A film cooling technique using a liquid film subjected to a hot gas flow in a turbulent condition is theoretically investigated. We successfully incorporate the two essential factors for the evaporating liquid film, droplet entrainment and three-dimensional film architecture, allowing for the physically consistent straightforward formulation. The validity of the present model is conveyed by reproducing combustion test results conducted for two types of flight-model bipropellant thrusters, in which the film length or dryout point shortens approximately inversely proportional to the combustion pressure. The underlying scenario to determine the film length is revealed. The gas flow initiates the originally smooth liquid film to be destabilized by Kelvin–Helmholtz instability in the axial direction and accelerates the wave crests leading to Rayleigh–Taylor instability in the transverse direction. Superposing the two types of waves produces three-dimensional cusps on the film as roots of entrained droplets. The convective heat transfer evaporating the liquid film is enhanced by the entrainment, reducing the net film flow rate, and by the cusp structure, enlarging the area of liquid/gas interface along the transverse direction in particular.
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