Dynamic interaction between a droplet and a wall heated beyond the Leidenfrost temperature

Spray systems are adopted as safety measures in most nuclear power plants. Considering that a spray can be represented by a collection of droplets, in this work we study the interaction between a single droplet and a hot wall. Our interest lies in the dynamic Leidenfrost effect, where the contact between an impacting droplet and a very hot wall (heated beyond the Leidenfrost temperature) is prevented by a vapor layer formed through the vaporization of the droplet. Under this condition, the heat removed from the wall is drastically reduced, which is very detrimental for safety systems based on spray cooling. In order to achieve a modest computational cost when analyzing the problem, we propose a simple model where the droplet is considered to be saturated, the heat transfer in the vapor layer is quasi-steady, and an improved lumped approach, based on Hermite-type approximations for integrals, is employed for the heat transfer in the hot wall. Furthermore, the lubrication approximation is applied to the fluid flow caused by the vaporization and movement of the droplet. Regarding the simplifications adopted, the most important is the use of a disk geometry to represent the shape of the droplet, where only vaporization on its lower surface is considered and the deformation due to movement and impact is disregarded. The implementation of the proposed model was done in the symbolic computing platform Mathematica®. Through the application of the model, the dynamics of the droplet was analyzed considering different initial temperatures of the wall. Parametric studies were also carried out to investigate the effects of initial droplet size and velocity on the interactions. Additionally, the effects of wall material and its temperature variation were evaluated by considering different materials and an isothermal case. As results, it was observed that, at impact, the thickness of the vapor layer decreases with the velocity of the droplet and increases with the wall temperature. Furthermore, more heat is removed from the wall by larger and faster droplets, and the cooling of the wall, which is inversely proportional to the thermal conductivity, showed negligible effects on the dynamics of the droplet. (author)