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

  • M. Heinrich
  • I. Teipel
Chapter

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 kε 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.

Keywords

Turbulence Model Mass Flux Algebraic Model Partial Load Radial Compressor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

D,ε

functions of the kε model

E

total specific internal energy

\(\vec{E}\)

flux vector in ξ-direction

f2,fµ

functions of the kε model

FKleb

Klebanoff intermittency function

FWake

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 * )

ro

impeller exit radius

Re

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

RT

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 \(\left( ={{u}^{*}}/\sqrt{\left( p/\rho \right)_{tot,\infty }^{*}} \right)\)

ui

velocity related to i-direction

us

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 * )

xi

Cartesian coordinate related to i-direction

δij

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

µl

dynamic viscosity (= (p/ρ)2/3)

µt

turbulent viscosity

w

vorticity-scale

ρ

density (= ρ*/ρ tot,∞ * )

τij

Cartesian stress tensor component

τw

wall shear stress

ξ,ŋ,ς

generalized curvilinear coordinates

ξx, ŋx..

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

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • M. Heinrich
    • 1
  • I. Teipel
    • 1
  1. 1.Institute for MechanicsUniversity of HannoverGermany

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