Turbulent jet mixing of supersonic flows in profiled flow-equalization channels

A numerical model for the calculation of gas dynamic systems with turbulent mixing of supersonic jets is proposed. The problem of designing a transitional flow-equalization channel of minimum length is solved for the viscous turbulent mixing of two parallel or mutually inclined supersonic flows. The problem is solved in two stages. In the first stage the flow-equalization channel is designed by solving the inverse problem in the ideal gas approximation. In the second stage the basic problem is solved for the channel thus obtained on the basis of the parabolized Navier-Stokes equations. Investigations have demonstrated the validity of this approach to the equalization of nonuniform flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–178, July–August, 1987.The authors are grateful to V. I. Kopchenov for supplying the program for solving the basic problem by a first-order Godunov method and to A. I. Kraiko and Yu. V. Kurochkin for their interest and advice.     

Mixing enhancement behind an oblique shock wave

The possibility of mixing enhancement when a design-condition cocurrent jet passes through a stationary oblique shock is investigated. In [4] the effect of such a shock on the mixing layer of flows with Mach numbers M = 3 and 5 was experimentally investigated and it was shown that behind the shock no turbulence is generated. However, irrespective of its effect on the turbulence characteristics, an oblique shock causes deformation of the jet, modifying its dimensions, and in the three-dimensional case the shape of the cross section. The effect of this deformation on mixing, which is shown to be fairly significant, has been investigated theoretically using a numerical method. An approximate relation describing the variation of the maximum admixture concentration in the jet behind the shock is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 61–68, March–April, 1992.The authors are grateful to V. A. Stepanov for useful discussions.     

Evolution of a cloud of low-temperature light gas in an open atmosphere

The problem of the evolution of a hydrogen-air cloud formed as a result of the spillage and evaporation of a certain amount of liquid hydrogen is formulated. The effect of various factors (initial shape and temperature, condensation of atmospheric moisture) on the dynamics of the cloud and its dangerous (from the standpoint of ignition and explosion) propties is analyzed by means of numerical modeling and an approximate method based on a thermodynamic adiabatic mixing scheme. The results of the approximate theory, the numerical calculations and physical experiments are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 92–101, May–June, 1991.The authors are grateful to I. A. Bolod'yan, V. I. Makeev, A. G. Frolov, and A. P. Chuguev for useful discussions and assistance.     

Numerical solution of the entrainment equation

An equation describing the change in body shape as a result of intense mass entrainment from the surface under the effect of convective aerodynamic heating under the simplest assumptions (dependence of the pressure on only the local slope of the surface, the method of local similarity to compute the heat fluxes) is considered. Mathematical questions originating during its numerical solution are investigated. The instability of explicit schemes is proved in the neighborhood of the stagnation point. A stable explicit-implicit scheme, suitable for a through computation of unsmooth solutions, is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 147–154, March–April, 1978.The author is grateful to V. V. Lunev for constant attention to the research and for useful discussions.     

Determination of the coefficient of longitudinal mixing in a undeformed porous medium in the presence of sorption

The article gives and analysis of an expression for the overall coefficient of longitudinal mixing in a porous undeformed medium and obtains analytical expressions for the initial and central moments. The distribution of the concentrations along the filtration channel for a fixed value of the time and the distribution of the concentrations at the outlet of a channel of fixed length are obtained in the form of Hermite polynomials (the forward problem). A method is outlined for determining the coefficient of longitudinal mixing from the experimental distributions and analytical expressions for the moments (the reverse problem). The article gives numerical values of the coefficient of longitudinal mixing found using the method under consideration.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 155–161, July–August, 1972.     

Nonlinear effects associated with the mutual displacement of two gases in a porous medium

The cyclic bidirectional process of isothermal flow of a binary singlephase compressible gas mixture in a porous medium accompanied by diffusion-dispersion mass transfer is considered. On the basis of the equations of multiphase multicomponent isothermal flow a system of two nonlinear partial differential equations with nonlinear boundary conditions corresponding to a given constant gas injection or takeoff rate is obtained and investigated. A numerical algorithm for solving the boundary-value problem obtained is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 64–71, November–December, 1991.In conclusion, the author wishes to thank V. M. Maksimov for taking a constant interest in the work and discussing the results.     

Possible flow regimes of a Newtonian fluid in pipes made of active material

A numerical study is made in the quasione-dimensional inertialess approximation of axisymmetric flow of a Newtonian fluid in a pipe of finite length made of nonlinear active material capable of reducing the corresponding deformations in response to an increase in the tensile stresses. This property is possessed, in particular, by the walls of the smallest arterial vessels, which are equipped with muscle layers. Data are given on the general laws of the exchange of flow regimes in dependence on the mean pressure, the length of the pipe, and certain theological parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 88–93, May–June, 1985.The author is grateful to S. A. Regirer for useful discussions.     

