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To investigate which component of the anisotropic permeability tensor of porous media influences turbulence over porous walls, direct numerical simulation of anisotropic porous-walled channel flows is performed by the D3Q27 multiple-relaxation-time lattice Boltzmann method. The presently considered anisotropic permeable walls have square pore arrays aligned with the Cartesian axes. Vertical, streamwise and spanwise pore arrays are systematically introduced to the walls to impose anisotropic permeability. Simulations are carried out at a friction Reynolds number of 111 and 230, which is based on the averaged friction velocity of the porous bottom and the smooth top walls. It is found that streamwise and spanwise permeabilities enhance turbulence whilst vertical permeability itself does not. In particular, the enhancement of turbulence is remarkable over porous walls with streamwise permeability. Over streamwise permeable walls, development of high- and low-speed streaks is prevented whilst large-scale intermittent patched patterns of ejection motions are induced. It is revealed by two-point correlation analysis that streamwise permeability allows the development of streamwise large-scale perturbations induced by Kelvin–Helmholtz instability. Spectral analysis reveals that this perturbation contributes to the enhancement of the Reynolds shear stress, leading to significant skin friction of the porous interface. Through the comparison between the two different Reynolds-number cases, it is found that, as the Reynolds number increases, the streamwise perturbation becomes larger and more organized. Consequently, owing to the enhancement of the large-scale perturbation, a significant Reynolds-number dependence of the skin friction of the porous interface can be observed over the streamwise permeable wall. It is also implied that the wavelength of the perturbation can be reasonably scaled by the outer-layer length scale.

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a b s t r a c tA three-dimensional twenty-seven (D3Q27) discrete velocity multiple-relaxation-time lattice Boltzmann method is developed. The proposed scheme is validated in fully developed turbulent channel, pipe and porous medium flows through direct and large eddy simulations. The direct numerical simulation of the turbulent channel flow confirms that the present scheme is as reliable as the spectrum method for simulating turbulence. Through the large eddy simulations of the pipe and porous medium flows, the present scheme shows its satisfactory accuracy for simulating turbulent flows bounded by circular walls that is failed by the three-dimensional nineteen (D3Q19) model.

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A numerical investigation of binary droplet collision has been conducted. The complete process of the collision of two liquid droplets is dynamically simulated by solving the incompressible Navier-Stokes equations coupled with the convective equation of the level set function that captures the interface between the liquid and the gas phases. The simulations cover four major regimes of binary collision: bouncing, coalescence, reflexive separation, and stretching separation. For water droplets in air, the numerical results are compared with the experiments by and Ashgriz and Poo [J. Fluid Mech. 221, 183 (1990)] on collision consequences. For hydrocarbon (C14H30) droplets in nitrogen gas, the simulated results are compared in detail with the time-resolved photographic images of the collision processes obtained by Qian and Law [J. Fluid Mech. 331, 59 (1997)] in every collision regime. The present numerical results suggest that the mechanism of a bouncing collision is governed by the macroscopic dynamics. However, the fact that the present macroscopic numerical model is unable to capture the collision regime of coalescence after minor deformation supports the speculation that its mechanism is related to the microscopic dynamics. Furthermore, the transition from bouncing to coalescence collisions has been predicted and agrees well with the analytical model. The mechanism of satellite droplet formation for head-on collision and stretching separation collision is also studied based on the detailed time-resolved dynamic simulation results. It is then confirmed that end pinching is the main cause of satellite formation in head-on collisions whereas the capillary-wave instability becomes dominant in large impact parameter cases. In the case of an intermediate impact parameter, the effects of twisting and stretching due to the angular momentum and the inertia of the colliding droplets are significant for the satellite formation.