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Proceedings of the 8th International Symposium

on Experimental and Computational

Aerothermodynamics of Internal Flows

Lyon, July 2007

Mihai Leonida NICULESCU: Ph.D. Student http://www.lmfa.ec-lyon.fr/ISAIF8/

Paper reference : ISAIF8-00125

Detailed Investigation of an Atomizing Air Compressor

Mihai Leonida Niculescu Valentin Silivestru Georgel Vizitiu Bogdan Gherman National Research & Development Institute for Gas Turbines COMOTI,

Iuliu Maniu 220 D, 061 126 Bucharest 6, Romania, P.O. 76, Phone: +4021 4340198; Fax: +4021 4340241

Sterian Dănăilă Corneliu Berbente

University POLITEHNICA of Bucharest, Faculty of Aerospace Engineering,Polizu 1-7, 011 061 Bucharest 1, Romania, Phone: +4021 4023814

The centrifugal atomizing air compressors are utilized in the industrial gas turbine as auxiliary systems in order to

increase the combustion efficiency. This solution seems to be widely used by General Electric although there is

very little documentation available at large public. The authors have not found any material that investigates the

aerodynamics of the centrifugal atomizing air compressors. For this reason, the authors consider that it is useful to

share their experience with other researchers.

Keywords: Atomizing Air Compressor, Impeller, Vaned Diffuser

Introduction

The atomizing air compressors are utilized in a closed

loop system between the turbine axial compressor dis-

charge and combustion chamber inlet of industrial gas

turbine. They receive their air supply from the discharge

of the turbine axial compressor. The atomizing air flow is

only a small portion, usually less than 5% of the total air

flow through the turbine. The role of the atomizing air

compressor is to boost the air pressure to the level re-

quired to obtain the energy required for proper atomizing

of the liquid fuel; usually the atomizing air compressor

pressure ratio is up to two. The atomizing air and fuel are

mixed together at the exit of the fuel nozzles and subse-

quently mixed with the main air flow in the combustion

chamber. Due to the lack of documentation with regard

the aerodynamics of centrifugal atomizing air compres-

sors, we have used the general compressor aerodynamic

books [1-2]

COMOTI has design and manufactured two atomizing

air compressors, one of them has three different vaned

diffusers whose vane angle at the leading edge are 18, 23

and 28 deg relative to tangential direction because it is

widespread industrial practice to combine an impeller

with different vaned diffusers in order to obtain the range

of operation required by customers [3]. These compres-

sors have tested in similitude conditions on a new test rig,

which still operates in an open circuit. Our research con-

cerning the atomizing air compressors was supervised,

approved and supported by the Romanian Education and

Research Ministry.

In order to increase the performance of its products,

COMOTI has developed in-house tools of designing cen-

trifugal compressors to increase their efficiency and us-

able range of flow rate at which they can operate and has

bought a license of Ansys CFX 10.0

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2 Proceedings of the 8th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows

Fig. 1 Industrial gas turbine with atomizing air compressor

One of the main objectives of this study is to investi-

gate the tip leakage flow that occurs in the impeller ofatomizing air compressor because it has a huge impact on

its performance.

Governing Equations

For a three-dimensional rotating Cartesian coordinate

system, the unsteady Reynolds-averaged Navier-Stokes

equations can be written in conservative form as [4-5]

( ) ( ) ( ) y y x x z z F G F G F GQ

S t x y z

∂ −∂ − ∂ −∂+ + + =

∂ ∂ ∂ ∂ (1)

where:

2 2 2

2 2

u

vQ

w

W r e

ρ

ρ

ρ

ρ

ρ

⎡ ⎤

⎢ ⎥⎢ ⎥⎢ ⎥

= ⎢ ⎥⎢ ⎥⎢ ⎥⎛ ⎞Ω⎢ ⎥+ −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(2)

2

2

2

x y z

u v w

u p vu wu

F F F uv v p wv

uw vw w p

uI vI wI

ρ ρ ρ

ρ ρ ρ

ρ ρ ρ

ρ ρ ρ

ρ ρ ρ

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥+⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥= = =+⎢ ⎥ ⎢ ⎥ ⎢ ⎥

+⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

(3)

Nomenclature

Aarea of cross-section normal to midspansurface of impeller (m

2)

Greek letters

b blade height (m) β angle relative to tangentialdirection (rad)

C p static pressure recovery coefficient ∆t physical timescale (s)

e internal energy (J/kg) η polytropic efficiency

f e external acceleration (m/s2) ϕ flow coefficient

F x , F y , F z vectors of convective components of flux κ thermal conductivity (W/(m.K))

G x , G y , G z vectors of diffusive components of flux µ dynamic viscosity (kg/(m.s))

I rothalpy (m2

/s2

) µ t eddy viscosity (kg/(m.s)) M u peripheral Mach ρ static density (kg/m3)

p static pressure (Pa) τ shear stress tensor (Pa)

