Solidification Layer Research Articles

Layer by layer solidification ofHe4in narrow porous media

We give a variational Monte Carlo description of $^{4}\mathrm{He}$ filling under pressure a porous material modeled by a smooth cylindrical nanopore. Our trial wave function is a shadow wave function which allows different degrees of correlation between $^{4}\mathrm{He}$ atoms depending on the distance from the pore wall but still preserving the full Bose symmetry. The radial density profile shows a strong layering of the $^{4}\mathrm{He}$ atoms which are located in concentric annuli. This system has a very rich phase diagram with at least four different phases. The layer in contact with the pore is always solid. For our narrow pore radius $(R=13\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$, as the density is increased, solidification takes place layer by layer, starting from the pore wall, as is confirmed by the static structure factors. The pore radius is too small to allow a bulklike solid to nucleate in the liquid region at the center of the pore, and in order to have a complete crystalline order in all the layers a pressure greater than $200\phantom{\rule{0.3em}{0ex}}\text{bar}$ is needed. Computing the one body density matrix we are able to estimate the condensate fraction, which is still nonzero even if all the layers are in the solid phase.

A moving boundary solution for solidification of lava lake and magma intrusion in the presence of time-varying contact temperature

During the solidification of a lava lake heat is released convectively from the top surface as well as conductively into the country rock from the base, leading to non-uniform solidification. The upper solidified layer grows at a faster rate than the lower solidified layer. Similarly, solidification of magma intrusion within the crust is also non-uniform due to the presence of thermal gradient in the crust. Available analytical solution for solidification of a melt layer assumes only symmetric cooling about the centre of the layer. In the present work a moving boundary solution for thermal evolution and non-uniform solidification of a melt layer incorporating time-varying contact temperature conditions at both of its boundaries is developed. The solution is obtained by using the Fourier spectral approach in the space domain and a modified finite difference scheme in the time domain, and is validated with available analytical solutions for simple cases and a semi-analytical solution for the case involving temperature gradient in the country rock. This solution can be used to analyse solidification of lava lakes and magma intrusions experiencing time-dependent temperature variation at their contacts with the country rock.

On the theory of glass solidification

The process of glass solidification is analyzed in the context of the fundamental principles of physicochemical kinetics. The concept of the emergence of “solidification seeds”, formation of “solidification layers” and their migration into the glass volume are discussed. It is demonstrated that the level of diathermancy of tinted glasses can characterize the force of the interaction between the colorant complexes and the main silicon-oxygen elements in glass and, consequently, can influence viscosity variation in solidifying. The proposed theoretical principles agree well with experimental and industrial data.

Evolution of microstructure in spray formed Al–18%Si alloy

Spray atomization and deposition process has emerged as an alternative to ingot and powder metallurgy routes. In the present investigation, we study the microstructural control during spray deposition of hypereutectic Al–Si alloy, employing different nozzle to substrate distances. Spray deposition is carried out using convergent–divergent close-coupled nozzle design at deposition distances of 200, 300, 450, and 550 mm. Microstructural characterization of oversprayed powders as well as spray formed deposits was performed. Microstructural features obtained at smaller deposition distance consist of co-existing primary Si phase and needle like eutectic Si. Dendrites of α-Al phase are observed indicating a large undercooling of the liquid pool prior to solidification. A large number of pre-solidified particles with very fine microstructure, embedded in a relatively coarse region, typically characterize those evolved at large deposition distances. However, at intermediate deposition distances, uniform and refined primary Si phases, 3–8 μm size, are observed. An undercooling effect is manifested in both the spray deposits as well as powder particles. These microstructural features have been discussed in light of a proposed model, which describes the presence of two layers (1) solidification layer and (2) interaction layer in the liquid pool.

Evolution of microstructure in spray formed Al?18%Si alloy

Spray atomization and deposition process has emerged as an alternative to ingot and powder metallurgy routes. In the present investigation, we study the microstructural control during spray deposition of hypereutectic Al–Si alloy, employing different nozzle to substrate distances. Spray deposition is carried out using convergent–divergent close-coupled nozzle design at deposition distances of 200, 300, 450, and 550 mm. Microstructural characterization of oversprayed powders as well as spray formed deposits was performed. Microstructural features obtained at smaller deposition distance consist of co-existing primary Si phase and needle like eutectic Si. Dendrites of α-Al phase are observed indicating a large undercooling of the liquid pool prior to solidification. A large number of pre-solidified particles with very fine microstructure, embedded in a relatively coarse region, typically characterize those evolved at large deposition distances. However, at intermediate deposition distances, uniform and refined primary Si phases, 3–8 μm size, are observed. An undercooling effect is manifested in both the spray deposits as well as powder particles. These microstructural features have been discussed in light of a proposed model, which describes the presence of two layers (1) solidification layer and (2) interaction layer in the liquid pool.

