# Cavitator Design for Straight-Running Supercavitating Torpedoes
## 2 Cavitator Design Procedure  
The cavitator design procedure was established based on operational concepts and design requirements. A straight-running supercavitating torpedo such as \"Shkval\" is known to operate in such a way that it rapidly accelerates up to the supercavitating speed immediately after being discharged from the launching tube and moves straight at a constant speed and depth corresponding to operational conditions. The torpedo was designed to fit the launching tube, and the design was implemented according to the operational conditions. The first step of cavitator design is to determine the design cavitation number defined as follows:  
\[\sigma\equiv(p_{\infty}-p_{c})/\frac{1}{2}\rho V^{2} \tag{1}\]  
where \(\rho\) represents the fluid density, \(V\) is the operational speed, and \(p_{\infty}\) and \(p_{c}\) are the ambient pressure at the operational depth and cavity pressure, respectively. If there is no ventilation system in the torpedo, the design cavitation number is determined only by the given operational speed and depth. However, when a ventilation system is used for supercavity generation, the designer may have multiple choices for the design cavitation number by adjusting the amount of ventilated gas. Generally, the cavitation number decreases with the increase in the ventilation flow rate, and a larger supercavity can be generated for a given cavitator. From a design perspective, it is advantageous to minimize the design cavitation number, allowing for a smaller cavitator to produce lower drag while maintaining the supercavity size. However, the minimum cavitation number achieved by ventilation is limited by the excessive ventilation rate, causing instability of the ventilated cavity [12]. This so-called \"cavity pulsation\" phenomenon, as shown in Figure 1, must be avoided because the motion stability of the torpedo might deteriorate considerably owing to this phenomenon, and the torpedo might become out of control under such a circumstance. Using a stability parameter \(\beta\) (\(\equiv\sigma_{v}/\sigma\), where \(\sigma_{v}\equiv(p_{\infty}-p_{v})/\frac{1}{2}\rho V^{2}\) represents the natural cavitation number and \(p_{v}\) the vapor pressure), [PERSON] [13] developed a theory on the stability of ventilated supercavities and proposed a criterion for its dynamic stability, in which the supercavities are stable in the range of \(1\leq\beta<\beta_{\text{cr}}=2.645\) and unstable at \(\beta\geq\beta_{\text{cr}}\)[12]. The range of the design cavitation number is accordingly determined as follows:  
\[\sigma_{v}/\beta_{\text{cr}}<\sigma\leq\sigma_{v} \tag{2}\]  
[PERSON] and [PERSON] [14] implemented [PERSON]'s model of cavity dynamics and predicted the critical value \(\beta_{\text{cr}}\) (\(\approx\)2.703) close to [PERSON]'s value for the cavitator alone. They also investigated the stability of ventilated supercavities when the body of a supercavitating vehicle existed and found that the presence of the body within the supercavity can result in a lower critical value of the stability parameter than that of the  
Figure 1: Cavity pulsation phenomenon. cavitator alone. Therefore, in practical design, it is desirable to adopt a design cavitation number sufficiently larger than its minimum value. Once the design cavitation number is determined, the next step is to identify an optimum cavitator that fulfills the design requirements mentioned in Section 1. First, the cavitator type should be determined. Disk- and cone-type cavitators are the most suitable for supercavitating vehicles. The designer must choose the better one of these two considering the operational concept of a supercavitating torpedo. For example, in the case of a long-range straight-running torpedo with a water-breathing ramjet propulsion system, the disk-type cavitator is more suitable because it facilitates the installation of a water intake system and has better static stability [15].