Length-scale assessments in unified k-ω model with transitional perspective

The SST k-ω model is transferred to a unified k-ω turbulence model using the Bradshaw-relation (an equilibrium assumption, entailing a con- stant structure parameter |−uv| /k. An elliptic relaxation (ER) function f_R-equation is solved in cooperation with the eddy damping function fμ and the eddy-viscosity equation to properly account for distinct effects of low-Reynolds number (LRN) and near-wall turbulence. To illustrate the innermost constancy of ER approach with the characteristic length scale, different hybrid length scales are introduced. Model coefficients are parameterized with f_R to imitate anisotropic characteristics of non-equilibrium turbulence. The overall contrivance represents the combination of wall-viscous (LRN) and wall-blocking (non-local) effects encountered in non-homogeneous flows. Moreover, a consistently formulated eddy-viscosity coefficient is incorporated in the eddy-viscosity relation. The ER function fR with different characteristic length scales replicates almost analogous results, indicating that the Kolmogorov length scale plays the vital role for wall-blocking. An algebraic intermittency function γ, formulated based on the “flow-structure-adaptive” structure parameter has been introduced to predict transitional flows. Computations demonstrate that the unified k-ω model maintains decent agreement with widely used turbulence models.