Numerical Study on Randomization in Late Boundary Layer Transition

Abstract

The mechanism of randomization in late boundary layer transition is a key issue of late boundary layer transition and turbulence theory. We studied the mechanism carefully by high order DNS. The randomization was originally considered as a result of large background noise and non-periodic spanwise boundary conditions. It was addressed that the large ring structure is affected by background noises first and then the change of large ring structure affects the small length scale quickly, which directly leads to randomization and formation of turbulence. However, what we observed is that the loss of symmetry starts from the middle level rings while the top and bottom rings are still symmetric. The nonsymmetric structure of second level rings will influence the small length scales at the boundary layer bottom quickly. The symmetry loss at the bottom of the boundary layer is quickly spread to up level through ejections. This will lead to randomization of the whole flow field. Therefore, the internal instability of multiple level ring structure, especially the middle ring cycles, is the main reason for flow randomization, but not the background noise. A hypothesis is given that the loss of symmetry may be caused by the shift from C-type transition to K-type transition or reverses. 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 1 PhD Student, AIAA Student Member, University of Texas at Arlington, USA

New Theories on Boundary Layer Transition and Turbulence Formation

“…Since the DNS study is focused on the mechanism of randomization and the DNS computation only allows use of two periods in the spanwise direction, we consider that the flow is randomized when the symmetry is lost and period is changed from π to 2π (Figures 38(a) and 38(b)): In real flow, there is no such a restriction of periodic boundary condition in the spanwise direction. A more detailed discussion about the mechanism of flow randomization will be given by another AIAA 2012 paper [36].…”