Showing papers on "Compressibility published in 2013"

Existence of a Weak Solution to a Nonlinear Fluid–Structure Interaction Problem Modeling the Flow of an Incompressible, Viscous Fluid in a Cylinder with Deformable Walls

Abstract: We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier–Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid–structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916–6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk–Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.

Structural change in molten basalt at deep mantle conditions

Abstract: The structure of molten basalt up to 60 GPa by means of in situ X-ray diffraction is described, with the coordination of silicon increasing from four under ambient conditions to six at 35 GPa, and subsequent reduced melt compressibility, which seems to affect siderophile-element partitioning Chrystele Sanloup and co-authors report on the structure of molten basalt at deep mantle conditions determined using in situ X-ray diffraction experiments in laser-heated diamond anvil cells They find that silicon coordination increases from 4 at ambient conditions to 6 at a pressure of 35 GPa, with the compressibility of the melt becoming lower above this transition Given that this pressure coincides with a marked change in the pressure evolution of nickel partitioning between molten iron and molten silicates, the authors conclude that melt compressibility may control siderophile-element partitioning These findings provide data that can be incorporated into quantitative models of the behaviour of silicate liquids deep in the Earth's mantle Silicate liquids play a key part at all stages of deep Earth evolution, ranging from core and crust formation billions of years ago to present-day volcanic activity Quantitative models of these processes require knowledge of the structural changes and compression mechanisms that take place in liquid silicates at the high pressures and temperatures in the Earth’s interior However, obtaining such knowledge has long been impeded by the challenging nature of the experiments In recent years, structural and density information for silica glass was obtained at record pressures of up to 100 GPa (ref 1), a major step towards obtaining data on the molten state Here we report the structure of molten basalt up to 60 GPa by means of in situ X-ray diffraction The coordination of silicon increases from four under ambient conditions to six at 35 GPa, similar to what has been reported in silica glass1,2,3 The compressibility of the melt after the completion of the coordination change is lower than at lower pressure, implying that only a high-order equation of state can accurately describe the density evolution of silicate melts over the pressure range of the whole mantle The transition pressure coincides with a marked change in the pressure-evolution of nickel partitioning between molten iron and molten silicates, indicating that melt compressibility controls siderophile-element partitioning

On a fractional Zener elastic wave equation

Abstract: This survey concerns a causal elastic wave equation which implies frequency power-law attenuation. The wave equation can be derived from a fractional Zener stress-strain relation plus linearized conservation of mass and momentum. A connection between this four-parameter fractional wave equation and a physically well established multiple relaxation acoustical wave equation is reviewed. The fractional Zener wave equation implies three distinct attenuation power-law regimes and a continuous distribution of compressibility contributions which also has power-law regimes. Furthermore it is underlined that these wave equation considerations are tightly connected to the representation of the fractional Zener stress-strain relation, which includes the spring-pot viscoelastic element, and by a Maxwell-Wiechert model of conventional springs and dashpots. A purpose of the paper is to make available recently published results on fractional calculus modeling in the field of acoustics and elastography, with special focus on medical applications.

A Continuum Model for Deformable, Second Gradient Porous Media Partially Saturated with Compressible Fluids

Abstract: In this paper a general set of equations of motion and duality conditions to be imposed at macroscopic surfaces of discontinuity in partially saturated, solid-second gradient porous media are derived by means of the Least Action Principle. The need of using a second gradient (of solid displacement) theory is shown to be necessary to include in the model effects related to gradients of porosity. The proposed governing equations include, in addition to balance of linear momentum for a second gradient porous continuum and to balance of water and air chemical potentials, the equations describing the evolution of solid and fluid volume fractions as supplementary independent kinematical fields. The presented equations are general in the sense that they are all written in terms of a macroscopic potential ψ which depends on the introduced kinematical fields and on their space and time derivatives. These equations are suitable to describe the motion of a partially saturated, second gradient porous medium in the elastic and hyper-elastic regime. In the second part of the paper an additive decomposition for the potential ψ is proposed which allows for describing some particular constitutive behaviours of the considered medium. While the potential associated to the solid matrix deformation is chosen in the form proposed by Cowin and Nunziato in [15], [33] and the potentials associated to water and air compressibility are chosen to assume a simple quadratic form, the macroscopic potentials associated to capillarity phenomena between water and air have to be derived with some additional considerations. In particular, two simple examples of microscopic distributions of water and air are considered: that of spherical bubbles and that of coalesced tubes of bubbles. Both these cases are suitable to describe capillarity phenomena in porous media which are close to the saturation state. Finally, an example of a simple microscopic distribution of water and air giving rise to a macroscopic capillary potential depending on the second gradient of fluid displacement is presented, showing the need of a further generalization of the proposed theoretical framework accounting for fluid second gradient effects.