Laminar boundary layer in a swirling flow on a permeable surface

Numerical and approximate analytic methods are used to investigate the three-dimensional nonself-similar swirling flow of a uniform gas on an axisymmetric permeable surface. For large values of the injection parameter (in the general case the injection velocity vector forms a nonzero angle with the vector of the outward normal to the flow surface) asymptotic expressions are obtained for the velocity and temperature profiles across the injection layer, the components of the friction stress and the heat flux at the surface. Certain results of a numerical solution of the problem obtained on a broad interval of variation of the injection parameter are presented. By comparing the numerical and asymptotic solutions the accuracy and region of applicability of the latter are estimated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 28–37, November–December, 1985.In conclusion, the author wishes to thank É. A. Gershbein (deceased) for useful discussion of his results.     

Parameters of streamer breakdown in xenon

It is known from experiments [1–3] that the velocity of streamers, induced in the center of the interelectrode gap and propagating to the electrodes under conditions when the streamer length is comparable with the distance between the electrodes, increases linearly as the streamer length increases. This relationship is in qualitative agreement with theory [4], Nevertheless, the velocity of streamers starting from the electrodes and propagating in a long interelectrode gap remains practically constant during the whole propagation process [5, 6], In the case of short gaps (2–5 cm), constancy of the velocity is observed during the stage of the process when the length of the streamer is much less (20%) than the length of the gap [7], Since the electric field at its end controls the streamer propagation, the constancy of the streamer velocity indicates that the controlling field is constant under these conditions. A number of theoretical models were proposed in [8–13] which describe uniformly moving anode- and cathode-directed streamers (henceforth called anode and cathode streamers). Comparison of experimental data with the corresponding theoretical model enables one to determine the streamer parameters: the electric field, the charged-particle density, the current density, the channel radius, etc. In the case of an anode streamer in Xe an attempt at such a comparison was made, in particular, in [6]. However, the lack of reliable data on the value of the drift velocity and the diffusion coefficient of electrons in Xe for E/p (10² – 10³) V/cm · mm Hg allowed only rough estimates to be made. In this paper a numerical calculation is made of the drift velocity, the diffusion coefficient of electrons in Xe, and the rate of excitation of Xe atoms in the resonance level in the range of values of E/p (10¹–10³) V cm · mm Hg, and the volt-ampere characteristic of the breakdown is measured under conditions described in [6] (p₀=300 mm Hg and E 10⁴–10⁵ V/cm). Using these results, the formulas for the velocity of anode [12] and cathode [13] streamers, and experimental data [6], the parameters of the streamers studied in [6] are determined.Translated from Zhurnal Prikladnoi Meknaniki i Tekhmcheskoi Fiziki, No. 3, pp. 6–11, May–June, 1976.The authors thank A. T. Rakhimov and A. N. Starostin for useful discussions, and A. V. Markov for help with the experiments.     

Stability of a compressible boundary layer relative to a localized disturbance

The problem of stability of an incompressible boundary layer relative to a localized disturbance is considered in a linear approximation. It is shown that the stability analysis reduces to the study of a discrete spectrum of eigenvalues of the corresponding boundary value problem. By means of numerical integration, analysis of the character of the emerging instability is carried out for an unstable mode for the Mach number M = 4.5.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, pp. 107–114, May–June, 1973.The author is grateful to V. V. Struminskii for his interest in this work; he is grateful to L. B. Aizin for useful discussion of the subjects broached, and to A. A. Maslov for the great help in carrying out the numerical calculations.     

Influence of the parameters of a cross-flow on the gain in a jet

A system of equations is proposed for calculating a turbulent axisymmetric jet in a cross-flow for gases with different physical properties. The mixing of carbon dioxide gas with excited nitrogen and helium in a gas-discharge laser has been investigated numerically. Vibrational relaxation of the mixed gases was taken into account. The calculated gain agrees satisfactorily with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 34–37, July–August, 1930.We thank A. P. Napartovich for helpful discussions and V. F. Gerasiaov for providing the experimental data.     

