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.

On Shinbrot’s conjecture for the Navier-Stokes equations

1993 ◽  
Vol 440 (1910) ◽  
pp. 537-540 ◽  
Keyword(s):  
Weak Solution ◽  
Fractional Derivatives ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Maximal Theorem

Marvin Shinbrot conjectured that the weak solution of the Navier-Stokes equations possess fractional derivatives in time of any order less than 1/2. In this paper, using the Hardy-Littlewood maximal theorem we prove that the conjecture is true in the two-dimensional case and it is true conditionally in the three-dimensional case.

scholarly journals A two-dimensional numerical and experimental study of piston and sloshing resonance in moonpools with recess

2019 ◽  
Vol 877 ◽  
pp. 142-166 ◽  
Author(s):  
Senthuran Ravinthrakumar ◽  
Trygve Kristiansen ◽  
Bernard Molin ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Numerical Methods ◽  
Eigenfunction Expansion ◽  
Natural Frequencies ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Surface Conditions ◽  
Body Boundary ◽  
Sloshing Mode ◽  
The Mean

The piston and first sloshing modes of two-dimensional moonpools with recess are investigated. Dedicated forced heave experiments are carried out. Different recess lengths are tested from $1/4$ to $1/2$ of the length of the moonpool at the mean waterline. A theoretical model to calculate the natural frequencies is developed based on linearized potential flow theory and eigenfunction expansion. Two numerical methods are implemented: a boundary element method (BEM) and a Navier–Stokes solver (CFD). Both the BEM and CFD have linearized free-surface and body-boundary conditions. As expected, the BEM over-predicts the moonpool response significantly, in particular at the first sloshing mode. The CFD is in general able to predict the maximum moonpool response adequately, both at the piston and first sloshing modes. Both numerical methods fail to predict the Duffing-type behaviour at the first sloshing mode, due to the linearized free-surface conditions. The Duffing behaviour is more pronounced for the largest recess. The main source of damping in the proximity of the first sloshing mode is discussed.

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

The Aerodynamics of Three-Dimensional Vaned Diffusers in Industrial Centrifugal Compressors

2005 ◽  
Author(s):  
Ahmed Abdelwahab
Keyword(s):  
Centrifugal Compressor ◽  
Dynamic Pressure ◽  
Three Dimensional ◽  
Pressure Recovery ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Two Dimensional ◽  
Blade Loading ◽  
Recovery Capacity ◽  
Close Proximity

Vaned diffusers have been used successfully as efficient and compact dynamic pressure recovery devices in industrial centrifugal compressor stages. Typically such diffusers consist of a cascade of two-dimensional blades distributed circumferentially at close proximity to the impeller exit. In this paper three low-solidity diffuser blade geometries are numerically investigated. The first geometry employs variable stagger stacking of similar blade sections along the blade span. The second employs linearly inclined stacking to generate blade lean along the diffuser span. The third geometry employs the conventional two-dimensional low-solidity diffuser geometry with no variable stagger or lean. The variable stagger blade arrangement has the potential of better aligning the diffuser leading edges with the highly non-uniform flow leaving the impeller. Both variable stagger and linearly leaned diffuser blade arrangements, however, have the effect of redistributing the blade loading and flow streamlines in the spanwise direction leading to improved efficiency and pressure recovery capacity of the diffuser. In this paper a description of the proposed diffuser geometries is presented. The results of Three-dimensional Navier-Stokes numerical simulations of the three centrifugal compressor arrangements are discussed. Comparisons between the performance of the two and three-dimensional diffuser blade geometries are presented. The comparisons indeed show that the variable stagger and leaned diffusers present an improvement in the diffuser operating range and pressure recovery capacity over the conventional two-dimensional diffuser geometry.

