CFD Online URL
[Sponsors]
Home > Wiki > Prandtl's one-equation model

Prandtl's one-equation model

From CFD-Wiki

Revision as of 12:45, 5 July 2007 by Jola (Talk | contribs)
Jump to: navigation, search
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  = k^{{1 \over 2}} l = C_D {{k^2 } \over \varepsilon }

Model


{{\partial k} \over {\partial t}} + U_j {{\partial k} \over {\partial x_j }} = \tau _{ij} {{\partial U_i } \over {\partial x_j }} - C_D {{k^{{3 \over 2}} } \over l} + {\partial  \over {\partial x_j }}\left[ {\left( {\nu  + {{\nu _T } \over {\sigma _k }}} \right){{\partial k} \over {\partial x_j }}} \right]


Closure Coefficients and Auxilary Relations


 \varepsilon  = C_D {{k^{{3 \over 2}} } \over l}

    C_D  = 0.08
[1]



   \sigma _k  = 1


where


\tau _{ij}  = 2\nu _T S_{ij}  - {2 \over 3}k\delta _{ij}

References

  • Wilcox, D.C. (2004), Turbulence Modeling for CFD, ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc..
  • Emmons, H. W. (1954), "Shear flow turbulence", Proceedings of the 2nd U.S. Congress of Applied Mechanics, ASME.
  • Glushko, G. (1965), "Turbulent boundary layer on a flat plate in an incompressible fluid", Izvestia Akademiya Nauk SSSR, Mekh, No 4, P 13.

Footnotes

  1. The exact constant used by Prandtl is currently unknown by the author. Wilcox mentions that other researchers (Emmons 1954 and Glushko 1965) have used a value ranging from 0.07 to 0.09. However, CHAM lists the constant as 0.1643 (see here)

Return to Turbulence modeling

My wiki