Inflexional disequilibrium of magnetic flux-tubes

In this paper, we prove that magnetic flux-tubes in inflexional configuration are in disequilibrium and evolve to an inflexion-free state. The magnetic field is defined in a tube of circular cross-section and is chosen so as to have toroidal and poloidal components contributing to the internal twist of the flux-tube. By using orthogonal curvilinear coordinates, we derive the equations for the Lorentz force associated with the magnetic flux-tube and use them to study the generic behaviour associated with passage through inflexional configuration. Inflexional state is attained when local curvature vanishes as the tube axis changes concavity. We check that the conditions for the equilibrium of the flux-tube in inflexional configuration are not satisfied and hence we prove disequilibrium. Inflexional disequilibrium makes magnetic flux-tubes evolve to an inflexion-free state. As a consequence, inflexional flux-tubes in free space evolve naturally to an inflexion-free configuration. This mechanism has important implications for the energetics of solar coronal loops and astrophysical flows.     

Gas-kinetic unified algorithm for plane external force-driven flows covering all flow regimes by modeling of Boltzmann equation

The nonequilibrium steady gas flows under the external forces are essentially associated with some extremely complicated nonlinear dynamics, due to the acceleration or deceleration effects of the external forces on the gas molecules by the velocity distribution function. In this article, the gas-kinetic unified algorithm (GKUA) for rarefied transition to continuum flows under external forces is developed by solving the unified Boltzmann model equation. The computable modeling of the Boltzmann equation with the external force terms is presented at the first time by introducing the gas molecular collision relaxing parameter and the local equilibrium distribution function integrated in the unified expression with the flow state controlling parameter, including the macroscopic flow variables, the gas viscosity transport coefficient, the thermodynamic effect, the molecular power law, and molecular models, covering a full spectrum of flow regimes. The conservative discrete velocity ordinate (DVO) method is utilized to transform the governing equation into the hyperbolic conservation forms at each of the DVO points. The corresponding numerical schemes are constructed, especially the forward-backward MacCormack predictor-corrector method for the convection term in the molecular velocity space, which is unlike the original type. Some typical numerical examples are conducted to test the present new algorithm. The results obtained by the relevant direct simulation Monte Carlo method, Euler/Navier-Stokes solver, unified gas-kinetic scheme, and moment methods are compared with the numerical analysis solutions of the present GKUA, which are in good agreement, demonstrating the high accuracy of the present algorithm. Besides, some anomalous features in these flows are observed and analyzed in detail. The numerical experience indicates that the present GKUA can provide potential applications for the simulations of the nonequilibrium external-force driven flows, such as the gravity, the electric force, and the Lorentz force fields covering all flow regimes.     

Certain problems concerning the origin and maintenance of cosmic magnetic fields

How regular magnetic fields in a plasma originated and are sustained is a question of considerable interest, since various objects in space such as spiral arms of galaxies, many stars, and planets have a regular magnetic field [1–3]. Several theoretical studies have been devoted to this theme [4–9]. However, because of the severe mathematical difficulties which arise in solving this problem, its study in the general form is still not possible, and its kinematic aspects are usually considered. In [5] a study is made of the induction of a toroidal magnetic field from the dipole field of a rotating spherical mass under the influence of radial convection. For the process to be undamped it is necessary to maintain a poloidal field, which according to the Cowling theorem may be induced by asymmetric motions from a toroidal field. Parker [6] suggested a specific model for the field increase by motions of the cyclonic type and indicated the possibility of self-regulation of the field maintenance process. Under certain conditions this process has a wave nature, the so-called dynamo-waves. In [7, 8] Braginskii considered the question of maintaining a quasi-stationary field by motions of the medium which differ little from axisymmetric motions. As a result of the large magnetic Reynolds numbers Re_m1 the field decays slowly, and a weak generation mechanism is adequate for maintaining the field.In [9] Birman and Schlüter suggested a fundamentally new mechanism for the formation of magnetic fields in a plasma as a result of the appearance under certain conditions of a vortical component of the mechanical electromotive force. It appears that this mechanism may be the reason for the appearance of cosmic magnetic fields.In the present paper we make a detailed study of the Birman mechanism for the origin of magnetic fields, and we derive the conditions which are imposed on the motion and the characteristics of the completely ionized plasma which are necessary for the appearance of a vortical emf. It is shown that in this case the axisymmetric motions of a highly conducting plasma may generate toroidal magnetic fields of considerable magnitude. Further, a kinematic solution is given of the problem of the determination of the magnetic field and currents which arise in the spherical plasma volume modeling a star. This volume rotates about some axis with a given angular velocity which depends on the spherical coordinates R and . Characteristics corresponding to the mean characteristics of the sun model are taken for specific calculations.     

