Study of Hydrodynamic Forces on Multiple Cylinders in Waves

Study of hydrodynamic Forces on Multiple Cylinders in WavesIntroductionIn the recent years, there know been increase in demand of production in the onshore industry. The extensive market scale of inshore structure business in c oer and gas production attracts interest for investors. Offshore structures atomic number 18 stationary structures located in the marine environment for production of natural re character references such as wind turbine for generating electricity, FPSO (Floating Production Storage Offload) for crude oil extraction and bore for drillships. These offshore structures fuel be either fixed or uncaringly blow. Floating offshore structures/platforms departing be use mooring strategy or dynamic attitudeing rule to float and hold its position in place. M any(prenominal) challenges atomic number 18 faced to withstand the position of the offshore structures due to oceankeeping and seethe load difficultys.As technology advance over the years, new imp lications and investigations are being carried out for offshore structures to to deal with seakeeping and oscillate load troubles. The implication of hydrodynamic lodge acting on an offshore structure became important due to various roam tons and fundamental interactions might yarn-dye the results of hydrodynamic absorbs greatly. The hydrodynamic forces determine how structures float with varying wave frequencies, wave height and etc. Large offshore structures such as semi-submersibles, offshore wind turbines and SPAR are often being investigated to correct their efficiencies by changing their shapes or dimensions.Large offshore cylindrical structures would affect hydrodynamic results due to their wave diffraction and light beam forces. Therefore, in this literature review, investigations of hydrodynamic forces on multiple cylinders are being studied. In pitch to rede how the hydrodynamic results vary, vagabond bodies with varying distance are being located in ideal roving, where hydrodynamic interactions will ca custom the influence by the scattered waves and the wave load will differ greatly by the presence of the neighbouring cylinders. Thus, to obtain accurate results, these hydrodynamic interactions are investigated from suppositional predictions, parcel mannikin analysis and model testing.The development of computer with memory skill and computational speed increases with the advance in technology. The use of these software simulation analysis helps to analyse the wave interactions amid multiple floating bodies in an ideal fluid. The software is dependant on the development of hydrodynamic theories. By using linear wave say-so theory, the diffraction and ray forces could be calculated.hydrodynamic Interaction phenomenaStudies of hydrodynamic interactions of multiple bodies have been on going over the past few decades. Hydrodynamic interaction created are due to wave actions the presence of neighbouring structures. A free floating consistency may escort six DOF (Degree of Freedom) due to surrounding condition, where ternion are translations (Surge, sway and heave) and three are whirlings (Roll, pitch and yaw). Vertical and longitudinal motions are the primary motions which are often experience by offshore structures.1 The interaction phenomena is due to diffraction and actinotherapy forces acting on the structures and forces created by the structures. The hurrying circumstancess and the motion of each embody merchant ship be obtain by the integrating of equation of motion.The interaction phenomena between two or more floating structures plays important billet on the performance of floating structure systems. It depends on the sepetration distance between the floating bodies and also on the direction of diminish with respect to the centerline of two floating bodies.2 This phenomena can be investigated by using twain hypothetic and experimentally(Model Test). For experimental, using a full scale model tests are desir equal but there are limitations due to controlled conditions and the high toll of production. Therefore, the need of associated computation tools for analysing these hydrodynamic forces to attain fast and accurate results. The complexity of multiple bodies solution increases with the amount of elements.(Research_3) Thus, the use of numerical method is passing recommended in this studies.http//www.ias.ac.in/sadhana/Pdf2004Dec/Pe1236.pdf 1http//www.dtic.mil/dtic/tr/fulltext/u2/a254627.pdf 2Potential TheoryThe knowledge of motion and wave bring forth forces of offshore mainly involves the structural design and its operation. Offshore structures in sea environment usually encounter environmental loads such as gravity, waves, wind and current. These are the basic information needed to evaluate the interaction of structures through the use of potential theory.(G. Moe, 1996)Potential theory can use to find out the general aspect of fluid flow problems in conjuncti on with Laplace equation. To revenge the solution of the Laplace equations, b put conditions of the fluid are set. Hydrodynamic forces in waves consist of radiation and diffraction forces where speeding potential is the key portion to satisfy the Laplace equation.Radiation and Diffraction occupationHydrodynamic forces is made up of diffraction and radiation forces. These forces includes the 6 degree of freedom that arises from the interaction of linear waves against any floating structure. In addition, these forces will provide information of hydrodynamic properties of floating structures, such as damping coefficient,added mass and wave excitation forces. The fluid must be assumed to be inviscid, incompressible and irrotational. Currently, there have been numerous theoretical and numerical studies on these problems. As the technology advances, researchers have obtained significant results on the phenomena, which made the study for these problems, such as structure and wave inter actions, perceptual constancy of floating structures aon going research.Diffraction ForceDiffraction force is the shove forces acting near the each structure, but due to multiple bodies and interaction of several bodies, the aspersion will affect the results of casualty wave.For free open problems with the Laplace equation as the governing equation, a first order or a second-order boundary condition can be obtain using a linearized free surface boundary conditionRadiation Force leaping Conditions presidency EquationThe motion response of a structure will suffice the fluid to oscillate, hence creating ram compasss in the fluid. In order to capture the motion response and the surrounding press champaigns, pep pill potential will be imposed. In addition, there are boundary conditions critition to be met. Drag forces are not being considered in the radiation and diffraction problems as it only occurs in slender body phenomena.With the assumption of having the structure plac ing in an ideal fluid with correct forward speed. In an ideal fluid condition, the fluid is irrotational and incompressible. The radiation condition should also be satisfied as it is to ensure that the waves propagate away from the structure. From the potential flow theory, it is made cognise that the amphetamine potential must satisfy the Laplace equations. Thus, the 3 boundary conditions constitute below must be satisfied.Body surfaceThe normal component of the fluid velocity is equal to the normal component of the heave force velocitySeafloorThe normal component of the fluid velocity equal to vigourWater surfaceThe fluid pressure is equal to the atmospheric pressure and fluid particles will always remain on the free-surface. Pressure will be constant across the free surface.These equations mention below will evidence the governing equation imposed on radiation and diffraction problems.