Introducing pre-impact air-cushioning effects into the Wagner model of impact theory

Moore, M. R.

doi:10.1007/s10665-021-10137-z

Cited by 16 publications

(9 citation statements)

References 50 publications

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“…This cushioning effect can soften the impact so much that the schlieren imaging cannot detect the pressure waves for some impacts (see, for example, Supplemental Movie 4 ). Previous studies do not agree on the magnitude of the pressure on the impacting surface when air cushioning is significant 29 – 31 , but we would expect the pressure to scale with 30 , which upon reflection off the free surface results in Daou et al 20 experimentally showed that even in the presence of an air layer, the pressure in the near field continues to scale with the water hammer pressure (i.e., ( 2 ) still applies). Hence, combining ( 1 ), ( 2 ) and ( 6 ) and simplifying shows that even at the lowest α the impact must exceed a critical velocity for cavitation to occur; As the ambient gas pressure, P a m b , affects the amount of trapped air, and the cushioning effect, the value of k 2 should change with gas properties, decreasing with lower P a m b .…”

Section: Resultsmentioning

confidence: 83%

“…This allows cavitation to occur at lower impact velocities and k 2 decreases to k 2 ≈ 0.0022 for P a m b ≤ 1/2 atm, corresponding to U o ≃ 3.3 m/s in water. Other studies have shown that the thinness of the air film and the rapid contact line motion cause the gas viscosity 31 , 32 , gas density 32 , rarefied gas effects 33 , and gas speed of sound 29 to affect the air cushioning. Hence, we expect that the minimum velocity for cavitation and k 2 likely depend on each of these parameters as well.…”

Section: Resultsmentioning

confidence: 99%

“…2 b, t = 30 μs). The curvature also changes the shape of the free surface depression 31 such that assuming a flat free surface no longer appears sufficient to approximate α . As these effects complicate the reflected pressure and the pressure field, additional modeling will be required to predicted the onset of cavitation for such variations in geometry.…”

Section: Resultsmentioning

confidence: 99%

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Cavitation upon low-speed solid–liquid impact

et al. 2021

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When a solid object impacts on the surface of a liquid, extremely high pressure develops at the site of contact. Von Karman’s study of this classical physics problem showed that the pressure on the bottom surface of the impacting body approaches infinity for flat impacts. Yet, in contrast to the high pressures found from experience and in previous studies, we show that a flat-bottomed cylinder impacting a pool of liquid can decrease the local pressure sufficiently to cavitate the liquid. Cavitation occurs because the liquid is slightly compressible and impact creates large pressure waves that reflect from the free surface to form negative pressure regions. We find that an impact velocity as low as ~3 m/s suffices to cavitate the liquid and propose a new cavitation number to predict cavitation onset in low-speed solid-liquid impact-scenarios. These findings imply that localized cavitation could occur in impacts such as boat slamming, cliff jumping, and ocean landing of spacecraft.

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Section: Resultsmentioning

confidence: 83%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Cavitation upon low-speed solid–liquid impact

et al. 2021

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“…The problem of droplet post-impact theory onto deformable surfaces has been tackled previously 13,15 by ignoring the air cushioning phase and the entrapped air. However, these features do influence the post-impact dynamics, 26,70 and so questions remain on how this occurs in impact on deformable surfaces. One possible alternative to the air cushioning model presented here and the classic Wagner model of impact theory would be to use direct numerical simulation to analyze how air cushioning effects influence post-impact dynamics.…”

Section: Discussionmentioning

confidence: 99%

Pre-impact dynamics of a droplet impinging on a deformable surface

2021

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The nonlinear interaction between air and a water droplet just prior to a high-speed impingement on a surface is a phenomenon that has been researched extensively and occurs in a number of industrial settings. The role that the surface deformation plays in an air cushioned impact of a liquid droplet is considered here. In a two-dimensional framework, assuming small density and viscosity ratios between the air and the liquid, a reduced system of integrodifferential equations is derived governing the liquid droplet free-surface shape, the pressure in the thin air film, and the deformation of the surface, assuming the effects of surface tension, compressibility, and gravity to be negligible. The deformation of the surface is first described in a rather general form, based on previous membrane-type models. The coupled system is then investigated in two cases: a soft viscoelastic case where the surface stiffness and (viscous) damping are considered and a more general flexible surface where all relevant parameters are retained. Numerical solutions are presented, highlighting a number of key consequences of surface deformability on the pre-impact phase of droplet impact, such as reduction in pressure buildup, increased air entrapment, and considerable delay to touchdown. Connections (including subtle dependence of the size of entrapped air on the droplet velocity, reduced pressure peaks, and droplet gliding) with recent experiments and a large deformation analysis are also presented.

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“…The effect of the air cushion is especially important for phenomena at the very initial stage, when the instantaneous Froude number is tremendously large. The detailed behaviour of the air cushion and its effect on various aspects of the impact, such as splash, pressure and force, are studied in, for example, Bouwhuis et al (2015), Jain et al (2021), Moore (2021), Hicks et al (2012).…”

Section: Introductionmentioning

confidence: 99%

The controlled impact of elastic plates on a quiescent water surface

Wang

Wong

et al. 2022

J. Fluid Mech.

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The impact of flexible rectangular aluminum plates on a quiescent water surface is studied experimentally. The plates are mounted via pinned supports at the leading and trailing edges to an instrument carriage that drives the plates at constant velocity and various angles relative to horizontal into the water surface. Time-resolved measurements of the hydrodynamic normal force ( $F_n$ ) and transverse moment ( $M_{to}$ ), the spray root position ( $\xi _r$ ) and the plate deflection ( $\delta$ ) are collected during plate impacts at 25 experimental conditions for each plate. These conditions comprise a matrix of impact Froude numbers ${Fr} = V_n(gL)^{-0.5}$ , plate stiffness ratios $R_D= \rho _w V_n^2 L^3D^{-1}$ and submergence time ratios $R_T= T_sT_{1w}^{-1}$ . It is found that $R_D$ is the primary dimensionless ratio controlling the role of flexibility during the impact. At conditions with low $R_D$ , maximum plate deflections on the order of $1$ mm occur and the records of the dimensionless form of $F_n$ , $M_{to}$ , $\xi _r$ and $\delta _c$ are nearly identical when plotted vs $tT_s^{-1}$ . In these cases, the impact occurs over time scales substantially greater than the plate's natural period, and a quasi-static response ensues with the maximum deflection occurring approximately midway through the impact. For conditions with higher $R_D$ ( $\gtrsim 1.0$ ), the above-mentioned dimensionless quantities depend strongly on $R_D$ . These response features indicate a dynamic plate response and a two-way fluid–structure interaction in which the deformation of the plate causes significant changes in the hydrodynamic force and moment.

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Introducing pre-impact air-cushioning effects into the Wagner model of impact theory

Cited by 16 publications

References 50 publications

Cavitation upon low-speed solid–liquid impact

Cavitation upon low-speed solid–liquid impact

Pre-impact dynamics of a droplet impinging on a deformable surface

The controlled impact of elastic plates on a quiescent water surface

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