and the iteration is converged.

is a turning function that varies the body force from zero at

the leading edge to maximum at the trailing edge. Other turning functions based on the local blade angle were investigated, but they often

resulted in non-physical supersonic throughflow velocities at flow

rates below the experimental rotor choking flow.

Body Force Unknowns

Either equation (11) or (19) can be used to find the magnitude of the

total tangential turning force. For convenience equation (11) will be

referred to as the turning model and equation (19) will be referred to

as the deviation model. Equation (13) gives the magnitude of the loss

force.

The term in (11) cannot be calculated using the axisymmetric equations, and the terms in (17) and in (19) cannot

be calculated from the Euler equations. Here these terms have been

modeled using results from steady Navier-Stokes calculations done

previously using the author’s CFD code SWIFT, see Chima [14, 15.]

However, these terms could also be calculated from experimental data

or design intent using the same formulation. The terms were approximated as a combination of spanwise reference profiles evaluated

θ

ΦθFθf

θ

+ ρ

vm

r

-----

∂(rv)

∂m

= = ------------

Tds = dh – dp ⁄ ρ

vm∂mh0rΩΦθ– Tvm∂m= s

+ u Fxf

x

( + ) v′ Fθf

θ

( + ) w Frf

r

+ + ( + )

h0

vm∂mh0rΩΦθ– Tvm∂ms u f

x

v′ f

θ w fr

= + ( + + )

∂ms f

i

vm

∂m

∂h0

rΩΦθrΩ Fθf

θ

= = ( + )

∂m

∂h0 Ω

∂(rv)

∂m

= ------------

Tvm∂ms u f

x

v' f

θ w fr

= –( + + ) = – f ⋅ V′

f

f T

vm

V′

-------

∂m

∂s

=

f

x

f

θ

f

r

Fθ Φθf

θ

= –

Fm

Fxand FrFm

(ξ)

FmFθ

vθ′

vm

------

 

  = – Fx

xξ

xξ

2

r

ξ

2

+

-------------------- Fm

= Fr

r

ξ

xξ

2

r

ξ

2

+

-------------------- Fm

=

β = χ + δ

χ δ

Φθ

β

V′

β + χ

Figure 2 — Nomenclature used for deviation model.

V′

(χ+ δ) V′ sin (χ+ δ)

v′

x

Fθ

n + 1

Fθ

n V′sin(χ + δ) – v′

∆t

-----------------------------------------

 

  φturn

= +

φturn

m mle–

mte mle–

= ---------------------

Fθ

n + 1

Fθ

n

=

φturn

∂(rv) ⁄ ∂m

∂s ⁄ ∂m δ

NASA/TM—2006-214117 4
upstream and downstream of each blade row at a single reference flow

near stall, and a scaling function that varied with corrected flow.

(20)

In (20), the terms labeled ref are the spanwise reference profiles.

They were evaluated from a single SWIFT solution and stored for

each blade at each spanwise location. The gradient terms were

evaluated along streamwise grid lines, although technically they

should be evaluated along streamlines. They were differenced

between stations upstream and downstream of a blade. Since and

are convected along streamlines, the exact axial location of these

stations is unimportant. Since the gradients were modeled as constants, the turning and loss vary linearly through the blade row. The

deviation was evaluated at blade trailing edges.

For a rotor the term can be calculated from Euler’s turbine equation (15.) For a stator it must be input directly.

The entropy gradient was evaluated using the canonical equation of

state written in terms of total conditions and integrated across a blade

row:

(21)

For a stator the temperature ratio equals one, and it can be shown

that , the total pressure loss coefficient.

The input reference profiles are shown at the top of Fig. 3 (the

SWIFT calculations are discussed later.) The turning profiles show

that the rotor adds swirl to the flow with overturning at the endwalls,

and that the stator removes most of the swirl. The entropy rise profiles

show that the rotor is especially lossy at the tip, and that the cantilevered stator is lossy at the hub. The deviation profiles are fairly uniform except at the endwalls. Since these profiles were evaluated by

averaging a 3-D Navier-Stokes solution, they inherently include

losses, blockage, and over- or under-turning due to shock-boundary

layer interaction, tip clearance flows, and secondary flows, all of

which are important for modeling stall in tip-critical blades.

In (20), the terms are normalized scaling functions used to

scale the reference profiles to other flow rates. They are defined as:

(22)

The overbar denotes a spanwise average, i.e.,

and . The deviation scaling function was evaluated at

midspan since the spanwise average deviation is poorly defined.

