Study of the Influence of Wall Roughness on Laminar-Turbulent Transition

The influence of 2D uniform roughness on laminar-turbulent transition in channel flow is studied using direct numerical simulation (DNS). Utilizing the Incompact3d code, the linear stability analysis (LEA) and the Immersed Boundary Method (IBM), two simulations are carried out using the same Reynolds number (i.e. the same flow rate): one with roughness on channel walls (Rough case) and the other with smooth walls (Smooth case). A comparative analysis between the Rough case and the Smooth case reveals common patterns in the evolution of the friction Reynolds number and Reynolds normal stresses along the streamwise direction: a quasi-laminar region downstream the inlet, followed by an increase in values of these quantities until reaching a peak, and subsequently, a decrease until achieving a fully developed turbulent state. In the present study, roughness increases the friction Reynolds number by a factor of 1.7 in the turbulent region. Furthermore, our findings, derived from the analysis of vortex structures and Reynolds normal stresses, reveal that roughness, combined with perturbed inflow conditions calculated from the LEA, has the potential to delay the onset of the transition with respect to the Smooth case. Additionally, it is found that roughness increases the magnitude of the friction Reynolds number and the Reynolds normal stresses downstream \(\approx 20\) channel half-heights after the channel inlet in comparison to the Smooth case. Finally, a roughness function of 9.1 is found for positions downstream the peak of the friction Reynolds number.