In this study, we aim to examine the influence of water entry velocity of a single and two tandem projectile(s) on the supercavitation flow and projectile loading under wave conditions using numerical simulation. The volume of fluid model, renormalization group (RNG) κ-ε turbulence model, and Schnerr–Sauer cavitation model are adopted to simulate the multiphase, turbulent, and cavitation flow, respectively. The projectile movement is considered using overlapping grids and a six-degree-of-freedom model. The results show that as the projectile velocity increases, both the dimensionless maximum radius and length of the cavity, as well as the yaw angle, also increase with the rising water entry velocity. For the two tandem projectiles, the cavity pattern on the second projectile varies as the projectile velocity changes. With a lower projectile velocity, the second projectile cannot directly access the front cavity, and there may be situations wherein the part of the second projectile is not enveloped by cavity. As the projectile velocity increases, the second one can directly enter the cavity of the first projectile without forming a separate cavity around itself. In all of the examined cases, the peak pressure on the first projectile is approximately an order of magnitude higher than that on the second one. Furthermore, with increasing projectile velocity, the pressure peak ratio between the first and second projectiles increases.

Water entry is an interesting subject but many of its physical aspects have remained unknown so far. Using computational fluid dynamics (CFD), this study investigates the dynamic stability of cylindrical projectiles in the oblique water entry at shallow angles in the presence of three phases of air, water and water vapor. The three-dimensional and transient numerical model has been verified using the former experimental results in the literature. In this study, the effects of projectile length-to-diameter ratio (L/D) and water entry angle on the projectile stability within cavity were investigated. Accordingly, the water entry of six projectiles was simulated with aspect ratios of 2 to 6 at three water entry angles of 6, 9 and 12 degrees with respect to the free surface with an initial velocity of 280 m/s. At each of the aforementioned angles, the critical L/D, where the projectile avoids tumbling inside the cavity at a larger value, was determined. This study showed that in the oblique water entry of a cylindrical projectile at the angles of 6, 9 and 12 degrees, the projectile tumbled within the cavity with a L/D of less than 5, 4 and 3. 5, respectively. The simulation results showed that increasing the L/D as well as the water entry angle relative to the free surface resulted in the improvement of the cylindrical projectile motion stability, which is in agreement with the experimental results. By analyzing the details of each simulation, it was found that the projectile stability within the cavity is correlated with the magnitude of the angular momentum which is generated in the projectile by the impact of the cavitator on the free surface and it was shown that the projectile with a specific L/D can withstand destabilizing angular momentum to a certain extent. Considering the fact that the atmospheric ballistics of gyroscopically stabilized projectiles lead to a limit for increasing L/D, this study showed that, for aluminum cylindrical projectiles in which air stability is achieved via the gyroscopic effect, the minimum water entry angle is 6° to attain the gyroscopic stability of the projectile in the air and stable motion inside the cavity. This fact is very important from a practical point of view.

The formation of supercavitation after a high-speed projectile enters water has a decisive impact on the underwater ballistic and penetration of the projectile. In this study, Ansysfluent19. 0 simulation software is used to study water entry of a chosen projectile at velocities of 300, 400, 500, and 600 m/s. The underwater cavitation characteristics, trajectories, and flow-field characteristics are analyzed for a 5. 8-mm caliber conical flat head projectile, as well as for t wo other projectiles of the same caliber and different head shapes — conical cone head and elliptical flat head — entering water vertically at the same velocities. The attenuation rate of water entry velocity increases with the increase of velocity. Within first 3ms, the velocity attenuation rate of the conical flat-head projectile with a water entry velocity of 600m / s is 55. 6 %, while the velocity attenuation rate of the projectile with a water entry velocity of 300m / s is only 16. 3 % within 3ms. Among the head shapes considered, the conical flat head projectile is the most stable for vertical water entry. The stability of an elliptical flat head projectile is worse, and the trajectory stability of a conical cone head projectile is still worse

Metaheuristic optimization algorithms are a relatively new class of optimization algorithms that are widely used for difficult optimization problems in which classic methods cannot be applied and are considered as known and very broad methods for crucial optimization problems. In this study, a new metaheuristic optimization algorithm is presented, the main idea of which is inspired by models in kinematics. This algorithm obtains better results compared to other optimization algorithms in this field and is able to explore new paths in its search for desirable points. Hence, after introducing the projectiles optimization (PRO) algorithm, in the first experiment, it is evaluated by the determined test functions of the IEEE congress on evolutionary computation (CEC) and compared with the known and powerful algorithms of this field. In the second try out, the performance of the PRO algorithm is measured in two practical applications, one for the training of the multi-layer perceptron (MLP) neural networks and the other for pattern recognition by Gaussian mixture modeling (GMM). The results of these comparisons are presented in various tables and figures. Based on the presented results, the accuracy and performance of the PRO algorithm are much higher than other existing methods.