Vol 51, No 6 (2016)

The results of a numerical investigation of the dynamics of a single air bubble rising in water are presented. The bubbles, 1, 2.5, 3, 5, 8, and 10 mm in diameter, are considered. An analysis is based on the numerical solution of the complete three-dimensional system of Navier–Stokes equations for a two-phase medium using an implicit approach with the automatic tracking of the gas-water interface by means of separating the volume fractions. Emphasis is placed on an examination of the local physical characteristics of the motion. The calculated mean rise velocities are compared with experimental data. The rising bubble trajectories are shown to be periodic, zigzag or helical in shape, which is due to the variation in their form and the generation of a characteristic turbulent wake behind them. The bubble rise velocities are correlated with the forces acting on the bubbles.

The procedure of incorporating the detached eddy method and a model of laminar-turbulent transition into the SSG/LRR-ω turbulence model is presented. The approach proposed can be regarded as the generalization of the existing models intended to perform calculations with the SST turbulence model to the case of their use with the SSG/LRR-ω model. The advantage of the approach developed over the RANS turbulence models based on the Boussinesq hypothesis is demonstrated with respect to the problems of flow past an airfoil and cold jet outflow.

The features of the dynamic processes related to the interaction between air shock waves and aqueous foam barriers accompanied by formation of vortex flows are simulated numerically and investigated. The method of solving is based on the two-phase gas-liquid mixture model generalized for solving spatial problems with the use of the equations of state in the analytic form which describe the thermodynamic properties of the mixture components.

The evaporation front moving with a constant velocity through a high-temperature geothermal reservoir is investigated. The solution in the form of a traveling wave is represented. The existence of a thermodynamically consistent solution and the solution with superheating of water ahead of the phase transition front is demonstrated. A boundary separating two types of the solutions is found in the domain of constitutive parameters. Stability of the solutions obtained is investigated by means of the normal mode method. It is shown that the criterion of superheating of water ahead of the boiling front and the criterion of linear stability of the front do not coincide.

Supersonic flow past an absorbing surface is considered. The flow past a plate set transverse to the oncoming stream is calculated on the basis of a model kinetic equation. It is found that the dependence of the drag coefficient on the surface adsorption coefficient qualitatively changes on transition from the free molecular to the continuum flow regime. It is shown that in dense media a drag coefficient maximum is reached at total gas absorption by the surface. Under these conditions the surface interacts with the undisturbed stream. The effect of the extent of the plate-produced disturbance region on the plate drag is investigated.

The structure of flow in the vicinity of a triple point in the problem of stationary irregular reflection of weak shock waves is numerically investigated within the framework of the Euler model, including the von Neumann paradox range. To improve the accuracy of the solution near singular points a new technology including a grid contracted toward the triple point and the discontinuity fitting is applied. It is shown that in the four-wave flow pattern the curvatures of the tangential discontinuity and the Mach front at the triple point are finite. The singularity is concentrated only in a sector between the reflected wave front and the expansion fan. When the three-wave flow pattern is realized, the curvatures of the tangential discontinuity and both wave fronts at the triple point are infinite. On the range of weak and moderate shock waves the logarithmic singularity in subsonic sectors near the triple point conserves up to transition to the regular reflection.

The three-dimensional formulation of the problem on the natural vibrations and stability of an elastic plate which interacts with a quiescent or flowing fluid is represented and a finite element algorithm of its numerical implementation is proposed. The governing equations, which describe vortex-free ideal fluid dynamics in the case of small perturbations, are written in terms of the perturbation velocity potential and transformed using the Bubnov–Galerkin method. The plate strains are determined on the basis of the Timoshenko theory. The variational principle of virtual displacements which takes into account the work done by inertial forces and the hydrodynamic pressure is used for the mathematical formulation of the dynamic problem of elastic structure. The solution of the problem is reduced to calculations and an analysis of complex eigenvalues of a coupled system of two equations. The effect of the fluid layer height on the eigenfrequencies and the critical velocities of the loss of stability is estimated numerically. It is shown that there exist different types of instability determined by combinations of the kinematic boundary conditions prescribed at the plate edges.