• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.9
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• pp.1-11
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• 2004

A comprehensive study has been made for the investigation of the convergence and stability characteristics of the LU scheme for solving the Euler equations on unstructured meshes. The von Neumann stability analysis technique was initially applied to a scalar model equation, and then the analysis was extended to the Euler equations. The results indicated that the convergence rate is governed by a specific combination of flow parameters. Based on this insight, it was shown that the LU scheme does not suffer any convergence deterioration at all grid aspect ratios, as long as the local time step is defined using an appropriate parameter combination.

• Journal of Energy Engineering
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• v.8 no.2
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• pp.224-232
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• 1999

Latent heat storage system using micro-encapsuled phase change material is effective method for floor heating of house and building. The temperature profile in capsule block and flow rate of hot water are important parameters for the development of heat storage system. In the present study, a mathematical model based on 3-D, non-steady state, Navier-Stokes equations, scalar conservation equations and turbulence model ($\kappa$-$\varepsilon$), is used to predict the temperature profiles in capsule and the velocity vectors in hot water pipe. The multi-block grids and fine grids embedding are used to join the circle in hot water pipe and square in capsule block. The phase change process of the capsule is quite complex not only because the size of phase change material is very small, but also because phase change material is mixed with the cement to form thermal storage block. In calculation, it's assumed that the phenomena of phase change is limited only the thermal properties of phase change material and the change of boundary is not happened in capsule. The purpose of this study is to calculate the temperature profiles in capsule block and velocity vectors in hot water pipe using the numerical calculation. Two kinds of thermal boundary condition were considered, the first (case 1) is the adiabatic condition for the both outside surfaces of the wall, the second (case 2) is the case in which one surface is natural convection with atmosphere and another surface is adaibatic. Calculation results are shown that the temperature profile in capsule block for case 1 is higher than that for case 2 due to less heat loss in adaibatic surface. Specially, in the domain of near Y=0, the difference of temperature is greater in case 1 than in case 2. The detailed experimental data of capsule block on the temperature profile and the thermal properties such as specific heat and coefficient of heat transfer with the various temperature are required to predict more exact phenomena of heat transfer.