Body Force Field Research Articles

Evaluation of Acoustic Sources in an Excited Unstable Laminar Shear Layer

The radiation of sound from artificial sources in a developing shear layer is studied numerically, in order to address an issue that arises in acoustic analogy models of jet noise: namely whether the unstable response of the mean-flow shear layer has a significant effect on sound radiation. Direct numerical simulation of a forced two-dimensional compressible laminar mixing layer has been carried out at a Reynolds number of 250, based on the mixing layer initial vorticity thickness and the upper free-stream velocity. The free-stream Mach numbers of the mixing layer are 0.9 and 0.45. The flow is excited with a single-frequency body force field that is acoustically compact and is derived from an applied-stress distribution. Sound radiation from the mixing layer is calculated at the forcing frequency, and compared with radiation from a uniform flow under the same forcing. Comparisons are shown for the most-unstable forcing frequency over a wide amplitude range. The pressure radiated on either side of the mixing layer differs very little from that radiated into a uniform flow of the same Mach number under the same forcing, although the higher forcing amplitudes used are sufficient to trigger the non-linear process of vortex roll-up in the case of the mixing layer. The dominant source position for the radiated pressure at the forcing frequency is estimated via a wavenumber-frequency domain analysis. It is found to be close to the location of the applied forcing, with little contribution from mixing-layer vortical structures that develop downstream.

Elastic theory of surface deformation in molecular physisorption

In molecular physisorption, beyond attractive and repulsive forces, a third contribution arises from the elastic deformation of the surface. In the present work the dimple appearing on a deformable surface upon physisorption of a foreign molecule is studied and its effect on the adsorption energy is calculated. The depth and shape of the physisorption dimple are studied on the basis of the theory of elasticity. The problem of the deformation of a semi-infinite elastic medium, subject to central body forces, is solved, with the centre (i.e., the molecule) placed outside the medium. A vectorial Poisson equation for the displacement field is solved with the boundary condition that no surface forces act. For a centrosymmetrical molecule the solution is obtained in two steps, whose results are then superposed: (1) the deformation field in an infinite elastic medium subject to a central body force field, whose centre coincides with the centre of the molecule, is evaluated (the solution generates mismatch of the boundary conditions); (2) a complementary homogeneous problem is solved with boundary conditions compensating the spurious contributions generated in step (1). Specific attention is given to methane adsorption both on a metal surface (Au) and on a molecular crystal surface (solid Ar). The shape function ζ( R) is always positive (indicating a bulging surface) if the distance z of the molecule (i.e., of the carbon atom) from the surface is large, but becomes largely negative for z smaller, showing a definite dimple. The minimum energy (adsorption equilibrium) corresponds to the latter case. The dimple depth turns out to be 10.0 pm in the case of Au, while for Ar we find a depth of 30.5 pm at 80 K and 25.6 pm at 0 K. A discussion of the asymptotic behaviour (proportional, off equilibrium, to R −1) of the deformation at long distances R from the adsorbed molecule is also given.

Componentwise energy amplification in channel flows

We study the linearized Navier–Stokes (LNS) equations in channel flows from an input–output point of view by analysing their spatio-temporal frequency responses. Spatially distributed and temporally varying body force fields are considered as inputs, and components of the resulting velocity fields are considered as outputs into these equations. We show how the roles of Tollmien–Schlichting (TS) waves, oblique waves, and streamwise vortices and streaks in subcritical transition can be explained as input–output resonances of the spatio-temporal frequency responses. On the one hand, we demonstrate the effectiveness of input field components, and on the other, the energy content of velocity perturbation components. We establish that wall-normal and spanwise forces have much stronger influence on the velocity field than streamwise force, and that the impact of these forces is most powerful on the streamwise velocity component. We show this using the relative scaling of the different input–output system components with the Reynolds number. We further demonstrate that for the streamwise constant perturbations, the spanwise force localized near the lower wall has, by far, the strongest effect on the evolution of the velocity field.

Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity

The present work deals with the uniqueness theorem for plane crack problems in solids characterized by dipolar gradient elasticity. The theory of gradient elasticity derives from considerations of microstructure in elastic continua [Mindlin, R.D., 1964. Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78] and is appropriate to model materials with periodic structure. According to this theory, the strain-energy density assumes the form of a positive-definite function of the strain (as in classical elasticity) and the second gradient of the displacement (additional term). Specific cases of the general theory employed here are the well-known theory of couple-stress elasticity and the recently popularized theory of strain-gradient elasticity. These cases are also treated in the present study. We consider an anisotropic material response of the cracked plane body, within the linear version of gradient elasticity, and conditions of plane-strain or anti-plane strain. It is emphasized that, for crack problems in general, a uniqueness theorem more extended than the standard Kirchhoff theorem is needed because of the singular behavior of the solutions at the crack tips. Such a theorem will necessarily impose certain restrictions on the behavior of the fields in the vicinity of crack tips. In standard elasticity, a theorem was indeed established by Knowles and Pucik [Knowles, J.K., Pucik, T.A., 1973. Uniqueness for plane crack problems in linear elastostatics. J. Elast. 3, 155–160], who showed that the necessary conditions for solution uniqueness are a bounded displacement field and a bounded body-force field. In our study, we show that the additional (to the two previous conditions) requirement of a bounded displacement-gradient field in the vicinity of the crack tips guarantees uniqueness within the general form of the theory of dipolar gradient elasticity. In the specific cases of couple-stress elasticity and pure strain-gradient elasticity, the additional requirement is less stringent. This only involves a bounded rotation field for the first case and a bounded strain field for the second case.

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equations that specify the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, the shear stresses, the interfacial momentum transfer and the wall friction, since these macroscopic effects govern the relative velocity between phases. A comparison of the models with existing experimental data shows a satisfactory agreement.

Generalized Airy Stress Functions

The classical Airy stress function in planar elastostatics cannot, in general, be a smooth function for multiply connected domains. Moreover, if a non-null body force field is active the classical Airy representation for the stress is not complete. Here, a generalized Airy representation for the stress is presented which preserves smoothness and which is complete. The generalized form identifies the explicit additional pieces that are needed for completeness in multiply connected domains and when a body force field is present.

Phase-field modeling of stress-induced instabilities.

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. Using a formulation that is independent of the state of reference chosen for the displacement field, we write down the elastic energy in an unambiguous fashion, thus obtaining an entire class of models. According to the choice of reference state, the particular model emerging from this class will become equivalent to one of the two independently constructed models on which brief accounts have been given recently [J. Müller and M. Grant, Phys. Rev. Lett. 82, 1736 (1999); K. Kassner and C. Misbah, Europhys. Lett. 46, 217 (1999)]. We show that our phase-field approach recovers the sharp-interface limit corresponding to the continuum model equations describing the Asaro-Tiller-Grinfeld instability. Moreover, we use our model to derive hitherto unknown sharp-interface equations for a situation including a field of body forces. The numerical utility of the phase-field approach is demonstrated by reproducing some known results and by comparison with a sharp-interface simulation. We then proceed to investigate the dynamics of extended systems within the phase-field model which contains an inherent lower length cutoff, thus avoiding cusp singularities. It is found that a periodic array of grooves generically evolves into a superstructure which arises from a series of imperfect period doublings. For wave numbers close to the fastest-growing mode of the linear instability, the first period doubling can be obtained analytically. Both the dynamics of an initially periodic array and a random initial structure can be described as a coarsening process with winning grooves temporarily accelerating whereas losing ones decelerate and even reverse their direction of motion. In the absence of gravity, the end state of a laterally finite system is a single groove growing at constant velocity, as long as no secondary instabilities arise (that we have not been able to see with our code). With gravity, several grooves are possible, all of which are bound to stop eventually. A laterally infinite system approaches a scaling state in the absence of gravity and probably with gravity, too.

Kinetics of Hygrothermal Treatment of Capillary Porous Materials

The kinetics of moisture and heat exchange between a capillary porous body and the surrounding single-phase gas–vapor medium is described. The physical aspects of various modes of the process are considered. The importance of taking into account the internal filtration of moisture under the action of the external field of body forces is demonstrated.

