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Advances in Fluid Mechanics and Turbomachinery pp 39–56Cite as

Flow Simulation in an Aerodynamic Diffusor of a High Loaded Radial Compressor using Different Turbulence Models

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Abstract

A two- and three-dimensional code solving the Reynolds-averaged compressible Navier-Stokes equations has been developed and successfully used for computation of the steady flow field in an aerodynamic diffuser of a high loaded centrifugal compressor. For the purpose of comparison the turbulence model of Baldwin and Lomax with and without an extension of Goldberg and Chakravarthy [1] for the determination of separated flow regions and the two equation k — ε model according to Kunz and Lakshminarayana [2, 3] are applied to compute the flow field of the diffuser on several operating points with the two-dimensional code. The three-dimensional solver in addition with the extended and unextended Baldwin-Lomax model has been applied to ascertain the three-dimensional flow field on the working point with the largest separation zone in the two-dimensional case. For comparison measured pressure distributions [4] of the examined operating points are presented likewise.

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Abbreviations

D,ε :

functions of the k — ε model

E :

total specific internal energy

\(\vec{E}\) :

flux vector in ξ-direction

f 2 ,f µ :

functions of the k — ε model

F Kleb :

Klebanoff intermittency function

F Wake :

wake function

\(\vec{F}\) :

flux vector in ŋ-direction

G :

Gaussian-distribution

J :

Jacobian

k :

turbulent kinetic energy(=k*/(p/ρ) * tot,∞ )

n :

wall distance

p :

static pressure (= p*/p * tot,∞ )

P :

production rate of k

Pr :

Prandtl-number

q :

Cartesian component of heat transfer

\(\vec{Q}\) :

vector of variables of state

r :

radius (= r*/r *DE )

r o :

impeller exit radius

Re :

Reynolds-number\(\left( ={{r}^{*}}DE\sqrt{\left( p\rho \right)_{tot,\infty }^{*}}/\mu _{l,\infty }^{*} \right)\)

R T :

local Reynolds-number

\(\vec{S}\) :

source term vector

t :

time \(\left( ={{t}^{*}}\sqrt{\left( p/\rho \right)_{tot,\infty }^{*}/r_{DE}^{*}} \right)\)

Tu :

turbulence rate

u :

velocity in x-direction \(\left( ={{u}^{*}}/\sqrt{\left( p/\rho \right)_{tot,\infty }^{*}} \right)\)

u i :

velocity related to i-direction

u s :

velocity-scale

U ∞ :

mean velocity at diffuser inlet

v :

velocity in y-direction (see u)

w :

velocity in z-direction (see u)

\(\vec{w}\) :

velocity vector

x,y,z :

Cartesian coordinates (related to r * DE )

x i :

Cartesian coordinate related to i-direction

δ ij :

Kronecker-symbol

ϵ :

dissipation rate of k

$$\left( ={{\varepsilon }^{*}}r_{DE}^{*}/{{\left[ \left( p/\rho \right)_{tot,\infty }^{*} \right]}^{1.5}} \right)$$
k :

isentropic coefficient

µ l :

dynamic viscosity (= (p/ρ)2/3)

µ t :

turbulent viscosity

w :

vorticity-scale

ρ :

density (= ρ*/ρ * tot,∞ )

τ ij :

Cartesian stress tensor component

τ w :

wall shear stress

ξ,ŋ,ς :

generalized curvilinear coordinates

ξ x , ŋ x ..:

partial derivatives ξ, ŋ,.. to x,y,..

∼ :

density weighted value

− :

time averaged value

+ :

modified value

*:

dimensionalized value

c :

inviscid

DE :

diffuser exit

i,j,k :

pointer related to x,y or z axis

v :

viscous

K :

suction duct upstream the compressor

tot :

total value

w :

wall

∞:

diffuser inlet

References

  1. Goldberg, U. C.; Chakravarthy, S. R.: Separated Flow Prediction Using a Hybrid k-L / Backflow Model. AIAA Journal, Vol. 28, NO. 6, Jun. 1990.

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  3. Kunz, R.; Lakshminarayana, B.: Three-Dimensional Navier-Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k — e Turbulence Model. ASME Paper 91-GT-146, 1991.

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Authors and Affiliations

  1. Institute for Mechanics, University of Hannover, Germany

    M. Heinrich & I. Teipel

Authors
  1. M. Heinrich
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  2. I. Teipel
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Editors and Affiliations

  1. Zentrum für angewandte Raumfahrttechnologie und Mikrogravitation, Universität Bremen, Am Fallturm, D-28359, Bremen, Germany

    Hans J. Rath  & Christoph Egbers  & 

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© 1998 Springer-Verlag Berlin Heidelberg

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Heinrich, M., Teipel, I. (1998). Flow Simulation in an Aerodynamic Diffusor of a High Loaded Radial Compressor using Different Turbulence Models. In: Rath, H.J., Egbers, C. (eds) Advances in Fluid Mechanics and Turbomachinery. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72157-1_4

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  • DOI: https://doi.org/10.1007/978-3-642-72157-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-72159-5

  • Online ISBN: 978-3-642-72157-1

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