P total pressure (Pa) Ω angular velocity (rad/s)

R Gas conconstant (J/(kg.K)) Subscripts r distance from the rotational axis (m) 1 impeller inletS vector of source term 2 impeller exit

s tip clearance (m) 3 vaned diffuser inletT static temperature (K) 4 vaned diffuser outlett time (s) t turbulentu, v, w Cartesian components of velocity (m/s) ts total-to-staticV absolute velocity (m/s) tt total-to-totalW relative velocity (m/s) Superscript

x, y, z Cartesian coordinates tot total (laminar + turbulent)

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Mihai Leonida NICULESCU et al. Detailed Investigation of an Atomizing Air Compressor 3

If we assume that the fluid is newtonian and the ther-

mal boundary layer is neglected, the diffusive flux G may

be written as

0tot

xx

tot

xy x tot

xz

tot tot tot

xx xy xz

G

T u v w k

x

τ

τ

τ

τ τ τ

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥

= ⎢ ⎥⎢ ⎥⎢ ⎥∂

+ + +⎢ ⎥⎢ ⎥∂⎣ ⎦

(4a)

0tot

xy

tot

yy

y tot

yz

tot tot tot

xy yy yz

G

T u v w k

y

τ

τ

τ

τ τ τ

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥

= ⎢ ⎥⎢ ⎥⎢ ⎥∂+ + +⎢ ⎥

∂⎢ ⎥⎣ ⎦

(4b)

0tot

xz

tot

yz z tot

zz

tot tot tot

xz yz zz

G

T u v w k

z

τ

τ

τ

τ τ τ

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥

= ⎢ ⎥⎢ ⎥⎢ ⎥∂

+ + +⎢ ⎥⎢ ⎥∂⎣ ⎦

(4c)

According to the Boussinesq hypothesis, the shear

stresses τtot may be written as

( )22

3

tot

xx t

u v w

x y z τ µ µ ⎛ ⎞∂ ∂ ∂= + − −⎜ ⎟∂ ∂ ∂⎝ ⎠

(5a)

( )2

23

tot

yy t

v u w

y x z τ µ µ

⎛ ⎞∂ ∂ ∂= + − −⎜ ⎟∂ ∂ ∂⎝ ⎠

(5b)

( )2

23

tot

zz t

w v u

z y xτ µ µ

⎛ ⎞∂ ∂ ∂= + − −⎜ ⎟∂ ∂ ∂⎝ ⎠

(5c)

( )tot tot

xy yx t

u v

y xτ τ µ µ

⎛ ⎞∂ ∂= = + +⎜ ⎟∂ ∂⎝ ⎠

(5d)

( )tot tot

xz zx t

u w

z xτ τ µ µ

∂ ∂⎛ ⎞= = + +⎜ ⎟∂ ∂⎝ ⎠

(5e)

( )tot tot

yz zy t

w v

y z τ τ µ µ

⎛ ⎞∂ ∂= = + +⎜ ⎟∂ ∂⎝ ⎠

(5f)

The Sutherland’s formula can be used to determine the

dynamic viscosity µ as function of temperature, while the

eddy viscosity µt is computed with a turbulence model.

For gases, the external force f e due to the gravitational

acceleration is very small, therefore it can be neglected.

Moreover, we can assume that the thermal conductivity is

the single heat source. If the Cartesian coordinate system

is rotating about z axis with constant angular-velocity Ω,

source term S could be written as

( )

( )

2

2

0

2

2

0

0

x v

S y u

ρ

ρ

⎡ ⎤⎢ ⎥

Ω + Ω⎢ ⎥⎢ ⎥

= Ω − Ω⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

(6)

The pressure is obtained from the equation of state,

p RT ρ = (7)

Numerical Simulation

The numerical simulations of the three-dimensional

viscous flow was carried out on an atomizing air impeller

combined with three vaned diffusers, with Ansys CFX

10.0 [6] and a quasi three-dimensional in-house code.

Table 1 Design

Property Atomizing impeller

Gas Air

Rotational speed 40 000 rpm

Mass flow rate 2.676 kg/s

Pressure ratio ≈ 1.5

Number of blades 17

Hub diameter

at leading edge42 mm

Tip diameter

at leading edge

65.7 mm

Outlet diameter 150 mm

Exit blade height 4 mm

Tip clearance at shroud 0.4 mm

Hub blade angle at

leading edge54 deg

Tip blade angle at

leading edge41 deg

Exit blade angle 55 deg

Inlet total pressure 12.273 bar

Inlet total temperature 380.37 K

Flow coefficient 0.0284

Peripheral Mach 0.8

The cross-section normal to midspan surface of cen-

trifugal and mixed impeller looks like lateral surface of a

frustum of a right circular cone (Fig. 2) cut by blades. We

have tried several meridional geometries in order to

minimize the area gradient of surface normal to midspan

surface of impeller until we have obtained an acceptable

area distribution as shown in Figs. 3 and 4. We have paid

a special attention to the chamber angle distribution (Fig.

