Real-time identification of parametric sloshing-induced heat and mass transfer in a horizontally oriented cylindrical tank

Abstract

Vertical forcing of partially filled tanks can induce parametric sloshing. Under non-isothermal conditions, the resulting mixing can disrupt the thermal stratification between liquid and vapor, leading to enhanced heat and mass transfer and large pressure fluctuations. This work presents an experimental investigation of sloshing-induced heat and mass transfer in a horizontally oriented cylindrical tank under vertical harmonic excitation. This configuration is particularly relevant for cryogenic fuel storage in aircraft and ground transportation, yet its thermodynamic response under parametric sloshing remains largely uncharacterized. The present study provides the first experimental characterization of the sloshing-induced pressure drop and associated heat and mass transfer in this geometry. Decoupled isothermal and non-isothermal experimental campaigns are carried out across multiple fill levels and forcing amplitudes, near resonance of the first longitudinal symmetric mode $(2,0)$, using a hydrofluoroether fluid (3M Novec HFE-7000). To quantify heat and mass transfer, a lumped thermodynamic model is combined with an Augmented-state Extended Kalman Filter (AEKF), enabling real-time, time-resolved inference of Nusselt numbers. A critical forcing threshold is identified: below it, the fluid remains quiescent and thermally stratified; above it, parametric resonance drives strong sloshing, complete thermal destratification, and a rapid pressure drop. At 50% fill, the dominant $(2,0)$ response intermittently alternates with a planar $(1,0)$ mode, indicating subharmonic mode interaction. The inferred Nusselt numbers increase by several orders of magnitude after destratification, and pressure-rate analysis confirms that condensation governs the pressure evolution.

Figures (21)

• Figure 1: Problem schematic: cylindrical tank of radius $R$, length $L$, dome radius $R_d$, wall thickness $\delta_w$ filled to height $H$, subjected to vertical harmonic excitation $Z(t)=z_e \cos(\omega_et)$ with qualitative representation of the initial fluid vertical thermal stratification. The tank wall has a thickness $\delta_w$ with inner and external surface averaged temperatures $T_{w,i}$ and $T_{w,e}$, respectively
• Figure 2: Dimensionless natural frequencies $\Omega_{ij}^2$ of a flat-ended horizontal cylinder of aspect ratio $L/R=5$ against fill height.
• Figure 3: Parametric‐instability regions for a harmonically excited horizontal cylindrical tank, shown in the non‐dimensional plane of acceleration $\hat{a}_v=\textrm{Fr}^2\frac{R}{z_e}=\frac{z_e\omega^2_e}{g}$ versus excitation frequency ratio $\omega_e/\omega_{1,0}$. Filled areas mark unstable solutions of Mathieu’s equation for three sloshing modes obtained from POD decomposition: $\omega_{(1,0)}$ (blue, \\\\\\ hatching), $\omega_{(2,0)}$ (orange, dot hatching), and $\omega_{(0,1)}$ (green, /// hatching). Experimental testing conditions are identified by blue dots and further detailed in Table \ref{['tab:ini_cond']}. Panels: \ref{['fig:stab_bound_theo_50_percent']} and \ref{['fig:stab_bound_theo_70_percent']} theoretical frequencies based on geometry with flat ends; \ref{['fig:stab_bound_exp_50_percent']} and \ref{['fig:stab_bound_exp_70_percent']} experimentally measured frequencies.
• Figure 4: Non-isothermal experimental set-up composed of the Pressuring tank (1), the sloshing cell (2), filling line (3), and pressuring line (4).
• Figure 5: Sloshing cell schematic. (a) Instrumentation layout: (1) relief valve; (2) flexible surface heaters; (3) vapor diffuser; (4) Type-T thermocouple T002; (5) ullage pressure transducer; (6) triaxial accelerometer; (7) differential-pressure transducer (fill level); (8) Type-K thermocouples T003--T012 (center probe and outer wall); (9) triaxial load cells. (b) Longitudinal mid-plane section showing the temperature probe and the vertical distribution of thermocouples T003--T012; elevations are listed in \ref{['tab:sensor-loc']}.