Uniform Density Gradient Research Articles

Experimental and numerical investigations on the effect of porosity and PPI gradients of metal foams on the thermal performance of a composite phase change material heat sink

This paper reports the results of an experimental and numerical study on the thermal performance of a metal foam based composite phase change material (PCM) heat sink cylindrical in shape with porosity and PPI (pores per inch) density gradients. Studies are conducted on different configurations of composite PCM made of an open-cell aluminum metal foams with porosities of 0.9, 0.94 and 0.97 and PPI of 8, 14 and 20 encapsulated with n-eicosane as the PCM. Experiments are carried out on the PCM heat sink heated from the bottom for different configurations of metal foams with a uniform porosity and non-uniform porosity created with layer wise arrangement of metal foams from the bottom to the top. Complementary three-dimensional numerical simulations have been conducted using the enthalpy porosity methodology with a non-thermal equilibrium model to understand the melting and solidification dynamics of PCM while melting (charging) and solidification (discharging) respectively. Heat sink configurations with uniform porosity, and porosity gradient created with bi-layer arrangement of metal foams have been simulated numerically. Further, the numerical simulations have been extended to study heat sink configurations containing metal foams with uniform PPI density and PPI density gradient. From the results, it is seen that the case of non-uniform variation in porosity (decreasing from the bottom to the top) with constant PPI density and the case of non-uniform PPI density (increasing from the bottom to the top) with constant porosity show superior performance up to 28 and 45% over the heat sink configurations with uniform porosity and PPI density respectively in the charging cycle in terms of the time to reach a setpoint temperature. From the numerical simulations, it is seen that the melt fraction of PCM significantly changes the convection velocity cells, which affects the melting dynamics of PCM. Additional numerical simulations have been conducted on PCM heat sink with non-uniform porosity (i.e. decreasing porosity from the bottom to the top) and non-uniform PPI density (i.e increasing PPI density from the bottom to the top) gradients created with three layers (tri-layer) of metal foams. The results show that the PCM heat sink with non-uniform porosity and non-uniform PPI density gradients created with tri-layer metal foams have almost the same performance as a bi-layer metal foam with enhancement ratio up to 4 and 4.4 times respectively over the base line case (i.e. PCM heat sink without metal foams). In the discharging cycle, it is seen that the porosity and PPI gradients do not have any effect on the thermal performance of the heat sink.

Terahertz radiation generated by shell electrons in the bubble regime via the interaction between an intense laser and underdense plasma

Backward terahertz radiation can be produced by a high-intensity laser normally incident upon an underdense plasma. It is found that terahertz radiation is generated by electrons refluxing along the bubble shell. These shell electrons have similar dynamic trajectories and emit similar backward radiations to vacuum. This scheme has been proved through electron dynamic calculations and by using an ionic sphere model. In addition, the bubble shape is found to influence the radiation frequency, and this scheme can be implemented in both uniform and up-ramp density gradient plasma targets. The terahertz radiation may be used for diagnosing the electron bubble shape in the interaction between an intense laser and plasma. All the results are presented via 2.5 dimensional particle-in-cell simulations.

Modelling mechanical heating in star-forming galaxies: CO and13CO Line ratios as sensitive probes

We apply photo-dissociation region (PDR) molecular line emission models, that have varying degrees of enhanced mechanical heating rates, to the gaseous component of simulations of star-forming galaxies taken from the literature. Snapshots of these simulations are used to produce line emission maps for the rotational transitions of the CO molecule and its 13CO isotope up to J = 4-3. We consider two galaxy models: a small disk galaxy of solar metallicity and a lighter dwarf galaxy with 0.2 \zsun metallicity. Elevated excitation temperatures for CO(1 - 0) correlate positively with mechanical feedback, that is enhanced towards the central region of both model galaxies. The emission maps of these model galaxies are used to compute line ratios of CO and 13CO transitions. These line ratios are used as diagnostics where we attempt to match them These line ratios are used as diagnostics where we attempt to match them to mechanically heated single component (i.e. uniform density, Far-UV flux, visual extinction and velocity gradient) equilibrium PDR models. We find that PDRs ignoring mechanical feedback in the heating budget over-estimate the gas density by a factor of 100 and the far-UV flux by factors of ~10 - 1000. In contrast, PDRs that take mechanical feedback into account are able to fit all the line ratios for the central < 2 kpc of the fiducial disk galaxy quite well. The mean mechanical heating rate per H atom that we recover from the line ratio fits of this region varies between $10^{-27}$ -- $10^{-26}$~erg s$^{-1}$.

