Transient axisymmetric motion of a floating cylinder

1985 ◽  
Vol 157 ◽  
pp. 17-33 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Frequency Domain ◽  
Impulse Response ◽  
Response Function ◽  
Time Domain ◽  
Impulse Response Function ◽  
Surface Effects ◽  
Added Mass ◽  
The Body ◽  
The Time Domain

A linear theory is developed in the time domain for vertical motions of an axisymmetric cylinder floating in the free surface. The velocity potential is obtained numerically from a discretized boundary-integral-equation on the body surface, using a Galerkin method. The solution proceeds in time steps, but the coefficient matrix is identical at each step and can be inverted at the outset.Free-surface effects are absent in the limits of zero and infinite time. The added mass is determined in both cases for a broad range of cylinder depths. For a semi-infinite cylinder the added mass is obtained by extrapolation.An impulse-response function is used to describe the free-surface effects in the time domain. An oscillatory error observed for small cylinder depths is related to the irregular frequencies of the solution in the frequency domain. Fourier transforms of the impulse-response function are compared with direct computations of the damping and added-mass coefficients in the frequency domain. The impulse-response function is also used to compute the free motion of an unrestrained cylinder, following an initial displacement or acceleration.

scholarly journals Convolution-based time-domain simulation for fluidelastic instability in tube arrays

2021 ◽  
Author(s):  
Mingjie Zhang ◽  
Ole Øiseth
Keyword(s):  
Impulse Response ◽  
Response Function ◽  
Time Domain ◽  
Impulse Response Function ◽  
Time Domain Simulation ◽  
Unit Step ◽  
Tube Arrays ◽  
Unit Impulse ◽  
The Time Domain ◽  
Unit Impulse Response

AbstractA convolution-based numerical algorithm is presented for the time-domain analysis of fluidelastic instability in tube arrays, emphasizing in detail some key numerical issues involved in the time-domain simulation. The unit-step and unit-impulse response functions, as two elementary building blocks for the time-domain analysis, are interpreted systematically. An amplitude-dependent unit-step or unit-impulse response function is introduced to capture the main features of the nonlinear fluidelastic (FE) forces. Connections of these elementary functions with conventional frequency-domain unsteady FE force coefficients are discussed to facilitate the identification of model parameters. Due to the lack of a reliable method to directly identify the unit-step or unit-impulse response function, the response function is indirectly identified based on the unsteady FE force coefficients. However, the transient feature captured by the indirectly identified response function may not be consistent with the physical fluid-memory effects. A recursive function is derived for FE force simulation to reduce the computational cost of the convolution operation. Numerical examples of two tube arrays, containing both a single flexible tube and multiple flexible tubes, are provided to validate the fidelity of the time-domain simulation. It is proven that the present time-domain simulation can achieve the same level of accuracy as the frequency-domain simulation based on the unsteady FE force coefficients. The convolution-based time-domain simulation can be used to more accurately evaluate the integrity of tube arrays by considering various nonlinear effects and non-uniform flow conditions. However, the indirectly identified unit-step or unit-impulse response function may fail to capture the underlying discontinuity in the stability curve due to the prespecified expression for fluid-memory effects.

Transient Motions of Floating Bodies at Zero Forward Speed

1987 ◽  
Vol 31 (03) ◽  
pp. 164-176 ◽  
Author(s):  
Robert F. Beck ◽  
Stergios Liapis
Keyword(s):  
Integral Equations ◽  
Impulse Response ◽  
Response Function ◽  
Time Domain ◽  
Linear Time ◽  
Impulse Response Function ◽  
Time Domain Analysis ◽  
The Body ◽  
Floating Body ◽  
Forward Speed

Linear, time-domain analysis is used to solve the radiation problem for the forced motion of a floating body at zero forward speed. The velocity potential due to an impulsive velocity (a step change in displacement) is obtained by the solution of a pair of integral equations. The integral equations are solved numerically for bodies of arbitrary shape using discrete segments on the body surface. One of the equations must be solved by time stepping, but the kernel matrix is identical at each step and need only be inverted once. The Fourier transform of the impulse-response function gives the more conventional added-mass and damping in the frequency domain. The results for arbitrary motions may be found as a convolution of the impulse response function and the time derivatives of the motion. Comparisons are shown between the time-domain computations and published results for a sphere in heave, a sphere in sway, and a right circular cylinder in heave. Theoretical predictions and experimental results for the heave motion of a sphere released from an initial displacement are also given. In all cases the comparisons are excellent.

scholarly journals Analytical and Numerical Analysis of the Dynamics of a Moonpool Platform–Wave Energy Buoy (MP–WEB)

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4083
Author(s):  
Kong ◽  
Liu ◽  
Su ◽  
Ao ◽  
Chen ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Wave Energy ◽  
Time Domain ◽  
Impulse Response Function ◽  
Radiation Force ◽  
Resonance Phenomenon ◽  
Hydrodynamic Performance ◽  
Wave Forces ◽  
Diffraction Radiation ◽  
The Time Domain

