Numerical-based theoretical analysis on effects of weak fluid acceleration of free-stream due to wind-tunnel blockage on grid-generated turbulence

We present a numerical-based theoretical analysis for effects of weak fluid acceleration of free-stream due to wind-tunnel blockage on grid-generated turbulence. The increasing of displacement thickness in the developing of the boundary layers due to wind-tunnel blockage reduces the effective area of the test section of the wind tunnel. Wind tunnel blockage, which often occurs in small wind tunnels, could accelerate the freestream in the wind tunnel and thereby affect the decay of grid-generated turbulence. A previous study proposed a mathematical form that validated the blockage effects on the grid-generated turbulence by demonstrating that the fluid acceleration is too weak to affect the anisotropy of the grid-generated turbulence. The previous study used the governing equation of the two-equation model based on the k−ϵ modeling. The present study have derived a mathematical form to describe the effects of weak fluid acceleration by using the governing equation used in the previous study with simple numerical simulation. The previous mathematical form has an applicable limit of St<0.2. Here, S is the streamwise nondimensional acceleration rate and is defined as S=(dU′/dx′)/(Uo/M), where U′, x′, Uo, and M are the streamwise mean velocity, the streamwise direction, the inflow velocity, and the mesh size, respectively. Moreover, t is the convection time normalized by the characteristic time M/Uo, which may be comparable to the normalized streamwise direction x/M for small S. The applicable limit in the present mathematical form is increased thirty-fold compared with that of the previous mathematical form. The effectiveness of the present scheme is then discussed using a scheme derived from the one-equation model as well as the previous scheme.