Hydrodynamic forces on fixed submerged cylinders

1992 ◽  
Vol 436 (1896) ◽  
pp. 13-32 ◽  
Keyword(s):  
Theoretical Calculations ◽  
Fluid Velocity ◽  
Longitudinal Velocity ◽  
Added Mass ◽  
Offshore Structures ◽  
Rate Of Change ◽  
Circular Cylinders ◽  
Inertia Force ◽  
Wave Loads ◽  
Zonal Harmonic

Wave loads on the cylindrical members of fixed offshore structures are generally calculated by using Morison’s Equation. The inertia force component of this equation is conventionally quoted in a form derived from theoretical calculations for a uniformly accelerating fluid. In this paper the correct form for the inertia force in a general fluid flow is derived from first principles by pressure integration and, independently, from earlier work, by energy arguments. It is shown that, for the thin cylinder limiting case, the transverse force on a circular cylinder is incorrectly given by the conventional approach, in that the product of transverse fluid velocity (in the direction of the required force) with the longitudinal velocity gradient should be added to the water particle acceleration, when computing the added-mass component of the force. Axial divergence, in other words, appears to play the role of a rate-of-change of added mass. It is shown that the mathematical origin of this extra term is the classical three-dimensional flow feature of a ‘zonal harmonic’, which produces a convective fluid acceleration but zero loading. A more elaborate formula is derived for non-circular cylinders, and the nature of point loads occurring at cylinder ends is also discussed.

A Numerical Investigation Into the Value of Added Mass Coefficient for Circular Cylinders

2005 ◽  
Author(s):  
H. Karadeniz
Keyword(s):  
Hydrodynamic Pressure ◽  
Added Mass ◽  
Offshore Structures ◽  
Circular Cylinders ◽  
Element Formulation ◽  
Fluid Structure Interactions ◽  
Shells Of Revolution ◽  
Fluid Structure ◽  
Mass Coefficient ◽  
Added Masses

This paper presents a general axi-symmetrical solid element to be used mainly for the calculation of added masses of water surrounding members of offshore structures, and in general, for multi-purposes such as analyses of shells of revolution, circular beams and plates, axi-symmetrical structures and soils, plane stress/strain problems. Since one element type is used for modeling of different media such as structures, soil and water, the element is very suitable to solve interaction problems. The element is derived parametrically so that changing values of parameters can generate flexible geometrical shapes in exact forms. In the element formulation, a constant shear locking is used to solve bending problems of beam like structures. A similar fluid element is also formulated to analyze fluid-structure interactions and to determine added masses of co-vibrating water. The added mass is calculated from hydrodynamic pressures, which are produced by fluid-structure interactions. In the paper, a special solution algorithm is presented for the coupled eigenvalue problem of the interaction. An analytic calculation of the added mass is also presented for members along which a constant variation of hydrodynamic pressure occurs. A couple of examples are provided to demonstrate applications of the elements explained. Added mass coefficients of offshore structural members (tubular members) are investigated for practical uses.

Effect of Air Fraction on Force Coefficients in Oscillatory Flow

2021 ◽  
Author(s):  
Malene Hovgaard Vested ◽  
Erik Damgaard Christensen
Keyword(s):  
High Speed ◽  
Offshore Structures ◽  
Air Injection ◽  
Wave Loads ◽  
Morison Equation ◽  
Force Coefficients ◽  
Air Content ◽  
Set Up ◽  
High Level ◽  
Spilling Breakers

Abstract The forces on marine and offshore structures are often affected by spilling breakers. The spilling breaker is characterized by a roller of mixed air and water with a forward speed approximately equal to the wave celerity. This high speed in the top of the wave has the potential to induce high wave loads on upper parts of the structures. This study analyzed the effect of the air content on the forces. The analyses used the Morison equation to examine the effect of the percentage of air on the forces. An experimental set-up was developed to include the injection of air into an otherwise calm water body. The air-injection did introduce a high level a turbulence. It was possible to assess the amount of air content in the water for different amounts of air-injection. In the mixture of air and water the force on an oscillating square cylinder was measured for different levels of air-content, — also in the case without air. The measurements indicated that force coefficients for clear water could be use in the Morison equation as long as the density for water was replaced by the density for the mixture of air and water.

