Showing papers on "Compressibility published in 1999"

Core-softened potentials and the anomalous properties of water

Abstract: We study the phase diagram of a system of spherical particles interacting in three dimensions through a potential consisting of a strict hard core plus a linear repulsive shoulder at larger distances. The phase diagram (obtained numerically, and analytically in a limiting case) shows anomalous properties that are similar to those observed in water. Specifically, we find maxima of density and isothermal compressibility as a function of temperature, melting with volume contraction, and multiple stable crystalline structures. If in addition a long range attraction between the particles is included, the usual liquid–gas coexistence curve with its critical point is obtained. But more interestingly, a first order line in the metastable fluid branch of the phase diagram appears, ending in a new critical point, as it was suggested to occur in water. In this way the model provides a comprehensive, consistent and unified picture of most of the anomalous thermodynamical properties of water, showing that all of them ...

Three-dimensional human head finite-element model validation against two experimental impacts.

Abstract: The impact response of a three-dimensional human head model has been determined by simulating two cadaver tests. The objective of this study was to validate a finite-element human head model under different impact conditions by considering intracranial compressibility. The current University Louis Pasteur model was subjected initially to a direct head impact, of short (6 ms) duration, and the simulation results were compared with published experimental cadaver tests. The model response closely matched the experimental data. A long duration pulse was chosen for the second impact and this necessitated careful consideration of the head–neck joint in order to replicate the experimental kinematics. The skull was defined as a rigid body and was subjected to six velocities. Output from the model did not accurately match the experimental results and this clearly indicates that it is important to validate a finite-element head model under various impact conditions to define the range of validity. Lack of agreement for the second impact is attributed to the nonlinearity in the dynamic behavior of intracranial stress, a problem that is not reported in the literature. © 1999 Biomedical Engineering Society.

Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble

Abstract: Coexistence curves of square-well fluids with variable interaction width and of the restricted primitive model for ionic solutions have been investigated by means of grand canonical Monte Carlo simulations aided by histogram reweighting and multicanonical sampling techniques. It is demonstrated that this approach results in efficient data collection. The shape of the coexistence curve of the square-well fluid with short potential range is nearly cubic. In contrast, for a system with a longer potential range, the coexistence curve closely resembles a parabola, except near the critical point. The critical compressibility factor for the square-well fluids increases with increasing range. The critical behavior of the restricted primitive model was found to be consistent with the Ising universality class. The critical temperature was obtained as Tc=0.0490±0.0003 and the critical density ρc=0.070±0.005, both in reduced units. The critical temperature estimate is consistent with the recent calculation of Caillol...

Two-dimensional navier-stokes simulation of breaking waves

Abstract: Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier–Stokes equation. The numerical modeling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account such as a nonisotropic stress tensor concentrated near the interface. Results concerning the time evolution of liquid–gas interface and velocity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Breaking processes including overturning, splash-up and gas entrainment, and breaking induced vortex-like motion beneath the surface and energy dissipation, are presented and discussed. It is found that strong vorticities are generated during the breaking process, and that more than 80% of the total pre-breaking wave energy is dissipated within three wave periods. The numerical results are compared with some laboratory measurements, and a favorable agreement is found.

Direct computation of the sound generated by vortex pairing in an axisymmetric jet

Abstract: The sound generated by vortex pairing in axisymmetric jets is determined by direct solution of the compressible Navier–Stokes equations on a computational grid that includes both the near field and a portion of the acoustic far field. At low Mach number, the far-field sound has distinct angles of extinction in the range of 60°–70° from the jet's downstream axis which can be understood by analogy to axisymmetric, compact quadrupoles. As the Mach number is increased, the far-field sound takes on a superdirective character with the dominant sound directed at shallow angles to the jet's downstream axis. The directly computed sound is compared to predictions obtained from Lighthill's equation and the Kirchhoff surface method. These predictions are in good agreement with the directly computed data. The Lighthill source terms have a large spatial distribution in the axial direction necessitating the introduction of a model to describe the source terms in the region downstream of the last vortex pairing. The axial non-compactness of the quadrupole sources must be adequately treated in the prediction method.