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Abstract: Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a "backward flow" is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.

Extended lattice Boltzmann method for numerical simulation of thermal phase change in two-phase fluid flow.

Abstract: In this article, a method based on the multiphase lattice Boltzmann framework is presented which is applicable to liquid-vapor phase-change phenomena. Both liquid and vapor phases are assumed to be incompressible. For phase changes occurring at the phase interface, the divergence-free condition of the velocity field is no longer satisfied due to the gas volume generated by vaporization or fluid volume generated by condensation. Thus, we extend a previous model by a suitable equation to account for the finite divergence of the velocity field within the interface region. Furthermore, the convective Cahn-Hilliard equation is extended to take into account vaporization effects. In a first step, a D1Q3 LB model is constructed and validated against the analytical solution of a one-dimensional Stefan problem for different density ratios. Finally the model is extended to two dimensions (D2Q9) to simulate droplet evaporation. We demonstrate that the results obtained by this approach are in good agreement with theory.

Molecular Understanding of the Compaction Behavior of Indomethacin Polymorphs

Abstract: Polymorphs enable us to gain molecular insights into the compaction behavior of pharmaceutical powders. Two polymorphs (α and γ) of indomethacin (IMC) were investigated for in-die and out-of-die compaction behavior using compressibility, tabletability and compactibility (CTC) profile, stress–strain relationship, and Heckel, Kawakita and Walker equations. Compaction studies were performed on a fully instrumented rotary tabletting machine. CTC analysis revealed that the γ-form has increased compressibility while the α-form showed greater compactibility. The α-form also showed increased tabletability over the γ-form at all the compaction pressures. Lower values of Py (Heckel parameter) and 1/b (Kawakita parameter) indicated increased deformation behavior of γ-form. Stress–strain analysis also supports the increased compressibility of γ-form. In addition, Walker analysis showed higher compressibility coefficient (W) for α-form, consistent with its greater tabletability. Thus, tabletability of IMC polymorphs w...

Rock deformation models and fluid leak-off in hydraulic fracturing

Abstract: SUMMARY Fluid loss into reservoir rocks during hydraulic fracturing is modelled via a poro-elastoplastic pressure diffusion equation in which the total compressibility is a sum of fluid, rock and pore space compressibilities. Inclusion of pore compressibility and porosity-dependent permeability in the model leads to a strong pressure dependence of leak-off (i.e. drainage rate). Dilation of the matrix due to fluid invasion causes higher rates of fluid leak-off. The present model is appropriate for naturally fractured and tight gas reservoirs as well as for soft and poorly consolidated formations whose mechanical behaviour departs from simple elastic laws. Enhancement of the leak-off coefficient by dilation, predicted by the new model, may help explain the low percentage recovery of fracturing fluid (usually between 5 and 50 per cent) in shale gas stimulation by hydraulic fracturing.

Serrin-Type Blowup Criterion for Full Compressible Navier–Stokes System

Abstract: The authors establish a Serrin-type blowup criterion for the Cauchy problem of the three-dimensional full compressible Navier–Stokes system, which states that a strong or smooth solution exists globally, provided that the velocity satisfies Serrin’s condition and that the temporal integral of the maximum norm of the divergence of the velocity is bounded. In particular, this criterion extends the well-known Serrin’s blowup criterion for the three-dimensional incompressible Navier–Stokes equations to the three-dimensional full compressible system and is just the same as that of the barotropic case.

Possible relation of water structural relaxation to water anomalies

Abstract: The anomalous behavior of thermodynamic response functions is an unsolved problem in the physics of water. The mechanism that gives rise to the dramatic indefinite increase at low temperature in the heat capacity, the compressibility, and the coefficient of thermal expansion, is unknown. We explore this problem by analyzing both new and existing experimental data on the power spectrum S(Q, ω) of bulk and confined water at ambient pressure. When decreasing the temperature, we find that the liquid undergoes a structural transformation coinciding with the onset of an extended hydrogen bond network. This network onset seems to give rise to the marked viscoelastic behavior, consistent with the interesting possibility that the sound velocity and response functions of water depend upon both the frequency and wave vector.

Uniform electron gas at finite temperatures

Abstract: We calculate the free energy of the quantum uniform electron gas for temperatures from near 0 to 100 times the Fermi energy, approaching the classical limit. An extension of the Vashista-Singwi theory to finite temperatures and a self-consistent compressibility sum rule is presented. Comparisons are made to other local-field correction methods, as well as recent quantum Monte Carlo simulation and classical map-based results. Accurate fits to the exchange-correlation free energy from both theory and simulation are given for future practical applications.

