One-dimensional steady magnetogasdynamic flow in oblique fields and the structure of shock waves

Summary An exact solution in closed form, in terms of elliptic functions, is obtained for the one-dimensional steady flow of a polytropic gas with finite constant electrical conductivity which is influenced by an oblique magnetic field and a transverse electric field in the absence of viscosity, thermal conductivity and all other non-electrical dissipative mechanisms. The solution is presented in terms of elementary functions and the many possible flow patterns are discussed in detail in the case when, at some position, the transverse momentum equals the transverse Maxwell stress; a case which is appropriate to the structure of switch-on and switch-off shock waves.The research reported in this paper was supported in part by the United States Air Force under Grant No. AF-EOAR-65-58 and monitored by the European Office, Office of Aerospace Research.     

Nonlinear problem of an electrical discharge in a flow

The nonlinear intial boundary value problem describing the relaxation of a quasi-neutral discharge in a gas flow with coplanar, heated and nonheated electrodes of finite extension is formulated in the diffusion approximation. Relaxation occurs from an initial breakdown to a steady-state or zero discharge in a weak electric field. A nonlinear transformation is applied to get an equivalent nonlinear problem, where nonlinearity is treated as a small perturbation. An analytic solution is obtained and criterions for existence and sustainment of a steady-state discharge against plasma losses due to convection, diffusion and recombination is discussed. Some numerical results are exhibited.     

A contribution to the theory of streamer breakdown

The development of a systematic theory of streamer breakdown of a gas requires the consideration of the transport of the region of ionization toward the ionized gas in an electric field depending on the form of the streamer, which in turn is determined by the transport mechanisms [1–3]. In this form the problem is very complicated,and the theory takes the path of investigation of different qualitative models of a streamer [4]. It is assumed in [4] that the rates of anode-directed and cathode-directed streamers are determined by the drift velocity of the electrons. The mechanism of propagation of anode-directed streamers is taken to be the development of avalanche from the leading front of the electrons traveling to the anode. On the side of the cathode, electrons before the front of the cathodedirected streamer are produced due to the transport of radiation from the ionized region [1]. It is shown in [5] that direct photo-ionization is ineffective because of the small range of the quantas, and a mechanism of development of cathode-directed streamer related to the associative ionization of excited atoms is proposed. These atoms are formed by long-span resonance photons from the wings of the spectral line. An interesting prediction of the theory [4] was a linear dependence of the velocity of the streamers on their length. This dependence was confirmed in experiments on the study of streamer breakdown initiated at the center of the discharge gap in spark chambers [6, 7]. At the same time, for streamers developing from avalanche initiated at one of the electrodes the velocity of propagation of the breakdown wave remains constant with a good accuracy in gaps having lengths of the order of 1 m. In the present work a qualitative theory is developed which permits one to calculate the velocity of the an ode-directed streamer in the case where it is independent of the length. Since for pressures of the order of atmospheric pressure the diffusion coefficient of excited atoms [8] is comparable with the electron diffusion coefficient, the effect of radiation transport is disregarded. The stability of the front of the streamer to infinitely small perturbations is investigated. It is shown that, when the finite thickness of the front is taken into consideration, the streamer is stable. It is unstable in the approximation of infinitely thin leading fronts.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 56–65, January–February, 1973.The authors thank A. A. Vedenov, E. P. Velikhov, A. P. Napartovich, and O. B. Firsov for valuable discussions.     

Ultra-high-frequency breakdown in irradiated parallel plate gaps

Summary U.h.f. breakdown stresses were measured in air, oxygen, nitrogen and hydrogen at frequencies 0.85 MHz to 11.5 MHz. Mid-gap irradiation by a distant (15 cm) auxiliary spark in the same gas was used. The breakdown stresses were independent of gap length. When the irradiating spark was to close to the test gap, the breakdown stress fell slightly. A qualitative explanation is offered.The authors wish to thank the Department of Scientific and Industrial Research for a maintenance grant (P. E. Lane) and the British Electrical and Allied Industries Research Association for generous financial help.     