The Effect of Working Fluid Inventory on the Performance of Revolving Helically Grooved Heat Pipes

The results of a recently completed experimental and analytical study showed that the capillary limit of a helically-grooved heat pipe (HGHP) was increased significantly when the transverse body force field was increased. This was due to the geometry of the helical groove wick structure. The objective of the present research was to experimentally determine the performance of revolving helically-grooved heat pipes when the working fluid inventory was varied. This report describes the measurement of the geometry of the heat pipe wick structure and the construction and testing of a heat pipe filling station. In addition, an extensive analysis of the uncertainty involved in the filling procedure and working fluid inventory has been outlined. Experimental measurements include the maximum heat transport, thermal resistance and evaporative heat transfer coefficient of the revolving helically grooved heat pipe for radial accelerations of |a⃗r|=0.0, 2.0, 4.0, 6.0, 8.0, and 10.0-g and working fluid fills of G=0.5, 1.0, and 1.5. An existing capillary limit model was updated and comparisons were made to the present experimental data.

Laboratory Study of Spherical Convection in Simulated Central Gravity

This work reports the first terrestrial laboratory study of thermal convection in a central body-force field. The force field is produced by gradients of magnetic field magnitude imposed on a spherical shell of heated, magnetizable fluid. Cells of thermal convection consistent with the notion of continental drift are detected using infrared imaging. Transitions of symmetry for the patterns of convection are observed in the range of Earth's Rayleigh number.

Particulate Stresses in Dense Disperse Flow

We review and discuss the progress as achieved to date in the matter of describing particulate stresses of different origins that occur in concentrated suspensions of solid particles. A few physical mechanisms of generating such stresses are explicitly recognized. First, these stresses appear as a result of direct momentum transport over a transient network of particles separated by thin lubricating films of the intervening fluid, so that a part of the apparent suspension viscosity must be attributed to its dispersed phase. Second, normal and tangential particulate stresses originate because of random fluctuations of particles caused by (1) their pair interactions as the particles are brought closer together and pass one another in mean shear flow, (2) the relative fluid flow and an external body force field as they interact with random fluctuations of suspension concentrations, and (3) random macroscopic flow patterns, such as bubbles rising in fluidized beds that produce a system of Reynolds-like stresses

Ensemble-average versus suspension-scale Cauchy continuum-mechanical definitions of stress in polarized suspensions: Global homogenization of a dilute suspension of dipolar spherical particles

The macroscale rheological properties of a dilute suspension exposed to a uniform external field and composed of identical, rigid, inhomogeneous, dipolar, spherical particles dispersed in an incompressible Newtonian fluid and possessing the same mean density as the latter fluid are derived from knowledge of its microscale properties by applying a global ensemble-averaging technique. Each dipole, which is permanently embedded in the particle, is assumed to be generated by the presence of an inhomogeneous external body-force field in the particle interior resulting from the action of the uniform external field on an inhomogeneous distribution of interior matter. It is shown that although the ensemble-average stress tensor is symmetric, the suspension nevertheless behaves macroscopically as if it possessed an asymmetric stress tensor. This seeming contradiction can be traced to the fact that the average body force acting on the contents of any arbitrarily drawn volume lying in the interior of the suspension does not vanish despite the fact that each particle is “neutrally buoyant.” That this force is not zero stems from the fact that some particles necessarily straddle the closed surface bounding that volume, and that the distribution of external body forces over the interiors of these particles is nonuniform. As such, that portion of the spherical particle lying outside of the surface enclosing the domain exerts a force on the remaining portion of the sphere lying within that domain. We then demonstrate that the natural macroscopic model, which is derived by equating the divergence of the suspension-scale stress appearing in that model to the ensemble-average external body-force field, and which predicts a symmetric stress tensor, is macroscopically deficient with respect to the more intuitive asymmetric stress model usually proposed by continuum mechanicians for such a suspension. It is shown that the latter, continuum-mechanical model recovers all the physically interesting properties of the suspension.