Solubilization of single-walled carbon nanotubes using a peptide aptamer in water below the critical micelle concentration.

The solubilizing ability of single-walled carbon nanotubes (SWCNTs) in water with several dispersants was investigated. Among the dispersants, including low-molecular-weight surfactants, peptides, DNA, and a water-soluble polymer, the peptide aptamer, A2 (IFRLSWGTYFS), exhibited the highest dispersion capability below the critical micelle concentration at a concentration of 0.02 w/v%. The dispersion of supernatant aqueous solution of SWCNTs containing aptamer A2 was essentially unchanged for several months after high-speed ultracentrifugation and gave rise to an efficient and stable dispersion of the SWCNTs in water. From the results of isothermal titration calorimetry and molecular dynamics simulations, the effective binding capability of A2 was due to π-π interaction between aromatic groups in the peptide aptamer and the side walls of SWCNTs. Interestingly, the peptide aptamer showed the possibility of diameter separation of semiconducting SWCNTs using a uniform density gradient ultracentrifuge. These phenomena are encouraging results toward an effective approach to the dispersion and separation of SWCNTs.

Transition through Rayleigh–Taylor instabilities in a breaking internal lee wave

AbstractResults of direct numerical simulations of the transitional processes that characterise the evolution of a breaking internal gravity wave to a fully developed and essentially steady turbulent patch are presented. The stationary lee wave was forced by the imposition of an appropriate bottom boundary shape within a density-stratified domain having a uniform upstream velocity and density gradient, and with the ratio of momentum to thermal (or other) diffusivity defined by$\mathit{Pr}=1$. An earlier paper considered the eventual, fully developed turbulent patch arising after the breaking process is complete (Yakovenkoet al.,J. Fluid Mech., vol. 677, 2011, pp. 103–133); the focus in this paper is on the instabilities in the breaking process itself. The flow is analysed using streamlines, density contours and temporal and spatial spectra, as well as second moments of the velocity and density fluctuations, for a Reynolds number of 4000 based on the height of the bottom topography and the upstream velocity. The computations (on a grid using in excess of$10^{9}$mesh points) yielded sufficient resolution to capture the fine-scale transition processes as well as the subsequent fully developed turbulence discussed earlier. It is shown that the major instability is of Rayleigh–Taylor type (RTI) with a resulting mixing region depth growing in a manner consistent with more classical RTI studies, despite the much more complicated environment. The resolution was sufficient to capture secondary Kelvin–Helmholtz-type instabilities on the developing RTI structures. Overall evolution towards the fully turbulent state characterised by a significant region of$-\frac{5}{3}$subrange in both velocity and density spectra is very rapid. It is much faster than the long time scale characterising the subsequent evolution of the turbulent patch; this latter time scale is sufficiently large that the turbulent patch can itself be viewed as essentially steady.

Impact of Tab Location on Large Format Lithium-Ion Pouch Cell Based on Fully Coupled Tree-Dimensional Electrochemical-Thermal Modeling

This paper presents extensive three-dimensional (3D) simulations of large LiFPO4 pouch cells. 3D simulations of the Li-ion battery behavior are highly nonlinear and computationally demanding. Coupling electrochemical modeling to thermal models represents an important step towards accurate simulation of the Li-ion battery. Non-uniform temperature, potential and current density through the battery induce non-uniform use of the active material and can have a negative impact on cell performance and lifetime. Different pouch cell designs, with different tab locations, have been investigated in term of performance, current density, potential and heat distributions. The model is first validated with experimental data at different current discharge rates. Afterwards, the electrochemical, thermal and electrical behaviors over each cell design under high discharge rate (4 It) are compared between configurations. It has been shown that the designs with symmetrical configurations show uniform potential and current density gradient, which minimize the ohmic heat and lead to more uniform active material utilization and temperature distributions across the cell surface.Introduction

The effect of small viscosity and diffusivity on the marginal stability of stably stratified shear flows