Construction and theoretical analysis of a direct-reading hot-wire vacuum gauge with zero point control

Summary A hot-wire vacuum gauge connected to a special bridge (fig. 2), indifferent to voltage fluctuations or changes in the temperature of the surroundings, is described. The balance point of the bridge can be controlled independently of the actual gas pressure in the vacuum system. The heating current is adjusted in the region of maximum sensitivity for very low pressures. The instrument has been calibrated from 10^–5 up to 0.1 mm Hg. Calibration curves for air, hydrogen, helium and argon are shown (fig. 6 and 7).A theoretical analysis of the gauge-bridge assembly is given. The calculated total sensitivity at very low pressures as a function of the heating current appeared to be in fair agreement with the experimental results (fig. 5). The calibration curve for air could be computed on the basis of a theoretical formula, assuming that the thermal conductivity of air remains directly proportional to the pressure in the whole region investigated. Factors, determining the pressure sensitivity of a gauge-bridge combination, are discussed.Communication of the Research Department of the N.V. KEMA at Arnhem     

Analytical Solutions to Gas Flow Problems in Low Permeability Porous Media

In most of conventional porous media the flow of gas is basically controlled by the permeability and the contribution of gas flow due to gas diffusion is ignored. The diffusion effect may have significant impact on gas flow behavior, especially in low permeability porous media. In this study, a dual mechanism based on Darcy flow as well as diffusion is presented for the gas flow in homogeneous porous media. Then, a novel form of pseudo pressure function was defined. This study presents a set of novel analytical solutions developed for analyzing steady-state and transient gas flow through porous media including effective diffusion. The analytical solutions are obtained using the real gas pseudo pressure function that incorporates the effective diffusion. Furthermore, the conventional assumption was used for linearizing the gas flow equation. As application examples, the new analytical solutions have been used to design new laboratory and field testing method to determine the porous media parameters. The proposed laboratory analysis method is also used to analyze data from steady-state flow tests of three core plugs. Then, permeability (k) and effective diffusion coefficient (D _e) was determined; however, the new method allows one to analyze data from both transient and steady-state tests in various flow geometries.     

Generation of nearly isotropic turbulence using two oscillating grids

Isotropic turbulence has unique properties and is impracticable to realize experimentally. Past experiments in this context have been performed by passing a uniform mean flow through a grid, which yields approximately isotropic decaying turbulence. Here an alternative approach of obtaining approximately isotropic stationary turbulence is described, which utilizes two monoplanar grids oscillating in a homogeneous fluid. It was found that the central region between the grids has certain properties similar to that of isotropic turbulence.The funding for the particle dispersion studies at Arizona State University (ASU) is provided by the Environmental Protection Agency (Office of Exploratory Research). The stratified and rotating flow research at ASU is funded by the Office of Naval Research and the National Science Foundation.     

The temporal evolution of a pair of streamwise vortices

A detailed investigation of the velocity and vorticity fields of a pair of vortices growing over a 75°-sweep delta wing is carried out through LDV measurements of three components of velocity and vorticity. Data are obtained along one of the vortices. The wing is undergoing a ramp-like pitch-up motion. The evolution of the flow field in four planes normal to the free-stream velocity is captured at 100 time instants through the wing motion. The delta wing is pitched through angles of attack ranging from 28° to 68°. From the velocity data at each incidence, the corresponding vorticity field is calculated. Hysteresis effects on vortex development and breakdown are studied through axial velocity and vorticity contours. The topologies of streamlines and vortex lines are compared with the corresponding topologies of the steady case. It is found that vortex breakdown can be detected first by a drastic reduction of the axial velocity. This phenomenon is developing in a non-axisymmetric fashion, beginning at the inboard side of the vortex. This is followed by a reduction of the axial vorticity component and finally by a reversal of the azimuthal vorticity component.This work was supported by the Air Force Office of Scientific Research, Project No. AFOSR-91-0310 and was monitored by Major Daniel Fant.     

