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The existing algorithm for determining mass flow in gas production and transportation systems from output pressure measurements is extended to the case where the internal section of the tube changes with time and is also to be determined in the course of solving the general problem. It is proposed to use this algorithm to determine the presence of hydrates in such systems. An example of determining the presence of hydrates in a main gas pipeline section in permafrost is considered.

Pressure filtration waves in cracks in porous permeable medium are studied. The effect of the porosity and permeability of the formation and crack, the crack width, and the rheological properties of the saturating fluid on the dynamics of perturbations in the crack are studied. It is shown that in a porous permeable formation, a crack is a wave channel through which low-frequency pressure fluctuations in wells propagate. Accurate solutions are obtained which describe the evolution of pressure fields in a crack with an instantaneous pressure change in the well by a constant value. Based on these solutions, the corresponding dependences of the fluid flow on time and the pressure at the boundaries are determined.

The operation of rapid-fire multi-rail electromagnetic launchers of solids in a burst mode is analyzed by numerical modeling in two-dimensional and three-dimensional nonstationary formulations. In the calculations, the launchers are powered from a Sakhalin pulsed magnetohydrodynamic generator. Launchers with three and five pairs of parallel rails connected in a series electrical circuit are considered. Bursts of different numbers of solids having different weight are modeled. It is established that the heating of rails is one of the main factors limiting the performance of launchers under such conditions is. It is shown, that the rate of heating of the rails is determined by the inhomogeneity of the current density distribution over the rail cross-section due to the nonstationary diffusion of the magnetic field into the rails. Calculations taking into account the nonstationary nature of the current density distribution in the rails of a multi-rail launcher have shown that a proper choice of the weight of the accelerated solids (up to 800 g), their number in the burst, and the material of the rails makes it possible to attain launching velocities of 1.8-2.5 km/s at moderate heating of the rails.

The flow of a hydrogen-methane mixture through heated coaxial cylindrical tungsten channels with a built-in tungsten wire is studied by the Direct Simulation Monte Carlo method. The purpose of the study is further development of the gas-phase method of deposition of diamond structures. The axial distributions of the concentrations of the components of the hydrogen-carbon mixture are calculated by means of solving a system of chemical kinetics equations. A series of experiments on deposition of diamond structures from various flows of the hydrogen-methane mixture is performed. The calculated results are compared with the experimental data. Based on these comparisons, it is concluded that numerical optimization of operation modes of gas-dynamic reactors can be used for deposition of diamond structures.

Evaporation rates of water droplets in high-temperature gases were experimentally determined using high-speed video recording cameras and low-inertia thermocouples (for heated air flow as an example). The experiments were carried out for droplets of initial size (radius) of 1-3 mm at an air temperature 500-1000 K. Dependences of the evaporation rate of water droplets on time and gas temperature for various initial droplet sizes were obtained.

Titanium dissolution in the aluminum melt and synthesis of an intermetallic compound at constant temperature and pressure are numerically simulated by the molecular dynamics method. Owing to titanium dissolution, the TiAl₃ intermetallic compound is formed near the interface between the titanium crystal and aluminum melt. Based on the theory of weak solutions, a mathematical model of titanium dissolution in the aluminum melt is constructed. Dependences of the diffusion coefficient, equilibrium concentration of titanium, and dissolution rate on temperature are obtained.

This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by the Legendre polynomial segments is used to obtain differential equations of the elastic layer. For the approximation of equilibrium equations and boundary conditions of three-dimensional theory of elasticity, several approximations of each desired function (stresses and displacements). The stresses at the internal points of the plate are determined from the defining equations for the orthotropic material, averaged with respect to the plate thickness. The construction of the bending equations of laminated plates for each layer is carried out with the help of the elastic layer equations and the conjugation conditions on the boundaries between layers, which are conditions for the continuity of normal stresses and displacements. The numerical solution of the problem of bending of the rectangular laminated plate obtained with the help of modified equations is compared with an analytical solution. It is determined that the maximum error in determining the stresses does not exceed 3%.

The constitutive equations of motion of an elastic medium with given initial stresses are formulated in the form of a hyperbolic system of differential equations of the first order. Equations describing the propagation of small perturbations in a prestressed isotropic medium with an arbitrary energy dependence of the elastic deformation in the strain tensor are derived, and equations for the quadratic dependence of elastic strain energy on the strain tensor are given.

This paper presents of an geometrically nonlinear analytical model of a flexible cylindrical frame (rim) of the transformable precision large-size reflector of space antennas made using polymer composite materials with form memory. A nonlinear boundary-value problem for the frame in a deformed (collapsed) state is formulated and exact analytic solutions in elliptic functions and integrals which describe the deformation modes of the rim. A geometrically nonlinear model us used to obtain exact analytical solutions which allow preliminary determination of the geometric dimensions and the optimal shape of the flexible frame and estimate the stored energy.

Numerical schemes for determining the shape and dimensions of radial cracks formed during confined explosions of linear charges located in a monolithic rock massif at a great depth and near its surface. The influence of the charge length on the dimensions of radial cracks in a confined explosion is studied. The amount of undercharging of a borehole or blast charge for which the area radial cracks is maximal is determined.