Disturbance convection velocity in turbulent jets under aeroacoustic excitation

The velocity of propagation of toroidal and oblique vortices formed in subsonic and supersonic turbulent jets under longitudinal internal and transverse external excitation by finite-amplitude saw-tooth acoustic waves is studied experimentally. It is demonstrated that the convection velocity of vortices is not constant, and the character of its variation depends on the vortex shape. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 21–25, September–October, 2007.     

A general treatment for non-Darcy film condensation within a porous medium in the presence of gravity and forced flow

Non-Darcy film condensation over a vertical flat plate within a porous medium is considered. The Forchheimer extended Darcy model is adopted to account for the non-Darcy effects on film condensation in the presence of both gravity and externally forced flow. A general similarity transformation is proposed upon introducing a modified Peclet number based on the total velocity of condensate, resulting from both gravitational force and externally forced flow. This general treatment makes it possible to obtain all possible similarity solutions including the asymptotic results in the four different limiting regimes, namely, Darcy forced convection regime, Forchheimer forced convection regime, Darcy body force predominant regime and Forchheimer body force predominant regime. Appropriate dimensionless groups for distinguishing these asymptotic regimes are found to be the micro-scale Grashof and Reynolds numbers based on the square root of the permeability of the porous medium. Correspondingly, the non-Darcy effect on the heat transfer rate are investigated in terms of these micro-scale dimensionless numbers.     

Force and flow characteristics of an intruder immersed in 3D dense granular matter

The motion of a projectile impact onto a granular target results in both the resistance force exerted on the projectile and rheology of granular media. A horizontal arrangement of cylinder quasistatically and dynamically intruding into granular media under different velocities and angles is simulated using discrete element method. Three distinguished drag force regimes are exhibited, including hydrostatic-like force independent of velocity, viscous force related to velocity, and inertial drag force proportional to the square of velocity. Meanwhile, the influence of penetration angles on drag force is examined for these three regimes, and a force model, which is related to penetration depth and angle, is proposed for quasi-static penetration. Then, flow characteristics of the granular media, such as velocity field, pressure field, packing fraction etc., are traced, and a rheology model of packing fraction and inertial number is established.     

Unsteady flow structure and vorticity convection over the airfoil oscillating at high reduced frequency