Modelling of passive heating for replication of sub-micron patterns in optical disk substrates

The transcribability of pit or land groove structures in replicating an optical disk substrate greatly affects the performance of a high-density optical disk. However, a solidified layer generated during the polymer filling worsens transcribability because the solidified layer prevents the polymer melt from filling the sub-micron patterns. Therefore, the development of the solidified layer during the filling stage of injection moulding must be delayed. For this delay, passive heating through an insulation layer has been used. In the present study, to examine the development of the solidified layer, delayed by passive heating, the flow of the polymer melt with passive heating was analysed. Passive heating delayed markedly the development of the solidified layer, reduced the viscosity of the polymer melt, and increased the fluidity of the polymer melt in the vicinity of the stamper surface with the sub-micron patterns. As a result, we predict that passive heating can improve the transcribability of an optical disk substrate. To verify our prediction, we fabricated an optical disk substrate by using passive heating of a mould and measured the transcribability of an optical disk substrate.

An experimental study of enhanced heat transfer in rectangular PCM thermal storage

The heat-transfer characteristics of a latent-heat storage unit with a finned surface have been experimentally studied in terms of the solidification and melting processes by comparing them with those of a heat-storage unit with a plain surface. Paraffin with a melting point of 30 °C was used in the investigations because it is appropriate for thermal storage applications in buildings. Time-based variations of the temperature distributions and heat flux are explained from the results of observations of the melting and the solidification layers. The dimensionless Nusselt number was calculated as a function of the Rayleigh number for natural convection in the paraffin for both the melting and the solidification processes. The effectiveness of the fins was calculated from the quotient of the heat flux with fins and the heat flux without fins.

단열층을 이용한 광디스크 기판의 서브 미크론 성형에 대한 수치 해석

Transcribability of pit or land groove structures in replicating an optical disk substrate greatly affects the performance of a high-density optical disk. However, a solidified layer, generated during the polymer filling, deteriorates transcribability because the solidified layer prevents the polymer melt from filling the sub-micro patterns. Therefore, the development of the solidified layer during filling stage of injection molding must be delayed. For this delay, passive heating by insulation layer has been used. In the present study, to examine the development of the solidified layer delayed by passive heating, the flow of polymer melt with passive heating was analyzed. Passive heating markedly delayed the development of the solidified layer, reduced the viscosity of the polymer melt, and increased the fluidity of the polymer melt in the vicinity of the stamper surface with the sub-micro patterns. As a result, we predict that passive heating can improve transcribability of an optical disk substrate. To verify our prediction, we fabricated an optical disk substrate by using passive heating of a mold and measured the transcribability of an optical disk substrate.

Size effect in cast-in insertion process

In the cast-in insertion process, the thermal conditions necessary for good bonding have been estimated by volume ratio. However, even with the same volume ratio, the bonding state varies with the size of the insert and the casting as well as with the location of the insert in the casting. Estimates of the effects of these geometrical conditions are useful to improve ease and reliability of this process. This study performed solidification analysis together with experiments to explain the size effect in cast-in insertion, and the results are discussed and compared. The model used in the study is a hollow cylindrical ductile iron casting and a mild steel ring insert located at the bottom of the cylinder. The standard size is about 80mm in diameter and height, and the scale was varied from 0.33 to 3 times the standard size for three volume ratios, 20, 25, and 30. The periods where the insert is in contact with liquidus melt (liquidus period) obtained by calculations were compared as the thermal condition. The calculations showed that, the liquid contact time is longer for larger sizes until about twice the standard size, but that it then decreases rapidly with even larger sizes. This is because the thick solidified layer formed by the large cooling effect of the insert does not remelt. Large size is not always advantageous to good bonding, and it is necessary to choose volume ratios suitable to the size of a casting.

OS12W0465 Strength evaluation of centrifugally cast steel pipes for gas equipment

Austenitic stainless steel pipes made by centrifugal casting have been used as burner material for heat-treatment furnaces and other industrial furnaces. This material has a high heat resistance, but brittle fracture can occur earlier than expected. Brittle fracture may start in the final solidification layer with micro cavitated structure formed on the inner surface of centrifugally cast pipes during manufacturing. In the present study, the strength of the specimens of an austenitic stainless steel machined from centrifugally cast pipes was studied with attention to the final solidification layer on the inner surface of the pipe. The strength decreased with increasing area of the final solidification layer. In order to predict the fracture strength of pipes with solidification layers under a variety of yielding scales, two-parameter method was proposed based on the combination of the stress intensity factor criterion and the gross sectional yielding stress criterion.

