Turbulence kinetic energy

In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured root-mean-square (RMS) velocity fluctuations.

In Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model. Generally, the TKE can be quantified by the mean of the turbulence normal stresses:

TKE can be produced by fluid shear, friction or buoyancy, or through external forcing at low-frequency eddy scales(integral scale). Turbulence kinetic energy is then transferred down the turbulence energy cascade, and is dissipated by viscous forces at the Kolmogorov scale. This process of production, transport and dissipation can be expressed as:

where:

Assuming density and viscosity both constant, the full form of the TKE equation is:

By examining these phenomena, the turbulence kinetic energy budget for a particular flow can be found.

In computational fluid dynamics (CFD), it is impossible to numerically simulate turbulence without discretizing the flow-field as far as the Kolmogorov microscales, which is called direct numerical simulation (DNS). Because DNS simulations are exorbitantly expensive due to memory, computational and storage overheads, turbulence models are used to simulate the effects of turbulence. A variety of models are used, but generally TKE is a fundamental flow property which must be calculated in order for fluid turbulence to be modelled.

Reynolds-averaged Navier–Stokes (RANS) simulations use the Boussinesq eddy viscosity hypothesis to calculate the Reynolds stresses that result from the averaging procedure:

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