Density Extremum Research Articles

Impact of titling angle and density extremum on transient convection in a porous chamber with sinusoidal heating

The aim of the present study is to investigate numerically the 2D unsteady transient convection of cold water near its highest density value in an inclined square porous enclosed space. The horizontal walls are kept in adiabatic condition. The temperature of left sidewall varies in sinusoidal manner whereas the opposing right sidewall is sustained with constant lower temperature. The range of angle of inclination is considered from 0° to 90°. The finite volume method (FVM) was applied to portray all mathematical equations. The special outcome of inclination angle, Darcy number, maximum density parameter and porosity are obtained in the present study with the use of Brinkmann–Forchheimer extended Darcy model. The change in the angle of inclination is noteworthy in the structure and direction of the flow of the fluid. The bicellular structure of the fluid is identified because of the density inversion effect. Increasing Darcy number and porosity values enhance the average rate of energy transport across the chamber. The lowest heat transfer is noticed for due to supreme density effect. Here the energy transfer from one cell to another cell is by conduction mode due to the existence of dual cell structure.

Diffusion equation based parameterization of light field and computational imaging model

The parameterization of light field is fundamental for the light field data acquisition and the computational imaging model. In this paper, we proposed the diffusion equation based parameterization of light field and established the computational imaging model via the proposed parameterized light field. Since the light propagation in the image space can be regarded as a diffusion process, the light field in the image space can be represented based on the diffusion equation in the lens imaging. The computational imaging model via the proposed light field parameterization consists of the forward model and the inverse problem. The forward model is the generation of the focal stack from the depth map and the all-in-focus (AIF) image. The inverse problem is to reconstruct the depth map and the AIF image from the focal stack. We clarify that the focal stack can be regarded as the scale spaces of the local region images. As a result, the depth reconstruction and the all-in-focus imaging from focal stack can be solved by detecting the extremum of the feature point density. In this paper, the simulated focal stack and the real captured focal stack data are used to verify the reconstruction method, and the high-precision scene depth map and the all-in-focus image are reconstructed.

Effects of Variable Properties on the Convective Flow of Water near Its Density Extremum in an Inclined Enclosure with Entropy Generation

The aim of the current numerical simulation was to understand the effects of the temperature-dependent properties of viscosity and thermal conductivity on the buoyant convection of cold water around its density extremum in a tilting chamber. The equations for thermal conductivity and viscosity were derived based on the reference temperature parameter. The entropy generation and cup mixing temperature were also calculated. The governing mathematical model was solved by the finite-volume-based iterative technique. The obtained results were deliberated for several values of inclination angles and for the density reversal parameter for variable viscosity and thermal conductivity cases. It was detected that density inversion has a strong effect on stream and thermal patterns through the development of a bi-cellular arrangement due to density inversion.

Characteristics and Underlying Physics of Bipolar Corona Discharge of Floating Conductor

Bipolar corona discharge is the fundamental phenomenon that preoccurs in air breakdown for nongrounded objects facing a high-voltage source, which sets important bases for aircraft protection crossing thunderclouds and improvement of high-voltage switches with floating conductors, while this phenomenon has not been fully understood to date. This article proposes a bipolar corona plasma model (BCPM) based on the plasma hydrodynamic process and the chemical reactions of air discharge. The numerical analysis of the charged particle distribution matches the experimental result of the bipolar corona discharge appearance. Furthermore, the characteristics of bipolar corona discharge are described from the perspective of electric field and electron current density at the two opposite ends of the floating conductor. Results show that, at the positive end, the corona discharge has a long columnar shape in a faint light blue. While at the negative end, the corona presents a spherical shape in a stronger luminous light purple. There exists a density extremum at the position 0.03 cm away from the conductor ends in the distribution of electrons, where a low electron density zone with a concentration of 0.42 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times \,\,10^{13}\,\,\text{m}^{-3}$ </tex-math></inline-formula> forms at the positive end, while electrons group to a high density of 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times \,\,10^{16}\,\,\text{m}^{-3}$ </tex-math></inline-formula> at the negative end. The geometric length of the high-density ions zone is enlarged by 2 times at the positive end compared to the negative end. The peak electric field at the negative end is about 1.5 times stronger than the electric field at the positive end, consistent with the space charge distribution at the positive and negative ends. The unbalance of the emission and entry of electron current results in a slightly positive polarity for the floating conductor. This study can be consulted for shedding light on the underlying physics of bipolar corona discharge of floating conductors.