Modeling of mixing during injection of an agent into oil reservoirs with development of fractal structures

A mathematical model of phase mixing in a subsurface reservoir during gas injection into an oil deposit with the objective of reducing the oil viscosity or modifying the phase state is investigated. The gas intrusion into the reservoir causes the development of fractal fields. To determine the mixing timet _*, it is proposed to divide the process into three stages, those of convective and diffusive mixing and the phase transition stage.The characteristic diffusive mixing time is orders of magnitude greater than the characteristic times of the other stages. This makes it possible to consider the stages as independent and use a successive alternation scheme. The convective mixing stage was described by the models of diffusion-limited aggregation or of invasion percolation with delayed action. For the stage of diffusive mixing, the problem of diffusion from a fractal was solved without account for phase transition. Relations for the characteristic times of total and partial mixing of the oil and gas were derived. It is shown that in some cases these times are of the order of several decades and are comparable with the oil field development duration.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 187–189, September–October, 1995.     

Nonequilibrium effects in the filtration of viscoelastic liquids

An experimental investigation was made of nonequilibrium effects with the filtration of viscoelastic petroleums and polymer solutions. A scheme is proposed to explain the effects obtained. A comparison between theoretical dependences and experimental data confirms the proposed scheme of the phenomenon. The filtration of viscoelastic liquids has recently attracted considerable attention. The interest in it is connected with the discovery of well-expressed elastic properties in several high-viscosity petroleums, as well as with the need to explain the laws governing the movement of solutions and polymer melts in a porous medium, with application to industrial chemical equipment and to the injection of polymer solutions into oil-bearing strata with the aim of increasing the yield of petroleum. Among articles devoted to the filtration of viscoelastic liquids, there should be mentioned the fundamental investigation of Marshall and Metzner [1], me theoretical article of Wissler [2], and me review of Savins [3]. Specifically, it is shown in [1] that, as a result of elastic effects, the filtration resistance in a steady-state flow rises in accordance with the relationship 1+A(V/r)² where V is the filtration rate; r is the mean pore radius; is the relaxation time; A is a constant on the order of magnitude of 10. In [1] this increase in the resistance is explained qualitatively by the action of specific, for elastic liquids, normal stresses in contracting and then expanding pore channels. A corresponding calculation (for a flat channel and a determined nonlinear model of a viscoelastic liquid) was made in [2] using the method of perturbation theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 76–83, September–October, 1973.     

Nonequilibrium stretching dynamics of dilute and entangled linear polymers in extensional flow

We propose an extension of the FENE-CR model for dilute polymer solutions [M.D. Chilcott, J.M. Rallison, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newtonian Fluid Mech. 29 (1988) 382–432] and the Rouse-CCR tube model for linear entangled polymers [A.E. Likhtman, R.S. Graham, Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation, J. Non-Newtonian Fluid Mech. 114 (2003) 1–12], to describe the nonequilibrium stretching dynamics of polymer chains in strong extensional flows. The resulting models, designed to capture the progressive changes in the average internal structure (kinked state) of the polymer chain, include an ‘effective’ maximum contour length that depends on local flow dynamics. The rheological behavior of the modified models is compared with various results already published in the literature for entangled polystyrene solutions, and for the Kramers chain model (dilute polymer solutions). It is shown that the FENE-CR model with an ‘effective’ maximum contour length is able to describe correctly the hysteretic behavior in stress versus birefringence in start-up of uniaxial extensional flow and subsequent relaxation also observed and computed by Doyle et al. [P.S. Doyle, E.S.G. Shaqfeh, G.H. McKinley, S.H. Spiegelberg, Relaxation of dilute polymer solutions following extensional flow, J. Non-Newtonian Fluid Mech. 76 (1998) 79–110] and Li and Larson [L. Li, R.G. Larson, Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow, Rheol. Acta 39 (2000) 419–427] using Brownian dynamics simulations of bead–spring model. The Rolie–Poly model with an ‘effective’ maximum contour length exhibits a less pronounced hysteretic behavior in stress versus birefringence in start-up of uniaxial extensional flow and subsequent relaxation.     

Direct Numerical Simulation of Statistically Stationary One- and Two-Phase Turbulent Combustion: A Turbulent Injection Procedure

A new turbulent injection procedure dedicated to fully compressible direct numerical simulation (DNS) or large eddy simulation (LES) solvers is proposed. To avoid the appearance of spurious acoustic waves, this method is based on an accurate tracking of the turbulent structures crossing the boundary at the inlet of the domain. A finite difference DNS solver has been coupled with a spectral simulation in which a statistically stationary homogeneous turbulence evolves to provide fluctuating boundary conditions.A new turbulence forcing method, dedicated to spectral solvers, has been developed as well to control the major properties of the injected flow (turbulent kinetic energy, dissipation rate and integral length scale). One-dimensional Navier–Stokes characteristic boundary conditions extended to non-stationary flows are coupled with the injection procedure to evaluate is potential in four various configurations: spatially decaying turbulence, dispersion of vaporizing sprays, propagation of one- and two-phase V-shape turbulent flames.     

