Exact Solution of Grid Produced Turbulence; New Approach
Keywords:Turbulent Energy, Kinetic Theory, Double Velocity Correlation, Grid Produced Turbulence, Final Period, Exact Solution
A new approach to the kinetic theory of grid produced turbulence in the final period of decay has been proposed. The governing equations are the two-point velocity correlation equations in which the triple-point correlations are neglected as the closure assumption, and the pressure-velocity correlations are discarded by considering the homogeneous turbulence. Without recourse to the isotropic conditions, these equations are found to be separable into a pair of Oseen type equations. As a result, the double velocity correlations are solved exactly as an initial value problem. It has been shown that the decay law for the turbulent energy in the final period becomes in the form,
≺(∆u)2/U2 = 3 [1 + 8(xx0/M)/(2Re)]-5/2,
where ≺(∆u)2≻/U2 is the normalized turbulent energy, U the main flow velocity, x the coordinate in the main flow direction, M the grid mesh size, x0 the point at which the initial condition is given, the constant determined by each the initial condition, and Re the Reynolds number based on U and M. The present theory shows reasonable agreement with the experiment.
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