∂(rv)

∂m

------------

∆(rv)

∆m

-------------

ref

φt m ̇

c

≈ ( )

∂s

∂m

------

∆s

∆m

-------

ref

φs m ̇

c

≈ ( )

δ δrefφδ m ̇

c

= + ( )

(∆′s)

rv

s

δref

∆(rv) ⁄ ∆m

∆s

R

-----

γ

γ – 1

-----------

T02

T01

-------

 

 

P02

P01

-------

 

  = ln – ln

∆s ⁄ R ≈ ω

φ mc

 ̇

( )

φt mc

 ̇

( )

∆(rv) mc

 ̇

( )

∆(rv) m ̇

c

( )

ref

= -------------------------------- φs mc

 ̇

( )

∆s m ̇

c

( )

∆s m ̇

c

( )

ref

= ------------------------

φδ m ̇

c

( ) δ m ̇

c

( ) δ m ̇

c

( )

ref

[ – ]

midspan

=

∆(rv) r

2

v2r

1

v1≈ –

∆s s

2

s

1

= –

0.20 0.30 0.40 0.50

|D(r*vth)|/(r*Utip)

0

20

40

60

80

100

Percent Span

Rotor

Stator

0.00 0.02 0.04 0.06 0.08 0.10

D(s)/R

0

20

40

60

80

100

Percent Span

Rotor

Stator

0.95 1.00 1.05 1.10

m/m_ref

−1.5

−1.0

−0.5

0.0

0.5

dev−dev_ref dg.

Rotor

Stator

0 5 10 15 20

Deviation [deg.]

0

20

40

60

80

100

Percent Span

Rotor

Stator

0.95 1.00 1.05 1.10

m/m_ref

0.70

0.80

0.90

1.00

1.10

d(rv)/d(rv)ref

Rotor

Stator

0.95 1.00 1.05 1.10

m/m_ref

0.4

0.6

0.8

1.0

1.2

ds/ds_ref

Rotor

Stator

Figure 3 — Top: Spanwise profiles of , , and deviation computed with SWIFT.

Bottom: Maps of 1-D variation of , , and deviation with corrected flow computed with SWIFT.

∆(rv) ∆s ⁄ R

∆(rv) ∆s ⁄ R

NASA/TM—2006-214117 5
The scaling functions vary with , the corrected mass flow at the

blade leading edges. They are normalized such that they have no

effect at the reference flow . They were evaluated using

SWIFT calculations of the stage speed line but could also be evaluated

using experimental data or design intent. The functions were input as

short tables for each blade row and interpolated linearly as needed.

The functions were extrapolated linearly outside the range of the input

data, but the mass flow was restricted to be less than the calculated

choking value and greater than some stall cutoff. When the code was

used to determine the stall point the cutoff was set very small. When it

was used to calculate behavior in stall the cutoff was set to about 80

percent of the computed stall flow. The input scaling functions are

shown at the bottom of Fig. 3. The turning, entropy rise, and deviation

all increase as flow rate decreases, as expected. Surprisingly, the

entropy rise is linear with flow rate for both blade rows.

For 3-D flows body forces were calculated independently on each

meridional grid plane. References profiles were the same for all planes

but scaling functions were determined for each plane based on the

inlet corrected flow per unit area for that plane. In that way body

forces could respond to circumferential variations in upstream conditions. Note that body forces are also functions of the local velocity and

thermodynamic properties that are computed as part of the solution.

Body Force Lag Model

The body force terms described above are functions of the corrected

mass flow calculated at blade leading edges and respond instantaneously everywhere to changes in that flow. In reality the blade forces

respond gradually to changes in flow or incidence. Time-lag models

are commonly used to simulate this finite response rate, (see Longley

[3] or Lindau, et al. [5].) The following time-lag model was used in

the present work:

(23)

where is a time scale associated with the blade response, typically

the throughflow time, F is or (the lag model is applied to

both,) and is the steady state value of the force. Computationally

the model is applied using,

. (24)

where is an under relaxation factor. For steady calculations

. For the unsteady calculations shown later the throughflow

time is about , so that .

NUMERICAL MODEL

The Euler equations (1–3) were transformed to body-fitted coordinates using finite-difference techniques described in Tweedt, et al.

[16.] Since the computational grid was uniform in the tangential direction, , the grid and metrics only required 2-D storage. The equations were discretized with either a central-difference

scheme or the AUSM+upwind scheme described by Chima, et al.

