Stefan Number-Insensitive Numerical Simulation of the Enthalpy Method for Stefan Problems Using the Space-Time Conservation Element and Solution Element Method

2004 ◽  
Author(s):  
Anahita Ayasoufi ◽  
Theo G. Keith ◽  
Ramin K. Rahmani
Keyword(s):  
Numerical Simulation ◽  
Phase Change ◽  
Numerical Simulations ◽  
Latent Heat ◽  
Space Time ◽  
Enthalpy Method ◽  
Stefan Problems ◽  
Stefan Number ◽  
Original Scheme ◽  
Solution Element

An improvement is introduced to the conservation element and solution element (CE/SE) phase change scheme presented previously. The improvement addresses a well known weakness in numerical simulations of the enthalpy method when the Stefan number, (the ratio of sensible to latent heat) is small (less than 0.1). Behavior of the improved scheme, at the limit of small Stefan numbers, is studied and compared with that of the original scheme. It is shown that high dissipative errors, associated with small Stefan numbers, do not occur using the new scheme.

scholarly journals Latent Heat Phase Change Heat Transfer of a Nanoliquid with Nano–Encapsulated Phase Change Materials in a Wavy-Wall Enclosure with an Active Rotating Cylinder

2021 ◽  
Vol 13 (5) ◽  
pp. 2590
Author(s):  
S. A. M. Mehryan ◽  
Kaamran Raahemifar ◽  
Leila Sasani Gargari ◽  
Ahmad Hajjar ◽  
Mohamad El Kadri ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Energy Storage ◽  
Phase Change ◽  
Latent Heat ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Wavy Wall ◽  
Governing Equations ◽  
Stefan Number ◽  
Change Material

A Nano-Encapsulated Phase-Change Material (NEPCM) suspension is made of nanoparticles containing a Phase Change Material in their core and dispersed in a fluid. These particles can contribute to thermal energy storage and heat transfer by their latent heat of phase change as moving with the host fluid. Thus, such novel nanoliquids are promising for applications in waste heat recovery and thermal energy storage systems. In the present research, the mixed convection of NEPCM suspensions was addressed in a wavy wall cavity containing a rotating solid cylinder. As the nanoparticles move with the liquid, they undergo a phase change and transfer the latent heat. The phase change of nanoparticles was considered as temperature-dependent heat capacity. The governing equations of mass, momentum, and energy conservation were presented as partial differential equations. Then, the governing equations were converted to a non-dimensional form to generalize the solution, and solved by the finite element method. The influence of control parameters such as volume concentration of nanoparticles, fusion temperature of nanoparticles, Stefan number, wall undulations number, and as well as the cylinder size, angular rotation, and thermal conductivities was addressed on the heat transfer in the enclosure. The wall undulation number induces a remarkable change in the Nusselt number. There are optimum fusion temperatures for nanoparticles, which could maximize the heat transfer rate. The increase of the latent heat of nanoparticles (a decline of Stefan number) boosts the heat transfer advantage of employing the phase change particles.

scholarly journals Correlations for Melting Time and Melt Fraction for Bottom Charged Tube in Tube Phase Change Material Heat Exchanger

2021 ◽  
Author(s):  
Lanka Sandeep Raj ◽  
Sane Sreenivas ◽  
Bandaru Durga Prasad
Keyword(s):  
Reynolds Number ◽  
Rayleigh Number ◽  
Phase Change ◽  
Latent Heat ◽  
Heat Storage ◽  
Melting Time ◽  
Time Step ◽  
Latent Heat Storage ◽  
Stefan Number ◽  
Hydraulic Behaviour

Abstract Multiple factors govern the Thermo-hydraulic behaviour of Latent heat storage devices. The correlation among these factors varies from case to case. In this work, a concentric tube in tube latent heat storage system is numerically modelled for the bottom charging case. Fixed grid enthalpy porosity approach is adopted to account for phase change. The numerical model’s independence is achieved by testing mesh size, time step, and maximum iterations per time step. The computational approach is validated against the experimental data. Non-dimensional parameters viz Rayleigh Number (3.04x105 to 65.75 x105), Stefan Number (0.2 to 1), Reynolds Number (600 to 3000), and L/D ratio (2 to 15) are varied in the respective ranges mentioned in parenthesis. Stefan number is found to have a major influence on the Melt Fraction and Melting time, compared to Rayleigh Number and Reynolds Number. Correlations are presented for quantifying the melt fraction and dimensionless melting time.