Numerical investigation of the growth of glowing discharges in two-dimensional geometry

It is known that a breakdown in gases can take place in two fundamental ways: by diffusion (the Townsend breakdown) or by forming a narrow current channel (the streamer breakdown). At present there are no reliable criteria for one or another of these mechanisms to occur. It is also an open question as far as the pressure region p < 10 mm Hg [I] is concerned. Even in the case of special preionization it is not always possible to avoid the streamer stage breakdown. It is obvious that the fundamental cause of a streamer breakdown is related to higher intensity of the electric field around the localized zone of higher conductivity [2]. In [3] the superiority was shown of using numerical methods in the analysis of an axisymmetric cathode directed streamer between two flat electrodes in nitrogen. In the present article the results are described of computations carried out to find out whether a mechanism is feasible for fusing the discharge at any early stage of ignition for the geometry of a flat electrode plane, which is the most favorable to an anode-oriented streamer. This effect was investigated within the framework of a nonstationary system of three equations in which the ionization processes, the recombinations in the balance of charged particles as well as the effect if space charge on the electric-field distribution have been taken into account [4], One has ignored the diffusion, which is also favorable to the streamer breakdown.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 49–54, September–October, 1978.The authors would like to express their thanks to A. A. Vedenov, A. P. Napartovich, and A. N. Starostin for their unceasing interest in this work and useful discussions.     

Effect of volume energy supply on swirled flows in a subsonic cocurrent stream

The results of a numerical investigation of the effect of thermal energy supply on a swirling viscous heat-conducting gas flow in a subsonic cocurrent stream are presented. The initial stage of development of the swirling flow in the neighborhood of the vortex axis with constant circulation in the outer flow region is considered for two different distributions of the streamwise velocity vector component which simulate a swirling jet-type flow and a wake flow with a streamwise velocity deficit. The effect of local volume energy supply in the neighborhood of the vortex axis, the circulation of the azimuthal velocity component, and the longitudinal pressure gradient in the inviscid stream on the development of the swirling flow and the process of breakdown of cocurrent vortex flows is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–53, November–December, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

Stability of nonlinearly elastic rods

This paper describes previously unknown stabilities and instabilities of planar equilibrium configurations of a nonlinearly elastic rod that is buckled under the action of a dead-load. The governing equations are derived from variational principles, including ones of isoperimetric type. Properties of stability are accordingly determined by study of the second variation. Stabilities to deformations both in the plane and out of the plane are considered.Among the newly discovered properties are: secondary bifurcation from the first buckled mode, marked differences between stability to two-dimensional and to three-dimensional variations, and the stabilizing influence of resistance to twist. In the isoperimetric examples, the analysis makes crucial use of a novel device to account for the dependence of the second variation on constraints.This research was supported by the U.S. National Science Foundation, the Army Research Office, the Air Force Office of Scientific Research, and the Office of Naval Research.     

A dynamic biaxial testing machine

The development of generalized constitutive equations for materials requires additional experimental data. A testing machine is described which is capable of applying biaxial, tension-torsion loading to thin-walled tubular specimens over a wide range in loading rates. Both components of the load are independently controlled. The objective is to obtain information on the effect of the rate of loading on viscoplastic or viscoelastic behavior of materials. Some preliminary data are given on the effect of loading rate on the yielding of mild steel. Paper was presented at 1966 SESA Spring Meeting held in Detroit, Mich., on May 4–6. The work presented herein was performed under Contract DA31-124-ARO-D-273 with the Army Research Office, Durham, Durham, N. C.     

