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C.J. Garrison

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Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 5–8, 1980

Paper Number: OTC-3760-MS

Abstract

ABSTRACT This paper presents a review of wave force predictions for rough and smooth cylinders. The Morison equation and some basic results for the drag and inertia coefficients in laboratory and ocean tests are reviewed. New results for rough cylinders at large Reynolds number are also presented. INTRODUCTION The correct values of the drag' and inertia coefficients to use in conjunction with Morison's equation for prediction of the design loading of offshore structures have been a topic of considerable interest and discussion for at least three decades. Many experiments have been conducted both in the ocean and in laboratory wave channels but with limited success. Test results have frequently shown rather extreme scatter, leaving the designer in the unfortunate position of possibly grossly over designing the structure or using coefficients which are less than the range of reported values. At the present time the state of knowledge remains incomplete although considerable progress has been made, particularly in the last decade. In this paper an attempt is made to review the Morison equation and discuss the results of various experiments regarding the coefficients of drag and inertia in relation to wave force calculations. particular emphasis is placed on recent results obtained from basic experiments in oscillatory, rectilinear flow past smooth and rough cylinders and the correlation of these results with results from ocean test platforms. MORISON'S EQUATION The so-called Morison's equation was apparently introduced by Morison et al. 1 in 1950 as a semi-intuitive expression for predicting the force exerted on a body in a viscous fluid under unsteady flow conditions. Since that time the general validity of the expression and, particularly, the validity in relation to wave-induced loads on circular cylinders has been questioned. Nonetheless, during the three decade interim since 1950 a more appropriate formula has not been found. Some insight into the appropriateness of Morison's equation can be gained through a dimensional analysis. For the sake of simplicity consider the force exerted on a circular cylinder placed in a simple rectilinear, harmonically oscillating flow. The instantaneous force is denoted by F and the cylinder is characterized by its diameter and roughness height, d and k, respectively. The pertinent fluid properties are its density, p, and kinematic viscosity, v. If the fluid motion is sinusoidal it may be completely characterized by the amplitude, a, and period, T. Thus, the instantaneous force per unit length of cylinder can be expressed as (Available in full paper)

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 1–4, 1977

Paper Number: OTC-2794-MS

Abstract

ABSTRACT This paper deals with the wave loading of several North Sea gravity platforms. A procedure based on diffraction theory and the Morison equation is outlined for determination of wave loads on practical platform configurations. The procedure is applied to several platforms proposed for the North Sea and calculations are compared with model test results. Also, a simplified diffraction theory which uses an approximate Green's function is compared with the general diffraction theory. INTRODUCTION Several papers, [Refs. 1–10], have reported on the theory and application of linear diffraction theory applied to the calculations of loads on large displacement structures. However, most of the reported comparisons of the theory with experiment deal with simple configurations such as cylinders and spheres without appendages. One of the purposes of this paper, therefore, is to demonstrate the application of diffraction theory to practical North Sea platform configurations which are composed of caissons with superstructures composed of smaller diameter members. The caisson is treated by use of diffraction theory using a source distribution over the immersed surface of the caisson and the superstructure loads are computed by use of the Morison equation. Suitable methods of coupling the source distribution and the superstructure are discussed and theoretical calculations are compared with wave channel test results for several proposed North Sea platforms. A second purpose of this paper is to examine the use of an approximate and much simpler Green's function (or source potential) which is valid in the limit as the wave period approaches infinity. Comparison of wave force results computed by use of the Green's function valid for arbitrary period and the asymptotic form indicates that the asymptotic form produces results which are valid for many practical situations. In fact, most typical North Sea platforms satisfy the criterion for application of the approximate Green's function. The advantage of the use of such a source potential is that it is much simpler than the general form valid for arbitrary period and, accordingly, requires considerably less computer time for numerical evaluations. REVIEW OF DIFFRACTION THEORY The problem statement which we wish to review is: To determine the pressures and resulting net force on a rigid immersed surface described by S(x,y,z)=0 due to a regular wave. The definition sketch indicating a rigid immersed surface in water of depth h is shown in Figure 1. The assumption of linearity (small amplitude wave motion) allows the total velocity potential associated with both the incident wave and the scattered wave to be represented as the sum, (Mathematical equation available in full paper) where ? w denotes the complex potential associated with the incident wave, and ? s denotes the complex scattering potential.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 5–7, 1974

