Modelling transition due to backward-facing steps using the laminar kinetic energy concept

Abstract

Boundary layer transition estimation and modelling is essential for the design of many engineering products across many industries. In this paper, the Reynolds-averaged Navier–Stokes are solved in conjunction with three additional transport equations to model and predict boundary layer transition. The transition model (referred to as the kT–kL–ω model) is based on the k–ω framework with an additional transport equation to incorporate the effects low-frequency flow oscillations in the form of a laminar kinetic energy (kL). Firstly, a number of rectifications are made to the original kT–kL–ω framework in order to ensure an appropriate response to the free-stream turbulence level and to improve near wall predictions. Additionally, the model is extended to incorporate the capability to model transition due to surface irregularities in the form of backward-facing steps with maximum non-dimensional step sizes of approximately 1.5 times the local displacement thickness of the boundary layer where the irregularity is located (i.e k/δ∗⪅1.5) at upstream turbulence intensities in the range 0.01<Tu(%)<0.8. A novel function is proposed to incorporate transition sensitivity due to aft-facing steps. This paper details the rationale behind the development of this new function and demonstrates its suitability for transition onset estimation on a flat plate at zero pressure gradient.