TRIGGERING OF DETONATION PROCESSES IN PROPULSION CHAMBER

The Navier-Stokes equations have been used for numerical modeling of chemically reacting gas flow in the propulsion chamber. The chamber represents an axially symmetrical plane disk. Fuel and oxidant were fed into the chamber separately at some angle to the inflow surface and not parallel one to another to ensure better mixing of species. The model is based on conservation laws of mass, momentum, and energy for nonsteady two-dimensional compressible gas flow in the case of axial symmetry. The processes of viscosity, thermal conductivity, turbulence, and diffusion of species have been taken into account. The possibility of detonation mode of combustion of the mixture in the chamber was numerically demonstrated. The detonation triggering depends on the values of angles between fuel and oxidizer jets. This type of the propulsion chamber is effective because of the absence of stagnation zones and good mixing of species before burning.

Modeling of Detonation Processes in Propulsion Engine

Numerical modeling of chemically reacting gas flow in the propulsion chamber using theNavier-Stokes equations has been performed. The simplest form of the chamber has been used, when thelast one represents axially symmetrical plane disk. Fuel and oxidant were fed into the chamber separatelywith outflow to the periphery. The directions of fuel and oxidizer jets are not at right angles to the inflowsurface and not parallel one to another to supply better mixing of species. The detonation triggeringdepends on the values of angles between fuel and oxidizer jets. At parallel directions of the jetssignificant part of not reacted gas components leaves the chamber. This type of the propulsion chamber ismore effective than one studied before, because of absence of stagnation zones and good mixing ofspecies before burning. The diameter of the chamber may be done less, since the largest part of fuelreacted at the inlet surface.

Rigid-body motion. Non-inertial coordinate systems

This chapter addresses the inertia tensor and its relation with the mass quadrupole moment tensor, the principal axes and the principal moments of inertia, evolution of the period of the Earth’s rotation around its axis due to the action of tidal forces, and the motion of the gyrocompass at a given latitude. The chapter also addresses precession of a symmetric top, the stability of rotations of an asymmetric top, “motion” of a plane disk which rolls in the field of gravity over a smooth horizontal plane, and the displacement from the vertical of a particle which is dropped from a given height with zero initial velocity. Finally, the chapter discusses the Lagrange point in the Sun-Jupiter system.

Rigid-body motion. Non-inertial coordinate systems

This chapter addresses the inertia tensor and its relation with the mass quadrupole moment tensor, the principal axes and the principal moments of inertia, evolution of the period of the Earth’s rotation around its axis due to the action of tidal forces, and the motion of the gyrocompass at a given latitude. The chapter also addresses precession of a symmetric top, the stability of rotations of an asymmetric top, “motion” of a plane disk which rolls in the field of gravity over a smooth horizontal plane, and the displacement from the vertical of a particle which is dropped from a given height with zero initial velocity. Finally, the chapter discusses the Lagrange point in the Sun-Jupiter system.

Researches of the of Gas Expiring From the Vortex Jet Gripping Device on the Flat Barrier

The interaction of the twisted stream of gas expiring from the vortex jet gripping device on a plane barrier is considered. The developed mathematical model allows defining a pattern of a current of a flow in the device camera, and also in a zone of contact with the retained object. Rarefaction in the field of capture and influence of different parameters on its value is defined. Value of forces of suction of a stream of compressed air allowing to retain a plane disk is received

MATHEMATICAL MODEL OF INTERACTION OF FREE ROLLING FLAT DISK WITH SOIL

When constructing a mathematical model for the interaction of a free-rotating plane disk with soil, it is necessary to take into account that the magnitude of its kinematic parameter, equal to the ratio of its circumferential velocity to the speed of translational movement of the disk, is not a given quantity, but a definite quantity. With uniform rotation of the disk and its translational movement at a constant speed, the kinematic parameter is determined from the equilibrium equation of external forces, applied to the disk. The generalized mathematical model of disk-soil interaction, proposed earlier, was taken into account, but in view of relative complexity it was not widely used. The aim of the study is to construct a simpler, but adequate mathematical model for the interaction of a free-spinning disc with soil. The model is constructed under the assumptions of the constancy of the translational velocity of the disk, the permanence of its penetration and the possibility of replacing the pressure on the disc’s lateral surfaces with its mean value and replacing the force per unit length of the blade with its mean value. Since the distribution of the elementary forces of soil reactions is ultimately determined by the distribution of the absolute velocities of the points of the disk in contact with the soil, the resultant reactions of the soil and their total moment are functions of the kinematic parameter of the disk and its relative burial. These functions are given by integrals, that are not expressed in terms of elementary functions by a finite number of operations. However, the proximity of the kinematic parameter of the free-spinning disk to unity makes it possible, with the help of an estimate of these integrals, to obtain approximate expressions in terms of elementary functions for the resultant reactions of the soil and their total angular momentum. It is shown that the accuracy of the approximations obtained is sufficient for engineering practice.