Dynamic pressure enhancement upon disk impact on a boiling liquid

Abstract

We experimentally investigate the impact of a flat, horizontal disk onto a boiling liquid, i.e., a liquid in thermal equilibrium with its vapor phase. We observe exceptionally high impact pressures deviating strongly from the inertial scaling found for impact in a non-condensable environment, coinciding with the rapid collapse of the vapor pocket entrapped below the disk. We explain our findings, which are relevant for the safe transportation of cryogenic fuels, as a result of vapor condensation, leading to accelerated vapor pocket contraction at high impact velocity and low vapor density.

Figures (4)

• Figure 1: (a) Schematic of the experimental setup. (b) Time evolution of the measured pressure $P_c$ at the center of the disk, on a logarithmic scale, for two different impact speeds $U_0 = 0.5$ and $2.0$ m/s at an ambient temperature $T_0 \approx 11.5$$^\circ$C. Here, $t_\text{a} = 0$ corresponds to the time at which the pressure signal at a reference pressure sensor near the disk edge rises above 10$\%$ of its maximum value. (c) Five re-aspected snapshots from the evolution of the entrapped vapor pocket under the impacting disk shown in (b). Note that, $t_\text{a} = 0$ coincides with the impact time, i.e., the time at which the disk is observed to make initial contact with the liquid surface from the high-speed recordings and $\tilde{t} = U_0t_\text{a}/R_0$ is the dimensionless time. (i) Gradual retraction of the liquid-vapor contact line from the disk edge at $T_0 \approx 11.5$$^{\circ}$C and $U_0 = 0.5$ m/s. The entrapped vapor pocket is punctured around the disk center only at a very late stage (see Supplementary video 1 supplemental). (ii) Rapid collapse of the entrapped vapor pocket at $T_0 \approx 11.5^{\circ}$C and $U_0$ = 2.0 m/s, where the entrapped vapor condenses into liquid around the disk center, resulting in the dark shaded wetted inner region of the disk that expands rapidly with time (see also in Supplementary video 2 supplemental). [Scale bar = 20 mm]
• Figure 2: Maximum central impact pressure $P_{\text{c,max}}$, rescaled with the inertial pressure scale $\rho_\text{L} U_0^2$ and plotted against the impact velocity $U_0$ at different ambient temperature $T_0$. Error bars show the standard deviation of the maximum impact pressure at the disk center over at least 5 repetitions of the experiment. The horizontal dashed blue line represents a fit to the data for water--air disk impact from jain2021air that follows the classic $\rho_\text{L} U_0^2$ scaling.
• Figure 3: Schematic of the model for the collapse of the entrapped vapor pocket upon impact. As the disk descends at constant impact velocity $U_0$ the pressure $p_\text{v}$ and temperature $T_\text{v}$ within the vapor pocket increase, whereas the temperature of the liquid bulk remains at the saturation level ($T_0$). Therefore, to restore equilibrium, the vapor pocket starts to condense at the liquid-vapor interface where the released latent heat is conducted into the liquid. Eventually, this process may cause the vapor pocket to collapse and the wetted area spreads in the radial direction over the disk surface.
• Figure 4: Plotting the rescaled maximum impact pressure $P_{\text{c,max}}/\rho_\text{L}U_0^2$ at the disk center from Fig. \ref{['fig:fig3']} against $U_{\text{sp}}/C_{\text{sound,L}}$ as derived from the proposed theoretical model gives a decent collapse of data. The maximum central impact pressure induced during boiling impact can be described as a result of vapor condensation that strongly depends on the impact velocity and vapor density of the boiling system. (Note that an additional data point for $U_0 = 2.25$ m/s at $T_{0} \approx 14.5^{\circ}$C is included here.)