(Page 44)The velocity potential, along each component(x, y and z) satisfies the Laplace eq uation in the fluid domain,The free-surface condition,Boundary condition on the sea floor,Boundary condition on body surface,Where k is depends on the motion (six DOF) that the body surface is expose to and nis the social unit vector normal to the body surface.Solving Boundary Value ProblemThe boundary conditions are all set in conjunction with velocity potential. The expression of linear hydrodynamic forces is derived from direct integration of the fluid pressure over the boundary of a body. By using the Greens theorem, part of the forces can be obtained with the declaration the scattering potential. Defining the field point at any point and the origination point for circulation, rotation and vorticity, the Green funtion will be presented in the form,WhereEquation 7 expresses the generator potential as a summation of a source in the exhaustible fluid and an image source above the free surface condition where . This shows that there will at .Equation 8 expresses the source potential is a summation of a source in unconditioned fluid and an image sink above free surface when . This satisfy the free surface condition where velocity potential equal zero on . Therefore, the solution of the velocity potential for a problem (e.g. force heave) can be written asThis source function is wedded for infinite water depth problem where is called the Green function.By using the Bernoullis equation, the total pressure could be fully derived with the use of velocity potential and the body motion amplitudes. Therefore, linear forces and moments are obtain from,We can consider component potentials such that the summation of hydrodynamic forces and moments areWhere it is flare into two components the wave excitation force due to diffraction and forces due to radiation force(In terms of added mass and damping coefficients).Given we want to find the force at mode j. The linear forces, also known as the first order wave excitation force, the force for mode j is denote as From Greens theorem, applying it to and a component of the radiation potential, we haveIt is show that those integrals on the seabed, over the free surface and at the far field disappeared due to the boundary conditions for and on these surfaces. Therefore, upon substituting the equation of boundary conditions, the Haskind likeness follows in the form ofBy using the equation of motion, the diffraction and radiation problem will be shed light ond.Calculation of Hydrodynamic forcesThe boundary value problem is solve, therefore the forces and moments can be evaluate. Panel method is use to solve the boundary value problem which is based on potential theory. Assumptions such that the wave amplitudes of the fluid is small as compared to the cross-sectional dimensions of the body are made. The tableling of the structure is done by plane quadrilateral elements in three dimensional problems.http//www.academia.edu/6937922/Computation_of_Ship_Hydrodynamic_Interaction_Forces_in_Restricte d_Waters_using_Potential_TheoryThe solution procedure can be generalize to any modes of motion, where added mass and damping matrix could be found. Solving the diffraction problem can be done by using the boundary condition (equation 5) where is the incident wave potential. From these solutions, we are able to derive the wave excitation loads such as wave excitation forces (surge, sway, heave) and wave excitation moments (roll, pitch, yaw). Therefore, solving the equation of motion and calculating the flow details such as hydrodynamic forces, by using the expression for velocity potential in terms of a three-dimensional source distribution.Past Researches OverviewWAMITWamit software is a diffraction/radiation panel political program developed to analyse the linear interaction of surface waves with several different types of submerged and floating structures. For this analysis of interaction, WAMIT uses a three-dimensional panel method and also quest some theoretical method. By u sing this software, it can help to define the conditions of the interactions such as, finite or infinite water depth, structures location on the free surface, attach on the seabed or submerged and whether the structures are fixed or freely floating with the motion of six degree of freedom.The fluid flow is assumed to be ideal and cartridge clip harmonic. WAMIT is able to deal with both first order and linearize analysis which includes second order forces. WAMIT is able to focus on the hydrodynamic interaction of multiple body with any restriction of condition of fluid environment. The use of integral equation obtained by Greens theorem will help solve the diffraction and radiation velocity potentials on the body wetted surface.WAMIT will be able to evaluate the following quantitiesHydrostatic coefficientsAdded-mass and damping coefficients for all modesWave excitation forces and moments using the Haskind relations, or without delay by pressure integration from the solutions of di ffraction or scattering problems.Motion amplitudes and phases for a freely floating bodyForces restraining a body which is freely floating in some but not all modesHydrodynamic pressure and fluid velocity on the body surface/fluid domainFree-surface elevationAll component of the drift force and moment by momentum integration over a control surfacehorizontal drift forces and mean yaw moment by momentum integration in the fieldAll components of the drift force and moment by local pressure integration over body surface go force and moment in bidirectional wavesTheoretical MethodThe method use by WAMIT will be a panel program designed to solve boundary-value problem for the interaction of waves phenomena with the pre-defining the bodies in finite or infinite water depth. Viscosity will not be considered. The time harmonic solutions are being solved for a given loaded state incident wave field which is assumed to be stand for by a superposition of a particular frequency components in t he absence of the body. The boundary value problem will be apply in conjunction with the integral equation using Greens theorem. These integral equation will be solved by panel method for the unknown velocity potential or strength source of the body surface. These integral equations of theoretical method could be found in .