AbstractThe effect of non-zero, but small, viscosity and diffusivity on the marginal stability of a stably stratified shear flow is examined by making perturbations around the neutral solution for an inviscid and non-diffusive flow. The results apply to turbulent flows in which horizontal and vertical turbulent transports of momentum and buoyancy are represented by eddy coefficients of viscosity and diffusivity that vary in the vertical ($z$) direction. General expressions are derived for the modified phase speed and the growth rate of small disturbances as a function of wavenumber. To first order in their coefficients, the effect on the phase speed of adding viscosity and diffusivity is zero. Growth rates are found for two mean flows when the horizontal or vertical coefficients of viscosity and diffusivity vary in $z$ in such a way that the rates can be found analytically. The first flow, denoted as a ‘Holmboe flow’, has a velocity and density interface: the mean horizontal velocity and the density are both proportional to $\tanh az$, where $a$ is proportional to the inverse of the interface thickness. The second, ‘Drazin flow’, has a similar velocity variation in $z$ but uniform density gradient. The analytical results compare favourably with numerical calculations. Small horizontal coefficients of viscosity and diffusivity may affect disturbances to the flow in opposite ways. Although the effect of uniform vertical coefficients of viscosity is to decrease the growth rates, and uniform vertical coefficients of diffusivity increase them, cases are found in which, with suitably chosen $z$ dependence, vertical coefficients of viscosity (or diffusivity) may cause a previously neutral disturbance to grow (or to diminish); viscosity may destabilize a stably stratified shear flow. The introduction of viscosity and diffusivity may consequently increase the critical Richardson number to a value exceeding $1/ 4$. While some patterns of behaviour are apparent, no simple rule appears to hold about whether flows that are neutral in the absence of these effects (viscosity or diffusivity) will be stabilized or destabilized when they are added. One such rule, namely our conjecture that viscosity is always stabilizing and that diffusivity is destabilizing, is explicitly refuted.

A turbulent patch arising from a breaking internal wave

Results of direct numerical simulations of the development of a breaking internal gravity wave are presented. The wave was forced by the imposition of an appropriate bottom boundary shape (a two-dimensional cosine hill) within a density-stratified domain having a uniform upstream velocity and density gradient. The focus is on turbulence generation and maintenance within the turbulent patch generated by the wave breaking. Pathlines, density contours, temporal and spatial spectra, and second moments of the velocity and density fluctuations and turbulent kinetic energy balance terms obtained from the data averaged over the span in the mixed zone are all used in the analysis of the flow. Typical Reynolds numbers, based on the vertical scale of the breaking region and the upstream velocity, were around 6000 and the fully resolved computations yielded sufficient resolution to capture the fine-scale transition processes as well as the subsequent fully developed turbulence. It is shown that globally, within the turbulent patch, there is an approximate balance in the production, dissipation and transport processes for turbulent kinetic energy, so that the patch remains quasi-steady over a significant time. Although it is far from being axially homogeneous, with turbulence generation occurring largely near the upstream bottom part of the patch where the mean velocity shear is particularly large, it has features not dissimilar to those of a classical turbulent wake.

A turbulent patch arising from a breaking internal wave

Results of direct numerical simulations of the development of a breaking internal gravity wave are presented. The wave was forced by the imposition of an appropriate bottom boundary shape (a two-dimensional cosine hill) within a density-stratified domain having a uniform upstream velocity and density gradient. The focus is on turbulence generation and maintenance within the turbulent patch generated by the wave breaking. Pathlines, density contours, temporal and spatial spectra, and second moments of the velocity and density fluctuations and turbulent kinetic energy balance terms obtained from the data averaged over the span in the mixed zone are all used in the analysis of the flow. Typical Reynolds numbers, based on the vertical scale of the breaking region and the upstream velocity, were around 6000 and the fully resolved computations yielded sufficient resolution to capture the fine-scale transition processes as well as the subsequent fully developed turbulence. It is shown that globally, within the turbulent patch, there is an approximate balance in the production, dissipation and transport processes for turbulent kinetic energy, so that the patch remains quasi-steady over a significant time. Although it is far from being axially homogeneous, with turbulence generation occurring largely near the upstream bottom part of the patch where the mean velocity shear is particularly large, it has features not dissimilar to those of a classical turbulent wake.