A Physically Based Model of Dissolution of Nonaqueous Phase Liquids in the Saturated Zone

The design of remediation strategies for nonaqueous phase liquid (NAPL) contaminants involves predicting the rate of NAPL dissolution. A physically based model of an idealized pore geometry was developed to predict nonaqueous phase liquid dissolution rate coefficients. A bundle of parallel pores in series model is used to represent NAPL dissolution as a function of three processes: pore diffusion, corner diffusion, and mixing and multiple contact. The dissolution rate coefficient is expressed in terms of the modified Sherwood number (Sh) and is a function of Peclet (Pe) number. The model captures the complex behavior of Sh versus Pe data for both water-wet (Powers, 1992) and NAPL-wet (Parker et al., 1991) media. For water-wet media, the observed behavior can be broken down into four distinct regions. Each region represents a different physical process controlling NAPL dissolution: the low-Pe region is controlled by pore diffusion; the low- to moderate-Pe region is a transition zone; the moderate-Pe region is controlled by mixing and multiple contact; and the high-Pe region is controlled by corner diffusion. For the high-Pe conditions typical of most column experiments, the model involves only one fitting parameter. For NAPL-wet media, NAPL dissolution is governed exclusively by corner diffusion, and the model again involves only one fitting parameter.     

Comprehensive Seepage Simulation of Fluid Flow in Multi-scaled Shale Gas Reservoirs

Shale gas seepage behaviour is a multi-field/-scale problem and makes transient pressure analysis a very challenging task. Non-Darcy flow in nanopores is prominent due to the broken of continuity hypothesis. Slippage effect and Knudsen diffusion are two important seepage mechanisms in nanopores, while recent studies show surface diffusion is another important transporting mechanism on surface of nanopores. Porous kerogen system contains large amounts of dissolved gas, which should not be overlooked. In this study, a comprehensive mathematical model was established by pseudo-quadruple porosity medium conception, coupling the effects of slippage flow, Knudsen diffusion, surface diffusion, ad-/desorption and gas transferring from kerogen to nanopore system, while fluid flow in fractures/macropores is described by Darcy’s law. Transient pressure behaviours of a multiple fractured horizontal well in box-shaped shale gas reservoir were studied, with nine possible flow regimes divided and parameters sensitivity analysed. Adsorbed constant and dissolved constant were defined to reflect the amount of adsorbed gas and dissolved gas, respectively. Research shows that adsorbed gas and dissolved gas are two important gas storage forms, neither of which should be neglected. The study can not only help us understand fluid flow mechanisms in nanopores from microscopic perspective, but enable us to analyse production performance and determine key operational parameters from macroscopic perspective.     

Subsonic electrically quasi-neutralweakly-ionized gas flow past a spherical probe

The electric characteristics of a sphere located in a flow of viscous, electrically quasi-neutral weakly-ionized gas containing electrons and monovalent ions are investigated theoretically and numerically. As in the majority of applications, the electrogasdynamic (EGD) interaction parameter is assumed to be small. This makes it possible to solve the gasdynamic and electric equations successively. The spherical surface is assumed to be conducting and heat-insulated. At low free-stream Mach numbers the gas temperature is almost constant in the region of flow past the sphere. This makes it possible to use the model of a viscous incompressible medium. The flow past a sphere is analyzed for gasdynamic Reynolds numbers varying over the interval 0 ≤ Re ≤ 1000. The electrodynamic equations in which the convection and diffusion of the electrons and ions and their electrical drift are taken into account are reduced to three elliptic equations for the electron and ion concentrations and the electric potential. A constant potential is assigned on the boundary of the computation region simulating infinity. The entire problem is simulated numerically using specially constructed grids. The charged-component, potential, and electric current fields are determined and the volt-ampere characteristics of the sphere are constructed for various gas velocities. The results obtained generalize the available data on the voltampere characteristics of a sphere (probe) in a weakly-ionized medium at rest.     

Inexpensive fluorescent particles for large-scale experiments using particle image velocimetry

Custom-produced fluorescent particles are presented and their use as tracers for particle image velocimetry is evaluated. The fabrication procedure is explained and the main properties of the particles are described. The advantages of using fluorescent particles over nonfluorescent ones are discussed, in particular, for applications involving large facilities, as those used in hydraulic research. Images using the produced particles are also shown. This work was done under the Grants N00014-05-1-0083, N00014-01-1-0540 and N00014-06-1-0661 from the U.S. Office of Naval Research.     

