Hydrodynamic Moments Research Articles

An AUV stability estimation method by considering rudder design parameters

Stability is a critical characteristic of Autonomous Underwater Vehicles (AUVs). During the initial design stage, selecting an appropriate rudder design is essential to ensure the overall stability performance of the AUV. This study introduces a method for predicting the stability of AUVs equipped with different rudder configurations. By parametric modeling based on the geometric characteristics of X-rudders, the rudder area, aspect ratio, and position parameters, which significantly impact AUV stability, were selected as the primary research objects. Formulas were derived to estimate the associated hydrodynamic forces and moments critical for assessing the stability index. Validation of this approach is conducted through comparison with Computational Fluid Dynamics (CFD) simulations. The results show that this method effectively predicts the hydrodynamic behavior of AUVs, facilitating stability assessments across various rudder designs.

The Hydrodynamic Similarity between Different Power Levels and a Dynamic Analysis of Ocean Current Energy Converter–Platform Systems with a Novel Pulley–Traction Rope Design for Irregular Typhoon Waves and Currents

In the future, the power of a commercial ocean current energy convertor will be able to reach the MW class, and its corresponding mooring rope tension will be very good. However, the power of convertors currently being researched is still at the KW class, which can bear less rope tension. The main mooring rope usually has a single cable and a single foundation. To investigate the dynamic response and rope tension of an MW-class ocean current generator mooring system, here, a similarity rule is proposed for (1) coefficients without any fluid–structure interaction (FSI) using the Buckingham theorem and (2) ones with FSI. The overall hydrodynamic drag and moment including the hydrodynamic coefficients in these two situations are represented in a Taylor series. Assuming similarity between the commercial MW-class and KW-class ocean current convertors, all hydrodynamic parameters of the MW-class system are estimated based on the known KW-class parameters and based on the similarity formula. In order to overcome the extreme tension of the MW-class system and to provide good stability, in this paper, we propose a pulley–rope design to replace the traditional single-traction-rope design. The static and dynamic mathematical models of this mooring system subjected to the impact of typhoon waves and currents are proposed, and analytical solutions are obtained. We find that the pulley–rope design can significantly reduce the dynamic rope tensions of the mooring system. The effect of the length ratio of the main traction rope, rope A, to the seabed depth on the dynamic tension of stabilizing converter rope D is significant. The length ratio is within a safe range, and the maximum rope dynamic tension is less than the fracture strength. In addition, if the rope length ratio is over the critical value, the larger the ratio, the higher the safety factor of the rope. In summary, the pulley–rope design can be safely used in an MW-level ocean current generator system.

Evaluation of hydrodynamic coefficients and sensitivity analysis of a work-class remotely operated vehicle using planar motion mechanism tests

This paper presents a comprehensive analysis of the hydrodynamic forces and moments relating to the drag on an open-frame work-class remotely operated vehicle (ROV) AUTO-1000. We describe the results of planar motion mechanism experiments conducted with the aim of modeling and simplifying the mathematical maneuverability model for such an ROV. The scale of the model is 1:4. Various experiments are performed in a nonlinear wave channel. The flow speeds in the static drag tests range from ±0.2–±0.5 m/s and the angle in the drift tests is less than 10°. The motion frequencies of the dynamic tests range from 0.25 to 3.14 rad/s. The amplitude of the translation motions is 0.03 m and the largest angular amplitude in the rolling tests is 5°. The viscous and inertial hydrodynamic coefficients are estimated. Normalized sensitivity coefficients are used to investigate the sensitivity of both the viscous and inertial hydrodynamic coefficients considering the multi-degree-of-freedom motion and velocity effect. The drag, drift, and stationary random motions are used to examine the sensitivity. A comparison of the motion simulation results given by simplified and complete models shows that a threshold normalized sensitivity coefficient value of 0.01 is suitable for filtering the ROV coefficients.

Exact hydrodynamic manifolds for the linear Boltzmann BGK equation I: spectral theory

We perform a complete spectral analysis of the linear three-dimensional Boltzmann BGK operator resulting in an explicit transcendental equation for the eigenvalues. Using the theory of finite-rank perturbations, we confirm the existence of a critical wave number kcrit\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_{\ extrm{crit}}$$\\end{document} which limits the number of hydrodynamic modes in the frequency space. This implies that there are only finitely many isolated eigenvalues above the essential spectrum at each wave number, thus showing the existence of a finite-dimensional, well-separated linear hydrodynamic manifold as a combination of invariant eigenspaces. The obtained results can serve as a benchmark for validating approximate theories of hydrodynamic closures and moment methods and provides the basis for the spectral closure operator.