Numerical study on influence of titling position and density extremum on convection in a porous cavity with sinusoidal heating

The aspiration of the present problem is to investigate numerically the 2D unsteady buoyancy convection of cold water near its highest density value in an inclined square porous enclosed space. Left sidewall temperature varies in sinusoidal manner whereas the opposing right sidewall is sustained with constant lower temperature. The walls along x axis and parallel to x axis are kept in adiabatic condition. The range of angle of inclination is considered from 0 degree to 90 degree. The finite volume method (FVM) was applied to portray all mathematical equations. The special outcome of inclination angle, Darcy number, maximum density parameter and porosity are obtained in the present study with the use of Brinkmann–Forchheimer extended Darcy model. The change in the angle of inclination is noteworthy in the structure and direction of the flow of the fluid. The bicellular structure of the fluid is identified because of the higher density effect.

Natural convection analysis of water near its density extremum between finite vertical plates: a differential transform approach

Using a two-dimensional differential transform method, we solve the steady natural convection problem of cold water between vertical isothermal plates of finite length. The cold water exhibits a density variation approximated as a quadratic function of temperature. Given the temperature-dependent viscosity, we present approximate analytical solutions in the form of power series for temperature, vertical flow velocity, and pressure defect. Numerical calculations are carried out for two cases of water temperature in which the following occur with respect to increases in temperature: 1) the density decreases monotonously; 2) the density increases and subsequently decreases. The numerical results reveal how the temperature-dependent properties affect the developing temperature and velocity profiles and pressure defect distribution along the streamwise direction.

The kinetic theory of the mesoscopic spacetime

At the mesoscopic scales — which interpolate between the macroscopic, classical, geometry and the microscopic, quantum, structure of spacetime — one can identify the density of states of the geometry, which arises from the existence of a zero-point length in the spacetime. This spacetime discreteness also associates an internal degree of freedom with each event, in the form of a fluctuating vector of constant norm. The equilibrium state, corresponding to the extremum of the total density of states of geometry plus matter, leads precisely to Einstein’s equations. In fact, the field equation can now be reinterpreted as a zero-heat-dissipation principle. The analysis of fluctuations around the equilibrium state (which is described by Einstein’s equations), will provide new insights about the quantum gravity.

Numerical modeling of solid-liquid phase change in a closed 2D cavity with density change, elastic wall and natural convection

In this paper, the solidification of water near its density extremum is simulated while taking into account the expansion of the phase change material resulting from the different density of the solid and liquid phases. A thermo-mechanical coupling is achieved through one of the boundaries of the cavity behaving as an elastic wall. A methodology is introduced in which the problem is adapted in order to be solved with commercial CFD software (ANSYS Fluent 17.0). It is shown that when both the density variations and interaction of the phase change material with its boundaries are taken into account, significant differences may be observed in the flow pattern and the thermal behavior of the system, as opposed to an approach where a free ceiling or a constant density would be used. The pressure buildup inside the cavity resulting from the expansion of the phase change material as it pushes against the elastic wall causes the melting temperature to drop, which hinders solidification. It is shown that this effect becomes more pronounced as the spring constant of the elastic wall increases. It is also demonstrated that, with the assumptions made in the present model, the pressure rise may significantly influence the buoyancy forces within the cavity and change the relative size of the two counter rotating convective cells in the liquid phase. In some cases, when the pressure rises very quickly, the density extremum in the cavity disappears which strongly changes the flow pattern, i.e., only a single counter-clockwise convective cell is present in the cavity. This, in turn, changes the shape and position of the solidification front considerably.

