A study on the effects of fluctuations of the supercavity parameters
Introduction
A supercavitating, under-water vehicle attains high forward speeds due to the great reduction in the drag achieved by enclosing most of the vehicle’s length within a ventilated supercavity [1], [2], [3]. A supercavity is a cavitation bubble that is larger than the body that causes it, and, generally, it is formed due to a reduction in the hydrodynamic pressure. The cavitation number σ is a dimensionless parameter that generally is used to characterize cavitating flows and to quantify the capability of the flow to produce cavitation. For an object moving in a fluid, this parameter is defined as:where P is the hydrostatic pressure, Pv is the vapor pressure, V is the object’s velocity, and ρ is the mass density of the fluid [4].
Although supercavitation may be a helpful phenomenon, it represents significant challenges for modeling, controlling, and maneuvering supercavitating vehicles.
Studies related to supercavitation have increased significantly over the past decade. The fact that supercavitation can be used to reduce drag on an underwater vehicle, has been known for some time, however, in recent years, several applications have emerged and there is now some demand for a refined design.
Supercavities can be formed and maintained either naturally or artificially. A natural supercavity can be produced when the underwater body is moving at such a high speed that the water vaporizes near the leading edge of the body; however, if such a high speed cannot be attained, an artificial supercavity could be created. Such a supercavity results from providing the cavity with gas at such a pressure that the pressure difference in Eq. (1) becomes small enough for σ to be sufficiently small to form supercavitation. Because of the limitations on the water’s velocity in the experimental water tunnel, using a ventilated cavity in the laboratory is a reasonable alternative.
Many researchers have worked in the area of “Generation, Maintenance, and Characterization of Cavity” [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. Wu and Chahine [18] characterized the content of the cavity behind a high-speed supercavitating body. They showed that the cavity-water interface was affected significantly by the air ventilation. Varyukhin [19] studied the deformation boundaries of an axisymmetric cavity by gas jets. In his work, he developed a method for calculating the shape of a ventilated cavity modeled by a wall with no penetration through the wall. Zhang et al. [20] conducted a series of projectile and water-tunnel experiments to investigate the characteristics of the shapes of natural and ventilated supercavities. They determined that the shape and dimensions of both the natural supercavities and ventilated ones were similar when the cavitation numbers were small and equal to each other. Shafaghat et al. [21] presented a formulation for the direct boundary element method for finding numerical solutions to axisymmetric supercavitating flows involving finite-length cavities. Nouri et al. [22] proposed a simple model for two-dimensional (2D) cavitating flows with artificial viscosity, the governing equations of which were the unsteady incompressible, viscous Navier–Stokes equations.
Supercavity is essentially a dynamic and unsteady phenomenon, and its characteristics, such as length L, diameter D, cavitation number σ, and cavity pressure P are all time dependent. The supercavity parameters vary periodically with random oscillations superimposed on this periodic motion. Therefore pressure of the cavity, and subsequently, the cavitation number will have both periodic and random components. Therefore the supercavitating vehicles are mostly accompanied by impact, oscillation, and pulsation of lift and drag forces which are applied on the cavitator, fins, and body of it. Thus, knowing the fluctuation patterns of the supercavity’s parameters would be useful and even essential for appropriately studying the dynamic of such vehicles. Some of the reasons for the dynamic nature of a supercavity are the re-entering jet, the shedding phenomenon and the generating and dissipating of vortices, all of which can have both periodic and random components.
Guoyu et al. [23] investigated the dynamics of attached turbulent cavitating flows. Jiazhong et al. [24] discussed the unsteady characteristics of cavitating flows. They showed that a low-frequency, pulsating phenomenon exists that is caused by the abrupt breakup of the cavity. Ito’s study [25] showed that the oscillations within the cavity were correlated with the shedding of the bubble cloud, which was the result of the breakup of the cavity. Sakagam [26] studied the influence of the segregated cavity on the pulsing of lift and drag forces. Sato [27] discussed the relationship between the characteristics of oscillation and the type of cavitation (e.g., sheet and cloud cavitation) by measuring the fluctuating pressure. Arndt et al. [28] investigated the unsteady partial cavitation and the partially ventilated one and supercavitating flows. In their research, they investigated the sensitivity of the dynamic model of a vehicle to changes in the fin-immersion ratio, the location of the center of gravity, speed, cavitator force, and cavitation number. They discovered that dynamics of the vehicle were mostly sensitive to variations in the fin-immersion ratio and the speed; they were relatively sensitive to changes in the cavitation number, cavitator, and variations in the force of the fin.
In this work, the dynamic characteristics of the supercavity and induced vibration due to the oscillations of its parameters were studied experimentally. An experimental setup with varying natural frequencies was designed, and a series of experiments were performed to determine the dynamics behavior of the ventilated cavity and its induced vibrations.
Section snippets
Theory of the problem
The supercavity is a dynamic phenomenon because its parameters are time dependent. Some of these parameters are length, diameter, pressure, and cavitation number. The time-dependent feature of the supercavity is due to the shedding of the bubble cloud (see Fig. 1a), re-entry of the jet (see Fig. 1b), and the periodic generation and dissipation of the vortex. Fig. 1a is part of this study and related to the natural cavity without ventilation. Fig. 1b is not part of this study however it is part
Water tunnel and its appurtenance
A ventilated supercavitation experiment was conducted in a ventilated water tunnel with a vibrational setup attached to it. All experiments were done at applied hydrodynamics laboratory of Iran University of Science and Technology. Fig. 2 shows the schematic presentation of water tunnel and its equipments. The test part of the water tunnel is 4 m long, with four separate window sections which the length of each is 1 m and its cross section area is 0.2 × 0.1 m2. In order to make the inside part
Results and discussion
As stated before, the variations of the supercavity’s parameters involved both harmonic and random terms. These parameters’ variations induced some excitations, both harmonic and random, to the adjacent structure. The random term excited the natural frequencies of the structure, and the harmonic term excited the system by its frequency. Both kinds of frequencies appeared in the response of the structure. Therefore, when the response of the plate is considered, three kinds of frequencies may
Applicability of the results
The results of these measurements can be extended to the range that the dimensional analysis experiments are valid. Dynamic behaviour of supercavity is just dependent on the cavitation condition. As it is known the cavitation condition just depends on cavitation and Froude numbers. Shedding frequency and random fluctuations are from supercavity dynamics and they can be a function of Froude number beside cavitation number; however when Froude number is very higher than one, the cavity and its
Conclusions
Supercavity is dynamic phenomena, and its parameters depend on time and have both periodic and random components. These fluctuations of the supercavity excite the adjacent structures and make them oscillate. An experimental setup was designed to estimate the excitations that are induced by a supercavity. This setup had the advantage of having its own variable natural frequencies. This means that the setup can be used to measure the responses of different structural systems to a statistically
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