Numerical Modelling of Phase Change in Freezing and Thawing Unsaturated Soil

1993 ◽  
Vol 24 (2-3) ◽  
pp. 95-110 ◽  
Author(s):  
H. Engelmark ◽  
U. Svensson
Keyword(s):  
Boundary Conditions ◽  
Phase Change ◽  
Change Process ◽  
Numerical Solutions ◽  
Time Dependent ◽  
Total Water Content ◽  
Total Water ◽  
Freezing And Thawing ◽  
Water Ice ◽  
Temperature Boundary

This paper presents a new method for handling the phase change process in numerical simultations of freezing and thawing soils. Moisture and heat transfer in soils subjected to both freezing and thawing are discussed. Simulated freezing results of temperature and total water content (water + ice) are compared with experimental data reported by Jame (1977). Simulated and experimental results were similar. The effects of different time-dependent temperature boundary conditions were evaluated and discussed. The method was used both with abrupt and smooth temperature boundary conditions and both resulted in stable numerical solutions. Finally, results from a simulation of a freezing and thawing cycle are presented and discussed qualitatively.

Integral Solutions of Phase Change With Internal Heat Generation

2004 ◽  
Author(s):  
Ali Siahpush ◽  
John Crepeau
Keyword(s):  
Differential Equation ◽  
Phase Change ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Melting Rate ◽  
Internal Heat Generation ◽  
Stefan Number ◽  
Temperature Boundary ◽  
Solid Liquid

This paper presents solutions to a one-dimensional solid-liquid phase change problem using the integral method for a semi-infinite material that generates internal heat. The analysis assumed a quadratic temperature profile and a constant temperature boundary condition on the exposed surface. We derived a differential equation for the solidification thickness as a function of the internal heat generation (IHG) and the Stefan number, which includes the temperature of the boundary. Plots of the numerical solutions for various values of the IHG and Stefan number show the time-dependant behavior of both the melting and solidification distances and rates. The IHG of the material opposes solidification and enhances melting. The differential equation shows that in steady-state, the thickness of the solidification band is inversely related to the square root of the IHG. The model also shows that the melting rate initially decreases and reaches a local minimum, then increases to an asymptotic value.

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

scholarly journals A finite volume-based model for the hydrothermal behavior of soil under freeze–thaw cycles

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0252680
Author(s):  
Tianfei Hu ◽  
Tengfei Wang
Keyword(s):  
Heat Transfer ◽  
Finite Volume ◽  
Fluid Transport ◽  
Numerical Solutions ◽  
Dynamic Equilibrium ◽  
Phase Changes ◽  
Freezing And Thawing ◽  
Water Ice ◽  
Freeze Thaw ◽  
Physics Model

Freeze–thaw cycles in soil are driven by water migration, phase transitions, and heat transfer, which themselves are closely coupled variables in the natural environment. To simulate this complex periglacial process at different time and length scales, a multi-physics model was established by solving sets of equations describing fluid flow and heat transfer, and a dynamic equilibrium equation for phase changes in moisture. This model considers the effects of water–ice phase changes on the hydraulic and thermal properties of soil and the effect of latent heat during phase transition. These equations were then discretized by using the finite volume method and solved using iteration. The open-source software OpenFOAM was used to generate computational code for simulation of coupled heat and fluid transport during freezing and thawing of soil. A set of laboratory freezing tests considering two thermal boundary conditions were carried out, of which the results were obtained to verify the proposed model. In general, the numerical solutions agree well with the measured data. A railway embankment problem, incorporating soil hydrothermal behavior in response to seasonal variations in surface temperature, was finally solved with the finite volume-based approach, indicating the algorithm’s robustness and flexibility.

scholarly journals Semi-derivative integral method (SDIM) to transient heat conduction: Time-dependent (power-law) temperature boundary conditions

2021 ◽  
pp. 143-143
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Power Law ◽  
Integral Method ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Time Dependent ◽  
Conduction Time ◽  
Parabolic Profile ◽  
Temperature Boundary

Transient heat conduction in semi-infinite medium with a power-law time-dependent boundary conditions has been solved by an integral-balance integral method applying to a semi-derivative approach. Two versions of the integral-balance method have been applied: Goodman?s method with a generalized parabolic profile and Zien?s method with exponential (original and modified) profile.

scholarly journals Non-Stationary Temperature Behavior of Spindle Assemblies and Ball Screw Gears for High Precision Metal Cutting Machines

2021 ◽  
Vol 248 ◽  
pp. 04020
Author(s):  
A.P. Kuznetsov
Keyword(s):  
Boundary Conditions ◽  
High Precision ◽  
Metal Cutting ◽  
Numerical Solutions ◽  
Time Dependent ◽  
Temperature Behavior ◽  
Ball Screw ◽  
Various Boundary Conditions ◽  
Thermophysical Parameters ◽  
Typical Temperature

Typical temperature and thermoelastic models of structures of spindle units and ball screw systems of metal-cutting machines were considered. The features of determining the geometric and thermophysical parameters of these models were described in some detail. Both analytical and numerical solutions for estimating time-dependent temperatures are presented. The solutions were obtained for thermoelastic displacements of spindles and ball screw systems for various boundary conditions and limitations of deformations during heating due to the design of these elements of metal-cutting machines.

scholarly journals Comparative investigation of phase change material on heat transfer characteristics under theoretical and practical periodic temperature boundary

2021 ◽  
pp. 351-351
Author(s):  
Yong Wang ◽  
Zhongsheng Zhang ◽  
Ting Liu ◽  
Yunsheng Fan ◽  
Jingmin Dai
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Phase Change ◽  
Phase Change Material ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Heat Transfer Characteristics ◽  
Temperature Boundary ◽  
Periodic Temperature ◽  
Change Material

In this paper, heat transfer characteristics of phase change material in rectangular containers are numerically analyzed. The inclination angles of the container refer to 0?, 90?, and 180?. Both theoretical and practical periodic temperature boundary conditions are taken into consideration, in which the periodic temperature boundary conditions include 50-80?C and 65-80?C. The comparison study is carried out through the liquid fraction and temperature histories during the heat transfer process under these different boundary conditions. It is indicated that there are large differences between the calculated results under the theoretical and the practical periodic temperature boundary conditions when the temperature boundary is 50-80?C, while the theoretical and the practical periodic temperature boundary conditions of 65-80?C have relatively little effect on the numerical results of the heat transfer process of the phase change material. Furthermore, compared with the temperature increasing stage, the numerical results calculated under the theoretical and the practical boundary conditions have more significant differences in the temperature decreasing stage. The research conclusion of this paper can provide a theoretical basis for the application of PCM under periodic temperature boundary conditions.

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