Freezing Front Research Articles

A General Analysis of Phase-Change Energy Storage for Solar Energy Applications

A unified approach is developed for the analysis of one, two, or three-phase melting or solidification of a semi-infinite medium with or without subcooling or superheating and imposed with constant, monotonic, or cyclic temperature or flux conditions. A source and sink method is presented in which a sink front is used to characterize a melt front while a source front is used to characterize a freeze front. An integrodifferential equation is then derived for the interface position which is linearized locally for numerical solution. This position is, in turn, used as input for the determination of the temperature distribution and energy storage and release in different phases of the medium. The numerical solution presented in this paper has shown to be unique, convergent, stable, and accurate. The analysis has been applied to the study of phase change in a subcooled paraffin wax imposed with a cyclic temperature condition. Test results yield some interesting phenomena related to the merging of phase-change fronts and hysteresis of energy storage and release, among others, which have not previously been reported in the literature. Their relations to the energy storage and release are particularly stressed in the paper.

Solution of Stefan problems imposed with cyclic temperature and flux boundary conditions

Stefan problems imposed with cyclic temperature and flux boundary conditions are solved by using source and sink methods. A source front is associated with a moving freeze front while a sink front is associated with a moving melt front. The solution is expressed in a set of coupled integrodifferential equations, which are solved numerically for interface positions, temperature profiles, and cumulative and instantaneous heat storage and release. The solution methods have been shown to be unique, convergent, stable, and accurate. While they are used to test one cycle each of the temperature and flux conditions, the developed methods are general and applicable to multiple cycles. The numerical results reveal interesting phenomena not previously reported in the literature. Their relevance to energy storage and material processing and treatment is also covered.

THEORIES OF THERMOELASTIC INSTABILITY DURINGSOLIDIFICATION BASED ON THE NEUMANNTEMPERATURE SOLUTION

The evolution of contact pressure at the metal/mold interface in an idealized, directional solidification process is examined using a thermohypoelastic stress function and the Neumann temperature solution. Nonuniform thermal distortion of the casting is established through the application of an oscillatory temperature profile at the mold interface. This is an attempt to study the effects of the often highly irregular cooling profiles in typical industrial casting processes (albeit in an idealized fashion). In many of these processes, it is virtually impossible to cool the ingot uniformly due to a variety of process conditions. Nonuniform thermal distortion causes the contact pressure at the mold interface as well as the macroscopic freezing front morphology to oscillate. If the contact pressure exceeds the hydrostatic pressure of the residual molten metal to the point where its net value is zero, then an air gap is nucleated. This represents a condition in which the casting and the mold surfaces locally b...

Dynamics of glass cooling applied to preform fabrication

The rapid change of viscosity with temperature in fluoride glass is often used to advantage in the making of preforms. In effect a freeze front moves in from the mould wall and, at the appropriate time, the central still-molten glass is allowed to drain. Core glass is then substituted to complete the preform. The dynamics of this operation are investigated by use of a computer model to obtain some general guidelines.

Numerical study of two-dimensional freezing in an annulus

An evaluation is made of the results of a numerical study on two-dimensional freezing in an annulus made up of an initially superheated phase-change medium. Numerical results are used to deduce a relation between the nondimensional discharge time and the other parameters. The velocity of the freeze front decreases with time because of the increase of interface area as the freezing proceeds radially outward, followed by a marginal decrease in the freezing rate due to the presence of the adiabatic surface; sensible cooling then occurs only where the freeze front has already reached the adiabatic surface. 6 refs.

Effects of Advancing Freeze Fronts on Distributions of Fine-grained Sediment Particles in Seawater- and Freshwater-Slush Ice Slurries

