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孔喉结构多孔介质内热质弥散的分形研究

Fractal Study of Heat and Mass Dispersion in Porous Media with Pore Throat Structure

【作者】 张杰

【导师】 张赛;

【作者基本信息】 昆明理工大学 , 机械工程(专业学位), 2022, 硕士

【摘要】 热弥散效应广泛存在于填充床反应器、地下含水层和多孔保温材料等多孔介质传热传质过程中,热弥散效应的强弱变化会影响多孔介质传热传质过程,研究热弥散效应与多孔介质微观结构参数的关系对多孔材料的设计制造具有重要的实际意义。在多孔介质对流传质研究领域,由于多孔介质空间结构的复杂性,很难全面详细地解释流体在多孔介质中的流动规律。多孔介质在一定特征尺度内具有分形特征,因此本文利用分形理论描述了多孔介质中的孔喉结构,对多孔介质内孔喉结构处流体的热质弥散过程进行了系统研究,建立了多孔介质对流传热传质过程的数学解析模型。主要研究内容如下:(1)建立了孔喉结构分形模型,分析了流体在孔喉结构处的流动特征和动力学能量损失,讨论了局部水头损失与流体速度之间的关系,推导出含有多孔介质结构参数(孔喉比、孔隙率、固体颗粒直径、迂曲分形维数和面积分形维数)的流体速度方程。(2)基于流体速度方程,结合菲克扩散定律和能量守恒定律,建立了无经验参数的多孔介质单相流体有效扩散系数模型和有效换热系数模型,通过实验对比验证了模型的准确性。分析了流体速度与多孔介质结构参数对有效扩散系数和有效换热系数的影响。(3)结合流体的运动方程和连续性方程,建立了单相流体速度弥散效应模型,根据热力学关系式,推导了热弥散系数表达式。与含有速度经验参数的常规模型对比,此表达式与实验数据更吻合。分析了结构参数、运动参数和热力学参数对热弥散系数的影响。(4)用分形理论描述非饱和多孔介质湿润相和非湿润相的微观结构,结合流体速度方程和流体速度弥散效应方程,建立了多孔介质多相流动的有效渗透率和有效热弥散系数模型。分析了饱和度、多孔介质结构参数与模型之间的关系。研究结果表明:在对流传热过程中,流体流动速度是影响传热传质过程的重要因素。流体速度越快,有效扩散系数越大,有效换热系数越大。流动速度与固体颗粒直径、孔隙率和面积分形维数呈正比关系,与孔喉比和迂曲分形维数呈反比关系。孔喉比值在1-150范围内对流体速度弥散效应影响较大。管道形状发生突变(如扩张、收缩和弯曲)时流体速度弥散效应增强,热弥散系数增大。在多相对流传热过程中,饱和度是影响各相流体空间分布的重要参数,相对渗透率和热弥散系数与饱和度、微观结构、流体物理性质和速度都有关。

【Abstract】 Thermal dispersion effect exists widely in the packed bed,underground aquifers and porous thermal insulation material such as heat and mass transfer process in porous media,the strength of the thermal diffusion effect change will affect the heat and mass transfer process of porous media,the thermal diffusion effect and micro porous media design and manufacture of the relationship between structural parameters of porous materials has important practical significance.In the field of mass transfer in porous media,due to the complexity of the spatial structure of porous media,it is difficult to fully explain the flow law of fluid in porous media in detail.Porous media has fractal characteristics in a certain characteristic scale,so this paper describes the pore-throat structure in porous media by using fractal theory,systematically studies the heat and mass dispersion process of fluid at the pore-throat structure in porous media,and establishes a mathematical analytical model for the process of convective heat and mass transfer in porous media.The main research contents are as follows:(1)the pore structure fractal model is established and analyzed the flow of the fluid in the pore structure characteristics and kinetic energy loss,discusses the relationship between local head loss and fluid velocity,containing the structural parameters of porous media is deduced(pore throat ratio,porosity,solid particle diameter,give dimension fractal dimension and surface integral form)of the fluid velocity equation.(2)Based on the fluid velocity equation,combined with Fick’s diffusion law and energy conservation law,the effective diffusion coefficient model and effective heat transfer coefficient model of single phase fluid in porous media without empirical parameters were established,and the accuracy of the model was verified by experimental comparison.The effects of fluid velocity and structure parameters of porous media on effective diffusion coefficient and effective heat transfer coefficient are analyzed.(3)Combined with the equation of motion and the equation of continuity of fluid,the velocity dispersion effect model of single-phase fluid is established,and the thermal dispersion coefficient expression is deduced according to the thermodynamic relation.Compared with the conventional model with the empirical parameters of velocity,this expression is in good agreement with the experimental data.The influence of structure parameters,motion parameters and thermodynamic parameters on thermal dispersion coefficient is analyzed.(4)Fractal theory was used to describe the microstructure of wet phase and non-wet phase in unsaturated porous media.Combined with fluid velocity equation and fluid velocity dispersion effect equation,effective permeability and effective thermal dispersion coefficient models of multi-phase flow in porous media were established.The relationship between saturation and structure parameters of porous media and the model is analyzed.The results show that fluid flow velocity is an important factor affecting heat and mass transfer in the process of convective heat transfer.The faster the fluid velocity,the greater the effective diffusion coefficient and the greater the effective heat transfer coefficient.The flow velocity is positively proportional to the solid particle diameter,porosity and surface integral dimension,and inversely proportional to the pore throat ratio and tortuous fractal dimension.The pore throat ratio has a great influence on the fluid velocity dispersion in the range of 1~150.When the pipe shape changes abruptly(such as expansion,contraction and bending),the velocity dispersion effect of the fluid increases and the thermal dispersion coefficient increases.In the process of multiphase convective heat transfer,saturation is an important parameter affecting the spatial distribution of each phase fluid.Relative permeability and thermal dispersion coefficient are related to saturation,microstructure,physical properties of fluid and velocity.

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