Two-structure thermodynamics for the TIP4P/2005 model of water covering supercooled and deeply stretched regions.

One of the most promising frameworks for understanding the anomalies of cold and supercooled water postulates the existence of two competing, interconvertible local structures. If the non-ideality in the Gibbs energy of mixing overcomes the ideal entropy of mixing of these two structures, a liquid-liquid phase transition, terminated at a liquid-liquid critical point, is predicted. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data for metastable, deeply supercooled water and simulations of molecular water models. However, existing TSEOSs were not designed to describe the negative pressure region and do not account for the stability limit of the liquid state with respect to the vapor. While experimental data on supercooled water at negative pressures may shed additional light on the source of the anomalies of water, such data are very limited. To fill this gap, we have analyzed simulation results for TIP4P/2005, one of the most accurate classical water models available. We have used recently published simulation data, and performed additional simulations, over a broad range of positive and negative pressures, from ambient temperature to deeply supercooled conditions. We show that, by explicitly incorporating the liquid-vapor spinodal into a TSEOS, we are able to match the simulation data for TIP4P/2005 with remarkable accuracy. In particular, this equation of state quantitatively reproduces the lines of extrema in density, isothermal compressibility, and isobaric heat capacity. Contrary to an explanation of the thermodynamic anomalies of water based on a "retracing spinodal," the liquid-vapor spinodal in the present TSEOS continues monotonically to lower pressures upon cooling, influencing but not giving rise to density extrema and other thermodynamic anomalies.

Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification.

Various spatial density profiles can develop in partially miscible stratifications when a phase A dissolves with a finite solubility into a host phase containing a dissolved reactant B. We investigate theoretically the impact of an A+B→C reaction on such density profiles in the host phase and classify them in a parameter space spanned by the ratios of relative contributions to density and diffusion coefficients of the chemical species. While the density profile is either monotonically increasing or decreasing in the nonreactive case, reactions combined with differential diffusivity can create eight different types of density profiles featuring up to two extrema in density, at the reaction front or below it. We use this framework to predict various possible hydrodynamic instability scenarios inducing buoyancy-driven convection around such reaction fronts when they propagate parallel to the gravity field.

Transient natural convection of cold water in a vertical channel

The two-dimensional differential transform method (DTM) is applied to analyse the transient natural convection of cold water in a vertical channel. The cold water gives rise to a density variation with temperature that may not be linearized. The vertical channel is composed of doubly infinite parallel plates, one of which has a constant prescribed temperature and the other of which is insulated. Considering the temperature-dependent viscosity and thermal conductivity of the water, approximate analytical (series) solutions for the temperature and flow velocity are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical computation is performed for the entire range of water temperature conditions around the temperature at the density extremum point, i.e.\( 4 {}^{\circ} C\) . Numerical results illustrate the effects of the temperature-dependent properties on the transient temperature and flow velocity profiles, volumetric flow rate, and skin friction. The DTM is a powerful tool for solving nonlinear transient problems as well as steady problems.

Rectilinear-motion space inversion-based detection approach for infrared dim air targets with variable velocities

Dim targets are extremely difficult to detect using methods based on single-frame detection. Radiation accumulation is one of the effective methods to improve signal-to-noise ratio (SNR). A detection approach based on radiation accumulation is proposed. First, a location space and a motion space are established. Radiation accumulation operation, controlled by vectors from the motion space, is applied to the original image space. Then, a new image space is acquired where some images have an improved SNR. Second, quasitargets in the new image space are obtained by constant false-alarm ratio judging, and location vectors and motion vectors of quasitargets are also acquired simultaneously. Third, the location vectors and motion vectors are mapped into the two spaces, respectively. Volume density function is defined in the motion space. Location extremum of the location space and volume density extremum of motion space will confirm the true target. Finally, actual location of the true target in the original image space is obtained by space inversion. The approach is also applicable to detect multiple dim targets. Experimental results show the effectiveness of the proposed approach and demonstrate the approach is superior to compared approaches on detection probability and false alarm probability. c 2016 Society of Photo-Optical Instrumentation Engineers (SPIE).

