Numerical simulation of oscillations of a monodisperse gas-particle mixture in a nonlinear wave field

This paper presents a numerical simulation procedure for the dynamics of a monodisperse gas-particle mixture in the nonlinear wave field of an acoustic resonator using a two-temperature two-velocity model ignoring phase transitions, particle collision, and possible coagulation. It is assumed that viscosity is present only in the carrier medium described by the Navier-Stokes equations for a compressible gas. The dispersed phase is described by the equation of conservation of mass, momentum, and energy. A monotonic solution is obtained by solving the equations of motion for the carrier medium and dispersed phase in generalized moving coordinates using the explicit McCormack method with splitting in the spatial directions and a conservative correction scheme. The method can be used to study nonlinear oscillations of two-phase mixtures in the vicinity of the first three eigenfrequencies in a flat channel.     

Two-layer quasi-one-dimensional model for calculating gas-particle mixture flow in nozzles

The one-dimensional approximation is widely used at the present time to calculate gas-particle (solid or liquid) mixture flows in nozzles within the framework of the two-velocity (or multi-velocity) continuum model. Other studies have been made [1–6] in which the calculations of the two-phase flow in the supersonic part of the nozzle was made by the method of characteristics, and, within the limits of the model adopted, these results may be considered exact. Comparison of the exact and approximate results [6] has shown that even for nozzles of quite simple form (nearly conical) the accuracy of the one-dimensional approximation in the case of mixture flow is considerably lower than for the pure gas, and the computation error increases with increase in the relative particle flow rate. This deterioration of the accuracy is to a considerable degree caused by flow stratification, which arises because of particle lag and leads to the formation of a wall region of pure gas. For high particle content, the wall layer, in which the gas is not subjected to thermal and dynamic input from the particles, has the nature of a low-entropy, low-temperature, high-velocity layer with parameters which differ significantly from the gas parameters in the region occupied by the particles.Therefore, in the present study a modification was made in the one-dimensional theory, based on separate averaging of the flow in the wall layer and in the core, where the gas flows together with the foreign particles. Comparison of the exact results with those obtained with the aid of conventional one-dimensional theory and the proposed two-layer model showed that this modification of one-dimensional theory led to a considerable reduction in the errors of calculation for the flow parameters.In conclusion, the authors wish to thank S. Yu. Krasheninnikov for suggesting this study and also N. S. Galyun, A. M. Konkin, and L. P. Frolov for assistance in the investigation.     

A laser-interferometric dilatometer for thermal-expansion measurements of composites

A high-precision, Fizeau-type laser-interferometric dilatometer system has been developed for low-expansion composite materials. The strain resolution is about one microstrain. The system is automated to operate over a large temperature range and record data during the test. A technique has been developed to reduce the data in real time. The dilatometer system is described and thermal-expansion measurements for several fiber-reinforced and particle-filled composites are presented. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Numerical solution of an inverse problem of nozzle theory for a two-phase gas-particle mixture

In the present paper gas flows with monodisperse and polydisperse particles in plane and axisymmetric nozzles are calculated by the inverse method [1, 2]. The gas velocity distribution is specified on the axis of symmetry of the nozzle, while the gas and particle parameters are specified in the entrance section. As a result of the numerical integration of a system of equations describing a flow of gas with condensate particles in it we determine the gas and particle parameters, the gas streamlines, and the particle trajectories with allowance for the mutual influence of the gas and particles. One of the gas streamlines is taken as the nozzle contour and the limiting trajectories and pure gas zone are found. A difference method is described which makes it possible to calculate the subsonic, transonic, and supersonic flow regions using a single algorithm, its features are noted, and the results of the calculation for monodisperse mixtures with particle diameters 1 and 5 m and fractions by weight 0.3 are given. A comparison is made with the results of calculations by other methods.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–114, July–August, 1986.The authors express their gratitude to N. B. Ponomarev and G. E. Dumnov for their useful discussions and help in carrying out the calculations.     

Strong explosion in a combustible gas mixture

Assume that a planar, cylindrical, or spherical point explosion takes place in a combustible mixture of gases. As a result of the explosion a strong shock wave develops and triggers chemical reactions with the release of heat. The solution of the problem for the case in which the thickness of the heat release zone is neglected (the infinitely thin detonation wave model) was obtained in [1–3].It was emphasized in [4] that these solutions can be considered only as asymptotic solutions for time and distance scales which are large in comparison with the scales which are characteristic for the chemical reactions, and under the assumption that as the overdriven detonation wave which is formed in the explosion is weakened by the rarefaction waves it does not degenerate into an ordinary compression shock. Here the question remains open of the possibility of obtaining such asymptotic solutions with account for finite chemical-reaction rates.In conclusion the authors wish to thank E. Bishimov for carrying out most of the computations for this study.     