[15.] The equations were solved using an explicit Runge-Kutta

scheme. For steady flows a two-stage scheme with spatially-varying

time step and implicit residual smoothing was used to accelerate convergence. For unsteady flows a second-order four-stage scheme with

constant time step was used.

Boundary Conditions

At the inlet the upstream-running Riemann invariant was extrapolated from the interior, and , and were specified. In all cases

was constant and . The inlet profile reflected the turbulent inlet boundary layer profiles and resulting blockage used in

SWIFT, but it was extrapolated to the wall on the coarser Euler grids

used in CSTALL to avoid problems with zero velocity at the wall. For

radial and circumferential distortion the inlet profile was modified

locally as described later.

At the exit, were extrapolated from the interior and

was set isentropically. The pressure was set using the radial equilibrium equation and a throttle model,

(25)

Here is a dimensionless throttle coefficient discussed later and

is the static pressure downstream of the throttle.

RESULTS

NASA Stage 35

NASA stage 35 is a transonic inlet stage for a core compressor and

was used here as a test case. The stage has a design pressure ratio of

1.82 at a mass flow of 20.19 kg/sec and a rotor tip speed of 455 m/sec.

The rotor has 36 multiple-circular-arc (MCA) blades with a maximum

radius of 9.94 cm and a tip clearance of ~0.2 percent of the span. The

cantilevered stator has 46 MCA blades with a hub clearance of ~0.5

percent span. The endwall clearances were much smaller than the grid

spacing used in Fig. 1, but the effects of the clearances were captured

by the reference profiles used in Fig. 3. Stage 35 was originally

designed and tested at NASA Glenn Research Center by Reid and

Moore [17.] Radial distributions of static and total pressure, total temperature, and flow angle were measured at axial stations located one

rotor axial chord upstream of the rotor and 2.43 chords downstream of

the stator. All calculations reported here were made at 100 percent

design speed to allow comparison with this data.

SWIFT – Navier-Stokes Analysis

The SWIFT code is a multiblock Navier-Stokes analysis code for

turbomachinery blade rows described by Chima, et al. [14, 15.] The

code solves the Navier-Stokes equations on body-fitted grids using an

explicit finite-difference scheme. It includes viscous terms in the

blade-to-blade and hub-to-tip directions, but neglects them in the

streamwise direction using the thin-layer approximation. The Baldwin-Lomax turbulence model was used for the present work. Multi

blade row calculations were made using a steady mixing plane

approach that transfers characteristic variables across the interface

between blade rows.

m ̇

c

m ̇

c

( )

ref

τ

∂F

∂t

------ F

ss

= ( – F)

τ

Fθf

F

ss

F

n + 1

(1 – r)F

n

rF

ss

= +

r = ∆t ⁄τ

r = 1

100∆t r = 0.01

(∆θ = constant)

P0T0, v

T0v = 0 P0

P0

u, v, and w ρ

pexp∞

Kt

2

-----ρVex

2 ρv

2

r

--------dr

rhub

r

∫

= + +

Ktp∞

NASA/TM—2006-214117 6
A central difference scheme was used. Artificial dissipation and

Eigenvalue scaling were used to capture shocks and to control point

decoupling. An explicit, four-stage Runge-Kutta scheme was used to

solve the flow equations. Calculations were run at a Courant number

of 5.6 using a spatially-varying time step and implicit residual

smoothing to accelerate convergence to a steady state.

Calculations for stage 35 were run using a grid with five blocks: an

H-block upstream, C-blocks around the rotor and stator, and O-blocks

for the rotor tip clearance and stator hub clearance. Tip clearance grids

had 9-11 points across the gap. The full grid had about 1.13 million

points. The calculations were run several years ago on the Cray C-90

at NASA Ames Research Center, on 6-8 processors. Cases near choke

were run 3,000 iterations, which took about 1.1 hours wall clock time.

Cases near stall were often run 3-4 times as long to ensure convergence.

CSTALL – Euler Analysis

CSTALL calculations were run on the axisymmetric grid shown in

Fig. 1. The grid had 147 points axially and 21 points spanwise, for a

total of 3,087 points. Steady 2-D cases were run with a 2-stage RungeKutta scheme on an SGI Octane2 with two processors. Cases near

choke were converged to machine zero in 3,000 iterations, which took

about 30 seconds. Cases near stall were often run 15-20,000 iterations

to ensure convergence.

3-D cases were run with 90 points evenly spaced in the circumferential direction, for a total of 278,830 points. Steady cases near choke

took about an hour. Unsteady 3-D cases were run with a 4-stage

Runge-Kutta scheme with a constant time step and no residual

smoothing. The time step was chosen to give a maximum Courant

number of about 2.5. One rotor revolution required 2,500 time steps,

which took about 40 minutes on the SGI. A dual time stepping

scheme could be used to reduce CPU time for unsteady cases but was

not used here.