Numerical Simulation of Two Phase Change Materials Melting Process

2014 ◽  
Vol 1049-1050 ◽  
pp. 94-100
Author(s):  
Bo Bo Zhang ◽  
Yu Ming Xing ◽  
Qiang Sheng
Keyword(s):  
Numerical Simulation ◽  
Energy Storage ◽  
Temperature Distribution ◽  
Phase Change ◽  
Latent Heat ◽  
Control Function ◽  
Melting Process ◽  
Thermal Control ◽  
Heat Energy ◽  
Two Phase

Phase change thermal control technology has gained increasing focus as an emerging technology for the thermal control of spacecraft. This literature focused on melting process inside a latent heat energy storage filled with phase change material (PCM) by numerical simulation. A matrix-based enthalpy porosity theory in a three-dimensional finite volume discretization is simulated. The temperature distribution during the melting process of PCM Cerrolow-136 and CH3COONa·3H2O is obtained, based on which the thermal control function and energy storage capacity is compared. The results show that Cerrolow-136 has better performance. In different states of phase change, the temperature distribution of Cerrolow-136 is fairly uniform. Thermal control face's temperature of Cerrolow-136 is closer to phase transition temperature. In the same heat flux of 3000 W/m2, The whole process of thermal control temperature getting to 80°C for Cerrolow-136 is longer. Cerrolow-136, for its excellent characteristics, has potentially broad application in the fields of latent heat energy storage and space vehicle electronics.

scholarly journals Direct Numerical Simulations of Flows With Phase Change

2002 ◽  
Author(s):  
Gretar Tryggvason ◽  
Nabeel AlRawahi ◽  
Asghar Esmaeeli
Keyword(s):  
Growth Rate ◽  
Phase Change ◽  
Numerical Simulations ◽  
Phase Boundary ◽  
Latent Heat ◽  
Volume Expansion ◽  
Front Tracking ◽  
Direct Numerical Simulations ◽  
Superheated Liquid ◽  
Simple Flows

During the last decade, direct numerical simulations of multiphase flow have emerged as a major research tool. It is now possible, for example, to simulate the motion of several hundred bubbles and particles in simple flows and to obtain meaningful average quantities that can be compared with experimental results. These systems are, however, still very simple compared to those systems routinely encountered in engineering applications. It is, in particular, frequently necessary to account for phase change, both between solid and liquid as well as liquid and vapor. Most materials used for manmade artifacts are processed as liquids at some stage, for example, and the way solidification takes place generally has major impact on the properties of the final product. The formation of microstructures, where some parts of the melt solidify faster than others, or solidify with different composition as in the case of binary alloys, is particularly important since the size and composition of the microstructure impact the hardness and ductility, for example, of the final product. Boiling is one of the most efficient ways of removing heat from a solid surface. It is therefore commonly used in energy generation and refrigeration. The large volume change and the high temperatures involved can make the consequences of design or operational errors catastrophic and accurate predictions are highly desirable. The change of phase from liquid to vapor and vice-versa usually takes place in a highly unsteady manner with a very convoluted phase boundary. Numerical simulations are therefore essential for theoretical investigations and while a few simulations of both problems have been published, the field is still very immature. In the talk the author gives a brief overview of the state of the art and discusses recent simulations of boiling and solidification in some detail. The progress made during the last few years in simulating the motion of multiphase flows without phase change has relied heavily on the so-called “one-fluid” formulation of the governing equations. In this approach one set of equations is written for all the phases involved. The formulation allows for different material properties in each phase and singular terms must be added at the phase boundaries to correctly incorporate the appropriate boundary conditions. The key challenge is to correctly advect the phase boundary and a number of methods have been proposed to do so. Those include the Volume-Of-Fluid (VOF), the level-set, the phase field methods, as well as front-tracking methods where the boundary is explicitly tracked by connected marker points [1]. The last approach, front tracking, has been particularly successful and is used for the examples shown here. In both boiling and solidification it is necessary to solve the energy equation, in addition to conservation equations for mass and momentum, and account for the release/absorption of latent heat at the phase boundary. The latent heat source also determines the motion of the phase boundary relative to the fluid. In boiling there is significant volume expansion as liquid is transformed into vapor and this expansion must be accounted for in the mass conservation equation. For solidification the volume expansion can often be neglected, but the transformation of the liquid into a stationary solid poses new computational challenges. An example of a bubble undergoing vapor explosion is shown in figure 1. The bubble is initially started as a small nearly spherical sphere in superheated liquid confined in a domain that is periodic in two directions, with a solid wall at the bottom and open on the top to allow outflow as the bubble expands. In this case the domain is resolved by a 643 grid. As the bubble grows, the interface becomes unstable, developing a corrugated shape (usually referred to experimentally as a “black bubble” since the corrugated surface is opaque). The increase in surface area greatly affects the growth rate of the bubble. Figure 2 shows one example of a simulation of the growth of a dendrite of pure material in uniform flow. The domain is a square resolved by a 2563 grid. A uniform inflow is specified on the left boundary, the top and bottom boundaries are periodic, and all gradients are set to zero at the outlet boundary. The temperature of the incoming flow is equal to the undercooled temperature and as latent heat is released at the phase boundary, the flow sweeps it from the front to the back. This results in a thinner thermal boundary layer at the tip of the upstream growing arm and a relatively uniform temperature in the wake. The growth rate of the upstream arm is therefore enhanced and the growth of the downstream arm is reduced.

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