Wave Resistance of a Surging Ship Hull Form

Scoping Study

Table of contents

Introduction

I.Overview of the background research and statement of the aims and objectives

i.History

ii.Key background literature

iii.Aims and Objectives

II.Methods to answer the objectives

i.Methodology

ii.Gantt Chart

III.Risk assessment

 

In recent years, there is a continuous need of developing new ship designs satisfying minimum fuel consumption and operating costs in order to meet economic, environmental and technical perspectives. Hence, estimation of ship propulsion power is essential in ship design process. To achieve this, the comprehension of resistance components on a ship hull is necessary. Indeed, the resistance of a ship is defined as the force required to tow the ship in calm water at constant speed. Thus, the understanding of the behaviour of this force is essential to reduce its impact on the ship motion.

The total resistance of a ship can be divided into several main components: frictional resistance, viscous pressure resistance and wave resistance. The Figure1 below shows a basic breakdown of the resistance components. (1)

Among all these components, the wave resistance of a ship, which corresponds from 10 % to 60 % of the total resistance in still water, is of particular interest for scientists. Indeed, observing a ship moving in water shows the creation of a wave pattern (Figure 2). This aspect of the flow absorbs energy from the hull and then generates a resistance force, commonly called wave resistance.

Consequently, wave resistance constitutes for a ship one of the most important feature to consider in order to minimise the fuel consumption of a vessel and then optimise its propulsive efficiency.

While at low speeds the wave resistance is virtually zero, it increases very quickly at higher speeds where it becomes dominant, and thus of significant interest for investigation.

Over the past year, the interest for high-speed crafts, mainly catamarans, has considerably increased. These types of hull have the particularity to be of slender hull form, which is characterised by a length to breadth ratio significantly higher than 1, typically between 6 and 12 for catamarans. Indeed, for ships at conventional speeds, the wave resistance generally decreases as the ship-length increases.

i. History

Before 1860, a little research was made about ship resistance. It all really began in 1870, when Froude first started investigating the discipline using experimental models. He discovered that the speed was proportional to the square root of the length, and invented the so-called Froude Number. Furthermore, he was one of the first who showed that the resistance of a ship was divided into two main components: the skin friction resistance and wave-making resistance (2).

In 1898, the Australian mathematician J.H Michell published a paper (3) providing a mathematical formulation for the wave resistance based on a triple integral, one integral in each length and draft directions and one integral with respect to the angle of propagation of the wave generated by the ship.

The resulting formula, based on the assumption of a thin ship and potential linearized theory, has not been improved upon this day and forms the basis of wave resistance theory. As an illustration, Michell’s integral can be evaluated easily for simple hulls defined by mathematical equations, such as Wigley hull forms[1] (4). The latter have analysed various hull shapes and concluded that the agreement found between Michell’s integral and the value of the wave resistance coefficient computed from towing tests was quite good.

Furthermore, in their study, Birkhoff and Kroukovsky (5) compared various model test results to Michell’s formulation and found a difference of around 10%.

In order to support theoretical approaches and obtain better understanding of the physical mechanism and, considerable work has been made concerning scaling methods and towing tank tests.

From the early 90’s, several model resistance tests have been carried out, comparing different hull forms. The International Towing Tank Conference, established in 1932, proposes a detailed description of appropriate experimental methodologies and uncertainty analysis. (6)

Nevertheless, the cost in terms of facilities and model construction along with the uncertainty associated with the test environment, the equipment and measurements constitute a real drawback of this method. Therefore, numerical methods have been developed to validate the experimental results, and to find better solutions more rapidly.

One of the most common approach to obtain the wave field around the hull is the application of ‘Thin Ship Theory’. In this theory, the body is assumed to be slender (ratio Length/Breadth >>1) and is represented by a planar array of sources on the hull centreline, with the assumption of linearized free-surface boundary conditions. This theory also assumes a ship undergoing at constant speed in calm water, of large depth and lateral extent. But main disadvantages of using slender body theory occur for wide beam hulls, near the limit of approximation. (1)

The wave resistance research has known a lot of progress since the beginning of the 19th century. Since the publication of the classic paper by Michell treating wave resistance analytically, much effort has been exerted in determining the applicability of his integral expressions.

ii. Key background literature

The application of thin ship theory, using numerical and experimental models to determine the wave resistance on simple slender hull forms such as Wigley hulls is widespread since this method can provide fast and accurate solutions.