Predicted Performance

Figure 4 compares static-to-total pressure ratio characteristics for

stage 35 as measured by Reid and Moore [17] with characteristics

computed by three different methods. The experimental data (solid

black circles) show a non-zero slope near the stall point of 18.2 kg/

sec. The characteristic computed with the SWIFT code (plus signs)

matches the experimental data closely but predicts stall at a higher

flow of 19.23 kg/sec. The reason for the discrepancy in predicted stall

point is unknown, but was found to be unaffected by changes in grid

resolution, differencing scheme, and turbulence model. CSTALL

solutions computed with the turning model (red squares) and the deviation model (black triangles) agree closely with each other and with

the SWIFT solution up to the stall point. However, the CSTALL

results predict stall at slightly lower flow than the experiment and a

much lower flow than SWIFT.

Since stall models typically require input of an axisymmetric characteristic that mimics stall, e.g. Gong [12,] it was not obvious in

advance whether the CSTALL formulation could even predict stall.

Subsequent results will show the mechanism responsible for stall in

the calculations. For now, note that the CSTALL solutions were computed using the scaling functions computed with SWIFT (Fig. 3,)

which were extrapolated linearly to the left of the predicted stall point

as necessary. It was found that the predicted stall point depended

strongly on the slopes of the scaling functions at the stall point. Small

changes in the slopes could be used to make the predicted stall points

match, but here the slopes were left as predicted by SWIFT.

16 17 18 19 20 21 22

Corrected Flow, kg/sec

1.10

1.20

1.30

1.40

1.50

1.60

1.70

Ps2/P01

Expt.

Swift

CSTALL−turn

CSTALL−dev

Figure 4 — Experimental and computed characteristics of

static-to-total pressure ratio for stage 35.

REF.

1.20 1.25 1.30 1.35 1.40

Total Temperature Ratio

0

20

40

60

80

100

Percent Span

Rotor 35

Expt.

Swift

CSTALL

0.90 0.92 0.94 0.96 0.98 1.00

Total Pressure Ratio

0

20

40

60

80

100

Percent Span

Stator 35

Expt

Swift

CSTALL

Figure 5 — Spanwise distributions of experimental and

computed total temperature ratio downstream of rotor 35.

Figure 6 — Spanwise distributions of experimental and

computed total pressure ratio downstream of stator 35.

NASA/TM—2006-214117 7
In general the turning and deviation models gave similar results at

stable operating points. However, at stalled operating points the turning model gave non-physical swings in flow angles while the deviation model held the flow angle close to the blade angle even when the

flow reversed direction. Hence the remainder of this paper will only

show results from the turning model at stable points and from the

deviation model at stalled points.

CSTALL solutions were computed using reference profiles from

the SWIFT solution at 19.74 kg/sec (labeled REF. on Fig. 4) and

should agree with SWIFT at that flow rate. Spanwise profiles of total

temperature ratio downstream of the rotor are compared in Fig. 5. The

SWIFT predictions (black line) agree closely with experimental data

(black circles) except near the tip, where a higher temperature ratio

was predicted. The CSTALL predictions (red squares) agree reasonably well with the SWIFT predictions, showing that the body forces

for turning are behaving correctly. Spanwise profiles of total pressure

ratio across the stator are compared in Fig. 6. The SWIFT predictions

(black line) are about a point higher than the data (black circles,) but

do show the large loss due to the stator hub clearance. The CSTALL

predictions (red squares) agree reasonably well with the SWIFT predictions, showing that the body forces for loss are also behaving correctly. Minor differences between SWIFT and CSTALL in Figs. 5 and

6 could be due to a number of modelling simplifications used in

CSTALL, such as estimation of the body forces using data along grid

lines rather than streamlines, neglect of losses in ducts, etc.

Stall Mechanism

CSTALL calculations of a speed line (Fig. 4) behave like most

Navier-Stokes calculations, with fast convergence near choke and

slow convergence near stall. When the exit pressure is raised above

the stall point the mass flow drops rapidly and large regions of reverse

flow develop. Investigation of the flow field at the stall point suggests

the mechanism by which the calculations predict stall. Figure 7 shows

predicted axial velocity contours within the stage at the last stable

operating point of Fig. 4. The plot shows a region of low axial velocity

on the casing from the rotor trailing edge to the stator leading edge.

