Abstract
The simplified analysis of the initial jetless stage of high-speed drop impingement onto a convex solid surface recently proposed by Burson-Thomas et al. (2019) has been extended to a concave surface with the radius of curvature larger than the drop radius. An approximate approach has also been proposed to incorporate the surface curvature into Heymann’s analysis (1969) based on the Rankine–Hugoniot equations. It has been shown that the simplified analysis predicts a significantly longer initial stage than Heymann’s analysis. As opposed to the convex surface, the duration of the initial jetless stage and the corresponding size of the contact area for the concave surface are larger than for the flat one. For both convex and concave surfaces, the effect of the surface curvature is significant when the radii of curvature of the surface and the drop are nearly equal, and is almost absent if the ratio of the radii is more than 10.
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REFERENCES
J. E. Field, M. B. Lesser, and J. P. Dear, ‘‘Studies of two-dimensional liquid-wedge impact and their relevance to liquid-drop impact problems,’’ Proc. R. Soc. London, Ser. A 401, 225–249 (1985).
C. B. Burson-Thomas, R. Wellman, T. J. Harvey, and R. J. K. Wood, ‘‘Importance of surface curvature in modeling droplet impingement on fan blades,’’ J. Eng. Gas Turbines Power 141, 031005-1–9 (2019).
K. Fujisawa, T. Yamagata, and N. Fujisawa, ‘‘Liquid droplet impingement erosion on groove roughness,’’ Nucl. Eng. Des. 330, 368–376 (2018).
W. F. Adler, ‘‘The mechanics of liquid impact,’’ in Erosion: Treatise on Materials Science and Technology, Ed. by C. M. Preece (Academic, New York, 1979), pp. 127–183.
W. Wu, Q. Liu, and B. Wang, ‘‘Curved surface effect on high-speed droplet impingement,’’ J. Fluid Mech. 909, A7 (2021).
F. Huang, Sh. Li, Y. Zhao, and Y. Liu, ‘‘Study on lateral jetting range during an arc-curved jet impacting nonplanar solid surfaces,’’ J. Fluids Eng. 140, 101201-1–11 (2018).
C. B. Burson-Thomas, R. Wellman, T. J. Harvey, and R. J. K. Wood, ‘‘Water droplet erosion of aeroengine fan blades: The importance of form,’’ Wear 426–427, 507–517 (2019).
F. J. Heymann, ‘‘High-speed impact between a liquid drop and a solid surface,’’ J. Appl. Phys. 40, 5113–5122 (1969).
M. B. Lesser, ‘‘Analytic solutions of liquid-drop impact problems,’’ Proc. R. Soc. London, Ser. A 377, 289–308 (1981).
J. M. Walsh, R. G. Shreffler, and F. J. Willig, ‘‘Limiting conditions for jet formation in high velocity conditions,’’ J. Appl. Phys. 24, 349–359 (1953).
K. Takizawa, T. Yabe, Y. Tsugawa, T. E. Tezduyar, and H. Mizoe, ‘‘Computation of free-surface flows and fluid-object interactions with the CIP method based on adaptive meshless Soroban grids,’’ Comput. Mech. 40, 167–183 (2007).
A. A. Aganin and T. S. Guseva, ‘‘Numerical simulation of liquid mass collision with a wall,’’ Progr. Comput. Fluid Dyn. Int. J. 19, 293–306 (2019).
F. Xiao, T. Yabe, T. Ito, and M. Tajima, ‘‘An algorithm for simulating solid objects suspended in stratified flow,’’ Comput. Phys. Commun. 102, 147–160 (1997).
J. E. Field, J. P. Dear, and J. E. Ogren ‘‘The effects of target compliance on liquid drop impact,’’ J. Appl. Phys. 65, 533–540 (1989).
ACKNOWLEDGMENTS
The author is thankful to Professor A. A. Aganin for useful discussions.
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(Submitted by D. A. Gubaidullin)
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Guseva, T.S. The Initial Stage of Liquid Drop Impingement onto a Curved Surface. Lobachevskii J Math 42, 2144–2150 (2021). https://doi.org/10.1134/S1995080221090146
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DOI: https://doi.org/10.1134/S1995080221090146