Mechanism Dominating the Generation of Sink-Mark and Residual Stress in a Press-Formed Glassware from a Thermal Engineering Viewpoint.

This paper deals with an experimental study on the generation of sink-mark and residual stress in a press formed glassware. Since both phenomena appear in the cooling process after pressing, it is considered that they were related with the growth of solidification layer on the press-formed surface. In this paper, the growth of solidification layer in a glassware and the generation of residual stress due to non-uniform shrinkage of glass, i.e. the generation of thermal tempering stress were numerically predicted, and the mechanism dominating the generation of sink-mark and residual stress frozen in a press-formed glassware was discussed by comparing the numerical results with those measured in actual glassware, which were press-formed in this study. The obtained results can be summarized as follows: (1) With elongating the pressing duration, both the sink-mark depth and the compressive residual stress at the pressed surface decrease while temperature at the pressed surface are little affected by the pressing duration. (2) The pressing-duration dependency of the sink mark and residual stress at the pressed surface is qualitatively explained well by a hypothesis that the thermal tempering stress starts to appear in the glass just after the deformation of the pressed surface, i.e. the generation of sink-mark stops due to the rigidity of solidification layer, and that the switchover timing becomes later as the pressing duration is elongated. (3) The compressive residual stress at the pressed surface is considered to consist of the thermal tempering stress due to non-uniform shrinkage of glass and the bending stress in the solidification layer due to sink mark generation.

Dynamics and control of solidification of molten metal flows

A solidified layer on the inside of a cooled flow channel can be used to control the flow rate of molten material through that channel. This concept can be used for flow rate control of molten furnace products in the metallurgical industry. In this study, internal solidification of molten metal flows has been modeled mathematically for both steady-state and dynamic cases. The model predicted solidified layer thickness and metal flow rate. Experimental verification of the mathematical model was obtained using molten tin. Novel design features of the experimental apparatus included the use of boiling heat transfer and the vertical mounting of the cooling section. Engineering knowledge regarding the design, operation, and control of a pilot scale (24 kg/s) molten metal circuit was obtained during the construction, commissioning, and operation of the experimental apparatus. Experimental results for tin flow rate from the experimental apparatus were within experimental error of the predictions of the mathematical model.

Vorticity transport in solidification boundary layers

A solidification boundary layer, where vorticity is concentrated, is shown to scale as δ ∼ (v/V) sin θ where θ is the angle that the solidification front makes with the oncoming flow, v is the kinematic viscosity of the melt, and V is the solidification rate. Key similarities with the suction boundary layer are outlined. Transport of vorticity, by diffusion and advection, in flows that solidify is discussed in the context of the planar-flow spin casting process, with special attention paid to how vorticity leaves the flow. Direct experimental evidence for a solidification layer in that application is reported.

Visualisation of Co-operation in the Construction of a Monolithic Building

When a monolithic construction is being erected, a strict regime must be followed on the thickness of a concrete layer and on the layer's solidification time. This regime can only be satisfied if all the cooperating ele ments (a concrete mixer, a crane, gangs working at the top of a building) harmonize. Assuming constant parameters of the co operating elements (but no constant increase of the construction within a 24-hour period is required), this paper presents the CoMB program, which dynamically visualizes this harmonization and reports the percentage of usage of co-operating elements. A didactic aspect of such a visualisation is outlined.

Effects of the Curvature on the Freezing Phenomena of a Laminar Water Flow in a Curved Channel

A numerical study is made on the ice-formation for a laminar flow in a curved channel. When the water flows through the curved channel with the walls specified below the freezing temperature, the ice layer has been formed on the curved surface, different from that of a straight channel. The fluctuation of ice layer has been predicted, considering the variation of velocity and temperature near the curved portion of channel. The study also takes into account the interaction existing between the laminar flow and the curved channel. In the solution strategy, the present study is substantially different from the existing works in that the complete set of governing equations in both the solid and liquid regions are resolved. The results from this study have been mainly presented, focusing on the variation of ice layer close to the curved portion. Numerical results have been obtained parametrically by varying the curved angle and the radius of curvature of channel, in addition to the variation of Reynolds numbers and wall temperatures of channel. The results show that the curved shape of channel has the great effect on the thickness of the solidification layer. The wave of ice layer thickness appears in the vicinity of curved portion. This behavior of ice layer has been amplified as is the increasing of curved angle and the radius of curvature of channel. In addition, the ice layer becomes thin as Reynolds numbers in increasing. And also, as the wall temperature of channel increases, the width of channel becomes to be shrunk due to the growth of ice layers in the upper and lower wall of channel.