ABSTRACT Experiments were performed to evaluate the effects of advancing freeze fronts on movements of fine-grained sediment particles in seawater- and freshwater-slush ice slurries. In the freshwater experiment, the horizontal migrations of clay-sized particles in response to a laterally advancing freeze front were documented photographically. Differential migration of particles as a function of their size was also noted. In the seawater-slush ice experiment involving downward movement of a freeze front through a sediment-laden slush ice layer, time-series measurements were taken for 1) accumulations of sediment released from the ice into the underlying water column, 2) decreases in temperature in the ice matrix, and 3) increases in salinity in the water beneath the ice. Results of the latter experiment support the contention that a downward congealing slush ice matrix can purge itself of at least a portion of an entrained sediment load during an evolving freezing process. However, most of the sediment load initially carried by the slush ice remained at the conclusion of the experiment. This observation has implications for the importance of spatial transport and deposition of ice-rafted sediments to overall sediment budgets in regions affected by sea ice. In summary, migration of sediment particles in congealing slush ice matrices due to freeze front advances can be important to geological, physical and biological processes as well as commercial activities in arctic marine and nearshore regions.

The ‘frozen front’: the Labour government, the division of Germany and the origins of the cold war, 1945–7

Scholars have long argued over the origins, nature and impact of the cold war. 1 During the 1950s and the early 1960s the West was held in thrall by the so-called traditionalist view of the cold war, expounded, in many cases, by those who had been active in government during these years. According to this school of thought, the desire of the Soviet Union to expand across Europe was held in check only by the defensive, protective policy of the United States. The cold war was in essence an American response to a Soviet challenge. During the Vietnam War and the crisis of American self-confidence that ensued, American scholars took a fresh look at the 1940s. These scholars' revisionism led them to depict the early cold war years as a period of the onward march of American capitalism, seeking power, influence and East European and world markets, using the myth of Soviet expansionism to mask the true nature of the United States' own foreign policy. Both these interpretations cast Britain in a supporting rather than a leading role. One reason for this is that Britain is seen in retrospect as a middle-ranking power, unlikely to have been capable of determining the course of events in Europe. It has, however, become increasingly clear since the opening of the relevant British archives that such a view is unhistorical. Whatever happened later, Britain was, and still regarded itself as, a major power in the immediate postwar years.2 This article, based mainly on the official British archives, will argue that to the extent that the cold war began with the division of Germany between East and West, Britain carries the responsibility for the cold war as much as Russia or America. It was not until 1948 that the lines of bipolar confrontation were publicly drawn, symbolized by the European Recovery Programme, the Berlin crisis and the formation of the North Atlantic Treaty Organization. In the postwar diplomatic negotiations about Germany, negotiations that shaped this superpower confrontation, Britain played a leading part.

Overwinter Soil Moisture Changes

ABSTRACT FIELD measurements of the overwinter soil moisture changes, those occurring from freeze-up up to the time of snowmelt, in the Canadian Prairies show that moisture losses are common from the shallow depth adjacent to the soil surface whereas, depending on the soil moisture content at the time of freezing, the amount of moisture in a 0 to 1 m soil layer remains unchanged or increases. It is shown that on irrigated areas the amount of moisture migration to a freezing front in the depth, 0 to 1 m, greatly exceeds snowmelt infiltration; in dryland areas overwinter changes represent, on the average, 20 to 50% of the soil moisture increase between fall and the end of snowmelt. The need for identifying the primary mode of transfer, liquid or vapor, is emphasized. Information is provided on the interrelationships between overwinter changes, fall soil moisture and soil temperature

A Simple Model of Ice Segregation Using an Analytic Function to Model Heat and Soil-Water Flow

For slowly moving freezing fronts in soil, the heat-transport equation may be approximated by the Laplacian of temperature. Consequently, potential theory may be assumed to apply and the temperature state can be approximated by an analytic function. The movement of freezing fronts may be approximated by a time-stepped solution of the phase-change problem, thus solving directly for heat flow across a freezing or thawing front. Moisture transport may approximated by using an exact solution of the moisture-transport equation assuming quasi-steady-state conditions, appropriate boundary conditions, and an exponential function relating unsaturated hydraulic conductivity (defined within the thawed zones) to pore water pressure (tension). This approach is used to develop a single model of ice segregation (frost-heave) in freezing soils. Applications to published and experimental one-dimension soil column freezing data show promising results.

