Fluid Mass Density Research Articles

Finite energy solutions to the isentropic Euler equations with geometric effects

Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical symmetry when the origin r = 0 is included. These partial differential equations are hyperbolic, but fail to be strictly hyperbolic when the fluid mass density vanishes and vacuum is reached. Furthermore, when geometric effects are taken into account, the sup-norm of solutions can not be controlled since there exist no invariant regions. To overcome these difficulties and to establish an existence theory for solutions with arbitrarily large amplitude, we search for solutions with finite mass and total energy. Our strategy of proof takes advantage of the particular structure of the Euler equations, and leads to a versatile framework covering general compressible fluid problems. We establish first higher-integrability estimates for the mass density and the total energy. Next, we use arguments from the theory of compensated compactness and Young measures, extended here to sequences of solutions with finite mass and total energy. The third ingredient of the proof is a characterization of the unbounded support of entropy admissible Young measures. This requires the study of singular products involving measures and principal values.

Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows

Within this paper the so-called artificial added mass effect is investigated which is responsible for devastating instabilities within sequentially staggered Fluid–structure Interaction (FSI) simulations where incompressible fluids are considered. A discrete representation of the added mass operator M A is given and ‘instability conditions’ are evaluated for different temporal discretisation schemes. It is proven that for every sequentially staggered scheme and given spatial discretisation of a problem, a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable. The analysis is quite general and does not depend upon the particular spatial discretisation schemes used. However here special attention is given to stabilised finite elements employed on the fluid partition. Numerical investigations further highlight the results.

Monte Carlo simulation results of some basic physical properties of Lennard–Jones fluids

Monte Carlo simulation is carried out for Lennard–Jones fluids for finding some of their basic physical properties under wide pressure and temperature changes. It is found from this simulation that for a given bulk fluid temperature the fluid mass density is linearly increased with the increase of fluid pressure, while for a given fluid pressure, the fluid mass density is linearly reduced with the increase of bulk fluid temperature. On the other hand, it is found that for a given fluid mass density the variation of fluid pressure is directly proportional to the variation of bulk fluid temperature. These findings support the corresponding results found and the statement made in the paper in Ref. [Y.B. Zhang, Industrial Lubrication and Tribology 58 (2006) 2], on which the theory of fluid shear strength is based.

Formation of macroscopic structures in partially ionized magnetoplasmas

It is shown that the governing nonlinear equations for a partially ionized magnetoplasma admit large-scale (in comparison with the ion skin depth) structures on a scale size that is controlled by the neutral fluid mass density. Implications of our investigation to macroscopic magnetic field structures in the interstellar plasma are discussed.

The influence of grains on the propagation and structure of C-type shock waves in interstellar molecular clouds

Grains contribute only about 1% to the mass of material in the interstellar medium (ISM). However, in dark clouds, where the charged component of the grains is believed to be a significant fraction of the total and the degree of ionization of the gas is low, the mass density of the charged grains is expected to greatly exceed that of the gaseous component. By the term ‘grains’, we understand both bulk materials, such as graphite or silicates, and large organic molecules (LOM), which may comprise polycyclic aromatic hydrocarbons. Grains are known to be important as both sources and sinks of molecules, notably H2. In the context of dynamics of the ISM, the charged grains may also be important for the modes of shock propagation. In particular, the formation of steady-state C-type shock waves is constrained by the requirement that the magnetosonic speed in the charged fluid, given (at zero temperature) by $$ v_{ims} = \frac{B} {{\left( {4\pi \rho _c } \right)^{\frac{1} {2}} }}, $$ (1) should exceed the shock speed, v s. In (1), B is the magnetic induction in the preshock gas, perpendicular to the direction of propagation of the shock wave, and ρc is the mass density of the charged fluid. As the mass density of charged grains dominates ρc in dark clouds, the fraction of the grains which is charged is an important parameter.

Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method

This paper reports the computer simulation of a flapping flexible filament in a flowing soap film using the immersed boundary method. Our mathematical formulation includes filament mass and elasticity, gravity, air resistance, and the two wires that bound the flowing soap film. The incompressible viscous Navier–Stokes equations, which are used to describe the motion of the soap film and filament in our formulation, are discretized on a fixed uniform Eulerian lattice while the filament equations are discretized on a moving Lagrangian array of points which do not necessarily coincide with the fixed Eulerian mesh points of the fluid computation. The interaction between the filament and the soap film is handled by a smoothed approximation to the Dirac delta function. This delta function approximation is used not only to interpolate the fluid velocity and to apply force to the fluid (as is commonly done in immersed boundary computations), but also to handle the mass of the filament, which is represented in our calculation as delta function layer of fluid mass density supported along the immersed filament. Because of this nonuniform density, we need to use a multigrid method for solving the discretized fluid equations. This replaces the FFT-based method that is commonly used in the uniform-density case. Our main results are as follows. (i) The sustained flapping of the filament only occurs when filament mass is included in the formulation of the model; within a certain range of mass, the more the mass of the filament, the bigger the amplitude of the flapping. (ii) When the length of filament is short enough (below some critical length), the filament always approaches its straight (rest) state, in which the filament points downstream; but when the length is larger, the system is bistable, which means that it can settle into either state (rest state or sustained flapping) depending on the initial conditions. This numerical result we observed in computer simulation is the same as that of the laboratory experiment even though the Reynolds number of the computations is lower than that of the laboratory experiment by two orders of magnitude.

Review of Environmental fluid mechanics by Hillel Rubin and Joseph Atkinson

Review of <i>Environmental fluid mechanics</i> by Hillel Rubin and Joseph Atkinson

Influence of coaxial-rod- and coaxial-blade-type baffles on bed expansion in gas–solid fluidization

Bed expansion data were obtained for unbaffled and two different types of baffled (coaxial rod and coaxial blade) gas–solid fluidized beds for varying operating parameters: fluid mass velocity, particle size, density and initial static bed heights. Correlations have been developed for the prediction of bed expansion. For this, the values of minimum fluidization mass velocity ( G mf) and settling mass velocity ( G S, considered as hindered settling) have been calculated with the help of available equations. The correlations developed are modified versions of those of Beranek and Sokol, where mass velocity ratio ( G R) has been used in place of velocity ( U): 1/R=f(G R ), where G R =(G f −G mf )/(G s −G mf ) Here, the entire range of G R has been divided into two regimes: 0< G R≤0.15 and 0.15< G R≤1.0.

The onset of Rayleigh–Taylor instabilities in magnetized partially ionized dense dusty plasmas

Onset criteria for unstable Rayleigh–Taylor modes in partially ionized dusty plasmas are derived for different density characteristics of the neutral gas and dust components across the interface where the modes are excited. The influences of a homogeneous equilibrium magnetic field and magnetic perturbations are taken into account. Dust–neutral gas collisions limit the range of unstable wave lengths. Different from (magneto)hydrodynamic modes in one-component neutral fully ionized fluids, increase of the mass density of the heavier fluid does not tend to a destabilization of all excited modes in the stratified fluid layer.

On the effective inertial mass density of a dissipative fluid

It is shown that the effective inertial mass density of a dissipative fluid just after leaving the equilibrium, on a time scale of the order of relaxation time, reduces by a factor which depends on dissipative variables. Prospective applications of this result to cosmological and astrophysical scenarios are discussed.

Instabilities in a Nonuniform Partially Ionized Isothermal Magnetoplasma

Electromagnetic modes and associated instabilities in a partially ionized, self-gravitating, nonuniform, isothermal, initially static magnetoplasma are theoretically investigated. The effects of the neutral fluid dynamics, the inhomogeneities in the external magnetic field and the background plasma number density, the self-gravitational field, the drag forces, the ionization and recombination, etc., on the dispersion properties of electromagnetic waves for different frequency regimes of interest are examined. It is shown that new types of instabilities, the first type of which is due to the combined effects of the self-gravitational and the drag forces, the second type of which is due to the combined effects of the plasma and the neutral fluid dynamics, and the third type of which is due to the drifting of electrons, exist in such a magnetoplasma. Furthermore, the effects of the external magnetic field and its inhomogeneity, the neutral fluid temperature, collisions of electrons or ions with neutrals, and the ionization play the stabilizing role, whereas the effects of the neutral fluid mass density, the plasma number density inhomogeneity, collisions of neutrals with electrons or ions, and the recombination play the destabilizing role. It is suggested that such instabilities could be responsible for the fragmentation of molecular clouds into substructures that in turn may fail to be supported against the self-gravity and may collapse to form the stars.

