Numerical Prediction of Impact-Related Wave Loads on Ships

2006 ◽  
Author(s):  
Thomas E. Schellin ◽  
Ould El Moctar
Keyword(s):  
Stokes Equations ◽  
Numerical Procedure ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Ship Motions ◽  
Normal Velocity ◽  
Wave Loads ◽  
Critical Areas ◽  
Strip Theory ◽  
A Chain

We present a numerical procedure to predict impact-related wave-induced (slamming) loads on ships. The procedure was applied to predict slamming loads on two ships that feature a flared bow with a pronounced bulb, hull shapes typical of modern offshore supply vessels. The procedure used a chain of seakeeping codes. First, a linear Green function panel code computed ship responses in unit amplitude regular waves. Wave frequency and wave heading were systematically varied to cover all possible combinations likely to cause slamming. Regular design waves were selected on the basis of maximum magnitudes of relative normal velocity between ship critical areas and wave, averaged over the critical areas. Second, a nonlinear strip theory seakeeping code determined ship motions under design wave conditions, thereby accounting for the ship’s forward speed, the swell-up of water in finite amplitude waves, as well as the ship’s wake that influences the wave elevation around the ship. Third, these nonlinearly computed ship motions constituted part of the input for a Reynolds-averaged Navier-Stokes equations (RANSE) code that was used to obtain slamming loads. Favourable comparison with available model test data validated the procedure and demonstrated its capability to predict slamming loads suitable for design of ship structures.

Numerical Prediction of Impact-Related Wave Loads on Ships

2006 ◽  
Vol 129 (1) ◽  
pp. 39-47 ◽  
Author(s):  
Thomas E. Schellin ◽  
Ould el Moctar
Keyword(s):  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Ship Motions ◽  
Normal Velocity ◽  
Wave Loads ◽  
Navier Stokes Equations ◽  
Critical Areas ◽  
Strip Theory ◽  
A Chain

We present a numerical procedure to predict impact-related wave-induced (slamming) loads on ships. The procedure was applied to predict slamming loads on two ships that feature a flared bow with a pronounced bulb, hull shapes typical of modern offshore supply vessels. The procedure used a chain of seakeeping codes. First, a linear Green function panel code computed ship responses in unit amplitude regular waves. Ship speed, wave frequency, and wave heading were systematically varied to cover all possible combinations likely to cause slamming. Regular design waves were selected on the basis of maximum magnitudes of relative normal velocity between ship critical areas and wave, averaged over the critical areas. Second, a nonlinear strip theory seakeeping code determined ship motions under design wave conditions, thereby accounting for the nonlinear pressure distribution up to the wave contour and the frequency dependence of the radiation forces (memory effect). Third, these nonlinearly computed ship motions constituted part of the input for a Reynolds-averaged Navier–Stokes equations code that was used to obtain slamming loads. Favorable comparison with available model test data validated the procedure and demonstrated its capability to predict slamming loads suitable for design of ship structures.

A mechanism for bypass transition from localized disturbances in wall-bounded shear flows

1993 ◽  
Vol 250 ◽  
pp. 169-207 ◽  
Author(s):  
Dan S. Henningson ◽  
Anders Lundbladh ◽  
Arne V. Johansson
Keyword(s):  
Shear Flows ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Normal Velocity ◽  
Bypass Transition ◽  
Nonlinear Interactions ◽  
Streamwise Vorticity ◽  
Low Velocity ◽  
Transfer Energy

The linear, nonlinear and breakdown stages in the transition of localized disturbances in plane Poiseuille flow is studied by direct numerical simulations and analysis of the linearized Navier–Stokes equations. Three-dimensionality plays a key role and allows for algebraic growth of the normal vorticity through the linear lift-up mechanism. This growth primarily generates elongated structures in the streamwise direction since it is largest at low streamwise wavenumbers. For finite-amplitude disturbances such structures will be generated essentially independent of the details of the initial disturbance, since the preferred nonlinear interactions transfer energy to low streamwise wavenumbers. The nonlinear interactions also give a decrease in the spanwise scales. For the stronger initial disturbances the streamwise vorticity associated with the slightly inclined streaks was found to roll up into distinct streamwise vortices in the vicinity of which breakdown occurred. The breakdown starts with a local rapid growth of the normal velocity bringing low-speed fluid out from the wall. This phenomenon is similar to the low-velocity spikes previously observed in transition experiments. Soon thereafter a small turbulent spot is formed. This scenario represents a bypass of the regular Tollmien–Schlichting, secondary instability process. The simulations have been carried out with a sufficient spatial resolution to ensure an accurate description of all stages of the breakdown and spot formation processes. The generality of the observed processes is substantiated by use of different types of initial disturbances and by Blasius boundary-layer simulations. The present results point in the direction of universality of the observed transition mechanisms for localized disturbances in wall-bounded shear flows.

