Eddy Heat Transfer by Secondary Görtler Instability

Experimental measurements of flow and heat transfer in a concave surface boundary layer in the presence of streamwise counter-rotating Görtler vortices show conclusively that local surface heat-transfer rates can exceed that of the turbulent flat-plate boundary layer even in the absence of turbulence. We have observed unexpected heat-transfer behavior in a laminar boundary layer on a concave wall even at low nominal velocity, a configuration not studied in the literature: The heat-transfer enhancement is extremely high, well above that corresponding to a turbulent boundary layer on a flat plate. To quantify the effect of freestream velocity on heat-transfer intensification, two criteria are defined for the growth of the Görtler instability: $Pz$ for primary instability and $Prms$ for the secondary instability. The evolution of these criteria along the concave surface boundary layer clearly shows that the secondary instability grows faster than the primary instability. Measurements show that beyond a certain distance the heat-transfer enhancement is basically correlated with $Prms$⁠, so that the high heat-transfer intensification at low freestream velocities is due to the high growth rate of the secondary instability. The relative heat-transfer enhancement seems to be independent of the nominal velocity (global Reynolds number) and allows predicting the influence of the Görtler instabilities in a large variety of situations.