Shock heating of plasma in a rapidly increasing magnetic field

The experimental excitation of intense collisionless shock waves (M 5) with subsequent plasma compression by the magnetic field of a shock coil is described. A magnetic plug > 20 kOe is produced in 100 × 10^–9 sec by a current generator, a long line with 250-kV water insulation and a characteristic impedance of l At an initial deuterium-plasma density of 2 × 10¹⁴ cm^–3, shock waves with a front width of 20c/₀₃and a velocity of 5 × 10₇ cm/sec are recorded. The ion energy after the accumulation, determined from the neutron yield, turns out to be 2 ke V. Axial shock waves excited by the plasma flow beneath the shock coil are observed.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, Vol. 11, No. 2, pp. 28–38, March–April, 1970.The authors thank G. I. Budker and R. Z. Sagdeev for formulating the problem, R. I. Soloukhin for interest in the study, and S. P. Shalamov for construction of the apparatus.     

Pressure pulsations on the surface of a sphere in a subsonic stream

Many data are available on the drag C_x and the distribution of the static pressure over the surface of a sphere [1, 2]. However, there are virtually no data on pulsations of the pressure over the surface of a sphere. In the present paper, the results are given of an investigation of the total and spectral levels of the pressure pulsations at different points of the surface of a sphere at M 0.5–1.0 and Re (1.7–2.7)·.10⁶. It was found that the strongest pressure pulsations occur on the side in the region of the angle 90°. In this region at M 0.6–0.8 the relative total level o/q where q is the velocity head in the oncoming stream, reaches values 0.18–0.22. It was established that at M = 0.7–0.9 narrow-band maxima occur in the spectra of the pressure pulsations at frequencies Sh fD/V = 0.2–0.3. Data are also presented on the pulsations of the base pressure behind a spherical segment with short cylindrical and conical trailing edges.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 164–168, September–October, 1981.     

Diagnosis of a hydrogen plasma by beams of helium atoms of different energy

The underlying theory is described for a method of diagnosing a hydrogen plasma by means of beams of helium atoms of different energy. The range of measured density is 10¹⁴ to 10¹⁶ cm^–3 with a length of plasma section probed 10 cm. The highest accuracy ( ± 20%) is attained in the middle of the range. The accuracy in measuring electron temperature from 10 to 50 eV is no worse than 10–30%. Higher temperatures can be determined with an accuracy of the same order. Methods have been developed in recent years for active diagnosis of a high-temperature plasma using beams of fast neutral particles [1–5]. These methods, in spite of involving somewhat unwieldy apparatus, promise to permit the study of a plasma in the range of parameters difficult to investigate by traditional methods (probes, microwave equipment, and so on). In addition, they have relatively high timewise and spatial resolutions and are noncontact methods in practice.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, Vol. 11, no. 2, pp. 7–11, March–April, 1970.     

Determination of laser plasma temperature from study of radiation in roentgen and visible regions of spectrum

A laser plasma temperature of T_e 20 eV is determined by the foil method from measurements in the region of soft roentgen radiation. Measurements of radiation intensity in the visible region of the continuous spectrum give values of the temperature of T 15 eV for the part of the plasma which is opaque in the visible region of the spectrum.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 114–117, January–February, 1972.The authors are grateful to V. E. Panchenko and M. Yu. Lel'chuk for aid in conducting the roentgen measurements, as well as to A. M. Orishich and A. I. Shusharo for participating in the experiments on optical diagnostics.     

Base-pressure pulsations behind a cylinder and disk in a subsonic stream flow

Base-pressure fluctuations behind a long cylinder (l/d 5–10) and the disk (l/ d 0.0) is investigated experimentally in this paper. The spectral and correlation characteristics of the base-pressure fluctuations behind axisymmetric bodies at a Mach number M 1.0 are generalized on the basis of the data obtained and the results of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 181–183, January–February, 1977.     

Investigation of plasma flux interaction with an axisymmetric magnetic field

The motion of the plasma flux in an axisymmetric magnetic field is examined for a magnetic Reynolds number R_m 10, magnetohydrodynamic interaction parameter N 1, and Hall parameter 1. Flux deceleration in a circular channel is studied at the entrance to the magnetic field because of the formation of azimuthal electrical current eddies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 37–39, May–June, 1972.     

