Wavesub Wave Energy Convertor: Reactor Design & Analysis
Info: 15464 words (62 pages) Dissertation
Published: 11th Dec 2019
Tagged: Energy
The renewable energy sector is currently going through a phase of increasing activity with a massive focus to discover, develop and implement new sustainable technologies. It is predicted that Wave Energy in particular can be at the forefront within the renewables sector with wave having the potential to supply a significant percentage of the overall renewable energy contribution.
Marine Power Systems (MPS) are a company based in Swansea, currently developing a novel Wave Energy converter called the WaveSub. The device consists of a power capturing float which is tethered by multiple flexible power take-off lines to a large barge like reactor. The lines are connected to a hydraulic power take-off system (PTO) which is used to capture energy from the relative movement between float and reactor which is then converted to electricity.
The WaveSub has a surface configuration for transport and a submerged configuration for power generation. In the surface configuration, the WaveSub reactor is filled with air and whilst in its submerged configuration it is filled with sea water. This project is directly linked to the design and analysis of this reactor.
Declaration of Authenticity………………………………………
Abstract…………………………………………………..
Acknowledgements…………………………………………..
Project Plan………………………………………………..
Table of Contents…………………………………………….
List of Figures……………………………………………….
1 Introduction………………………………………………
1.1 Scope and Objectives……………………………………
2 Literature Review………………………………………….
2.1 Ocean Energy – Wave……………………………………
2.2 Wave Energy Resource (UK)……………………………….
2.3 Wave Energy Converters………………………………….
2.3.1 Oscillating Water Columns………………………………
2.3.2 Oscillating Body Columns……………………………….
2.3.3 Overtopping Devices…………………………………..
2.4 Material Selection……………………………………….
2.4.1 Steel………………………………………………
2.4.2 Aluminium………………………………………….
2.4.3 Composites…………………………………………
2.5 Finite Element Analysis…………………………………..
2.5.1 What is Finite Element Analysis?………………………….
3 Reactor Concept 1
3.1 General Design………………………………………..
3.2 Computational Modelling & Analysis………………………….
3.2.1 3D Geometry………………………………………..
3.2.2 Assumptions………………………………………..
3.2.3 Loadcase Summary……………………………………
3.2.4 Mesh Settings……………………………………….
3.2.5 Mechanical Properties………………………………….
3.3 Simulation Results – Concept 1……………………………..
3.3.1 Simulation 1 – External Pressure On Outer Chambers…………..
3.3.2 Simulation 2 – External Pressure On Inner Chambers……………
3.3.3 Simulation 3 – Internal Pressure on Outer Chambers……………
3.3.4 Simulation 4 – Internal Pressure on Inner Chamber……………..
3.3.5 Simulation 5 – Power Take Off Loads (Operational)…………….
3.3.6 Simulation 6 – Towing………………………………….
3.3.7 Simulation 7 – Lifting…………………………………..
3.3.8 Simulation 8 – Mooring…………………………………
3.3.9 Simulation 9 – Central Tether…………………………….
4 System Design Change………………………………………
4.1 Reactor Design Change…………………………………..
4.2 Alternative Concept……………………………………..
5 Reactor Concept 2
5.1 General Design………………………………………..
5.2 Computational Modelling & Analysis………………………….
5.2.1 3D Geometry………………………………………..
5.2.2 Assumptions………………………………………..
5.2.3 Loadcase Summary……………………………………
Simulation Title…………………………………………….
Minimum Safety Factor………………………………………
5.2.4 Mesh Settings……………………………………….
5.2.5 Mechanical Properties………………………………….
5.3 Simulation Results………………………………………
5.3.1 Simulation 1 – Storm Loads with Float in Cradle……………….
5.3.2 Simulation 2 – PTO Storm Loads………………………….
5.3.3 Simulation 3 – PTO Operational Loads………………………
5.3.4 Simulation 4 – Lifting Points……………………………..
5.3.5 Simulation 5 – Towing………………………………….
6 Manufacturing Cost Comparison………………………………..
7 Conclusion……………………………………………….
7.1 Future Work…………………………………………..
References…………………………………………………
Appendix 1 – WaveSub Specification………………………………
Appendix 2 – Computational Loadcases…………………………….
