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수평으로 인접한 유체층과 공극률이 변하는 다공질층에서 열적 불안정성

Thermal Instabilities in Horizontally Superposed Fluid and Porous Layer with Variable Porosity

변석훈 황인국 최창균

Byun SH Hwang IG Choi CK

HWAHAK KONGHAK, December 1997, 35(6), 921-927(7), NONE

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Abstract

수평을로 인접하고 있는 유체층과 유체로 포화된 다공질층이 밑면으로부터 가열되고 있는 계에 대해 다공질층의 공극률의 변화를 고려하여 자연대류의 임계조건을 조사하였다. 선형안정성 이론을 적용하여 다공질층의 깊이와 다공질층을 구성하는 입자직경의 비 d_m/d_p, 다공질층과 유체층 깊이의 비 ^d가 대류발생 임계조건에 주는 영향을 수치해법으로 구하였다. d_m/d_p가 10³보다 작을 때에는 공극률의 변화로 인해 임계조건이 영향받는다는 결과를 얻었다. ^d가 큰 경우에는 대류발생은 다공질층이 지배적이며 d_m/d_p가 감소함에 따라 임계 Darcy-Rayleight 수는 감소하였다. 이는 다공질층의 입자 직경이 커짐에 따라 벽면에서의 공극률이 증가하여 유동이 더 자유로워지기 때문에 다공질층이 열적으로 더 불안정해짐을 나타낸다.

The critical conditions to mark the onset of natural convection in the horizontally superposed fluid and porous layer, cooled from below, with variable porosity were investigated. By using the linear stability theory the effects of d_m/d_p(ratio of porous layer thickness to particle diameter) and ^d(ratio of porous layer thickness to fluid layer thickness) on the critical conditions are obtained numerically. The results show that the critical conditions are influenced by the variation of porosity when the value of d_m/d_p is smaller than 10³. For large values of ^d the onset of convection is dominant in the porous layer and the critical Darcy-Rayleigh number decreases with decreasing the vale of d_m/d_p. It means that as the particle diameter becomes larger, the porosity becomes larger near the surface and the fluid inthe porous layer becomes more mobile, i.e., more unstable.

Keywords

Natural Convection Porous Layer Variable Porosity Linear Stability Theory Darcy-Rayleigh Number

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