Vol 53, No 4 (2018)

The problem of water permeability of a thin impervious screen made of a polymeric geomembrane with flaws (damages) is considered. The screen consists of a covering layer and a ground base underlaid by a drainage bed. The solution is implemented using methods of theory of flow through a porous medium by means of the conformal mapping and velocity hodograph methods. The characteristic feature of this solution is the study of free pressurized–pressureless flow in a porousmediumthrough a continuous slit in the plane formulation. The basic computational dependences are presented and the calculations of the water permeability are carried out by means of the formulas obtained in comparison with the well-known dependences for a particular case.

The two-dimensional variational problem for a gas-lubricated slider bearing is considered. In the gas layer the pressure field is described by the linear Reynolds equation which corresponds to low compressibility numbers. The boundary conditions are the conditions of vanishing the excess pressure on the boundaries of the domain. The load capacity acts as the functional of the variational problem. The system of necessary conditions of extremum which underlies the calculation algorithm is analyzed qualitatively. The present study develops radically and supplements the results of author’s studies at the modern level of theoretical and computational possibilities.

It is known that turbulence is characterized by intermittence which is closely related to the development of unsteady nonisotropic intense small-scale vortex structures. In this study, small fluid particles from the inertial range of isotropic turbulence are considered. It is shown that the phenomenon of rotation intensification and stretching of the particles can be analyzed theoretically. In recent experimental and numerical studies, where this phenomenon was called “the pirouette effect”, its significance in the mechanism of the intense small-scale structures generation was discussed. In this study, a linear stochastic Lagrangian model for the effect is developed. In this model, the kinetic equation for the distribution function of the squared cosine of the angle between the vorticity and the eigenvector of the strain rate tensor of a fluid particle is derived and time history asymptotics of this quantity are analytically calculated at large and small times. The results are in good agreement with the recent experiments and numerical calculations. An analysis made in this study shows that the linear processes probably play the crucial role in certain processes in the isotropic turbulence, which is known to be a principally nonlinear phenomenon. The model developed makes it possible to analyze the statistics of the Lagrangian dynamics of small fluid particles in the inertial range which can be useful in some computational approaches to turbulence.

Flow past a simplified model of the civil aircraft is numerically investigated in the landing regime. The numerical modeling is performed within the framework of the Reynolds equations. The aerodynamic characteristics of the model are studied. Regimes with the static hysteresis are found.

Disturbance propagation in laminar boundary layers is investigated at large freestream velocities. An integral relation determining the disturbance propagation velocity in the weak hypersonic interaction regime is obtained for the first time.

The propositions of the development of reactor systems using UF₆ as the nuclear fuel were put forward in USSR and USA already in the fifties of the last century, while from the beginning of the seventies the UF₆-based reactors have become considered as the power sources for spaceborne nuclear power plants (NPP). The application of UF₆ circulating in the closed NPP contourmakes it possible to realize the potential advantages of the flow-through design due to the gaseous fuel mobility compared with the existing NPPs with solid cores. At different plant designs, reactor arrangements, and special flow organization in fuel elements the power range from hundreds of kilowatts to tens megawatts can be realized. The areas of application of power plants with circulating UF₆ can, in particular, include the spaceborne NPPs of wide power range for electric and plasma rocket engines used in the manned flight to Mars, the reactor-laser with direct pumping of gaseous laser mixtures with nuclear fission products, and the on-ground nuclear electric power plants of new generation with high performance with respect to the fuel cycle and safety. On the basis of an analysis of the results of investigations performed in USSR and USA to the end of the nineties of the last century and presented in this overview it can be concluded that from the standpoint of the physics of working processes and constructional materials resistant in the UF₆ environment, there are no insurmountable obstacles for developing the NPPs with circulating UF₆. The list of problems, whose solution can favor the further development of this line of research, if it would be implemented, is formulated. In Section 1 the fuel element designs are described and the techniques of flow organization in them are experimentally validated. In Section 2 the computational and experimental support of the programs is presented. It includes the calculations of the fluid dynamics and heat and mass transfer, the thermal and transport properties of uranium hexafluoride, the special properties of uranium hexafluoride as a working body, and the uranium hexafluoride effect on the constructionalmaterials. In Section 3 the projects of spaceborne power plants of closed and open type on a wide power range are reviewed. In Section 4 one of the promising lines in the field of the nuclear energy use, namely, the reactor-laser development, is presented. Section 5 overviews the on-ground plants, where, apart from the electric power plants, of interest are transport power plants, high-temperature engineering systems, in particular, for hydrogen production, the plants for producing high neutron fluxes, and some others. Section 6 presents considerations concerning the realization of rig reactor experiments with uranium hexafluoride circulating in the reactor core, whose criticity is fully ensured by the gaseous UF₆. These experiments could be the final stage in corroborating the power source of the new type both under space and on-ground conditions. Section 7 contains an analysis of the available publications on the state of the art of investigations in the United States, which allows one to suppose that in USA a vast program of studies on the use of nuclear reactors with circulating UF₆ in the space and on-ground energetics is being systematically performed. In Section 8 some problems which need to be solved in developing the power plants with circulating uranium hexafluoride are listed; they require a vast amount of scientific research. The work on the determination of the design of the power plants with circulating UF₆ and hydrodynamic processes occurring in them were conducted in the Keldysh Research Center (before 1976 the Institute of Thermal Processes) under the supervision of A.A. Pavel’ev, who was the author of many ideas in the field of hydrodynamic stability and turbulence realized in experimental setups and computationmethods. In memory of his invaluable contribution into this line of research the authors dedicate to him this overview.