Shrinkage induced flow during directional solidification of pure substance in a bottom cooled cavity: A study on flow reversal phenomena
TL;DR: In this article, a numerical model was proposed to capture the shrinkage induced flow during directional solidification of a pure substance in a bottom-cooled cavity, which indicated the existence of an unprecedented flow reversal phenomenon during the progression of the solidification process caused by the opposing nature of shrinkage and buoyancy effects.
Abstract: Development and proposition of a numerical model to capture the shrinkage induced flow during directional solidification of a pure substance in a bottom cooled cavity are carried out. A novel numerical scheme involving fixed grid-based volume fraction updating is proposed to track the solid–liquid interface, considering the inclusion of the shrinkage effect. Directional solidification in bottom cooled orientation is of particular interest since shrinkage and buoyancy effects oppose each other. The results from the proposed numerical model indicated the existence of an unprecedented flow reversal phenomenon during the progression of the solidification process, caused by the opposing nature of shrinkage and buoyancy effects. The flow reversal phenomena predicted by the numerical model are validated by conducting experiments involving directional solidification of coconut oil in a bottom cooled cavity. Qualitative and quantitative measurements of the velocity field and interface growth are obtained using the particle image velocimetry technique and compared with three dimensional numerical results. Once the flow reversal phenomena are established through numerical and experimental evidences, case studies are performed, considering varying material properties, cold boundary temperatures, initial temperatures of the melt, and cavity heights to find the effect of each of these parameters on flow reversal phenomena. The parametric study also allowed us to check the robustness and consistency of the proposed model. The proposed model will serve as an important milestone toward the development of numerical models for capturing macro-scale shrinkage defects and prediction of composition heterogeneity during directional alloy solidification.
Citations
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TL;DR: In this paper , a segment of the heat exchanger is numerically modelled to analyse the temporal behaviour of the latent heat energy storage system during the cycle of discharging, and transient numerical computation incorporates an iterative, finite volume method based on enthalpy-porosity technique for numerically model the phase change phenomena.
Abstract: The present study endeavours to represent a latest concept of utilizing similar heat transfer fluid (HTF) and phase change material (PCM) in a direct contact type PCM heat exchanger (DCHEX). This technique has been found more effective during melting process. In the following investigation, a segment of the heat exchanger is numerically modelled to analyse the temporal behaviour of the latent heat energy storage system during the cycle of discharging. The transient numerical computation incorporates an iterative, finite volume method based on enthalpy-porosity technique for numerically model the phase change phenomena. For the analysis, water is used as working fluid. To show the performance enhancement of this technique during melting process, a series of simulations are performed to examine the impact of varying HTF inlet condition and flow rates. The changes in the configuration of the heat exchanger are studied. Heat exchanger parameters such as difference between inlet and outlet temperature (ΔT), heat release rate (Q), temperature effectiveness (θ) and volumetric heat transfer coefficient (Uv) are evaluated for all such cases. A uniform exit temperature of the HTF is observed for most of the time with significant increase in the heat transfer in the direct contact type heat exchanger. Three distinct stages namely initial, intermediate and final phases are observed during the melting process. During the initial phase the parameters exhibits uniform behaviour. In the intermediate phase there is significant drop and rise in the parameters while during the final phase the value of parameters diminishes except for Uv. Increasing HTF flow rate promotes increment in heat transfer rate while increasing the inlet temperature of HTF is more desirable to increase the overall heat transfer coefficient.
3 citations
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TL;DR: In this paper, a fixed grid-based numerical scheme involving volume averaging of conserved parameters is proposed to investigate the effect of shrinkage induced flow (SIF) on freckling phenomena during bottom-up solidification of binary alloys.
Abstract: Freckle formation during directional solidification of binary alloy is a well-researched subject area. However, the influence of shrinkage induced flow (SIF) on freckling phenomena is barely reported. The focus of this work is to investigate this effect during bottom-up solidification of binary alloys. A fixed grid-based numerical scheme involving volume averaging of conserved parameters is proposed. The solidification geometry under consideration is a two-dimensional mold cavity with a central riser allowing continuous melt flow into the cavity. Model validation is obtained against existing numerical results involving directional solidification of Al-4.1 wt. % Cu alloy. However, heavier solute (Cu) rejection in the melt during solidification renders the validation case study devoid of freckling phenomena. The postvalidation investigations involve bottom up solidification of Al-30 wt. % Mg alloy with lighter solute (Mg) rejection, leading to solutal instability and freckle formation. The effect of SIF on solutal instability, channel formation, and overall macro-segregation is investigated. The intensity of SIF hinges on both cooling condition and opening size. The penetration depth of SIF into the solidification domain gives rise to either early or late onset of solutal instability. SIF penetration depth till the melt domain adjacent to the mushy layer promotes early onset of solutal instability. However, SIF penetration into the mushy layer itself triggers redistribution of solute-rich melt inside this layer, leading to delayed onset of solutal instability. Since the macro-segregation is a direct consequence of advection of solute inside and adjacent to the mushy region, the influence of SIF is manifested by unprecedented macro-segregation pattern.