On the equilibration of a symmetrically unstable front via a secondary shear instability

The equilibration of a symmetrically unstable density front is examined using linear stability theory and nonlinear numerical simulations. The initial state, chosen to approximate conditions in the surface ocean, consists of a weakly stratified mixed layer above a strongly stratified thermocline. Each layer has a uniform horizontal density gradient and a velocity field in thermal wind balance. The potential vorticity (PV) in the mixed layer is negative, indicating conditions favourable for symmetric instability. Once the instability reaches finite amplitude, a secondary Kelvin–Helmholtz (K-H) instability forms. Linear theory accurately predicts the time and the wavenumber at which the secondary instability occurs. Following the secondary instability, small-scale turbulence injects positive PV into the mixed layer from the thermocline and from the upper boundary, resulting in a rapid equilibration of the flow as the PV is brought back to zero. While the physical parameters used in this study correspond to typical conditions near a surface ocean front, many of the conclusions apply to symmetric instabilities in the atmosphere.

Frontogenesis in turbulent flow through porous media using non-linear Forchheimer equation

We present here both one- and two-dimensional models for turbulent flow through heterogeneous unbounded fluid saturated porous media using non-linear Forchheimer extended Darcy (DF) equation in the presence of gravitational field. The fluid is initially at rest and sets in motion due to a uniform horizontal density gradient. It is shown that a purely horizontal motion develops satisfying non-linear DF equation. Analytical solutions of this non-linear Initial Value Problem are obtained and limiting solutions valid for the Darcy regime in the case of laminar flow are derived. A measure of the stability of the flow is discussed briefly using Richardson number. The comparison between the nature of the solutions satisfying the non-linear and linear initial value problems are made. We found that even in the case of turbulent flow the vertical density gradient varies continuously both with space z and time t but the horizontal density gradient remains unchanged. The existence and uniqueness theorem of the Initial Value Problem is proved. The stability of these solutions are discussed and it is shown that the solutions are qualitatively and quantitatively different for z < 1 4 and z > 1 4 in the upper and lower half of the region. In particular, we have shown that the solution which is stable for infinitesimal perturbations is also stable for arbitrary perturbations both in time and space. In the case of two-dimensional motion, a piecewise initial density gradient with continuous distribution of density, stream function formulation is used and the solutions are obtained using time-series analysis. In this case solution shows crowding of the density profiles in the lower-half of the channel reflecting an increase in density gradient and incipient of frontogenesis there, because of the increase in circulation of the flow due to piecewise initial density gradient.

Fluid–body interaction in the presence of uniform vorticity and density gradient

We consider the case of a rigid or deformable body moving in a linear shear flow of an inviscid, incompressible and inhomogeneous fluid with a uniform density gradient. The body is impulsively introduced into the nonuniform ambient flow field possessing time-dependent vorticity. In order to make the analysis amenable, it is further assumed that the size of the body is small with respect to the inhomogeneity of the ambient flow. By integrating the Euler equation it is shown that analytic expressions can be obtained for the hydrodynamical reactions (forces and moments) acting on the body which determine its trajectories. In addition to the traditional purely inertial quadratic terms, three new types of interaction modes are thus revealed: Vorticity-inertia, density gradient-inertia, and vorticity-density gradient. The first two modes have been considered separately just recently but the third one is presented here for the first time. It is finally demonstrated that all three modes of interaction can be obtained from a relatively straightforward unified approach.

Gravitational instability of miscible fluids in a Hele-Shaw cell

We revisit the Rayleigh–Taylor instability when the two fluids are miscible and in the geometry of a Hele-Shaw cell. We provide analytical dispersion relations for the particular cases of either a sharp front between the two fluids or of a uniform density gradient stratification and for various fluid flow models, including an unbounded geometry, a two-dimensional gap-averaged Navier–Stokes–Darcy equation, and an effective porous medium. The results are compared to three-dimensional lattice BGK simulations, based on which the relevance of the various models in different wavelength regimes is discussed.

