Technical University Braunschweig
Leichtweiss-Institute for Hydraulic Engineering and Water Resources
Department of Coastal Engineering, Student research project
June 2006

Breaking wave load of a vertical slender
cylinder within a cylinder group

von: Jeanette Juilfs

Contents

1. Introduction 1

2. State of knowledge  4

2.1. Problem statement and procedure of analysing the state of knowledge 4
2.2. Flow around a cylinder  4

2.2.1. Steady flow 5
2.2.2. Oscillatory flow 8

2.3. Forces on a single cylinder 8

2.3.1. Drag force  9
2.3.2. Mass force 10
2.3.3. Drag and mass coefficient  13

2.4. Breaking waves  14
2.5. Single cylinder in breaking waves  18
2.6. Cylinder group  20

2.6.1. Tandem arrangement  21
2.6.2. Side by side arrangement 24

2.7. Experimental investigations with cylinder groups  27
2.8. Summary of existing results  35

3. Experimental investigation 37

3.1. Experimental set-up 37
3.2. Measuring instruments  39
3.3. Cylinder group configurations 40
3.4. Testing programme  41

4. Evaluation of the experimental results  48

4.1. Wave kinematics 48

4.1.1. Wave height  48
4.1.2. Wave celerity  53
4.1.3. Wave length  55

4.2. Total force on single cylinder 56
4.3. Total force on cylinder groups 60

4.3.1. Tandem arrangement  60
4.3.2. Side by side arrangement 62

5. Summary and concluding remarks  68

6. Acknowledgements 71

7. References  72
 

1. Introduction

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.

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A coefficient C is going to be developed which describes the increase or decrease of the wave load on the measuring cylinder in the group compared to the single cylinder. The coefficient C will be analysed as a function of the breaking wave conditions, the configuration and the spacing between the cylinders. In this paper only a selection of the fifteen performed tests is going to be analysed. The following flow chart shows the problem statement, the objective and the proceeding of this paper.

Fig. 3-1 Problem statement, objective and proceeding [figure only in downloadfile]

As required in the task, the state of knowledge is first described in chapter 2. Therein the required report of previous experiments is given. The recent experiments in Hanover are reported in chapter 3. Therein the experimental set-up, the measurement techniques and the testing programme are briefly described. The fourth chapter deals with the evaluation of these experiments. Finally, in chapter 5, the main results are briefly summarised. A required comparison with the published results of previous experiments is also given in chapter 5. The same chapter includes furthermore a prospect with continuative aspects for further research.

2. State of knowledge

2.1. Problem statement and procedure of analysing the state of knowledge

The Morison equation gives a simple engineering tool to determine the wave force acting on slender cylinders. Slender means, that the structure with a certain diameter D is sufficiently small compared to the wave length L (D/L < 0.05). In this case diffraction effects are negligible. The equation is applicable for vertical, circular, slender cylinder with a smooth surface without neighbouring cylinders. In an arrangement of closely spaced cylinders the influence of the neighbouring cylinders on the surrounded fluid field is likely to be expected. As the Morison equation is only applicable for single cylinder, the need of a modification of the given equation in order to consider this interaction is obvious and proposed in Morison et al. (1950).

In this chapter the basic principles of single cylinders in a fluid flow are first described. Furthermore the wave kinematics of breaking waves are studied especially the breaking point as an important parameter in the following examination. Afterwards it is made use of the investigation of single cylinder subjected to breaking waves for further interpretation of cylinder groups. Afterwards the previous knowledge about cylinder groups is presented. Previous publications describing experimental investigations with different configurations of cylinders in breaking and non-breaking waves are briefly reviewed and analysed furthermore. Tab. 3-4 summarises the main parameters of the wave and model set-up of these past investigations. A conclusion closes this chapter.

2.2. Flow around a cylinder

In this paragraph the description of the flow around a cylinder is separated into two different flow types, namely the steady flow and the oscillating flow. In a steady flow the fluid is characterised by a smooth uniform movement with a locally constant velocity. The oscillating flow is characterised by acceleration of the water particles.

2.2.1. Steady flow

A steady flow is described by the Reynolds number Re and undergoes tremendous changes as the Reynolds number increases from zero. The Reynolds number is formulated as:

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umax= maximum horizontal water particle velocity [m/s], D= diameter of the cylinder [m], ν= kinematic viscosity [m²/s] (1.0*10-6 m²/s at 20°C) While considering a smooth circular cylinder in a steady current, two different flow regions are established, namely the wake and the boundary layer. A definition sketch is given in Fig. 3-2. The wake region extends over a wide distance, which is comparable with the diameter D, while the boundary layer extends over a comparatively small thickness (Sumer and FredsØe, 1997).

Fig. 3-2 Definition sketch (modified from Sumer and FredsØe, 1997) [figure only in downloadfile]

In Fig. 3-2 the separation point locates the separation of the boundary layer from the surface of the structure. For small values of Reynolds number no separation occurs. The separation first appears when the Reynolds number becomes 5. At that value the appearance of a fixed pair of vortices at the rear part of the cylinder is found. The next range is characterised by a laminar vortex street (40 < Re < 200). The wake becomes partly turbulent where 200 < Re < 300. At Reynolds numbers greater than 300 the following three ranges could be described: the subcritical flow regime where 300 < Re < 3*105, the transitional flow regime where 3*105< Re <3.5*105 and the supercritical flow regime where 3.5*105 < Re < 5*105. The subcritical range is characterised by a completely turbulent wake but the boundary layer over the cylinder surface remains laminar. The next Reynolds number regime, the so called transitional flow regime, shows a turbulent boundary layer separation at one side of the cylinder. The boundary layer separation becomes turbulent at both sides of the cylinder in the supercritical flow regime, but the boundary layer is not completely turbulent. The transition to turbulence is located somewhere between the stagnation point and the separation point. The boundary layer becomes turbulent at one side when the Reynolds number reaches the value of about 1.5*106. When the Reynolds number finally increases over a value of 4.5*106 the boundary layer becomes turbulent over the whole cylinder surface. This flow regime is called transcritical flow regime (Sumer and FredsØe, 1997). A detailed classification with a brief description of each flow regime is given in Fig. 3-3, which shows examples of flow patterns and occurring vortex shedding at all Reynolds numbers.

Fig. 3-3 Flow patterns around a circular cylinder (Sumer and FredsØe, 1997) [figure only in downloadfile]

As described above, vortex shedding occurs when the Reynolds number reaches values greater than 40. For these values the boundary layer is separated by the surface of the cylinder and a shear layer is formed. A significant amount of vorticity contained in the boundary layer is fed into the shear layer and causes it to roll up into a vortex. Likewise a vortex is formed at the other side of the cylinder, which rotates in the opposite direction (Sumer and FredsØe, 1997).

2.2.2. Oscillatory flow

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