Natural convective diffusion between two nonconcentric spheres

A study is made of the natural convective diffusion in a nonconcentric spherical layer formed by a ball of radius R₁ in a sphere of radius R₂. The centers of the ball and sphere are separated by a distance d R₁. The spherical layer is filled with a binary electrolyte, and the outer surface of the ball and the inner surface of the sphere serve as the anode and cathode, respectively, of an oxidation—reduction reaction. It is assumed that the reaction proceeds in accordance with diffusion kinetics, i.e., the current in the circuit limits the rate at which the reacting substances reach the electrodes [1]. If a current passes in the system, a concentration gradient develops in the reacting substances, and in a gravitational field a convective motion of the fluid is generated, which changes the rate at which the reacting substances arrive at the electrodes. For a binary eletrolyte in the leading approximation in the small parameter r_D(R₂ – r₁)^–1, where r_D is the Debye radius, the migration current can be eliminated, and one need consider only the diffusion and convective fluxes of the ions [2]. If the centers of the ball and the sphere coincide, the integrated diffusion flux at small Grashof numbers is not changed, and there is merely a local redistribution.[3–5]. At small Grashof numbers, a strong dependence of the integrated diffusion flux on the eccentricity of the spherical layer must be expected. In the present paper, the hydrodynamic velocity field of the fluid, and also the change in the integrated diffusion flux due to the convective transport of the ions are found in the linear approximation in the small parameter = d/R₁.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 151–154, January–February, 1984.     

Numerical investigation of convective motion in a closed cavity

The investigation of thermal convection in a closed cavity is of considerable interest in connection with the problem of heat transfer. The problem may be solved comparatively simply in the case of small characteristic temperature difference with heating from the side, when equilibrium is not possible and when slow movement is initiated for an arbitrarily small horizontal temperature gradient. In this case the motion may be studied using the small parameter method, based on expanding the velocity, temperature, and pressure in series in powers of the Grashof number—the dimensionless parameter which characterizes the intensity of the convection [1–4]. In the problems considered it has been possible to find only two or three terms of these series. The solutions obtained in this approximation describe only weak nonlinear effects and the region of their applicability is limited, naturally, to small values of the Grashof number (no larger than 10³).With increase of the temperature difference the nature of the motion gradually changes—at the boundaries of the cavity a convective boundary layer is formed, in which the primary temperature and velocity gradients are concentrated; the remaining portion of the liquid forms the flow core. On the basis of an analysis of the equations of motion for the plane case, Batchelor [4] suggested that the core is isothermal and rotates with constant and uniform vorticity. The value of the vorticity in the core must be determined as the eigenvalue of the problem of a closed boundary layer. A closed convective boundary layer in a horizontal cylinder and in a plane vertical stratum was considered in [5, 6] using the Batchelor scheme. The boundary layer parameters and the vorticity in the core were determined with the aid of an integral method. An attempt to solve the boundary layer equations analytically for a horizontal cylinder using the Oseen linearization method was made in [7].However, the results of experiments in which a study was made of the structure of the convective motion of various liquids and gases in closed cavities of different shapes [8–13] definitely contradict the Batchelor hypothesis. The measurements show that the core is not isothermal; on the contrary, there is a constant vertical temperature gradient directed upward in the core. Further, the core is practically motionless. In the core there are found retrograde motions with velocities much smaller than the velocities in the boundary layer.The use of numerical methods may be of assistance in clarifying the laws governing the convective motion in a closed cavity with large temperature differences. In [14] the two-dimensional problem of steady air convection in a square cavity was solved by expansion in orthogonal polynomials. The author was able to progress in the calculation only to a value of the Grashof numberG=10⁴. At these values of the Grashof numberG the formation of the boundary layer and the core has really only started, therefore the author's conclusion on the agreement of the numerical results with the Batchelor hypothesis is not justified. In addition, the bifurcation of the central isotherm (Fig. 3 of [14]), on the basis of which the conclusion was drawn concerning the formation of the isothermal core, is apparently the result of a misunderstanding, since an isotherm of this form obviously contradicts the symmetry of the solution.In [5] the method of finite differences is used to obtain the solution of the problem of strong convection of a gas in a horizontal cylinder whose lateral sides have different temperatures. According to the results of the calculation and in accordance with the experimental data [9], in the cavity there is a practically stationary core. However, since the authors started from the convection equations in the boundary layer approximation they did not obtain any detailed information on the core structure, in particular on the distribution of the temperature in the core.In the following we present the results of a finite difference solution of the complete nonlinear problem of plane convective motion in a square cavity. The vertical boundaries of the cavity are held at constant temperatures; the temperature varies linearly on the horizontal boundaries. The velocity and temperature distributions are obtained for values of the Grashof number in the range 0<G4·10⁵ and for a value of the Prandtl number P=1. The results of the calculation permit following the formation of the closed boundary layer and the very slowly moving core with a constant vertical temperature gradient. The heat flux through the cavity is found as a function of the Grashof number.     

