Density Inversion Of Water Research Articles

Entropy Generation, Heat Transfer of Water Near Density Inversion Region with Relative Positions of Hot and Cold Walls: Numerical Analysis

This study investigates the entropy generation and heat transfer of water density inversion region in a square cavity with the different relative positions of hot and cold walls by numerical simulation. Mathematical models are solved using the EES (Engineering Equation Solver) program. A physical model is a 38 mm square cavity filled with water, with cold and hot wall temperatures maintained at 0oC and 10oC. Results indicated that the Nusselt number of cases 1 (cold and hot walls on both sides) is higher than case 2 (hot wall above, cold wall below) and case 3 (cold wall above, hot wall below) by 1.582 and 1.059 times, respectively. The average total generation per unit volume in case 1 increases by 1.577 times and 1.059 times, respectively, compared to cases 2 and 3, which almost correspondingly increase with heat transfer capacity. Entropy generation by fluid friction is negligible

Supercritical convective flows of melt water in an open horizontal rectangular cavity with a prescribed vertical heat flux

The influence of the intensity of heating, expressed by the Grashof number, on supercritical regimes of thermal convection of melt water in a horizontal rectangular cavity with an aspect ratio of two is investigated. On the lateral solid boundaries, the thermal insulation conditions are satisfied, and a constant vertical heat flux is set on the lower solid and upper free horizontal and non-deformable edges. Under conditions when the cavity-average temperature is close to the temperature of water density inversion in the cavity, a state of mechanical equilibrium is possible, when a stably stratified layer is located on top of an unstable stratified layer. For two cases of the position of the horizontal boundary between these layers, the structure of stationary planar supercritical thermal convection is investigated. The calculations were carried out by the finite-difference method on a square grid with 128 nodes along the horizontal coordinate and 64 along the vertical one. Calculations have shown that, with an equal thickness of unstable and stably stratified layers, supercritical convection in the region up to about six supercriticalities has a two-cell structure in the horizontal direction with two (large at the bottom and weaker at the top) vortices in each of the cells. With an increase in supercriticality, this two-cell structure turns into a four-cell structure in a hysteresis manner. For the case when the thickness of the stably stratified layer is three times less than the thickness of the unstable stratified layer, the supercritical convective flow has the general form of a single-vortex cell elongated horizontally. With an increase in the Grashof number up to about a hundredfold supercriticality, it remains generally single-vortex and does not experience bifurcations.

Modeling Coupled Conduction–Convection Ice Formation on Horizontal Axially Finned and Unfinned Tubes

The freezing of water around immersed unfinned and finned horizontal tubes is simulated numerically. The impact of natural convection as well as the water density inversion with temperature is considered. The equations governing both fluid flow and heat transfer around the tubes and through the solid–liquid interface are solved using finite difference schemes. To follow the moving solid–liquid boundary, dynamic grid generation is performed using the elliptic partial differential equation method with iterative interpolating smoothing to avoid divergence. For validation, the present results for unfinned tubes are compared with experimental studies reported in the literature. The present numerical simulations are aimed at improving our understanding of the parameters affecting the freezing process around both finned and unfinned tubes. The results showed that the flow patterns are similar in both tube configurations with one main vortex in the liquid region when there is no inversion in the water density. The presence of fins complicates the distribution of local Nusselt number along the solid–liquid interface in comparison with the unfinned tube. The impact of natural convection on the rate of ice formation is limited to the initial period of the freezing process. The results also show the freezing enhancement when utilizing fins. An accumulated ice mass correlation is developed for each tube configuration. This model can be used to optimize the design of both finned and unfinned tubes in energy storage systems, which are viable tools for air conditioning load shifting and leveling.

Density maximum effects on mixed convection in a square lid-driven enclosure filled with Cu-water nanofluids

In this paper, the authors investigate the laminar mixed convection flow of Cu-water nanofluid near density maximum of water in a lid-driven enclosure. The governing equations based on the Boussinesq and non-Boussinesq homogenous models are solved using a pressure-based finite volume method. Four different lid-driven cases are simulated when volume fractions of nanoparticles range from 0.0, 0.03 and 0.05 and the Richardson (Ri) number varies from 0.01, 0.1, 1, 10 and 100 under both the Boussinesq and non-Boussinesq approximations. Streamlines, isotherms, mid-plane velocities, mid-plane temperature and the average Nusselt (Nu) number in various boundary conditions have been analyzed. Results show that the flow pattern and thermal behavior of the nanofluid strongly depend on the density inversion of water and the presence of nanoparticles. Further, the findings indicate that the density inversion phenomenon leads to a lower average Nu number under the non-Boussinesq approximation compared to the Boussinesq approximation, suggesting that studies with the Boussinesq approximation may overestimate heat transfer performance. In addition, the average Nu number increases as the volume fractions of nanoparticles increase. Finally, the maximum value of the average Nu number can be achieved under the Boussinesq approximation when the shear-driven force is aligned with the buoyancy force.