VLF oscillation mechanism analysis of underwater vehicle based on overlapping grid

ABSTRACT The present study aims to investigate the VLF oscillation mechanism of underwater vehicles motion by conducting numerical simulation on the AFF-1. The straight-line simulations of AFF-1 were performed using RANS equations with a Reynolds stress turbulence model at different speeds, and an initial flow field with converged resistance results was obtained. Meanwhile, the accuracy of the numerical model and input parameters were validated by the resistance results. The sinuous motion of AFF-1 was simulated based on dynamic fluid body interaction (DFBI) and overlapping grid. The results indicated that the inherent instability of the AFF-1 significantly impacts its motion dynamics. Specifically, when AFF-1was in straight-line motion at a constant forward velocity, it was subjected to the influence of pressure component of hydrodynamic force and moment, resulting in slow trajectory divergence motion of AFF-1. In scenarios where manual manipulation is employed, this instability leads to the emergence of VLF oscillations.

Hydrodynamic mechanism for dynamical structure formation of a system of rotating particles

Based on the hydrodynamic mechanism, which takes into account the interaction of all particles, a numerical simulation of the formation of a dynamical structure in a viscous fluid was carried out. This structure is a result of the collective dynamics of rotating particles in the fluid. It is supposed that the particles have a magnetic moment and are driven into rotation by an external variable uniform magnetic field. The results of numerical modeling of collective dynamics are presented for three initial structures that can be formed by interacting dipole particles in the absence of an external magnetic field. Such equilibrium structures are a straight chain, a closed chain, and a periodic structure in the form of a flat system of particle chains. The rotation of particles sets the surrounding fluid in motion, whose flow creates hydrodynamic forces and moments that move the particles. The collective dynamics of a system of rotating particles leads to the formation of a new dynamical structure from the original one, and this new structure has its own characteristic features for each case considered. A qualitative comparison of the results of the dynamics for a particles’ system set in motion due to the action of an external moment or an external force is carried out. The proposed hydrodynamic mechanism for the formation of a dynamical structure as a result of the collective dynamics of a rotating particles’ system can be used to control structure formation in a liquid-particle system.

Simulation and Controller Design for a Fish Robot with Control Fins.

In this paper, a nonlinear simulation block for a fish robot was designed using MATLAB Simulink. The simulation block incorporated added masses, hydrodynamic damping forces, restoring forces, and forces and moments due to dorsal fins, pectoral fins, and caudal fins into six-degree-of-freedom equations of motion. To obtain a linearized model, we used three different nominal surge velocities (i.e., 0.2 m/s, 0.4 m/s, and 0.6 m/s). After obtaining output responses by applying pseudo-random binary signal inputs to a nonlinear model, an identification tool was used to obtain approximated linear models between inputs and outputs. Utilizing the obtained linearized models, two-degree-of-freedom proportional, integral, and derivative controllers were designed, and their characteristics were analyzed. For the 0.4 m/s nominal surge velocity models, the gain margins and phase margins of the surge, pitch, and yaw controllers were infinity and 69 degrees, 26.3 dB and 85 degrees, and infinity and 69 degrees, respectively. The bandwidths of surge, pitch, and yaw control loops were determined to be 2.3 rad/s, 0.17 rad/s, and 2.0 rad/s, respectively. Similar characteristics were observed when controllers designed for linear models were applied to the nonlinear model. When step inputs were applied to the nonlinear model, the maximum overshoot and steady-state errors were very small. It was also found that the nonlinear plant with three different nominal surge velocities could be controlled by a single controller designed for a linear model with a nominal surge velocity of 0.4 m/s. Therefore, controllers designed using linear approximation models are expected to work well with an actual nonlinear model.

Rans investigation on the hydrodynamic performance of a ship moving obliquely in shallow and narrow channel

ABSTRACT The ship traveling in restricted waterways often experiences larger hydrodynamic forces and moments, together with larger sinkage, trim and heel, compared with that in open water. The hydrodynamic performance of an oil tanker moving obliquely in a shallow and narrow channel is investigated by using a RANS (Reynolds-Averaged Navier-Stokes) method in this work. The effects of ship-bank distance, water depth, etc. on hydrodynamic performance are analysed. When the ship gets closer to the channel bank or the inclination of the channel bank becomes steeper, the blockage effects due to the channel become more considerable. The effects of shallow water and ship drift motion will augment bank effects. The captive model test for a ship moving obliquely in a shallow and narrow channel are numerically carried out in both Circulating Water Channel (CWC) and Towing Tank (TT). The bank effects showed by TT are more considerable than that by CWC.