2 citations
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TL;DR: In this paper, the effect of shrinkage voids during the solidification of binary alloy as phase change material (PCM) on the thermal performance of a latent heat thermal energy storage is studied.
Abstract: In this paper, the effect of shrinkage voids during the solidification of binary alloy as phase change material (PCM) on the thermal performance of a latent heat thermal energy storage is studied. Al-Cu 4.1% wt., Al-Si 7% wt., and Al-Mg 30% wt. are the three binary alloys considered as the PCMs. A generalized numerical model considering differences in density, thermal conductivity, and specific heat between liquid and solid phases is developed. A novel method of fluid fraction update scheme is employed to account for the change in volume fraction due to concentration variation induced due to shrinkage and buoyancy flows. The proposed numerical model is validated using reported numerical and experimental results. The density ratio is found to have a pronounced effect on the solidification of binary alloys. With an increasing density ratio, a faster solidification rate along with a thicker mushy region is observed. This effect of density ratio is found to be much more prominent for higher cold wall temperatures. The performance of three binary alloys, namely, Al-Cu 4.1% wt., Al-Si 7% wt., and Al-Mg 30% wt. is examined. Al-Cu 4.1% wt. alloy is found to solidify much earlier with the release of higher energy, followed by Al-Si and Al-Mg, respectively. The model is further used to predict the size and shape of shrinkage void produced for the binary alloys.
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TL;DR: In this paper, the influence of the Marangoni convection on the trajectory of a dendrite fragment in the alloy melt and compare with the experimental observations is numerically simulated and the experimentally observed rotation behavior of the fragmented side-arm in transparent SCN-0.24% H2O, observed from the PFMI video, shows a good agreement with simulation results.
Abstract: During directional solidification of alloys in the microgravity environment of the International Space Station (ISS), growth of dendritic array is expected to be under purely diffusive transport conditions. The resulting microstructure is expected to make up uniformly arranged primary dendrites on sample cross-sections without any defects, such as macrosegregation and spurious (misoriented) grains. However, spurious grains have been seen in recently directionally solidified Al-7 wt% Si samples under the joint NASA-ESA project (MICAST) and also in SCN-0.24 wt% H2O samples grown under the NASA-PFMI project. Careful examination of both these experiments shows the presence of voids at the melt-crucible interface which are the likely source of the convective flows responsible for the fragmentation of dendrite-side arms, and their rotation which creates the nucleus for the spurious grains. In this paper, we assume that side-arm of a primary dendrite has gotten detached from the primary trunk during remelting and isothermal hold, prior to the onset of directional solidification on the Space Station, in the vicinity of a pore at the melt-crucible interface. We numerically simulate the influence of the Marangoni convection on the trajectory of such a dendrite fragment in the alloy melt and compare with the experimental observations. The experimentally observed rotation behavior of the fragmented side-arm in transparent SCN-0.24 wt% H2O, observed from the PFMI video, shows a good agreement with simulation results. The predicted rotational speeds of broken-off secondary arm in the Al-7 wt% Si (MICAST) samples is significantly higher than those in the SCN-0.24 wt% H2O (PFMI). The strength of the convection is dependent on the Marangoni Number and location of the surface pore relative to the Mushy zone. Marangoni convection is strong enough to force the rotation of broken-off side arms and should be considered an important source of microstructural inhomogeneity during terrestrial solidification processing applications.
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TL;DR: In this paper , the effect of solute expansion coefficient on the natural convection and freezing front propagation is investigated by performing three-side cooled solidification experiments, where four different aqueous salt solutions, and different compositions thereof, were employed for experimentation.