Natural convection of Cu–water nanofluid near water density inversion in horizontal annulus with different arrangements of discrete heat source – Sink pair

In this paper, natural convection heat transfer is studied in two-dimensional horizontal concentric cylindrical annulus with discrete source-sink pairs. The effects of Cu nanoparticles on natural convection of water near its density maximum were considered in numerical simulations. Geometry consisting of two hot and cold sources (constant temperature) with different arrangements and the remained parts were assumed to be adiabatic. The governing equations were formulated using both the Boussinesq (B) and non-Boussinesq (NB) homogenous models and were solved on a non-uniform mesh using a pressure-based finite volume method. The computations were carried out for Pr=13.31, Rayleigh number from 104 to 5×105 and volume fraction of nanoparticles from 0 to 0.08. This work with pure fluid and nanofluid was validated by previous studies and the results were shown in three cases under investigation. The results were presented from streamlines and isotherms flow field, local and average Nusselt number. It was found that different arrangements by different angles and density inversion affected founding best state of heat transfer in each case and general enhancement of heat transfer was obtained by adding volume fractions of nanoparticles, so average Nusselt number increased and an optimum design was also found. It was concluded that the B approximation in comparison to NB approximation gave rise to the higher heat transfer rate. The findings showed that which of cases was applicable to optimization design in industry and especial in heat exchanger.

Entropy generation and natural convection of nanoparticle-water mixture (nanofluid) near water density inversion in an enclosure with various patterns of vertical wavy walls

Entropy generation due to laminar natural convection of Cu–water nanofluid near the density maximum of water in a two-dimensional enclosure with various patterns of vertical wavy walls is investigated numerically. In order to study the nature of irreversibility in terms of entropy generation in the presence of nanoparticle near water density inversion, the second law of thermodynamics is applied. The governing equations are formulated using both the Boussinesq and non-Boussinesq homogenous models and solved on a non-uniform mesh using a pressure-based finite volume method. The calculations are performed for Ra number of 105, 106 and a range of nanoparticle volume fraction from 0 and 0.05. The results are presented and discussed in terms of streamlines, isotherms patterns, contours of local entropy generation, average Nusselt number and average entropy generation. It was found that both the density inversion and the presence of nanoparticles play a significant role in the flow field structure, heat transfer characteristics and entropy generation. It was concluded that the Boussinesq approximation gave rise to the higher average heat transfer rate and entropy generation as compared to non-Boussinesq approximation. In addition, the average Nusselt number and entropy generation were found to decrease as the volume fraction of nanoparticle increased. Finally, the formation of bi-cellular flow structure substantiates the effective role of density inversion of water in the free convection characteristics.

Onset of convective instabilities in under-ice melt ponds

The onset of double-diffusive natural convection in under-ice melt ponds is investigated through a linear stability analysis. The three-layer configuration is composed by a fluid layer (melt pond) overlying a saturated porous medium (ice matrix), which in turn overlies another fluid layer (under-ice melt pond). Water density inversion is taken into account by adopting a density profile with a quadratic temperature dependence and a linear concentration dependence. We show that the key parameter affecting stability is the depth of the ice matrix, while the depths of the upper and lower fluid layers play a marginal role. A Hopf bifurcation is observed in the whole range of parameters studied, and the size of the convection cells depends on ice permeability. The influence of the external temperature gradient is investigated by means of the definition of an extra thermal parameter accounting for the relative position of the density maximum. It is shown that convection is favored by larger temperature gradients, which occur during Arctic summer.

Natural convection of nanoparticle–water mixture near its density inversion in a rectangular enclosure

Natural convection of mixture of nanoparticles and water near its density maximum in a rectangular enclosure is studied numerically. A non-Boussinesq homogenous model is used in mathematical formulations of governing equations. The finite volume method is used to solve the governing equations. The results are presented graphically in the form of streamlines, isotherms and velocity vectors and are discussed for various nanoparticle volume fractions. It is observed that flow and temperature field is affected significantly in the presence of nanoparticles. The average heat transfer rate considering a non-Boussinesq temperature-dependent density (inversion of density) is lower than considering a Boussinesq temperature-dependent density. The average Nusselt number increases with an increase of nanoparticle volume fraction. It is observed that the density inversion of water leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. The properties of nanoparticles also affect the fluid flow and heat transfer.