Unsteady vortex structures and vorticity convection over the airfoil (NACA 0012), oscillating in the uniform inflow, are studied by flow visualization and velocity measurements. The airfoil, pivoting at one-third of the chord, oscillates periodically near the static stalling angle of attack (AOA) at high reduced-frequency. The phase-triggering and modified phase-averaged techniques are employed to reconstruct the pseudo instantaneous velocity field over the airfoil. During the down stroke cycle, the leading-edge separation vortex is growing and the vortex near the trailing edge begins to shed into the wake. During the upstroke cycle, the leading-edge separation vortex is matured and moves downstream, and the counter clockwise vortex is forming near the trailing edge. Convection speeds and wavelength of the unsteady vortex structure over the airfoil equal to that of the counter clockwise vortex shed into the wake. This kind of vortex structure is termed as “synchronized shedding” type. The wavelength of unsteady vortex structure over the airfoil is significantly different from that at low reduced-frequency. Consistent convection speeds of the leading-edge separation vortex are acquired from the spatial-temporal variations of local circulation and local surface vorticity generation, and equals that predicted from flow visualization. Spatial-temporal variations of the local surface vorticity generation clearly reveal the formation and passage of the leading-edge separation vortex only in the region where the flow does not separate completely from the surface. Significant amounts of the surface vorticity are generated within the leading-edge region of the airfoil during the upstroke cycle. Only negligible amount of surface vorticity is produced within the region of complete flow separation. During the down stroke cycle, the surface vorticity generation is mild along the airfoil surface, except the leading-edge region where a small scale leading-edge separation vortex is forming and growing.     

Experimental laminar Rayleigh-Bénard convection in a cubical cavity at moderate Rayleigh and Prandtl numbers

Rayleigh-Bénard convection in a cubical cavity with adiabatic or conductive sidewalls is experimentally analyzed at moderate Rayleigh numbers (Ra ≤ 8 × 10⁴) using silicone oil (Pr=130) as the convecting fluid. Under these conditions the flow is steady and laminar. Three single-roll-type structures and an unstable toroidal roll have been observed inside the cavity with nearly adiabatic sidewalls. The sequence from the conductive state consists of a toroidal roll that evolves to a diagonally oriented single roll with increasing Rayleigh number. This diagonal roll, which is stabilized by the effect of the small but finite conductivity of the walls, shifts its axis of rotation towards to two opposite walls, and back to the diagonal orientation to allow for the increase in circulation that occurs as the Rayleigh number is further increased. Conduction at the sidewalls modifies this sequence in the sense that the two initial single rolls finally evolve into a four-roll structure. Once formed, this four-roll structure remains stable when decreasing the Rayleigh number until the initial single diagonally oriented roll is again recovered. The topology and the velocity fields of all structures, characterized with visualization and particle image velocimetry, respectively, are in good agreement with numerical results reported previously for the cavity with adiabatic walls, as well as with the numerical predictions obtained in the present study for perfectly conducting lateral walls. Received: 10 August 1998/Accepted: 1 August 2000     

No slip boundary effects in non-Darcian mixed convection from a vertical wall in saturated porous media. Analytical solution

An analytical study is made for wall effects in non-Darcy mixed convection from vertical impermeable surfaces embedded in a saturated porous medium. The governing equations are transformed into a dimensionless form by non-similar transformation to cover both forced and natural convection dominated regimes. Two different dimensionless parameters that measure the strength of mixed convection were found in both regimes. The parameters of forced convection dominated regime can be related to those of natural convection dominated regime. An approximate analytical solution for the governing equations was obtained. Temperature and velocity profiles for both regimes are presented. Received on 9 September 1997     

Simulation of the Onset of Nonstationarity and Chaos in a Hydrodynamic System Governed by a Small Number of Degrees of Freedom

The hypothesis of the onset of nonstationarity and chaos in a hydrodynamic system as a result of the nonlinear interaction of a small number of degrees of freedom is verified experimentally with reference to fluid convection in a toroidal channel. Regimes of motion of a fluid medium which correspond qualitatively to the Lorenz model are obtained experimentally. These include steady-state regimes, their bifurcations, nonuniqueness and instability, unsteady periodic and stochastic regimes. The spectral and statistical characteristics of the and unsteady processes are investigated, the nature of the onset of chaos is analyzed, and the results are compared with calculations. The mathematical model of the problem is refined.     

Spectral methods for the simulation of incompressible flows in spherical shells

A spatial discretization of the incompressible Navier–Stokes equation is presented in which the velocity is decomposed using poloidal and toroidal scalars whose spatial dependence is given in terms of spherical harmonics and Chebychev polynomials. The radial resolution needs to be large enough at any given angular resolution in order to avoid instability in the simulation of rotating flows. Several semi‐implicit time steps are discussed. The most accurate scheme is an integrating factor technique. Copyright © 1999 John Wiley & Sons, Ltd.     

