Heat Transfer Analysis in a Flow Over Concave Wall With Primary and Secondary Instabilities

Abstract The centrifugal instability mechanism in boundary layers over concave surfaces is responsible for the development of counter- rotating vortices, aligned in the streamwise direction, known as Gortler vortices. These vortices create two regions in the spanwise direction, the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer towards the wall, increasing the drag coefficient and the heat transfer rate. The upwash region does the opposite. The Gortler vortices distort the streamwise velocity profile in the spanwise and the wall-normal directions. These distortions generate inflections in the distribution of streamwise velocity that are unstable to unsteady disturbances giving rise to secondary instabilities. In these flows the secondary instabilities can be of varicose or sinuous mode. The present paper analyses the heat transfer in a flow over a concave wall subjected to primary and secondary instabilities. The research is carried out by a Spatial Direct Numerical Simulation. The adopted parameters mimic the experimental parameters of Winoto and collaborators 17,18 and the Prandtl number adopted was Pr = 0.72. The results show that the varicose mode is the dominant secondary instability for the adopted parameters and that the spanwise average heat transfer rates can reach higher values than the turbulent ones. The higher heat transfer is caused by the mean flow distortion induced by the vortices, and this is present before high–frequency secondary instability sets in. Hence there is no direct connection to secondary instability. Possibly low–frequency modes undergo instability earlier.