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Flow Simulation in a High-Loaded Radial Compressor

  • W. Evers
  • M. Heinrich
  • I. Teipel
  • A. R. Wiedermann
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NONUFM, volume 48)

Summary

A two- and three-dimensional Euler and Navier-Stokes code has been developed and successfully used for the computation of the flow field in a high loaded centrifugal compressor. For the purpose of comparison, the algebraic turbulence model of Baldwin and Lomax, a modification of the Baldwin-Lomax model with an extension according to Goldberg and Chakravarthy [1] for the determination of separated flow regions and the two-equation κ — ε model according to Kunz and Lakshminarayana [2, 3] are applied to simulate the flow field of the diffuser with the two-dimensional Navier-Stokes code. The three-dimensional solver in addition to the extended and original Baldwin-Lomax model has been applied to obtain the three-dimensional flow field of the diffuser and the impeller.

Keywords

Mass Flux Algebraic Model Radial Compressor Reynolds Stress Model Splitter Blade 
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.

Abbreviations

Nomenclature

D, ε

functions of the κ — ε model

e

specific internal energy

Erot

relative total specific internal energy

\(\overrightarrow{E}\)

flux vector in direction of the curvilinear coordinates

f2, fμ

functions of the κ — ε model

F Kleb

Klebanoff intermittency function

FWake

wake function

G

Gaussian distribution

J

Jacobian

k

turbulent kinetic energy \((=k^\star/(\rho/\rho)^\star_{tot,\infty})\)

l

length scale of the Baldwin-Lomax model

n

wall distance

p

static pressure \((=p^\star/p^\star_{tot,\infty})\)

P

production rate of k

Pr

Prandtl number

qi

Cartesian component of heat transfer

\(\vec{Q}\)

vector of variables of state

r

radius \((=r^\star/r^\star_{DE})\)

Re

Reynolds number \((r^\star_{DE}\sqrt{(p\rho)^\star_{tot,\infty}/\mu^\star_{l,\infty}}\)

RT

local Reynolds number

\(\overrightarrow{S}\)

source term vector

t

time \((t^\star\sqrt{(p/\rho)^\star_{tot,\infty}/r^\star_{DE}})\)

u

relative velocity in x-direction, \(u=u_1(=u^\star/\sqrt{(p/\rho)^\star_{tot,\infty}})\)

us

wall friction velocity, velocity scale

Ui

contravariant velocities

v, w

relative velocities in y and z direction, v=v 2, w=u 3 (see u)

\(\overrightarrow{w}\)

velocity vector

x,y,z

relative Cartesian coordinates, x=x 1, y=x 2, z=x 3 \((x_{i}^{\star}/r^\star_{DE})\)

δij

Kronecker delta

ε

dissipation rate of \(k(=\varepsilon^\star r^\star_{DE})/[(p/\rho)^\star_{tot,\infty}]^{1.5})\)

κ

isentropic coefficient

μl

dynamic viscosity \((=\mu_{l}^{\star}/\mu^\star_{l,\infty})\)

μt

turbulent viscosity

ξi

generalized curvilinear coordinates

ρ

density \((=\rho^\star/\rho^\star_{tot,\infty})\)

τij

Cartesian stress tensor component

τw

wall shear stress

ψ

function in Eqn. (1)

ω

vorticity scale

Ω

angular velocity of relative frame of reference \((=\Omega^\star r^\star_{DE}/\sqrt{(p/\rho)^\star_{tot,\infty}})\)

Superscripts and subscripts

~

density weighted value

time averaged value

+

modified value

dimensionalized value

a,b,BL

layer pointer in the algebraic turbulence models

c

inviscid

DE

diffuser exit

i

layer pointer in the algebraic turbulence models

i, j, k

axis pointer

K

suction duct upstream the compressor

o

layer pointer in the algebraic turbulence models

tot

total value

w

wall

v

viscous

0

impeller exit

diffuser inlet

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References

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Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996

Authors and Affiliations

  • W. Evers
    • 1
  • M. Heinrich
    • 1
  • I. Teipel
    • 1
  • A. R. Wiedermann
    • 1
  1. 1.Institute for MechanicsUniversity of HannoverHannoverGermany

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