Showing papers on "Compressibility published in 1980"

SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries

Abstract: In this report a simple, but powerful, computer program is presented for the solution of two-dimensional transient fluid flow with free boundaries The SOLA-VOF program, which is based on the concept of a fractional volume of fluid (VOF), is more flexible and efficient than other methods for treating arbitrary free boundaries SOLA-VOF has a variety of user options that provide capabilities for a wide range of applications Its basic mode of operation is for single fluid calculations having multiple free surfaces However, SOLA-VOF can also be used for calculations involving two fluids separated by a sharp interface In either case, the fluids may be treated as incompressible or as having limited compressibility Surface tension forces with wall adhesion are permitted in both cases Internal obstacles may be defined by blocking out any desired combination of cells in the mesh, which is composed of rectangular cells of variable size SOLA-VOF is an easy-to-use program Its logical parts are isolated in separate subroutines, and numerous special features have been included to simplify its operation, such as an automatic time-step control, a flexible mesh generator, extensive output capabilities, a variety of optional boundary conditions, and instructive internal documentation

Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid

Abstract: Analytical and numerical analyses have been made of the physical behaviour of a collapsing bubble in a liquid. The mathematical formulation takes into account the effects of compressibility of the liquid, non-equilibrium condensation of the vapour, heat conduction and the temperature discontinuity at the phase interface. Numerical solutions for the collapse of the bubble are obtained beyond the time when the bubble reaches its minimum radius up to the stage when a pressure wave forms and propagates outward into the liquid. The numerical results indicate that evaporation and condensation strongly influence the dynamical behaviour of the bubble.In addition, the propagation of the stress wave, both in a solid and a liquid, due to the collapse of the bubble has been observed by means of the dynamic photoelasticity. It is clearly demonstrated that the stress wave in a photoelastic specimen is caused by impact of the pressure wave radiated from the bubble.

An equation of state for hard dumbell fluids

Abstract: Monte Carlo simulations are reported for 45 state points of the hard dumbell system covering elongations l/σ from 0·2 to 1·0 and densities σd 3 from 0·2 to 0·9 (l is the bond length, σ the atom diameter and the d the diameter of a sphere with the same volume as the dumbell). The calculated compressibility factors, P/ρkT, together with the second virial coefficients reported by Isihara, have been used in a least squares evaluation of the constants in an equation of state that expresses the compressibility factor as a function of elongation and density. The fitted equation reproduces the virial coefficients to within about 0·2 per cent and the compressibility factors to within about 0·4 per cent. For the limiting case of hard spheres (l = 0) it reduces to the Carnahan-Starling equation. Expressions have been derived for calculating the isothermal compressibility, residual free energy and residual chemical potential from the equation.

Critical Behavior of a Micellar Solution

Abstract: The static and dynamic critical properties of a nonionic amphiphile aqueous solution showing a lower consolution point are investigated by laser-light scattering. The osmotic isothermal compressibility and the correlation length of the concentration fluctuations diverge with mean-field-theory critical exponents. The behavior of the mass diffusion constant in the hydrodynamic region is in good agreement with the predictions of the mode-mode-coupling theory.

Dielectric formulation of strongly coupled electron liquids at metallic densities. II. Exchange effects and static properties

Abstract: Static and thermodynamic properties of strongly coupled electron liquids at metallic densities are investigated on the basis of the general dielectric formulation developed in previous work The contribution of exchange effects to the local field correction is singled out, and the remaining Coulomb contribution is explicitly calculated The resulting set of self-consistent integral equations is numerically solved over the range of the density parameters, $0l~{r}_{s}l~20$ The static structure factor, the radial distribution function, the local field correction, the correlation energy, and the isothermal compressibility are computed and compared with other existing theories

Dynamic response of embankment, concrete-gravity and arch dams including hydrodynamic interaction

Abstract: An analysis procedure in the frequency domain for determining the earthquake responses of a dam was developed. The procedure inclides hydrodynamic interaction and water compressibility effects. Linear responses of idealized, two dimensional gravity dams and three dimensional dams, including arch dams were obtained. For an infinite uniform region a finite element discretization provides for a proper transmission of pressure waves. Hydrodynamic effects are equivalent to an added mass and added load in the frequency domain equations of motion of the dam. Complex frequency response functions for acceleration at the dam crest are presented for two dimensional concrete gravity and earth dams and for a three dimensional arch dam. Water compressibility and fluid foundation interaction significantly influence the response of concrete gravity dams and are even more important for each dam.

Gravitational flows of granular materials with incompressible grains

Abstract: A theory of flowing granular materials with incompressible grains is presented which is similar to one proposed by Goodman and Cowin in 1972. Using a nonlinear version of the theory, boundary‐value problems corresponding to gravity flow in a closed vertical channel and in a channel with a free surface inclined at various angles from the vertical are considered in detail. In analyzing these problems, the dependence of the free energy and viscosity on the volume fraction are specialized to agree with those proposed as a result of recent experimental work. Solutions of these problems demonstrate many of the characteristics normally assumed in other treatments of granular materials. In particular, for vertical flow, when the volume fraction is greater than (less than) the critical volume fraction, a compressive (tensile) force must be exerted on the walls to maintain isochoric flow. Pluglike regions in which the velocity is almost constant develop, and there is a relatively thin shear region near the wall. For the flow with a free surface, as grain size or angle of inclination increases, the solutions tend to two rigid motions separated by a thin shear layer.

