卷 54, 编号 7 (2019)

This work investigates the stability of steady flows of ideal (inviscid and nonconductive) gas in channels with variable cross sections, in the diverging part of which a Chapman-Jouguet detonation wave (DW_CJ) is located. Steady and unsteady flows are described by equations in a one-dimensional approximation with the detonation wave represented by a planar discontinuity surface, normal to the channel axis. The combustible mixture before the detonation wave and the combustion products behind it are perfect gases with constant heat capacities, which, like additive constants in terms of the internal energy and enthalpy, are different before and after the wave. Since the Mach number behind the DW_CJ is equal to unity, it can stand only in the diverging part of the channel in the steady flow. Moreover, depending on the conditions at the channel exit, the flow behind it can be either super- or subsonic. In the first case, the initial Pertubation can reach the DW_CJ only from the left (the gas moves from left to right), and, in the second case it can come from both sides. When investigating the stability, is it is assumed, first, that after the initial perturbation, the detonation wave, which is slightly shifted, remains a DW_CJ. In this case, analysis of stability reduces to calculating the derivative of the Mach number of DW_CJ from the Mach number of the steady flow in front of the wave. In this formulation, the derivative value is always such that the flow under consideration is unstable. Small perturbations of the DW_CJ make it slightly overcompressed. However, even taking this into account, a steady flow with a DW_CJ in a diverging channel is always unstable.

In this study, using the Euler equations, we investigate 3D stationary flows behind a detached bow shock produced in a supersonic flow around a body with a smooth convex bow. The supersonic free stream was considered to be uniform. Maximal entropy on the body surface is substantiated. The streamline that ends at the front stagnation point on the body (the stagnation streamline) is shown to cross the bow shock at the point where the plane tangent to it is perpendicular to the free stream direction. This means that the entropy value on the body surface is calculated by the free stream parameters and is equal to the entropy value behind a normal shock at the point of the stagnation streamline onset.

Using the methods of high-resolution photo- and video recording, this work studied the fine structure of the flows in the cavity center and on the growing splash tip, which disturb the smooth surface of the liquid after the crown falls. The surface geometry reflects the complexity of the pattern of fine flows in the near-surface fluid layer. The geometrical parameters of the structure formed by smooth spikes separated by thin depressions are determined. The structure formation is associated with the action of various exchange mechanisms between the kinetic, potential, and internal energy in a fluid with a free surface.

In this work we studied the structure and dynamics of a two-dimensional flow of a continuously stratified fluid near a horizontal wedge using numerical methods. A mathematical model and a method of numerical implementation were developed. This allows for the simultaneous study of all the elements of multiscale stratified flows without additional hypotheses and connections. The numerical solution is implemented in the OpenFOAM open source package. The calculations were performed in the parallel mode with the use of computing resources of the UniHUB web-laboratory. The laws governing the flow formation are analyzed and the physical mechanisms that are responsible for the vortex formation in areas with high density gradients near the edges of the streamlined wedge are determined.

The structure and dynamics of flows near a horizontal and inclined plates in stratified and homogeneous fluids in a transient vortex regime are studied for various angles of inclination of the plate to the horizon and various geometrical modifications of its front and rear edges. This study is based on high-precision numerical modeling of the fundamental system of equations, which allows calculations of both stratified and homogeneous viscous liquids in a unified formulation. Instantaneous patterns of the vorticity fields, pressure gradient, and density, as well as the values of forces and moments acting on the surface of the plate are analyzed at different inclination angles, curvature radii of the front edge of the plate, and sharpness coefficients of the rear part. The pressure field consists of multi-scale spotted structures with a negative values of pressure, corresponding to the positions of vortical elements of the flow, whose spatial and time scales, geometric features, manifestation level, and dissipation rate essentially depend on the angle of inclination of the plate to the horizon, geometrical modification of its edges, and the type of the fluid. Special attention is paid to the fine structure of the flow near the front edge of the plate, which is the area with the most diverse scales of the flow, in which both large-scale and small-scale vertical structures form and actively interact.

In this work we study the effect of the exponential temperature dependence of the incompressible fluid viscosity on the critical parameters of the flow hydrodynamic stability in a flat channel at various specified values of the wall temperature. The temperature field perturbations are thought to be absent. The eigenvalue spectra for the generalized Orr-Sommerfeld equation are constructed at sufficiently large Peclet numbers. The spectra structure, neutral stability curves, and the critical Reynolds number are shown to largely depend on the fluid properties that are determined by the exponential viscosity function.

When simulating incompressible flow around airfoil using vortex methods of computational hydrodynamics, it is necessary to solve the boundary integral equation with respect to the intensity of the vortex sheet at the airfoil surface line. For its approximate solution, the Galerkin method with a piecewise-constant and piecewise-linear representation of the solution on the airfoil surface line can be applied. The coefficients of the system of linear equations, arising from the procedure of discretization of the integral equation, e xpress the influence of the vortex sheet located on the panels of the airfoil surface line on other panels; the components of the right-hand side vector express the influence of point vortices that simulate a vortex wake in the flow domain. For the case of the airfoil surface line approximation with a polyline consisting of rectilinear panels, exact analytical expressions are obtained for the coefficients of the matrix and the right-hand side vector; for the case of taking into account the curvature of the panels, an approach for their approximate calculation is proposed and all the necessary formulae are derived.