Movement of Deposited Water on Turbomachinery Rotor Blade Surfaces

A theoretical approach for calculating the movement of liquid water following deposition onto a turbomachine rotor blade is described. Such a situation can occur during operation of an aero-engine in rain. The equation of motion of the deposited water is developed on an arbitrarily oriented plane triangular surface facet. By dividing the blade surface into a large number of facets and calculating the water trajectory over each one crossed in turn, the overall trajectory can be constructed. Apart from the centrifugal and Coriolis inertia effects, the forces acting on the water arise from the blade surface friction, and the aerodynamic shear and pressure gradient. Nondimensionalization of the equations of motion provides considerable insight and a detailed study of water flow on a flat rotating plate set at different stagger angles demonstrates the paramount importance of blade surface friction. The extreme cases of low and high blade friction are examined and it is concluded that the latter (which allows considerable mathematical generalization) is the most likely in practice. It is also shown that the aerodynamic shear force, but not the pressure force, may influence the water motion. Calculations of water movement on a low-speed compressor blade and the fan blade of a high bypass ratio aero-engine suggest that in low rotational speed situations most of the deposited water is centrifuged rapidly to the blade tip region.