Structure and thermodynamics of a simple fluid

Abstract: Monte Carlo results are found for a simple fluid with a pair potential consisting of a hard-sphere core and a Lennard-Jones attractive tail. They are compared with several of the most promising recent theoretical treatments of simple fluids, all of which involve the decomposition of the pair potential into a hard-sphere-core term and an attractive-tail term. This direct comparison avoids the use of a second perturbation scheme associated with softening the core, which would introduce an ambiguity in the significance of the differences found between the theoretical and Monte Carlo results. The study includes the optimized random-phase approximation (ORPA) and exponential (EXP) approximations of Andersen and Chandler, an extension of the latter approximation to nodal order three (the N3 approximation), the linear-plus-square (LIN + SQ) approximation of H\o{}ye and Stell, the renormalized hypernetted chain (RHNC) approximation of Lado, and the quadratic (QUAD) approximation suggested by second-order self-consistent $\ensuremath{\Gamma}$ ordering, the lowest order of which is identical to the ORPA. As anticipated on the basis of earlier studies, it is found that the EXP approximation yields radial distribution functions and structure factors of excellent overall accuracy in the liquid state, where the RHNC results are also excellent and the EXP, QUAD, and LIN + SQ results prove to be virtually indistinguishable from one another. For all the approximations, however, the thermodynamics from the compressibility relation are poor and the virial-theorem results are not uniformly reliable. Somewhat more surprisingly, it is found that the EXP results yield a negative structure factor $S(k)$ for very small $k$ in the liquid state and poor radial distribution functions at low densities. The RHNC results are nowhere worse than the EXP results and in some states (e.g., at low densities) much better. In contrast, the N3 results are better in some respects than the EXP results but worse in others. The authors briefly comment on the RHNC and EXP approximations applied to the full Lennard-Jones potential, for which the EXP approximation appears somewhat improved in the liquid state as a result of the softening of the potential core.

Unsteady Flow of a Dusty Incompressible Fluid between Two Parallel Plates under an Impulsive Pressure Gradient

Abstract: In the present investigation, an attempt is made to study the unsteady flow or an incompressible viscous fluid with uniform distribution of dust particles between two parallel plates under an impulsive pressure gradient. Analytical expressions for velocities of the fluid and the dust particles have been obtained. The variation of total fluxes for fluid and dust particles has been discussed. The influence on skin friction has been noticed.

Dynamics of classical ionic plasmas in an electron gas

Abstract: The Bohm-Staver treatment of electronic screening of the long-wave-length ionic motions in a classical plasma is re-examined and extended to ionic mixtures. In the case of a pure ionic plasma, the Bohm-Staver formula for the speed of sound is brought to consistency with the Ornstein-Zernike compressibility by the inclusion of two (largely compensating) corrections arising from the thermodynamics of the bare plasma and from local pseudopotential effects. Attenuation of sound waves by viscosity in the bare plasma is also displayed. A parallel treatment is given of the effects of electronic screening on the longitudinal excitation spectrum of a bare ionic mixture at long wave-lengths, which contains an ionic plasma mode broadened by collisions as well as a relaxation mode of finite width. Electronic screening transforms the plasma mode into a sound wave mode and yields an interdiffusion relaxation peak whose width vanishes with the square of the wave number and is directly proportional to the interdiffusion coefficient of the two ionic species. The hydrodynamic behaviour of the screened ionic mixture is thus shown to be similar to that of a neutral mixture.

Modal methods in finite element fluid-structure eigenvalue problems

Abstract: The technique of fixed-interface modal synthesis used to solve large structural eigenvalue problems is extended to fluid-structure eigenvalue problems with a view to efficient solution of problems involving localized modifications. Three cases are considered: namely, those fluid or fluid-structure vibration problems directly analogous to the structural case; the modification of the fluid model of a structure enclosing a compressible fluid; and the modification of fluid and structural models of a structure enclosing an incompressible fluid. Examples of the three cases are given, as are estimates of the computation that can be saved when using the methods to avoid resolving modified eigenvalue problems. It is also shown that the hard-walled modes of a fluid enclosure can be used to modify the incompressible-fluid modes of the fluid-structure system to account for a degree of compressibility in the fluid. An example and computation estimates are given.

On mechanics of saturated granular materials

Abstract: A continuum theory of saturated granular materials is formulated. The basic balance laws for the solid phase as well as for the fluid phase are presented. The constitutive equations are derived and the basic equations of motion of the solid and fluid continua are obtained. Several cases of interest, such as incompressible granules saturated with liquids are discussed. It is shown that the theory contains, as its special cases, the Mohr-Coulomb criterion for a granular material as well as Darcy's law of flow through porous media.

A review of the experimental data from the high pressure phase in polyethylene

Abstract: The experimental techniques are enumerated which were up to present used to investigate the high pressure phase in linear polyethylene. The crystallographic data of this phase which is hexagonal are tabulated. In part they come from wide angle X-ray scattering, in part they are calculated from dilatometric results discussed in detail. The thermodynamic quantities given encompass the phase diagramm including the slope of the curves, the changes in volume, entropy and enthalpy and the linear compressibility and the linear expansion coefficient of the hexagonal phase. Further results are reported found by microscopy, ultrasonic measurements and Raman spectroscopy.