Capturing transition and non-transition flows with a new shear stress transport model

A new Shear Stress Transport (SST) k - ω model is devised to integrate salient features of both the non-transitional SST k - ω model and correlation-based γ - Re_θ transition model. An exceptionally simplified approach is applied to extend the New SST (NSST) model capabilities toward transition/non-transition predictions. Bradshaw’s stress-intensity factor $R_b=|-\overline{uv}|/k$ can be parameterized with the wall-distance dependent Reynolds number $R{e}_y=\sqrt{k}y/v$; however, as the Re_y is replaced by a “flow-structure-adaptive” parameter $R_{\mu }=v_{\mathrm{T}}/v$, the resulting R_b is capable of capturing various transition phenomena naturally. The prospective stress-intensity parameter $R_b=R_b\left(R{e}_y,R_{\mu }\right)$ is incorporated in the constitutive relations for eddy-viscosity v_T and production termP_k. The proposed formulation is intrinsically plausible, having a dramatic impact on the prediction of bypass, separation-induced and natural transitions together with non-transitional flows. An extra viscous-production term P_k^lim is added with the k-equation to ensure proper generation of k at the viscous sublayer when computing separation-induced transition over a Low-Reynolds Number (LRN) airfoil. Results demonstrate that the NSST k - ω model maintains an excellent consistency with both SST k - ω and γ - Re_θ models.