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence

1997 ◽  
Vol 347 ◽  
pp. 37-70 ◽  
Author(s):  
J. R. RISTORCELLI
Keyword(s):  
Mach Number ◽  
Large Scale ◽  
Single Point ◽  
Longitudinal Velocity ◽  
Rate Of Change ◽  
Constitutive Relationship ◽  
Compressible Turbulence ◽  
Velocity Correlation ◽  
Turbulent Reynolds Number ◽  
Simple Scaling

The mathematical consequences of a few simple scaling assumptions regarding the effects of compressibility are explored using a singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure–dilatation and dilatational dissipation appearing in single-point moment closures for compressible turbulence are obtained. The results obtained, in as much as they come from the same underlying procedure, represent a unified development for both dilatational covariances. While the results are expressed in the context of a statistical turbulence closure they provide, with very few phenomenological assumptions, an interesting and clear mathematical model for the ‘scalar’ effects of compressibility. For homogeneous turbulence with quasi-normal large scales the expressions derived are – in the small turbulent Mach number squared isotropic limit – exact. The expressions obtained contain constants that have a precise physical significance and are defined in terms of integrals of the longitudinal velocity correlation. The pressure–dilatation covariance is found to be a non-equilibrium phenomenon related to the time rate of change of the kinetic energy and internal energy of the turbulence; it is seen to scale with α2M2t εs [Pk/ε−1] (Sk/εs)2. Implicit in the scaling is a dependence on the square of a gradient Mach number, S[lscr ]/c. A new feature indicated by the analysis is the appearance of the Kolmogorov scaling coefficient, α, suggesting that large-scale quantities embodied in the well-established ε∼u˜3/[lscr ] relationship provide a link to the structural dependence of the effects of compressibility. The expressions for the dilatational dissipation are found to depend on the turbulent Reynolds number and scale as M4t (Sk/εs)4R−1t. The scalings for the pressure–dilatation are found to produce an excellent collapse of the pressure–dilatation data from direct numerical simulation.

Wave Action on Double-Cylinder Structure With Perforated Outer Wall

2003 ◽  
Author(s):  
Yucheng Li ◽  
Lu Sun ◽  
Bin Teng
Keyword(s):  
Numerical Experiments ◽  
Fluid Velocity ◽  
Wave Interaction ◽  
Outer Wall ◽  
Wave Force ◽  
Wave Loads ◽  
Linear Solution ◽  
Perforated Wall ◽  
Physical Experiments ◽  
Run Up

Based on an eigenfunction expansion of velocity potential and a linear model between the pressure difference between two sides of a perforated wall and the fluid velocity inside it, a semi-analytic linear solution has been acquired for wave interaction with a combined cylinder with an solid interior column surrounded by a coaxial exterior column with perforated wall at a section in azimuthal direction. Numerical experiments have been carried out to examine the influences on the wave force and wave run-up on the combined cylinders with perforated wall by the porous coefficient, the size of the perforated section, and the ratio between the radii of the interior and the exterior columns. This paper also presents the comparison between the numerical experiments results and the physical experiments results. It is acceptable of the comparison of these two results. The combined cylinder may reduce both the wave run-up and the wave loads on it through combination of certain parameters.

Model Tests of a Spar-Type Floating Wind Turbine Under Wind/Wave Loads

2015 ◽  
Author(s):  
Fei Duan ◽  
Zhiqiang Hu ◽  
Jin Wang
Keyword(s):  
Wind Turbine ◽  
Model Test ◽  
Wind Wave ◽  
Wave Model ◽  
Offshore Structures ◽  
Model Tests ◽  
Wave Loads ◽  
Scaled Model ◽  
Floating Wind Turbine ◽  
Wave Effects

Wind power has great potential because of its clean and renewable production compared to the traditional power. Most of the present researches for floating wind turbine rely on the hydro-aero-elastic-servo simulation codes and have not been exhaustively validated yet. Thus, model tests are needed and make sense for its high credibility to master the kinetic characters of floating offshore structures. The characters of kinetic responses of the spar-type wind turbine are investigated through model test research technique. This paper describes the methodology for wind/wave model test that carried out at Deepwater Offshore Basin in Shanghai Jiao Tong University at a scale of 1:50. A Spar-type floater was selected to support the wind turbine in this test and the model blade was geometrically scaled down from the original NREL 5 MW reference wind turbine blade. The detail of the scaled model of wind turbine and the floating supporter, the test set-up configuration, the mooring system, the high-quality wind generator that can create required homogeneous and low turbulence wind, and the instrumentations to capture loads, accelerations and 6 DOF motions are described in detail, respectively. The isolated wind/wave effects and the integrated wind-wave effects on the floating wind turbine are analyzed, according to the test results.

Three-Dimensional CFD Analysis of Two Circular Cylinders Arranged Perpendicular to Each Other

2005 ◽  
Author(s):  
Karl W. Schulz ◽  
Tommy Minyard ◽  
William Barth
Keyword(s):  
Structural Dynamics ◽  
Three Dimensional ◽  
Offshore Structures ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Cfd Analysis ◽  
Flow Conditions ◽  
Tandem Cylinders ◽  
Dynamics Response ◽  
The University

A three-dimensional numerical method combining solution of the incompressible Reynolds Averaged Navier-Stokes (RANS) equations with a rigid body structural dynamics response has been developed previously to aid in the prediction of the loads and motions of offshore structures. In this paper, we use the tool to compute the hydrodynamic flow around two tandem cylinders oriented perpendicularly to each other. The flow conditions and gap distances between the cylinders are chosen to match a set of water tunnel experiments carried out at the University of Queensland. Comparisons of Strouhal frequencies and example flowfield visualizations are presented between the experimental measurements and associated CFD results.

