Simulations of turbulence

Definition of a turbulent flow

Turbulence is a physical phenomenon which arises in the majority of the industrial flows but also in nature. The passenger of a plane can, sometimes, try out trepidations of the apparatus crossing a zone of strong atmospheric turbulence. The turbulent flow of a river downstream from a pillar of bridge, the emanating mixture of smoke of a chimney in the atmosphere, constitute other examples of manifestation of the phenomenon of turbulence in a flow. A flow is known as turbulent if:

• the variables of the flow (speeds, temperature, concentrations) are non stationary and random. The velocity measurement at a point given in a turbulent flow strongly oscillates around a median value, from where randomness. However the flow contains coherent structures, the space and temporal localization of these structures giving this randomness to him.

• the flow presents a strong vorticity, ∇ × V ,
• the flow contains coherent but random structures,
• the flow is associated with a strong mixture of species (particles, gas), of heat and momentum, because of an increase in the diffusive character compared to a laminar flow.

In general, a flow becomes turbulent when the inertias large are compared with the forces of viscous diffusion, or when the Reynolds number, Re, is large. The Reynolds number is defined by Re = U L/ν or Re = ρ U L/ Μ

Turbulence is a characteristic of the flow and not fluid. In the majority of the flows more the small scales of turbulence are rather broad (compared with the intermolecular distance from collision) so that the assumption of continuity of the fluid particles is valid. So the Navier-Stokes equations can be used.

Navier-Stokes equations

The Navier-Stokes equations contain of the mass and the momentum conservation equations. In a Cartesian frame of reference, noted $x\_i$ I = 1. 3, the vector of the fields speeds is noted $\backslash \; scriptstyle\; \backslash \; vec\; \{V\}\; =U\_i$ for I = 1. 3.

• Conservation equation of the mass

For an incompressible flow, the density of the fluid is uniform, the conservation equation of the mass is summarized with a null divergence of the Flight Path Vector. By using the convention of summation of Einstein for the repeated indices:

$\backslash \; frac\; \{\backslash \; partial\; partial\; U\_i\}\; \{\backslash \; x\_i\}$

• Conservation equation of the momentum (qdm)

Taking into account the conservation of the mass, the conservation equation of momentum (qdm) for an incompressible flow is written:

$\backslash \; rho\; \backslash \; frac\; \{\backslash \; partial\; U\_i\}\; \{\backslash \; partial\; T\}\; +\; \backslash \; rho\; \backslash \; frac\; \{\backslash \; partial\; (U\_i\; U\_k)\}\{\backslash \; partial\; x\_k\}\; =\; -\; \backslash \; frac\; \{\backslash \; partial\; P\}\; \{\backslash \; partial\; x\_i\}\; +\; \backslash \; driven\; \backslash \; frac\; \{\backslash \; partial^2\; partial\; U\_i\}\; \{\backslash \; x\_i^2\}$ Equation in which, ρ is the density of the fluid, P the pressure, μ dynamic viscosity.

• Conservation equation of energy

The conservation equation of energy in a volume of control can be written in various forms.

Modeling RANS (Reynolds Averaged Navier-Stokes)

Modeling THEM (Broad-Eddy Simulation)

Direct simulation (DNS)

Random links:

Vallisneria | Supercoupe of Switzerland of football | Roger Hammond | William Calley | Siri Gamage | Gopalapuram

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org