5) in order to minimize the secondary and leakage flows,

which condition largely efficiency, pressure ratio and

stable operation range of impellers.

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Fig. 2 View of cross-section normal to midspan surface,

in a centrifugal impeller

Fig. 4 Dimensionless area distribution of cross-section normal

to midspan surface, in the atomizing air impeller,

computed with in house-code

The investigated vaned diffusers consist of two parallel

walls and 14 circular-arc vanes whose vane angle at the

leading edge are 18, 23 and 28 deg relative to tangential

direction. The center of the leading edge is at radius r 3 / r 2

= 1.16 and the center of the trailing edge is at radius r 4 / r 3

= 1.721. The width of each vaned diffuser is only 4 mm,

therefore the viscous effects are very important.

Firstly, we have studied the impeller and vaneless dif-

fuser as shown in Fig. 6 and after that, we have investi-

gated the atomizing air compressor with open impeller,

vaneless diffuser and vaned diffuser as shown in Fig. 7.

For the atomizing air compressor with the open im-

peller and without the vaned diffuser, the computational

domain generated in Ansys ICEM CFD 10.0 was split

into six blocks to facilitate the building of a fully struc-

tured mesh. One passage is divided into six domains: one

H-grid upstream of the blade, two H-grids for the passage

between the blade, one H-grid downstream of the blade,

one H-grid in the center of tip gap and one O-grid around

the blade as shown in Figs. 8 and 9. Two meshes were

tested, with 1 192 690 and respectively 868 890 nodes. A

Fig. 3 Meridional view of the atomizing air impeller

Fig. 5 Chamber angle distribution

in the atomizing air impeller

special attention was paid to the tip clearance because the

ratio s2/b2 = 0.1 is very high. For this reason, the fine

mesh has 10 points in the tip-to-shroud direction and 36 in

the hub-to-tip direction. COMOTI has tried but it has not

succeeded to decrease the tip clearance at impeller exit

under 0.4 mm due to the vibrations and technological

constraints.

For the vaned diffusers, the computational domain

generated in Ansys ICEM CFD 10.0 was split into five

blocks to facilitate the building of a fully structured mesh.

One passage is divided into five domains: one H-grid

upstream of the vane, two H-grids for the passage be-

tween the vane, one H-grid downstream of the vane and

one O-grid around the vane. Two meshes were tested for

each vaned diffuser, with about 300 000 and respectively

200 000 nodes.

In Ansys CFX 10.0, the numerical solution of Rey-

nolds-Averaged Navier-Stokes (RANS) equations was

obtained with an implicit time marching technique. It is

worthwhile to notice that, in the implicit or explicit

time-stepping schemes, the steady-state solution is not

dependent by the time step; therefore, this stepping is

βhub

βshroud

Leading

edgeTrailing

edgeDimensionless meridional distance

ω

A r e a o f c r o s s - s e c t i o n n o r m a l t o

m i d s p a n s u r f a c e o f i m p e l l e r / A 1

R a d i u s ( m m

)

Rotational axis mm

Leading

edgeTrailing


C h a m b e r a n g l e β (

d e g )

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Mihai Leonida NICULESCU et al. Detailed Investigation of an Atomizing Air Compressor 5

Leading


R e l a t i v e v e l o c i t y / u

2

Trailing

edge

W/u2 near shroud, mid-channel

W/u2 at midspan, mid-channel

Wm/u2 at midspan, mid-channelWθ/u2 at midspan, mid-channel

amenable to convergence acceleration techniques. In or-

der to reduce the computational cost, we employed a

physical timescale ∆t = 1/Ω = 0.23 ms, which has assured

a good convergence rate. Convective fluxes of the discre-

tized equations are handled using a second order upwindscheme. The authors considered that the steady-state so-

lution was achieved when the reduction of the root mean

square of the norm of residuals was five decades.

Fig. 6 Isometric view of computational domain of atomizing

air compressor without vaned diffuser

Fig. 8 Grid detail showing shroud modeling

Fig. 10 Atomizing air rotor

(designed and manufactured by COMOTI)

The flow is assumed fully turbulent and it has simulated

in Ansys CFX 10.0 with the shear-stress transport (SST)

k-ω based model, which was developed by Menter [6-7]

in order to combine the advantages of the robust and ac-

curate formulation of the Wilcox k-ω model in the near-wall region with the free-stream independence of the k-ε

model in the far field. To achieve this, the k-ε model is

converted into a k-ω formulation.