In this work the hydrodynamic performance of a novel wave energy converter configuration was analytically and numerically studied by combining a moonpool and a wave energy buoy, called the moonpool platform–wave energy buoy (MP–WEB). A potential flow, semi-analytical approach was adopted to assess the total (incident, diffraction, radiation) wave forces acting on the device, and the wave capture and energy efficiency performance of this configuration was assessed, both in the time and frequency domain. The performance of the two configurations, single float and double float, were analyzed and compared in terms of diffraction force, added mass radiation force, motion, and power in the frequency domain. Using an impulse response function-based (IRF) method, the frequency domain results were converted in the time domain. The same parameters in the time domain were derived and the main results were confirmed. Wave energy conversion efficiency was significantly increased due to the resonance phenomenon inside the moonpool.

scholarly journals Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory

2015 ◽  
Author(s):  
Godine Kok Yan Chan ◽  
Paul D. Sclavounos ◽  
Jason Jonkman ◽  
Gregory Hayman
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Wind Turbines ◽  
Time Domain ◽  
The Body ◽  
Nonlinear Loads ◽  
Frequency Wave ◽  
Linear And Nonlinear ◽  
The Time Domain ◽  
Nonlinear Free Surface

A hydrodynamics computer module was developed to evaluate the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The new formulation allows linear and nonlinear loads on floating bodies to be computed in the time domain. It also avoids the computationally intensive evaluation of temporal and spatial gradients of the velocity potential in the Bernoulli equation and the discretization of the nonlinear free surface. The new hydrodynamics module computes linear and nonlinear loads — including hydrostatic, Froude-Krylov, radiation and diffraction, as well as nonlinear effects known to cause ringing, springing, and slow-drift loads — directly in the time domain. The time-domain Green function is used to solve the linear and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.

A Numerical Method for Representing Retardation Functions With Complex Exponentials

2017 ◽  
Author(s):  
Fushun Liu ◽  
Lei Jin ◽  
Jiefeng Chen ◽  
Wei Li
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Memory Effects ◽  
Floating Structure ◽  
Frequency Dependent ◽  
Laplace Domain ◽  
The Time Domain ◽  
Frequency Domain Techniques

Numerical time- or frequency-domain techniques can be used to analyze motion responses of a floating structure in waves. Time-domain simulations of a linear transient or nonlinear system usually involve a convolution terms and are computationally demanding, and frequency-domain models are usually limited to steady-state responses. Recent research efforts have focused on improving model efficiency by approximating and replacing the convolution term in the time domain simulation. Contrary to existed techniques, this paper will utilize and extend a more novel method to the frequency response estimation of floating structures. This approach represents the convolution terms, which are associated with fluid memory effects, with a series of poles and corresponding residues in Laplace domain, based on the estimated frequency-dependent added mass and damping of the structure. The advantage of this approach is that the frequency-dependent motion equations in the time domain can then be transformed into Laplace domain without requiring Laplace-domain expressions of the added mass and damping. Two examples are employed to investigate the approach: The first is an analytical added mass and damping, which satisfies all the properties of convolution terms in time and frequency domains simultaneously. This demonstrates the accuracy of the new form of the retardation functions; secondly, a numerical six degrees of freedom model is employed to study its application to estimate the response of a floating structure. The key conclusions are: (1) the proposed pole-residue form can be used to consider the fluid memory effects; and (2) responses are in good agreement with traditional frequency-domain techniques.

Transient Free-Surface Hydrodynamics Using Rational Approximation of the Green’s Function

1999 ◽  
Vol 43 (02) ◽  
pp. 95-106 ◽  
Author(s):  
Christopher J. Damaren
Keyword(s):  
Free Surface ◽  
Frequency Domain ◽  
Source Function ◽  
The Body ◽  
Floating Body ◽  
Order Ordinary Differential Equation ◽  
Radiation Impedance ◽  
Rational Dependence ◽  
The Time Domain ◽  
Domain Source

Rational approximations in the frequency domain are developed for the source function of linear free-surface hydrodynamics using the recently uncovered fourth-order ordinary differential equation (ODE) satisfied by the time-domain source function. The radiation problem for a floating body in deep water is formulated using a source plus wave-free potential expansion for the fluid. The inherent rational dependence on frequency of the wave-free potentials as well as the source approximation are used to develop a system of constant-coefficient ODE's for the radiation impedance which can be used to develop the motion of the body in a simple manner. The technique is applied to the heaving motion of a floating sphere with good results. The application to more general body geometries is explored by formulating the frequency-domain problem using the variational principle of Chen and Mei and exploiting its polynomial dependence on frequency.

