Control of separation phenomena in a high-speed flow by means of the surface electric discharge

The results of an experimental and theoretical investigation of the interaction between a surface electric discharge and a supersonic air flow in a constant cross-section channel are given. The features of the generation of the surface discharge in the flow are described. A model of the interaction is proposed. The regime of gasdynamic screening of a mechanical obstacle on the channel wall is investigated. Data on the change in the main flow parameters as a result of the generation of a surface discharge are given. The experimental results are compared with the results of calculations based on a simplified model of the interaction.     

Turbulent mixing of relaxing gases in a supersonic nozzle

Processes of turbulent mixing of hot nitrogen and carbon dioxide gas (CO₂) in a supersonic nozzle are investigated in connection with gasdynamic lasers with selective thermal excitation. The actual flow pattern in the nozzle and cavity is simulated by the system of equations of a turbulent boundary layer. The results of calculations of the gain profile, the CO₂ concentration, and the laser power agree satisfactorily with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 156–160, March–April, 1981.We are very grateful to B. S. Aleksandrov and V. K. Pozdyshev for numerous helpful discussions.     

Physical and mathematical modeling of a supersonic flow around a cylinder with a porous insert

Results of numerical and experimental modeling of a supersonic flow (M_∞ = 4.85) around a model of a streamwise-aligned cylinder with a cellular-porous insert permeable for the gas on the frontal face of the cylinder are described. Experimental data on the influence of the pore structure and the length of the porous cylindrical insert on the model drag, pressure on the frontal face of the cylinder, and flow pattern are obtained. Numerical modeling includes solving Favre-averaged Navier-Stokes equations, which describe the motion of a viscous compressible heat-conducting gas. The system is supplemented with a source term taking into account the drag of the porous body within the framework of the continuum model of filtration. Data on pressure and velocity fields inside the porous body are obtained in calculations, and the shape of an effective pointed body whose drag is equal to the drag of the model considered is determined. The calculated results are compared with the measured data and schlieren visualization of the flow field.     

Experimental and numerical investigations of fluid flow and heat transfer in a cryogenic tank at loss of vacuum

The transient process of thermal stratification in liquid nitrogen (LN₂) induced by lose of vacuum in a multi-layer insulated cryogenic tank is investigated both experimentally and numerically. In the experiments, distribution and evolution of the liquid temperature is obtained using thermocouples. Then, two-dimensional numerical computations are performed, using the two-fluid model together with nucleate boiling model as the closure correlations. Comparison of the numerical results against the experimental data illustrates that the process of thermal stratification forming and weakening, as well as the liquid temperature field are satisfactorily simulated. The computed results of liquid flow field contribute to the understanding of this transient process. It is also demonstrated that the two-phase flow in the tank plays an important role on thermal stratification.     

Numerical analysis of transient laminar forced convection of nanofluids in circular ducts

In this study, forced convection heat transfer characteristics of nanofluids are investigated by numerical analysis of incompressible transient laminar flow in a circular duct under step change in wall temperature and wall heat flux. The thermal responses of the system are obtained by solving energy equation under both transient and steady-state conditions for hydro-dynamically fully-developed flow. In the analyses, temperature dependent thermo-physical properties are also considered. In the numerical analysis, Al₂O₃/water nanofluid is assumed as a homogenous single-phase fluid. For the effective thermal conductivity of nanofluids, Hamilton–Crosser model is used together with a model for Brownian motion in the analysis which takes the effects of temperature and the particle diameter into account. Temperature distributions across the tube for a step jump of wall temperature and also wall heat flux are obtained for various times during the transient calculations at a given location for a constant value of Peclet number and a particle diameter. Variations of thermal conductivity in turn, heat transfer enhancement is obtained at various times as a function of nanoparticle volume fractions, at a given nanoparticle diameter and Peclet number. The results are given under transient and steady-state conditions; steady-state conditions are obtained at larger times and enhancements are found by comparison to the base fluid heat transfer coefficient under the same conditions.     

