The impact of compressible liquid droplet on hot rigid surface

The processes arising when a high-velocity liquid nitrogen drop impacts a hot rigid wall have been studied by means of numerical simulation. An extremely thin near-wall layer of fluid undergoing heating and liquid–vapor phase transition is clearly distinguished in the droplet, the rest of the liquid remaining cold. A model for the layer, based on the reduced compressible Navier–Stokes equations with a two-phase equation of state, has been constructed and adjusted to the known model for the cold liquid part of the drop, based on the barotropic liquid Lagrangian equations with the Tait equation of state. A predictor-corrector finite-difference scheme for the thin layer equations has been devised and coupled with the finite-element method for the barotropic liquid. Drop shapes and flow field distributions in the layer have been obtained for the impacts of nitrogen droplets of different sizes with an initial velocity 186 m/s and different wall temperatures. The influence of the vapor layer on the drop has been analyzed. The heat flux on the wall has been calculated. An analytic formula has been derived for the heat flux, which is in agreement with the calculations for droplets up to 0.1 mm radius.