Paper Number: OTC-2067-MS

Abstract

ABSTRACT A numerical scheme is developed utilizing a Green's function and digital computer calculations to determine the excitation forces and moments as well as added mass and damping coefficients for floating bodies. The analysis is carried out within the framework of linear theory for bodies of arbitrary shape, either submerged or semi-submerged, in water of finite depth. The calculated hydrodynamic coefficients associated with both the wave excitation and response of the body are utilized in conjunction with the equations of motion in order to determine the response of a free-floating body to wave excitation. In addition, the steady-state drift force and uplift force are discussed for the case of free-floating and fixed bodies. Numerical results are presented for several configurations. INTRODUCTION The usual procedure for the placement of large concrete gravity structures involves construction in dry dock, floatation and towing of the structure to the deployment site followed by sink age through controlled ballasting. During the towing and sinking stages it is necessary to know the response of the structure to wave excitation. This is particularly true during sinking when the structure approaches and ventually sits on the bottom. There is also another interesting feature of the floating body problem discussed herein. As waves interact with a floating structure, not only a periodic excitation force results, but in addition, the wave interaction results in a steady-state or time-independent horizontal force, vertical force and pitching moment. The steady-state horizontal force is usually referred to as drift force in ship hydrodynamics and generally causes an unrestrained floating body to drift in the direction of wave propagation. The time-independent uplift force may be important during the sinking of large structures since additional ballast beyond that needed for the calm water case must be provided for in order to sink the structure. This effect is particularly important in the case of structures which have small or no stabilizing waterline areas. In the past the primary application of research relevant to the wave induced response of floating bodies has been in the area of surface ships. In view of the elongated shape of typical ships, a two-dimensional hydrodynamic analysis (strip theory) is generally employed. The assumption of infinite depth is also common to most of the published work in ship hydrodynamics. However, large ocean gravity structures are generally not constructed in the form of elongated bodies as in the case of ships and, therefore, strip theory is invalid, making a truly three-dimensional analysis of the fluid/structure necessary. Moreover, during the sinking operation the large object approaches and eventually rests on the ocean floor, and consequently, the bottom proximity or finite depth effect is also of interest. These features of the floating body problem have received little attention in the past by naval architects. Several papers have treated the hydrodynamic coefficients for the two-dimensional problem associated with cylinders oscillating in water of infinite depth. Examples include those of Russell, Porter, Vogt?s, and Pauling and Richardson4 Equivalent data for three -dimensional shapes is much more limited, but Havelock5 has theoretically determined added mass and damping coefficients for a floating sphere, and ellipsoidal bodies oscillating on the free surface have been considered by Kim 6 . In a later paper Kim 7 calculated the heave, surge, and pitch response for the same scherzo idol bodies to wave excitation. Barakat 8 also treated the vertical motion of a sphere as induced

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 30–May 2, 1972

Paper Number: OTC-1554-MS

Abstract

Abstract When bottom mounted structures of large displacement are immersed in the sea, earthquake induced hydrodynamic loads may become important design factors. Specifically, as the earth oscillates, a bottom mounted structure is forced to describe time dependent motion in an otherwise still fluid. As a result, hydrodynamic loads in addition to the inertial loads of the structure itself are induced. In this paper, a theoretical approach to the calculation of these hydrodynamic loads is outlined and numerical results are presented for several submerged configurations. Practical geometries considered include a submerged oil storage tank configuration and a conical configuration as has been proposed for offshore drilling rig designs for deployment in the Arctic. Also, computations were carried out for a sphere and vertical circular cylinder and various comparisons with classical results are made. Numerical results for these submerged structures are presented in the form of a dimensionless hydrodynamic load parameter or added mass coefficient. Results corresponding to a number of different water depths are presented to show the rather sizable effect of the relative water depth on the hydrodynamic force. It is shown that for typical earthquake frequencies, the effect of the free water surface is to reduce the hydrodynamic loads in comparison to the corresponding infinite depth values. Experimental results obtained by vibration testing are presented for a submerged sphere and a vertical circular cylinder. These results show excellent agreement with the theoretical results. Introduction Principal attention in earthquake engineering has been given to the generation of tsunami waves, the shoreline run-up and damage caused by these waves, as well as the damage to dry land structures caused by strong ground motion. With the increased deployment of large submerged structures, an additional facet of this important problem has come to light. Namely, if a large bottom mounted structure submerged in the ocean is excited by oscillatory ground motion, hydrodynamic loads in addition to its own inertia forces come into play. As the structure is caused to move through the water, hydrodynamic forces which are dependent upon the size and shape of the structure as well as the water depth and frequency of oscillation arise. On account of the large density of water, these forces are often quite large and have considerable influence on the structural design. When an object is accelerated through a fluid there are, in general, two types of forces that are recognized, one being a drag component and a second, the inertial component. The nature of the flow produced by the time dependent motion of the immersed rigid object and the relative contribution of these two components of force is generally considered to be strongly dependent on the amplitude of the relative fluid motion in comparison to the characteristic lineal dimension of the object. For example, Keulegan and Carpenter [1] found that, for harmonic motion of the fluid past a fixed circular cylinder, major flow separation did not occur and the forces were well represented by potential flow values provided the amplitude of the motion was less than about a half diameter.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 30–May 2, 1972