Important work has been done on the subject particularly on high speed displacement and semi-displacement hull forms, such as catamarans. Indeed, as stated before, the wave making resistance is significant at high speed, i.e. at high Froude number and thus, particular attention is given to high speed vessels.

Insel and Molland (7) (8) studied the resistance components in calm water for high speed displacement and semi-displacement catamarans with symmetric demi-hulls. In this work, the wave resistance was calculated from the description of the far-field wave system using Eggers coefficients for a source in a finite channel, and an experimental investigation was conducted for a serie of hull forms. Catamaran resistance components present a complex phenomenon due to the interference between the two demi-hulls, which is not considered throughout the study of mono-hulls. The results of this investigation give a better understanding of the behaviour of wave resistance for catamaran hull forms in uniform motions.

Nevertheless, problems have been experienced when applying such methods on transom-stern hulls. From Insel work, Dr. A.F. Molland published a paper providing an improved method for the theoretical prediction of the wave resistance of transom-stern hulls using a slender body approach. (9)

Hence, from Insel and Molland works, a better understanding of the wave resistance for single or double-hulled vessels undergoing uniform motions is available.

Although ships spend most of their operational time navigating at constant speed, there are circumstances when unsteady effects can be important. These are during the acceleration and deceleration phases. This concept of ships wave resistance undergoing non-constant speed has not been raised by the previous studies. Indeed, it appears to be little literature about theory or measurements on this subject.

Lunde (10), proposed a linearized theory for the wave resistance in steady and accelerated motions. He appears to be the first researcher who developed the analysis of the ship-wave problem including the unsteady effects. In the case of unsteady motion, a triple integral is required to calculate the wave resistance: a double integral over the longitudinal and transverse wave-number domain and an integral over the time, from the start of the motion. This mathematical expression constitutes the foundation of the unsteady wave resistance theory.

Wehaussen (11) used the Lunde’s theory as a basis and developed asymptotic formulas for the unsteady wave resistance of a thin ship in order to estimate the effect of the initial acceleration of a ship model. Through his work, he tried to determine how long the influence of the initial acceleration persists and what form it takes. Furthermore, Çalisal (12) amplified Wehausen’s work by including the effect of deep water and infinitely wide towing tank upon the wave pattern caused by initial acceleration.

Additionally, oscillatory motions upon ship hull forms have raised some interests. The study of oscillatory motions concerns especially rowing shells, and limited number of studies are available. Scrag and Nelson (13) studied the unsteady effects on racing shell due to their non-uniform motions on water. The rowing hull form was considered as a slender body (L/B=30), and then was analysed using thin ship theory, including shallow water effects. They established that the unsteady effects upon the hull increased the total resistance between 2% to 5%. Hence, these type of hull forms are particularly subject to unsteady hydrodynamic effect due to non-uniform motions.

A limited number of computational studies of rowing shells have been carried out. Tuck and Lazauskas (14) used steady-speed thin ship theory to study optimal shaped for rowing shells. Furthermore, Formaggia (15) computed the effect heave and pitch motions on resistance using a potential flow theory.

Based on the works from Lunde and Wehausen, Doctors (16)  recently published a paper in which he investigated the effect of oscillatory motions upon the wave resistance in order to understand the unsteady hydrodynamics of a racing shells. In this study, the ship model was towed with a harmonic velocity component. It was proved in that work that the unsteady wave resistance varies considerably from the traditional average value. Furthermore, the unsteady linearized wave resistance theory, developed by Lunde and Wehaussen was used with high degree of accuracy. However, the results were not presented at high frequency oscillation, more relevant to the rowing.

Moreover, Day and Clelland (17) investigated the unsteady hydrodynamic effect of a single scull, by demonstrating the strong link existing between turbulence and acceleration. The effect of unsteady speed on wave-making resistance is more pronounced in shallow water, especially close to the critical depth Froude number of 1.0. They examined the impact of unsteady effects on laminar-turbulent transition comparing the results obtained in both field trials and towing tank tests.

