Direct numerical simulations of turbulent channel flow over ratchet roughness

Abstract

AbstractThe influence of the orientation of ratchet-type rough surfaces on their fluid dynamic roughness effect is investigated using direct numerical simulations of turbulent channel flow at $$Re_{\tau }=395$$ R e τ = 395 . The ratchet length-to-height ratio is varied from $$\ell /k=2$$ ℓ / k = 2 to 16 for a fixed ratchet height of $$k/\delta =0.1$$ k / δ = 0.1 where $$\delta$$ δ is the mean channel half-height. The results show that both roughness function and mean flow and turbulence statistics strongly depend on the ratchet orientation. Existing empirical formulae, which estimate the roughness function $$\Delta U^+$$ Δ U + or the equivalent sand-grain roughness $$k_s$$ k s based on surface-slope related parameters such as the effective slope or the Sigal-Danberg parameter, fail to accurately predict the differences between ratchet surfaces with high windward slopes and ratchet surfaces with high leeward slopes.