Density variations of galactic cosmic rays in magnetic clouds

Galactic cosmic ray behavior features in events when magnetic clouds that have been observed in interplanetary disturbances near the Earth are investigated. It is shown in most cases (but not in all) that the cosmic ray density behavior in the magnetic cloud near the Earth can be described by a simple parabolic distance dependence measured in gyroradii. Most magnetic clouds modulate cosmic rays by reducing their density, but there is a group of events (about 1/5) in which the cosmic ray density in the magnetic cloud increases. The extremum (minimum or maximum) of the cosmic ray density is often located closer to the cloud center rather than its edges. A number of factors that contribute to the model description are considered, and the contributions are estimated.

Galactic Cosmic Ray Density Variations in Magnetic Clouds

We investigate the characteristics of Galactic cosmic rays in events associated with magnetic clouds that reach Earth. A mathematical model, capable of describing the distribution of the cosmic-ray density in a magnetic cloud is considered. We show that in most cases the behavior of the cosmic-ray density within magnetic clouds at 1 AU can be described accurately by a parabolic function of the distance to the center of the magnetic cloud measured in gyroradii. As expected, the majority of magnetic clouds modulate cosmic rays, resulting in a reduction of their density. However, there is a group of events (about one fifth of the total sample) in which the density of cosmic rays in a magnetic cloud increases. Furthermore, the extremum (a minimum or a maximum) of the cosmic-ray density is found closer to the cloud center and not at its edges. We consider a number of the factors contributing to the model and estimate the effect of each factor.

Rossby-wave instability in viscous discs

The Rossby wave instability (RWI), which depends on the density bumps and extremum in the vortensities in the differentially rotating discs, plays an important role in the evolution of the protoplanetary discs. In this article, we investigate the effect of viscosity on the non-axisymmetric RWI in the self-graviting accretion discs. For this purpose, we add the viscosity to the work of Lovelace and Hohlfeld (2013). Consideration of viscosity complicates the problem so that we use the numerical method to investigate the stable and unstable modes. We consider three ranges of viscosities: high viscosity in the ranges $0.1\leq \alpha\leq 0.4$, moderate viscosity in the ranges $0.01\leq \alpha < 0.1$, and low viscosity in the ranges $\alpha < 0.01$. The results show that the occurrence of the RWI is related to the value of viscosity so that the effect of high viscosity is important, while the low viscosity is negligible. These results may be applied for the study of the RWI role in planet formation and angular momentum transport for different kinds of the protoplanetary discs with different viscosities.

Minimum-density anomaly and spatial ordering of softly repulsive particles in a narrow channel

We performed an extensive numerical investigation of a system of repulsive Gaussian particles confined in a thin cylindrical pore. In this setting, the fluid phase can be cooled down to very low temperatures, thus bypassing the freezing transition. Focusing on the thermal behavior of the average number density, we find a range of pressures within which, upon cooling, the system density first approaches a maximum that is then followed by a minimum at lower temperatures. As the width of the pore is reduced, the density minimum shifts to larger pressures, in line with what happens in the same model in one dimension. As far as the system structure is concerned, a pronounced layering is observed at the wall; moreover, when the pore radius is not too small, the relative fraction of solid-like (i.e., well coordinated) particles increases overall on cooling, in a somewhat larger amount when crossing the region bounded by the two density extrema. On account of this phenomenology, we surmise that the anomalous behavior of the system density stems from the smoothening of the density jump occurring at the three-dimensional freezing point. By analogy, our findings suggest that the essential driving mechanism leading to the volumetric anomaly exhibited by supercooled water confined in silica nanopores at ambient pressure is an effective soft repulsion between water molecules at short distances.

