On invariants in grid turbulence at moderate Reynolds numbers

The decay characteristics and invariants of grid turbulence were investigated by means of laboratory experiments conducted in a wind tunnel. A turbulence-generating grid was installed at the entrance of the test section for generating nearly isotropic turbulence. Five grids (square bars of mesh sizes M D 15, 25 and 50 mm and cylindrical bars of mesh sizes M = 10 and 25 mm) were used. The solidity of all grids is sigma = 0.36. The instantaneous streamwise and vertical (cross-stream) velocities were measured by hot-wire anemometry. The mesh Reynolds numbers were adjusted to Re-M = 6700, 9600, 16 000 and 33 000. The Reynolds numbers based on the Taylor microscale Re-lambda in the decay region ranged from 27 to 112. In each case, the result shows that the decay exponent of turbulence intensity is close to the theoretical value of -6/5 (for the M = 10 mm grid, -6(1 + p)/5 similar to -1.32) for Saffman turbulence. Here, p is the power of the dimensionless energy dissipation coefficient, A(t) similar to t(.)(p) Furthermore, each case shows that streamwise variations in the integral length scales, L-uu and L-vv, and the Taylor microscale lambda grow according to L-uu similar to 2L(vv) proportional to (x/M - x(0)/M)(2/5) (for the M = 10 mm grid, L-uu proportional to (x/M - x(0)/M)(2(1+p)/5) similar to (x/M - x(0)/M)(0.44)) and lambda proportional to (x/M - x(0)/M)(1/2), respectively, at x/M > 40-60 (depending on the experimental conditions, including grid geometry), where x is the streamwise distance from the grid and x(0) is the virtual origin. We demonstrated that in the decay region of grid turbulence, u(rms)(2) L-uu(3) and v(rms)(2) L-vv(3), which correspond to Saffman's integral, are constant for all grids and examined Re-M values. However, u(rms)(2) L-uu(5) and v(rms)(2)L(vv)(5) which correspond to Loitsianskii's integral, and u(rms)(2)L(uu)(2) and v(rms)(2)L(vv)(2), which correspond to the complete self-similarity of energy spectrum and < u(2)> similar to t(-1), are not constant. Consequently, we conclude that grid turbulence is a type of Saffman turbulence for the examined Re-M range of 6700-33 000 (Re-lambda = 27-112) regardless of grid geometry.