On the Interaction of Waves With Intake/Discharge Flows Originating From a Freely-Floating Body

2003 ◽  
Vol 125 (1) ◽  
pp. 41-47 ◽  
Author(s):  
B. Padmanabhan ◽  
R. C. Ertekin
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Floating Body ◽  
Wave Forces ◽  
Linear Potential ◽  
Two Dimensional ◽  
Rankine Source ◽  
Total Potential ◽  
Linear Potential Theory ◽  
Steady Potential

A linear theory is developed to obtain the motions of a two-dimensional, freely floating body (from which steady intake/discharge flows originate) that encounters incoming waves. The boundary-value problem is formulated within the assumptions of linear potential theory by decomposing the total potential into its oscillatory and steady components. The steady potential is further decomposed into the double-model and perturbation potentials. The time-harmonic potential is coupled with the steady potential through the free-surface condition. The potentials are obtained by use of the quadratic boundary-element method based on the Rankine source. The effect of the steady intake/discharge flows on the diffraction loads, hydrodynamic force coefficients, as well as the motions of a two-dimensional prismatic body floating on the free surface are presented. It is shown that the exciting wave forces and the hydrodynamic coefficients other than the damping coefficients are not appreciably affected in the case of low intake/discharge Froude numbers that are estimated, for example, for a 100 MW floating OTEC plant.

On the Interaction of Waves With Intake/Discharge Flows Originating From a Freely-Floating Body

2002 ◽  
Author(s):  
B. Padmanabhan ◽  
R. C. Ertekin
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Floating Body ◽  
Wave Forces ◽  
Linear Potential ◽  
Rankine Source ◽  
Total Potential ◽  
Low Froude Number ◽  
Linear Potential Theory ◽  
Steady Potential

This work is motivated by the many instances of intake/discharge flows from openings on floating or submerged ocean vessels and structures that may affect the wave field around them. Damaged vessels may release oil, or water may enter these vessels through openings. In oil skimming operations, for example, a very thin layer of oil must be skimmed off a large surface area, and therefore, oil skimming vessels require large intakes. Floating OTEC plants also require large intake and discharge volumes to sustain their operations. A linear theory is developed to obtain the motions of a 2-dimensional, freely floating body (from which steady intake/discharge flows originate) that encounters incoming waves. The boundary-value problem is formulated within the assumptions of linear potential theory by decomposing the total potential into its oscillatory and steady components. The steady potential is further decomposed into the double-model and perturbation potentials. The time-harmonic potential is coupled with the steady potential through the free-surface condition. The potentials are obtained by use of the quadratic boundary-element method based on the Rankine source. The effect of the steady intake/discharge flows on the diffraction loads, hydrodynamic force coefficients, as well as the motions of a 2-dimensional prismatic body floating on the free surface are presented. It is shown that the exciting wave forces and the hydrodynamic coefficients other than the damping coefficients are not appreciably affected by the intake/discharge flows of low Froude number for a 100MW floating OTEC plant.

Interaction of Waves With Steady Intake/Discharge Flow Emanating From a 3-D Body

2007 ◽  
Author(s):  
Bala Padmanabhan ◽  
R. Cengiz Ertekin
Keyword(s):  
Steady Flow ◽  
Surface Condition ◽  
Linear Potential ◽  
Intake Rate ◽  
Mooring Lines ◽  
Incoming Wave ◽  
Total Potential ◽  
Warm Surface Water ◽  
Linear Potential Theory ◽  
Steady Potential

It has been proposed that the warm surface-water intake pipes distributed around an OTEC plant can generate adequate momentum to globally position a platform to overcome the second-order drift forces, thereby eliminating the need for additional power for thrusters or for mooring lines. It is evident that if the intake rate of the flow is high, there will be interaction among the locally created steady flow due to the intake, the incoming wave and the ensuing platform motions. In this work, we address such concerns by developing a linear theory for obtaining the motions (in the presence of incoming waves) of arbitrary 3-D bodies from which there is a steady intake/discharge. The boundary-value problem is formulated within the assumption of linear potential theory by decomposing the total potential into oscillatory and steady components. The steady potential is further decomposed into double-model and perturbation potentials. The time harmonic potential is coupled with the steady potential through the free-surface condition. The potentials are obtained using the quadratic boundary-element method. The effect of the steady flow on hydrodynamic force coefficients and RAOs are studied.

Interaction of Waves With a Steady Intake/Discharge Flow Emanating From a 3D Body

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Bala Padmanabhan ◽  
R. Cengiz Ertekin
Keyword(s):  
Steady Flow ◽  
Surface Condition ◽  
Linear Potential ◽  
Intake Rate ◽  
Mooring Lines ◽  
Incoming Wave ◽  
Total Potential ◽  
Warm Surface Water ◽  
Linear Potential Theory ◽  
Steady Potential

It has been proposed that the warm surface-water intake pipes distributed around an OTEC plant can generate adequate momentum to globally position a platform to overcome the second-order drift forces, thereby eliminating the need for additional power for thrusters or for mooring lines. It is evident that if the intake rate of the flow is high, there will be interaction among the locally created steady flow due to the intake, the incoming wave, and the ensuing platform motions. In this work, we address such concerns by developing a linear theory for obtaining the motions (in the presence of incoming waves) of arbitrary 3D bodies from which there is a steady intake/discharge. The boundary-value problem is formulated within the assumption of the linear potential theory by decomposing the total potential into oscillatory and steady components. The steady potential is further decomposed into double-model and perturbation potentials. The time harmonic potential is coupled with the steady potential through the free-surface condition. The potentials are obtained using the quadratic boundary-element method. The effect of the steady flow on hydrodynamic force coefficients and response amplitude operators is studied.

Towards Fully Non-Linear Floating Body Simulations by a Potential Method

2012 ◽  
Author(s):  
Heinrich Söding
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Computing Time ◽  
Potential Method ◽  
The Body ◽  
Floating Body ◽  
Rankine Source ◽  
Exact Boundary ◽  
Approximate Wave ◽  
Steep Waves

A 3-dimensional Rankine source panel method for simulating a rigid floating body in steep waves is being developed. The aim is to obtain the same quality as free-surface RANSE methods, which are well suited for this application, but to require only a small fraction of the computing time needed by RANSE methods. The body may have forward speed or perform maneuvering motions. The exact boundary conditions are satisfied at the actual location of the fluid boundaries. The waves are generated not by a material wave maker, but by an approximate wave potential which needs not satisfy the exact free-surface condition. No wave damping regions are required. Whereas for steep waves without a body the method appears satisfactory, it needs further improvements if a body is present.

Computation of Wave Added Resistance by Control Surface Integration

2016 ◽  
Author(s):  
Zhiyuan Pan ◽  
Torgeir Vada ◽  
Kaijia Han
Keyword(s):  
Free Surface ◽  
Near Field ◽  
Momentum Conservation ◽  
Ship Hull ◽  
Control Surface ◽  
Floating Body ◽  
Added Resistance ◽  
Time Step ◽  
Rankine Source ◽  
Linearization Methods

A time domain Rankine source solver is extended to compute the wave added resistance of ships. The proposed approach applies the momentum conservation principle on the near field fluid volume enclosed by the wet surface of a floating body, the free surface and a control surface. The wave added resistance is then calculated by the integration over the control surface of the fluid velocities and free surface elevations. To be able to incorporate the proposed method with the Rankine source code, an interpolation scheme has been developed to compute the kinematics for the off-body points close to (or on) the free surface. Two Wigley ship models, a containership model S175 and a tanker model KVLCC2 are used to validate the present method. In general good agreement is found comparing with the model test data. The convergence behavior is examined for the proposed method including the selection of the time step and location of the control surface. Both Neumann-Kelvin and double body linearization methods are evaluated with the proposed method. It is found that the Neumann-Kelvin linearization can only be applied for slender ship hull, whereas double body method fits also for blunt ships. It is suggested to apply the proposed method with double body linearization to evaluate the wave added resistance of ships with a control surface close to the ship hull.

Numerical Analysis of a Floating Body With Two-Dimensional Moonpool Including Piston Mode

2010 ◽  
Author(s):  
Jaekyung Heo ◽  
Jong-Chun Park ◽  
Moo-Hyun Kim ◽  
Weon-Cheol Koo
Keyword(s):  
Free Surface ◽  
Viscous Flow ◽  
Experimental Results ◽  
Floating Body ◽  
Navier Stokes ◽  
Linear Potential ◽  
Navier Stokes Equation ◽  
Nonlinear Potential ◽  
Heave Motion ◽  
Piston Mode

In this paper, the potential and viscous flows are simulated numerically around a 2-D floating body with a moonpool (or a small gap) with particular emphasis on the piston mode. The floating body with moonpool is forced to heave in time domain. Linear potential code is known to give overestimated free-surface heights inside the moonpool. Therefore, a free-surface lid in the gap or similar treatments are widely employed to suppress the exaggerated phenomenon by potential theory. On the other hand, Navier-Stokes equation solvers based on a FVM can be used to take account of viscosity. Wave height and phase shift inside and outside the moon-pool are computed and compared with experimental results by Faltinsen et al. (2007) over various heaving frequencies. Pressure and vorticity fields are investigated to better understand the mechanism of the sway force induced by the heave motion. Furthermore, a nonlinear potential code is utilized to compare with the viscous flow. The viscosity effects are investigated in more detail by solving Euler equations. It is found that the viscous flow simulations agree very well with the experimental results without any numerical treatment.