Convection of a heat-generating fluid in a rotating horizontal cylinder

Thermal convection of a fluid in a horizontal cylinder rotating about its own axis with uniformly volume-distributed internal heat sources is experimentally investigated. The enclosure boundary temperature was kept constant. The threshold of the excitation of convective flows and their structure are studied as functions of the heat-release intensity and the rotation velocity. The experiments are performed with water and water-glycerin solutions. It is shown that rapidly rotating fluid is in a stable quasiequilibrium state, namely, the temperature distribution is axisymmetric and has a maximum at the center of the enclosure. It is found that with decrease in the rotation velocity a convective flow arises thresholdwise, in the form of vortex cells periodically arranged along the axis. The thermal convection in the rotating enclosure is shown to be determined by the effects of two different mechanisms. One of these is due to the centrifugal force of inertia and plays the stabilizing role, while the other, thermovibrational mechanism is connected with nonisothermal fluid oscillations under the action of gravity in the enclosure-fitted reference frame and is responsible for the occurrence of mean thermal convection. The boundaries of the convection generation are plotted in the plane of the governing dimensionless parameters and the heat transfer in the supercritical region is studied.     

Local nonsimilarity solution for the impact of the buoyancy force on heat and mass transfer in a flow over a porous wedge with a heat source in the presence of suction/injection

Combined heat and mass transfer in free, forced and mixed convection flows along a porous wedge with internal heat generation in the presence of uniform suction or injection is investigated. The boundary-layer analysis is formulated in terms of the combined thermal and solute buoyancy effect. The flow field characteristics are analyzed using the Runge-Kutta-Gill method, the shooting method, and the local nonsimilarity method. Due to the effect of the buoyancy force, power law of temperature and concentration, and suction/injection on the wall of the wedge, the flow field is locally nonsimilar. Numerical calculations up to third-order level of truncation are carried out for different values of dimensionless parameters as a special case. The effects of the buoyancy force, suction, heat generation, and variable wall temperature and concentration on the dimensionless velocity, temperature, and concentration profiles are studied. The results obtained are found to be in good agreement with previously published works.     

Electric effects on the rheology of insulating oils in electrodes with flocked fabric

The rheological behavior of insulating oils is studied in nonuniform electric fields which are generated by an electrode covered with flocked fabric. Although the oils show no electrorheological effects in uniform fields between metal electrodes with smooth surfaces, the flocked fabric leads to a striking increase of viscosity in steady shear. The viscosity enhancement increases with decreasing zero-field viscosity and decreasing conductivity of oils. In the limit of zero shear rate, the oils with low conductivity behave as solids with yield stress. When a very small quantity of fine particles is introduced into electrified oils without shear, a rapid and large-scale motion of particles is observed between the tips of fibers and the plate electrode. The local motion of fluids in high electric fields is referred to as electrohydrodynamic (EHD) convection. Periodic patterns of circulation flow are formed in static oils. The electric energy which is dissipated during the circulation motion contributes to holding the periodic flow in static oils. When the stress is very low, the periodic patterns are not broken down. The yield stress corresponds to the force required to rupture the domain structures of EHD convection. In shear fields, the additional energy may be required to change the periodic patterns of EHD convection. The striking increase of viscosity in steady shear can be attributed to the interactions between EHD convection and external shear. Received: 31 August 1998 Accepted: 17 February 1999     

Linear theory of unsteady gas flow under the influence of nonpotential external forces

We determine in the linear formulation the velocity and pressure fields excited in a compressible medium by a lifting filament that displaces and deforms arbitrarily. For general unsteady motion of such a filament we give explicit formulas that express the velocity at a given point in terms of the intensity of the free vortices entering the audio signal audibility zone constructed for this point. We examine gas flow caused by an arbitrary external body force field.Studies devoted to the determination of gas velocity fields for flow past slender bodies relate primarily to translational motion of a body with a dominant constant velocity [1–3]. Gas velocities for helical motion of a rectilinear lifting filament within the gas have been examined in [4].     

