本文選題：Navier-Stokes方程 + 可變質(zhì)源　； 參考：《哈爾濱工業(yè)大學(xué)》2017年碩士論文

【摘要】：Navier-Stokes方程是描述流體運(yùn)動(dòng)的基本方程,有著廣泛的應(yīng)用,如:船舶、石油、航空航天以及地球物理科學(xué)等領(lǐng)域。近年來(lái),由于廢氣污染日益嚴(yán)重,Navier-Stokes方程在描述有化學(xué)反應(yīng)的氣體吸收過(guò)程中有了新應(yīng)用,例如:二氧化碳的化學(xué)吸收過(guò)程。由于氣體的不斷輸入,使流體的濃度和質(zhì)量不斷變化,而傳統(tǒng)的Navier-Stokes方程(無(wú)質(zhì)源)僅能描述質(zhì)量不變的流體,不能準(zhǔn)確的描述氣體吸收的過(guò)程。因此,本文引入了帶質(zhì)源項(xiàng)的Navier-Stokes方程來(lái)研究氣體的吸收過(guò)程。本文的主要研究?jī)?nèi)容如下:首先,本文第二章通過(guò)對(duì)常規(guī)無(wú)質(zhì)源項(xiàng)的Navier-Stokes方程的敘述,引出了化學(xué)反應(yīng)中有質(zhì)源項(xiàng)的Navier-Stokes方程。在第二章的基礎(chǔ)上,第三章通過(guò)給出可變質(zhì)源Navier-Stokes方程的近似方程組,并對(duì)該近似方程組的弱解進(jìn)行了定義,再通過(guò)能量估計(jì)法證明了該近似方程組弱解的存在,最后由強(qiáng)收斂性得到原可變質(zhì)源Navier-Stokes方程組的全局弱解存在。由于可變質(zhì)源Navier-Stokes方程的解析求解幾乎不可能,本文的第四章以可變質(zhì)源Navier-Stokes方程在燃煤電廠二氧化碳吸收中的應(yīng)用為例,通過(guò)表面更新模型來(lái)描述質(zhì)源,采用SIMPLE算法和PISO算法分別對(duì)可變質(zhì)源的Navier-Stokes方程組進(jìn)行數(shù)值求解。驗(yàn)證了PISO算法在瞬態(tài)問(wèn)題中的優(yōu)越性,獲得了反應(yīng)中填料表面反應(yīng)產(chǎn)物及乙醇胺的摩爾濃度分布云圖,和不同時(shí)間點(diǎn)上的二氧化碳吸收率,并討論了影響CO2吸收率的主要因素。此外,還比較了SIMPLE算法和PISO算法在不同迭代步長(zhǎng)下的收斂性,分析了不同算法下收斂時(shí)間不同的原因以及計(jì)算精度的差異。
[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.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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