The paper focuses on a study of turbulence decay in flow with streamwise gradient. For the first time, an analytical solution of this problem was obtained based on the k‐ε model of turbulence in one‐dimensional (1D) approximation, as well as on the symmetry properties of the system of differential equations. Lie group technique enabled reducing the problem to a linear differential equation. The analytical solution enabled parametric studies, which are computationally cheap in comparison to CFD based simulations. The lattice Boltzmann method (LBM) in two‐dimensional approximation (2D) was used to validate the analytical results. Large eddy simulation (LES) Smagorinsky approach was used to close the LBM model. Computations revealed that the rate of turbulence decay is significantly different for the cases of positive and negative streamwise pressure gradient. The further comparisons showed that the analytical solution underpredicts the predictions by the numerical methodology, which can be attributed to the simplified problem statement used to derive the closed‐form analytical solution. Comparisons of calculations with experiments revealed that the theoretical models used in the study underpredict the measurements for flows with a positive pressure gradient. Hence it can be concluded that the LBM technique combined with the LES Smagorinsky model requires the further modification.
Abstract
The paper represents an analysis of convective instability in a vertical cylindrical porous microchannel performed using the Galerkin method. The dependence of the critical Rayleigh number on the Darcy, Knudsen, and Prandtl numbers, as well as on the ratio of the thermal conductivities of the fluid and the wall, was obtained. It was shown that a decrease in permeability of the porous medium (in other words, increase in its porosity) causes an increase in flow stability. This effect is substantially nonlinear. Under the condition Da > 0.1, the effect of the porosity on the critical Rayleigh number practically vanishes. Strengthening of the slippage effects leads to an increase in the instability of the entire system. The slippage effect on the critical Rayleigh number is nonlinear. The level of nonlinearity depends on the Prandtl number. With an increase in the Prandtl number, the effect of slippage on the onset of convection weakens. With an increase in the ratio of the thermal conductivities of the fluid and the wall, the influence of the Prandtl number decreases. At high values of the Prandtl numbers (Pr > 10), its influence practically vanishes.
The focus of this paper was Jouguet detonation in an ideal gas flow in a magnetic field. A modified Hugoniot detonation equation has been obtained, taking into account the influence of the magnetic field on the detonation process and the parameters of the detonation wave. It was shown that, under the influence of a magnetic field, combustion products move away from the detonation front at supersonic speed. As the magnetic field strength increases, the speed of the detonation products also increases. A dependence has been obtained that allows us to evaluate the influence of heat release on detonation parameters.