Energy transfer in a fluid with a uniform density gradient

Energy transfer via resonance in a stratified fluid with a constant Brunt–Väisälä frequency is studied through the Manley–Rowe relation and direct numerical simulations. The objectives of this study are two-fold. One is to determine if there is a limitation on the lengthscale of small-scale waves to which primary energy can be effectively transferred. The other is to study factors affecting the growth of parametric subharmonic instability. Resonantly interacting modes are classified into three groups: local sum modes, quasi-subharmonic modes and remote parametric subharmonic instability modes (characterized by interaction with very small-scale waves). The latter two involve energy transfer from a primary wave to secondary waves with half the frequency. Most energy transfer is through local sum resonant modes and quasi-subharmonic modes. Energy cannot effectively transfer to higher wavenumber modes since dynamical systems are altered as wavenumbers of excited modes increase. In the remote modes, the solution is sinusoidal with high angular frequency and very small energy capacity. As a consequence, these modes are inactive in energy transfer despite their high energy growth rates. Effects of non-uniform white noise amplitude and primary mode propagation angle on the quasi-subharmonic modes are also investigated. Implications for energy transfer in the ocean are discussed.

Effect of the stratified ocean of the core upon the Chandler wobble

It is supposed that a stably stratified layer exists at the top of the fluid core; we call it the stratified ocean of the core (SOC). The assumed model of the SOC has a sharp density drop at the boundary with the bulk of the core, and a uniform internal density gradient. The influence of the SOC upon the Chandler wobble is considered. It is shown that the action of Archimedean buoyancy forces in the SOC creates inside this layer an additional fluid velocity of order of ( C H/2 σ)v τ . Here C H is the relative density deficit in the SOC, v τ is the velocity associated with the Chandler wobble without the SOC, and σ∼1/400 is the frequency of the Chandler wobble measured in cycles per day. The effect of the SOC on the Chandler wobble is small: it increases the wobble period by ∼0.1 day, and its contribution to the dissipation of the wobble energy is about six orders of magnitude smaller than the observed dissipation. A change of seismic velocity in the SOC due to the greater concentration of the light admixture is discussed. A comparison of the conditions in the SOC with the conditions at the inner core boundary shows that the extra amount of the light fluid in the layer increases the seismic velocity; therefore, the SOC is a high-velocity layer.

Amplification of fluctuations and current dynamo due to helical and chiral effects in geophysical and plasma-like media

Dynamo effect is considered in more general case than well known one when not only mean motion but also conducting components possess nonzero mean helicity. Dispersion equation for helical motions is studied, including inhomogeneous case. Criteria for development of instability are found. Interaction between large-scale internal wave and small-scale helical turbulence in plane Couette flow of fluid with statically stable uniform density gradient in gravitational field is studied basing on a set of equations for scalar and quasi-scalar wave fields and for helicity of turbulence. This system of equation describes acceleration of wave growth due to its backward action on turbulence, i.e. wave-turbulent instability. Chiral media are further considered and effects topologically close to helical ones are analyzed. It is shown that in such media ranges of scales exist, in which fluctuations of electric field can be anomalously amplified.

Enhanced stratification in the lower Chesapeake Bay following northeasterly winds

Density data from a lower Chesapeake Bay transect obtained after two northeasterly wind events were used to describe the effects of these events on the density field in the lower estuary. The first northeaster occurred in early August 1995 and the second northeaster was related to the passage of hurricane Felix off the lower bay in mid-August 1995. The latter northeaster prolonged a period of persistent winds from the N and NE that began in early August and caused storm surges of similar magnitude to the former northeaster. The salinity fields observed after the early August event suggested encroachment of coastal waters into the lower bay as reflected by high salinities throughout the transect. Two days after weakening of the winds related to Felix, the density distribution across the lower bay showed strongly stratified conditions. This behavior suggested that the inflow of coastal water into the lower bay and the wind mixing related to Felix combined to produce a vertically uniform density gradient perpendicular to the bay entrance that relaxed after the winds weakened. This weakening of the winds coincided with neap tidal currents, which were not energetic enough to maintain vertical homogeneity and must have allowed the self-adjustment of the density gradient and the seaward advection of relatively buoyant waters near the surface. These mechanisms were illustrated with simplified numerical experiments. The findings of this study are used to propose the hypothesis that, in general, enhanced stratification and flushing in the lower bay will ensue the relaxation of a northeasterly wind event, provided that this relaxation coincides with a weak friction regime, i.e., neap tides.