Cellular structure in a natural convection loop and its chaotic behaviour: II. Theory

A theoretical study of thermal convection in a vertically oriented thin toroidal loop which is placed in a uniform negative vertical temperature gradient is reported. The Boussinesq approximation is employed, and the first-order perturbed fields from a steady conduction state are obtained in the form of a double Fourier series. The critical Rayleigh number for the onset of convection is determined and various types of steady convective patterns, including cellular structure, are examined. Four typical modes are superposed to express the time-dependent velocity and temperature fields, whose mode-amplitudes constitute an extended version of the Lorenz model. Numerical simulation shows a sequence of transitions from steady to periodic, quasi-periodic, and chaotic states as the Rayleigh number is increased. The present model successfully explains our experimental results.     

Numerical study on magneto-convection of cold water in an open cavity with variable fluid properties

The aim of the present study is to understand the problem of buoyancy and thermocapillary induced convection of cold water near its density maximum in an open cavity with temperature dependent properties in the presence of uniform external magnetic field. The governing equations are solved by the finite volume method. The results are discussed for various values of reference temperature parameter, density inversion parameter, Rayleigh, Hartmann and Marangoni numbers. It is observed that the temperature of maximum density leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. Convection heat transfer is enhanced by thermocapillary force when buoyancy force is weakened.     

On centrifugal separation of particles of two different sizes

We consider flow in a centrifugal force field of a non-dilute suspension with particles or droplets of two sizes. The volume fraction and the velocity fields are determined assuming small convection and shear terms. The resulting flow field is quite different from that in a gravitational settling of a similar mixture. In particular, the volume fraction is a function of time and radius in the sectors separated by kinematic shocks and the settling velocity is a non-monotonic function of the particle size.     

Effects of heat generation on g-Jitter induced natural convection flow in a channel with isothermal or isoflux walls

This paper discusses the behavior of g-jitter induced free convection in microgravity under the influence of a transverse magnetic field and in the presence of heat generation or absorption effects for a simple system consisting of two parallel impermeable infinite plates held at four different thermal boundary conditions. The governing equations for this problem are derived on the basis of the balance laws of mass, linear momentum, and energy modified to include the effects of thermal buoyancy, magnetic field and heat generation or absorption as well as Maxwell's equations. The fluid is assumed to be viscous, Newtonian and have constant properties except the density in the body force of the balance of linear momentum equation. The governing equations are solved analytically for the induced velocity and temperature distributions as well as for the electric field and total current for electrically-conducting and insulating walls. This is done for isothermal–isothermal, isoflux–isothermal, isothermal–isoflux and isoflux–isoflux thermal boundary conditions. Graphical results for the velocity amplitude and distribution are presented and discussed for various parametric physical conditions.     

Structure of Sidewall Thermoconcentration Convection in the Flow Formation and Disintegration Regimes

The transformation of the structure of the density, optical refractive index, temperature, and salinity fields in the regimes of formation and disintegration of convection flows under uniform sidewall cooling of a continuously stratified fluid is investigated using optical and probe techniques. Although the height of the individual cells is almost constant in the various stages of the process, the field patterns change significantly. In the formation stage the contributions of the temperature and salinity to the density distribution compensate each other, the density profile is smooth and the optical refractive index profile is stepped. In the disintegration stage the density profile also becomes stepped. At large times a new convection flow is formed on the external boundaries of the cells due to the temperature difference between the cooled inner fluid and the warmer outer (undisturbed) fluid, and this flow maintains the structure contrast as the motion degenerates.