Appendix 3 –Operational Requirements…………………………….
Appendix 4 – Reactor Concept 1 Cost Breakdown……………………..
Appendix 5 – Reactor Concept 2 Cost Breakdown……………………..
Figure 1. WaveSub Equipment Overview
Figure 2. Classification of wave energy converters (3)
Figure 3. OWC Working Principle (9)
Figure 4. Ocean Power Technology Powerbuoy Device (14)
Figure 5. Wave Dragon Overtopping Device (17)
Figure 6. Initial Reactor Concept Design
Figure 7. Plan View of Reactor Chamber Layout
Figure 8. Isometric View of Reactor Showing Internal Steel Structure (all plates removed)
Figure 9. Isometric view of reactor fabrication (side plate removed for clarity)
Figure 10. Fully constrained faces
Figure 11. Faces selected for external pressure loads
Figure 12. Von Mises stress results
Figure 13. Displacement Results
Figure 14. Safety Factor Results
Figure 15. Fully constrained faces
Figure 16. Faces selected for internal pressure loads
Figure 17. Von Mises stress results
Figure 18. Displacement results
Figure 19. Safety Factor Results
Figure 20. Fully constrained faces
Figure 21. Faces selected for internal pressure loads
Figure 22. Von Mises stress results
Figure 23. Displacement results
Figure 24. Safety Factor Results
Figure 25. Fully constrained faces
Figure 26. Faces selected for internal pressure loads
Figure 27. Von Mises stress results
Figure 28. Displacement results
Figure 29. Safety Factor Results
Figure 30. Fully Constrained faces
Figure 31. Faces selected for corner PTO loads & central tether line
Figure 32. Von Mises stress results
Figure 33. Displacement results
Figure 34. Safety factor results
Figure 35. Fully constrained faces
Figure 36. Faces selected for towing loads
Figure 37. Von Mises stress results
Figure 38. Displacement results
Figure 39. Safety factor results
Figure 40. Fully constrained faces
Figure 41. Faces selected for top deck loads
Figure 42. Von Mises stress results
Figure 43. Fully constrained faces
Figure 44. Safety factor results
Figure 45. Fully constrained faces
Figure 46. Face selected for mooring load
Figure 47. Von Mises stress results
Figure 48. Displacement results
Figure 49. Safety factor results
Figure 50. Fully constrained faces
Figure 51. Von Mises stress results
Figure 52. Displacement results
Figure 53. Safety factor results
Figure 54. Wavesub Assembly With Depth Setting Floats
Figure 55. Updated Reactor Concept
Figure 56. Updated Reactor Frame
Figure 57. Model Constraints (blue) and Loads (Yellow)
Figure 58. Von Mises Stress Results
Figure 59. Displacement Results
Figure 60. Safety Factor Results
Figure 61. Constraints, Central PTO & Corner PTO Storm Loads
Figure 62. Von Mises Stress Results
Figure 63. Displacement Results
Figure 64. Safety Factor Results
Figure 65. Constraints, Central PTO & Corner PTO Operational Loads
Figure 66. Von Mises Stress Results
Figure 67. Displacement Results
Figure 68. Safety Factor Results
Figure 69. Lifting Constraints and Loadings
Figure 70. Von Mises stress results
Figure 71. Displacement Results
Figure 72. Safety factor results
Figure 73. Faces selected for towing loads
Figure 74. Von Mises stress results
Figure 75. Displacement results
Figure 76. Safety factor results
Figure 77. Low Cost Of Energy Equation (20)
List of Tables
Table 1 – Concept 1 Minimum Safety Factors
Table 2- Concept 1 Simulation Mesh Settings
Table 3 – Simulation Material Properties for Mild Steel Grade 275
Table 4 – Simulation Material Properties for Mild Steel Grade 355
Table 5 – Chamber Option Comparison
Table 6 – Concept 2 Minimum Safety Factors
1 Introduction
A topic that is continuously causing global debate is Energy with a massive emphasis on forms of renewables. It is well known that the current non-renewable resources are depleting at a rapid rate and only relevantly recently have countries started to push forward various forms of renewables accepting that change is needed. Renewable sources such as solar and wind have had significant financial backing by the government for over 20 years. It is arguably of this early period of financial support that wind is well ahead of other forms of renewable energy technologies.
