Reynolds number dependency of turbulent flow over ratchet surfaces

As the Reynolds number (Re) increases and the size of the roughness height relative to the viscous length scale grows, rough surfaces go through different regimes, i.e., hydraulically smooth, transitionally rough, and fully rough. In the fully rough regime, the friction factor becomes independent of Re and the roughness function ΔU⁺ increases linearly with κ^-1ln(k_s⁺), where k_s⁺ is the equivalent sand-grain roughness. While most surfaces adhere to the fully rough behaviour, there are some surfaces that do not conform to this conventional trend.

In the present study, ratchet roughness composed of spanwise triangular bars with a scalene cross-section is investigated using direct numerical simulations of turbulent channel flow. Two orientations of the same surface are considered, namely ‘favourable’, i.e., with the low-slope sides facing the flow, and ‘adverse’, where the high-slope sides face the flow. The aim is to establish the differences in the Reynolds number dependency for the two orientations and to gain insight into the underlying physical mechanisms. Preliminary results indicate that while the ratchet surface in the ‘favourable’ orientation attains fully rough behaviour, in the ‘adverse’ orientation the same surface exhibits atypical behaviour at high Re.