This low-speed region is directly related to the high entropy rise

across the rotor at the tip (Fig. 3, top center.) Figure 8 plots the axial

velocity on the casing vs. axial distance. The upper plot is for the next

to the last stable operating point on Fig. 4 and the lower plot is for the

stall point. It is apparent that the axial velocity at the casing goes to

zero quickly as the flow approaches stall, and that the stage stalls

when the velocity reaches zero.

Effect of Throttle Boundary Condition

The static-to-total pressure ratio characteristics shown in Fig. 4

were calculated using radial equilibrium at the exit (eq. 25) but not the

throttle model, i.e., The throttle coefficient for the stage 35

experiment was estimated to be using SWIFT results at

the grid exit and assuming that the throttle exhausted back to the

ambient. Another characteristic was calculated by holding

constant and varying . The throttle characteristic at

the stall point (black line) and the compressor characteristics predicted with and without the throttle boundary condition are shown in

Fig. 9. The throttle boundary condition reduced the predicted stall

point from 17.1 kg/sec (red squares) to 16.4 kg/sec (blue triangles.)

The slope of the static-to-total pressure ratio characteristics remained

negative over the entire flow range. Since the CSTALL results predict

a stall point slightly lower than the experiment even with , the

throttle boundary condition was not used for subsequent calculations.

Kt= 0.

Kt≈ 1.314

Kt= 1.314 p∞

−5 0 5 10 15

Axial position [cm]

0.00

0.10

0.20

0.30

0.40

0.50

0.60

Casing Vx/c0

Stable

R1 S1

At Stall

Figure 7 — Axial velocity component contours at stall.

Figure 8 — Axial velocity along the casing of stage 35 at flow

rates before stall (stable) and at stall.

0 5 10 15 20 25

Mass Flow, kg/sec

1.10

1.20

1.30

1.40

1.50

1.60

1.70

Static Pressure Ratio

Expt.

Throttle Line

CSTALL, Kt=0

CSTALL, Kt=1.314

Figure 9 — Effect of throttle exit boundary condition on the stall

point.

Kt= 0

NASA/TM—2006-214117 8
Radial Distortion

CSTALL requires input for a few operating points of a compressor.

This input can be derived from steady Navier-Stokes calculations of

periodic blade rows with clean inflow. Once this input is available

CSTALL can be used to investigate the effects of inlet distortion on

the performance of the compressor without the need for further

Navier-Stokes computations.

Radial distortion can have a big impact on compressor stability but

it is easy to model with CSTALL. It was modeled by running

CSTALL in a 2-D mode with the specified inlet total pressure profile

modified as shown in Fig. 10. Figure 11 compares the predicted staticto-total pressure ratio characteristic with radial distortion to the computed and measured characteristics with clean flow shown previously.

Radial distortion greatly reduces the actual mass flow and exit static

pressure from their clean flow values, but the normalized characteristic of static-to-total pressure ratio versus corrected mass flow (red triangles) collapses onto the clean flow characteristic (blue squares.) The

main effect of radial distortion is to increase the predicted stall flow

from 17.1 kg/sec. to 18.8 kg/sec.

Circumferential Distortion

Circumferential distortion is a 3-D problem that requires analysis of

the entire annulus. This is costly to compute with a Navier-Stokes

code but easy to compute with CSTALL because CSTALL uses an

Euler formulation and a much coarser grid. Circumferential distortion

was modeled by running CSTALL in a 3-D mode with the inlet total

pressure profile reduced by 13 percent over a 120 degree segment of

the inlet boundary. Figure 12 compares the predicted static-to-total

pressure ratio characteristic with circumferential distortion to the

computed and measured characteristics with clean flow shown previously. Like radial distortion, circumferential distortion reduces the

actual mass flow and exit static pressure from their clean flow values.

Unlike radial distortion, the normalized static-to-total pressure ratio

versus corrected mass flow characteristic does not collapse onto the

clean characteristic, but becomes lower everywhere.

At operating points near stall it was noted that many circumferential

locations in the distorted region were well below the stall point on the

body force calibration curves (Fig. 3.) In this case a parallel compressor model would predict that the stage would be stalled, but the

present model predicts stable operation.

0.81 0.85 0.89 0.93 0.97 1.01

Inlet Total Pressure

0

20

40

60

80

100

Percent Span

Clean

Rad. Dist.

Figure 10 — Inlet total pressure profiles specified for stage 35.