Gas transfer at the air–water interface: experiments with different turbulence forcing mechanisms

Most environmentally important gases (such as oxygen or carbon dioxide) have low solubility. The transfer process of such gases across the air–water interface is controlled by molecular diffusion and turbulence, concentrated within a very thin layer in the water side. A challenge for a better understanding of the problem is to be able to elucidate the transport processes happening within this thin layer. We used non-invasive measurement techniques to study the interaction between the gas transfer process and the hydrodynamic condition in the water phase with two different turbulence forcing mechanisms, namely grid-stirred and buoyant-convective turbulence. The experimental setup for the turbulence generation and the measurement techniques are described. The different dominating turbulent transport mechanisms of the two cases were discussed, and a comparison of the different measured scales between the two cases is also presented.     

Full three-dimensional measurements of the cross-flow separation region of a 6:1 prolate spheroid

The flow in the cross-flow separation region of a 1.37 m long, 6:1 prolate spheroid at 10° angle of attack was investigated with a novel 3-D fiber-optic Laser Doppler Velocimeter (LDV). The probe was used to measure three simultaneous, orthogonal velocity components from within the model. The design and operation of this LDV probe is described and velocity, Reynolds stress, and velocity triple-product measurements are presented from the inner boundary layer through the boundary-layer edge. Development of the 6:1 prolate spheroid model was funded by the Office of Naval Research, Mr. James A. Fein, program manager. Development of miniature, 3-D, fiber-optic, boundary layer probe and research into the flow around this body was sponsored by the Defense Advanced Research Projects Agency, Mr. Gary W. Jones, program manager.The authors gratefully acknowledge the support of these agencies.     

On the smallest scale for the incompressible Navier-Stokes equations

We prove that, for solutions to the two- and three-dimensional incompressible Navier-Stokes equations, the minimum scale is inversely proportional to the square root of the Reynolds number based on the kinematic viscosity and the maximum of the velocity gradients. The bounds on the velocity gradients can be obtained for two-dimensional flows, but have to be assumed in three dimensions. Numerical results in two dimensions are given which illustrate and substantiate the features of the proof. Implications of the minimum scale result, to the decay rate of the energy spectrum are discussed.Research was supported in part by the National Acronautics and Space Administration under NASA Contract No. NAS1-18107, while the second author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665. Additional support was provided by the National Science Foundation under Grant DMS-8312264 and the Office of Naval Research under Contract N-00014-83-K-0422.     

Estimate of the amplitudes of the fields created by an unsteady gamma source

It is known [1–4] that an unsteady gamma source gives rise to an electromagnetic field in the surrounding space. Most of the studies of the characteristics of such fields have been performed in the approximation which is linear in the field [1–3]. An exception is [4] in which the slowing down of Compton electrons by the electric field is taken into account. It follows from [1, 2] that the characteristic scale of the fields created close to the source is of the order of 3 · 10⁴ V/m. Although this value is appreciably lower than the value of breakdown fields in air, electric discharges are observed [5] in the vicinity of a gamma source, indicating the presence of substantially larger fields. One effect not taken into account in the latter approximation which could lead to an increase in the field is the increase in electron termperature due to the electric field [6]. On the one hand, this decreases the electron mobility and consequently also the conductivity of the system, On the other hand, it is known that the electron attachment coefficient for electronegative molecules strongly affects the characteristics of electric fields and depends on the electron energy. Therefore, the electron balance equation must take account of the dependence of on the electric field through the electron energy, and this leads to a further change in conductivity. We take account of these effects on the shaping of electric fields in air in the vicinity of the source. It is assumed that electron lifetimes are determined solely by their attachment to molecules. This is a good approximation for air pressures near normal [1–3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 163–170, July–August, 1976.