Abstract: In this work, the effect of solute expansion coefficient on the natural convection and freezing front propagation is investigated by performing three-side cooled solidification experiments. Four different aqueous salt solutions, and different compositions thereof, were employed for experimentation. The mixtures were solidified to analyze the effect of solute expansion coefficients on the convection currents, and the composition distribution in the bulk. The initial compositions were chosen such that all cases have the same primary solid fraction at eutectic temperature, for obtaining similar compositional changes in the bulk liquid at various stages. Similar cooling conditions were also maintained to ensure that the variation in convection strength is caused primarily by different solute expansion coefficients. A distinct observation of the free surface freezing before the bulk, termed bridging, is reported in certain cases. Further analysis revealed that the bridging could be attributed to a difference in solute convection caused by the solute expansion coefficient. Numerical simulations were performed to further ascertain the plausible initiation mechanisms for bridging. The predicted compositional and solid fraction distribution revealed lesser solute accumulation near the surface, for the lower solute expansion cases, and the resulting increase in the tendency of freezing at the top. An upper limit for the ratio of solutal to thermal Rayleigh numbers in the experimental conditions has been identified for the occurrence of bridging in high Prandtl number fluids.
References
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TL;DR: In this paper, a new technique is described for the numerical investigation of the time-dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free The full Navier-Stokes equations are written in finite-difference form, and the solution is accomplished by finite-time step advancement.
Abstract: A new technique is described for the numerical investigation of the time‐dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free The full Navier‐Stokes equations are written in finite‐difference form, and the solution is accomplished by finite‐time‐step advancement The primary dependent variables are the pressure and the velocity components Also used is a set of marker particles which move with the fluid The technique is called the marker and cell method Some examples of the application of this method are presented All non‐linear effects are completely included, and the transient aspects can be computed for as much elapsed time as desired
5,841 citations
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TL;DR: In this paper, a method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described.
Abstract: A method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described. The flow field is discretized by a conservative finite difference approximation on a stationary grid, and the interface is explicitly represented by a separate, unstructured grid that moves through the stationary grid. Since the interface deforms continuously, it is necessary to restructure its grid as the calculations proceed. In addition to keeping the density and viscosity stratification sharp, the tracked interface provides a natural way to include surface tension effects. Both two- and three-dimensional, full numerical simulations of bubble motion are presented.
2,154 citations
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TL;DR: In this paper, a front-tracking method for multiphase flows is presented, which is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties.
Abstract: Direct numerical simulations of multiphase flows, using a front-tracking method, are presented. The method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties. Interfacial terms are accounted for by adding the appropriate sources as δ functions at the boundary separating the phases. The unsteady Navier–Stokes equations are solved by a conventional finite volume method on a fixed, structured grid and the interface, or front, is tracked explicitly by connected marker points. Interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid. Advection of fluid properties such as density is done by following the motion of the front. The method has been implemented for fully three-dimensional flows, as well as for two-dimensional and axisymmetric ones. First, the method is described for the flow of two or more isothermal phases. The representation of the moving interface and its dynamic restructuring, as well as the transfer of information between the moving front and the fixed grid, are discussed. Applications and extensions of the method to homogeneous bubbly flows, atomization, flows with variable surface tension, solidification, and boiling are then presented.
1,817 citations
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TL;DR: In this article, an enthalpy formulation based fixed grid methodology is developed for the numerical solution of convection-diffusion controlled mushy region phase-change problems, where the basic feature of the proposed method lies in the representation of the latent heat of evolution, and of the flow in the solid-liquid mushy zone, by suitably chosen sources.
Abstract: An enthalpy formulation based fixed grid methodology is developed for the numerical solution of convection-diffusion controlled mushy region phase-change problems. The basic feature of the proposed method lies in the representation of the latent heat of evolution, and of the flow in the solid-liquid mushy zone, by suitably chosen sources. There is complete freedom within the methodology for the definition of such sources so that a variety of phase-change situations can be modelled. A test problem of freezing in a thermal cavity under natural convection is used to demonstrate an application of the method.
1,527 citations
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TL;DR: In this article, the melting of pure gallium in a rectangular cavity has been numerically investigated using the enthalpy-porosity approach for modeling combined convection-diffusion phase change.
Abstract: The melting of pure gallium in a rectangular cavity has been numerically investigated using the enthalpy-porosity approach for modeling combined convection-diffusion phase change. The major advantage of this technique is that it allows a fixed-grid solution of the coupled momentum and energy equations to be undertaken without resorting to variable transformations. In this work, a two-dimensional dynamic model is used and the influence of laminar natural-convection flow on the melting process is considered. Excellent agreement exists between the numerical predictions and experimental results available in the literature. The enthalpy-porosity approach has been found to converge rapidly, and is capable of producing accurate results for both the position and morphology of the melt front at different times with relatively modest computational requirements. These results may be taken to be a sound validation of this technique for modeling isothermal phase changes in metallurgical systems.
1,110 citations