Stresses in buried conduits caused by freezing front

A laboratory experiment modeling the buried conduit problem was performed to study the stress changes in the conduit as a result of frost penetration in the soil. The model consisted of a large-scale soil container insulated on all sides except the top. The level and temperature of the ground water in the container, and the end restraints of the buried conduit, could be controlled. The model was placed in a cold room where the air temperature could be reduced to −25°C. The experimental results, supplemented by the available field data, demonstrate the influence of soil freezing on pipe bending stresses. Maximum frost depth, which can vary with the rate of freezing even for comparable air freezing indexes, is a significant soil thermal parameter that correlates with pipe stresses. Availability of ground water significantly increases pipe stresses while pipe-end restraints tend to decrease them slightly. The results suggest that the water expulsion by the advancing freezing front causes loss of soil stiffness due to the increased pore water pressures and decreased effective stresses in the soil.

Application of Dual-Energy Gamma-Ray Technique for Nondestructive Soil Moisture and Density Measurement During Freezing

Frost heave is a phenomenon unique to freezing soils. To study frost heave, a dual-energy gamma-ray technique has been adapted to determine nondestructively the soil bulk density variation and moisture migration that occur as the soil freezes and heaves. The technique uses two radioactive sources for simultaneous measurement of density and moisture content. Test results show good agreement between measured and calculated data for density and moisture content. The test data indicate that the dual-energy gamma-ray technique can accurately and reliably provide continuous nondestructive monitoring of both density and moisture content variations along a freezing soil column. Freeze front location can also be determined.

Analysis of Propagation of Freezing and Thawing Fronts

ABSTRACTThe modified isotherm migration method (MIMM) is used to calculate the temperature profiles and freezing (thawing) times for symmetrically cooled (heated) slabs with meat‐like thermal properties. MIMM, which is reviewed briefly is not restricted to the usual idealizations such as zero surface resistance, uniform critical temperature distribution, and infinitely large sample. Dimensional analysis is used to identify the dimensionless groups controlling freezing and thawing front propogation in slabs, cylinders, and spheres having uniform thermal properties and constant freezing temperature. The MIMM results provide a basis for evaluating the qualitative origins and the quantitative extent of the success of Plank's (1913) old model. The freezing times predicted by the moving front model used here agree with those predicted by the empirical correlation found by Cleland and Earle for the Karlsruhe test substance.

Numerical Method For the Two-dimensional Freezing Problem Around a Horizontal Cylinder Encompassing a Density Inversion Point

A numerical method for the two-dimensional freezing problem around a horizontal cylinder involving a maximum density point was presented. This problem offers a complex one involving the natural convection flow around the freezing front and the heat conduction inside it, and no exact analysis of it has been performed so far. The present numerical method utilizes the so-called boundary fixing method in which both the boundaries of body and freezing front are immobilized and it is applicable to general multi-dimensional moving boundary problems. Example calculations are made for steady freezing front shape, temperature distribution in solid phase, and also isotherms, streamlines, and Nusselt number distribution around the cylinder

Instability of the Planar Freeze Front During Solidification of an Aqueous Binary Solution

A model describing the heat transfer, solute redistribution, and interface stability during the planar solidification of an aqueous binary solution has been developed. The temperature field was calculated using a modified Ka´rma´n-Pohlhausen integral technique. With this technique, the averaged heat conduction equation was solved with the full set of boundary conditions using an assumed spatial variation of the temperature profile. The concentration field was solved for analytically. The stability of the planar freezing morphology was determined using the Mullins-Sekerka stability criterion, in which the time variation of a sinusoidal perturbation of the planar interface was calculated. Application of this criterion to the freezing of saline indicates that for any practical freezing rate the planar interface was unstable. This represents an indictment of the planar freezing model and indicates the tendency for aqueous solutions to freeze dendritically.

Eddy current study of solidification in lead and lead 20 pct tin

The use of eddy currents to nondestructively evaluate metallic solidification is modelled in one dimension. Calculated responses of the reflected signals show characteristics that can be identified with different solidification morphologies, the extent of freezing, and temperature changes. Experimental verification of the calculated results is done with lead and a lead-20 tin alloy. Morphological details of the solidification for both lead and lead-20 tin alloy are extracted from the eddy current responses in real time. Features such as uniform freezing front motion in pure lead and phase formation in the alloy are detected. Finally, compensation for the thermal gradients in the copper mold and the phase shift in the balancing network allow for good agreement between the eddy current response and the calculated response for freezing.

