On Invariants in Energy Decay Region in Grid Turbulence

Abstract

Decaying characteristics of grid turbulence are investigated by means of the laboratory experiments using a wind tunnel. Turbulence-generating grids are installed at the entrance to the test section to generate nearly isotropic turbulence. Four grids (mesh size M = 10, 15, 25 and 50 mm) are used. Instantaneous streamwise velocity is measured by a hot wire anemometer. The mesh Reynolds numbers are adjusted to Re M = 6,700, 9,600, 16,000 and 33,000. In this study, decaying characteristics and invariants of grid turbulence for four grid sizes and Re M are mainly investigated. The result for each case shows that the decay exponent of turbulent intensity is close to a theoretical value of-6 5 for Saffman turbulence. Each case also shows that streamwise variation of integral length scale L uu and Taylor microscale λ grow as L uu ∝ (x M − x 0 M) 2 5 and λ ∝ (x M − x 0 M) 1 2 at (x M − x 0 M) > 50, where x 0 is the virtual origin. Consequently, it is concluded that in the decaying region of grid turbulence, u 2 r.m.s L 3 uu , which corresponds to Saffman's integral, are constant for all grids and Re M examined. However, u 2 r.m.s L 5 uu , which corresponds to Loitsianskii's integral, is not constant.