Application of the γ -Re θ Transition Model to Simulations of the Flow Past a Circular Cylinder

Based on the finite volume method, the flow past a two-dimensional circular cylinder at a critical Reynolds number (Re = 8.5 × 10 5 ) was simulated using the Navier-Stokes equations and the γ -Re θ transition model coupled with the SST k − ω turbulence model (hereinafter abbreviated as γ -Re θ model). Considering the effect of free-stream turbulence intensity decay, the SST k − ω turbulence model was modified according to the ambient source term method proposed by Spalart and Rumsey, and then the modified SST k − ω turbulence model is coupled with the γ -Re θ transition model (hereinafter abbreviated as γ -Re θ -SR model). The flow past a circular cylinder at different inlet turbulence intensities were simulated by the γ -Re θ -SR model. At last, the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers were each simulated by the γ -Re θ -SR model, and the three flow states were analyzed. It was found that compared with the SST k − ω turbulence model, the γ -Re θ model could simulate the transition of laminar to turbulent, resulting in better consistency with experimental result. Compared with the γ -Re θ model, for relatively high inlet turbulence intensities, the γ -Re θ -SR model could better simulate the flow past a circular cylinder; however the improvement almost diminished for relatively low inlet turbulence intensities The γ -Re θ -SR model could well simulate the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers.