Lagrangian Expressions of the Hydrodynamic Forces Acting on a Rigid Body in the Presence of a Free Surface

1985 ◽  
Vol 29 (01) ◽  
pp. 12-22
Author(s):  
G. A. Athanassoulis ◽  
T. A. Loukakis
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Hydrodynamic Pressure ◽  
Hydrodynamic Forces ◽  
Ship Motions ◽  
Analytical Dynamics ◽  
Motion Equations ◽  
Hydromechanical System ◽  
Complete Set ◽  
Virtual Velocity

The formalism of classical analytical dynamics is used in conjunction with the principle of virtual velocity to derive Lagrangian expressions for the hydrodynamic forces acting on a rigid body moving through an in-viscid and incompressible liquid with a free surface. Simultaneously, a corresponding Lagrangian expression is derived for the hydrodynamic pressure acting on the free surface itself. The expressions for the hydrodynamic forces degenerate to the classical ones if the free surface is not present, and the expression for the pressure is reduced to that obtained by Milder if the rigid boundaries are all kept fixed. The derived Lagrangian expressions for the hydrodynamic reactions are used to obtain a complete set of motion equations for the examined hydromechanical system, and to discuss another Lagrangian approach to the ship-motions problem, presented by Wang.

scholarly journals Coupling Between Flexible Ship and Liquid Sloshing Using Potential Flow Analysis

2010 ◽  
Author(s):  
Youngbum Lee ◽  
Mingyi Tan ◽  
Pandeli Temarel ◽  
Shihua Miao
Keyword(s):  
Rigid Body ◽  
Potential Flow ◽  
Coupling Effect ◽  
Flow Analysis ◽  
Hydrodynamic Forces ◽  
The Body ◽  
Liquid Sloshing ◽  
Ship Motions ◽  
Resonance Frequencies ◽  
Body Boundary

The significant increase in demand for Liquefied Natural Gas (LNG) and the economic aspects of its transportation resulted in increases in the number and size of LNG carriers. One of the design issues for LNG carriers is the sloshing phenomenon because containment systems widely used nowadays have no internal structures. Furthermore, because the weights of ship and cargo are comparable and ship operators want more flexible operations allowing partial fillings in tanks, the coupling effect between ship motions and sloshing requires further investigation, including the effect of ship distortion. The previous study on coupling between rigid body and sloshing shows good agreement between methods of prediction and measurements [1,2]. Hence, in this paper the potential flow approach adopted for the coupling effect between rigid body ship motion and sloshing is extended to flexible ship-partially filled tank system, using the desingularised Rankine source method. In this case, the global deflection of the flexible ship is used for application of the body boundary condition on the partially filled tank. The aim of this paper is to investigate the influence of hull flexibility on the hydrodynamic forces and moments associated with liquid sloshing and vice versa, as well as the dynamic characteristics (e.g. resonance frequencies) of the whole system. As there are no experimental results available, the method is validated by comparing hydrodynamic forces from sloshing obtained using rigid and flexible body approaches. The coupling effect between flexible ship and sloshing in partially filled tanks is investigated for an idealized LNG Carrier in beam regular waves, considering different partial filling scenarios.

scholarly journals Numerical Analysis of Hydrodynamic Loads on Passing and Moored Ships in Shallow Water

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 558
Author(s):  
Ji-Yong Park ◽  
Bo Woo Nam ◽  
Yonghwan Kim
Keyword(s):  
Free Surface ◽  
Surface Effect ◽  
Hydrodynamic Pressure ◽  
Simulation Method ◽  
Separation Distance ◽  
Hydrodynamic Forces ◽  
Surface Boundary ◽  
Surface Boundary Conditions ◽  
Surface Models ◽  
Force Time

In this study, hydrodynamic interactions between passing and moored ships were studied by applying a time-domain numerical simulation method. The boundary value problem for a fluid domain was formulated based on a potential flow theory. A numerical method was developed based on a finite element method with an efficient re-mesh algorithm. Regarding the free-surface boundary conditions, both double-body and free-surface models were considered for examining the free-surface effect on the hydrodynamic forces due to the passing ship. First, numerical results were validated by comparison with the model test results of Kriebel et al. (2005), where generic Series 60 hulls were considered as the target model for the passing and moored ships. In addition, hydrodynamic pressure fields and force time-series were investigated to understand the passing ship problem. Second, a series of numerical simulations were performed to study the effects of the passing ship speed, separation distance, water depth, and relative vessel size, which were used to compare the peak values of hydrodynamic forces. The applicability and limitations of the double-body and free-surface models are discussed for predicting passing ship loads.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

scholarly journals HYDRODYNAMIC FORCES ACTING ON A SUBMERGED OBSTRUCTION IN STEADY FREE SURFACE FLOWS

2004 ◽  
Vol 48 ◽  
pp. 877-882
Author(s):  
Mirei SHIGE-EDA ◽  
Juichiro AKIYAMA ◽  
Masayuki NONAKA ◽  
Takanori ASANO
Keyword(s):  
Free Surface ◽  
Free Surface Flows ◽  
Hydrodynamic Forces ◽  
Surface Flows

The Forced Oscillations of Submerged Bodies

2003 ◽  
Vol 125 (4) ◽  
pp. 710-715
Author(s):  
Angel Sanz-Andre´s ◽  
Gonzalo Tevar ◽  
Francisco-Javier Rivas
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Central Point ◽  
Modal Testing ◽  
Forced Oscillations ◽  
Motion Equations ◽  
Marine Applications

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.

