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.
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Abbreviations
- 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 \((=\Omega^\star r^\star_{DE}/\sqrt{(p/\rho)^\star_{tot,\infty}})\)
- ~:
-
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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© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Evers, W., Heinrich, M., Teipel, I., Wiedermann, A.R. (1996). Flow Simulation in a High-Loaded Radial Compressor. In: Hirschel, E.H. (eds) Flow Simulation with High-Performance Computers II. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89849-4_33
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DOI: https://doi.org/10.1007/978-3-322-89849-4_33
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