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

Sloshing Effects Accounting for Dynamic Coupling Between Vessel and Tank Liquid Motion

2007 ◽  
Author(s):  
Mirela Zalar ◽  
Louis Diebold ◽  
Eric Baudin ◽  
Jacqueline Henry ◽  
Xiao-Bo Chen
Keyword(s):  
Coupling Effect ◽  
Scale Model ◽  
Small Scale ◽  
Induced Response ◽  
Linear Potential ◽  
Dynamic Coupling ◽  
Liquid Motion ◽  
Violent Behaviour ◽  
Standard Size ◽  
Vessel Motion

Sloshing, a violent behaviour of liquid contents in tanks submitted to the forced vessels’ motion on the sea represents one of the major considerations in LNG vessels design over several past decades. State of the art of sloshing analysis relies on small-scale sloshing model tests supported by extensive developments of CFD computation techniques, commonly studying one isolated tank submitted to the forced motion without their mutual interaction. In reality, wave-induced response of the vessel carrying liquid cargo is affected by internal liquid motion, and consequently, tank liquid flow is altered by the vessel motion in return. An efficient numerical model for dynamic coupling between motions exerted by tank liquid (sloshing) and rigid body motions of the vessel (seakeeping) was developed in Bureau Veritas, formulated under the assumptions of linear potential theory in frequency domain. As already experienced with anti-rolling tanks, strong coupling effect is perceived on the first order transverse motions. However, consequences of coupled motions on sloshing loads have not been explored yet. This paper presents comparative analysis of sloshing effects induced by coupled and non-coupled vessel motion, introduced as the excitation to 6 d.o.f. small-scale model test rig. Possible risk of coupled effects is demonstrated on the example of standard size of LNG carrier operating with partly filled cargo tanks.

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.

scholarly journals A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180642 ◽  
Author(s):  
H. Alemi Ardakani ◽  
T. J. Bridges ◽  
F. Gay-Balmaz ◽  
Y. H. Huang ◽  
C. Tronci
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Variational Principle ◽  
Stream Function ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Euclidean Group ◽  
Fluid Sloshing ◽  
Pressure Boundary Condition ◽  
Vessel Motion

A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler–Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically.

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

A Study of Anti-Rolling Tank on Floating Vessel

2016 ◽  
Author(s):  
Kyung Sung Kim ◽  
Byung Hyuk Lee ◽  
Moo-Hyun Kim ◽  
Jong-Chun Park ◽  
Han Suk Choi
Keyword(s):  
Volterra Series ◽  
Three Dimensional ◽  
Ship Motion ◽  
Simulation Program ◽  
Linear Potential ◽  
Hydrodynamic Coefficients ◽  
Acceleration Data ◽  
Moving Particle ◽  
Vessel Motion ◽  
External Forces

Active anti-rolling tank (ART) is sophisticated equipment on a floating vessel to reduce roll motion for the slender ship-shape vessel. Three-dimensional panel based diffraction and radiation linear potential program employed to obtain hydrodynamic coefficients of floating vessel. For the ship motion, a BEM (Boundary Element Method)-based ship motion program was used and inner sloshing effects were conducted by a particle-based CFD (Computational Fluid Dynamics) program which is the Moving Particle Semi-implicit (MPS). By using panel program, the hydrodynamic coefficients were obtained in frequency domain, and then were converted into time domain ship motion simulation program. In this procedure, time memory effect was considered by Volterra series expansion. The ship motion program and sloshing program was coupled dynamically; inner tank received displacement, velocity and acceleration data from ship motion program and use them for inner tank motion, while the ship motion program was waiting external forces due to sloshing impact loads and inertia forces/moments from sloshing simulation program. Thus, two programs run simultaneously and allowed real time coupling effects of inner sloshing on vessel motion. By comparing response amplitude operator (RAO) of the vessel without anti-rolling tank, it was shown both values have good agreement. And then comparing between vessels with and without anti-rolling tank, it is shown that the effects of ART changed and shift RAOs. Furthermore, by changing the location of ART, location effects of ART were also investigated.

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