Bruce J. Muga

Particle-in-Cell Method

In Chapter Particle-in-Cell Method, it was stated that “if the exact distribution of \(\vec v\) were known everywhere in the control volume surrounding the cylinder, then the integrals of the momentum theorem, and thus FT could be evaluated without the need for the experimental constants.” As a natural extension of this statement, it should be pointed out that there is a way for determining what amounts to the “exact distrubution” of “ \(\vec v\). This approach, although not widely used, for a number of reasons which will be pointed out later, is the subject of this chapter. The original method (known as Particle-In-Cell (PIC)) was developed by Harlow (1955) and by Evans and Harlow (1957), and has been greatly extended by Welch, Harlow, Shannon and Daly (1966). The latter treatment is known as the Marker and Cell (MAC) method. For a complete and thorough discussion, the reader should consult the original references. However, because of its importance and potential application to a wide range of problems involving ocean structures, a brief review of the method is given herein.

Wave Forces Induced on Very Large Crude Carriers

Describes a theoretical method for predicting the forces induced by irregular waves on very large crude carriers, in which the hull section is modeled as a prismatic elliptic cylinder. Diffraction of the wave around the elliptic cylinder is taken into account and results are presented for surge and sway force and yaw moment for incident wave angles from 0 degree (head-on) to 90 degrees (broadside-on) at several increments and water depth to draft ratios. Thus, the effect of underkeel clearance is taken into account. In order to verify the method, an experimental study utilizing the captive model technique was carried out at the Netherlands Ship Model Test Basin (NSMB). In this study, forces (and moments) in the surge, sway and yaw directions were measured as the real tanker shape models were subjected to irregular waves incident from 0 degree to 90 degrees at several values. The comparisons, which are presented in terms of the non-dimensional force (or moment) ratios, are considered to be excellent. The procedure described herein can be employed to synthesize external loading histories due to irregular waves acting on very large crude carriers of specified dimensions for a variety of incident wave angles and water depth/draft ratios. The technique can also be employed to derive added mass and damping coefficient functions for the specified tanker. The procedure is an intermediate step in the process of determining the behaviorial response of the moored vessel. The vessel can be considered as moored to conventional piers in relatively protected areas or to sea islands or sea berths in exposed locations. The combination of low computational cost and reasonable accuracy makes it an ideal procedure to employ for a number of engineering applications.

Evaluation Of Drift Force Computation Methods.

Moored-ship and/or platform system designers are often faced with the problem of deciding between different drift force computation methods. This paper is intended to assist in this decision making by providing a comparative evaluation of the two major categories of computation methods. The methods for calculating drift forces (second order) on vessels fall into two (2) major categories. In one method, the problem is reduced to the computation of the potential far away from the vessel. This is known as the far-field approximation as described and developed by Maruo (1960), Newman (1967) and Faltinsen and Michelsen (1974). In the other method, known as the near-field or close-in approximation, the integration is performed directly on the vessel hull as developed by Salvesen (1974) and Pinkster and Van Oortmerssen (1977). Following the approach of the first mentioned category, a computer program has been prepared which calculates drift forces and moments on vessels of arbitrary hull geometry. No assumptions regarding the hull geometry are included in the underlying theory. The second category, however, includes some mild slenderness assumptions (Salvesen (1974)). Based on the drift force program outlined in this paper, some selected results for various hull geometries are presented. These results are compared, where applicable, with existing results obtained from application of the near-field method. These comparisons permit: (a) determination of the range of compatibility of the two methods, and (b) the influence of hull geometry on the applicability of the near-field approximation. Moored-ship system designers thus have a systematic procedure from which drift force calculations can be evaluated.

The One Degree of Freedom and Continuous Beam Models

This chapter deals with the statistics for the vibration responses of a one degree of freedom model and also a simple beam model. In the first case, a tall offshore structure fixed to the ocean floor is assumed to vibrate in its first mode only when subjected to random wave forces. In the second case, a uniform, horizontal cross beam on a fixed ocean structure is assumed to vibrate in all modes under random forces. In each case, the statistical vibration analysis follows a definite pattern. Since the steps are rather lengthy, it is often easy to lose sight of the design goals of such an analysis. These steps to be followed are summarized: 1. Set up a reasonable mathematical model of the structure and formulate the governing equations of motion for this model. 2. Calculate the complex frequency response function where the applied force is harmonic« Deduce the response to a nonharmon-ic force. 3 Calculate the unit impulse response function where the applied force is step pulse. From this« deduce the response to a general type of force input. 4. Assume that the random input force is stationary and ergodic, and use the results of steps 2 and 3 to calculate the system’s responses.