Time-Domain Simulations of Multi-Body Systems in Deterministic Wave Trains

2006 ◽  
Author(s):  
Katja Jacobsen ◽  
Gu¨nther F. Clauss
Keyword(s):  
Frequency Domain ◽  
Impulse Response ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Wave Length ◽  
Impulse Response Function ◽  
Impulse Response Functions ◽  
Hydrodynamic Coupling ◽  
Lift Off ◽  
Multi Body

A growing amount of reports on heavy lift operations involving huge crane vessels prove that investigations on the motion behavior of multi-body systems are vital regarding the combined aspects of safety and economics. In this paper a method of transforming frequency-domain into time-domain results is presented. With the panel program WAMIT (WAMIT Inc.) the Response Amplitude Operators (RAO) of the motions in six degrees of freedom of the structures involved in a lift operation are calculated. The multi-bodies RAOs differ significantly from those of the single structures (without interaction effects). The consideration of hydrodynamic coupling is therefore essential for the prediction of accurate relative motions between the structures. Frequency-domain results are still important when determining operational limitations. But only with simulations in time-domain the relation between cause and reaction can be studied in detail. Results from simulations provide for example decision support for finding uncritical starting points of the lift off operation. By Fouriertransforming the RAOs the impulse-response functions are obtained. Having the impulse-response function the time-dependent system responses in arbitrary deterministic wave registrations are determined by convolution. This method allows fast and effective time-domain simulations of multi-body systems. Results are presented for a crane semisubmersible and a conventional transport barge. The influence, particularly the sensitivity of wave height and wave length on the response is shown in wave packets.

Noncausality of the discrete‐time magnetotelluric impulse response

Geophysics ◽  
1992 ◽  
Vol 57 (10) ◽  
pp. 1354-1358 ◽  
Author(s):  
Gary D. Egbert
Keyword(s):  
Magnetic Fields ◽  
Frequency Domain ◽  
Impulse Response ◽  
Discrete Time ◽  
Time Domain ◽  
Linear Relation ◽  
External Source ◽  
The Time Domain ◽  
Treat All ◽  
Time Invariant

Under the assumption that the external source magnetic fields are uniform, the electric (E) and magnetic (H) fields observed at the surface of the conducting earth satisfy a time‐invariant linear relation, which may be expressed as multiplication in the frequency domain, [Formula: see text], Eq. (1), or as convolution in the time domain, [Formula: see text], Eq. (2). Here the tilde denotes quantities in the frequency domain; e.g., [Formula: see text] is the frequency‐domain magnetotelluric (MT) impedance, and Z the corresponding time‐domain impulse response. For simplicity in the following discussion, I treat all quantities as scalars, although the operations in equations (1) and (2) generally involve vectors and tensors.

scholarly journals Time-Domain Analysis of Substructure of a Floating Offshore Wind Turbine in Waves

2016 ◽  
Author(s):  
Zi Lin ◽  
Jianmin Yang ◽  
Longbin Tao ◽  
P. Sayer ◽  
Dezhi Ning
Keyword(s):  
Wind Turbine ◽  
Impulse Response ◽  
Response Function ◽  
Incident Wave ◽  
Time Domain ◽  
Wave Spectrum ◽  
Impulse Response Function ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Floating Offshore Wind Turbine

This paper aims to analyze the hydrodynamics of a floating offshore wind turbine (FOWT) in waves. Instead of modeling the incident random wave with the traditional wave spectrum and superposition theory, an impulse response function method was used to simulate the incident wave. The incident wave velocity was evaluated by a convolution of the wave elevation at the original point and the impulse response function in the domain. To check the validity of current wave simulation method, the calculated incident wave velocities were compared with analytical solutions; they showed good agreement. The developed method was then used for the hydrodynamic analysis of the substructure of the FOWT. A direct time-domain method was used to calculate the wave-rigid body interaction problem. The proposed numerical scheme offers an effective way of modeling the incident wave by an arbitrary time series.

scholarly journals Frequency-domain elastic wavefield simulation with hybrid absorbing boundary conditions

2019 ◽  
Vol 16 (4) ◽  
pp. 690-706
Author(s):  
Zhencong Zhao ◽  
Jingyi Chen ◽  
Xiaobo Liu ◽  
Baorui Chen
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Time Domain ◽  
Absorbing Boundary Conditions ◽  
Elastic Media ◽  
Absorbing Boundary ◽  
Wavefield Simulation ◽  
The Time Domain

Abstract The frequency-domain seismic modeling has advantages over the time-domain modeling, including the efficient implementation of multiple sources and straightforward extension for adding attenuation factors. One of the most persistent challenges in the frequency domain as well as in the time domain is how to effectively suppress the unwanted seismic reflections from the truncated boundaries of the model. Here, we propose a 2D frequency-domain finite-difference wavefield simulation in elastic media with hybrid absorbing boundary conditions, which combine the perfectly matched layer (PML) boundary condition with the Clayton absorbing boundary conditions (first and second orders). The PML boundary condition is implemented in the damping zones of the model, while the Clayton absorbing boundary conditions are applied to the outer boundaries of the damping zones. To improve the absorbing performance of the hybrid absorbing boundary conditions in the frequency domain, we apply the complex coordinate stretching method to the spatial partial derivatives in the Clayton absorbing boundary conditions. To testify the validity of our proposed algorithm, we compare the calculated seismograms with an analytical solution. Numerical tests show the hybrid absorbing boundary condition (PML plus the stretched second-order Clayton absorbing condition) has the best absorbing performance over the other absorbing boundary conditions. In the model tests, we also successfully apply the complex coordinate stretching method to the free surface boundary condition when simulating seismic wave propagation in elastic media with a free surface.

Sign in / Sign up

Export Citation Format

Share Document