Dynamics of sprinkler jets

The problem of the motion of droplet-air sprinkler jets is examined. On the basis of the equations of a turbulent two-phase boundary layer the trajectories and range of these jets are calculated. A comparison of the calculation results with experiment indicates satisfactory agreement. It is shown that the expression for the range of a body projected at an angle to the horizontal gives exaggerated values for the range, while calculating the range for a single droplet with allowance for the air resistance gives values that are much too low. It has been established that in calculating the motion of sprinkler jets it is necessary to take into account the air resistance to the water droplets reduced as a result of the acceleration of the air in the immediate vicinity of the preceding droplets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 60–67, September–October, 1985.     

Flow of a binary gas mixture with arbitrary accommodation of the tangential momentum

The system of BGK (Bhatnagar, Gross, Krook) equations describing the isothermal flow of a binary gas mixture in a capillary with arbitrary accommodation of the tangential momentum is solved by the Bubnov-Galerkin method. General expressions are given for the kinetic thermodynamic coefficients which are valid in the whole range of Knudsen numbers and have the correct free-molecule and viscous limits. The diffusion-slip coefficients, calculated by using test values of the fraction of diffuse reflection, are compared with the experimental results.     

Measurement of translational temperature in low-density jets

A technique and method for measuring the velocity-distribution function of the atoms in rarefied gas flows are described. Some results obtained with flows of binary gas mixtures behind a sonic nozzle are presented. The temperature of the light component (helium) is determined from the half width of the distribution function. Incomplete restoration of the helium temperature occurs in the Mach disk. This effect is examined in relation to concentration. A qualitative explanation is proposed for the effect in question.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 30–34, January–February, 1973.     

Mach reflection of weak shock waves from a rigid wall

On the basis of experimental observations and theoretical analysis of flow structure in the neighborhood of the triple point, it is shown that one should reject the condition for equality of the angle of deflection of flows passing through the Mach front and the two other fronts and replace it with some supplementary condition. The system of consistency equations in the indicated region is closed by an equation which is obtained under the assumption of the extremality of the deflection angle of a flow passing through the incident and reflected fronts. Calculations of the pressure drops behind the shock fronts agree with experimental data in this case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 26–33, September–October, 1973.The authors thank S. A. Khristianovich for consideration of the work and advice.     

Inverted population of Co2 molecules in expanding gas streams

The system of equations of hydrodynamics, which describes the process of escape of the mixtures CO₂ + N₂ + He, H₂O from a nozzle, is solved numerically in conjunction with the equations of the kinetics of the excitation of the vibrational degrees of freedom of the molecules. It is found that an inverted population of the CO₂ molecules with respect to the transition [00 °1] – [10 °0], is produced under certain conditions at the exit from the nozzle. The magnitude of the inversion depends both on the nozzle configuration and on the initial values of the gas temperature and pressure. It is shown that for a specified nozzle configuration there exist optimal values of these parameters, at which the inverted population of the CO₂ molecules reaches approximately 10¹⁵ cm^–3.Translated from Zhumal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 24–34, September–October, 1971.     

Plane-parallel supersonic flow with a discontinuity

This article considers a plant-parallel supersonic flow, with a shock wave terminating within the flow; the shock wave is regarded as a distortion. A line of discontinuity is located ahead of the shock wave in the supersonic zone. The problem is solved by the method of indeterminate coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 95–100, July–August, 1970.The authors thank S. V. Fal'kovich for his valuable advice and for his evaluation of the results obtained.     

An application of the operational calculus to the equations of the Rayleigh Problem in MHD

Summary The operational calculus in the form developed by Van der Pol and Bremmer is applied to obtain some solutions for the equations of the Rayleigh Problem in MHD. The diffusivities in these solutions can have arbitrary values. A limiting case of the solutions is studied, and it is shown that the solutions have some advantages as compared to the integrals of Chang and Yen, and of Hide and Roberts. Finally an example of Ludford is used to verify that the integrals obtained here will make their appearance in the solution of some boundary value problems.MHD stands for magnetohydrodynamics.     

Effect of particles suspended in a fluid flow on the decay of isotropic turbulence

Dynamic equations have been obtained for the two-point double correlations of the fluctuation velocities of a fluid and the particles suspended in it at low volume concentrations of the solid phase. In the case of uniform isotropic turbulence these equations can be considerably simplified. The final period of decay of isotropic turbulence has been studied in detail. At this stage in the case of high-inertia particles the inhomogeneous-fluid turbulence is similar to the turbulence of a homogeneous fluid (without particles) in the sense that the presence of the particles affects only the fluctuation energy but leaves unchanged the spatial scales of turbulence and the spatial energy spectrum function. The suspended particles lead to exponential damping of the turbulent pulsations.Little theoretical information is available on the hydrodynamics of a suspension of fine particles in a turbulent liquid or gas. Research has been mainly confined to the behavior of the individual particles in a given turbulence field [1]. The problem of the turbulent motion of the mixture as a whole has been examined by Barenblatt [2], who derived the equations of motion of the mixture, using Kolmogorov's hypothesis to close them. Hinze [3] has also attempted to derive equations for turbulent pulsations of the mixture. However, as Murray showed [4], Hinze' s equations contradict Newton' s third law.The effect of suspended particles on the turbulence of a two-phase flow is governed by the noncorrespondence of the local velocities of the particles and the medium. The forces of resistance to the motion of the particles relative to the fluid lead to additional dissipation of fluctuation energy and decay of turbulence [2]. On the other hand, if the averaged velocities of particles and medium do not correspond, the suspended particles may also have a destabilizing effect [5, 6], causing energy transfer from the averaged to the pulsating motion. Below we shall consider the case where the averaged velocities of the two phases coincide, i.e., we shall deal only with the first of the two above-mentioned effects.The authors thank G.I. Barenblatt for his useful advice.     

Experimental investigations of the compressibility of argillaceous soils subjected to underground explosions

The results of experimental investigations of the compressibility of argillaceous soils (loess loams, loams, and clays) subjected to underground explosions are discussed. The data concerning the deformation at the shock-wave front, and their comparison with data concerning residual deformations indicate that the viscoplastic soil properties strongly influence the soil compressibility for short-term loads originating from underground explosions. The conclusions which were previously drawn in [1] are qualitatively and quantitatively confirmed.     

Generation of beams of three-dimensional periodic internal waves by sources of various types

The energy and force characteristics of periodic internal wave beams in a viscous exponentially stratified fluid are analyzed. The exact solutions of linearized problems of generation obtained by integral transformations describe not only three-dimensional internal waves but also the associated boundary layers of two types. The solutions not containing empirical parameters are brought to a form that allows a direct comparison with experimental data for generators of various types (friction, piston, and combined) of rectangular or elliptic shape. The stress tensor and force components acting on the generator are given in quadratures. In the limiting cases, the solutions are uniformly transformed to the corresponding expressions for the problems in a two-dimensional formulation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 12–23, May–June, 2006