Boiling liquid model

Представлена модель вскипающей жидкости, построенная на базе ранее предложенной автором обобщенно-равновесной модели смеси. В модели учтена сжимаемость жидкой фракции. Проведен характеристический анализ уравнений модели и показана их гиперболичность. Приведены расчетные формулы узлового метода характеристик, с использованием которого рассчитано течение при распаде произвольного разрыва во вскипающей жидкости. A model of a boiling liquid is presented, built on the basis of a one-speed two-temperature mixture model previously proposed by the author, in which the forces of interfractional interaction are taken into account. The liquid fraction was considered compressible. A characteristic analysis of the equations of the model is carried out and their hyperbolicity is shown. Relations for characteristic directions and differential relations along these lines are written. An analytical formula for calculating the speed of sound in a boiling liquid is obtained. It is noted that the speed of sound in a liquid when taking into account phase transformations is somewhat lower than is predicted by the Wood formula. The calculation formulas of the iterative algorithm of the nodal method of characteristics are presented, which implies that the flow is calculated during the decay of an arbitrary rupture in a boiling liquid. In the calculations, it was assumed that the phase transition during the boiling process occurs under conditions of an overheated state, when the temperature of the liquid exceeds the saturation temperature. It is shown that taking phase transformation into account leads to a significant increase in the vapor concentration in the unloading wave, as well as to a small increase in both the speed of the mixture and pressure. The concentration of the vapor fraction behind the shock front decreases.

Unloading wave in the cylindrical network from nonlinear elastic fibers

Aims of research. Investigation of a wave of unloading in a cylindrical network of nonlinear elastic fibers. Given the many options for wave propagation in cylindrical networks, an attempt is made to solve the problem of continuous waves. Methods. The movement of the network in the axial direction is cornsidered. nonlinear elastic fibers; To a basis of a cylindrical system are accepted: an individual vector i r parallel wave of unloading; cylindrical network; to a cylinder axis, j r · an individual vector of a tangent to cross-section section continuous waves of the cylinder, k · an individual vector perpendicular to the previous ones, x - is the coordinate in the direction of the axis of the cylinder, y - is the length of an arc of the circumference of the cylinder. The problem reduces to a hyperbolic system of equations under appropriate conditions. Since the wave speed increases when the net is stretched, the stretch wave will obviously be discontinuous. In order to study continuous waves, the problem of wave propagation is solved when unloading a pre-stretched cylinder from a nonlinear basis. The problem is solved by the method of characteristics. Results. The results are illustrated with calculations and can be used at calculations of various flexible pipes, including flexible drilling.

Mechanochemical mechanism for reaction of aluminium nano- and micrometre-scale particles

A recently suggested melt-dispersion mechanism (MDM) for fast reaction of aluminium (Al) nano- and a few micrometre-scale particles during fast heating is reviewed. Volume expansion of 6% during Al melting produces pressure of several GPa in a core and tensile hoop stresses of 10 GPa in an oxide shell. Such stresses cause dynamic fracture and spallation of the shell. After spallation, an unloading wave propagates to the centre of the particle and creates a tensile pressure of 3–8 GPa. Such a tensile pressure exceeds the cavitation strength of liquid Al and disperses the melt into small, bare clusters (fragments) that fly at a high velocity. Reaction of the clusters is not limited by diffusion through a pre-existing oxide shell. Some theoretical and experimental results related to the MDM are presented. Various theoretical predictions based on the MDM are in good qualitative and quantitative agreement with experiments, which resolves some basic puzzles in combustion of Al particles. Methods to control and improve reactivity of Al particles are formulated, which are exactly opposite to the current trends based on diffusion mechanism. Some of these suggestions have experimental confirmation.