An analytical simulation of solidification behavior within deposited preform during spray forming process

Abstract Solidification within spray deposited preform is one of the key processing stages of spray forming, which has a substantial influence on the formation of the final microstructure of the preform. For the sake of optimizing the process and getting desired microstructure and properties of the preform, the solidification behavior should be fully understood. In this investigation, a concept of ‘virtual’ solidification layer was applied to establish an analytical model to simulate the solidification behavior within the preform during spray forming process, which will provide clearer physical pictures of the solidification behavior. According to the model developed, a simulation of the solidification behavior was performed for a typical Al–Cu alloy. The results show that both the processing parameters (such as deposition rate and temperature of spray cone at the point of impingement) and the thermophysical properties of the material are the important factors controlling the solidification behavior. Even for the same thermodynamic state of spray cone at the point of impingement, the top surface temperature of the preform will change conspicuously as variation of the processing parameters or thermophysical properties of the material takes place, which will cause the variation of microstructure and properties of the preform. Therefore, the principle of taking the thermodynamic state of spray cone at the point of impingement as the key factor controlling the spray deposition process should be modified adequately. A new parameter (the surface temperature of the preform) for the processing control of spray forming was proposed.

Natural convection heat transfer of the low prandtl number fluid with solidified layer formation

Experimental and analytical studies have been performed on natural convection heat transfer in the low Prandtl number fluid of the molten metal with a rapid solidified layer formation. The experimental results on the relationship between the Nusselt number and Rayleigh number were compared with the existing correlations. The temperature distribution and the heat transfer rate have been evaluated using the numerical model. The experimental study has shown that a solidified layer formation leads to a decrease of natural convection heat transfer rate in the metal pool, due to the solidified layer's action as a conducting thermal barrier. The experimental results are more similar to Globe and Dropkin's correlation than any others. Even though the Rayleigh number rapidly decreases due to an increase of the solidified layer thickness, the Nusselt number does not rapidly decrease because of the aspect ratio effect. The numerical results on the temperature profile and the heat transfer rate in the metal pool region match well with the experimental data.

Numerical Simulation of Dynamic Layer Solidification for a Eutectic Binary System.

Direct numerical simulations of layer solidification for unsteady condition have been carried out for a eutectic binary fluid of lauric acid and myristic acid, which exhibits a laminar flow between two parallel walls of different temperatures. Two-dimensional differential equations for momentum, heat and mass transfer are solved simultaneously using non-orthogonal coordinate systems. The boundary-fit grid is generated according to the time-changed shape of the solid-liquid interface. The predictions are discussed with reference to the time-changes of the shape of the solid-liquid (S-L) interface, the growth rate, the concentration at the S-L interface, the super-cooled layer adjacent to the S-L interface, and the concentration in the solid.

Compressible flow analysis of filling and postfilling in injection molding with phase-change effect

In order to predict the shrinkage, warpage and mechanical properties of the injection molded parts, it is necessary to know the history of the flow field during injection-molding processes. In the present investigation a numerical simulation program was developed to predict the flow field in filling and post-filling stages of injection molding. To simulate the real molding conditions more accurately, a generalized Hele-Shaw model for a non-Newtonian fluid was assumed considering the effects of phase change and compressibility of the resin. A finite-element-finite-difference (FEM-FDM) hybrid scheme with control volume approach was employed as the solving technique. For modeling the viscosity of the resin, a modified Cross model was used with a double-domain Tait equation of state being employed in describing the compressibility of the resin during molding. The energy balance equation, including latent-heat dissipation for semicrystalline materials, was solved in order to predict the solidified layer and temperature profile in detail. For verification of the numerical results obtained from the developed program, the simulation results were compared with the experimental results obtained from the test mold set designed in the current study using commercial-grade PP and the data available in the literature. Based on a comparison between experiments and simulations, it was found that the currently developed program was useful in unified simulations of filling and post-filling in injection-molding processes when considering the phase-change effect.

A numerical analysis of solid-liquid phase change heat transfer around a single and two horizontal, vertically spaced cylinders in a rectangular cavity

In the present study, a new numerical model is proposed to analyze solid-liquid phase change heat transfer in a complicated geometry. The present model can treat the solid/liquid phase change heat transfer with/without porous media, as well as conventional transient natural convection with/without porous media. Solidification calculations of pure water (without porous media) around a single cylinder and two cylinders were performed to check the validity of the model. The interaction of two solidification layers were examined, and the effects of natural convection in the melt on the solidification process were also studied. The numerical results were found to be in excellent agreement with experimental data. It was also shown that for the initial water-temperature, Ti, of 0°C the solidification progresses more rapidly for the single cylinder than that for the two cylinders, but the reverse is true for Ti ⩾ 4°C.