Английская Википедия:Cebeci–Smith model

Содержание

Текст

Текст

Текст

Текст

Текст

Текст

Текст

Текст

Текст

The Cebeci–Smith model, developed by Tuncer Cebeci and Apollo M. O. Smith in 1967, is a 0-equation eddy viscosity model used in computational fluid dynamics analysis of turbulence in boundary layer flows. The model gives eddy viscosity, <math>\mu_t</math>, 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, it is not suitable for large regions of flow separation and significant curvature or rotation. Unlike the Baldwin-Lomax model, this model requires the determination of a boundary layer edge.

Equations

In a two-layer model, the boundary layer is considered to comprise two layers: inner (close to the surface) and outer. The eddy viscosity is calculated separately for each layer and combined using:

<math>

\mu_t = \begin{cases} {\mu_t}_\text{inner} & \mbox{if } y \le y_\text{crossover} \\ {\mu_t}_\text{outer} & \mbox{if } y > y_\text{crossover} \end{cases} </math>

where <math>y_\text{crossover}</math> is the smallest distance from the surface where <math>{\mu_t}_\text{inner}</math> is equal to <math>{\mu_t}_\text{outer}</math>.

The inner-region eddy viscosity is given by:

<math>

{\mu_t}_\text{inner} = \rho \ell^2 \left[\left(

\frac{\partial U}{\partial y}\right)^2 +
\left(\frac{\partial V}{\partial x}\right)^2

\right]^{1/2} </math>

where

<math>

\ell = \kappa y \left( 1 - e^{-y^+/A^+} \right) </math>

with the von Karman constant <math>\kappa</math> usually being taken as 0.4, and with

<math>

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

The eddy viscosity in the outer region is given by:

<math>

{\mu_t}_\text{outer} = \alpha \rho U_e \delta_v^* F_K </math>

where <math>\alpha=0.0168</math>, <math>\delta_v^*</math> is the displacement thickness, given by

<math>

\delta_v^* = \int_0^\delta \left(1 - \frac{U}{U_e}\right)\,dy </math>

and F_K is the Klebanoff intermittency function given by

<math>

F_K = \left[1 + 5.5 \left( \frac{y}{\delta} \right)^6

 \right]^{-1}

</math>

References

• Smith, A.M.O. and Cebeci, T., 1967. Numerical solution of the turbulent boundary layer equations. Douglas aircraft division report DAC 33735
• Cebeci, T. and Smith, A.M.O., 1974. Analysis of turbulent boundary layers. Academic Press, Шаблон:ISBN
• Wilcox, D.C., 1998. Turbulence Modeling for CFD. Шаблон:ISBN, 2nd Ed., DCW Industries, Inc.

External links

• This article was based on the Cebeci Smith model article in CFD-Wiki