Investigation of ventilation demand variation in unsteady supercavitation
Introduction
Ventilated supercavitation refers to the formation of an artificial gas pocket in water flow created by air injection behind a flow separation device, i.e., cavitator in such a way that the so-formed cavity is large enough to surround an immersed vehicle. This phenomenon has been broadly investigated for its potential applications in the drag reduction for high-speed operation of underwater vehicles [1]. Due to the complex multi-phase interactions involved in cavitating flows, which are sensitive to flow conditions, a significant amount of research has been conducted on characterizing the behaviors of ventilated supercavities [2] as well as on mechanical control strategies [3]. However, despite numerous research reported on the characterization of general behaviors of ventilated supercavities [4], an area that has not hitherto received significant attention, is the ventilation strategy, i.e. optimally controlling the ventilation rate for the supercavity to be formed and sustained under various flow conditions.
Compared to several investigations that report general cavity behaviors, such as geometry, shape, and cavity closure, only a handful of studies focus on the ventilation requirements associated with the supercavity formation and its sustenance upon formation. For instance, Karn et al. [5], explored the ventilation hysteresis phenomenon in great detail and established that the ventilation demands to form and to sustain a supercavity may be significantly different, the latter being much smaller than the former. In a followup work, Karn et al. [6] investigated the ventilation demands of the supercavity under various flow settings and provided a detailed explanation of the cavity formation and collapse processes, relating each with bubble coalescence proficiency and pressure balance near the closure. Their research has been conducted for a backward-facing model (BFM) with only a disk type cavitator. However, there is an inherent limitation with this type of cavitator configuration – it neglects the effects of the cavitator shape or the presence of the mounting strut, both of which have been shown to noticeably affect the cavity behaviors [7], [8], [9], especially the supercavity formation process [10]. Recently, Shao et al. [11] studied the ventilation demands for a forward-facing model (FFM) with a variety of cavitator geometries (cone, disk, and non-axisymmetric) to consider both the cavitator shape and the mounting strut effects. They have found out that the cone type cavitator required the least ventilation flow to form and sustain a cavity. They have also observed that the interaction between the mounting strut and the air–water interface leads to a noticeable change in collapse ventilation demand compared to that of the BFM case. Their detailed analysis on the momentum balance between the air injection and the estimated re-entrant jet at the closure further supported that the re-entrant jet governs the cavity collapse process. However, although it has been reported that the ventilation demand depends crucially on the flow unsteadiness [6], which may significantly alter the operation of the supercavitating object [3], [12], the investigations on ventilation demand and ventilation hysteresis to date have been limited to the steady flow conditions only. Therefore, to connect the lab-scale experiments with the practical situations of underwater vehicles encountering surface waves, experimental investigations exploring the role of different cavitator shapes and mounting strut effects in unsteady flows is needed, not only to understand general cavity behaviors, but to investigate the underlying physics with an express emphasis on the ventilation demand and ventilation hysteresis.
Though mostly limited to the general cavity behaviors or the ventilation demands of the BFM supercavity, a few recent studies investigated ventilated supercavitation under unsteady flows by using a gust generator that consists of flapping hydrofoils [6], [12], [13], [14]. Such a setup was deployed to simulate unsteady incoming flows by controlling either the angle of attack (AoA) or the flapping frequency () of the hydrofoils. In particular, it has been reported that for the unsteady flows the cavity dimensions and cavitation number () periodically change [12] and closure variation is observed between twin-vortex and re-entrant jet [13]. Shao et al. [14] further classified FFM supercavity into five distinct states (namely stable, wavy, pulsating 1, pulsating 2, and collapsing states), characterizing each state based on the simultaneous pressure measurement and high-speed imaging. They observed transitions across these states with a change in either AoA or and further proposed a stability criterion for these state transitions. Karn et al. [6] studied the formation and collapse ventilation demand trends with respect to the change in AoA and for BFM and observed that all these demands increase with higher flow unsteadiness. They noted that such flows impose a vertical perturbation to the individual bubble movements that lead to the increased formation ventilation demand. They also commented on the internal pressure fluctuation that leads to higher collapse ventilation demand. However, their explanations of the observed trends heavily relied on the implications of flow perturbation and pressure fluctuation but lacked visual evidence.
Therefore, as a follow-up study of Shao et al. [11], we present a systematic examination of unsteady flow conditions, generated by the gust generator, on the formation and sustenance ventilation demand of FFM model (including the mounting strut effect) with a cone type cavitator which has shown to require the least ventilation demand to form and sustain the supercavity. The rest of the sections are as follows: Section 2 provides detailed explanation on the experimental methods. The results of our study are presented in Section 3. Specifically, 3.1 Ventilation demands in low, 3.2 Ventilation demands in high demonstrates the results of cone cavitator with different flow regimes. Section 3.3 provides a quantitative estimation of change in the collapse ventilation demand due to the flow unsteadiness. Section 4 provides a summary of the current study.
Section snippets
Experimental setup and methodology
The experiments are conducted in the high-speed cavitation water tunnel at Saint Anthony Falls Laboratory (SAFL), University of Minnesota. As shown in Fig. 1, the flow facility consists of a closed recirculating tunnel with a large volume dome-shaped settling chamber located upstream of the test section, designed for fast bubble removal during the ventilation experiments. The dimension of the test section is (length, height, and width), and the bottom and the two side windows
Ventilation demands in low Fr regime
As shown in Fig. 3, at low Fr regime are plotted from steady to various unsteady incoming flow conditions. It should be noted that the uncertainty in the measurement at each condition, at a maximum of , is less than of the mean value presented in the figure. The error bars on the data points are extremely small to be noticeable. In this regime, trends (dashed lines) show a slight increase with but are minimally influenced by AoA. plot shows a similar increasing
Summary and conclusion
In this study, we have investigated the ventilation characteristics of a supercavity generated by a forward-facing cone-type cavitator under unsteady flows. Flow unsteadiness is adjusted by changing either the angle of attack (AoA) or the frequency () of the flapping foils located upstream of the test section. At a lower free stream velocity, the formation ventilation demand () and collapse ventilation demand () both increase with flow unsteadiness except for the collapse demand at the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work is supported by the Office of Naval Research (Program Manager, Dr. Thomas Fu) under Grant No. N 000141612755.
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