Modeling Mixed Flow in Storm Sewers

Abstract: The blowing off of storm manhole covers may be attributed to the severe pressure transients that can occur during and after the transition from free-surface to pressurized flow in a sewer system. Observations from a physical sewer model with a submerged outlet indicate that the pressure transients were composed of an initial low frequency water hammer type pressure surge and a subsequent high frequency pressure fluctuation due to the release of trapped air at the upstream manhole. A mathematical model, which was based on the assumption of rigid water columns and a compressible air bubble, was derived to simulate the pressure transients. The frequency of pressure transients predicted by the calibrated mathematical model is in close agreement with that recorded during the laboratory experiments. The attenuation of the pressure fluctuations, however, is underestimated. This may be attributed to the superposition of various air release processes observed during the experiments and the assumption of a steady-state friction factor used in the mathematical model.

A Generalized Model for the Thermodynamic Properties of Mixtures

Abstract: A mixture model explicit in Helmholtz energy has been developed which is capable of predicting thermodynamic properties of mixtures containing nitrogen, argon, oxygen, carbon dioxide, methane, ethane, propane, n-butane, i-butane, R-32, R-125, R-134a, and R-152a within the estimated accuracy of available experimental data. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single generalized equation which is applied to all mixtures studied in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures at various compositions including dew and bubble point properties and critical points. It incorporates accurate published equations of state for each pure fluid. The estimated accuracy of calculated properties is ±0.2% in density, ±0.1 % in the speed of sound at pressures below 10 MPa, ±0.5% in the speed of sound for pressures above 10 MPa, and ±1% in heat capacities. In the region from 250 to 350 K at pressures up to 30 MPa, calculated densities are within ±0.1 % for most gaseous phase mixtures. For binary mixtures where the critical point temperatures of the pure fluid constituents are within 100 K of each other, calculated bubble point pressures are generally accurate to within ±1 to 2%. For mixtures with critical points further apart, calculated bubble point pressures are generally accurate to within ±5 to 10%.

Influence of clay fraction on pore-scale properties and hydraulic conductivity of experimentally compacted mudstones

Abstract: We report the results of a series of hydraulic conductivity tests carried out on seven natural, well-characterised specimens of London Clay mudstone. The clay fractions of the samples range from 27% to 66% and enabled a test of the influence of clay fraction on the hydraulic conductivity, pore size distribution, compressibility and specific surface area of natural mudstones. Hydraulic conductivities were determined at effective stresses between 1.5 and 33 MPa. Hydraulic conductivities of clay-rich samples (49–66% clay fraction) decreased from ∼10−11 m s−1 to ∼10−14 m s−1 over a porosity range of 48% to 25%. At a given porosity the hydraulic conductivities of two silt-rich samples (27 and 33% clay fraction) were 40–250 times greater than those of the five clay-rich samples. Variations in hydraulic conductivity are directly related to pore size distributions and are accurately predicted by a model which uses pore size distribution as its primary input. Clay-rich samples have unimodal pore size distributions with modal throat radii around 60–120 nm. Silt-rich samples have bimodal pore throat size distributions. One modal size is similar to that observed in clay-rich samples with a second modal value at 3–6 μm. Compaction under effective stresses up to 10 MPa results in the preferential collapse of larger pores, so that the rate of loss of hydraulic conductivity is greater in the silt-rich samples. Differences in hydraulic conductivity between silt-rich and clay-rich mudstones therefore decline with decreasing porosity. The range of porosity-hydraulic conductivity relationships means that hydraulic conductivity is not easily predicted from porosity alone; additional constraining parameters such as grain and pore size distributions are required.

A Physical Introduction to Fluid Mechanics

Abstract: Fluid Statics. Introduction to Fluid Motion I. Introduction to Fluid Motion II. Equations of Motion in Integral Form. Differential Equations of Motion. Incompressible, Irrotational Flows. Dimensional Analysis. Viscous Internal Flows. Viscous External Flows. Open Channel Flow. Compressible Flow. Turbomachines. Environmental Fluid Mechanics. Historical Notes. Appendices. Answers to Selected Problems. Index.