Instabilities of self-gravitating dusty clouds in magnetized plasmas

A rigorous theoretical investigation has been made of electromagnetic modes and associated filamentational instabilities in a nonuniform, partially ionized, self-gravitating, dusty magnetoplasma, taking into account the effects of the neutral fluid dynamics, inhomogeneities in the external magnetic field and the plasma density, the drag forces, the ionization and recombination, etc. It is found that there exist two new types of filamentational instabilities; one type is due to the combined effects of collisions of dust particles or ions with stationary neutrals and the self-gravitational force, and the other type is due to the combined effects of the dusty plasma and the neutral fluid dynamics. Furthermore, the effects of the external magnetic field and its inhomogeneity, the neutral fluid temperature, collisions of dust particles with neutrals, and the ionization play the stabilizing role, whereas the effects of the neutral fluid mass density, the plasma number density inhomogeneity, collisions of ions with neutrals, and the recombination play the destabilizing role. The newly found instabilities may be responsible for the formation of stars in galaxies via fragmentation or filamentation of interstellar dense molecular clouds.

Gravitational waves around a naked singularity: Odd-parity perturbation of Lemaître-Tolman-Bondi space-time

The motion of a spherical dust cloud is described by the Lemaitre-Tolman-Bondi solution and is completely specified by initial values of distributions of the rest mass density and specific energy of the dust fluid. From generic initial conditions of this spherically symmetric collapse, there appears a naked singularity at the symmetric center in the course of the gravitational collapse of the dust cloud. So this might be a counter example to the cosmic censorship hypothesis. To investigate the genericity of this example, we examine the stability of the `nakedness' of this singularity against odd-parity modes of non-spherical linear perturbations for the metric, i.e., linear gravitational waves. We find that the perturbations do not diverge but are well-behaved even in the neighborhood of the central naked singularity. This means that the naked singularity formation process is marginally stable against the odd-parity modes of linear gravitational waves.

Scaling of transient hydrodynamic interactions in hard sphere suspensions

Analyses of retarded hydrodynamic interactions between pairs of spheres, computed in Fourier space over the full frequency range, have been performed to investigate scaling of the time-dependent self-diffusion coefficient ${D}_{s}(t,\ensuremath{\varphi}).$ It appears that up to intermediate volume fractions $(\ensuremath{\varphi}l~0.15)$ ${D}_{s}(t,\ensuremath{\varphi})$ shows scaling behavior when both the characteristic time \ensuremath{\tau} is appropriately rescaled and ${D}_{s}(t,\ensuremath{\varphi})$ is normalized by the short-time self-diffusion coefficient of the suspension ${D}_{s}{=D}_{0}(1\ensuremath{-}1.83\ensuremath{\varphi}).$ The rescaled characteristic time is based on matching of the long-time tail of the velocity autocorrelation function with the single-particle result. Scaling is observed for a range of particle to fluid density ratios (for $0l~\ensuremath{\sigma}l~2,$ $\ensuremath{\sigma}={\ensuremath{\rho}}_{s}/\ensuremath{\rho},$ with ${\ensuremath{\rho}}_{s}$ the particle density and \ensuremath{\rho} the fluid mass density). Scaling for higher volume fractions, which is already present when the characteristic time is computed by optimal fitting, might be improved by including three-particle hydrodynamic interactions. The present results support the conclusion that modification of correlation functions in hard sphere suspensions, in order to include effects of two-particle hydrodynamic interactions, is already sufficient to show the existence of scaling of ${D}_{s}(t,\ensuremath{\varphi}).$

Study on the Vibrational Characteristics of a Tube Array Caused by Two-Phase Flow. Part II: Fluidelastic Vibration

Fluidelastic vibration of tube arrays caused by two-phase flow has been studied before. The critical flow velocity is usually estimated with a simple Connors-type criterion which is based on an average flow velocity, an average fluid mass density and damping in two-phase flow. However, there is no explanation of why this simple criterion is applicable or how fluidelastic instability occurs in two-phase flow. This paper presents experimental results on the fluidelastic vibration caused by air-water flow and by steam-water two-phase flow in condition of up to 7·0 MPa pressure and temperature reaching 284°C. A new criterion, based on an assumption of energy balance per cycle of oscillation, is introduced using the "true" flow velocity. However, comparison with the experimental data indicates that, in the slug or froth flow regimes, the speed of the intermittently rising slugs, introduced in Part I of this study, should be used; hence, a new modified criterion for the slug and froth flow regimes is derived. In addition, the new criterion is compared with the usual Connors-type criterion which greatly depends on the estimation of the damping in two-phase flow. The agreement between the two criteria is found to be within the uncertainty introduced by the variance in the unknown parameters in the Connors criterion.