Liquid–liquid critical point in supercooled silicon

A novel liquid-liquid phase transition has been proposed and investigated in a wide variety of pure substances recently, including water, silica and silicon. From computer simulations using the Stillinger-Weber classical empirical potential, Sastry and Angell [1] demonstrated a first order liquid-liquid transition in supercooled silicon, subsequently supported by experimental and simulation studies. Here, we report evidence for a liquid-liquid critical end point at negative pressures, from computer simulations using the SW potential. Compressibilities exhibit a growing maximum upon lowering temperature below 1500 K and isotherms exhibit density discontinuities below 1120 K, at negative pressure. Below 1120 K, isotherms obtained from constant volume-temperature simulations exhibit non-monotonic, van der Waals-like behavior signaling a first order transition. We identify Tc ~ 1120 +/- 12 K, Pc -0.60 +/- 0.15 GPa as the critical temperature and pressure for the liquid-liquid critical point. The structure of the liquid changes dramatically upon decreasing the temperature and pressure. Diffusivities vary over 4 orders of magnitude, and exhibit anomalous pressure dependence near the critical point. A strong relationship between local geometry quantified by the coordination number, and diffusivity, is seen, suggesting that atomic mobility in both low and high density liquids can usefully be analyzed in terms of defects in the tetrahedral network structure. We have constructed the phase diagram of supercooled silicon. We identify the lines of compressibility, density extrema (maxima and minima) and the spinodal which reveal the interconnection between thermodynamic anomalies and the phase behaviour of the system as suggested in previous works [2-9]

Mixed Convection in Water Near the Density Extremum Along a Vertical Plate with Sinusoidal Surface Temperature Variation Embedded in a Porous Medium

A steady laminar boundary layer flowing along a vertical plate immersed in a Darcy–Brinkman porous medium saturated with water at 4°C is studied. The plate temperature varies sinusoidally along the plate between 0 and 8°C where the density of water varies parabolically and is almost symmetrical at about 4°C. Except for the existence of the buoyancy force, it is assumed that either the plate moves upwards or the ambient water moves upwards (moving stream). The results are obtained with the direct numerical solution of the boundary layer equations taking into account the temperature dependence of water thermophysical properties (ρ, μ and c p). Results are presented for the wall temperature gradient and the wall shear stress along the plate for free convection and mixed convection. Temperature and velocity profiles are also presented.

A note on mixed convection of laminar plane water plumes at temperatures around the density extremum

In all studies concerning mixed convection in plane laminar plumes a linear relationship between fluid density and temperature has been used. However, it is known that the water density-temperature rela- tionship is non-linear at low temperatures with a density maximum at 3.98 ◦ C for pure water. In this note the problem of plane laminar water plume in a coflowing vertical free stream has been investigated taking into account the non-linearity between density and temperature. This is the first work in the literature which treats plane mixed convection plumes with nonlinear relation between density and temperature. Both rising and descending plumes have been investigated. It was found that the ambient water temperature plays an important role on the results. When the ambient temperature is greater than maximum density temperature (Ta > Tm), the water plume behavior is similar to that of the classical plume with linear density-temperature relationship. However, when the ambient temperature is equal or lower than the maximum density temperature the water plume behavior is completely different from the classical plume with linear density-temperature relationship. The centerline velocity shows a series of maxima and minima which are produced by the combination of the nonlinear density-temperature relation and the free stream.

Double diffusive convection of anomalous density fluids in a porous cavity

A numerical study has been performed to analyze the combined effect of temperature and species gradients on the buoyancy-driven natural convection flow of cold water near its density extremum contained in a porous cavity. The governing equations are descretized using the finite volume method. The results of the investigation are presented in the form of steady-state streamlines, velocity vectors, isotherms, and isoconcentrationlines. The results are discussed for different porosities, Darcy numbers, and Grashof numbers. The heat and mass transfer rates calculated are found to behave nonlinearly with hot wall temperature. The heat and mass transfer are increased with increasing Darcy number and porosity. It is found that the convective heat and mass transfer rate are greatly affected by the presence of density maximum.