Laminar mixing of planar supersonic chemically reacting jets of unequal pressure

A study is made of the influence of a transverse pressure gradient on the mixing of reacting jets of fluorine and hydrogen. The real picture is simulated by a system of simplified Navier-Stokes equations. A comparison is made with calculations based on the complete Navier-Stokes equations and also boundary layer equations. Features of the shock waves are analyzed under conditions of strong heat release in the mixing layer. The influence of these features on the gain in laser situations is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 18–23, May–June, 1982.We thank G. N. Volchkova, Yu. P. Golovachev, V. A. Pospelov, M. Kh. Strel'ts, and M. L. Shur for helpful discussions.     

Turbulent mixing at an accelerating interface between liquids of different density

Gravitational turbulence, arising at the interface between incompressible liquids in the field of gravity is discussed. Qualitative differences from shear turbulence are evaluated. The results of experiments on determination of constant mixing and the distribution profiles of the density are given. Two-dimensional calculations are used to set up numerical experiments on mixing. The experiments and calculations are compared with each other and with the theoretical results of [1, 2].Presented at the Fourth Conference on Theoretical and Applied Mechanics, Kiev, May 21–28 (1976).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 157–160, November–December, 1978.In conclusion, the authors thank R. I. Ardashev, S. I. Balabin, V. E. Kotlyar, and G. O. Tomashev for their aid in carrying out the experiments.     

Conditions of pulsed starting of supersonic diffusers of wind tunnels

In the framework of an ideal gas and quasi-one-dimensional approach, a study is made of the unsteady processes associated with the starting of supersonic unregulated diffusers of pulsed wind tunnels. Application of Chisnell's hypothesis to the reversed shock wave propagating through the inhomogeneous flow, allowance for the interaction of this wave with the perturbations reflected from the diffuser, and also the assumption of quasistationarity of the flow in the concluding stage make it possible to obtain finite relations for the optimal conditions of pulsed starting of the diffuser. The starting limit found in this manner agrees well with numerical calculations based on a more complete model when the relative length of the convergent part of the diffuser is short. The obtaining of the starting conditions for other cases requires the introduction into the proposed model of a correction for the extent of the region of interaction of the reversed shock wave with the perturbations reflected from the diffuser. This correction was found on the basis of some numerical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–141, January–February, 1982.I thank A. N. Kraiko and V. T. Grin' for constant interest in the work and helpful advice.     

Dynamics of nanofibres conveyed by low Reynolds number flow in a microchannel

In this paper we aim to create an experimental and numerical model of nano and micro filaments suspended in a confined Poiseuille flow. The experimental data obtained for short nanofibres will help to elucidate fundamental questions concerning mobility and deformation of biological macromolecules due to hydrodynamic stresses from the surrounding fluid motion. Nanofibres used in the experiments are obtained by electrospinning polymer solutions. Their typical dimensions are 100–1000 μm (length) and 0.1–1 μm (diameter). The nanofibre dynamics is followed experimentally under a fluorescence microscope. A precise multipole expansion method of solving the Stokes equations, and its numerical implementation are used to construct a bead-spring model of a filament moving in a Poiseuille flow between two infinite parallel walls. Simulations show typical behaviour of elongated macromolecules. Depending on the parameters, folding and unfolding sequences of a flexible filament are observed, or a rotational and translation motion of a shape-preserving filament. An important result of our experiments is that nanofibres do not significantly change their shape while interacting with a micro-flow. It appeared that their rotational motion is better reproduced by the shape-preserving Stokesian bead model with all pairs of beads connected by springs, omitting explicit bending forces.     

Investigation of the starting process in the shaped nozzle of a large-diameter shock tube

The characteristics of flow formation in the shock-wave starting process of a shaped nozzle with a developed subsonic section are analyzed on the basis of numerical calculations in the inviscid two-dimensional formulation. It is shown that in this case the use of steady-state boundary conditions in the throat section can lead to a significant error in determining the startup time. The results of the calculations are compared with experimental data obtained over a broad interval of the leading parameters. The results of the comparison help to explain the part played in the starting process by flow separation from the nozzle walls, which was not taken into account in the numerical investigation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 88–95, September–October, 1986.The authors wish to express their thanks to R. I. Serikov and V. M. Khailov for the wind tunnel nozzle blowdown data and to V. P. Stulov for useful advice and discussions.