Similarity in the flow of a magnetized plasma around a plate and a cylinder

The article is devoted to a verification of the law of similarity in the flow of a rarefied magnetized plasma around a body under conditions which simulate the conditions of flow around artificial earth satellites in the ionosphere. The law of similarity for flow around plates and cylinders of different sizes (R₀/_i0.5–1, V₀/V_i1.5–2) is confirmed experimentally. It is shown that the patterns of flow around a plate and a cylinder coincide at small values of the parameter (=R₀/z_H). The effect of the potential of the bodies on their flow patterns is studied.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 3–12, March–April, 1973.The authors thank A. V. Gurevich for constant cooperation and valuable advice, and K. Tinchurin for help in the measurements.     

Laser heating of its erosional low-temperature plasma in the process of gasdynamic motion

A study is made of the gasdynamical and optical properties of erosional laser plasma jets in the presence and absence of laser radiation. It is shown that in processes of plasma formation during the action of laser radiation of moderate intensity (q 10⁷ W/cm²) on absorbing materials, the heating of the disintegration products by the attacking laser radiation plays an important role. The temperature distribution is obtained along the plasma jet which forms during the laser attack counter to its propagation in a quartz tube confining the dispersion. The temperature maximum is found at the exit from the tube, is caused by the heating of the erosional laser plasma by the incident laser radiation in the process of its one-dimensional gasdynamical motion, and indicates the screening of the surface from the laser radiation. It is established that the screening is affected by the gasdynamical structure of the plasma jet and by the spacing of the plasma clusters corresponding to the regular pulses of laser radiation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 13–18, January–February, 1974.The authors are grateful to M. A. El'yashevich for his interest in the work.     

Unsteady one-dimensional flow in a saturated porous medium with a volume heat source

The one-dimensional process of the heating of a saturated porous medium by a volume heat source as a result of the absorption of the energy of a high-frequency (frequency R~ 10¹–10³ MHz) electromagnetic wave is investigated. It is assumed that in the initial state the saturating (second) component is in the high-viscosity liquid or solid state. Under the action of the heat it is heated, melts, expands, becomes less viscous and under the pressure head created may flow relative to the stationary rock skeleton (first component). On the basis of the mathematical model proposed the basic laws of the process are analyzed and numerically investigated in the case of one-dimensional axisymmetric motion. It is shown that under actual conditions the dimensions of the thermal influence zone may be very considerable. Thus, by varying certain external factors it is possible to modify the dynamics of the process and the distributions of the temperature, pressure and phase velocity fields.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 115–124, July–August, 1991.     

Mixed Convection in a Horizontal Channel with Local Heating from Below

Mixed convection induced in the entrance region of a horizontal plane channel by a bottom heat source of finite dimensions is considered. The calculations were performed for the Prandtl number Pr = 1, Grashof numbers ranging from 4 · 10³ to 3.2 · 10⁴, and Reynolds numbers varying from 0 to 10. The dimensions of the heat source and its location were also varied. The results were obtained from a numerical solution of the 2D unsteady Navier-Stokes equations in the Boussinesq approximation, written in vorticity – stream function – temperature variables. The solution was found by the Galerkin finite element method.     

