Turbulence modeling

Turbulence modeling

Turbulence modeling is the area of physical modeling where a simpler mathematical model than the full time dependent Navier-Stokes Equations is used to predict the effects of turbulence.There are various mathematical models used in flow modelling to understand turbulence.

Joseph Boussinesq was the first practitioner of this, introducing the concept of eddy viscosity. In this model, the additional turbulent stresses are given by augmenting the molecular viscosity with an eddy viscosity. This can be a simple constant eddy viscosity (which works well for some free shear flows such as axisymmetric jets, 2-D jets, and mixing layers). Later, Ludwig Prandtl introduced the additional concept of the mixing length, along with the idea of a boundary layer. For wall-bounded turbulent flows, the eddy viscosity must vary with distance from the wall, hence the addition of the concept of a 'mixing length'. In the simplest wall-bounded flow model, the eddy viscosity is given by the equation:

: u_t = kappa left|frac{partial u}{partial y} ight|l^2

:where:

:kappa is the von Karman constant (0.41);

:frac{partial u}{partial y} is the partial derivative of the streamwise velocity (u) with respect to the wall normal direction (y);

:l is the distance from the wall.

This simple model is the basis for the "Law of the Wall", which is a surprisingly accurate model for wall-bounded, attached (not separated) flow fields with small pressure gradients.

More general have evolved over time, with most modern turbulence models given by field equations similar to the Navier-Stokes equations.

Among many others, Joseph Smagorinsky (1964) proposed a useful formula for the eddy viscosity in numerical models, based on the local derivatives of the velocity field and the local grid size:

: u_t = Delta x Delta y sqrt{left(frac{partial u}{partial x} ight)^2 + left(frac{partial v}{partial y} ight)^2 + frac{1}{2}left(frac{partial u}{partial y} + frac{partial v}{partial x} ight)^2}

References

* [http://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=0521298199| Townsend, A.A. (1980) "The Structure of Turbulent Shear Flow" 2nd Edition (Cambridge Monographs on Mechanics)]
* [http://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=0080166210| Bradshaw, P. (1971) "An introduction to turbulence and its measurement" (Pergamon Press)]
* [http://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=0963605100| Wilcox C. D., (1998), "Turbulence Modeling for CFD" 2nd Ed., (DWC Industries, La Cañada) ]
* [http://www.ebi-edu.com/Entreprises/Recherche/documents/Absi%20R%20J%20WW%20ASCE%202006.pdf Absi, R. (2006), "Discussion of One-Dimensional Wave Bottom Boundary Layer Model Comparison: Specific Eddy Viscosity and Turbulence Closure Models" Journal of Waterway, Port, Coastal and Ocean Engineering, American Society of Civil Engineers (ASCE), Vol. 132, No. 2, pp. 139-141.]
* [http://www.jstage.jst.go.jp/article/jscejb/62/4/62_437/_article Absi, R. (2006), "A Roughness and time dependent mixing length equation", Journal of Hydraulic, Coastal and Environmental Engineering, (Doboku Gakkai Ronbunshuu B), Japan Society of Civil Engineers (JSCE), Vol. 62, No. 4, pp.437-446.]


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Turbulence — In fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and… …   Wikipedia

  • Atmospheric dispersion modeling — Industrial air pollution source Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that solve the mathematical equations and algorithms… …   Wikipedia

  • Roadway air dispersion modeling — is the study of air pollutant transport from a roadway or other linear emitter. Computer models are required to conduct this analysis, because of the complex variables involved, including vehicle emissions, vehicle speed, meteorology, and terrain …   Wikipedia

  • Computational fluid dynamics — Computational physics Numerical analysis  …   Wikipedia

  • Fluid dynamics — Continuum mechanics …   Wikipedia

  • Charles Speziale — Charles G. Speziale Born June 16, 1948(1948 06 16) Newark, New Jersey, United States …   Wikipedia

  • Modélisation des turbulences — La modélisation de la turbulence (et non des turbulences ) est une branche de la dynamique des fluides consistant, pour la simulation numérique des écoulements turbulents, à représenter l influence de la turbulence sur l écoulement moyen… …   Wikipédia en Français

  • Joseph Valentin Boussinesq — (born March 13 1842 in Saint André de Sangonis (Hérault département ), died February 19 1929 in Paris) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.John… …   Wikipedia

  • Von Kármán constant — A unitless constant describing the logarithmic velocity profile of a turbulent fluid near a no slip boundary. The equation for such boundary layer flow profiles is:u=frac{u {star{k}lnfrac{z}{z 0}where u is the velocity at height z above the… …   Wikipedia

  • Boussinesq approximation — may refer to: * Boussinesq approximation (buoyancy) for buoyancy driven flows for small density differences in the fluid * Boussinesq approximation (water waves) for long waves propagating on the surface of a fluid layer under the action of… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”