All these previous works raise an important interest on the consequences of non-uniform flow upon the wave resistance. As it has been explained before, only few studies tried to analyse the unsteady effects on model hulls undergoing non-constant speed. The present project will have the aim to validate and extend the researches done in the past with respect to this subject, by answering the following research question:

What are the effects of non-uniform flow upon the wave resistance of a thin ship hull model?

iii. Aims and Objectives

To answer the previous question, the following aims are defined:

• To evaluate the wave resistance on slender ship hull forms undergoing non-constant speed and investigate its unsteady behaviours on the hull.
• To compare the results with the wave resistance of steady speed hull forms, and draw appropriate conclusions.

In order to achieve these aims, several objectives have to be attained:

1. To review the knowledge regarding the theory of thin ships wave resistance undergoing uniform and non- uniform motions.
2. To numerically predict the wave resistance of slender ship hull forms undergoing steady and accelerating motion.
3. To conduct experiments in a Towing Tank to validate the predicted wave resistance under steady and accelerating motion.
4. To analyse the effects of control parameters such as speed, acceleration, water depth, model sinkage and trim on wave resistance.
5. To compare the wave resistance of a ship travelling at constant speed with one who’s average speed is the same but undergoing unsteady motion.

i. Methodology

In order to correctly undertake this project, and answer all the defined objectives, it is essential to identify the principal deliverables and milestones and to organize them in a Gantt Chart. The principal key stages of the project are listed below.

• Literature review

The first step to complete in order to fully understand the project background is the literature review. Indeed, the exhaustive literature study written up will allow to fully understand the subject. It will be based on the references stated previously and will explain in detail all the key aspects of the subject: definitions, theories, past experiments…

Hence, it is the first deliverable that need to be achieved.

• Numerical analysis

Once the literature review is finished and the theoretical background of the subject well understood, a numerical analysis will be carried out using Matlab software. To accomplish this, a precise definition of the models and features analysed must be done upstream.

• Experimental testing and analysis

The towing tank experiment is the core of this project and should be carried out as soon as possible, taking into account the tank availabilities and the principal deadlines of the project. It will consist of wave resistance tests using longitudinal wave cuts.

The time planned for the experiment is from 3 to 5 working days and the time for the analysis of data should be around 15 days. It will be conducted in the University of Solent towing tank.

Furthermore, to achieve the testing, existing models will be used in order to optimize the time schedule.

• Comparison of the results

The last important step of this project, before the finalization of the report writing up, will be to compare the experimental and theoretical results and to raise the appropriate conclusion about the subject. This step will be done once all the experimental data are analysed.

ii. Gantt Chart

The different steps of the project are summarised in Table1. These steps, as well as the sub-steps are all coordinated in a time-scale and are available in the Figure3.

Table 1: Main key-stages of the project

Task name	Start	Finish
Project Start/ First meeting with M. Taunton	Mon 30/01/17	Mon 30/01/17
Scoping study	Mon 30/01/17	Thu 30/03/17
Scoping Report submission	Thu 30/03/17	Thu 30/03/17
Project progress report	Mon 03/04/17	Fri 16/06/17
Project Progress Report submission	Fri 16/06/17	Fri 16/06/17
Experimental part of the project	Sat 17/06/17	Mon 31/07/17
Poster design and preparation of the presentation	Mon 03/07/17	Tue 18/07/17
MSc Poster Presentation	Tue 18/07/17	Tue 18/07/17
Numerical Analysis	Sat 17/06/17	Mon 14/08/17
Draft Project submission	Fri 01/09/17	Fri 01/09/17
Feedback on drafts	Tue 12/09/17	Tue 12/09/17
Final report writing up	Tue 12/09/17	Sat 23/09/17
MSc Dissertation submission	Sat 23/09/17	Sat 23/09/17
Report writing up	Fri 16/06/17	Sat 23/09/17
Meeting with the supervisor to discuss the project’s progress (every week or every two weeks)	Mon 30/01/17	Fri 08/09/17

Figure 3: Gantt Chart of the project

As part of managing the health and safety of people, a risk assessment is indispensable when a project is started. It allows to identify and prevent the risks and hazards during the project progress. The risk matrix is used here to assess the risks present in the working environment. (18)

The risk matrix is one of the most common tool used for risk evaluation and consider two major parameters:

• A hazard: anything that may cause harm.
• The risk: the chance, high or low, that somebody could be harmed by these hazards together with an indication of how serious the harm could be.