Viscosity in Seakeeping

2018 ◽  
Vol Vol 160 (A2) ◽  
Author(s):  
M Pawłowski
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Ship Motions ◽  
Hydrodynamic Coefficients ◽  
Reynolds Stresses ◽  
Navier Stokes Equations ◽  
Inviscid Fluids ◽  
Strip Theory ◽  
Linear Problems

Application of strip theory for the prediction of ship motions in waves relies on sectional hydrodynamic coefficients; i.e. the added mass and damping coefficients. These coefficients apply to linearised problems and are normally computed for inviscid fluids. It is possible to account for viscosity but this cannot be done by the RANS equations, as in linear problems there is no room for turbulence. The hydrodynamic coefficients can include the effect of viscosity but this can be done rightly through the classic Navier–Stokes equations for laminar (non-turbulent) flows. For solving these equations commercial RANS software can be used, assuming no Reynolds stresses.

scholarly journals Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

2013 ◽  
Vol 737 ◽  
pp. 440-465 ◽  
Author(s):  
S. Cherubini ◽  
J.-C. Robinet ◽  
P. De Palma
Keyword(s):  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Control Procedure ◽  
Normal Velocity ◽  
Optimal Control Strategy ◽  
Navier Stokes Equations ◽  
Target Time ◽  
Layer Flow ◽  
Laminar State

AbstractThe present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimization and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier–Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: (i) a wall-normal velocity compensation at small times; (ii) a rotation-counterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account.

VISCOSITY IN SEAKEEPING

2021 ◽  
Vol 160 (A2) ◽  
Author(s):  
M Pawłowski
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Ship Motions ◽  
Hydrodynamic Coefficients ◽  
Reynolds Stresses ◽  
Navier Stokes Equations ◽  
Inviscid Fluids ◽  
Strip Theory ◽  
Linear Problems

Application of strip theory for the prediction of ship motions in waves relies on sectional hydrodynamic coefficients; i.e. the added mass and damping coefficients. These coefficients apply to linearised problems and are normally computed for inviscid fluids. It is possible to account for viscosity but this cannot be done by the RANS equations, as in linear problems there is no room for turbulence. The hydrodynamic coefficients can include the effect of viscosity but this can be done rightly through the classic Navier–Stokes equations for laminar (non-turbulent) flows. For solving these equations commercial RANS software can be used, assuming no Reynolds stresses.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

scholarly journals Numerical simulation of Faraday waves

2009 ◽  
Vol 635 ◽  
pp. 1-26 ◽  
Author(s):  
NICOLAS PÉRINET ◽  
DAMIR JURIC ◽  
LAURETTE S. TUCKERMAN
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Oscillation Period ◽  
Finite Amplitude ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Faraday Waves ◽  
Temporal Behaviour ◽  
Two Fluids ◽  
Front Tracking Method

We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier–Stokes equations are solved using a finite-difference projection method coupled with a front-tracking method for the interface between the two fluids. The critical accelerations and wavenumbers, as well as the temporal behaviour at onset are compared with the results of the linear Floquet analysis of Kumar & Tuckerman (J. Fluid Mech., vol. 279, 1994, p. 49). The finite-amplitude results are compared with the experiments of Kityk et al (Phys. Rev. E, vol. 72, 2005, p. 036209). In particular, we reproduce the detailed spatio-temporal spectrum of both square and hexagonal patterns within experimental uncertainty. We present the first calculations of a three-dimensional velocity field arising from the Faraday instability for a hexagonal pattern as it varies over its oscillation period.

Subsidence of the Ekofisk Platforms: Wave in Deck Impact Study — Various Wave Models and Computational Methods

2002 ◽  
Author(s):  
Bogdan Iwanowski ◽  
Henrik Grigorian ◽  
Ingar Scherf
Keyword(s):  
Computational Methods ◽  
Stokes Equations ◽  
Type Equation ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Wave Loads ◽  
Wave Impact ◽  
Navier Stokes Equations ◽  
Wave Models ◽  
Displacement Approach

Subsidence of the Ekofisk platforms creates several operational challenges. For safety of the platforms, it is of great importance to find the wave impact loads acting on the platforms’ decks. The paper describes how such loads can be computed. Three theoretical wave models are discussed in the paper: the Airy wave, Airy wave modified through Wheeler stretching and the 5th order non-linear Stokes wave. The wave loads for these wave models are computed by various methods. The method based on momentum displacement approach and Morison-type equation developed by Dr. Kaplan is used as a reference point. The loads are also computed through a solution of complete Navier-Stokes equations, with the Volume of Fluid (VOF) method used to trace motion of the fluid’s free surface. Results of different wave models and different computational methods are compared and discussed.

scholarly journals Numerical simulation of complex 3D compressible viscous flows through rotating blade passage

2003 ◽  
pp. 55-82
Author(s):  
M. Despotovic ◽  
Milun Babic ◽  
D. Milovanovic ◽  
Vanja Sustersic
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Convergence Acceleration ◽  
Design Tool ◽  
Navier Stokes ◽  
Internal Flows ◽  
Navier Stokes Equations ◽  
Rotating Blade ◽  
Compressible Viscous Flows

This paper describes a three-dimensional compressible Navier-Stokes code, which has been developed for analysis of turbocompressor blade rows and other internal flows. Despite numerous numerical techniques and statement that Computational Fluid Dynamics has reached state of the art, issues related to successful simulations represent valuable database of how particular tech?nique behave for a specifie problem. This paper deals with rapid numerical method accurate enough to be used as a design tool. The mathematical model is based on System of Favre averaged Navier-Stokes equations that are written in relative frame of reference, which rotates with constant angular velocity around axis of rotation. The governing equations are solved using finite vol?ume method applied on structured grids. The numerical procedure is based on the explicit multistage Runge-Kutta scheme that is coupled with modem numerical procedures for convergence acceleration. To demonstrate the accuracy of the described numer?ical method developed software is applied to numerical analysis of flow through impeller of axial turbocompressor, and obtained results are compared with available experimental data.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

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