## 1 Introduction  
The diesel engine is criticized in current and future developments due to its excellent reliability and economy. The emerging energy industry currently has, more or less, problems [1; 2; 3; 4; 5] and cannot replace diesel engines in the short term [6]. Due to the complex composition of diesel fuel and the oxygen-rich combustion characteristics of diesel engines, the exhaust gas contains a large number of pollutants, such as carbon monoxide, nitrogen oxides (NOx), unburned hydrocarbons (uHC), and particulate matter (PM). To control the NOx emission level of diesel engines, selective catalytic reduction (SCR) technology is currently used in combination with an ammonia slip catalyst (ASC). In addition, to ensure the operation of a diesel oxidation catalyst (DOC) and diesel particulate filter (DPF), an SCR system is usually located downstream of an after-treatment system in accordance with emission regulations. [PERSON] et al. conducted a study on the emissions of a marine diesel engine burning bio-diesel under different operating conditions. The marine after-treatment system used in the study employs a DPF+SCR arrangement, which can effectively reduce PM and NOx emissions levels [7; 8]. At present, an SCR system generally sprays a urea water solution (UWS) into an exhaust gas. Ammonia is produced during the pyrolysis and hydrolysis processes, providing a reducing agent for NOx catalytic conversion reactions. In ideal conditions, the droplets of UWS can completely evaporate and decompose with the help of exhaust heat. However, when the operating condition changes, the increase in ammonia demand leads to an increase in spray volume and the diameter of urea droplets. The UWS cannot be completely evaporated on the short spray path, and the droplets fall on the mixer wall to form a urea film. A thicker urea film cannot completely bring urea molecules back into the exhaust during evaporation, forming urea crystals. [PERSON] et al. 's research indicates that urea crystallization mainly occurs in areas such as the urea nozzle, nozzle seat, exhaust pipe wall, and the inlet surface of the carrier in the SCR system [9]. It is generally believed that urea crystal is developed from the film formed by spray hitting the wall [9; 10]. The evaporation characteristics of droplets can also change at different ambient temperatures. When the ambient temperature is above 300 \({}^{\circ}\)C, UWS droplets will undergo deformation, hollowing, and slight explosion phenomena. By integrating the above research, the urea droplet evaporation process can be divided into two stages, namely, the water evaporates first, and then the urea begins direct pyrolysis [11]. However, some researchers also believe that water and urea are evaporated synchronously, and ammonia in the SCR system is obtained from the decomposition of urea vapor in the gas phase [12; 13]. The hanging single droplet evaporation pyrolysis test can only reflect the variation process of UWS droplets in the exhaust airflow, while the crystallization process on the wall is slightly different. If the urea spray fails to completely decompose in the exhaust, the spray may hit the wall. Spray wall impingement is a precondition for the formation of wall film, so researchers have carried out detailed research and analysis on different wall impingement behaviors. Through the spray wall impact test, [PERSON] divided the wall impact behavior of droplets into seven types: spherical attachment, spreading attachment, complete rebound, crushing rebound, complete crushing, splash, and boiling crushing, and these seven types of behaviors are mainly divided by the Weber number of droplets and the temperature difference between the droplets and the wall surface [14]. [PERSON] further divided the region using two dimensionless numbers K and T, where the parameter K is calculated from the Weber number and Laplace number of the droplet, while T is calculated from the wall temperature and droplet saturation temperature [15].