One form of renewable energy which has seen a recent increase in investment and development is wave. Wave energy has a huge potential to become one of the leading technologies in renewables. Wave energy is the transfer of then energy within oceans waves into electricity.
Marine Power Systems (MPS) are developing a novel Wave Energy converter called the WaveSub (see figure 1 below). The device consists of a power capturing float which is tethered by multiple flexible power take-off lines to a large barge like reactor. The lines are connected to a hydraulic power take-off system (PTO) which is used to capture energy from the relative movement between float and reactor which is then converted to electricity.
The WaveSub has a surface configuration for transport and a submerged configuration for power generation. In the surface configuration, the WaveSub reactor is filled with air and whilst in its submerged configuration it is filled with sea water. Please contact us for further details of the WaveSub concept and device if needed.
MPS are designing a sea-going 1/4 scale (reactor barge approximately 13.5m x 8.5m x 2.5m) prototype of the device. A critical component of this is the reactor, a large barge like structure comprising of floodable flotation/Ballast chambers.
Power Capturing float
Corner PTO System
Central Tether
Reactor
1.1 Scopeand Objectives
Marine Power Systems was founded in 2008 with the sole purpose of developing a novel wave energy converter called Wavesub. A critical Part of this device is the Reactor. A fabricated steel structure which will provide the sub frame to mount all auxiliary components and subsystems as well as being the main body to react with a power capturing float when in operation.
The purpose of this project was to produce an optimised ¼ scale Reactor design in line with the overall system specification. Finite Element Analysis (FEA) studies were carried out on the design to determine maximum stress, Stress distribution and displacement in several load cases.
Manufacturability, cost of manufacture, maintainability, weight and scalability were key drivers in the design activity.
2 Literature Review
2.1 Ocean Energy – Wave
It is clear by simply looking out at the sea that there is a massive energy potential stored within the oceans. It is this huge energy resource that holds the potential to provide clean sustainable energy, not only to the United Kingdom, but globally.
Wave energy has the highest energy density amongst renewable energies, and directly follows seasonal demands in temperate climates. The seas and therefore waves are much more energetic and turbulent in the colder months of autumn and winter, providing more energy extraction potential. Whereas, in the warmer months of spring and summer, the seas are much calmer.
2.2 Wave Energy Resource (UK)
Circumpolar storms near the Atlantic Ocean generate the most attractive climate for waves as well as the seas off western Europe (1). These areas lie between 30 and 60 degrees’ latitude, with power levels ranging between 20 kW/m and 70 kW/m. The UK lies perfectly within this attractive wave climate, and with the unrestricted coastal border, marine energy production seems a logical for future energy resources in the UK and Europe
- Annual Mean Significant Wave Height (2)
Figure 2 shows the annual mean significant wave height in waters surrounding the UK, highlighting the great potential for wave energy. It is estimated that the UK has the potential wave power resource of 7-10GW. The UK grid has a capacity of around 80 GW and a peak demand of approximately 65 GW. by taking these figures it can be estimated that wave energy can produce up to 15% of the overall UK energy demand.
