Numerical Study of Mechanism of U-shaped Vortex Formation

This paper illustrates the mechanism of U-shaped vortex formation which is found both by experiment and DNS. The main goal of this paper is to explain how the U-shaped vortex is formed and further develops. According to the results obtained by our direct numerical simulation with high order accuracy, the U-shaped vortex is part of the coherent vortex structure and is actually the tertiary streamwise vortices induced by the secondary vortices. The new finding is quite different from existing theories which describe that the U-shaped vortex is newly formed as the head of young turbulence spot and finally break down to small pieces. In addition, we find that the U-shaped vortex has the same vorticity sign as the original λ-shaped vortex tube legs and serves as a second neck to supply vorticity to the ring-like vortex when the original vortex tube is stretched and multiple rings are generated. 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 2 A = amplitude of 2D inlet disturbance d 3 A = 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