On the Hydrodynamic Interaction Between Ship and Free-Surface Motions on Vessels With Moonpools

2019 ◽  
Author(s):  
Senthuran Ravinthrakumar ◽  
Trygve Kristiansen ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Linear Potential ◽  
Two Dimensional ◽  
Sloshing Mode ◽  
Vessel Motion

Abstract Coupling between moonpool resonance and vessel motion is investigated in two-dimensional and quasi three-dimensional settings, where the models are studied in forced heave and in freely floating conditions. The two-dimensional setups are with a recess, while the quasi three-dimensional setups are without recess. One configuration with recess is presented for the two-dimensional case, while three different moonpool sizes (without recess) are tested for the quasi three-dimensional setup. A large number of forcing periods, and three wave steepnesses are tested. Boundary Element Method (BEM) and Viscous BEM (VBEM) time-domain codes based on linear potential flow theory, and a Navier–Stokes solver with linear free-surface and body-boundary conditions, are implemented to investigate resonant motion of the free-surface and the model. Damping due to flow separation from the sharp corners of the moonpool inlets is shown to matter for both vessel motions and moonpool response around the piston mode. In general, the CFD simulations compare well with the experimental results. BEM over-predicts the response significantly at resonance. VBEM provides improved results compared to the BEM, but still over-predicts the response. In the two-dimensional study there are significant coupling effects between heave, pitch and moonpool responses. In the quasi three-dimensional tests, the coupling effect is reduced significantly as the moonpool dimensions relative to the displaced volume of the ship is reduced. The first sloshing mode is investigated in the two-dimensional case. The studies show that damping due to flow separation is dominant. The vessel motions are unaffected by the moonpool response around the first sloshing mode.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

Unsteady thrust, lift and moment of a two-dimensional flapping thin airfoil in the presence of leading-edge vortices: a first approximation from linear potential theory

2018 ◽  
Vol 851 ◽  
pp. 344-373 ◽  
Author(s):  
R. Fernandez-Feria ◽  
J. Alaminos-Quesada
Keyword(s):  
Potential Theory ◽  
Leading Edge ◽  
Input Power ◽  
Linear Potential ◽  
Two Dimensional ◽  
Thin Airfoil ◽  
Reduced Frequency ◽  
Large Phase ◽  
Linear Potential Theory ◽  
Oscillating Foil

The effect of a leading-edge vortex (LEV) on the lift, thrust and moment of a two-dimensional heaving and pitching thin airfoil is analysed within the unsteady linear potential theory. First, general expressions that take into account the effect of any set of unsteady point vortices interacting with the oscillating foil and unsteady wake are derived. Then, a simplified analysis, based on the Brown–Michael model, of the initial stages of the growing LEV from the sharp leading edge during each half-stroke is used to obtain simple expressions for its main contribution to the unsteady lift, thrust and moment. It is found that the LEV contributes to the aerodynamic forces and moment provided that a pitching motion exists, while its effect is negligible, in the present approximation, for a pure heaving motion, and for some combined pitching and heaving motions with large phase shifts which are also characterized in the present work. In particular, the effect of the LEV is found to decrease with the distance of the pivot point from the trailing edge. Further, the time-averaged lift and moment are not modified by the growing LEVs in the present approximation, and only the time-averaged thrust force is corrected, decreasing slightly in most cases in relation to the linear potential results by an amount proportional to$a_{0}^{2}k^{3}$for large$k$, where$k$is the reduced frequency and$a_{0}$is the pitching amplitude. The time-averaged input power is also modified by the LEV in the present approximation, so that the propulsion efficiency changes by both the thrust and the power, these corrections being relevant only for pivot locations behind the midchord point. Finally, the potential results modified by the LEV are compared with available experimental data.

Influence of Free Surface on Hydrodynamic Lift Using a High-Order Boundary Element Method

2015 ◽  
Author(s):  
Amanda J. Costa ◽  
Daniel Kowalyshyn ◽  
Kevin Tuil ◽  
Yin Lu Young ◽  
William Milewski ◽  
...  
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Boundary Element ◽  
High Order ◽  
Linear Potential ◽  
Surface Boundary ◽  
Ship Hulls ◽  
Surface Boundary Conditions ◽  
Linear Potential Theory ◽  
Element Method

This paper presents the results of hydrofoil simulations at varying depths below the free surface, in surface piercing conditions, and integrated with ship hulls. It focuses on the influence of the free surface on the hydrodynamic loads, susceptibility to cavitation, and resulting surface wave patterns. A fast, high-order, NURBS (Non Uniform Rational B-Spline) based boundary element method has been developed that includes both free surface boundary conditions and steady and unsteady iterative pressure Kutta conditions for simulating lift. Results from this method will be compared to published experimental results, analytical solutions based on linear potential theory, and numerical results from viscous simulations obtained using the commercial CFD solver, ANSYS CFX.

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