2.3 Wave Energy Converters
Wave energy devices have generally been classified according to size, location and working principle (1). Falcao (2) proposed a working principle classification of wave energy devices. He identified three main classes of devices;
- Oscillating Water columns (Fixed and Floating Structures).
- Oscillating Bodies (Submerged and Floating Structures).
- Overtopping devices (Fixed and Floating Structures).
These are then divided further into various sub categories;
- Location: Onshore, Offshore, and Near-shore.
- Device Size: Attenuator, Point-Absorber and Terminator.
- Working Principle: Pressure Differential, Floating structures, Overtopping devices and Impact devices.
There are over one thousand ocean wave energy device patents (4), many more ideas are being developed each varying in complexity from the others.
2.3.1 Oscillating Water Columns
The oscillating water column [OWC] wave energy device is one of the most popular and researched upon categories of wave energy converters. Some of these devices have reached prototype testing (5,6,7) and commercial deployment such as the Limpet deployed in the Isle of Islay of Scotland, Ocean Power Technologies Powerbuoy (8) and a few others. The basic principle of these devices is to take advantage of wave movement to cause a rise and fall in the water level in an air chamber. This in turn causes a variation in the height of the air column which is then used to drive an air turbine as shown Below.
These devices typically consist of two parts; an upper part which forms the air chamber and a bottom part which is open to allow the wave action oscillate the internal water column. They can either be free floating (such as Yoshio Masuda’s buoys) or bottom fixed structures. Lopez classifies the bottom fixed variation as Archimedes effect converters, these use the pressure created by the wave crests passing over top part of the device to compress the air chamber, and the reduced pressure of the wave troughs causes the chamber to rise again (10).
2.3.2 Oscillating Body Columns
This class of devices are floating bodies which move relative to wave motion and a fixed reference such as the sea bed or an external structure (single body systems) or the relative motion between multiple floating bodies (multi-body systems) (11). These are offshore devices and are typically deployed at depths greater than 40 m, and hence present maintenance and life-cycle challenges due to the more demanding nature of deep sea conditions, and the additional cost of transmission cables. But they can make use of the more abundant wave energy resource in these locations (12).
An example of an oscillating body system is Ocean Power Technologies’ Power buoy (Figure 4 below) which has recently been approved for commercial deployment in the United States after tests off the coast of Scotland. It has a design life of 25 years and rated peak power output of 866kW (13). It is slack moored to the sea-bed and hence is free to oscillate with the motion of the waves, with the upper (float) part moving upwards and downwards with respect to the rest of the body under the sea.
2.3.3 Overtopping Devices
Overtopping WEC’-s are more direct in their approach to extracting energy from waves. They work by causing water from waves to flow over the top of a structure into a reservoir which is at a higher level than the free surface of the nearby ocean; this water is then allowed to flow back into the sea thus creating a ‘mini dam’. This allows for a steady flow of water to the turbines. The energy from the water flowing back into the sea is then used to power hydraulic turbines (12,15,16).
These devices have enjoyed a bit more success than oscillating body systems, due to their minimisation of moving parts (the turbines being the major components) or their relative simplicity, but they also face the challenge of low head values from the reservoirs which can’t be too high above the sea level depending on the height of the incident waves, and as the amount of energy available from a stored body of water is directly proportional to its height above the turbine’s level, this makes the efficiency of the turbines a critical part in the overall efficiency of the WEC.
The Wave Dragon is a slack-moored offshore overtopping device. The waves are concentrated over a ramp by two wave adjustable deflectors onto a reservoir higher than the surrounding sea level. Originally developed in Denmark, a 57m wide grid connected prototype was deployed in 2003 off the coast of Denmark and run for a number of years (12). A full scale Wave dragon demonstrator was being developed for deployment in Wales off St. Ann’s head with a rated power output of 7MW depending on the amount of wave energy available at the site of deployment (15).
