Numerical Study On Surface Friction and Boundary Layer Thickening in Transitional Flow

The skin friction on a surface is a major concern by engineers. It is widely accepted that turbulent flow has higher friction than laminar flow due to the higher mixing in boundary layer. However, our new high order DNS found that the high friction is generated in a laminar zone in a transitional flow. Whenever the small length scales are generated, the velocity shear becomes very large in the laminar sub-layer which is caused by increment of momentum. Then the surface friction quickly jumps to a very high level even when the flow is still laminar. Since the viscous coefficient is a constant for incompressible flow, there is no direct co-relation between high surface friction and mixing or turbulence. Therefore, high surface friction is only directly related to velocity gradient which is immediately enlarged by small length scale generation near the wall. It is also well-known that the turbulent boundary layer is much thicker than laminar boundary layer. This paper presents the mechanism that how the multiple level ring cycles overlap and the boundary layer becomes thicker. Our new high order DNS found that the second multiple ring cycle would overlap with the first multiple ring cycle due to the higher speed of the ring head and lower speed of the ring legs. The second ring cycle does not mix with the first ring cycle although they have same sign. The overlapping of multiple ring cycles leads to thickening of the transitional boundary layer. Nomenclature ∞ M = Mach number Re = Reynolds number in δ = inflow displacement thickness w T = wall temperature ∞ T = free stream temperature in Lz = height at inflow boundary out Lz = height at outflow boundary Lx = length of computational domain along x direction Ly = length of computational domain along y direction in x = distance between leading edge of flat plate and upstream boundary of computational domain d A 2 = amplitude of 2D inlet disturbance d A 3 = amplitude of 3D inlet disturbance ω = frequency of inlet disturbance 2 3 d d , α α = two and three dimensional streamwise wave number of inlet disturbance β = spanwise wave number of inlet disturbance R = ideal gas constant γ = ratio of specific heats ∞ µ = viscosity