Spatial Kinetics Model of Supercavitating Vehicles Reflecting Conic‐Like Oscillation

Abstract

A spatial kinetics model for supercavitating vehicles including the coupled motion of pitch, yaw, and rolling was presented. Mathematical simulations were performed to investigate dynamic performance of supercavitating vehicles. An intrinsic conic-like oscillation in the motion of supercavitating vehicles was discovered. A lakebed experiment was carried out to validate the oscillation. Good agreement is achieved between simulation and experiment in terms of the amplitude and frequency of attitude angles. The steady phase difference between the motions in different planes is also accurately captured which is about π/2. The conic-like oscillation is attributed to the occurrence of the tail-slap motion in the vertical and horizontal planes and the steady phase difference.

Design Methodology of Conical Section Shape for Supercavitating Vehicles considering Auto-Oscillation Characteristics

“…ey pointed out that the SV system has complex phenomena, such as coexistence of stable equilibrium point and limit cycle, coexistence of limit cycle and chaotic attractor, and coexistence of multiple limit cycles. e authors of the present work also discovered the intrinsic conic-like oscillation in the motion of SVs [21] and pointed out that conic-like oscillation is attributed to the occurrence of the tail-slap motion in the vertical and horizontal planes and the steady phase difference. e basic configuration of the vehicle itself is still the major question concerning maneuvering SVs [15].…”

“…According to the literature [21,37], the kinetic equations based on the assumptions above are presented as follows.…”

“…where r zwA is the amplitude of r zw , and r zwA � ������ r 2 y + r 2 z , describing the deviation between the cavity and the vehicle at the stern plane. Here, r y and r z are the components of the vector from the stern plane center to cavity centerline, as shown in Figure 2, where O b x b y b z b is the body-fixed coordinate system, the expressions of which are given in the Appendix [21,37].…”

Predictive Control of a Supercavitating Vehicle Based on Time-Delay Characteristics

“…In [9], the author created an integrated dynamic model of a supercavitating vehicle, and constructed a 6-DOF equation of motion. In [10], the author proposed a spatial kinetics model for supercavitating vehicles that considered the coupled motions of pitch, yaw, and roll.…”

“…To expand the initial feasible region of the system, free control variables can be introduced into the infinite time domain. Knowing the state quantities at time k are x(k|k) = x(k) and x(k − d|k) = x(k − d) , the state space prediction model of the supercavitation system can be derived according to (10) as follows:…”