Analysis of singular perturbations on the Brinkman problem for fictitious domain models of viscous flows

Abstract: We show the justification of a formulation by fictitious domain to study incompressible viscous flows inside fluid–porous–solid systems by using the Brinkman model in a heterogeneous fictitious porous medium covering the whole auxiliary domain. The singular perturbations of this problem are analysed when the permeability of the medium tends to infinity in the fluid domain and/or to zero in the solid domain. In addition, the viscosity inside the solid body may possibly tend to infinity. The strong convergence of the solutions is established. Some error estimates on the solution are derived as a function of the penalty parameter. The error bound on the resulting applied force for the flow around a bluff obstacle is also given. Copyright © 1999 John Wiley & Sons, Ltd.

An explicit finite element algorithm for convection heat transfer problems

Abstract: A finite element algorithm is presented for the simulation of steady incompressible fluid flow with heat transfer using triangular meshes. The continuity equation is modified by employing the artificial compressibility concept to provide coupling between the pressure and velocity fields of the fluid. A standard Galerkin finite element method is used for spatial discretization and an explicit multistage Runge‐Kutta scheme is used to march in the time domain. The resulting procedure is stabilized using an artificial dissipation technique. To demonstrate the performance of the proposed algorithm a wide range of test cases is solved including applications with and without heat transfer. Both natural and forced convection applications are studied.

Surface Activity−Compressibility Relationship of Proteins at the Air−Water Interface

Abstract: The surface concentration versus surface pressure relationship of 39 proteins under dynamic adsorption conditions at the air−water interface has been studied. It was found that the slope of these plots, ϑ (in ergs/mg), which is defined as surface activity, showed a positive correlation (r = 0.86) with the adiabatic compressibility of the proteins. The linear regression line passed almost through the origin, suggesting that, theoretically, rigid and inflexible globular proteins would not be able to reduce the surface tension of water even at a saturated monolayer coverage. Some empirical equations were derived for the estimation of the ϑ values of unknown proteins on the basis of their amino acid compositions as well as secondary structure contents. The compressibility values predicted from these calculated ϑ values agreed with the experimental values. The experimental ϑ values of globular proteins also showed a negative linear correlation (r = 0.77) with the ΔG° of thermal unfolding of the proteins. The r...

Compressibility and Fractal Dimension of Fine Coal Particles in Relation to Pore Structure Characterisation Using Mercury Porosimetry

Abstract: Mercury porosimetry has been applied to characterize the pore structure of fine coals particles. Interparticle voids and compressibility effects on the mercury intrusion data were examined. It is found that coal compressibility has a significant effect on mercury porosimetry data when pressure P > 20 MPa. The compressibility of the two coals used was determined to be 3.13 x 10(-10) m(2) N-1 and 2.50 x 10(-10) m(2) N-1 for CA and GO coals, respectively. Fractal dimension analysis provides a fingerprint to distinguish the effect of coal compression from the pore filling process during mercury intrusion. It is shown that fractal dimension can be evaluated from the compressibility corrected pore volume data. Results from the present study suggest that statistic self-similarity of the fractal dimension perspective is limited by certain artificial effects, such as crushing and grinding. Different surface irregularities exist over different pore size ranges, and a single fractal dimension value can only be used to describe the surface irregularity within a limited pore size range. The average fractal dimensions in the pore size range of 6-60 nm were found to be 2.71 and 2.43 for CA and GO coals, respectively.

