Predicting distributed roughness induced transition with a four-equation laminar kinetic energy transition model

A four-equation laminar kinetic energy transition model is developed to predict the distributed roughness induced transition using local variables. Based on the laminar kinetic energy transition model (k_T-k_L-ω model), three key improvements are devised in the work. Firstly, an additional transport equation for roughness amplification factor is combined with the laminar kinetic energy transition model. Secondly, the effective length scale is modified through the roughness amplification factor to consider the enhancement of the first and second unstable mode characteristic timescale. Additionally, for the sake of modeling the roughness effects in the full turbulent zone, the wall boundary condition for the specific turbulence dissipation rate is amended. Numerical results, including flat plate with distributed roughness, sharp biconic configuration with large roughness and hemisphere with different roughness heights, demonstrate that the proposed four-equation transition model is competent for accurate transition prediction at different roughness heights and Reynolds numbers. Besides, with the modification for the wall boundary condition of the specific turbulence dissipation rate, the present model outperforms the original model in simulating turbulent augmentations of skin friction and turbulent heating over rough surfaces. Thus, the present model has attraction and feasibility for simulating distributed roughness induced transition. While more physical mechanisms of roughness induced transition should be considered to further refine this four-equation laminar kinetic energy transition model.