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The Baldwin-Lomax model is a two-layer algebraic model which gives 
as a function of the local boundary layer velocity profile. The eddy-viscosity, , is given by:
![\mu_t = \left\{
\begin{array}{ll}
{\mu_t}_{inner} & y \leq y_{crossover} \\[1.5ex]
{\mu_t}_{outer} & y > y_{crossover}
\end{array}
\right.](/W/images/math/6/2/a/62aea5700d426d32d39f008c74eb985f.png)
| (1) |
Where 
is the smallest distance from the surface where 
is equal to 
:
| (2) |
The inner region is given by the Prandtl - Van Driest formula:
| (3) |
Where
- Failed to parse (unknown function\renewcommand): \renewcommand{\exp}[1]{e^{#1}} l = k y \left( 1 - \exp{\frac{-y^+}{A^+}} \right)
| (4) |
| (5) |
| (6) |
The outer region is given by:
| (7) |
Where
| (7) |
and 
are determined from the maximum of the function:
| :Failed to parse (unknown function\renewcommand): \renewcommand{\exp}[1]{e^{#1}} F(y) = y \left| \Omega \right| \left(1-\exp{\frac{-y^+}{A^+}} \right)
| (32) |
is the intermittency factor given by:
:![F_{KLEB}(y) = \left[1 + 5.5 \left( \frac{y \, C_{KLEB}}{y_{MAX}} \right)^6
\right]^{-1}](/W/images/math/9/b/d/9bde77641b7e232fa3e083d3e59795c4.png) | (32) |
is the difference between maximum and minimum speed in the profile. For boundary layers the minimum is always set to zero.
: | (32) |
\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Failed to parse (syntax error): A^+<math> & <math>C_{CP}<math> & <math>C_{KLEB}<math> & <math>C_{WK}<math> & <math>k<math> & <math>K<math> \\ \hline 26 & 1.6 & 0.3 & 0.25 & 0.4 & 0.0168 \\ \hline \end{tabular} \caption{Model Constants, Baldwin-Lomax Model} \end{center} \end{table} Table 1 gives the model constants present in the formulas above. Note that <math>k<math> 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, <math>k<math>, present in the governing equations, is set to zero. == References == ''Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows'' by B. S. Baldwin and H. Lomax, AIAA Paper 78-257, 1978