On boundary layer flow of a Sisko fluid over a stretching sheet

Abstract: In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions. Keywords: Sisko fluid, boundary layer flow, non-linear stretching sheet, analytical solution Quaestiones Mathematicae 36(2013), 137–151

On thermodynamics in the primary power conversion of oscillating water column wave energy converters

Abstract: The paper presents an investigation to the thermodynamics of the air flow in the air chamber for the oscillating water column wave energy converters, in which the oscillating water surface in the water column pressurizes or de-pressurises the air in the chamber. To study the thermodynamics and the compressibility of the air in the chamber, a method is developed in this research: the power take-off is replaced with an accepted semi-empirical relationship between the air flow rate and the oscillating water column chamber pressure, and the thermodynamic process is simplified as an isentropic process. This facilitates the use of a direct expression for the work done on the power take-off by the flowing air and the generation of a single differential equation that defines the thermodynamic process occurring inside the air chamber. Solving the differential equation, the chamber pressure can be obtained if the interior water surface motion is known or the chamber volume (thus the interior water surface motion) if the chamber pressure is known. As a result, the effects of the air compressibility can be studied. Examples given in the paper have shown the compressibility, and its effects on the power losses for large oscillating water column devices.

Compressibility Considerations for Kappa-Omega Turbulence Models in Hypersonic Boundary Layer Applications

Abstract: The ability of kappa-omega models to predict compressible turbulent skin friction in hypersonic boundary layers is investigated. Although uncorrected two-equation models can agree well with correlations for hot-wall cases, they tend to perform progressively worse - particularly for cold walls - as the Mach number is increased in the hypersonic regime. Simple algebraic models such as Baldwin-Lomax perform better compared to experiments and correlations in these circumstances. Many of the compressibility corrections described in the literature are summarized here. These include corrections that have only a small influence for kappa-omega models, or that apply only in specific circumstances. The most widely-used general corrections were designed for use with jet or mixing-layer free shear flows. A less well-known dilatation-dissipation correction intended for boundary layer flows is also tested, and is shown to agree reasonably well with the Baldwin-Lomax model at cold-wall conditions. It exhibits a less dramatic influence than the free shear type of correction. There is clearly a need for improved understanding and better overall physical modeling for turbulence models applied to hypersonic boundary layer flows.

Mass and Volume Conservation in Phase Field Models for Binary Fluids

Abstract: The commonly used incompressible phase field models for non-reactive, binary fluids, in which the Cahn-Hilliard equation is used for the transport of phase variables (volume fractions), conserve the total volume of each phase as well as the material volume, but do not conserve the mass of the fluid mixture when densities of two components are different. In this paper, we formulate the phase field theory for mixtures of two incompressible fluids, consistent with the quasi-compressible theory [28], to ensure conservation of mass and momentum for the fluid mixture in addition to conservation of volume for each fluid phase. In this formulation, the mass-average velocity is no longer divergence-free (solenoidal) when densities of two components in the mixture are not equal, making it a compressible model subject to an internal con-straint. In one formulation of the compressible models with internal constraints (model 2), energy dissipation can be clearly established. An efficient numerical method is then devised to enforce this compressible internal constraint. Numerical simulations in confined geometries for both compressible and the incompressible models are carried out using spatially high order spectral methods to contrast the model predictions. Numerical comparisons show that (a) predictions by the two models agree qualitatively in the situation where the interfacial mixing layer is thin; and (b) predictions differ significantly in binary fluid mixtures undergoing mixing with a large mixing zone. The numerical study delineates the limitation of the commonly used incompressible phase field model using volume fractions and thereby cautions its predictive value in simulating well-mixed binary fluids.

Modeling gas-particle two-phase flows with complex and moving boundaries using DEM-CFD with an immersed boundary method

Abstract: An immersed boundary method (IBM) has been developed and incorporated into the coupled discrete element method and computational fluid dynamics (DEM-CFD) approach to model particulate systems consisting of a compressible gas and solid particles with complex and/or moving boundaries. The IBM is used to deal with the interaction between gas and complex and moving boundaries by using simple rectangular grids to discretize the fluid field. The developed method has been applied to simulate some typical powder handling processes (e.g., gas fluidization with an immersed tube, segregation in a vertically vibrated bed, and pneumatic conveying). Good agreement is achieved between the present simulation results and the experimental ones reported in the literature. It has been demonstrated that the capacity of DEM-CFD is enhanced with the incorporation of IBM, which can be used to simulate a wide range of problems that could not be handled with the conventional DEM-CFD method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1075–1087, 2013