Gasdynamics of a Convergent Air-Intake with a Nose Compression Surface

A model configuration of a hypersonic vehicle realizing the principle of compression convergence along spatially-convergent directions of the entire jet captured by an air-intake is studied. The configuration includes a convergent air-intake, whose gasdynamic design is performed using the axisymmetric supersonic flow in an internal convergent channel. The air-intake is integrated with the swept transversely-concave nose surface of the vehicle, which forms at high supersonic velocities a three-dimensional compression flow, also convergent. The results of numerical and experimental studies at freestream Mach numbers 4 and 6 are presented; they reveal the salient features of the gasdynamic pattern of the flows near the nose and the external compression wedge of the air-intake, as well as in the internal channel.     

Subsonic Radiation Gas Dynamics in a Laser Plasma Generator Channel

The radiation gasdynamic processes in the channel of an air laser plasma generator operating at atmospheric pressure are analyzed. In the multigroup approximation a numerical radiation gasdynamic model is formulated on the basis of the equations of motion of a viscous heat-conducting gas and the selective thermal radiation transport equation. Laminar and turbulent subsonic generator operation regimes are considered.For the purpose of approximately describing the turbulent gas and plasma mixing the Navier-Stokes equations averaged after Reynolds and the k-ε turbulence model are used. The problem is solved in the time-dependent two-dimensional axisymmetric formulation.Strong radiation-gasdynamic interaction regimes are investigated. In these regimes the energy losses due to radiation from the high-temperature region of the laser plasma and the absorption of its thermal self-radiation by the surrounding plasma and gas layers (radiation reabsorption) appreciably affect the gasdynamic flow structure. Two methods of integrating the selective thermal radiation transport equation in the generator channel are discussed. In one of these the thermal radiation transport is calculated inside the heated volume and in the other the radiation heat fluxes are calculated on the surfaces bounding the volume. The results of calculating the spectral and integral radiation heat fluxes on the inner surface of the generator are given.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 126–143.Original Russian Text Copyright © 2005 by Surzhikov.     

Approximate calculation of channel flows under force and energy actions

Gasdynamic channel flows under force and energy actions are considered. An approximate method is proposed for solving the gasdynamic equations that describe these flows. Themethod includes the separation of an “active” flow volume in which the integral electric force and applied power, whose densities are assumed to be uniform, are concentrated and the numerical integration of the system of hydrodynamic equations over the entire channel (in laminar and turbulent variants) with the piecewise constant force and energy sources obtained. The results of experimental investigation are presented for the flow that arises after two accessories mounted on the opposite walls of the vertical rectangular channel of constant cross-section, which create a dielectric barrier discharge (DBD actuators). This flow is numerically simulated using the method developed. On the basis of the method proposed the flow characteristics are determined for a model subsonic diffuser on whose lower wall, immediately in front of the separation zone, the DBD actuator is mounted. The efficiency of this accessory in reducing the gasdynamic losses is demonstrated.     

Numerical Simulation of a Turbulent Thermal

Ascent of a large-scale thermal in a standard atmosphere is calculated with the use of the Reynolds equations and the k model of turbulence, which takes into account temperature inhomogeneity and vorticity of the flow, and the Euler equations. Results of numerical calculations of a flow examined experimentally are presented. Gas-dynamic and turbulent flow parameters obtained in calculations and experiments are compared.     

Similarity with the outflow of strongly unexpanded jets into a hypersonic wake

The article discusses the outflow of a nonviscous gas from a strongly unexpanded supersonic nozzle into a supersonic wake. Under the assumption that the radius of the outlet cross section of the nozzle is negligibly small in comparison with the characteristic dimensions of the jet, expressions are obtained for the transverse and longitudinal dimensions of the jet, as well as similarity criteria determining the dimensionless gasdynamic functions. The satisfaction of the similarity criteria was verified by comparison with numerical calculations. Similarity with the outflow of strongly unexpanded jets was discussed in [1–3], where, specifically, the characteristic dimension of the flow was determined. In [4] it was demonstrated that the experimentally observed structure of the jet can be best described with the introduction of two characteristic dimensions, longitudinal and transverse. The effective construction of these two characteristic dimensions for the case of nonviscous outflow into a flooded space was carried out in [5], in which it was shown that using the longitudinal and transverse dimensions the geometries of the flow and the gasdynamic parameters are found to depend on the adiabatic index of the outflowing gas and on a parameter formed from the integral characteristics of the nozzle. The present work is a generalization of the results of [5] for the outflow of a jet into a hypersonic wake.     