16 17 18 19 20 21 22

Corrected Flow, kg/sec

1.10

1.20

1.30

1.40

1.50

1.60

1.70

Ps2/P01

Expt. (clean)

CSTALL (clean)

Rad. Dist

Figure 11 — Experimental and computed characteristics of

static-to-total pressure ratio with and without radial distortion.

16 17 18 19 20 21 22

Corrected Flow, kg/sec

1.10

1.20

1.30

1.40

1.50

1.60

1.70

Ps2/P01

Expt. (clean)

CSTALL (clean)

Theta Dist

Figure 12 — Experimental and computed characteristics of

static-to-total pressure ratio for stage 35 with and without

circumferential distortion.

16 17 18 19 20 21 22

Corrected Flow, kg/sec

1.10

1.20

1.30

1.40

1.50

1.60

1.70

Ps2/P01

Expt. (clean)

CSTA LL (clean)

Theta Dist

Figure 13 — Computed characteristic of static-to-total pressure

ratio for stage 35 with circumferential distortion during stall and

stall recovery.

NASA/TM—2006-214117 9
The calculations were pushed from the last stable operating point

into stall by increasing the specified exit static pressure ratio from

1.49 to 1.50. An unsteady rotating stall pattern developed gradually.

After 16 rotor revolutions the exit pressure ratio was decreased to 1.10

and the calculations were run another 14 revolutions to simulate stall

recovery to a high flow point. Figure 13 shows the locus of the

unsteady operating points on the static-to-total pressure ratio characteristics. During stall there was a large variation in inlet mass flow but

little variation in pressure ratio which is effectively set by the inlet and

exit boundary conditions.

Figure 14 (top) shows the unsteady history of the inlet mass flow

plotted against rotor revolutions. The increase in exit pressure reached

the inlet boundary in about one revolution and the mass flow began to

drop. An oscillation developed in the mass flow after several revolutions and became periodic after 10-12 revolutions. The exit pressure

was decreased at 16 revolutions and the inlet mass flow began to

increase about one revolution later. The oscillations are still evident at

30 revolutions but are decaying asymptotically towards zero. The bottom of Fig. 14 shows unsteady casing pressure traces at the rotor leading edge at 12 evenly spaced circumferential locations. Pressure

oscillations grew gradually over about 10 revolutions then decayed

slowly after the exit pressure was decreased at 16 revolutions. The

four traces in the center are in the distorted flow region and show more

variation in the signal. Analysis of the pressure traces shows that there

are two stall sells that rotate at .

Figure 15 shows axial velocity contours on an unwrapped surface

near the casing. Flow is from top to bottom, rotation is left to right,

and the low total pressure distorted inflow is at the center. The upper

figure shows a stable operating point where the distorted inflow is

transported slightly in the direction of the rotation. The lower figure

shows the flow during rotating stall where two stall cells are evident in

the rotor. Since the tip speed is transonic these cells generate

upstream-running shocks that produce the large pressure oscillations

seen in Fig. 14.

Figure 16 shows entropy contours on an annular surface near the

rotor trailing edge. Rotation is counterclockwise. The left figure

shows a stable operating point where the high entropy distorted inflow

that started upstream at bottom center has been transported a few

blade pitches counterclockwise. The right figure shows the flow during rotating stall. Animations have shown that the flow first becomes

unsteady at the 4 o’clock position where the rotor leaves the distorted

region. The flow remains quite unsteady at that location as two partspan stall cells form and rotate around the annulus.

SUMMARY AND DISCUSSION

A 3-D unsteady CFD code called CSTALL was developed and used

to investigate distortion and stall phenomena in compressors. The

code uses a body force formulation that can be calibrated easily from

a few steady Navier-Stokes calculations. CSTALL was used in a 2-D

throughflow mode to predict operating maps and estimate stall points

quickly and to predict the effects of radial distortion. It was used in a

3-D steady mode to predict the effects of circumferential distortion on

the operating map. Finally, CSTALL was used in a 3-D unsteady

mode to model rotating stall and recovery from stall. The following

observations can be made about the code:

• Marble’s formulation of body forces for turning and loss [6] provided an elegant framework for deriving body force information

from CFD solutions or experimental data. The body forces gave

physically realistic spanwise distributions of turning, deviation, and

loss, which are important for accurate prediction of tip-critical stall.

Marble’s formulation was used for stable operating points, but an

iterative scheme developed by Stewart [7] for turning the flow to a

specified flow angle was found to be useful for stalled operating

points.

