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.     

Flow and Heat Transfer in Underexpanded Air Jets Issuing from the Sonic Nozzle of a Plasma Generator

We present the results of an experimental investigation and numerical simulation of the gasdynamic structure of underexpanded dissociated-air jets and the heat transfer in these strongly nonequilibrium flows under the test conditions realized in the 100-kW electrodeless VGU-4 plasma generator of the Institute for Problems in Mechanics of the Russian Academy of Sciences (IPM RAS). The flow and heat transfer analysis is carried out on the basis of measurements of the static pressure in the plenum chamber, at the sonic nozzle exit, and on the low-pressure chamber wall, the stagnation pressure on the jet axis using a Pitot tube, and the heat transfer at the stagnation points of water-cooled models placed along the jet axis. The numerical simulation, based on complete Navier-Stokes equations, includes the calculation of (1) equilibrium air plasma flows in the discharge channel of the VGU-4 plasma generator; (2) underexpanded nonequilibrium dissociated-air jet outflow into the ambient space; and (3) axisymmetric jet flow past cylindrical models.     

HF-plasmatron experiment and numerical simulation of heat transfer in underexpanded dissociated-nitrogen jets

Experiments on heat transfer in underexpanded supersonic jets of high-enthalpy nitrogen are performed on the VGU-4 induction high-frequency plasmatron at a pressure of 10.4 GPa in a compression chamber. At gas flow rates of 2.4 and 3.6 g/s and HF generator powers of 45 and 64 kW the heat fluxes to the copper, stainless steel, MPG-7 graphite, and quartz surfaces are measured at the stagnation point of a water-cooled cylindrical, flat-ended model, 20 mm in diameter. In the same regimes the stagnation pressures are measured. The effect of the surface catalyticity with respect to nitrogen atom recombination on the heat flux is demonstrated and the qualitative catalyticity scale of the studied materials is established. In the supersonic regimes nonequilibrium nitrogen plasma flow in the discharge channel of the plasmatron and the underexpanded jet flow past the model are numerically simulated for the experimental conditions. The experimental and calculated data on the stagnation pressures and the heat fluxes to cooled surfaces of the metals, graphite, and quartz are compared.     

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.     

Supersonic Flow Past a Thermal Source

The results of an experimental investigation and numerical simulation of a gasdynamic structure formed as a result of supersonic flow past a pulsating thermal source are presented. Heat was supplied to the flow by producing a limited plasma volume as a result of the breakdown of the focused radiation of a CO₂ laser operating in the pulse periodic regime. On the basis of the experimental data obtained, a thermal source model was developed and accepted for further numerical calculations. The calculations were carried out within the framework of the inviscid gas model using the TVD scheme and nonreflecting boundary conditions. The effect of the relevant gasdynamic and energetic parameters on the flow pattern associated with the studied phenomenon is established. Data on the flow parameter distributions in the wake of the thermal source are obtained as a function of the freestream Mach number.     

Extended thermodynamics of molecular ideal gases

The objective of extended thermodynamics of molecular ideal gases is the determination of the 17 fields ofmass density, velocity, energy density, pressure deviator, heat flux, intrinsic energy density and intrinsic heat flux. The intrinsic energy represents the rotational or the vibrational energy of the molecules. The necessary field equations are based upon balance laws and the system of equations is closed by constitutive relations which are characteristic for the gas under consideration. The generality of the constitutive relations is restricted by theprinciple of material frame indifference, and by the entropy principle. These principles reduce the constitutive coefficients of all fluxes to the thermal and caloric equation of state of the gas and provide inequalities for the transport coefficients. The transport coefficients can be related to the shear viscosity, the heat conductivity, and the coefficients of self-diffusion and attenuation of sound waves, so that the field equations become quite specific. The theory is in perfect agreement with the kinetic theory of molecular gases. It is shown that in non-equilibrium the temperature is discontinuous at thermometric walls. The dynamic pressure and the volume viscosity, are discussed and it is shown how extended thermodynamics and ordinary thermodynamics are related.     

