Fluid dynamics and heat transfer in the wake of a sphere

Abstract Direct numerical simulation and large-eddy simulation have been performed for a heated sphere at Reynolds numbers of R e = 1000 and R e = 10 4 , respectively. The Prandtl number for both simulations has been P r = 0.7 . Measurements of the local and average Nusselt number are performed and compared with literature available experimental results. Average and front stagnation point Nusselt numbers increase with the Reynolds number, while the minimum value moves towards the sphere apex as the flow enters the sub-critical regime. Differences in both viscous and thermal boundary layers are observed, while the shape factor at Reynolds number R e = 10 4 behaves similarly to that observed in circular cylinders at comparable Reynolds numbers. It is shown that as the Reynolds number increases, the increase in turbulent kinetic energy promotes the entrainment of irrotational flow thus enhancing the temperature mixing in the zone. The near wake, between 5 ≤  x / D  ≤ 15, spreads at a faster rate at R e = 1000 with a slope close to x / D 1/2 , while at R e = 10 4 it follows a trend close to x / D 1/3 .