The high-speed projectile moving near the sea level will significantly suffer from the effects of waves. The water entry and exit of a high-speed projectile crossing a wave are investigated by detached-eddy simulation. Three simulations with different altitudes through the wave are conducted to analyze the altitude's influence on the cavity dynamics. To validate the numerical model, a water-entry experiment is carried out in a wave tank for comparison. The projectile crossing the wave forms a cavity channel from water entry to exit. Because the water below the cavity is more difficult to displace than the atmosphere with the water surface under the cavitation effects, the downward expansion of vapor is blocked, and the wave surface is lifted. Consequently, the cavity above the projectile expands more strongly until breaking through the water surface, while the cavity below the projectile keeps closed, and the projectile is wetted. Thus, a nose-up pitching moment is generated at water entry, while the drag force is gradually enhanced during the water exit, and a lift force acts toward the atmosphere. As the altitude increases, the upper cavity becomes more open, but the lower cavity shrinks, leading to the augmentation of the lift force.

Tail slapping is considered to be a prominent mode for facilitating the movement of supercavitating projectiles underwater. Stability mechanism of the tail slapping and stability criterion of projectiles was numerically investigated in this paper. A numerical method was conducted to calculate the free flight of projectiles by combining the finite volume method, the mixture multiphase model, and a dynamic meshing scheme. The accuracy and applicability of the numerical calculation method are verified by experiments. Three typical stability modes of tail slapping motion, namely, stable, conditionally stable, and unstable, were identified through the free flight numerical simulations of projectiles with varying length-to-diameter ratios under different initial angular velocities. The stability criterion of projectiles was proposed, indicating that the tail slapping stability can be determined by analyzing the curve of the moment variation with the angle of attack at any velocity above 200 m/s. Furthermore, it was found that the stable projectiles possess inherent motion states that are exclusively determined by their structural features and are unaffected by the initial motion conditions.

In this paper, the modes of vortex shedding in the wake of a stationary sphere with the Lorentz force, which can be generated by the actuators in weakly conductive fluids and is parallel to the sphere surface, are numerically investigated at Re = 300. The relations among the wake structures, the vorticity distribution, and the motions of the rear stagnation point and the separation point are discussed before and after the application of Lorentz force. From this, the mechanism of mode transformations in the sphere wake is revealed. The results indicate that the fluid near the sphere surface is accelerated with the application of Lorentz force. The rear stagnation point and the separation point move rearward and become steady. Therefore, the vorticity on the rear surface of the sphere gradually decays and becomes steady, which leads to the periodic shedding mode of hairpin vortex replaced by the steady double-thread wake structure. Moreover, the wake structure varies with the interaction parameter N of the Lorentz force. When the Lorentz force is relatively small (N = 0.04), the vibration amplitude of hairpin vortex is weakened, and the vortex heads disappear with vortex legs and necks left. The wake is still periodic due to the hairpin vortex shedding. As N increases to 0.08, the hairpin vortex is suppressed completely, while the double-thread wake appears. The wake is steady due to the suppression of the hairpin vortex shedding. As N further increases to 0.20, a spanwise vortex ring is formed around the double-thread wake.

A direct numerical simulation (DNS) is performed to investigate the control effect and mechanism of turbulent channel flow with the distribution of spanwise Lorentz force. A sinusoidal distribution of constant spanwise Lorentz force is selected, of which the control effects, such as flow characters, mean Reynolds stress, and drag reductions, at different parameters of amplitude A and wave number k _x are discussed. The results indicate that the control effects vary with the parameter A and k _x . With the increase of A, the drag reduction rate D _r first increases and then decreases rapidly at low k _x , and slowly at high k _x . The low drag reduction (or even drag increase) is due to a weak suppression or even the enhancements of the random velocity fluctuation and mean Reynolds stress. The efficient drag reduction is due to the quasi-streamwise vortex structure induced by Lorentz force, which contributes to suppressing the random velocity fluctuation and mean Reynolds stress, and the negative vorticity improves the distribution of streamwise velocity. Therefore, the optimal control effect with a drag reduction of up to 58% can be obtained.

In this paper, electromagnetic force on two degrees of freedom vortex-induced vibration (VIV) of an elastically mounted sphere for vibration suppression is numerically achieved at Re = 300. The relations between the wake structures, velocity and pressure distributions, force coefficients, and sphere displacement are investigated by varying the interaction parameter (N) of electromagnetic force. With the increase in N, the momentum of the fluid near the sphere is enhanced to control the flow separation. Therefore, both the rotation radii of the rear stagnation point (RSP) and the separation line (SL) decrease, causing the spiral vortices to become thinner. This leads to a reduction in the fluctuation amplitude of the lift coefficient and mitigates the VIV. As N exceeds 0.5, the periodic spiral vortices transform into a steady double-thread wake due to the stopping of RSP and SL rotation. Therefore, a constant lift is generated in the z-direction due to the asymmetric flow field in the x–z plane, which is accompanied by the VIV fully suppressed. Moreover, the effect of electromagnetic locations (θm) on vibration suppression is examined. With the increase of θm, the vibration suppression efficiency increases first and then decreases, which achieves the maximum vibration suppression efficiency at θm = 125°. The reason is that the electromagnetic force covers the location of the half-circle-shaped SL, which has a significant effect on the control of the flow separation.

In this paper, the electro—magnetic control of a cylinder wake in shear flow is investigated numerically. The effects of the shear rate and Lorentz force on the cylinder wake, the distribution of hydrodynamic force, and the drag/lift phase diagram are discussed in detail. It is revealed that Lorentz force can be classified into the field Lorentz force and the wall Lorentz force and they affect the drag and lift forces independently. The drag/lift phase diagram with a shape of “8 consists of two closed curves, which correspond to the halves of the shedding cycle dominated by the upper and lower vortices respectively. The free stream shear (K > 0) induces the diagram to move downward and leftward, so that the average lift force directs toward the downside. With the upper Lorentz force, the diagram moves downwards and to the right by the field Lorentz force, thus resulting in the drag increase and the lift reduction, whereas it moves upward and to the left by the wall Lorentz force, leading to the drag reduction and the lift increase. Finally the diagram is dominated by the wall Lorentz force, thus moving upward and leftward. Therefore the upper Lorentz force, which enhances the lift force, can be used to overcome the lift loss due to the free stream shear, which is also obtained in the experiment.