Abstract
The prime objective of this study is to answer the question: How large is the pressure developed at the instant of a spherical liquid droplet impact on a solid surface? Engel first proposed that the maximum pressure rise generated by a spherical liquid droplet impact on a solid surface is different from the one-dimensional water-hammer pressure by a spherical shape factor (Engel 1955 J. Res. Natl Bur. Stand. 55(5), 281–298). Many researchers have since proposed various factors to accurately predict the maximum pressure rise. We numerically found that the maximum pressure rise can be predicted by the combination of water-hammer theory and the shock relation; then, we analytically extended Engel’s elastic impact model, by realizing that the progression speed of the contact between the gas–liquid interface and the solid surface is much faster than the compression wavefront propagation speed at the instant of the impact. We successfully correct Engel’s theory so that it can accurately provide the maximum pressure rise at the instant of impact between a spherical liquid droplet and solid surface, that is, no shape factor appears in the theory.
Highlights
An understanding of liquid droplet impact onto a rigid solid surface is needed in a number of technological situations such as cleaning of surfaces, spray coating, spray cooling and ink-jet printing
We contrast the liquid droplet impact pressure with the water-hammer pressure rise in later sections; we briefly review a couple of previous one-dimensional models used in the estimation of impact pressure
We examine whether the liquid impact pressure rise can be reduced by the stiffened-gas pressure rise (equation (2.10)) when the interface that impacts on a solid surface has a finite radius of curvature using the numerical analysis
Summary
An understanding of liquid droplet impact onto a rigid solid surface is needed in a number of technological situations such as cleaning of surfaces, spray coating, spray cooling and ink-jet printing. They investigated the impact process of cylindrical, spherical and conical water droplets on a solid plane surface using numerical methods They found that the impact pressure rise reaches a peak of 0.7r0c0V. Sanada et al [23] carried out a numerical simulation of an axisymmetric spherical liquid droplet impact on a solid surface, using the ghost fluid method [24] They found that the maximum pressure rise of the point closest to the solid surface can be well predicted by equation (1.2). Sanada et al [25] and Kondo & Ando [26] numerically studied axisymmetric and cylindrical droplet impact on a solid surface, respectively, using the shock-interface capturing scheme [27] Their results support Engel [6], i.e. equation (1.1). We correct Engel’s elastic impact model to find that the factor aE/2 appearing in equation (1.1) converges to 1 at the instant of the impact
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