可变质源Navier-Stokes方程弱解的存在性及其在气体吸收中的应用

发布时间：2018-04-27 22:19

本文选题：Navier-Stokes方程 + 可变质源　；参考：《哈尔滨工业大学》2017年硕士论文

【摘要】：Navier-Stokes方程是描述流体运动的基本方程,有着广泛的应用,如:船舶、石油、航空航天以及地球物理科学等领域。近年来,由于废气污染日益严重,Navier-Stokes方程在描述有化学反应的气体吸收过程中有了新应用,例如:二氧化碳的化学吸收过程。由于气体的不断输入,使流体的浓度和质量不断变化,而传统的Navier-Stokes方程(无质源)仅能描述质量不变的流体,不能准确的描述气体吸收的过程。因此,本文引入了带质源项的Navier-Stokes方程来研究气体的吸收过程。本文的主要研究内容如下:首先,本文第二章通过对常规无质源项的Navier-Stokes方程的叙述,引出了化学反应中有质源项的Navier-Stokes方程。在第二章的基础上,第三章通过给出可变质源Navier-Stokes方程的近似方程组,并对该近似方程组的弱解进行了定义,再通过能量估计法证明了该近似方程组弱解的存在,最后由强收敛性得到原可变质源Navier-Stokes方程组的全局弱解存在。由于可变质源Navier-Stokes方程的解析求解几乎不可能,本文的第四章以可变质源Navier-Stokes方程在燃煤电厂二氧化碳吸收中的应用为例,通过表面更新模型来描述质源,采用SIMPLE算法和PISO算法分别对可变质源的Navier-Stokes方程组进行数值求解。验证了PISO算法在瞬态问题中的优越性,获得了反应中填料表面反应产物及乙醇胺的摩尔浓度分布云图,和不同时间点上的二氧化碳吸收率,并讨论了影响CO2吸收率的主要因素。此外,还比较了SIMPLE算法和PISO算法在不同迭代步长下的收敛性,分析了不同算法下收敛时间不同的原因以及计算精度的差异。
[Abstract]:Navier-Stokes equation is the basic equation to describe fluid motion, and has been widely used in many fields, such as ship, oil, aerospace, geophysical science and so on. In recent years, the Navier-Stokes equation has been applied to describe the absorption of gases with chemical reactions, such as the chemical absorption of carbon dioxide. Because of the constant input of gas, the concentration and mass of the fluid are constantly changing, but the traditional Navier-Stokes equation (without mass source) can only describe the fluid with constant mass, and can not accurately describe the process of gas absorption. Therefore, the Navier-Stokes equation with mass source term is introduced to study the gas absorption process. The main contents of this paper are as follows: firstly, in the second chapter, the Navier-Stokes equation with prime source term in chemical reaction is derived by describing the Navier-Stokes equation of the conventional non-prime source term. On the basis of the second chapter, in chapter 3, the approximate equations of Navier-Stokes equation with metamorphic source are given, the weak solutions of the approximate equations are defined, and the existence of weak solutions of the approximate equations is proved by the energy estimation method. Finally, by strong convergence, the existence of global weak solutions for Navier-Stokes equations with metamorphic sources is obtained. Because it is almost impossible to solve the Navier-Stokes equation of metamorphic source, the application of Navier-Stokes equation of metamorphic source in carbon dioxide absorption of coal-fired power plant is taken as an example, and the surface renewal model is used to describe the source. The SIMPLE algorithm and the PISO algorithm are used to solve the Navier-Stokes equations of the metamorphic source. The superiority of PISO algorithm in transient problem was verified. The distribution of reaction products and ethanolamine on the surface of fillers and the carbon dioxide absorptivity at different time points were obtained. The main factors affecting the absorption rate of CO2 were discussed. In addition, the convergence of SIMPLE algorithm and PISO algorithm under different iteration steps are compared, and the reasons of different convergence time and the difference of calculation accuracy are analyzed.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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