A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

We discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi‐steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well‐balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed–load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump‐shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi‐steady approach only when the bed–load rapidly interacts with the hydrodynamics. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

Self-Localization of the Energy Supply During Pulse Ionization of a Supersonic Flow

The pulse ionization of the time-dependent quasi-two-dimensional flow developed during diffraction of a shock wave on a wedge is investigated experimentally. The redistribution of the pulse volume discharge plasma subjected to preionization by ultraviolet radiation from plasma sheets is investigated when the discharge is initiated in different stages of the time-dependent gas dynamic flow. Images of the plasma flow are compared with the corresponding fields of the gas dynamic flow parameters. It is shown that the pulse discharge plasma flows can be controlled due to the phenomenon of self-localization in a given flow zone of known shape. The local energy supply to the gasdynamic flow is simulated numerically using the experimental data.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 144–156.Original Russian Text Copyright © 2005 by Znamenskaya, Ivanov, Kryukov, and Kuli-Zade.     

Simultaneous temperature and 2D velocity measurements in a turbulent heated jet using combined laser-induced fluorescence and LDA

 This paper presents an efficient technique for the characterization of thermal transport properties in turbulent flows. The method is based on the temperature dependence of fluorescence, induced by laser radiation, of an organic dye. The laser-induced fluorescence technique is combined with 2D laser Doppler anemometry, in order to measure in the same sample volume simultaneously and instantaneously the temperature and velocity. The technique is demonstrated on a turbulent heated round jet: the mean and fluctuating dynamic and thermal fields are investigated, and the temperature-velocity cross-correlations are determined in order to characterize the turbulent diffusivity and the turbulent Prandtl number. Received: 30 October 1997/Accepted: 14 July 1998     

Interaction of surface radiation with conjugate mixed convection from a vertical channel with multiple discrete heat sources

Important results of a numerical study performed on combined conduction–mixed convection–surface radiation from a vertical channel equipped with three identical flush-mounted discrete heat sources in its left wall are provided here. The channel has walls of identical height with the spacing varied by varying its aspect ratio (AR). The cooling medium is air that is considered to be radiatively transparent. The heat generated in the channel gets conducted along its walls before getting dissipated by mixed convection and radiation. The governing equations for fluid flow and heat transfer are considered without boundary layer approximations and are transformed into vorticity–stream function form and are later normalized. The resulting equations are solved, along with relevant boundary conditions, making use of the finite volume method. The computer code written for the purpose is validated both for fluid flow and heat transfer results with those available in the literature. Detailed parametric studies have been performed and the effects of modified Richardson number, surface emissivity, thermal conductivity and AR on various pertinent results have been looked into. The significance of radiation in various regimes of mixed convection has been elucidated. The relative contributions of mixed convection and radiation in carrying the mandated cooling load have been thoroughly explored.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.     

Interaction between a shock wave and a longitudinal low-density gas layer

The problem of the interaction between a shock wave and a semi-infinite longitudinal plane layer or a cylindrical channel of finite thickness filled with a low-density gas is studied on the basis the Euler equations. The flow gasdynamics, including qualitatively new, regular and irregular, interaction regimes, are described. New gasdynamic flow elements, such as high-pressure jets with an internal wave structure and layered vortices, are found to exist. It is revealed that the gasdynamic precursor growth is decelerated at long time intervals, due to the flow chocking effect and the vorticity development behind its front.     

On the optimal distribution of the flow rate of gas blown through the side walls of the channel of a de plasmotron (plasma generator)

It is well known that the blowing of cold gas through the side walls of the channel of a dc plasmotron (plasma generator) with longitudinal blowing over the arc leads to an increase in the useful power of the plasmotron [1]. The increase is due to the increase in the combustion voltage of the arc and also the decrease in the heat fluxes to the wall of the channel. The present paper solves the problem of the optimal distribution of the flow rate of gas blown through the side walls into the channel of a dc plasmotron of arbitrary shape F(x). The flow in the main channel and in the ducts in the side walls is described by the quasi-one-dimensional gas-dynamic equations investigated qualitatively in [2] and verified experimentally in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 120–124, May–June, 1981.     

Experimental and Numerical Investigation of Heat Exchange between Underexpanded High-Enthalpy Air Jets and Cylindrical Models

Experiments on heat transfer in supersonic underexpanded high-enthalpy air jets are conducted on the VGU-4 induction plasmatron at the pressure in the compression chamber of 8.5 hPa. At the air flow rate of 3.6 g/s and the high-frequency generator powers of 45 kW(regime 1) and 64 kW (regime 2) the heat fluxes to the copper surface at the stagnation point of watercooled cylindrical models along the axes of dissociated air jets are measured. The models, 30 mm in diameter, could have a flat face or a hemispherical nose. In the same regimes, the stagnation pressures are measured using the Pitot tube in the shape of a cylinder, 30 mm in diameter, having either a flat face or a hemispherical bluntness with a receiving hole, 14 mm in diameter. For the experimental conditions calculations of flows in the plasmatron discharge channel and supersonic underexpanded jets issuing from the discharge channel are performed within the framework of the Navier–Stokes and Maxwell equations. The heat fluxes to the experimental models are computed and compared with the experimental data.     