The role of the turbulent scales in the settling velocity of heavy particles in homogeneous isotropic turbulence

The average settling velocity of heavy particles under a body force field is studied numerically in stationary homogeneous isotropic turbulent flows generated by the direct numerical simulation and the large eddy simulation of the continuity and Navier–Stokes equations. The flow fields corresponding to different selected ranges of turbulent scales are obtained by filtering the results of the direct numerical simulation, and employed for calculating the particle motion. Wang & Maxey (1993) showed that as a consequence of the particle accumulation in the low vorticity region and the preferential sweeping phenomenon, the average settling rate in turbulence is greater than that in still fluid. In the present study, the phenomenon of particle accumulation in the low vorticity region is found to be controlled mainly by the small scales with wavenumber kω corresponding to the maximum of the dissipation (vorticity) spectrum. However, the increase of the average settling rate, 〈ΔvS〉, also depends strongly on the large energetic eddies. The small eddies with wavenumber greater than 2.5kω have essentially no effect on the particle accumulation and the average settling velocity. The large eddy simulation is thus adequate for the present study provided the smallest resolved scale is greater than 1/(2.5kω). Detailed calculations show that 〈ΔvS〉 is maximized and is of order u′/10 when τp/τk≈1 and vd/u′≈0.5 for Rλ=22.6–153, where τp is the particle's relaxation time, τk is the Kolmogorov timescale, vd is the settling rate in still fluid, u′ is the root mean square of the velocity fluctuation, and Rλ is the Reynolds number based on the Taylor microscale.

On the Average Settling Rate of Heavy Particles in Decaying Homogeneous Isotropic Turbulence

ABSTRACTThe average settling rate of spherical solid particles, 〈vs〉, under a body force field is studied numerically in decaying homogeneous isotropic turbulent flows generated by the direct numerical simulation of the continuity and Navier-Stokes equations. The increase of the average settling rate, 〈Δvs〉, is maximized when Tp/Tk ≈ 1 and vd/u′ ≈ 0.5, and is of order 0.lu′, which is qualitatively similar to that in stationary turbulence. Here 〈Δvs〉 = 〈vs〉 − vd, Tp is the particle's relaxation time, Tk is the Kolmogorov time scale, vd is the settling rate of particles in still fluid, and u′ is the root mean square of the fluid velocity fluctuation. However, the magnitude of the maximum value of 〈Δvs〉 in decaying turbulence is substantially greater (about 40%) than that in the corresponding stationary turbulence due to the inertia response of particles to turbulence decay. Although 〈Δvs〉/u′ does not reach a stationary state as the flow is evolving, it is a slowly time varying function for the parameters of interest as Tp (≈ Tk when 〈Δvs〉 is maximized) is in general of one order less than the time scale of turbulence decay.

The Effects of Transverse Acceleration-Induced Body Forces on the Capillary Limit of Helically Grooved Heat Pipes

A helically grooved copper heat pipe with ethanol as the working fluid has been fabricated and tested on a centrifuge table. The heat pipe was bent to match the radius of curvature of the table so that uniform transverse (perpendicular to the axis of the heat pipe) body force fields could be applied along the entire length of the pipe. By varying the heat input (Qin = 25 to 250 W) and centrifuge table velocity (radial acceleration |a⃗r| = 0 to 10g), information on dry out phenomena, circumferential temperature uniformity, heat lost to the environment, thermal resistance, and the capillary limit to heat transport was obtained. Due to the geometry of the helical grooves, the capillary limit increased by a factor of five when the radial acceleration increased from |a⃗r| = 0 to 6.0g. This important result was verified by a mathematical model of the heat pipe system, wherein the capillary limit to heat transport of each groove was calculated in terms of centrifuge table angular velocity, the geometry of the heat pipe and the grooves (including helix pitch), and temperature-dependent working fluid properties. In addition, a qualitative study was executed with a copper-ethanol heat pipe with straight axial grooves. This experimental study showed that the performance of the heat pipe with straight grooves was not improved when the radial acceleration was increased from |a⃗r| = 0 to 10.0g.

