Cebeci-Smith model

**Turbulence modeling**
	Turbulence
	RANS-based turbulence models Linear eddy viscosity models Algebraic models Cebeci-Smith model ; Baldwin-Lomax model ; Johnson-King model ; A roughness-dependent model ; ; One equation models Prandtl's one-equation model ; Baldwin-Barth model ; Spalart-Allmaras model ; ; Two equation models k-epsilon models Standard k-epsilon model ; Realisable k-epsilon model ; RNG k-epsilon model ; Near-wall treatment ; ; k-omega models Wilcox's k-omega model ; Wilcox's modified k-omega model ; SST k-omega model ; Near-wall treatment ; ; Realisability issues Kato-Launder modification ; Durbin's realizability constraint ; Yap correction ; Realisability and Schwarz' inequality ; ; ; ; Nonlinear eddy viscosity models Explicit nonlinear constitutive relation Cubic k-epsilon ; EARSM ; ; v2-f models model ; model ; ; ; Reynolds stress model (RSM) ;
	Large eddy simulation (LES) Smagorinsky-Lilly model ; Dynamic subgrid-scale model ; RNG-LES model ; Wall-adapting local eddy-viscosity (WALE) model ; Kinetic energy subgrid-scale model ; Near-wall treatment for LES models ;
	Detached eddy simulation (DES)
	Direct numerical simulation (DNS)
	Turbulence near-wall modeling
	Turbulence free-stream boundary conditions Turbulence intensity ; Turbulence length scale ;

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The Cebeci-Smith [Smith and Cebeci (1967)] is a two-layer algebraic 0-equation model which gives the eddy viscosity, $\mu_t$ , as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace applications. Like the Baldwin-Lomax model, this model is not suitable for cases with large separated regions and significant curvature/rotation effects. Unlike the Baldwin-Lomax model, this model requires the determination of of a boundary layer edge.

Equations

$\mu_t = \begin{cases} {\mu_t}_{inner} & \mbox{if } y \le y_{crossover} \\ {\mu_t}_{outer} & \mbox{if } y > y_{crossover} \end{cases}$

(1)

where $y_{crossover}$ is the smallest distance from the surface where ${\mu_t}_{inner}$ is equal to ${\mu_t}_{outer}$ :

$y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer}$

(2)

The inner region is given

${\mu_t}_{inner} = \rho l^2 l \left[\left( \frac{\partial U}{\partial y}\right)^2 + \left(\frac{\partial V}{\partial x}\right)^2 \right]^{1/2},$

(3)

where

$l = \kappa y \left( 1 - e^{\frac{-y^+}{A^+}} \right)$

(4)

with the constant $\kappa = 0.4$ and

$A^+ = 26\left[1+y\frac{dP/dx}{\rho u_\tau^2}\right]^{-1/2}.$

(5)

The outer region is given by:

${\mu_t}_{outer} = \alpha \rho U_e \delta_v^* F_{KLEB}(y;\delta),$

(6)

where $\alpha=0.0168$ , $\delta_v^*$ is the velocity thickness given by

$\delta_v^* = \int_0^\delta (1-U/U_e)dy,$

(7)

and $F_{KLEB}$ is the Klebanoff intermittency function given by

$F_{KLEB}(y;\delta) = \left[1 + 5.5 \left( \frac{y}{\delta} \right)^6 \right]^{-1}$

(8)

Model variants

Performance, applicability and limitations

Implementation issues

References

Smith, A.M.O. and Cebeci, T. (1967), "Numerical solution of the turbulent boundary layer equations", Douglas aircraft division report DAC 33735.
Wilcox, D.C. (1998), Turbulence Modeling for CFD, ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc..

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 == Model variants ==

Cebeci-Smith model

From CFD-Wiki

Revision as of 17:23, 17 September 2007

Contents

Equations

Model variants

Performance, applicability and limitations

Implementation issues

References

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