Laval nozzle flow calculation

The inverse problem of the theory of the Laval nozzle is considered, which leads to the Cauchy problem for the gasdynamic equations; the streamlines and the flow parameters are found from the known velocity distribution on the axis of symmetry.The inverse problem of Laval nozzle theory was considered in 1908 by Meyer [1], who expanded the velocity potential into a series in powers of the Cartesian coordinates and constructed the subsonic and supersonic solutions in the vicinity of the center of the nozzle. Taylor [2] used a similar method to construct a flowfield which is subsonic but has local supersonic zones in the vicinity of the minimal section. Frankl [3] and Fal'kovich [4] studied the flow in the vicinity of the nozzle center in the hodograph plane. Their solution, just as the Meyer solution, made it possible to obtain an idea of the structure of the transonic flow in the vicinity of the center of the nozzle.A large number of studies on transonic flow in the vicinity of the center of the nozzle have been made using the method of small perturbations. The approximate equation for the transonic velocity potential in the physical plane, obtained in [3–6], has been studied in detail for the plane and axisymmetric cases. In [7] Ryzhov used this equation to study the question of the formation of shock waves in the vicinity of the center of the nozzle, and conditions were formulated for the plane and axisymmetric cases under which the flow will not contain shock waves. However, none of the solutions listed above for the inverse problem of Laval nozzle theory makes it possible to calculate the flow in the subsonic and transonic parts of the nozzles with large gradients of the gasdynamic parameters along the normal to the axis of symmetry.Among the studies devoted to the numerical calculation of the flow in the subsonic portion of the Laval nozzle we should note the study of Alikhashkin et al., and the work of Favorskii [9], in which the method of integral relations was used to solve the direct problem for the plane and axisymmetric cases.The present paper provides a numerical solution of the inverse problem of Laval nozzle theory. A stable difference scheme is presented which permits analysis with a high degree of accuracy of the subsonic, transonic, and supersonic flow regions. The result of the calculations is a series of nozzles with rectilinear and curvilinear transition surfaces in which the flow is significantly different from the one-dimensional flow. The flowfield in the subsonic and transonic portions of the nozzles is studied. Several asymptotic solutions are obtained and a comparison is made of these solutions with the numerical solution.The author wishes to thank G. D. Vladimirov for compiling the large number of programs and carrying out the calculations on the M-20 computer.     

Flow of gas mixtures with vibrational energy relaxation in plane and axisymmetric nozzles

A method is described for the calculation of plane and axisymmetric flows of gas mixtures with vibrational energy relaxation in the subsonic, transonic, and supersonic regions of the nozzle. The method is based on numerical solution of the inverse problem of nozzle theory. Results are given for the flow of a C0₂-N₂-H₂O-He mixture with vibrational relaxation and compared with the results of one-dimensional calculations. It is found that vibrational-energy relaxation has a significant effect on the gasdynamic parameters of flow in nozzles with large, relative expansion and therefore in choosing a nozzle shape, especially in the supersonic region, it is necessary to calculate the nonequilibrium flow. It is shown that the geometry of the transonic and supersonic regions of the nozzle has a considerable effect on the distribution of the inverse population of the level and the amplification factor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 125–131, September–October, 1977.     

Interference of stationary and non-stationary shock waves

The mathematical model of a gasdynamic discontinuity is used in the area of study concerning gas flows with large gradients of gasdynamic functions. Gasdynamic functions before and after the discontinuity meet non-linear algebraic equations called the dynamic compatibility conditions on the discontinuities. Different modes of shock wave structures forming as a result of regular or irregular interference of the incoming discontinuities of different types are described. Ranges of the initial flow parameters definition such that either shock wave structures of different modes take place or interference equations have no solutions are determined. Most attention is given to arbitrary triple shock-wave configurations. Their classification is proposed. Differential characteristics of the steady flow are studied. The notion “differential characteristics” includes first derivatives of the fundamental gasdynamic parameters with respect to natural coordinates and curvatures of the discontinuities surfaces. Effect of unsteadiness on the triple-shock configuration is examined. Some problems arising at creation of complete local theory of steady and propagating gasdynamic discontinuities interference are formulated.     

