Efficient prediction method for Kelvin-Helmholtz instability growth on transcritical droplet surface in composite coordinate system

Traditional methods for analyzing the Kelvin-Helmholtz instability on the surface of droplets that dominate the formation mass of combustible mixtures are difficult to achieve effective predictions over a wide range of critical conditions for the actual operation of hybrid internal combustion engines. In this paper, the composite coordinate system method was used to establish an efficient prediction model of equivalent droplet instability in a transcritical strong convection environment. The global diffusion dynamics model, thermodynamics control model, and tangential instability model of local droplet surface were used, respectively. The analytical solution could be obtained by the modal coordinate transformation in the global coordinate system model, and the potential function was introduced in the local coordinate system to improve the solution speed. To realize a practical fluid computational simulation model, the dimensionless physical parameters were used to describe the changes in aerodynamic force, inertial force, viscous force, surface tension, and other control factors under different transcritical conditions and analyze their influence on the growth of tangential and normal unstable waves on the droplet surface. The results show that the aerodynamic forces on the droplet surface still dominate the development of tangential unstable waves on the droplet surface under transcritical conditions. When the pressure increases, the decrease in the flow characteristics controlled by Reynolds number in liquid phase and the decrease in the viscous force of the droplet controlled by Ornisol number basically offset. With the increase in ambient temperature, the contribution of flow characteristics controlled by Reynolds number to the growth of the Kelvin-Helmholtz wave becomes small, and the influence of the inertial force of the droplet becomes weak.