A new low-Reynolds-number nonlinear two-equation turbulence model for complex flows

A new nonlinear, low-Reynolds-number k–ε turbulence model is proposed. The stress–strain relationship is formed by successive iterative approximations to an algebraic Reynolds-stress model. Truncation of the process at the third iteration yields an explicit expression for the Reynolds stresses that is cubic in the mean velocity gradients and circumvents the singular behaviour that afflicts the exact solution at large strains. Free coefficients are calibrated – as functions of y* – by reference to direct numerical simulation (DNS) data for a channel flow. By using the nonlinear stress–strain relationship, the sublayer behaviour of all turbulent stresses is reproduced. The extension to nonequilibrium conditions is achieved by sensitising the model coefficients to strain and vorticity invariants on the basis of formal relations derived from the algebraic Reynolds-stress model. The new model has been applied to a number of complex two dimensional (2-D) flows, and its performance is compared to that of other linear and nonlinear eddy-viscosity closures.