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.     

Flow and coupled heat transfer in the cavity between the rotor and stator

The turbulent flow and coupled heat transfer in the cavity between the rotor and stator is numerically simulated. Reynolds-averaged Navier-Stokes equations closed with equations of the k-ɛ turbulence model are used to calculate the viscous compressible gas flow characteristics and heat transfer; the unsteady heat conduction equation is used to calculate the temperature field in the metal. The influence of the mass flow rate of the coolant on the flow structure and efficiency of cooling of the rotor and stator walls is studied. The calculated results are compared with experimental data.     

Boundary layer development in supersonic MHD generators

A numerical model of the turbulent boundary layers in the gas dynamic channel of a supersonic MHD generator is constructed. This model describes the development and structure of the layers in the nozzle, on the electrode and insulating walls of the duct, in the two-dimensional approximation. The characteristics of the boundary layers in various generator operating regimes are investigated numerically. The integral boundary layer thicknesses characterizing the nonuniformity of the gas dynamic and electrodynamic quantities are calculated. The limits of applicability of the integral calculation method are determined for typical MHD generator operating conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 35–41, May–June, 1990.The authors wish to thank A. B. Vatazhin, V. A. Bityurin, and V. A. Zhelnin for discussing the formulation of the problem, A. A. Yakushev for participating in the discussion of the results, and Yu. V. Rakseeva and L. V. Yashina for preparing the article.     

Heat exchange between a selectively emitting liquid and a laminar gas flow in the presence of an external source of radiation

An investigation is conducted in the solution of a number of practical problems of the radiative and combined heat exchange in nonuniform systems having widely different physical properties. The processes of thermal interaction between the ocean and the atmosphere have been treated in the paper [1], the effect of thermal radiation on the melting and solidification of semitransparent crystals has been investigated in [2], the flow of a selectively emitting gas around the lateral surface of an object evaporating under the action of radiative heating has been discussed in [3], and heat transfer from a jet to the molten mass of glass in a glassmaking furnace tank has been investigated in [4]. The radiative and combined heat exchange between a selectively emitting liquid and a transparent heat-conducting laminar gas flow in the case of a specified external thermal radiation field is discussed in this paper. The energy conservation equations are set up taking into account the heat transfer by radiation, convection, and molecular thermal conduction. A differential approximation is used in calculating the values of the radiation fluxes. A system of fundamental computational equations is solved by the method of finite differences and iterations and by the Runge-Kutta method. The results of the calculations are presented in the form of graphs.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 116–122, May–June, 1976.     

An experimental study of gasdynamic windows for gas lasers

The working pressure in the cavities of most gas lasers varies from 30 to 100 torr. Thus, in transmitting the laser light into the atmosphere, the problem arises of isolating the cavity from atmospheric pressure. In low-power lasers (N l kW/cm², where N is the laser output power) optical windows of monocrystalline NaC1 (CO₂ laser), CaF₂ (CO laser), and so on, are used for this purpose [1], The absorption coefficient for radiant energy of such optical windows averages 0.02–0.2%; thus, at cw laser powers of order 3 kW/cm² or more it is difficult to send the beam out through monocrystalline windows because they are heated excessively due to absorption of radiation and, consequently, broken. In this casa so-called gasdynamic windows (shutters) with transverse gas pump-through [2] or ejector-type gasdynamic windows, which ensure the required pressure difference and tolerable return flows of gas between the laser cavity and the surrounding medium, are used in place of monocrystalline windows. Here we shall describe the design of gasdynamic windows, their characteristics, and operating regimes, and we shall present data from experimental studies of the operation of gasdynamic windows with transverse gas pumpthrough over a wide range of variation of the window size and gas-flow parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 192–196, March–April, 1977.In conclusion, we thank Kh. M. Faizulin, V. M. Abramov, S. A. Danilushkin, B. Ya. Lyubimov, and L. V. Bol'shov for help in doing the experiments and for useful discussions.