Study on the Vibrational Characteristics of a Tube Array Caused by Two-Phase Flow—Part 2: Fluidelastic Vibration

Fluidelastic vibration of a tube array caused by two-phase flow has been reported in some papers. The critical flow velocity is usually estimated with a simple Connors-type criterion which is based on average flow velocity, average fluid mass density and damping in two-phase flow. However, there is no explanation why this simple criterion can be used or how the fluidelastic instability occurs by two-phase flow. This paper shows the experimental results on the fluidelastic vibration both by air-water two-phase flow and by steam-water flow in the condition of up to 7.0 MPa in pressure and to 284°C in temperature, and a new criterion based on an assumption of energy balance is here introduced using a “true” flow velocity. However, the comparison with the experimental data indicates that an intermittently rising slug speed, which has been introduced in Part 1, in slug or in froth flow region, should be used, and a modified new criteria for slug or froth flow region is derived. In addition, the new criteria is compared with the usual Connors-type criteria, which greatly depend on the estimation of the damping in two-phase flow. The agreement of both criteria is revealed to be in the vicinity of the variance of the unknown parameters in the usual criteria.

Biphasic blood volume changes with lower body suction in humans

We recorded blood and plasma mass density and hematocrit of antecubital venous blood in 12 subjects in the supine position before, during, and after 20-40 min of lower body subatmospheric pressure (LBNP) of -35 mmHg. Mass density values decreased during the first minutes of LBNP, indicating a transient 2.8% blood volume gain before they rose as expected. After LBNP, a pronounced further density increase, indicating a further 1.5% hemoconcentration, preceded the return toward control. This pattern suggests reflex-driven transient filtration effects. Computed mass density of fluid exchanged between blood and extravascular space was 1,007.2 +/- 4.4 milligrams (37.0 degrees C); mass density of erythrocytes remained unaltered. We conclude that sudden unloading of central pressure receptors with LBNP causes microvascular fluid gain preceding fluid loss (hemoconcentration) during LBNP, and receptor loading after LBNP additionally causes fluid loss preceding inward filtration (hemodilution) during recovery. These effects can be quantified with high-precision blood and plasma mass densitometry performed by the mechanical oscillator technique.

Cellular and oscillatory self-induced methane migration

Methane genesis from kerogen maturation can induce kilometer-scale flow in a porous medium due to the fluid mass density dependence on methane concentration. The decrease in density with increasing methane content in solution may destabilize a water column, and initiate convective overturns. Conditions favoring these buoyancy-driven flows include a narrow thermal-depth window for methanogenesis and a large initial organic matter content. The self-organizing aspects of methanogenesis-induced flow are explored via the numerical simulation of reaction-transport equations. Cellular convection is demonstrated, and under certain conditions, the flow velocities are found to oscillate in time. For systems with initially random kerogen distribution the convection cells organize into one of a discrete set of well ordered convection cell patterns despite the initial disorder. Simulations initialized with heterogeneous porosity and permeability show that varying sizes and patterns of convection flows may develop which reflect the interplay between the inherent tendency toward self-organization and the nonuniformities in hydraulic properties.

Cellular and oscillatory self-induced methane migration

Methane genesis from kerogen maturation can induce kilometer-scale flow in a porous medium due to the fluid mass density dependence on methane concentration. The decrease in density with increasing methane content in solution may destabilize a water column, and initiate convective overturns. Conditions favoring these buoyancy-driven flows include a narrow thermal-depth window for methanogenesis and a large initial organic matter content. The self-organizing aspects of methanogenesis-induced flow are explored via the numerical simulation of reaction-transport equations. Cellular convection is demonstrated, and under certain conditions, the flow velocities are found to oscillate in time. For systems with initially random kerogen distribution the convection cells organize into one of a discrete set of well ordered convection cell patterns despite the initial disorder. Simulations initialized with heterogeneous porosity and permeability show that varying sizes and patterns of convection flows may develop which reflect the interplay between the inherent tendency toward self-organization and the nonuniformities in hydraulic properties.

Apparatus to determine the complex mass density of a viscous fluid contained in a rigid porous solid from acoustic pressure measurements

Two experimental techniques to determine the frequency‐dependent complex mass density of a viscous fluid contained in a rigid porous solid are being investigated. The fluid‐filled solid is contained within a small (≪λ) cylindrical cavity. In one technique the moving mass of the fluid is sensed by the effect it has on the measured input electrical impedance of a moving coil transducer. In the second technique the moving mass is extracted from the measured pressure required for the fluid to oscillate with a known amplitude through the porous solid. Preliminary results have been reported for the impedance method [Grant et al., J. Acoust. Soc. Am. Suppl. 1 84, S176 (1988)]. Preliminary results for the pressure technique and a comparison of the two methods will be presented. [Work sponsored by NRL‐USRD and the Naval Postgraduate School.]