The condensation or evaporation of droplet is a phase change process, which is not only an efficient heat and mass transfer process, but also has a close relation with the change of the environmental climate. Experimental results show that the electrostatic field has a big influence on the formation of droplet, and it is an effective way to enhance heat and mass transfer and it’s also related to the formation of lightning and rain. Based on the phase equilibrium theory, this paper derived the mathematical expressions of pressure difference, vapor pressure and equilibrium radius of spherical dielectric droplet under electrostatic field by using the thermodynamic equations with the effects of electric field. By means of numerical calculations, it analyzed the formation process of droplet with these mathematical expressions. The results show that the pressure difference, vapor pressure and equilibrium radius of dielectric droplet under electrostatic field are increased compared with those without electric field. The increase of vapor pressure and equilibrium radius will accelerate the evaporation process of droplet, so the electrostatic field can promote the evaporation of droplet. This conclusion is consistent with the experiments and can provide reference for related theoretical researches and engineering applications.

Optical imaging detection technology is an important subject in the study of precision guided weapons. The aero-optical effects has a big influence on the guidance precision, and it can make the vehicle off the target position, or even off the target. The interaction between the aircraft and the incoming flow leads to a very complex flow field structure around it. The existence of shock waves, expansion waves and turbulent boundary layer makes the refractive index of the flow field unevenly distributed in space and high frequency jitter in time. Among them, the aero-optical distortion caused by the boundary layer rotation process is the biggest problem to be solved urgently. Boundary layer transition, as a process of boundary layer flow from laminar to turbulent state, is a strong nonlinear complex flow physical phenomenon influenced by multi-factor coupling, and has been a hot topic in turbulence research field.The transition region of the supersonic boundary layer is very unsteady and random, and the pulsation frequency is high, so the refractive index distribution is extremely complex. The light passing through this layer will be deflected, and there will be imaging blur and energy dispersion which seriously affect the accuracy of imaging guidance. It is difficult to reduce this effect by optical correction. This paper attempted to reduce or even eliminate the effect of supersonic boundary layer transition on optical transmission performance by delaying boundary layer transition. Taking the boundary layer flow field around the optical window of the supersonic rotary vehicle as the research object, the study carried out numerical simulation on the variation law of the aero-optical effect of the boundary layer by using the flow control method of adding perturbation plates. The results show that with the increase of the angle of attack, the distribution of optical path difference gradually changes from the symmetrical distribution along the symmetry plane to the change along the flow direction, and gradually flattens. After the turbulence control is applied, the transition position of the boundary layer above the optical window moves backward, and the flow field above the window gradually changes from the transition area to the laminar flow area, which has a significant effect on suppressing the aero-optical effect.

It is of great significance to study the geometric structure and characteristics of random packings for understanding the macroscopic physical properties of disordered systems such as granular matter, foam, colloid, etc. Combining with experiments and computer simulations, researchers have explored the random packings of particles with different shapes and dimensions. In theory, some models based on statistical geometry, mean field approximation or stochastic process were proposed to investigate the volume fraction and average coordination number of random packings. However, due to the complex constraints of packing structure, the difficulty of setting a criterion for the disorder, etc., it is difficult to perform rigorous analysis and calculation even for monodisperse disk packings. For the volume fraction of the random closed packing, different studies provided different results. In this paper，a statistical Voronoi model was proposed for the theoretical research of the geometric properties of the monodisperse disk packings. The Voronoi network was used to describe the configuration of a packing and an area formula of the Voronoi network was deduced for general case. Based on the concepts of excluded circle and Voronoi circle, several theorems were given for determining the Voronoi nearest neighbor relationship between rigid disks. For balanced and stable disk packings, based on the relationships between the features of a Voronoi cell and the contact structure of nearest neighbor disks, this paper derived several formulae such as the volume fraction of a symmetric Voronoi cell varying with the contact number, the area of a Voronoi cell and the geometric coordination number varying with angles of neighbor contact lines. Finally, this paper derived the integral formulae for the average geometric coordination number and the average reduced free volume with respect to the probability distribution of the contact line angle by using the statistical analysis of Voronoi network. Theoretical calculation results show that the volume fraction of a Voronoi cell increases both with the increase of its symmetry and its contact number, the average contact number is 4 and the average volume fraction is π²/12 for the random closed packing. These results can be used to understand the geometric structure and feature of the frictionless disk packing.