Mixing and Diffusion in Regular/Fractal Grid Turbulence

Abstract

Scalar mixing in turbulent flows is widely observed in nature as well as in industrial plants. In this chapter, we deal with three topics related to mixing and diffusion in grid-generated turbulence. The first topic (shown in Sect. 1) is experimental research on an axisymmetric CO\(_2\) jet issuing into free-stream turbulent flows generated by a square-mesh biplane round-rod grid (referred to as a regular grid in Sect. 1) and a square fractal grid. The CO\(_2\) jet issues from a small pipe located in the decaying region of these grid turbulences. A composite probe consisting of two concentration-sensitive I-type hot-wire sensors is used. For both flows, the mesh Reynolds number in the free stream is 6,000, and the jet Reynolds number based on the relative velocity between the free stream and the exit velocity of the jet is 5,000. The Taylor Reynolds numbers are about 100 and 35 for the square fractal grid and the regular grid, respectively. The results show that the half-widths of the mean velocity and concentration of the jets increase more rapidly, and the root mean square velocity and concentration in the axial direction decay more slowly for stronger free-stream turbulence. The second topic (shown in Sect. 2) is the development of a mixing layer of a high-Schmidt-number passive scalar in turbulent flows generated by a square-mesh biplane square-bar grid (referred to as a regular grid in Sect. 2) and a square fractal grid with the same mesh Reynolds number of 2500. A uniform passive scalar (Rhodamine B) is supplied only from the lower stream; therefore, scalar mixing layers with an initial step profile develop downstream of the grids. Particle image velocimetry and planar laser-induced fluorescence are used to investigate the velocity and concentration statistics. It is reconfirmed that the square fractal grid produces a higher turbulence intensity than the regular grid. The eddy diffusivity of the mass in the square fractal grid turbulence is approximately 4.2 times larger than that in the regular grid turbulence. The third topic (shown in Sect. 3) is direct numerical simulation of the mixing layer developed in grid turbulence. The simulations include the heat transfer in turbulent flows generated by four types of grid: (a) a square-mesh biplane square-bar grid (referred to as a regular grid in Sect. 3), (b) a square-mesh single-plane square-bar grid, (c) a composite grid consisting of parallel square-bars and (d) a square fractal grid. Two fluids at different temperatures are provided separately in the upper and lower streams upstream of the grids, generating a thermal mixing layer behind the grid. For grid (a), simulations with two different Prandtl numbers of 0.71 and 7.1, corresponding to air and water flows, respectively, are performed. The results show that the typical grid turbulence and thermal mixing layer can be simulated downstream of the grids, and a larger vertical turbulent heat flux is observed when the Prandtl number is large. Next the mixing layers in regular and square fractal grid turbulences are compared. In particular, the effects of the ratio of the largest to the smallest bar for the fractal grid, \(t_r\), are investigated. The results show that turbulent mixing is enhanced to a greater extent in fractal grid turbulence than in regular grid turbulence, especially at large \(t_r\). In Sect. 4, the conclusion and future prospects are presented.