Numerical Study on Natural Convection of Water Near Its Density Maximum in Horizontal Annulus

In this paper, numerical simulations for natural convection of water near its maximum-density in horizontal annulus with isothermal walls are performed with the finite volume method. The results show that there are different steady-state flow patterns for different control parameters in the range of calculation for concentric horizontal annulus. Furthermore, the effects of the non-dimensional parameters, which include the radius ratio and density inversion parameter, on the temperature and flow fields are discussed, and the variation of the average Nusselt number is analyzed at different conditions. It is found that density inversion of water has a great effect on natural convective heat transfer in horizontal annulus.

Effect of temperature dependent properties on MHD convection of water near its density maximum in a square cavity

Natural convection of water near its density maximum in the presence of magnetic field in a cavity with temperature dependent properties is studied numerically. The viscosity and thermal conductivity of the water is varied with reference temperature and calculated by cubic polynomial. The finite volume method is used to solve the governing equations. The results are presented graphically in the form of streamlines, isotherms and velocity vectors and are discussed for various combinations of reference temperature parameter, Rayleigh number, density inversion parameter and Hartmann number. It is observed that flow and temperature field are affected significantly by changing the reference temperature parameter for temperature dependent thermal conductivity and both temperature dependent viscosity and thermal conductivity cases. There is no significant effect on fluid flow and temperature distributions for temperature dependent viscosity case when changing the values of reference temperature parameter. The average heat transfer rate considering temperature-dependent viscosity are higher than considering temperature-dependent thermal conductivity and both temperature-dependent viscosity and thermal conductivity. The average Nusselt number decreases with an increase of Hartmann number. It is observed that the density inversion of water leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. The heat transfer rate behaves non-linearly with density inversion parameter. The direction of external magnetic field also affect the fluid flow and heat transfer.

Buoyancy-driven convection of water near its density maximum with time periodic partially active vertical walls

The effect of density inversion on transient natural convection heat transfer of cold water in a square cavity with partially active vertical walls is studied numerically. The governing equations are solved by control volume method with power law scheme. In the hot location the temperature is varied sinusoidally and in the cold location uniform temperature is maintained. Nine different positions of the active zones are considered. Results are discussed for various values of the amplitude, period and different Grashof numbers and presented graphically in the form of isotherms, streamlines, mid-height velocity profile and average Nusselt number. It is found that density inversion of water affects natural convection flow and heat transfer. Heat transfer rate is enhanced upto 80% when the heating location is in the middle of the hot wall.

Modelling ice melting processes: numerical and experimental validation

PurposeThis work is devoted to the experimental analysis, numerical modelling and validation of ice melting processes.Design/methodology/approachThe thermally coupled incompressible Navier‐Stokes equations including water density inversion and isothermal phase‐change phenomena are assumed as the governing equations of the problem. A fixed‐mesh finite element formulation is proposed for the numerical solution of such model. In particular, this formulation is applied to the analysis of two different transient problems.FindingsThe numerical results computed with the finite element formulation have been found to be very similar to the corresponding predictions, also obtained in this study, provided by a finite volume enthalpy‐based technique. Both numerical results, in turn, satisfactorily approached the available experimental measurements expressly conducted in the context of this work for validation purposes.Research limitations/implicationsThey are mainly due to some model simplifications (e.g. no volume changes are considered during the solid‐liquid transformation) and to the inherent difficulties associated with the experimental measurements.Practical implicationsThis study may be relevant for a better understanding of the phenomena occurring in different engineering applications involving phase‐change in water: food freezing, ice formation in pipes, freezing/melting processes in soils, ice growth in plane wings, etc.Originality/valueThe study is mainly focused on the validation of the numerical predictions obtained with the finite element formulation mentioned above with other results provided by a well‐known finite volume technique and, in addition, with available laboratory measurements carried out in the context of this work.