Computational Fluid Dynamics Investigation of Hydrodynamic Forces and Moments Acting on Stern Rudder Plane Configurations of a Submarine

This study presents the predicted hydrodynamic characteristics of different rudder plane configurations on the stern of a full-scale submarine in deep water, which are obtained using the Reynolds-Averaged Navier–Stokes method in Ansys Fluent Solver. First, the results obtained for the X-rudder plane configuration are verified according to previous numerical and experimental results in order to assess the accuracy of the simulation procedure. The X-rudder plane, Y-rudder plane, and Cross-rudder plane configurations in deep water with deflection angles ranging from −21 degrees to +21 degrees are then simulated. Next, the hydrodynamic forces and moments of the Cross-plane, X-plane, and Y-plane rudder configurations obtained through simulation are analyzed using Taylor’s expansion to estimate the hydrodynamic coefficients. The obtained results demonstrate that the X-force of the X-plane rudder configuration is larger than the corresponding forces acting on the Cross-plane rudder and Y-plane rudder configurations. Meanwhile, the Y-force and Z-force of the X-plane rudder configuration are significantly greater than the corresponding forces of the left configurations. The same tendency can be seen in the moment of the X-plane rudder about the y- and z-axes. However, the roll moment induced by the Y-plane and Cross-plane rudder configurations is significantly larger than that under the X-plane rudder configuration.

Dynamic response of multi-unit floating offshore wind turbines to wave, current, and wind loads

Motion of a multi-unit wind-tracing floating offshore wind turbine (FOWT) to combined wave–current and wind is obtained in the frequency-domain. The linear diffraction wave theory with a Green function for small current speeds and the blade-element momentum method are used for the hydrodynamic and aerodynamic analysis, respectively. A finite-element method is coupled with the hydrodynamic and aerodynamic equations to obtain the elastic responses of the FOWT to the environmental loads. The wind-tracing FOWT consists of three 5 MW wind turbines installed at the corners of an equilateral triangular platform. The platform is connected to the seabed through a turret-bearing mooring system, allowing the structure to rotate and face the dominant wind direction; hence, the multi-unit FOWT is called the wind-tracing FOWT. In this study, rigid-body responses of the wind-tracing FOWT to waves and wind are compared with those to combined wave, current, and wind loads for several current speeds and various wave heading angles. For a chosen current speed and wave heading angle, hydro- and aeroelastic responses of the wind-tracing FOWT to combined waves, current, and wind are obtained and compared with those of the rigid structure. Discussion is provided on the effect of the wave–current interaction on the motion and elastic responses of the wind-tracing FOWT. The numerical results show that under the rated wind speed, the motion of the wind-tracing FOWT is mainly governed by the wave-induced hydrodynamic forces and moments and the presence of current results in larger elastic motion of the FOWT to the environmental loads.

Validation of 4DOF maneuvering coefficients optimization using hydrodynamic force and moment estimated from free-running model test results

The present study concerns validation of data-driven modeling for ship dynamics from free-running model test results, in terms of estimation of hydrodynamic force and moment, maneuvering coefficients, and maneuver simulation results. An estimation method for the hydrodynamic force and moment from the acceleration of a surface combatant model ship is suggested and compared with the conventional ship dynamics modeling. The hull dynamics modeling relates the motion and hydrodynamic force and moment is developed by optimizing maneuvering coefficients which leads to minimum loss function of hydrodynamic force and moment and maneuvering criteria. The maneuvering coefficients of the dynamics model is compared with a conventional system-based dynamics model. Lastly, the maneuvering simulation results are compared to the free-running model test results. The suggested model adequately predicts hydrodynamic force and moment in highly coupled sway and yaw motion.