Whole-field measurement of gas density from two simultaneously recorded interferograms

The visualization technique presented herein is based on white light differential interferometry using large Wollaston biprisms. The particularity of our set-up is that it yields two instantaneous interferograms, taken at precisely the same time, on which the interference fringes are differently oriented. Thus, the instantaneous fields of two different partial derivatives of density are simultaneously recorded and it is possible, through the use of both interferograms, to obtain the value of the density in domains where this cannot be done using a single interferogram. This method has been successfully tested in the two-dimensional unsteady flow past a cylinder.List of symbols d diameter of the cylinder - Oxy Cartesian reference system - t time - M upstream Mach number - gas density - P pressure - P pressure fluctuation - N vortex street frequency - birefringence angle - double-prism median plane - biprism abscissa corresponding to any colour - ₀ biprism abscissa corresponding to the background colour - E optical thickness - E _e optical thickness corresponding to the background colour - dE difference of optical thickness - _x deviation angle of light rays along Ox - _y deviation angle of light rays along Oy - D diameter of the spherical mirror - R radius of curvature of the spherical mirror - L virtual distance from the middle of the test section to the spherical mirror - T time between the trigger and the recording of interferograms     

Waves in a liquid mixture with gas bubbles

The one-dimensional nonstationary motion of a mixture of an ideal incompressible liquid with gas bubbles in a tube behind a moving piston is considered. An exact solution is obtained. Shock-wave propagation is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 143–145, July–August, 1976.The author thanks L. I. Sedov for his evaluation of the study and advice.     

Light-induced drift of a binary gas mixture in a channel

A simple qualitative model, a generalization of the well-known Hamel model [6], suitable for any gas density ratio is constructed; a passage in the limit to the strong collision model is demonstrated. Light-induced diffusion in a plane channel is examined within the framework of the model proposed for arbitrary Knudsen numbers and various gas density ratios; velocity profiles are obtained; the effect of the relative cross section of the excited molecules and the radiation power on the velocities of the active and buffer gases is investigated; the role of the wall in the variation of the total momentum of the mixture is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 159–165, March–April, 1990.The author is grateful to M. N. Kogan for discussing the trend of his research.     

Studies on gas turbulence and particle fluctuation in dense gas-particle flows

Particle fluctuation and gas turbulence in dense gas-particle flows are less studied due to complexity of the phenomena. In the present study, simulations of gas turbulent flows passing over a single particle are carried out first by using RANS modeling with a Reynolds stress equation turbulence model and sufficiently fine grids, and then by using LES. The turbulence enhancement by the particle wake effect is studied under various particle sizes and relative gas velocities, and the turbulence enhancement is found proportional to the particle diameter and the square of velocity. Based on the above results, a turbulence enhancement model for the particle-wake effect is proposed and is incorporated as a sub-model into a comprehensive two-phase flow model, which is then used to simulate dilute gas-particle flows in a horizontal channel. The simulation results show that the predicted gas turbulence by using the present model accounting for the particle wake effect is obviously in better agreement with the experimental results than the prediction given by the model not accounting for the wake effect. Finally, the proposed model is incorporated into another two-phase flow model to simulate dense gasparticle flows in a downer. The results show that the particle wake effect not only enhances the gas turbulence, but also amplifies the particle fluctuation.     

Instantaneous density measurement in two-dimensional gas flow by high speed differential interferometry

The aim of this paper is to present an experimental set-up using a Wollaston prism differential interferometer producing up to twenty successive short exposure white light interferograms at a high framing rate. It is shown that, through optical component calibration, the interferograms can be analysed to yield the instantaneous density field. This method has been successfully tested in the two-dimensional unsteady flow generated by the interaction of a mixing layer and a cavity.List of symbols h height of the downstream edge of the cavity - H height of backward facing step - M Mach number - t time - t time interval between two successive frames - N frequency - double-prism median plane - birefringence angle - _p pressure fluctuation - C _p pressure coefficient - biprism abscissa corresponding to any colour - ₀ biprism reference abscissa corresponding to background colour - _y deviation of light rays - R radius of curvature of spherical mirror - L virtual distance from the middle of the test section to the spherical mirror - E optical thickness - E _e optical thickness corresponding to background colour - d _E difference of optical thickness - d _x abscissa difference - gas density - ₀ stagnation gas density - _e gas density of background colour     

Shock adiabats in a mixture of gas and particles

Shock waves in a mixture of a gas and incompressible drops or particles are considered. We construct the shock adiabat connecting the states in front of and behind a discontinuity, on which the processes of interaction of the phases are assumed to be frozen. It follows from analysis of this adiabat that when particles are present in the gas pressure discontinuities of infinite intensity are impossible, which distinguishes this adiabat from the Hugoniot adiabat in gas dynamics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–167, September–October, 1979.I thank V. V. Gogosov, and also V. A. Naletov and G. A. Shaposhnikov for assistance in the work and R. I. Nigmatulin for valuable comments.