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 equations Reynolds-averaged Navier–Stokes (RANS) simulations use the Boussinesq
eddy viscosity hypothesis to calculate the
Reynolds stress that results from the averaging procedure: \overline{u'_i u'_j} = \frac23 k \delta_{ij} - \nu_t \left( \frac{\partial \overline{u_i}}{\partial x_j} + \frac{\partial \overline{u_j}}{\partial x_i} \right), where \nu_t = c \cdot \sqrt{k} \cdot l_m. The exact method of resolving TKE depends upon the turbulence model used;
– (k–epsilon) models assume isotropy of turbulence whereby the normal stresses are equal: \overline{(u')^2} = \overline{(v')^2} = \overline{(w')^2}. This assumption makes modelling of turbulence quantities ( and ) simpler, but will not be accurate in scenarios where anisotropic behaviour of turbulence stresses dominates, and the implications of this in the production of turbulence also leads to over-prediction since the production depends on the mean rate of strain, and not the difference between the normal stresses (as they are, by assumption, equal).
Reynolds-stress models (RSM) use a different method to close the Reynolds stresses, whereby the normal stresses are not assumed isotropic, so the issue with TKE production is avoided.
Initial conditions Accurate prescription of TKE as initial conditions in CFD simulations are important to accurately predict flows, especially in high Reynolds-number simulations. A smooth duct example is given below. k = \frac32 ( U I )^2, where is the initial turbulence intensity [%] given below, and is the initial velocity magnitude. As an example for pipe flows, with the
Reynolds number based on the pipe diameter: I = 0.16 Re^{-\frac{1}{8}}. Here is the turbulence or eddy length scale, given below, and is a – model parameter whose value is typically given as 0.09; \varepsilon = {c_\mu}^\frac34 k^\frac32 l^{-1}. The turbulent length scale can be
estimated as l = 0.07L, with a
characteristic length. For internal flows this may take the value of the inlet duct (or pipe) width (or diameter) or the hydraulic diameter. ==References==