Slender cylinders are widely used as a structural element in offshore structures. Oil platforms, jetties and piers are often supported by group of cylinders, which are arranged closely spaced. The Morison equation (Morison et al., 1950) constitutes a simple tool to calculate the wave force on one single cylinder. To what extent the cylinders, which are arranged in a group, affect each other is extensively unclear. As these group interference effects are not considered in the Morison equation there is a lack of a generally accepted formula to calculate the individual forces on cylinders within cylinder groups.
In this student research project the special loading case of breaking waves acting on cylinder groups is examined. Breaking waves developed from wave superposition during a storm may cause great impact loads also in deep water. The investigation of breaking waves leads to the upper bound of possible loads on offshore structures. A closer analysis of the so called impact force and the validation of former assumptions of considering it is not part of this paper. The main focus lies on the interactions between cylinders arranged in groups when a single breaking wave impinges the group or a part of it.
These interactions are investigated based on large-scale experiments, which have been performed in summer 2004 in the Large Wave Flume (GWK) at the Coastal Research Centre (FZK) in Hanover. Fifteen configurations of cylinder groups have been examined, including one configuration with one single cylinder and fourteen configurations of groups up to three cylinders arranged in row or transversely. The single cylinder and one cylinder in each cylinder group are equipped with strain gauges on the top, which measure the bending moments during the tests. These measuring cylinders, in the single arrangement and in the group arrangements, have the same position in the wave flume. Therefore the comparison of the measured bending moments of the single cylinder with those of the cylinder in the group provides information about the influence of the adjacent elements in a cylinder group. The results of the single cylinder test can be taken as a reference for the results of the cylinder group’s tests.
Table of Contents
1. Introduction
2. State of knowledge
2.1. Problem statement and procedure of analysing the state of knowledge
2.2. Flow around a cylinder
2.2.1. Steady flow
2.2.2. Oscillatory flow
2.3. Forces on a single cylinder
2.3.1. Drag force
2.3.2. Mass force
2.3.3. Drag and mass coefficient
2.4. Breaking waves
2.5. Single cylinder in breaking waves
2.6. Cylinder group
2.6.1. Tandem arrangement
2.6.2. Side by side arrangement
2.7. Experimental investigations with cylinder groups
2.8. Summary of existing results
3. Experimental investigation
3.1. Experimental set-up
3.2. Measuring instruments
3.3. Cylinder group configurations
3.4. Testing programme
4. Evaluation of the experimental results
4.1. Wave kinematics
4.1.1. Wave height
4.1.2. Wave celerity
4.1.3. Wave length
4.2. Total force on single cylinder
4.3. Total force on cylinder groups
4.3.1. Tandem arrangement
4.3.2. Side by side arrangement
5. Summary and concluding remarks
Research Objectives and Themes
The primary objective of this research is to examine the interaction effects between slender cylinders within a group subjected to breaking waves, specifically by developing a coefficient C to quantify the change in wave loading on a cylinder within a group compared to a isolated single cylinder.
- Large-scale experimental analysis in the Large Wave Flume (GWK).
- Evaluation of force interactions in tandem and side-by-side cylinder configurations.
- Analysis of the influence of breaking wave conditions and cylinder spacing on loads.
- Comparison of experimental results with established Morison equation models for single cylinders.
Excerpt from the Book
2.6. Cylinder group
The assumption that a cylinder arranged in a group behaves in an identical manner like a single one is only justified if the cylinders are sufficiently apart. Otherwise the interference effects between closed spaced cylinders drastically changes the surrounded flow and produces unexpected forces, pressure distributions and intensifies or suppresses vortex shedding (Zdravkovich, 1977). A cylinder group is defined as a conglomeration of at least two cylinders. Related to the wave direction the cylinders can be arranged staggered or in row. Latter may be aligned as a tandem arrangement, where the cylinders are arranged one behind the other at any longitudinal spacing, or as a side-by-side arrangement, where the cylinders face the flow at any transverse spacing. In this paper only cylinders in row are taken into consideration. A tandem arrangement of two cylinders with its parameters and designation used in the following is shown exemplarily in Fig. 3-14. The figure shows the cylinder group subjected to horizontal wave forces due to breaking waves, which are investigated in this paper. The spacing between the cylinders was differently defined in former investigations. Therefore a clear unique definition is required. The spacing SC describes the centre spacing of the cylinders. The gap between the cylinders is designated with SG.
Summary of Chapters
1. Introduction: Presents the problem of estimating wave forces on grouped cylinders in offshore structures and defines the project’s focus on large-scale testing of breaking wave impacts.
2. State of knowledge: Reviews the fundamental theories of fluid flow around cylinders, the Morison equation, and previous experimental findings regarding cylinder groups in both regular and breaking wave conditions.
3. Experimental investigation: Details the Large Wave Flume (GWK) test setup, the configurations tested, measurement instrumentation, and the specific test program involving plunging breakers.
4. Evaluation of the experimental results: Analyzes the wave kinematics and compares the bending moments measured on grouped cylinders against the reference single cylinder results, deriving the coefficient C.
5. Summary and concluding remarks: Consolidates the findings regarding the sheltering effects in tandem arrangements and the heightened force effects observed in side-by-side arrangements, while providing recommendations for future research.
Keywords
Coastal engineering, Breaking waves, Cylinder groups, Large-scale experiments, Wave loading, Morison equation, Tandem arrangement, Side by side arrangement, Interference effects, Sheltering effect, Impact force, Wave kinematics, Structural analysis, Offshore structures, Bending moments
Frequently Asked Questions
What is the core focus of this research?
This study investigates how slender cylinders arranged in groups influence each other when subjected to the high-impact loads of breaking waves, a scenario where standard formulas like the Morison equation fall short.
What are the primary cylinder configurations examined?
The research analyzes cylinders in row configurations, specifically focusing on tandem (one behind the other) and side-by-side arrangements at various center spacings.
What is the primary objective or research question?
The main goal is to determine the interference effects between cylinders and develop a coefficient C that describes the increase or decrease in wave load on a grouped cylinder compared to an isolated single cylinder.
Which scientific methodology is utilized?
The research relies on large-scale laboratory experiments conducted in the Large Wave Flume (GWK) in Hanover, utilizing strain gauges to measure bending moments and wave gauges to characterize wave kinematics.
What does the main body of the paper address?
The main body covers the theoretical state of knowledge, a detailed account of the experimental setup and testing program, and an extensive evaluation of how wave height, celerity, and loading cases affect the measured moments on different configurations.
Which keywords characterize this work?
Key terms include breaking waves, coastal engineering, cylinder groups, interference effects, wave loading, and offshore structure design.
How do tandem arrangements differ from side-by-side arrangements in terms of load?
The study finds that tandem arrangements generally result in a sheltering effect (reduced load) for the downstream cylinder, while side-by-side arrangements typically experience a heightening of wave forces on the center cylinder.
Why was the "pile-up effect" noted in the research?
The pile-up effect describes the accumulation of water at the cylinder edge which can lead to premature immersion of pressure transducers, causing potential inaccuracies in force duration measurements if not properly accounted for.
- Quote paper
- Jeanette Juilfs (Author), 2006, Breaking wave load of a vertical slender cylinder within a cylinder group, Munich, GRIN Verlag, https://www.grin.com/document/61677