• Body force data was input at one operating point and was scaled to

other operating points using normalized characteristic maps. This

procedure gave good predictions of the entire operating line, but

other formulations are possible. For example, data could input at

many operating points and interpolated directly, or body force

unknowns could be correlated with local incidence along the span.

These formulations might improve predictions of stall but would

complicate the input to the code.

• CSTALL predicted compressor stall without specification of a

stalled characteristic. The predicted stall point was at a slightly

lower flow than the experiment and a much lower flow than NavierStokes calculations used for calibration. It was found that the predicted stall point was sensitive to the slopes of the normalized characteristic maps used to scale the body force data to other mass

flows. These maps were extrapolated linearly into stall, giving the

correct trends for loss and deviation but probably not for .

Further calculations will be needed to find the best way to calculate

the normalized characteristic maps and to extend them into stall.

• A throttle exit boundary condition was shown to decrease the predicted mass flow at which the compressor stalled. Since that mass

flow was low even without the throttle condition, the throttle condition was not used for most cases shown here. It would be interesting

to see if this boundary condition can be used to stabilize NavierStokes calculations.

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Rotor Revolutions

−0.1

1.1

(Ps−P(t=0))/Po

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Rotor Revolutions

17

18

19

20

21

Corrected Mass Flow [kg/sec]

0.94 Ω

Figure 14 — Top: Inlet corrected mass flow for stage 35 during

stall and stall recovery.

Bottom: Casing static pressures at 12 circumferential locations

at the leading edge of rotor 35 during stall and stall recovery.

0.94 Ω

∆(rv)

NASA/TM—2006-214117 10
Rotor

Stator

Low P0 Flow

Stall cell Stall cell

Shock Shock

Figure 16 — Entropy contours at the trailing edge of rotor 35.

Left: Steady flow with circumferential distortion over 120 deg.

Right: Stalled flow.

Clean

Clean

Stalled

Very

Rotation

Stalled

Unsteady

Distortion Distortion

Rotation

Figure 15 — Axial velocity contours on an unwrapped surface near the tip of stage 35.

Top: Steady flow with circumferential distortion over 120 deg.

Bottom: Stalled flow.

NASA/TM—2006-214117 11
• One useful feature of CSTALL was its ability to predict the effects

of inlet distortion on a compressor quickly without the need for further Navier-Stokes computations. Radial distortion was analyzed

and was shown to reduce the stable flow range of the compressor

without affecting the shape of the normalized operating characteristic. Circumferential distortion also reduced the stable flow range of

the compressor, but it reduced the static-to-total pressure ratio at all

flow rates as well.

• Unsteady calculations showed the ability of the model to predict

rotating stall inception and recovery. These calculations used a

body force lag equation to model the delayed response of body

forces to changes in flow. The model required a time lag parameter

that is usually taken to be the blade row throughflow time. Unsteady

calculations seemed to be insensitive to changes in this parameter,

but further calculations are needed to determine its full effect. It

may also be possible to calibrate this parameter using 2-D unsteady

Navier-Stokes cascade calculations.

• Further calculations are planned to validate CSTALL predictions of

rotating stall and to investigate casing injection flow control for stall

prevention and recovery.

REFERENCES

[1] Pampreen, R. C., 1993, Compressor Surge and Stall, Concepts

ETI, Inc., Norwich, VT.

[2] Takata, H. and Nagano, S., 1972, “Nonlinear Analysis of Rotating

Stall,” J. Engineering for Power, Oct. 1972, pp. 279-293.

[3] Longley, J. P., 1997, “Calculating the Flowfield of High-Speed

Multi-stage Compressors,” ASME Paper 97-GT-468.

[4] Demargne, A. A. J., Longley, J. P., 1997, “Comparisons Between

Measured and Calculated Stall Development in Four High-Speed

Multi-Stage Compressors,” ASME Paper 97-GT-467.

[5] Lindau, J. W., Owen, A. K., 1997, “Nonlinear Quasi-ThreeDimensional Modeling of Rotating Stall and Surge,” AIAA Paper 97-

2772.

[6] Marble, F. E., 1964, “Three-Dimensional Flow in Turbomachines,” in High Speed Aerodynamics and Jet Propulsion, Vol X, Aerodynamics of Turbines and Compressors, Hawthorne, W. R., ed.

Princeton University Press, Princeton, NJ., pp. 83–165.

[7] Stewart, M. E. M., 1995, “Axisymmetric Aerodynamic Numerical

Analysis of a Turbofan Engine,” ASME Paper 95-GT-338.

