For the purpose of simulating roughness induced transition

the boundary conditions of turbulent dissipation rate and eddy viscosity for rough surface were added to Langtry's γ-Reθ transition model; furthermore

equivalent sand surface roughness height was introduced to rewrite the correlation equations of the transition momentum thickness Reynolds number

making it appropriate for roughness-induced transition. Numerical simulation was made by referring to the wind tunnel data of several rough flat plate experiments and variable-pressure-gradient plate experiment

in which the results were satisfactory. Main conclusions are made as follows:surface roughness will enhance the heat transfer

increase the skin friction coefficient and shift the transition position upstream in general compared with smooth cases; effects for natural transition is significant

as surface roughness of 0.15 mm could shift the transition position upstream about 40%; while affect for separating induced transition is weaker; with the increase of surface roughness

transition position and separating bubble position are shifted backwards a little

the strength of separating bubble becomes weaker while the friction coefficient increases.