Fig. 7 Isometric view of computational domain of atomizing

air compressor with vaned diffuser whose vane angle

at the leading edge is 23 deg

Fig. 9 Grid detail showing clearance modeling

Fig. 11 Dimensionless relative velocity, at design point, in the

shrouded atomizing air impeller, computed with in-house code

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At the inlet, a uniform stagnation pressure (12.273 bar)

and temperature (380.37 K) are imposed, turbulence in-

tensity is 5%, turbulent viscosity ratio µt/µ is 10 and the

flow is normal to inlet. Downstream classical boundary

condition (uniform static pressure) is inadequate tosimulate the atomizing air compressor due to the highly

non-uniform flow at the exit boundary. For this reason,

the mass flow rate is imposed at the outlet because this

boundary condition leads to a non-uniform static pressure

distribution at the outlet. All the walls have been assumed

adiabatic.

The interface between the impeller and vaned diffuser

(Fig. 7) is simulated with a version of mixing plane ap-

proach called stage [6] because the unsteady flow,

multi-blade-row CFD analysis are still prohibitive and

limited by the available computing resources. On mix-

ing-plane, the momentum and energy fluxes are averagedtangentially to provide a spanwise profile of pressure,

momentum and energy. Stage averaging between blade

passages takes account for time average interaction ef-

fects between them. Basing on the hypothesis that the

relative motion between blade rows is sufficiently large to

Fig. 12 Streamlines at 95% span from the hub, in the open

impeller, at design point, computed with Ansys CFX 10.0

Fig. 14 Total-to-total polytropic efficiency, at design speed,

computed with Ansys CFX 10.0

cause any upstream velocity profile to mix out prior en-

tering the downstream machine component, the stage

approach models the loss that occurs as the flow is mixed

between stationary and rotating components. The major

lack of this approach is that it neglects transient interac-tion effects between blade rows.

The atomizing air impeller has studied in three con-

figurations: open, with no gap and with stationary shroud

and shrouded (with rotating shroud), in order to investi-

gate the importance of tip leakage on its performance as

shown in Figs. 11, 12, 13, 14 and 15. Also, we have

studied the atomizing air compressor with three different

vaned diffusers whose vane angle at the leading edge are

18, 23 and 28 deg relative to tangential direction and with

the open impeller as shown in Figs. 16, 17, 18 and 19.

Because the flow is compressible at the impeller exit,

the static pressure recovery coefficient C p is defined as2

2 2

p

p pC

P p

−=

− (8)

to show the effect of the vaneless and vaned diffuser on

static pressure recovery as shown in Figs. 18 and 19.

Fig. 13 Total pressure ratio of open and close impeller,

at design speed, computed with Ansys CFX 10.0

Fig. 15 Total-to-static polytropic efficiency, at design speed,

computed with Ansys CFX 10.0

Flow coefficient ϕ

I m

e l l e r

t o t a l

r e s s u r e r a t i o

T o t a l - t o - t o t a l p o l y t r o p i c e f f i c i e

n c y

Flow coefficient ϕ

Flow coefficient ϕ

T o t a l - t o - s t a t i c p o l y t r o p i c e f f i c i e n c y

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exit blade angle of the atomizing air impeller is 55 deg

relative to tangential direction.

The impellers and vaneless diffusers have a signifi-

cant stabilizing role. Unfortunately, the vaneless dif-

fusers are much bigger than vaned diffusers that realizethe same static pressure rise. Moreover, at design point,

the total pressure loss is much larger in the vaneless

diffusers than in the vaned diffusers, which achieve the

same static pressure recovery.

Acknowledgement

The study could not be completed without the sup-

port received from University “POLITHENICA” Bu-

charest – Aerospace Engineering Faculty and National

Institute for Research and Development Gas Turbines

COMOTI.

References

[1] N.A. Cumpsty, Compressor Aerodynamics, Longman

Scientific & Technical, 1989

[2] V. Pimsner, Turbomachines (in Romanian), EdituraTehnica Bucharest, 1988

[3] R. Hunziker, G. Gyarmathy, The Operational Stability

of a Centrifugal Compressor and Its Dependence on the

Characteristics of the Subcomponents, Journal of Tur-

bomachinery, Vol. 116, April 1994

[4] S. Dănăilă, C. Berbente, Numerical Methods in Fluid

Dynamics (in Romanian), Publishing House of Roma-

nian Academy, 2003

[5] C. Hirsch, Numerical Computation of Internal and Ex-

ternal Flow, Volume 2: Computational Methods for In-

viscid and Viscous Flows, John Wiley and Sons, New

York, 1990

[6] Ansys Inc, Ansys CFX-Solver, Release 10, Ansys In-

corporated, 2005[7] F.R. Menter, Two-Equation Eddy-Viscosity Turbulence

Models for Engineering Applications, AIAA Journal,

32(8), pg. 1598-1605, August 1994

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