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Baldwin-Barth model

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Turbulence modeling
Turbulence
RANS-based turbulence models
  1. Linear eddy viscosity models
    1. Algebraic models
      1. Cebeci-Smith model
      2. Baldwin-Lomax model
      3. Johnson-King model
      4. A roughness-dependent model
    2. One equation models
      1. Prandtl's one-equation model
      2. Baldwin-Barth model
      3. Spalart-Allmaras model
    3. Two equation models
      1. k-epsilon models
        1. Standard k-epsilon model
        2. Realisable k-epsilon model
        3. RNG k-epsilon model
        4. Near-wall treatment
      2. k-omega models
        1. Wilcox's k-omega model
        2. Wilcox's modified k-omega model
        3. SST k-omega model
        4. Near-wall treatment
      3. Realisability issues
        1. Kato-Launder modification
        2. Durbin's realizability constraint
        3. Yap correction
        4. Realisability and Schwarz' inequality
  2. Nonlinear eddy viscosity models
    1. Explicit nonlinear constitutive relation
      1. Cubic k-epsilon
      2. EARSM
    2. v2-f models
      1. \overline{\upsilon^2}-f model
      2. \zeta-f model
  3. Reynolds stress model (RSM)
Large eddy simulation (LES)
  1. Smagorinsky-Lilly model
  2. Dynamic subgrid-scale model
  3. RNG-LES model
  4. Wall-adapting local eddy-viscosity (WALE) model
  5. Kinetic energy subgrid-scale model
  6. Near-wall treatment for LES models
Detached eddy simulation (DES)
Direct numerical simulation (DNS)
Turbulence near-wall modeling
Turbulence free-stream boundary conditions
  1. Turbulence intensity
  2. Turbulence length scale

Contents

Kinematic Eddy Viscosity

 \nu _t  = C_\mu  \nu \tilde R_T D_1 D_2

Turbulence Reynolds Number


{\partial  \over {\partial t}}\left( {\nu \tilde R_T } \right) = U_j {\partial  \over {\partial x_j }}\left( {\nu \tilde R_T } \right) = \left( {C_{\varepsilon 2} f_2  - C_{\varepsilon 1} } \right)\sqrt {\nu \tilde R_T P}  + \left( {\nu  + {{\nu _T } \over {\sigma _\varepsilon  }}} \right){{\partial ^2 } \over {\partial x_k \partial x_k }} - {1 \over {\sigma _\varepsilon  }}{{\partial \nu _T } \over {\partial x_k }}{{\partial \left( {\nu \tilde R_T } \right)} \over {\partial x_T }}


Closure Coefficients and Auxilary Relations


   C_{\varepsilon 1}  = 1.2

    C_{\varepsilon 2}  = 2.0

   C_\mu   = 0.09

   A_o^ +   = 26

   A_2^ +   = 10



 {1 \over {\sigma _\varepsilon  }} = \left( {C_{\varepsilon 2}  - C_{\varepsilon 1} } \right){{\sqrt {C_\mu  } } \over {\kappa ^2 }}



    \kappa  = 0.41



P = \nu _T \left[ {\left( {{{\partial U_i } \over {\partial x_j }} + {{\partial U_j } \over {\partial x_i }}} \right){{\partial U_i } \over {\partial x_j }} - {2 \over 3}{{\partial U_k } \over {\partial x_k }}{{\partial U_k } \over {\partial x_k }}} \right]



   D_1  = 1 - e^{{{ - y^ +  } \over {A_o^ +  }}}

  D_2  = 1 - e^{{{ - y^ +  } \over {A_2^ +  }}}



   f_2  = {{C_{\varepsilon 1} } \over {C_{\varepsilon 2} }} + \left( {1 - {{C_{\varepsilon 1} } \over {C_{\varepsilon 2} }}} \right)\left( {{1 \over {\kappa y^ +  }} + D_1 D_2 } \right)\left[ {\sqrt {D_1 D_2 }  + {{y^ +  } \over {\sqrt {D_1 D_2 } }}\left( {{{D_2 } \over {A_o^ +  }}e^{{{ - y^ +  } \over {A_o^ +  }}}  + {{D_1 } \over {A_2^ +  }}e^{{{ - y^ +  } \over {A_2^ +  }}} } \right)} \right]

References

  1. Wilcox, D.C. (2004), Turbulence Modeling for CFD, ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc.
  2. Baldwin, B.S. and Barth, T.J. (1990), A One-Equation Turbulence Transport Model for High Reynolds Number Wall-Bounded Flows, NASA TM 102847.
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