Spray jet impingement is widely used to cool hot solids in iron-and steel-making processes. Numerous droplets impinge onto a solid at random and interact with each other. The present study treats the deformation behavior of two liquid drops one by one impinging coaxially onto a solid. The system of Navier-Stokes equations for incompressible fluid flow in the axial coordinate system is solved by means of a finite difference method. The effect of surface tension, gravity, and wettability between the liquid and the solid is taken into account. First, the deformation behavior of a single drop onto a solid is examined and compared to the experimental data for model validation. Then, the collision of two drops in tandem with the solid is simulated. The effect of the distance between two drops on the deformation behavior is studied. The physics of interaction phenomena of droplets is investigated theoretically.KEY WORDS: spray cooling; numerical analysis; collision dynamics of droplets onto a solid; interaction of droplets. first droplet after a time interval, d . In the present study, the effect of the time interval, d , on the merged liquid motion is investigated in detail theoretically.The liquid motion is assumed to obey the Navier-Stokes equations for incompressible viscous fluid in the axis symmetrical system. The effects of gravity, viscosity, surface tension, and wettability between the liquid and the solid are taken into account. The wettability is specified by means of the contact angle at the liquid/solid interface. The heat transfer between the droplets and the solid is neglected. In addition, the effect of airflow surrounding the droplets is not taken into account. Since the liquid density (ϭ1 000 kg/m 3 ) is approximately 830 times larger than the gas density (ϭ1.2 kg/m 3 ) at atmospheric pressure and temperature, the momentum of the surrounding airflow is negligibly small compared to the liquid. Thus, it is reasonable to consider that the liquid motion is little affected by the momentum transfer between the airflow and the liquid.Every variable is normalized using the initial droplet diameter, p , and/or the impact velocity of the first droplet, 0 as the following forms, ........ (1) where t, (r, z), (u, v), and p represent the dimensionless time, coordinates, velocity components, and pressure, respectively.denotes the liquid density. Also, overbars mean the dimensional variables. The dimensionless conservation equations are given as the following forms: The boundary conditions are explained next. At the symmetric boundary (rϭ0), the symmetric condition is imposed. No-slip condition is used at the liquid/solid boundary. At the free liquid surface, the following Laplace equation is used to determine the surface pressure. (8) where is the surface tension. At the contact line, which is defined by the free liquid surface at the solid, the advancing contact angle is specified when the contact line advances. In the present study, the advancing contact angle is set to 110 degrees.The conservation equations are...