Influence of Density Inversion on Thawing Around a Cylinder in a Frozen Saturated Porous Medium

An analytical study is made of the convective flow field produced when a warm cylinder maintained at a fixed temperature above freezing is buried in saturated frozen porous medium. The flow field is shown to have a double cell pattern due to the density inversion of water at ~ 4°C, with downward convection of heat dominating at cylinder temperatures of below ~ 10°C and upward heat convection dominating at temperatures greater than this. The analysis uses a perturbation technique to determine the first-order convective correction to the flow and temperature fields around the cylinder for a quasi-static case. It demonstrates that the porous medium permeability and the cylinder temperature are the dominant factors in determining the point at which convection heat transfer becomes significant, with convection expected to be insignificant for Darcy permeabilies lower than 10−5 m/s. The analysis also gives an indication of the rates of thawing occurring in different directions without resorting to numerical methods. The practical implications of a thawing pattern significantly different to that predicted by conduction theory only are discussed briefly with respect to the problem of differential thaw settlement of arctic pipelines.

Visualization of Solidification in a Simulated Czochralski System

[S0022-1481(00)04003-2]

2719 密度逆転領域を含む水の自然対流における 3 次元数値解析

2719 密度逆転領域を含む水の自然対流における 3 次元数値解析

Effect of water density inversion on the plane-parallel flow and heat transfer in a channel of constant width

The results of a numerical study of the effect of cold-water density inversion (Prandtl number Pr=11.59) on the flow and heat transfer in a horizontal plane-parallel channel with isothermal top and bottom walls are presented. The calculations were performed for the Grashof number Gr=3·104, the Reynolds number Re=10, and the channel segment length-to-height ratiol/d=40. The wall temperature was so varied that the temperature difference between the top and bottom walls remained constant.

Transient Cooling of Water around Two Cylinders in a Rectangular Cavity. The Effect of the Spacing between the Cylinders.

Transient cooling of water around two cooled horizontal cylinders placed in a rectangular enclosure has been studied. The governing equations were solved by a finite difference method, and the flow structure and temperature distributions have been predicted. The purpose of the present study is to examine the effects of the spacing between the cylinders and the initial temperature of water on the cooling process of water. The initial water temperature was varied at 4, 6, 8 and 12°C, and timewise variations of the temperature field and the velocity field as well as the mean Nusselt numbers on the cylinder surfaces were compared. The effect of a change in the spacing between the cylinders on the cooling process appears earlier stage as the initial temperature of water is increased. Complicated flow patterns are observed for initial water temperatures larger than 4°C due to the density inversion of water, irrespective of the extent of the spacing.

Heat transfer characteristics of a rectangular natural circulation loop containing water near its density extreme

This article presents results of a theoretical and experimental study concerned with steady-state characteristics of a rectangular natural circulation loop with vertical heat transfer sections containing water near its density extreme. A one-dimensional model has been developed to simulate heat transfer behavior of the rectangular loop, with particular attention to unravel effect of density inversion of water near 4°C. In parallel to the theoretical simulations, supporting experiments have been undertaken to obtain data to verify the model. Fairly good agreement was found between the predicted and measured temperature distribution along the loop. Influence of density inversion effect has been clearly demonstrated to be substantially significant and needs to be taken into account when the operating temperature of the natural circulation loop filled with water encompassing its density-extreme temperature.

EFFECT OF DENSITY INVERSION ON COOLING OF WATER AROUND A CYLINDER IN A RECTANGULAR CAVITY

Transient natural convection in water around a cooled horizontal cylinder placed at the center of a rectangular enclosure has been studied. The governing equations were solved by a finite difference method, and the flow structure and temperature distributions have been predicted. The purpose of the present study was to examine the effects of the density inversion and the initial temperature of water on the cooling process. The initial water temperature was varied at 4, 6, 8, and 12°C, white the temperature of the cylinder surface was fixed at 0°C. The timewise variations of the temperature field and the velocity field as well as the mean and local Nusselt numbers on the cylinder surface were compared. Change in the initial water temperature largely affects fluid flows due to the density inversion of water. Complicated flow patterns are observed for initial water temperature higher than 4°; C. Cooling of water is most effective for an initial water temperature of 12°; C.

Transient Natural Convection of Water around a Cylinder in a Rectangular Cavity. Effect of the Density Inversion on Cooling of Water.

Transient natural convection in water around a cooled horizontal cylinder placed at the center of a rectangular enclosure has been studied. The governing equations were solved by a finite difference method, and the flow structure and temperature distributions have been predicted. The purpose of the present study was to examine the effects of the density inversion of water and the initial temperature of water on the cooling process of water. The initial water temperature was varied 4, 6, 8 and 12°C, and the timewise variations of the temperature field and the velocity field as well as the mean and local Nusselt numbers on the cylinder surface were compared. The change in the initial water temperature largely affects fluid flows due to the density inversion of water. Complicated flow patterns are observed for initial water temperatures larger than 4°C. The cooling of water is most effective for an initial water temperature of 12°C.