ALBERT

Description: 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 = 15, 25 and 50 mm and cylindrical bars of mesh sizes M = 10 and 25 mm) were used. The solidity of all grids is σ = 0.36. The instantaneous streamwise and vertical (cross-stream) velocities were measured by hot-wire anemometry. The mesh Reynolds numbers were adjusted to ReM = 6700, 9600, 16 000 and 33 000. The Reynolds numbers based on the Taylor microscale Reλ 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 ∼ -1.32) for Saffman turbulence. Here, p is the power of the dimensionless energy dissipation coefficient, A(t) ∼ tp. Furthermore, each case shows that streamwise variations in the integral length scales, Luu and Lνν, and the Taylor microscale λ grow according to Luu ∼ 2Lνν ∝ (x/M - x0/M)2/5 (for the M = 10 mm grid, Luu ∝ (x/M - x0/M)2(1+p)/5 ∼ (x/M - x0/M)0.44) and λ ∝ (x/M - x0/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 x0 is the virtual origin. We demonstrated that in the decay region of grid turbulence, urms2Luu3 and νrms2Lνν3, which correspond to Saffman's integral, are constant for all grids and examined ReM values. However, urms2Luu5 and νrms2Lνν5, which correspond to Loitsianskii's integral, and urms2Luu2 and νrms2Lνν2, which correspond to the complete self-similarity of energy spectrum and 〈u2〉 ∼ t-1, are not constant. Consequently, we conclude that grid turbulence is a type of Saffman turbulence for the examined ReM range of 6700-33 000 (Reλ = 27-112) regardless of grid geometry. © 2013 Cambridge University Press.

Description: In many turbulent flows near obstacles or in ducts, the turbulence is inhomogeneous in two directions perpendicular to the main flow direction. In convective flows, there may initially be no mean motion. In both types of flow the gradients of Reynolds stresses drive mean motions in directions of inhomogeneity. Using the method of rapid distortion theory developed by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, p. 209), we analyse these gradients where homogeneous isotropic turbulence is impinging onto two semi-infinite flat rigid surfaces intersecting at right angles. The mean velocity is assumed to be uniform (i.e. the surfaces move at free-stream velocity, or the boundary layers are very thin). The inhomogeneous spectra, variances and Reynolds-stress gradients are evaluated. For isotropic free-stream turbulence with mean square velocity u2∞1̄, the mean square velocity fluctuation at a high Reynolds number in the corner is u2 ∞1̄(X, 0, 0) = 2.121u2∞1̄ , independent of the form of the spectrum. This is explained by estimating how the free-stream eddies are blocked by the two walls. The gradients of Reynolds stresses force a mean secondary flow to develop; its direction is into the corner, and its magnitude at time t is of order tu2 ∞1̄/L∞, where L∞ is the integral scale. These results are tested in a wind tunnel experiment. A turbulence-generating grid installed at the entrance to the test section generates nearly isotropic, grid-generated turbulence. A corner plate with faces parallel to the mean flow and sharp edges is placed downstream of the grid so that shear-free turbulence impinges onto the corner plate. The turbulent Reynolds number based on (L∞), (ReL=u 2∞1̄L∞/v, is 1400 at the leading edge of the plate. A hot-wire anemometry is used to measure instantaneous velocities. The experimental results are consistent with the rapid distortion theory estimates for the variances and the secondary mean motion, which is in the same direction and has the same order of magnitude as Prandtl's analysis of shear-driven secondary flow (of the second kind). We conclude that the blocking mechanism adds to the shear effects and has a significant and sometimes dominant contribution to the crossflows wherever it acts in two non-parallel directions, such as convection in a corner. Consequently, mean transport into corners occurs for most kinds of distorted flow with weak viscous stresses, which has many engineering and environmental implications. There are also implications for the chaotic nature of many confined flows near corners. © 2010 Cambridge University Press.