Spectral Green's Dyadic for Point Sources in Poroelastic Media

A fairly detailed derivation of the spectral Green's dyadic for point sources in unbounded poroelastic media is presented. It is assumed that the motion of the poroelastic medium is governed by Biot's theory of poroelasticity; thus in a source-free unbounded space the wave field consists of two (fast and slow) longitudinal waves and a transverse wave. Considering a three-dimensional source-receiver system and then through a decomposition of the displacement and body force fields, the dilatational and rotational components of motion are separated. Separation yields two sets of systems of two partial differential equations representing scalar wave equations of poroelasticity, which unlike the case of elastic propagation are still coupled in terms of the motion of the pore fluid and that of the frame material, respectively. General solutions are derived from the fundamental eigenvalue problems of poroelasticity, which are associated with the systems of the homogeneous wave equations. Singular solutions for point sources are then obtained by superimposing the latter with particular solutions of the inhomogeneous wave equations. Consistent with previous studies, the spectral Green's dyadic shows that the body force singularity generates three distinct waves. These waves are radiating from the source with wave speeds, attenuations, and amplitudes, which depend on frequency and consequently on the level and type of dissipation in the two-phase medium.

Calculation of Mechanical, Thermodynamic and Transport Properties of Metallic Glass Formers

AbstractRecently, we have parametrized Sutton-Chen type empirical many body force fields for FCC transition metals to study the thermodynamic, mechanical, transport and phase behavior of metals and their alloys. We have utilized these potentials in lattice dynamics calculations and molecular dynamics simulations to describe the structure, thermodynamic, mechanical and transport properties of pure metals and binary alloys in solid, liquid and glass phases. Here, we will describe these applications: mechanical properties of binary alloys (Pt - Rh) and viscosity of a binary alloy, (Au - Cu), as a function of composition, temperature, and shear rate, crystal-liquid, liquid-crystal phase transformation in (Ni - Cu), liquid to glass transformation in a model glass former, (Ag - Cu).

Crystallization of aluminum alloys in the presence of vertical electromagnetic force fields

The influence of vertical and steady electromagnetic force fields applied during the solidification of representative aluminum alloys was investigated. The experiments were performed both in the absence and in the presence of electromagnetic body force fields, oriented either upward or downward, and for various degrees of heat extraction rate. Several physical mechanisms of magnetohydrodynamic origin, acting on the macro- and microstructure of these alloys, have been revealed. It has been established that the stirring and liquid-solid-phase separation phenomena results in a decided grain refinement and, under certain conditions, in the segregation of the most part of the eutectic phase from the primary solid.

A simple description of some inertia effects in the behaviour of heavy particles in a turbulent gas flow

The effects of some inertia parameters and the influence of non-linear drag in the behaviour of heavy particles in a turbulent gas flow are investigated by examining th properties of their streamwise fluctuating motion. The particles are suspended in a stationary homogeneous turbulent gas flow, under the influence of an external body force field, which implies a non-zero mean slip velocity between the two phases. Two kinds of methods, the results of which are compared, are used. The first method is based on a simplified kinematic simulation of the fluid velocity fluctuation in the streamwise direction, according to a known turbulence spectrum. The second method is a classical Lagrangian tracking technique. The presence of an external body force field makes the particle turbulent response depend on three dimensionless parameters, among them the conventional Stokes number St and the particle Reynolds number Re p , based on the mean relative velocity between the fluid and the particle, are found to be the most influential ones for heavy particles. A particle response diagram is built, leading to an approximate expression for the particle-to-fluid turbulent intensity ratio in terms of a modified Stokes number which embodies the effects of both St and Re p . Numerical predictions are provided in the case of an upward vertical flow, in a large range of particle mean Reynolds numbers exceeding unity. A significant influence of the drag non-linearity can be observed. The main conclusion is that the effect of non-linear drag may surpass the well-known crossing-trajectory effect, in causing the particle mean-square velocity to increase with increasing mean relative velocity, contrary to what is generally expected for small inertia particles.

Properties of the particle pseudogas in a vertical fluid-particle flow

The rheological equations of state of the dispersed medium are obtained for one-dimensional flows of monodisperse systems in which the acceleration of the external body force field and the average interphase slip velocity are collinear, on the basis of an analysis of the pseudoturbulence properties.