Baldwin-Lomax model

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Revision as of 12:29, 8 September 2005

The Baldwin-Lomax model is a two-layer algebraic model which gives the eddy-viscosity, $\mu_t$ , as a function of the local boundary layer velocity profile.

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

(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 by the Prandtl - Van Driest formula:

${\mu_t}_{inner} = \rho l^2 \left| \Omega \right|$

(3)

Where

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

(4)

$\left| \Omega \right| = \sqrt{2 \Omega_{ij} \Omega_{ij}}$

(5)

$\Omega_{ij} = \frac{1}{2} \left( \frac{\partial u_i}{\partial x_j} - \frac{\partial u_j}{\partial x_i} \right)$

(6)

The outer region is given by:

${\mu_t}_{outer} = \rho \, K \, C_{CP} \, F_{WAKE} \, F_{KLEB}(y)$

(7)

Where

$F_{WAKE} = MIN \left( y_{MAX} \, F_{MAX} \,\,;\,\, C_{WK} \, y_{MAX} \, \frac{u^2_{DIF}}{F_{MAX}} \right)$

(8)

$y_{MAX}$ and $F_{MAX}$ are determined from the maximum of the function:

$F(y) = y \left| \Omega \right| \left(1-e^{\frac{-y^+}{A^+}} \right)$

(9)

$F_{KLEB}$ is the intermittency factor given by:

$F_{KLEB}(y) = \left[1 + 5.5 \left( \frac{y \, C_{KLEB}}{y_{MAX}} \right)^6 \right]^{-1}$

(10)

$u_{DIF}$ is the difference between maximum and minimum speed in the profile. For boundary layers the minimum is always set to zero.

$u_{DIF} = MAX(\sqrt{u_i u_i}) - MIN(\sqrt{u_i u_i})$

(11)

Model constants

The table below gives the model constants present in the formulas above. Note that $k$ is a constant, and not the turbulence energy, as in other sections. It should also be pointed out that when using the Baldwin-Lomax model the turbulence energy, $k$ , present in the governing equations, is set to zero.

$A^+$	$C_{CP}$	$C_{KLEB}$	$C_{WK}$	$k$	$K$
26	1.6	0.3	0.25	0.4	0.0168

References

"Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows" by B. S. Baldwin and H. Lomax, AIAA Paper 78-257, 1978

@@ Line 1: / Line 1: @@
-The Baldwin-Lomax model is a two-layer algebraic model which gives the eddy-viscosity <math>\mu_t</math> as a function of the local boundary layer velocity profile:
+The Baldwin-Lomax model is a two-layer algebraic model which gives the eddy-viscosity, <math>\mu_t</math>, as a function of the local boundary layer velocity profile.
 <table width="100%"><tr><td>
@@ Line 109: / Line 109: @@
 == References ==
-* ''Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows'' by B. S. Baldwin and H. Lomax, AIAA Paper 78-257, 1978
+* ''"Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows"'' by B. S. Baldwin and H. Lomax, AIAA Paper 78-257, 1978

Baldwin-Lomax model

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Revision as of 12:29, 8 September 2005

Model constants

References

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