[논문]PARAMETRIC INVESTIGATIONS ON THE DOUBLE DIFFUSIVE CONVECTION IN TRIANGULAR CAVITY

Kwon, SunJoo; Oh, SeYoung; Yun, Jae Heon; Chung, Sei-Young

PARAMETRIC INVESTIGATIONS ON THE DOUBLE DIFFUSIVE CONVECTION IN TRIANGULAR CAVITY 원문보기

Kwon, SunJoo (Nuclear Fuel Cycle Strategy Research Lab Korea Atomic Energy Research Institute) , Oh, SeYoung (Department of Mathematics Chungnam University) , Yun, Jae Heon (Department of Mathematics Chungnam University) , Chung, Sei-Young (Department of Mathematics Chungnam University)

Double-diffusive convection inside a triangular porous cavity is studied numerically. Galerkin finite element method is adopted to derive the discrete form of the governing differential equations. The first-order backward Euler scheme is used for temporal discretization with the second-order Adams-Bashforth scheme for the convection terms in the energy and species conservation equations. The Boussinesq-Oberbeck approximation is used to calculate the density dependence on the temperature and concentration fields. A parametric study is performed with the Lewis number, the Rayleigh number, the buoyancy ratio, and the shape of the triangle. The effect of gravity orientation is considered also. Results obtained include the flow, temperature, and concentration fields. The differences induced by varying physical parameters are analyzed and discussed. It is found that the heat transfer rate is sensitive to the shape of the triangles. For the given geometries, buoyancy ratio and Rayleigh numbers are the dominating parameters controlling the heat transfer.

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문제 정의

However, the temperature fields show the slightly concentrated isotherms toward the high temperature wall. Both the concentration and temperature profiles show iso-lines perpendicular to the bottom wall because of the no flux boundary condition adopted in this study. The buoyancy induced flow in the triangles show more mass flux near the walls compared to the center since the temperature differences are specified along the wall without any internal heat sources.
[6] investigate the viscous flow characteristics in the triangular cavity. In their study, numerical assessment results are shown for the unique viscous flow characteristics in the triangular cavity by using finite difference formulation, The numerical treatment of the singular points of the triangle was the major concern of their study. So far, to our knowledge, the double-diffusive convection in a triangular cavity has not been addressed by any researchers.
Thus far, literatures on the double-diffusive convection are ample, however, there are very few literatures addressing the double-diffusive convection in triangle geometry even though its possible wide applications in the engineering problems. The purpose of our present study is to investigate the double-diffusive phenomena in triangular geometries.
The purpose of this study is parametric investigation on the double-diffusive convection in triangular cavities. Three different types of triangle cavity shapes are considered in order to show the geometric effects on the double-diffusive convection.

제안 방법

In order to avoid difficulties arising from specifying boundary conditions for the pressure, we adopt the stream-function formulation in this study. The stream-function(Ψ) is defined by using the velocity as
Thus, the verification of the present numerics is revered to [4]. Since our main purpose of this study is to explore the effect of triangular geometry on the double-diffusive convection phenomena, we will focus our attention on three equilateral triangles with bottom length Lb = 1 and its side angles β = 0.15π, 0.33π, and 0.45π. Three different β values are used to examine the geometric effects.

이론/모형

The nondimensional form of the governing equations are presented and solved in the triangular meshes. Galerkin finite element method is used in order to avoid the special treatments on the triangular shape in the finite difference method[6].
Galerkin finite element method is used to spatially discretize the governing equations. In the finite element method, the calculation domain is subdivided into number of sub-domain element.

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PARAMETRIC INVESTIGATIONS ON THE DOUBLE DIFFUSIVE CONVECTION IN TRIANGULAR CAVITY 원문보기

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