Development and Optimization of Mathematical Model of High Speed Planing Dynamics

2015 ◽  
Author(s):  
Prin Kanyoo ◽  
Dominic J. Taunton ◽  
James I. R. Blake
Keyword(s):  
Relative Velocity ◽  
High Speed ◽  
Lift Force ◽  
Hydrodynamic Pressure ◽  
Physical Nature ◽  
Ship Motions ◽  
Additional Contribution ◽  
Forward Speed ◽  
Planing Craft ◽  
Hydrostatic Force

The primary difference between a planing craft and a displacement ship is that the predominant force to support the conventional or displacement craft is hydrostatic force or buoyancy. While in the case of planing craft, the buoyancy cedes this role to hydrodynamic lift force caused by flow and pressure characteristics occurring when it is travelling at high forward speed. However, the magnitude of hydrostatic force is still significant that cannot be completely neglected. Due to the high forward speed and trim angle, the flow around and under the planing hull experiences change of momentum and leads to the appearance of lift force according to the 2ndlaw of Newton. In other words, there is a relative velocity between the craft hull and the wave orbital motion that causes hydrodynamic pressure generating hydrodynamic lift force act on the hull surface. Then, in case of behaviors in waves, an additional contribution of ship motions is necessary to be considered in the relative velocity, resulting in nonlinear characteristic of its physical nature.

Utilizing the Effort/Motion Approach in the Simulation of Interconnected Rigid Body Systems

1997 ◽  
Author(s):  
N. Duke Perreira
Keyword(s):  
Numerical Simulation ◽  
Rigid Body ◽  
Multibody Systems ◽  
Invariant Form ◽  
Second Law ◽  
Orthogonal Projections ◽  
Gauge Invariant ◽  
Motion Equations ◽  
Newton's Second Law ◽  
Constraint Surface

Abstract The effort/motion approach has been developed for use in designing, simulating and controlling multibody systems. Some aspects of each of these topics are discussed here. In the effort/motion formulation two sets of equations based on the orthogonal projections of a dimensional gauge invariant form of Newton’s Second Law occur. The projections are onto the normal and tangent directions of a dimensional gauge invariant constraint surface. The paper shows how these equations are obtained for a particular linkage with redundant effort and motion actuation. Two alternative Runga-Kutta based approaches for numerical simulation of the effort/motion equations are developed and applied in simulating the motion and determining the effort generated in the example linkage under various conditions. Oscillation about equilibrium positions, solutions with constant motion and with constant effort are given as examples of the approach.

scholarly journals Combinatory Attitude Determination Method for High Rotational Speed Rigid-Body Aircraft

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Liangliang An ◽  
Liangming Wang ◽  
Ning Liu ◽  
Jian Fu
Keyword(s):  
Rigid Body ◽  
Rotational Speed ◽  
Attitude Determination ◽  
Unscented Kalman Filter ◽  
The State ◽  
Determination Method ◽  
State Equations ◽  
High Rotational Speed ◽  
Motion Equations ◽  
Accuracy Measurement

In this paper, we present a novel multisensor combinatory attitude determination method that enables high-accuracy measurement of the attitude of a high rotational speed rigid-body aircraft. We analyze the external moments of the aircraft during flight and develop the method using theoretical deductions based on the motion equations of a rigid body rotating around the centroid. The proposed method fuses the data measured from GPS, gyrometer, and magnetometer and uses the improved unscented Kalman filter (UKF) algorithm to perform filtering. First, appropriate assumptions and simplifying approximations are made for around-centroid motion equations of a rigid body according to the motion characteristics of the high rotational speed aircraft. Using these assumptions and approximations, the constraint equations between the Euler attitude angles and flight-path angle, trajectory deflection angle are derived to serve as the state equation. Second, the roll angle with error is calculated using the geomagnetic field model and the geomagnetic intensity measured by a three-axis magnetometer and then fused with the angular velocity information obtained from the gyroscope for constructing the measurement equations. Finally, the state equations are discretized using the Runge–Kutta method during the UKF prediction stage, improving the prediction accuracy. Simulation results show that the proposed method can effectively determine the attitude information of the high rotational speed aircraft, achieving high level of reliability and accuracy thanks to the combination of information from GPS, gyroscope, and magnetometer.

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