[8] Escuret, J. F., Garnier, V., 1994, “Numerical Simulations of Surge

and Rotating Stall in Multi-Stage Axial-Flow Compressors,” AIAA

Paper 94-3202.

[9] Hale, A., and O’Brien, W. O., 1998, “A Three-Dimensional Turbine Engine Analysis Compressor Code (TEACC) For Steady State

Inlet Distortion,” J. Turbomachinery, Vol. 120, pp. 422-430.

[10] Hale, A., Davis, M., and Sirbaugh, J., 2004, “A Numerical Simulation Capability for Analysis of Aircraft Inlet–Engine Compatibility,”

ASME Paper GT-2004-53473.

[11] Gong, Y., Tan, C. S., Gordon, K. A., Greitzer, E. M., 1998, “A

Computational Model for Short Wavelength Stall Inception and

Development in Multistage Compressors,” ASME Paper 98-GT-476.

[12] Gong, Y., 1998, “A Computational Model for Rotating Stall

Inception and Inlet Distortions in Multistage Compressors,” Ph. D.

dissertation, Massachusetts Institute of Technology.

[13] Hsiao, E., Naimi, M., Lewis, J. P., Dalbey, K., Gong, Y., and Tan,

C., 2001, “Actuator Duct Model of Turbomachinery Components for

Powered-Nacelle Navier-Stokes Calculations,” J. Propulsion and

Power, Vol. 17, No. 4, pp. 919-927.

[14] Chima, R. V., 1998, “Calculation of Multistage Turbomachinery

Using Steady Characteristic Boundary Conditions,” AIAA Paper

AIAA-98-0968. Also NASA TM-1998-206613.

[15] Chima, R. V., and Liou, M.–S., 2003, “Comparison of the

AUSM+ and H-CUSP Schemes for Turbomachinery Applications,”

AIAA Paper AIAA-2003-4120. Also NASA TM-2003-212457.

[16] Tweedt, D. L., and Chima, R. V., 1996, “Rapid Numerical Simulation of Viscous Axisymmetric Flow Fields,” AIAA Paper AIAA-96-

0449. Also NASA TM-107103.

[17] Reid, L., and Moore, R. D., 1978, “Performance of a SingleStage Axial-Flow Compressor With Rotor and Stator Aspect Ratios of

1.19 and 1.26, Respectively, and With Design Pressure Ratio of 1.82,”

NASA Technical Paper 1338.

NASA/TM—2006-214117 12
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

REPORT DOCUMENTATION PAGE

2. REPORT DATE

19. SECURITY CLASSIFICATION

 OF ABSTRACT

18. SECURITY CLASSIFICATION

 OF THIS PAGE

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

12b. DISTRIBUTION CODE

8. PERFORMING ORGANIZATION

 REPORT NUMBER

5. FUNDING NUMBERS

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

6. AUTHOR(S)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS

17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Technical Memorandum

Unclassified

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135–3191

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

February 2006

NASA TM—2006-214117

GT2006–90040

E–15452

WBS 561581.02.08.03.02.01

18

A Three-Dimensional Unsteady CFD Model of Compressor Stability

Rodrick V. Chima

Turbomachinery; Compressor; Stall; Inlet distortion; CFD; Computational fluid dynamics;

Unsteady flow

Unclassified -Unlimited

Subject Category: 07

Prepared for Turbo Expo 2006 sponsored by the American Society of Mechanical Engineers, Barcelona, Spain,

May 8–11, 2006. Responsible person, Rodrick V. Chima, e-mail: Rodrick.V.Chima@nasa.gov, organization code

RTC, 216-433–5919.

A three-dimensional unsteady CFD code called CSTALL has been developed and used to investigate compressor

stability. The code solved the Euler equations through the entire annulus and all blade rows. Blade row turning, losses,

and deviation were modeled using body force terms which required input data at stations between blade rows. The input

data was calculated using a separate Navier-Stokes turbomachinery analysis code run at one operating point near stall,

and was scaled to other operating points using overall characteristic maps. No information about the stalled characteristic

was used. CSTALL was run in a 2–D throughflow mode for very fast calculations of operating maps and estimation of

stall points. Calculated pressure ratio characteristics for NASA stage 35 agreed well with experimental data, and results

with inlet radial distortion showed the expected loss of range. CSTALL was also run in a 3–D mode to investigate inlet

circumferential distortion. Calculated operating maps for stage 35 with 120 degree distortion screens showed a loss in

range and pressure rise. Unsteady calculations showed rotating stall with two part-span stall cells. The paper describes

the body force formulation in detail, examines the computed results, and concludes with observations about the code.