Baldwin-Lomax model
From CFD-Wiki
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- | The Baldwin-Lomax model is a two-layer algebraic model which gives <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> | <table width="100%"><tr><td> | ||
:<math> | :<math> | ||
- | \mu_t = | + | \mu_t = |
- | \begin{ | + | \begin{cases} |
- | {\mu_t}_{inner} & y \ | + | {\mu_t}_{inner} & \mbox{if } y \le y_{crossover} \\ |
- | {\mu_t}_{outer} & y > y_{crossover} | + | {\mu_t}_{outer} & \mbox{if} y > y_{crossover} |
- | \end{ | + | \end{cases} |
- | + | ||
</math></td><td width="5%">(1)</td></tr></table> | </math></td><td width="5%">(1)</td></tr></table> | ||
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<table width="100%"><tr><td> | <table width="100%"><tr><td> | ||
:<math> | :<math> | ||
- | + | l = k y \left( 1 - e^{\frac{-y^+}{A^+}} \right) | |
- | l = k y \left( 1 - | + | |
</math></td><td width="5%">(4)</td></tr></table> | </math></td><td width="5%">(4)</td></tr></table> | ||
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F_{WAKE} = MIN \left( y_{MAX} \, F_{MAX} \,\,;\,\, | F_{WAKE} = MIN \left( y_{MAX} \, F_{MAX} \,\,;\,\, | ||
C_{WK} \, y_{MAX} \, \frac{u^2_{DIF}}{F_{MAX}} \right) | C_{WK} \, y_{MAX} \, \frac{u^2_{DIF}}{F_{MAX}} \right) | ||
- | </math></td><td width="5%">( | + | </math></td><td width="5%">(8)</td></tr></table> |
<math>y_{MAX}</math> and <math>F_{MAX}</math> are determined from the maximum of the function: | <math>y_{MAX}</math> and <math>F_{MAX}</math> are determined from the maximum of the function: | ||
- | <table width="100%"><tr><td>:<math> | + | <table width="100%"><tr><td> |
- | + | :<math> | |
- | F(y) = y \left| \Omega \right| \left(1- | + | F(y) = y \left| \Omega \right| \left(1-e^{\frac{-y^+}{A^+}} \right) |
- | </math></td><td width="5%">( | + | </math></td><td width="5%">(9)</td></tr></table> |
<math>F_{KLEB}</math> is the intermittency factor given by: | <math>F_{KLEB}</math> is the intermittency factor given by: | ||
- | <table width="100%"><tr><td>:<math> | + | <table width="100%"><tr><td> |
+ | :<math> | ||
F_{KLEB}(y) = \left[1 + 5.5 \left( \frac{y \, C_{KLEB}}{y_{MAX}} \right)^6 | F_{KLEB}(y) = \left[1 + 5.5 \left( \frac{y \, C_{KLEB}}{y_{MAX}} \right)^6 | ||
\right]^{-1} | \right]^{-1} | ||
- | </math></td><td width="5%">( | + | </math></td><td width="5%">(10)</td></tr></table> |
<math>u_{DIF}</math> is the difference between maximum and minimum speed in the profile. For boundary layers the minimum is always set to zero. | <math>u_{DIF}</math> is the difference between maximum and minimum speed in the profile. For boundary layers the minimum is always set to zero. | ||
- | <table width="100%"><tr><td>:<math> | + | <table width="100%"><tr><td> |
+ | :<math> | ||
u_{DIF} = MAX(\sqrt{u_i u_i}) - MIN(\sqrt{u_i u_i}) | u_{DIF} = MAX(\sqrt{u_i u_i}) - MIN(\sqrt{u_i u_i}) | ||
- | </math></td><td width="5%">( | + | </math></td><td width="5%">(11)</td></tr></table> |
+ | |||
+ | |||
+ | == Model constants == | ||
+ | |||
+ | The table below 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. | ||
- | + | <table cellpadding="5" cellspacing="1" border="1"> | |
- | + | <tr> | |
- | + | <td><math>A^+</math></td> | |
- | + | <td><math>C_{CP}</math></td> | |
- | <math>A^+<math> | + | <td><math>C_{KLEB}</math></td> |
- | + | <td><math>C_{WK}</math></td> | |
- | 26 | + | <td><math>k</math></td> |
- | + | <td><math>K</math></td> | |
- | + | </tr> | |
- | + | <tr> | |
- | + | <td>26</td> | |
- | + | <td>1.6</td> | |
+ | <td>0.3</td> | ||
+ | <td>0.25</td> | ||
+ | <td>0.4</td> | ||
+ | <td>0.0168</td> | ||
+ | </tr> | ||
+ | </table> | ||
- | |||
== References == | == 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 |
Revision as of 12:28, 8 September 2005
The Baldwin-Lomax model is a two-layer algebraic model which gives the eddy-viscosity as a function of the local boundary layer velocity profile:
| (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
| (4) |
| (5) |
| (6) |
The outer region is given by:
| (7) |
Where
| (8) |
and are determined from the maximum of the function:
| (9) |
is the intermittency factor given by:
| (10) |
is the difference between maximum and minimum speed in the profile. For boundary layers the minimum is always set to zero.
| (11) |
Model constants
The table below gives the model constants present in the formulas above. Note that 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, , present in the governing equations, is set to zero.
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