Paper Number: OTC-1555-MS

Abstract

Abstract Wave forces exerted on large submerged bottom-mounted structures is a topic of current interest. Particularly in the design of submerged oil-storage vessels, where the structure generally has limited net negative buoyancy, the wave forces are of considerable importance in the design. This paper deals with the interaction of a train of regular surface waves with a large submerged oil-storage tank resting on the ocean floor in water of finite depth. Linear wave theory is used to describe the incident wave, and viscous effects are neglected on the basis that the size of the submerged object is large compared to the height of the incident wave. The problem is formulated in the form of a potential flow problem, and to solve this problem, point wave sources are distributed over the immersed surface. The strengths of these sources are then adjusted to satisfy the no-flow condition at the surface of the object. Results from a computer program based on these theoretical concepts are compared with experimental results from wave channel testing. Reference Garrison, C. J. and Chow, P. Y.: "Forces Exerted on a Submerged Oil storage Tank by Surface Waves", J. of the Waterways, Harbor and Coastal Engineering Division, ASCE. Civil Engineering Abstract Diffraction theory for submerged objects of arbitrary shape is applied to calculate the wave forces acting on a submerged oil-storage tank. The computer-generated numerical results for both the horizontal and vertical force components are compared with experimental results. Introduction A new concept in the production of oil offshore involves the use of large submerged storage tanks. Oil is stored in the tanks during production at the offshore site and at certain intervals the accumulated oil is loaded aboard a tanker. Since the tanks used in this concept are very large, relatively light when submerged, and usually deployed in relatively shallow water, the forces induced by surface waves are of considerable importance in their design. It is, therefore, the intent of this paper to describe a basic experimental and theoretical study of the horizontal and vertical components of the forces induced by surface waves on certain practical storage-tank configurations. It is generally accepted that the Morison equation 1 is a valid approximation for the calculation of wave forces acting on objects whose lineal dimensions are small in comparison to the wave length of the incident wave. This equation, which involves both a drag and inertial component of force, assumes that the object is so small as not to disturb the incident wave. However, as the size of the object in comparison to the incident wave length increases, scattering occurs and the Morison equation becomes invalid. Moreover, the object may not be deeply submerged and the effect of the free surface, also disregarded in the Morison equation, may be important. Thus, in the case of large submerged objects the simplified theory based on the Morison equation becomes invalid, and a more basic approach that includes these additional factors must be taken.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 21–23, 1970

Paper Number: OTC-1278-MS

Abstract

ABSTRACT Theoretical and experimental results for gravity wave interaction with a hemispherical object resting on the ocean floor are presented. The hydrodynamic problem of wave interaction with large submerged objects such as submerged oil storage tanks is approached by means of diffraction theory. Numerical results for horizontal and vertical force coefficients and corresponding phase shift angles are presented. These results are compared with results, obtained from a simpler approach to show where the effects due to the proximity of the free surface and the relative size of the object become significant. Also, corresponding experimental results are presented for comparison with the theory. INTRODUCTION In recent years ever increasing attention is being given to the exploitation of natural resources in the coastal waters of the oceans. Such exploitation is predicated at least partly on the ability to design and build large scale structures offshore. For this purpose, it is necessary to have a better understanding of the forces induced by surface gravity waves on structures such as large submerged oil storage tanks. This paper contributes towards such understanding by taking a basic approach to the problem of wave interaction with a large hemispherical tank. Although the shape considered is somewhat idealized, it is representative of practical shapes and the results provide some insight and understanding into the fundamental problem. Wave forces acting on such objects as piles 1 , submerged pipe lines 2 , or other shapes such as small spheres 3 , have been the subject of investigation for nearly two decades. A common feature of all of these studies is the condition that the object size is small compared to the length of the incident wave. This condition, which prevails in most practical applications, simplifies the general problem of wave/structure interaction in that it allows the assumption that the presence of the object has no effect on the incident wave. Accordingly it may be assumed that the flow field existing at the center of the object extends to infinity and the force can be represented as the sum of two components, drag and inertia. The component due to dragis proportional to the product of a drag coefficient, C d , and the square of the velocity. The component due to inertia, on the other hand, is proportional to the product of the inertia coefficient, (1+C m ), where C m is the added-mass coefficient, and the local fluid acceleration. The, expression for wave force which involves these two terms was originally applied by Morison, Johnson and O'Brien 1 in the study of wave forces on piles and; consequently, has come to be known as the "Morison equation". However, as the size of the object in relation to the wave length increases, the simplifying assumptions upon which the Morison equation is based are eventually violated and this simple relationship no longer yields valid results.