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Baldwin-Lomax model

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

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}

The inner region is given by the Prandtl - Van Driest formula:

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


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

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

\Omega_{ij} = \frac{1}{2}
 \frac{\partial u_i}{\partial x_j} -
 \frac{\partial u_j}{\partial x_i}

The outer region is given by:

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


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

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)

F_{KLEB} is the intermittency factor given by:

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

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})

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


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