Solution Of General Dynamic Equation For Nanoparticles In Turbulent Flow Considering Fluctuating Coagulation

All scientific problems can be studied from macro and micro perspectives. In reality, people are more concerned with the overall movement of a large number of particles. That is the macroscopic state of matter, such as temperature, pressure, velocity, density, etc. In order to study these macroscopic states, scientists have developed thermodynamics and statistical mechanics. These two subjects have become the cornerstone of modern science, and in many areas, they have a deep influence. Fluid mechanics which is an independent branch of science also based on the foundation of this. In many research problems of fluid mechanics, the research of two-phase flow is particularly important. Two phase flow is a flow system which consisting of two phases. If the phase of matter in the flow system is more than two, it is called multiphase flow. Our atmosphere is a multiphase flow system. The atmosphere is just as important to humans as water is to fish, and it provides the oxygen which is necessary for people. With the rapid development of economy, a large number of industrial waste gas and automobile exhaust gas are discharged into the atmosphere, resulting in the increase of particulate matter in the atmosphere. When the particles are beyond the carrying capacity of the environment, they will produce haze and cause other environmental problems. It will also do harm to production and human life. The atmosphere is composed of tiny particles that we call it the aerosol system. If we can know the dynamic behavior of the particles in the aerosol system, we can understand the generation, propagation and evolution of atmospheric pollutants better, and solve the problem of air pollution in a better way. Brownian coagulation is the process of collision between particles due to Brownian motion. It is one of the most important processes in the dynamics of aerosol particles. In the study of aerosol particles, the research of nanoparticles is the most important one. The nanoparticles refer to particles larger than lnm and smaller than 100nm. The study object of nanoparticles in the multi-phase flow is its dynamic evolution characteristics, and the interaction between the particles and the fluid field. There are two approaches to examine the modeling of nanoparticle evolution, namely Eulerian and Lagrangian. In the Eulerian framework, the starting point lies within the following General Dynamic Equation (GDE) which can include nucleation, coagulation, condensation, breakage and so on. In many practical applications, nanoparticles exist in turbulent flow. In this case, the effects of turbulence on particle convection, diffusion, nucleation, and coagulation must be taken into account. Many scientists have done a lot of research work on the evolution of the nanoparticles in the turbulent flow based on GDE. The general dynamic equation for turbulent flow is derived by making the Reynolds assumption that the fluid velocity and size distribution function can be written as the sum of mean and fluctuating components. When particle coagulation is considered, the fluctuating coagulation term which is the contribution to coagulation resulting from the fluctuating concentrations will appear after averaging the equation. In the previous studies, the fluctuating coagulation term, consisting of correlation between two fluctuating particle size distribution function, is neglected. The new averaged general dynamic equation for nanoparticles in turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The corresponding experiments are performed and numerical results of particle size distribution correlate well with the experimental data. The results show that, for turbulent nanoparticle flow, the fluctuating coagulation term should be included in the averaged particle general dynamic equation. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds number is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with smaller Schmidt number and the flow with higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher with considering fluctuate coagulation than that without considering fluctuating coagulation.