In diesel engines, fuel mixing is an important process in determining the combustion efficiency and emissions level. One of the measures used to achieve fuel mixing is controlling the nature and behavior of the fuel spray by shaping the injection rate. The mechanism underlying the behavior of the spray with varying injection rates before the start of combustion is not fully understood. Therefore, in this research, the fuel injection rate shape is investigated to assess the spraying and mixing behavior. Diesel sprays with different ambient temperatures and injection pressures are modeled using the CONVERGE-CFD software. The validation is performed based on experimental data from an Engine Combustion Network (ECN). The verified models are then used to analyze the characteristics of the diesel spray before and after the end-of-injection (EOI) with four fuel injection rate shapes, including a rectangular injection rate shape (RECT), a quick increase gradual decrease injection rate shape (QIGD), a gradual increase gradual decrease injection rate shape (GIGD), and a gradual increase quick decrease injection rate shape (GIQD). The spray vapor penetrations, liquid lengths, evaporation ratios, Sauter mean diameter (SMDs), distributions of turbulence kinetic energy, temperatures, and equivalence ratios were compared under different injection rate shapes. The results show that the QIGD injection rate shape can enhance mixing during injection, while the GIQD injection rate shape can achieve better mixing after the EOI.

Common rail systems have been widely used in diesel engines due to the stricter emission regulations. The advances in injector technology and ultrahigh injection pressure greatly promote the development of multiple-injection strategy, leading to the shorter injection duration and more variable injection rate shape, which makes the mixing process more significant for the formation of pollutant emission. In order to study the mixing process of diesel sprays under variable injection rate shapes and find the optimized injection strategy, a one-dimensional spray model was modified in this paper. The model was validated by the measured spray penetrations based on shadowgraphy experiments with the varying injection rate. The simulations were performed with five injection rate shapes, triangle, ramping-up, ramping-down, rectangle and trapezoid. Their spray penetrations, entrainment rates and equivalence ratios along spray axial distance are compared. The potentials of multiple-injection and gas-jet after end-of-injection (EOI) to improve mixing process and emission reduction are discussed finally. The results indicated that ramping-up injection rate obtains the highest entrainment rate after EOI, and it needs 1.5 times of injection duration for the entrainment wave to arrive at the spray tip. For the other four injection rates, the sprays can be treated as a steady-like state, needing twice of injection duration from EOI to the time the entrainment wave reaches the spray tip. The multiple-injection with proper injection rate shape enhanced the entrainment rate, and the gas-jet after EOI affected the mixture distribution and entrainment rate in spray tail under ramping-down injection rate.