Dual transition scheme on k-equation model

The proposed model integrates two transition mechanisms into the turbulent kinetic energy ($k$-equation) turbulence framework, assisted by transition representatives. These include a “flow-structure-adaptive” stress-intensity parameter, which induces the pre-transitional/pseudo-laminar state before transition, and an intermittency factor, which facilitates the prediction of flow transition onset and completion with a feasible growth rate and a logical transition length. The algebraic transition model introduces new functions and correlations, which are based on theoretical and experimental evidence. These elements stimulate multiple transition phenomena in a suitable and credible way due to their reliance on local flow information for initiating and controlling the transition growth rate. With the employment of an algebraic closure for the dissipation rate, the $k$-equation directly anticipates the free-stream turbulence intensity instead of the free-stream “eddy-to-laminar” viscosity ratio ($R_{\mu \infty }$). This approach avoids the “trial-and-error” inconsistency typically associated with most correlation-based and physics-based transition models when initiating appropriate computations. The independence of the algebraic transition model from $R_{\mu \infty }$ offers substantial benefits in predictive capability over traditional transition models. However, the quality of performance might fluctuate, contingent on the closure approximations adopted. This detail is of immense importance for accurately depicting the pertinent physical characteristics of the flow, such as bypass, natural, and separation-induced transitions. Numerical results indicate that the current model, whether equipped with algebraic transition additives or not, aligns well with both existing experimental data and commonly used transition and non-transition models. The new transition model has decent agreement with the transitional boundary layer on a flat plate, and transitional flow over an airfoil with laminar and turbulent separation bubbles.