Liquid drop impact on solid surface with application to water drop erosion on turbine blades, Part I: Nonlinear wave model and solution of one-dimensional impact

Water drop erosion is regarded as one of the most serious reliability concerns in the wet steam stage of a steam turbine. The most challenging aspect of this problem involves the fundamental solution of the transient pressure field in the liquid drop and stress field in the metal substrate, which are coupled with each other. We solve the fundamental problem of high-speed liquid-solid impact both analytically and numerically. In Part I of this paper, the governing equations based on a nonlinear wave model for liquid are derived. Analytical and approximate solutions of one-dimensional liquid-solid impact are given for both linear and nonlinear models, which provide critical insights into the water drop erosion problem. Both continuous and pulsant impacts on rigid and elastic substrates are analyzed in detail. During continuous impact, the maximum impact pressure is always higher than the water hammer pressure. Upon pulsant impact and at a particular instant related with the impact duration, the maximum tensile stress appears at a certain depth below the solid surface, which can be readily related with the erosion rate. In Part II of this paper, two-dimensional (axisymmetric) liquid-solid impact is solved numerically, from which the most dangerous impact load/duration time and the most likely crack positions are deduced. Based on our recent solution of the water drop impact statistics (associated with the fluid flow in the blade channel), a comprehensive numerical study of the water drop erosion (fatigue) on a turbine blade is carried out.