Comparative compressibilities of calcite-structure carbonates; deviations from empirical relations

Abstract: Room-temperature volume measurements of the complete set of calcite-structure carbonates in the pressure range 0-8.1 GPa revealed systematic differences in compressibilities that depend on cation type, resulting in significant deviations from empirical relations of an inverse linear correlation between K o and V o . The bulk modulus for MgCO 3 lies approximately 18 GPa below the trend for the 3d transition metal carbonates, which show an expected inverse linear correlation of bulk modulus with ambient cell volume (and M-O bond length). The bulk modulus of CdCO 3 , whose M-O bond length and cell volume are only slightly smaller than those of CaCO 3 , lies up to 10 GPa above the trend of the 3d transition metal carbonates and about 30 GPa above that of calcite. These deviations in compressibility trends as a function of cell volume (or M-O bond length) are expressed as differences in a axis compressibility but not in c axis compressibility, which shows a nearly linear increase with M-O distance. Hence, systematic behavior is apparently limited to subsets of carbonates in which metal ions share the same valence electron character (i.e., s vs. 3d vs. 4d) and is primarily attributed to unexpected compressibility differences along the a axis. Crystal-field effects, beyond those reflected in the M-O distances, cannot account for the observed compressibilities. Nonbonded interactions also fail to explain the deviations from predicted trends. Variations of electronegativity and vibrational frequency with ionic radius for the relevant metal ions show differences that are qualitatively similar to the observed trends of bulk modulus, suggesting that differences in bonding character may contribute to the different behaviors among the subsets of calcite-structure carbonates. However, it is most likely that a combination of factors is necessary to account fully for the observed behavior.

Maxwell fluid suction flow in a channel

Abstract: Two-dimensional, steady and incompressible suction flow of the upper-convected Maxwell fluid in a porous surface channel has been studied The combined effects of viscoelasticity and inertia are considered A similarity solution is assumed, resulting in a nonlinear system of ODEs that describes the relations between the two velocity components, the three deviatoric stresses and the pressure gradient This system is solved using two methods: an analytical solution, based on a power series method in terms of the transverse coordinate across the channel, and a fourth-order Runge–Kutta numerical integration scheme We first find the existing Newtonian flow solutions for suction and injection For the Maxwell fluid, the solutions of the power series and the numerical integration are in complete agreement in the range of Reynolds and Deborah numbers 0 ≤ Re ≤ 30 and 0 ≤ De ≤ 03 They show that the suction flow exhibits a flattening of the longitudinal velocity profile near the centerline and the establishment of boundary layers near the porous surfaces as Reynolds number increases It is also observed that when Deborah number increases, with a fixed Reynolds number, viscoelasticity affects the velocity profiles in the same way as inertia in a Newtonian fluid The application of the self-similar solution to the injection flow of the Maxwell fluid is also discussed

Finite Elastic Deformations in Liquid-Saturated and Empty Porous Solids

Abstract: Based on the Theory of Porous Media (TPM), a formulation of a fluid-saturated porous solid is presented where both constituents, the solid and the fluid, are assumed to be materially incompressible. Therefore, the so-called point of compaction exists. This deformation state is reached when all pores are closed and any further volume compression is impossible due to the incompressibility constraint of the solid skeleton material. To describe this effect, a new finite elasticity law is developed on the basis of a hyperelastic strain energy function, thus governing the constraint of material incompressibility for the solid material. Furthermore, a power function to describe deformation dependent permeability effects is introduced.

Magnetic reconnection with Sweet-Parker characteristics in two-dimensional laboratory plasmas

Abstract: Magnetic reconnection has been studied experimentally in a well-controlled, two-dimensional laboratory magnetohydrodynamic plasma. The observations are found to be both qualitatively and quantitatively consistent with a generalized Sweet-Parker model which incorporates compressibility, downstream pressure, and the effective resistivity. The latter is significantly enhanced over its classical values in the collisionless limit. This generalized Sweet-Parker model also applies to the case in which a unidirectional, sizable third magnetic component is present.