Pressure fluctuations and heating of a gas by the inflow of a supersonic jet into a cylindrical cavity

The formation of pressure fluctuations at the inflow of a jet into a cavity (or the so-called resonance tube) was first observed by Hartmann. Further investigations showed that at the same time there is a heating of the gas in the cavity [1, 2]. It was established in [1, 2] that at subsonic and slightly supersonic velocities (M < 2.0) the cavity air can be heated up to 500–700 °K. Further investigations [4, 6] showed that by using monatomic gases inside the cavity one can reach even higher temperatures (T 800–900 °K). The resonance tubes find an application as powerful sound sources. There is also a possibility of their use in thermochemistry, and for the plasma production [6], In the literature, there is an absence of data on the resonance tube characteristics for large Mach numbers. In the present work we investigate the resonance tubes for M = 3.2–4.0. These investigations have shown that pressure oscillations can occur at these Mach numbers with the peak-to-peak amplitude of P 0.4·P_o, where P_o is the total pressure in the inflowing jet. Depending on the clearance between the nozzle and the cavity, both low- and high-frequency oscillations can be set up. It is established that the most intense shock-wave heating of the gas takes place at high-frequency fluctuations, although their amplitude is smaller in comparison with the low-frequency ones. It is shown that the cold air inside the cavity can be heated by means of the fluctuations up to T 1600 °K or more.Translated from Izvestiya Akamemii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–111, September–October, 1977.     

Drag measurements on V-grooved surfaces on a body of revolution in axial flow

In water flows with velocities of up to 9 m/s the friction drag of a body of revolution in axial flow was investigated for dependence on the body surface structure. This was done for different types of riblet film fixed on the surface with the riblet direction aligned with the flow. The lateral spacing between the triangular shaped riblets varied between 0.033 mm and 0.152 mm. In all cases the riblet spacing was equal to the riblet height. For comparison a smooth reference film was used.Depending on the Reynolds number and the non-dimensional riblet spacings ⁺, a turbulent drag reduction of up to 9% could be achieved with riblets in comparison with the flow over a smooth surface.In the region of transition to turbulent flow and with non-dimensional riblet spacings ofs ⁺10–15 drag reductions of up to 13% were obtained. It is therefore conjectured, that in addition to hampering the near wall momentum exchange, the riblets can delay the development of initial turbulent structures in time and space.     

Multi-mode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers

A novel LDA system using laser diode arrays and multi-mode fibers in the transmitting optics is presented. The use of high numerical aperture multi-mode step-index fibres results in measurement volumes with, for example, 80 µm length and minimal speckle effects. Because of the high spatial resolution and low relative fringe spacing variation of d/d5×10^–4 the multi-mode fibre LDA is predestined for investigating turbulent flows. Boundary layer measurements carried out show excellent agreement with theoretical velocity profiles.     

Method of singular perturbations in the problem of free convection with constant heat flux on a vertical surface

The process of laminar free convection for medium values of the Grashof number is examined. An asymptotic solution which accounts for the effect of the leading edge and interaction of the boundary layer with the external flow is constructed, A comparison with experimental data shows that the solution obtained is applicable for Ra 10².Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 129–136, March–April, 1977.     

Percolation approach to the problem of hydraulic conductivity in porous media

While percolation theory has been studied extensively in the field of physics, and the literature devoted to the subject is vast, little use of its results has been made to date in the field of hydrology. In the present study, we carry out Monte Carlo computer simulations on a percolating model representative of a porous medium. The model considers intersecting conducting permeable spheres (or circles, in two dimensions), which are randomly distributed in space. Three cases are considered: (1) All intersections have the same hydraulic conductivity, (2) The individual hydraulic conductivities are drawn from a lognormal distribution, and (3) The hydraulic conductivities are determined by the degree of overlap of the intersecting spheres. It is found that the critical behaviour of the hydraulic conductivity of the system,K, follows a power-law dependence defined byK (N/N _c–1)^x, whereN is the total number of spheres in the domain,N _c is the critical number of spheres for the onset of percolation, andx is an exponent which depends on the dimensionality and the case. All three cases yield a value ofx1.2±0.1 in the two-dimensional system, whilex1.9±0.1 is found in the three-dimensional system for only the first two cases. In the third case,x2.3±0.1. These results are in agreement with the most recent predictions of the theory of percolation in the continuum. We can thus see, that percolation theory provides useful predictions as to the structural parameters which determine hydrological transport processes.     

