The Existence Of Weak Solution Of Navier-stokes Equations With The Mass Source Item And Its Application To Gas Absorption

The Navier-Stokes equations are the basic equations for describing motion of fluid.They have a wide range of applications,such as ships,petroleum,aerospace,and geophysics.In recent years,since gas pollution are serious,Navier-Stokes equations have a new application in the description of the chemical reaction of the gas absorption process,such as carbon dioxide absorption process.Due to the constant input of the gas,the concentration and quality of the fluid are constantly changing.However,the traditional Navier-Stokes equations(no mass source)can only describe the fluid of constant quality,so that they can not accurately describe the process of gas absorption.Therefore,this paper introduces the Navier-Stokes equations with the mass source item to study the gas absorption process.The major of this study are as shown below:First,the qualitative Navier-Stokes equations are introduced in the second chapter.On the basis of the second chapter,the approximate equations of the Navier-Stokes equations with the variable mass source are given in the third chapter.The definition of the weak solutions for the approximate equations is also given.The energy estimation method is used in the proof of the existence of the weak solution of the approximation equations.The global weak solution of the original Navier-Stokes equations with the variable mass source is obtained by the strong convergence.Since giving the analytic solution of the Navier-Stokes equations is almost impossible.In the fourth chapter,Navier-Stokes equations with the variable mass source are applied in the carbon dioxide absorption of coal-fired power plants.The surface renewal model is used to describe the mass source.The SIMPLE algorithm and PISO algorithm are respectively used to solve the Navier-Stokes equations with variable mass source.The results show that the PISO algorithm has the superiority in the transient problem.The concentration of the reaction product and the ethanolamine on the filler surface,and the carbon dioxide absorption rate at the different time points are given.The factors that affect the CO2 absorption rate are also discussed.In addition,the convergence of SIMPLE algorithm and PISO algorithm under different iterative steps are compared.The reasons of different convergence time under different algorithms are analyzed.And the difference of calculation accuracy between SIMPLE algorithm and PISO algorithm is compared.