Inclusion of Thermobaricity in Isopycnic-Coordinate Ocean Models

Abstract: Buoyancy anomalies caused by thermobaricity, that is, the modulation of seawater compressibility by potential temperature anomalies, underlie a long-standing argument against the use of potential-density-framed numerical models for realistic circulation studies. The authors show that this problem can be overcome by relaxing the strict correspondence between buoyancy and potential density in isopycnic-coordinate models. A parametric representation of the difference between the two variables is introduced in the form of a ‘‘virtual potential density,’’ which can be viewed as the potential density that would be computed from the in situ conditions using the compressibility coefficient for seawater of a fixed (but representative) salinity and potential temperature. This variable is used as a basis for effective dynamic height computations in the dynamic equations, while the traditionally defined potential density may be retained as model coordinate. The conservation properties of the latter assure that adiabatic transport processes in a compressibility-compliant model can still be represented as exactly two-dimensional. Consistent with its dynamic significance, the distribution of virtual potential density is found to determine both the local static stability and, to a lesser degree, the orientation of neutrally buoyant mixing surfaces. The paper closes with a brief discussion of the pros and cons of replacing potential density by virtual potential density as vertical model coordinate.

Progress in Favre-Reynolds Stress Closures for Compressible Flows

Abstract: A closure for the compressible portion of the pressure-strain covariance is developed. It is shown that, within the context of a pressure-strain closure assumption linear in the Reynolds stresses, an expression for the pressure-dilatation can be used to construct a representation for the pressure-strain. Additional closures for the unclosed terms in the Favre–Reynolds stress equations involving the mean acceleration are also constructed. The closures accommodate compressibility corrections depending on the magnitude of the turbulent Mach number, the mean density gradient, the mean pressure gradient, the mean dilatation, and, of course, the mean velocity gradients. The effects of the compressibility corrections on the Favre–Reynolds stresses are consistent with current DNS results. Using the compressible pressure-strain and mean acceleration closures in the Favre–Reynolds stress equations an algebraic closure for the Favre–Reynolds stresses is constructed. Noteworthy is the fact that, in the absence of mean velocity gradients, the mean density gradient produces Favre–Reynolds stresses in accelerating mean flows. Computations of the mixing layer using the compressible closures developed are described. Favre–Reynolds stress closure and two-equation algebraic models are compared to laboratory data for the mixing layer. Experimental data from diverse laboratories for the Favre–Reynolds stresses appears inconsistent and, as a consequence, comparison of the Reynolds stress predictions to the data is not conclusive. Reductions of the kinetic energy and the spread rate are consistent with the sizable decreases seen in these classes of flows.

Change of Compressiblity at the Glass Transition and Prigogine-Defay Ratio in ZrTiCuNiBe Alloys

Abstract: The change of the compressibility at the glass transition Tg is evaluated from pressure experiments in the liquid and the glassy state of the ZrTiCuNiBe bulk metallic glass forming system. Via the enthalpy recovery method, we derive an increase of Tg with pressure of 3.6 K/GPa. Comparing the changes of the compressibility, the specific heat capacity, and the thermal expansion coefficient at Tg, we estimate for the first time a Prigogine-Defay ratio in metallic systems. This ratio is about 2.4 for the present alloy and compares well with known nonmetallic glass forming systems.

A first-order model for bubble dynamics in a compressible viscoelastic liquid

Abstract: The radial dynamics of a spherical bubble in a compressible viscoelastic liquid is studied by means of a simplified singular-perturbation method to first-order in the bubble-wall Mach number. The three-parameter linear Oldroyd model is adopted to describe the viscoelastic properties of the liquid. The equation of motion for the bubble radius and the pressure equation are derived and numerical calculations are conducted for the case of bubble collapse in a constant-pressure field. It is concluded that the rheology of the liquid strongly influence the behaviour of bubbles only for values of the Reynolds number ( Re =R 0 p ∞ ρ ∞ /η where R 0 is the initial radius, p ∞ is the undisturbed liquid pressure, ρ ∞ is the liquid density and η is the liquid viscosity) smaller than 10 2 while for Re ≥ 10 2 , sound emission is the main damping mechanism in spherical bubble dynamics. In both cases, the 1/ r law of pressure attenuation through the liquid is not affected by the viscoelastic properties of the liquid. The effect of polymer additives on spherical bubble collapse is also discussed.