Convective stability of a weakly conducting liquid in an electric field

In an inhomogeneously heated weakly conductive liquid (electrical conductivity 10^–12–1 cm^–1) located in a constant electric field a volume charge is induced because of thermal inhomogeneity of electrical conductivity and dielectric permittivity. The ponderomotive forces which develop set the liquid into intense motion [1–6]. However, under certain conditions equilibrium proves possible, and in that case the question of its stability may be considered. A theoretical analysis of liquid equilibrium stability in a planar horizontal condenser was performed in [2, 4]. Critical problem parameters were found for the case where Archimedean forces are absent [2]. Charge perturbation relaxation was considered instantaneous. It was shown that instability is of an oscillatory character. In [4] only heating from above was considered. Basic results were obtained in the limiting case of disappearingly small thermal diffusivity in the liquid (infinitely high Prandtl numbers). In the present study a more general formulation will be used to examine convective stability of equilibrium of a vertical liquid layer heated from above or below and located in an electric field. For the case of a layer with free thermally insulated boundaries, an exact solution is obtained. Values of critical Rayleigh number and neutral oscillation frequency for heating from above and below are found Neutral curves are constructed. It is demonstrated that with heating from below instability of both the oscillatory and monotonic types is possible, while with heating from above the instability has an oscillatory character. Values are found for the dimensionless field parameter at which the form of instability changes for heating from below and at which instability becomes possible for heating from above.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–23, September–October, 1976.In conclusion, the author thanks E. M. Zhukhovitskii for this interest in the study and valuable advice.     

Stability of convective motion caused by inhomogeneously distributed internal heat sources

The stability of steady convective plane-parallel flow in a vertical layer of viscous incompressible liquid of thickness h is investigated. The motion is caused by heat sources distributed in the liquid with volume density Q = Q₀exp (^–x) (the x axis is taken perpendicular to the boundary layer). The region of instability is determined for various values of the Prandtl number and the parameter N = h characterizing the inhomogeneity of the internal sources. It is shown that with increase in N there is qualitative rearrangement of the stability limit for perturbations of hydrodynamic type and incremental thermal waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–144, May–June, 1977.     

Mixed convection flow over a vertical plate with localized heating (cooling), magnetic field and suction (injection)

An analysis is carried out to study the effects of localized heating (cooling), suction (injection), buoyancy forces and magnetic field for the mixed convection flow on a heated vertical plate. The localized heating or cooling introduces a finite discontinuity in the mathematical formulation of the problem and increases its complexity. In order to overcome this difficulty, a non-uniform distribution of wall temperature is taken at finite sections of the plate. The nonlinear coupled parabolic partial differential equations governing the flow have been solved by using an implicit finite-difference scheme. The effect of the localized heating or cooling is found to be very significant on the heat transfer, but its effect on the skin friction is comparatively small. The buoyancy, magnetic and suction parameters increase the skin friction and heat transfer. The positive buoyancy force (beyond a certain value) causes an overshoot in the velocity profiles.A mass transfer constant - B magnetic field - C_fx skin friction coefficient in the x-direction - C_p specific heat at constant pressure, kJ.kg^–1.K - C_v specific heat at constant volume, kJ.kg^–1.K^–1 - E electric field - g acceleration due to gravity, 9.81 m.s^–2 - Gr Grashof number - h heat transfer coefficient, W.m².K^–1 - Ha Hartmann number - k thermal conductivity, W.m^–1.K - L characteristic length, m - M magnetic parameter - Nu_x local Nusselt number - p pressure, Pa, N.m^–2 - Pr Prandtl number - q heat flux, W.m^–2 - Re Reynolds number - Re_m magnetic Reynolds number - T temperature, K - T_o constant plate temperature, K - u,v velocity components, m.s^–1 - V characteristic velocity, m.s^–1 - x,y Cartesian coordinates - thermal diffusivity, m².s^–1 - coefficient of thermal expansion, K^–1 - , transformed similarity variables - dynamic viscosity, kg.m^–1.s^–1 - ₀ magnetic permeability - kinematic viscosity, m².s^–1 - density, kg.m^–3 - buoyancy parameter - electrical conductivity - stream function, m².s^–1 - dimensionless constant - dimensionless temperature, K - w, conditions at the wall and at infinity