Assessment of Numerical Captive Model Tests for Underwater Vehicles: The DARPA SUB-OFF Test Case

During the early design stage of an underwater vehicle, the correct assessment of its manoeuvrability is a crucial task. Conducting experimental tests still has high costs, especially when dealing with small vehicles characterized by low available budget. In the current investigation, virtual towing tank tests are simulated using the open-source OpenFOAM library in order to assess the reliability of CFD methods for the prediction of hydrodynamic forces and moments. A well-known case study, the Defence Advanced Research Projects Agency (DARPA) SUB-OFF model, is used, and the outcomes are compared to the experimental results available in the literature. Five different configurations are investigated for pure drift tests, rudder tests and pure rotation in both vertical and horizontal plane. The results show an overall good agreement with the experimental data with a quite low demanding mesh arrangement of 3M cells, a favourable balance between accuracy and computational time. In more detail, the expected error in the most significant forces during manoeuvres is less than 2% for the fully appended configuration (the submarine real operative condition), whereas the accuracy is moderately reduced for the barehull configuration (a case not representative of a real hull) with an expected error of 15%. A possible reason for the differences observed could be attributed to the description of the two streamwise vortices generated when manoeuvring. Apart from the lateral force and yaw moment, the results of the longitudinal force are also presented, having a greater disparity when compared to the experimental data. Nevertheless, the longitudinal force has no important role for the purpose of making stability and control predictions. The study contributes to the validation and consolidation of CFD methods, offering insights into their accuracy and limitations for practical applications in underwater vehicles.

High Accurate Investigation of the Nuclear Hydrodynamical Moment of Inertia

A method for investigating the non-axial moments of inertia within the framework of the hydrodynamical model is developed to give a high accurate formula of the hydrodynamical moments of inertia. In these investigations the third order of the deformation parameter is taken into account.

Reduced order modeling of hydrodynamic interactions between a submarine and unmanned underwater vehicle using non-myopic multi-fidelity active learning

Several efforts have been dedicated to developing computational tools capable of predicting the hydrodynamic forces and moments of Unmanned Underwater Vehicles (UUVs). However, there is no method at the moment that allows for real-time computational modeling of all the complex hydrodynamic interaction forces and moments that a UUV experiences when operating in close proximity to a moving submarine. Real-time modeling of these hydrodynamic interactions is essential to simulate the motion required to launch and recover UUVs from submarines. Potential flow models are often fast enough to be used in real time, but lack the accuracy of Computational Fluid Dynamics (CFD) simulations, which often take hours or days to solve. Here, we formulate the problem in the context of machine learning, specifically active learning. The goal is to develop a surrogate model capable of predicting the UUV and submarine hydrodynamic interactions in real time using a very small number of carefully selected CFD simulations. We introduce a new active learning framework called Non-Myopic Multi-Fidelity Active Learning for Gaussian Process (GP) regression that accelerates the convergence of the surrogate model by utilizing the low cost of the low fidelity simulations to explore the domain, as well as optimally selected high fidelity simulations to improve the model accuracy. The resulting surrogate model can be integrated into UUV control and autonomy systems and motion simulators to further enable UUV launch and recovery from submarines. This new active learning method may also be used to create higher accuracy and lower cost surrogate models in other real world applications.

Experimental and numerical study of the hydrodynamics of a flapping fin at zero speed

The flapping fins can be used as effective actuators of roll stabilizers at zero speed. They provide anti-roll torques to reduce the roll motion of ships in waves. The effects of roll amplitude, flapping frequency and aspect ratio on the hydrodynamic forces and moments at zero speed have been studied through experiments and numerical simulations. It is found that the forces and moments can be described using the added mass forces and damping forces respectively. Empirical formulas to calculate the forces and moments have been derived. The flapping frequency has no significant effects on the force coefficients and moment coefficients. The drag coefficients can be described by an exponential function of KC number, the added mass coefficients are the function of roll amplitude and aspect ratio due to the 3D flow separation.

Effects of pitch angle on a near free surface underwater vehicle

Simulations of an underwater vehicle were conducted to investigate the effects of steady pitch angle, Froude number, and submergence depth. A shallow submerged (D* = 1.1) to a deeply submerged (D* = 6.6) SUBOFF was investigated over a range of steady pitch angles and Froude numbers. Results show that proximity to the free surface causes increased resistance, heave and pitch moment and that free surface effects diminish rapidly with increased submergence depth. Even though D* = 3.3 is typically quoted as being the deeply submerged threshold, free surface effects can still be observed especially at large pitch angles. At pitch angle, asymmetry can be seen between the pressure distribution of the upper and lower surfaces of the SUBOFF, with a phase shift of the hydrodynamic forces and moments. At smaller pitch angles, the changes in hydrodynamic forces and moments stay relatively linear at an offset from zero degrees. At larger pitch angles, the hydrodynamic forces and moments become non-linear due to crossflow separation and air entrainment over the bow/stern. Additionally, the potential of the stern planes to cope with free surface effects were investigated, showing the safety threshold with respect to Froude number, submergence depth, and hull pitch angle.

