Coherent turbulent heat transfer over a wall under pressure gradients with and without organized roughness

Bumps with roughness are prevalent in nature and technology. We study via DNS the flow over a heated wall of a channel having a simple large-scale spanwise bump overlaid with fine-scale longitudinal grooves (GW) used as an idealized roughness. Also, data are compared with a bump wall without grooves (SW). In SW, negative turbulent heat flux near the wall is found in the region of negative turbulence production despite also being where a local maximum of wall heat flux (q_w) and wall shear stress (t_w) occurs – notably further accentuated in GW. Another maximum of q_w occurs at the point of flow reattachment downstream of the bump, with a higher magnitude in GW. In GW, q_w decreases upstream of the bump and in the separation bubble (SB) region downstream of the bump; the thermal boundary layers are thicker in GW than in SW. The lower q_w upstream is caused by the upstream streamline curvature-induced steady SB. In the SB downstream of the GW bump q_w is particularly lower where secondary minibubbles, counter-rotating to SB appear – hence the decrease in q_w under the entire SB. The turbulent Prandtl number (Pr_t) ranges from ~0.5 in the shear layer past the bump peak to ~2.5 in regions of adverse pressure gradient for both SW and GW – the peak of Pr_t is 25% higher in SW than in GW. q_w/t_w varies from 0.5 to 2.5 over the bump similarly in both SW and GW. This ratio upstream of the bump is 30% higher in GW. The instantaneous distributions of temperature, turbulent heat transfer and Pr_t are explained in terms of coherent structures in the vortical and thermal fields.