饱和多孔介质自然对流数学模型与实验研究

Mathematical Model for Natural Convection in a Saturated Porous Medium and Its Experimental Study

以饱和多孔介质内流体流动、流体和固体传热为研究对象,考虑流体密度随温度变化和局部热平衡,引入Brinkman-Forchheimer的扩展Darcy模型进行修正,建立固体随机堆积饱和多孔介质自然对流数值模型,采用有限体积法计算。利用自主研制的两侧恒温差立方体多孔介质实验台,对所建数值模型进行实验验证。综合数值计算和实验结果表明:多孔介质方腔内最大流速随温差和瑞利数Ra增大而增大,且最大流速出现在高温壁面和低温壁面附近;随着Ra增大,温度等值线由近似平行于高低温壁面变为近似垂直于高低温壁面;高温壁面上Nu从上至下呈线性增加趋势;高温壁面Nu随Ra增大而增大,当Ra<102时,Nu维持在12以内;当102<Ra<106,Nu增加迅速,由11.4增加到276.4;当Ra>106,Nu增加速率很小。

With the fluid flow and heat transfer between a fluid and a solid serving as the object of study and changes of the density of the fluid with the temperature being taken into account,the local heat balance was corrected by introducing the Brinkman-Forchheimer extended Darcy model,a numerical model for natural convection of saturated porous media randomly deposited was set up and a calculation was performed by using finite volumetric method. By making use of a self-developed cubic porous medium test rig having a constant temperature difference at both sides,the authors conducted an experimental verification of the numerical model in question. The comprehensive numerical calculation and test results show that the maximum flow speed inside the square cavity of the porous medium will increase with an increase of the temperature difference and Ra number and appear at a location nearing both high temperature wall surface and low temperature one. With an increase of the Ra number,the isolines of the temperature will change from being almost parallel to the high and low temperature wall surface to being closely perpendicular to them. Nu number on the high temperature wall surface will assume a linear ascending tendency and the Nu on the high temperature wall surface will increase with an increase of Ra. When Ra < 102,Nu will maintain within 12.When 102 < Ra < 106,Nu will rapidly increase from 11. 4 to 276. 4. When Ra > 106,Nu will increase at a very small speed.