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

Abstract 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.

[1]  Brad Lee Boyce,et al.  The residual stress state due to a spherical hard-body impact , 2001 .

[2]  F. J. Heymann,et al.  High‐Speed Impact between a Liquid Drop and a Solid Surface , 1969 .

[3]  F. G. Hammitt,et al.  Hydrodynamic Phenomena During High-Speed Collision Between Liquid Droplet and Rigid Plane , 1973 .

[4]  N. Fleck,et al.  Mechanisms governing the high temperature erosion of thermal barrier coatings , 2004 .

[5]  Y. Ventikos,et al.  Computational study of high-speed liquid droplet impact , 2002 .

[6]  O. G. Engel,et al.  Waterdrop collisions with solid surfaces , 1955 .

[7]  M. B. Lesser,et al.  Analytic solution of liquid-drop impact problems , 1981, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  John W. Hutchinson,et al.  Particle impact on metal substrates with application to foreign object damage to aircraft engines , 2002 .

[9]  Brad Lee Boyce,et al.  On the application of the Kitagawa-Takahashi diagram to foreign-object damage and high-cycle fatigue , 2002 .

[10]  John E. Field,et al.  The contribution of the Cavendish Laboratory to the understanding of solid particle erosion mechanisms , 2005 .

[11]  B. Staniša,et al.  Erosion behaviour and mechanisms for steam turbine rotor blades , 1995 .

[12]  Ho-Young Kim,et al.  Imaging the high-speed impact of microdrop on solid surface , 2003 .

[13]  William F. Adler,et al.  Analysis of water-drop impacts on layered window constructions , 1994, Optics & Photonics.

[14]  Branko Staniša,et al.  Erosion behaviour of turbine rotor blades installed in the Krsko nuclear power plant , 2003 .

[15]  Joseph B. Franzini,et al.  Fluid Mechanics with Engineering Applications. 6th Ed. By R. L.DAUGHERTY and J. B. FRANZINI. McGraw-Hill. 1965. 574 pp. $9.95 or 80s. Fluid Dynamics. By J. W. DAILY and D. R. F. HARLEMAN. Addison Wesley. 1966. 454 pp. $12.50 or 94s. , 1967, Journal of Fluid Mechanics.

[16]  P. Lush,et al.  Liquid impact on a bilinear elastic-plastic solid and its role in cavitation erosion , 1987, Journal of Fluid Mechanics.

[17]  William F. Adler,et al.  Waterdrop impact modeling , 1995 .

[18]  Kazuyoshi Takayama,et al.  The measurement of impact pressure and solid surface response in liquid-solid impact up to hypersonic range , 1995 .

[19]  D. Bonn,et al.  Singular jets and bubbles in drop impact. , 2006, Physical review letters.

[20]  Angus R. Simpson,et al.  Water hammer with column separation: A historical review , 2006 .

[21]  Stanley S. Cook.  Erosion by Water-Hammer , 1928 .

[22]  Frederick G. Hammitt,et al.  High-Speed Impact Between Curved Liquid Surface and Rigid Flat Surface , 1975 .

[23]  Y. Ito,et al.  Analysis of Brittle Target Fracture from a Subsonic Water Drop Impact , 1979 .

[24]  John E. Field,et al.  High‐speed photography of surface geometry effects in liquid/solid impact , 1988 .

[25]  O. G. Engel.  Damage produced by high‐speed liquid‐drop impacts , 1973 .

[26]  John E. Field,et al.  The effects of target compliance on liquid drop impact , 1989 .

[27]  A. Fedorchenko,et al.  Effect of capillary and viscous forces on spreading of a liquid drop impinging on a solid surface , 2005 .

[28]  D. V. Boger,et al.  Influence of fluid elasticity on drops impacting on dry surfaces , 2000 .

[29]  R. M. Blowers.  On the Response of an Elastic Solid to Droplet Impact , 1969 .

[30]  Xiangshan Chen,et al.  Water Drop Erosion on Turbine Blades: Numerical Framework and Applications , 2008 .

[31]  F. J. Heymann,et al.  On the Shock Wave Velocity and Impact Pressure in High-Speed Liquid-Solid Impact , 1968 .

[32]  J. E. Field,et al.  ELSI conference: invited lecture: Liquid impact: theory, experiment, applications , 1999 .