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

Quasi-analytical solutions of a turbulence-modeling equation on the robustness of decaying homogeneous turbulence

“…Therefore, the above analytical solution may not be suitable to calculate a value of f ( t ) directly. Moreover, the previous analytical solutions of f ( t ) 17,35 are based on an exponential function and differ significantly from the above analytical solution. Thus, the above analytical solution may not be discussed using the previous analytical solutions.…”

“…In addition, this refined analytical solution could be discussed using the previous analytical solutions. 17,35 Thus, the present study uses the refined analytical solution of equation (13). An analytical solution of g ( t ) can also be obtained from f ( t ) using the approximation of h ( t ) …”

“…Moreover, C ϵ 1 is the model coefficient, and the other model coefficient C ϵ 2 10 is described as C ϵ 2 = ( n + 1 ) / n . Using the axisymmetric anisotropy of the homogeneous turbulence, the term P is the production term and is given as P = ( 1 / 2 ) ( − 2 〈 u 2 〉 + 〈 v 2 〉 + 〈 w 2 〉 ) ( dU / dx ) , 17,35 where dU / dx is the longitudinal gradient of the streamwise mean velocity U , and x is the streamwise direction. Previous studies of grid-generated turbulence 1 used the anisotropy parameter a , which is defined as follows: a = 〈 v 2 〉 / 〈 u 2 〉 = 〈 …”

“…This constant variation is the same as that used in previous studies. 17,35 The second temporal variation is a linear variation. The linear variation of S ( t ) is given as follows: S ( t ) = d t St , where d t S is a linear gradient of the variations.…”

“…In an actual experimental situation, this weak fluid acceleration could be caused by the blockage of a wind tunnel. 33,34 Few previous studies examined the effects of the weak fluid acceleration, 17,35,36 the small strain of the mean flow, due to wind tunnel blockage of the grid-generated turbulence, whereas there are several previous studies that examined the effects of wind tunnel blockage on the flow around an obstacle or a wind turbine. 37–41 In a recent experiment on grid-generated turbulence using a wind tunnel, the blockage effects, which may be equivalent to the effects of weak fluid acceleration, were confirmed to be negligible.…”