# Simulation of Aerosol Evolution within Background Pollution for Nucleated Vehicle Exhaust via TEMOM
## 1 Introduction  
The health effects of particulate matter (PM) air pollution have long been a matter of widespread concern [1, 2, 3, 4]. Much of this work focuses on measurements of aerosols at different times of the day. This method can identify periods when particle concentrations are highest directly to judge the degree of its impact on health. However, this research method cannot analyze the factors affecting the evolution of aerosols and the origin of aerosols. The reason is that the pollution sources, temperature, humidity, etc., change with time during the day. All of these changes affect the evolution of aerosols as the aerosol evolves over the day. Therefore, the factors cannot be decoupled. Therefore, simulation plays an essential role in solving how physical quantities affect the evolution of aerosols. Simulation can keep irrelevant variables unchanged and only change the target variable. The coupling of fine particles and macroscopic flow field belongs to multiphase flow in fluid mechanics. In this study, there are only two phases: air and particles. When dealing with the multiphase flow, the continuous phase is generally described by Navier-Stokes equation, and there are many options for the discrete phase. There are generally three choices. First, the discrete phase is equivalent to the continuous phase, which is the same as the continuous phase and is described by the NS equation. Second, use Lagrangian particles for tracking; third, use the PBE (Population Balance Equation) equation to describe the discrete phase. We are using the third method here. [PERSON]'s work [5] has shown that these particulate matters, especially with diameters below 100 nm, have a more adverse influence on human health than ultrafine and coarse particles. The first study found the effect on background aerosol, including coagulation, condensation, and nucleation, coupled with Navier-Stokes equation. By comparing withthe simulation data, the effect of background aerosol on the evolution process is investigated. We have set up six cases to evaluate the effect of background pollution on nucleation. The simulation method had been proved with a good agreement by [PERSON] [6]. Many studies have reported aerosol's evolution under pollution conditions [7; 8; 9]. The background of pollution has a significant impact on the evolution of aerosols, which has reached a consensus. However, these studies are mainly based on experiments and measurements. They do not involve the quantitative analysis of the aerosol evolution process of the background physical quantities of the pollution background. [PERSON] [10] uses the thermodynamically consistent theory to treat the binary nucleation rate as a function of temperature, relative humidity, and acidity. Compared with the classical approach, they increased the computational efficiency of simulated nucleation by 25 times. Then, [PERSON] [11] extended the applicable temperature range of the work to the high-temperature range, which led to applying this research to simulate vehicle emissions. The evolution of vehicle emissions will be diluted in three-dimensional space due to the consideration of the flow field. The temperature, concentration, etc. will change accordingly. This can lead to significant changes in particle size and its distribution. This is also the reason why the Euler-Euler model is challenging to track the particle phase. It is complicated to consider multiple processes at the same time. Thus, researchers have separately studied the influence of a single process on the single properties of particle population. For example, [PERSON] [12; 13] studied the effect of environmental dilution on the particle size distribution and concentration changes of the carrier by taking the particle size distribution as a function of time. [PERSON] studied the influence of turbulent kinetic energy on coagulation [14], dilution on number concentration, and the relationship between internal combustion engine operating state and particle size [15].