An improved lattice Boltzmann model for high gas and liquid density ratio in composite grids

Lattice Boltzmann method is one of the widely used in multiphase fluid flow.However,the two main disadvantages of this method are the instability of numerical calculations due to the large density ratio of two phases and impossibility of the temperature distribution to be fed back into the velocity distribution function when the temperature is simulated.Based on the combination prescribed by Inamuro,the large density ratio two-phase flow model and thermal model makes the density ratio of the model simulation to be increased to 2778:1 by optimizing the interface distribution function of two-phase which improves the accuracy of differential format.The phase transition term is added as source term into the distribution function controlling two phase order parameters to describe the temperature effect on the gas-liquid phase transition.The latent heat generated from the phase change is also added as a source term into the temperature distribution function which simulates the movement of the flow under the common coupling of density,velocity,pressure and temperature.The density and the temperature distribution of single bubble are simulated.Comparison of the simulation results with experimental results indicates a good agreement pointing out the effectiveness of the improved model.     

Applicability of a one-dimensional model to the calculation of the properties of a plasma generator

Most engineering methods for calculating the properties of plasma generators use similarity theory to derive dimensionless equations to generalize experimental results [1]. Although their accuracy is acceptable for practical calculations, the equations cannot be used for a physical analysis of the local phenomena occurring in the working channel of a plasma generator. In the present paper the experimental data are compared with the results of a calculation of the local and integrated heat and gasdynamic properties of a dc plasma generator with a longitudinally injected arc. The basis of the computational method is a quasi-one-dimensional gasdynamic model of the flow of an electrically conducting gas in the channel of the plasma generator developed and studied in [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–126, July–August, 1977.In conclusion, the authors thank G. A. Lyubimov for valuable remarks.     

Hypersonic flow past a flat-plate/beveled-whistle system

The results of an experimental and numerical investigation of unsteady hypersonic nitrogen flow (M_∞ = 21 and the unit Reynolds number Re_∞1 = 6×10⁵ m^?1) past an integrated flat-plate/beveled whistle model are presented. The calculations using the ANSYS Fluent package are carried out for different geometries of the whistle cavity and angles of incidence of the model. The conditions under which fluctuations occur in the whistle are determined and the fields of the mean flow and fluctuations in the shock layer on the plate are obtained. In the experiments performed in the T-327A hypersonic nitrogen wind tunnel of the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences the dependence of the pressure fluctuations on the plate surface on the angle of attack of the model are obtained. The calculated and measured results are compared.     

Stagnation region of a blunt body in two-phase hypersonic flow

The fluid-mechanics equations of a two-velocity, two-temperature medium are used to investigate flow near the stagnation point of a blunt body washed by a hypersonic stream of gas containing solid or liquid deformed particles. The effect of particles of the gasdynamic flow parameters is analyzed. A relaxation layer was found to occur near the body, with marked changes in the gas parameters. It is shown that the presence of particles in the flow reduces the shock stand-off distance. The results of computations on the dynamics and heating of particles in the shock layer are discussed. A solution in finite form is obtained in the limiting case of fine particles by the method of asymptotic expansions. The motion of solid or liquid particles in hypersonic shock layers has been the subject of several papers [1–6], in which particle dynamics was examined, assuming that the particles have a negligible influence on the gasdynamic flow parameters. The solutions obtained are therefore limited to the case of low mass particle concentration in the incident flow. A numerical solution not subject to this limitation was obtained in [7] for supersonic two-phase flow over a wedge.     

Gasdynamic structure of the initial section of supersonic jets of the plasma of a magnetoplasmodynamic source

An experimental investigation was made of the gasdynamic structure of the initial section of supersonic jets of a plasma of argon and helium with outflow into a rarefied medium from a source of the magnetoplasmodynamic type. A study is made of the dependence of the gasdynamic structure on the kind of gas, the pressure in the surrounding medium, the inductance of the external magnetic field, the stagnation enthalpy, the mass flow rate, and the means used for feeding the gas.