Disk impact on a boiling liquid: Dynamics of the entrapped vapor pocket

TL;DR

This work investigates how a condensable vapor pocket entrapped under a circular disk during impact on a boiling liquid governs the impact loads, contrasting with non-condensable air cushions. Using a temperature-controlled chamber and a combination of pressure sensors, hydrophone, and high-speed imaging with TIR visualization, the study maps pre- and post-impact vapor-pocket dynamics across ambient temperatures, impact speeds, disk heating, and tilt. Key findings include a Rayleigh-like initial retraction of the pocket, condensation-induced rapid collapse at high $U_0$ and low $T_0$ that can produce localized pressures far beyond gas-cushion predictions, and the demonstrated ability to mitigate such loads by heating the disk or increasing tilt to hinder proper entrapment. The work advances understanding of boiling-liquid impacts with phase-change interfacial layers and informs design considerations for cryogenic fuel containment and related multiphase systems.

Abstract

Upon the impact of a flat disk on a boiling liquid, i.e., a liquid that is in thermal equilibrium with its own vapor, a thin vapor layer is entrapped under the disk. Due to the tendency of vapor to undergo phase change under pressure variation upon impact, the dynamics of this entrapped vapor pocket are different from those of a non-condensable air pocket. In this work, we experimentally investigate the dynamics of the entrapped vapor pocket, more specifically its time evolution and its subsequent influence on the hydrodynamic loads at different equilibrium ambient temperatures and impact velocities. We find that the retraction of the vapor pocket at high ambient temperature and small impact velocity is slow, occurring from the disk edge, and driven by the dynamic pressure $ρ_{\text{L}}U_0^2$. In contrast, at lower ambient temperatures and large impact velocities, after a short initial stage, the vapor pocket will collapse rapidly due to condensation. This scenario is confirmed by conducting experiments where, by heating the disk, the vapor pocket collapse is observed to slow down. We attribute this to the vaporization of liquid near the three-phase contact line region that frustrates the condensation process and reduces the impact pressure on the disk. The violent collapse of the vapor pocket may impart additional instantaneous momentum, but the overall pressure and force impulses are still found to be closely associated with the liquid added mass. Finally, we found that at a high tilt angle of the disk, the three-phase contact line movement over the disk surface may hinder the proper entrapment and compression of the vapor pocket, which results in a lower central impact pressure as rapid condensation at the central disk region does not occur.

Figures (10)

• Figure 1: Schematic of the experimental setup.
• Figure 2: (a) Cross section of the temporal deformation of the free liquid surface before the impact of a $R_0 =$ 0.040 m circular flat disk at (i) $T_0 \approx 24.5^{\circ}\text{C}$ and $U_0 =$ 2.0 m/s and (ii) $T_0 \approx 11.5^{\circ}\text{C}$ and $U_0 =$ 1.0 and 2.0 m/s. The vertical dashed lines denote the location of the disk edge and $\tau$ is defined as the time before impact, where $\tau$ = 0 is the moment at which the disk makes initial contact with the deformed surface around the disk edge. The initial thickness of the entrapped vapor pocket $h_0$ is taken as the difference between $h(r = R_0$) and $h(r = 0)$ at $\tau =$ 0.033 ms. (b) Plot of the initial thickness of the entrapped vapor pocket $h_0$ against the density ratio between the vapor and liquid $\rho_{\text{v,0}}/\rho_{\text{L}}$. The black solid line shows the direct proportionality of $h_0$ with $R_0 \left(\rho_{\text{v,0}}/\rho_{\text{L}}\right)$, where $\lambda = 2.1$ is a fitted prefactor based on the experimental data. Meanwhile, the red dashed line $h_0 \sim R_0 (\rho_{\text{v,0}}/\rho_{\text{L}})^{0.872}$ represents the dependence of $h_0$ on the density ratio at $t^{\dagger} =$ 0.9998 predicted by the integration of Eq. (5.6) in peters2013splash. The light blue diamond marker at $\rho_\text{v,0}/\rho_\text{L} = 1.2 \times 10^3$ is the initial thickness of an entrapped air pocket under a $R_0 = 0.040$ m flat disk before impacting towards a water bath at $U_0 = 1.0$ m/s, taken from jain2021total.
• Figure 3: (a) Six (re-aspected) snapshots of the evolution of the entrapped vapor pocket at (i) $U_0$ = 1.0 m/s and (ii) $U_0$ = 2.0 m/s at $T_0 \approx$ 16.5$^{\circ}\text{C}$. The time $\tilde{t}$ is the time after impact $t$ normalized by the inertial time scale $t_{\text{i}} = R_0/U_0$, where $\tilde{t}$ = 0 is the moment at which the disk edge first contacted the deformed liquid surface. The scale bar indicates a length of 20 mm. (b) The maximum expansion speed $U_{\text{e,max}}$ of the wetted area from the central disk region for selected $T_{0}$ and $U_0$ where the entrapped vapor pocket collapses. The inset shows a phase diagram where red circular markers indicate that the vapor pocket is observed to collapse at the central region in the experiment for the corresponding ambient temperature $T_0$ and impact velocity $U_0$, while the cross markers indicate cases where no collapse at the central region was registered. The black dashed line indicates the speed of sound $C_{\text{sound,L}}$ in liquid Novec 7000 at different temperatures from aminian2022ideal. (c) Plot of the effective radius $R_{\text{eff}}$ of the vapor pocket against time after impact $t$. Here, symbols indicate the different impact velocities and colors the different ambient temperatures (see legend).
• Figure 4: Normalized radius $R_\text{eff}/R_\text{eff,i}$ of the entrapped vapor pocket against normalized time $t/t_\text{tc}$ for selected representative ambient temperatures and impact velocities from Fig. \ref{['fig:Reff']}c. The radius of the vapor pocket $R_{\text{eff}}$ is normalized by its initial radius $R_{\text{eff,i}}$ while the time after impact $t$ is normalized by the Rayleigh collapse time $t_{\text{tc}}$ (see text). The black solid line is the solution of the Eq. \ref{['eq:rayleigh']}. The data for different ambient temperatures and impact velocity collapse well at the initial stage of the retraction.
• Figure 5: (a) Time series of the pressure signal $p(t)$ at the center (red lines) and near the edge (black lines) of the disk at $T_{0} \approx$ 16.5 $^{\circ}$C and (i) $U_0 =$ 1.0 m/s (ii) $U_0 =$ 2.0 m/s and (iii) $T_{0} \approx$ 11.5 $^{\circ}$C, $U_0 =$ 2.0 m/s. The pressure signals are centered at $t_{\text{p}} =$ 0 ms when the impact pressure at the disk center $P_{\text{c}}$ is maximum. The maximum pressure at the disk center $P_{\text{c,max}}$ at $T_{0} \approx$ 11.5 $^{\circ}$C is about 4 times larger than $T_{0} \approx$ 16.5 $^{\circ}$C, at the same impact velocity $U_0 =$ 2.0 m/s. The blue dashed lines represent the theoretical gas pressure under the approaching disk center computed with Eq. (5.4) from peters2013splash, for comparison. (b) Pressure in the liquid bulk measured by a hydrophone located approximately 0.12 m from the center of the disk at two different ambient temperatures and impact velocities.