Most nuclear power plants adopt spray systems as safety measures, 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 is prevented by a vapor layer formed through the vaporization of the droplet. A simple model is proposed, consisting of an improved lumped approach based on Hermite-type approximations for integrals for the transient heat transfer in the droplet and the wall, an integral method to model the transient heat transfer in the vapor layer, and a lubrication approximation that considers the effects of inertia for the flow caused by the vaporization and the motion of the droplet. The proposed model was implemented in the symbolic computing platform Mathematica® and used to analyze the droplet dynamics considering different initial wall temperatures. Parametric studies were carried out to investigate the effects of initial droplet size and velocity on the interactions. The effects of wall material and its temperature variation were also evaluated by considering different materials and an isothermal case. As results, the behavior of the droplet is verified to change continuously over time until it takes-off from the wall just before complete vaporization. Furthermore, at the impact, 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.
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