Fluid-Induced Forces

The traditional method of determining the forces induced on structural elements has been to consider the force to be due to linear combination of an inertial contribution and a drag contribution, or FT = FI + FD Each of these time-varying components has then been formulated in terms of (i) geometrical properties of the structure, (ii) fluid properties describing the flow field and (iii) some “variable constants” which have been determined empirically. A great deal of effort has been devoted to an improved description of the flow field as discussed in Part I of this text and perhaps even more effort has been expended on correlations of the empirically determined “variable constants”. The purpose of this chapter is to describe and illustrate how these constants may be estimated and to indicate to what extent these predictions may be in error. To a large degree, these empirically determined constants exhibit a good deal of scatter in the data as published in the pertinent literature but usually (there are some notable exceptions) the scatter is not accounted for except in terms of experimental error in the acquisition of data.

Wave Forecasting and Hindcasting

The purpose of this chapter is not that of providing instruction on how to make wave forecasts and/or hindcasts, but rather to illustrate the basic concepts and procedures which are employed by-specialists who regularly furnish forecasting services. The objective here is that of providing sufficient insight into the mechanics of wave forecasting and the underlying premises so that information contained in the forecast and/or hindcast can be used to maximum advantage.

A Review of Some Statistical Concepts

The forces measured on existing ocean structures have rarely had simple time histories• As a result, the structural responses such as deflection, strain, and acceleration to these “random” type forces do not have simple time histories either. Typical data for either the time behavior of a force or the response to that force at a point on an ocean structure might look like the trace shown in Fig. 9.1, where, for generality, the ordinate is designated as z = z(t). At first glance, such a trace appears to have no definite frequency of fluctuation, although there appears to the an upper bound for z. If z were identified as a force, one might be tempted to simply use the upper bound for z and design a structure according to classical static methods. One might ask, the, what if an approximate forcing frequency could be associated with z over a short time period and what if this frequency were tuned to the natural frequwncy of the structure? Could no the structural deflections then exceed the static design conditions? It is the purpose of this chapter to define som of the statistical tools with an engineer can obtain some answers to these questins. Crandall and Mark (1964) elaborate on these ideas.

Surface Gravity Water Waves

Of all of the forces induced by the ocean environment on structures, those due to surface gravity waves are the most important and at the same time the most difficult to determine. The critical evaluations to be made are: (i) what is the likelihood (or probability) of the occurrence of waves of a given magnitude, frequency (of the wave’s, and duration (of this wave intensity) at a given location during the proposed life of the structure; (ii) how can this ‘time history’ of waves be interpreted as a ‘time history’ of forces (or loads) acting on the structure; and, finally, (iii) what are the effects of the force history on the structure (i.e., the behavioral response of the structure). The first question is largely discussed in Chapter v of Part I. Part II is devoted to a discussion of the second question, and Part III treats the final question in a general manner. The behavioral response of specific structures are discussed in Part IV. The remainder of this chapter and the next chapter deal with the description of ocean water gravity waves and various methods of analyzing these waves.

A Specific Nonlinear Application

In this chapter, nonlinear effects are considered. These effects become more pronounced (1) when wave lengths are short compared with a characteristic length of the vessel (length when waves are head-on and beam when waves are beam-on), (2) when vessel is moored in shallow water so that draft/depth ratio is significant and (3) when natural period of mooring assembly is long relative to dominant wave period.

Dynamic Behavior of Materials in an Environment

In the first part of this chapter, mechanical properties of engineering metals and the tests used to characterize them are briefly reviewed. Since standard mechanical tests are generally performed in non-corrosive laboratory environments, the structural designer can use such test results with a degree of confidence only if the structure has corrosion protection. As this protection wears away, the integrity of the exposed structure is severely threatened. In the second part of this chapter, the common mechanisms of these destructive corrosion attacks are summarized. In the third section, materials suitable for both present and future ocean structures are surveyed, and several methods of corrosion protection are discussed. In the last sections, a statistical approach is used to describe the damage accumulation in materials subjected to random type loads and to corrosive environments. Numerical examples are included which illustrate the use of the theory to estimate probable lifetimes of certain ocean structures.