Interactions Between Vertical Structures in Waves

2005 ◽  
Author(s):  
J. Wang ◽  
S. M. Calisal ◽  
W. Qiu
Keyword(s):  
Energy Conversion ◽  
Wave Energy ◽  
Numerical Solutions ◽  
Theoretical Calculations ◽  
Hydrodynamic Interactions ◽  
Circular Cylinders ◽  
Diffraction Effect ◽  
Validation Data ◽  
Conversion System ◽  
Energy Conversion System

This paper presents experimental and theoretical results obtained during the hydrodynamic study of a multi-cylinder system. The main focus of the study was to quantify hydrodynamic interactions between heaving vertical cylinders of a conceptual wave energy conversion system. Several identical circular cylinders representing platforms in an energy conversion system and a parabolic shaped wave reflector were tested in a wave flume tank. Wave heaving forces, radiation and diffraction effects were studied experimentally and numerically. The theoretical calculations were carried out for hydrodynamic coefficients, the radiation and diffraction effect analysis. Experimental results for multi-cylinders were compared with the numerical solutions by a panel-free method in the frequency domain. One main objective of the experimental tests was to calibrate the experimental set up, obtain validation data for numerical calculations. The diffraction studies showed that the hydrodynamic interactions could be constructive or destructive for heave wave forces. The positive magnification of the wave exciting force can be significant if a parabolic shaped reflector is used. It was observed that the wave force magnification and the wave energy absorption depend on incoming wavelength, and the cylinder to wavelength ratio. It has been found in the radiation tests that heave added mass and damping coefficients compare well with the calculations based on potential flow calculations.

scholarly journals Efficient Wave Modeling Using Nonhydrostatic Pressure Distribution and Free Surface Tracking on Fixed Grids

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Hans Bihs ◽  
Arun Kamath ◽  
Ankit Aggarwal ◽  
Csaba Pakozdi
Keyword(s):  
Stokes Equations ◽  
Wave Model ◽  
Offshore Structures ◽  
3D Simulation ◽  
Wave Forces ◽  
Wave Loads ◽  
Two Phase ◽  
New Approach ◽  
2D Simulation ◽  
Numerical Wave

For the estimation of wave loads on offshore structures, relevant extreme wave events need to be identified. In order to achieve this, long-term wave simulations of relatively large scales need to be performed. Computational fluid dynamics (CFD) based numerical wave tanks with an interface capturing two-phase flow approach typically require too large computational resources. In this paper, a three-dimensional (3D) nonhydrostatic wave model is presented, which solves the Navier–Stokes equations and employs an interface tracking method based on the continuity of the horizontal velocities along the vertical water column. With this approach, relatively fewer cells are needed in the vicinity of the air–water interface compared to CFD-based numerical wave tanks. The numerical model solves the governing equations on a rectilinear grid, which allows for the employment of high-order finite differences. The capabilities of the new wave model are presented by comparing the wave propagation in the tank with the CFD approach in a two-dimensional (2D) simulation. Further, a 3D simulation is carried out to determine the wave forces on a vertical cylinder. The calculated wave forces using the new approach are compared to those obtained using the CFD approach and experimental data. It is seen that the new approach provides a similar accuracy to that from the CFD approach while providing a large reduction in the time taken for the simulation. The gain is calculated to be about 4.5 for the 2D simulation and about 7.1 for the 3D simulation.

Nonlinear Wave Loads Acting on Cylinder Array Slowly Oscillating in Diffraction and Radiation Wave Fields

2005 ◽  
Author(s):  
Weiguang Bao ◽  
Takeshi Kinoshita ◽  
Motoki Yoshida
Keyword(s):  
Nonlinear Wave ◽  
Perturbation Expansion ◽  
Low Frequency ◽  
Added Mass ◽  
Wave Loads ◽  
Wave Fields ◽  
Wave Drift ◽  
Cylinder Array ◽  
Radiation Wave ◽  
Low Frequency Motion

The problem of a circular cylinder array slowly oscillating in both diffraction and radiation wave fields is considered in the present work. As a result of the interaction between the wave fields and the low-frequency motion, nonlinear wave loads may be separated into the so-called wave-drift added mass and damping. They are force components proportional to the square of the wave amplitude but in phase of the acceleration and velocity of the low-frequency motion respectively. The frequency of the slow oscillation is assumed to be much smaller than the wave frequency. Perturbation expansion based on two time scales and two small parameters is performed to the order to include the effects of the acceleration of the low-frequency motion. Solutions to these higher order potentials are suggested in the present work. Wave loads including the wave drift added mass and damping are evaluated by the integration of the hydrodynamic pressure over the instantaneous wetted body surface.

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