Statically unstable layers produced by overturning internal gravity waves

Internal waves in a uniformly stratified fluid of sufficiently large amplitude develop tilted layers in which the fluid is statically unstable. To investigate the evolution and subsequent development of this structure, experiments are made in which a horizontal rectangular tube containing a fluid of uniform density gradient is gently rocked at a selected frequency about a horizontal axis normal to the tube length. Large-amplitude standing internal gravity waves of the first mode are generated, and these steepen and overturn, the isopycnal surfaces folding to produce a vertically thin and horizontally extensive layer in which the fluid is statically unstable. In experiments with relatively small forcing, the layer persists for some 6 buoyancy periods, with no detected evidence of secondary instability, and static stability is re-established as the periodic flow reverses. The layer however breaks down, with consequent diapycnal mixing, when greater forcing is applied.The scale and growth rates of instability in the overturning internal gravity waves are estimated using the theory developed in a companion paper by Thorpe (1994a). For the parameters of the laboratory experiments with relatively small forcing, the growth rates are small, consistent with the absence of signs of secondary instability. Larger growth rates and disturbance amplification factors of about 70 are predicted for the conditions in the experiment in which mixing was observed to occur. The experimental observations are consistent with an instability having a longitudinal structure.We conclude that the form and development of breaking in internal gravity waves will vary according to the circumstances in which waves break, but depend on the Prandtl number of the fluid and, in particular, on the Rayleigh and Reynolds numbers of regions of static instability which develop as the waves overturn.

Instability of stratified fluid in a vertical cylinder

In a previous paper we analysed the stability to small disturbances of stationary stratified fluid which is unbounded. Various forms of the undisturbed density distribution were considered, including a sinusoidal profile and a function of the vertical coordinate z which is constant outside a central horizontal layer. Both these types of stratification are so unstable that the critical Rayleigh number is zero. In this sequel we make the study more complete and more useful by taking account of the effect of a vertical circular cylindrical boundary of radius a which is rigid and impermeable. As in the previous paper we assume that the undisturbed density distribution is steady.The case of fluid in a vertical tube with a uniform density gradient is useful for comparison, and so we review and extend the available results, in particular obtaining growth rates for a disturbance which is neither z-independent nor axisymmetric. A numerical finite-difference method is then developed for the case in which dρ/dz = ρ0kA cos kz. When ka [Lt ] 1 the relation between growth rate and Rayleigh number approximates to that for a uniform density gradient of magnitude ρ0kA; and when ka [Gt ] 1 the tilting-sliding mechanism identified in the previous paper is relevant and the results approximate to those for an unbounded fluid, except that the smallest Rayleigh number for a neutral disturbance is not zero but is of order (ka-1. In the case of an undisturbed density which varies only in a central layer of thickness l, the same mechanism is at work when the horizontal lengthscale of the disturbance is large compared with l, resulting in high growth rates and a critical Rayleigh number which vanishes with l/a. Estimates of the growth rate are given for some particular density profiles.

Stability of an oscillated fluid with a uniform density gradient

Instabilities in a fluid with a constant density gradient that is subject to arbitrarily oriented oscillatory accelerations are considered. With the Boussinesq approximation and for the case of an unbounded fluid, transformation to Lagrangian coordinates allows the reduction of the problem to an ordinary differential equation for each three-dimensional wavenumber. The problem has three parameters: the nondimensional amplitude R of the base-state oscillation, the nondimensional level of background steady acceleration, which for some cases can be represented in terms of a local (in time) Richardson number Ri, and the Prandtl number Pr. Some general bounds on stability are derived. For Pr = 1 closed-form solutions are found for impulse (delta function) accelerations and a general asymptotic solution is constructed for large R and general imposed accelerations. The asymptotic solution takes advantage of the fact that at large R wave growth is concentrated at 'zero points'. These are times when the effective vertical wavenumber passes through zero. Kelvin-Helmholtz instabilities are found to dominate at low R, while Rayleigh-Taylor instabilities dominate at high R. At high R, the uniform shear of the Kelvin-Helmholtz case tends to distort and weaken instability waves. With unsteady flows, Ri = 1/4 is no longer an instability limit. Significant instabilities have been found for sinusoidal forcing for Ri up to 0.6.