A model for frost heave including overburden

A mathematical model for coupled mass and energy transfer in freezing soils has been developed that accounts for the effects of overburden. Heaving is allowed to occur wherever the ice pressure is at least as large as the overburden. The ice pressure is calculated from the temperature and water pressure using the generalized Clapeyron equation. The one-dimensional energy and mass balances are solved using a fully implicit, Galerkin procedure. The model predicts the observed rapid decline of heave rate with increasing overburden. Comparisons of predictions with the recent data by Penner and Ueda indicate that the model predicts too much heave at low overburdens and too much heave at high temperature gradients. There is apparently some other mechanism for limiting heave when a thin frozen fringe is expected between the freeze front and the lens. In order to match the experimental heave, the thickness of the frozen fringe had to be increased by about one mm. in addition to that normally predicted by the model.

Pore Water Pressure and Consolidation in Unfrozen Soil near the Freezing Front

When the soft soil freezes accompanying with the water suction, the effective stress increases with the lowering of pore water pressure that takes place near the freezing front, and thereby the unfrozen soil adjacent to it is subjected to a fairly strong dewatering consolidation. In this paper pore water pressure distribution in front of unidirectional freezing front penetrating at a constant rate is analyzed theoretically, and it is found that the lowering of pore water pressure is larger than expected. Therefore the lowering of the pressure may explain a soft soil subsidence after thawing and sludge dewatering by freezing. Influence region of dewatering consolidation, δs, is given by Cυ/U, and transitional time attaining to a steady state, τt, is given by A·Cυ/U2. Here Cυ is coefficient of consolidation, U is frost penetration rate and A is a positive constant.In the case of soil which is relatively low in the degree of consolidation, the freezing expansion and dewatering consolidation take place simultaneously, and at far from δs in unfrozen soil the result of their mutually subtracted effect is observed as the amount of frost heave. Then, frost heave ratio, ξ, is given approximately by ξ0+nfΓ. Here ξ0is a characteristic constant of the soil, nf is free water content of soil at freezing temperature andΓ is nondimensional volumetric expansion ratio of water at freezing ≅ 0. 09.

Exact solution for freezing of humid porous half-space

New Stephan-like problem is defined and exact solutions for temperature and moisture distributions as well as the position of the moving freezing front in a humid porous half-space are obtained. The analytical solution is programmed in BASIC and some illustrative examples are plotted.

Reticulate Ice Veins in Permafrost, Northern Canada: Discussion

'Paper by Mackay, J . R. Can. Geotech. J . 11(2), p p 230-237. In these soils horizontal ice lenses are rarely observed by themselves except as sub-horizontal lenses in the active layer. The discussers would like to expand upon one theory noted by the author, by suggesting two mechanisms for reticulate ice vein growth that cause cracking in the unfrozen soil ahead of the advancing freezing front. Water is drawn into, or forced into, these cracks where, in time, it is frozen by the 0 O C isotherm. It is to be noted that while the writers agree with Maskay

Importance of Arc Gap Control in Vacuum Consumable Arc Remelting of Superalloys

In vacuum consumable arc remelting, control over the ingot solidification rate is of paramount importance to optimum product quality. In general, solidification rate is very dependent upon ingot size and melting current which help to define the general characteristics of the molten pool geometry and that of the advancing freezing front within the ingot. However, control of these parameters is achieved by precisely monitoring arc gap throughout the melting operation. By having a close control over the arc gap, the vacuum melter can eliminate variations in solidification rate which can cause localized harmful segregates. There are several types of controls used in the vacuum melting industry today and these are discussed, including the hash control used at Special Metals Corporation. The important features of the control are outlined with respect to their influence on arc gap, including speed of feed, voltage limitation, and basic hash/arc gap relationships. The importance of controlling the arc gap in Udimet 718 is shown by illustrating the effect of intentional controlled variations in arc gap at several melting currents on the formation of several types of segregates. The method of programming arc melt cycles to gain the most control over arc gap to ensure a reproducible, high quality product is discussed.