A numerical investigation on ship-ship overtaking interactions in confined waterways

The whole process of a KCS container ship overtaking a low-speed Neo-Panamax container ship is numerically simulated by solving the unsteady Reynolds Averaged Navier-Stokes (URANS) equations. The dynamic overset mesh technique is adopted to simulate the relative motions between the two ships and the ship attitude variations. The free-surface elevations, ship attitudes, as well as hydrodynamic forces and moments on the two ships are predicted. In order to discuss the effects of different navigation parameters on the ship-ship interactions, a set of ship speeds, lateral distances and water depths are simulated. The results illustrate that the overtaken ship is more significantly impacted by the interaction than the overtaking ship, and the drawdown generated by the overtaking ship is the key factor during the overtaking process. The increase of ship speed, the decrease of lateral distance or water depth can lead to more intense drawdown, and hence even more significant ship-ship interaction effects.

Detachment of inclined spheroidal particles from flat substrates

The detachment of fine particles attached to a solid substrate or rock surface significantly affects colloidal transport in porous media. The work is devoted to quantifying the detachment conditions for inclined oblate spheroids subjected to creeping viscous flow. A numerical and a laboratory study were conducted to systematically evaluate the impact of the orientation (pitch) angle towards the hydrodynamic moment, adhesive DLVO force, contact area, and critical detachment velocity. The methodology developed to produce stretched latex polystyrene particles reduces the geometric uncertainty of nonspherical fines. The geometry of the produced oblate spheroids is fully determined by the semi-major and semi-minor axes. For inclined attached particles, an explicit formula has been derived for the detaching velocity, where the detaching drag torque exceeds the attaching adhesion torque. The probabilistic distribution of the model parameters for the detachment velocity of the inclined particles attached to the plane substrate provides upscaling for fines detachment from the particle to porous media scale.

Hydrodynamic Analysis of Shallow Water Sloshing in Ship Chamber Under Longitudinal Earthquake

Shallow water sloshing-structure interaction under the coupled longitudinal and pitch motions resulted by the longitudinal earthquake directly affects the structural safety of the shiplift. However, no matter in shiplift or other related fields, there is little research on this aspect at present. As a basis of structural dynamics analysis and earthquake resistant design, an analytical method including a developed modal system and new engineering formulas is presented to predict the hydrodynamic moment and force in the ship chamber. Based on the linear modal theory, a modal system describing shallow water sloshing under longitudinal earthquake is developed with infinite set of modal functions. Then, new engineering formulas for calculating the hydrodynamic moment and force are proposed with only retaining the lowest sloshing mode (n=1). Case simulations suggest that the maximum error of hydrodynamic moment and force between n=1 and n=100 are lower than 1.3% and 10.5%, respectively. In addition, the hydrodynamic moment resulting from pressure on the walls can be reasonably ignored, which accounts for less than 0.5% percent of total hydrodynamic moment. With respect to the currently used Housner model, the presented formulas are greatly improved in computational accuracy and rationally supplement the missing part in the seismic design part of the Design code for shiplift.

Shallow water effects on circular motion tests using an efficient and robust approach

This paper presented an efficient and robust numerical approach for conducting circular motion tests (CMTs) with fully appended ship under deep and shallow water conditions. A 135 m long benchmark inland waterway ship was selected for systematic investigations. By comparing predictions obtained from the widely applied moving grid and rotating reference frame approaches for CMTs, the proposed rotating flow approach attained predictions equally as accurate as the moving grid approach, but computationally significantly more efficient. By coupling the rotating flow approach with the free surface, the ship’s trim and sinkage were also accounted for. Grid independence study and comparison with physical CMTs carried out at HSVA validated the proposed approach. The influence of the free surface and the action of the propellers on hydrodynamic forces and moments was demonstrated by performing CMTs at water depth to draft ratios of 8.0 and 1.2. Effects of the free surface and the propellers were more pronounced in shallow water. In the end, systematic CMTs were carried out with the free surface and operating propellers across four different water depths, employing water depth to draft ratios of 1.2, 1.5, 2.0, and 3.0, and demonstrated the influence of shallow water on maneuvering forces and on the associated turning ability of the investigated ship.