In the present case, two principal aspects of the work are considered. The first one is the experiment which will be carry out in a towing tank, and the second one include the office work.

The risk assessment is presented in the below table listing all the potential hazards and harms that could happened during this project associated with the likelihood and severity risk factors.

Task	Hazard	Harm	Who could be affected?	Existing measures to control risk	Likelihood Risk Factor	Severity Risk Factor	Risk Score
Towing tank experiment	Chemicals present in the water	Poisoning or other illness Chemicals skin burns	People participating to the experiment	To wash hands after the experiment	3	3	9
Carrying, pushing, pulling, sliding, lifting of models or other objects during towing tank testing	Manual handling	Back injury Bruising	People participating to the experiment	To not move objects alone	4	2	8
Towing tank experiment	Water	Fall into water/Drowning Drop objects in the tank Risk to slip	People participating to the experiment	Protective barrier along the tank	2	2	4
Towing tank experiment	Electrical	Electrical shock/burn	People participating to the experiment	Protect and isolate all electrical features	2	3	6
Towing tank experiment	Fire	Burns Smoke inhalation	People participating to the experiment	Fire extinguisher present in the tank Emergency exists Evacuation plan	2	3	6
Carriage moving during towing tank tests Hand tools	Machinery and equipment	Crushing, trapping, cuts To lean over the carriage	People participating to the experiment	Demonstration on how to use the equipment. Help from experimented people	1	4	4
Towing tank experiment	Confined spaces	Asphyxiation Illness due to breathing harmful air or vapours	People participating to the experiment	2	4	8
Report writing up	Computer	Can cause posture problems and pain, discomfort Headaches and sore eyes can also occur	4	2	8
Working alone on the project	Psychological	Stress	Student working on the project	4	2	8

 

References

1. Molland, A.F., Turnock, S.R. and Hudson, D.A. Ship Resistance and Propulsion. University of Southampton : Cambridge University Press, 2011.

2. Froude, W. Experiments upon the effect produced on the wave-making resistance. s.l. : Transactions of the Royal Institution of Naval Architects, 1877.

3. Michell, J.H. The wave resistance of a ship. 1898.

4. Journée, J.M.J. Experiments and Calculations on 4 Wigley Hull Forms in Head Waves. s.l. : Delft University of Technology , 1992.

5. Birkhoff, G., K.Kroukovsky, V. and Kotik, J. Theory of the Wave Resistance of Ships. pp. 359-396.

6. ITTC. International Towing Tank Conference- Recommended procedures. 2002.

7. Insel, M. An Investigation into the Resistance Components of High Speed Displacement Catamarans. Southampton. University of Southampton : Ph.D. Thesis, 1990.

8. Insel, M. and Molland, A.F. An investigation into the resistance components of high speed. s.l. : Transactions, Royal institution of Naval Architects, 1992.

9. Molland, A.F., Wellicome, J.F. and Couser,, P.R. An improved method for the theoretical prediction of the wave. s.l. : University of Southampton, 1998.

10. Lunde, J.K. Linearised Theory of Wave Resistance for Displacement Ship in Steady and Accelerated Motion. 1951.

11. Wehausen, J.V. Effect of the initial acceleration upon the wave resistance of ship models. s.l. : University of California, 1961.

12. Calisal, S. Effect of Initial Acceleration on Ship Wave Pattern and Wake Survey Methods. 1977. pp. 239-247. Vol. 21.

13. Scragg, C. A and Nelson, B. D. The design of an eight-oared rowing shell. s.l. : Marine Technol, 1993.

14. Tuck, E.O. and Lazauskas, L. Low drag rowing shell. 1996.

15. Formaggia, L., et al. Fluid-structure interaction problems in free surface flows. 2007.

16. Doctors, L.J., Day, A.H. and Clelland, D. Resistance of a Ship Undergoing Oscillatory Motion. 2010.

17. Day, A.H., et al. An experimental study of unsteady hydrodynamics of a single scull. s.l. : SAGE, 2011.

18. Executive, Health and Safety. http://www.hse.gov.uk/risk/controlling-risks.htm.

[1] A Wigley hull: hull defined by a three variables parametric function