2.4 Material Selection
Material selection is one of the most important factors in any engineering design project, a poor material selection can be the ultimate failing of a device/product. This is even more true in the marine environment, where the operating conditions could be described as extreme compared to land based operation. Some factors that should be considered within the marine environment include; increased corrosion from salt content, bio-fouling, and large forces from energetic seas. In the context of wave power devices, there are a few potential material options which can be manipulated to protect against the extreme marine environment. The cost of materials is also important as to decrease the overall cost of the generation of electricity. The Carbon
Trust provide guidelines for the design and operation of wave energy converters, including material selection (18).
2.4.1 Steel
Steel is the most commonly used material in the manufacture of wave power devices. It is relatively inexpensive compared to other materials, and is relatively easy to source. Steel is produced from iron ore, with the addition of carbon.20 It is manufactured into many forms at steel work locations around the UK, and globally. Steel has a large density of around 7800 kg/m3, and therefore a substantial mass. Within the marine environment, the use of steel would require watertight welds to increase the strength of the device (19).
There are concerns about the use of steel in the marine environment. One being related to corrosion. Steel is known to rust and corrode when subjected to moisture. With this corrosion, the steel not only loses aesthetical values, but also loses structural integrity. The corrosion can be prevented, with the use of anti-corrosion coatings and other systems such as cathodic protection.
2.4.2 Aluminium
An alternative material for wave power devices is aluminium, which is the 3rd most abundant element on Earth, easily extracted from bauxite ore. Its ductility means that it can be readily cast and machined. Aluminium is much less dense (approximately 1/3 of the density), but also much weaker (1/3 of the stiffness) than steel. Aluminium has a favourable strength to weight ratio than steel, and is not susceptible to rust (19).
2.4.3 Composites
Composites are increasingly used in the marine industry, being used to manufacture; hulls, kayaks, canoes, jet skis, along with others. The most common composite used in the industry is Fibre Reinforced Polymers (FRP), which gives huge resistance to corrosion, the environment and electrical and thermal conductivity. FRP has good formability, toughness, reduced mass, making it a popular choice for the marine industry, with the introduction of structural foam to add buoyancy. Composites are however, extremely expensive to manufacture.
2.5 Finite Element Analysis
In mechanical design, some form of structural analysis is usually required as part of the design process. Traditionally this has been done by engineering hand calculations, but nowadays this has evolved immensely and is now done by using highly complex computer programmes which are relatively easy to use. Even so it is still very important that designers have a good understanding of mechanical failure mechanisms and understand how loads are transmitted through structures.
Design packages have moved on tremendously since they were first used in design and many now have some form of structural analysis built into them as standard (especially 3d design packages). The main computer aided design packages include:
- Autodesk Inventor
- Solid Works
- Solid Edge
- Siemens NX
All of the programmes above are continuously improving their software, and most are updated every 6 to 12 months. As you can imagine, the competition in this field is very fierce and each one is trying to offer something the other cannot as standard, which works out great for the end user.
2.5.1 What is Finite Element Analysis?
Finite Element Analysis (FEA) was first developed in 1943 by R. Courant (22), who utilized the Ritz method of numerical analysis and minimization of variational calculus to obtain approximate solutions to vibration systems. Shortly thereafter, a paper published in 1956 by M. J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp established a broader definition of numerical analysis. The paper centered on the “stiffness and deflection of complex structures”. By the early 70’s, FEA was limited to expensive mainframe computers generally owned by the aeronautics, automotive, defence, and nuclear industries.
Since the rapid decline in the cost of computers and the phenomenal increase in computing power, FEA has been developed to an incredible precision. Present day supercomputers are now able to produce accurate results for all kinds of parameters. FEA consists of a computer model of a material or design that is stressed and analyzed for specific results. It is used in new product design, and existing product refinement. A company is easily able to verify a proposed design will be able to perform to the client’s specifications prior to manufacturing or construction. Modifying an existing product or structure is utilized to qualify the product or structure for a new service condition. In case of structural failure, FEA may be used to help determine the design modifications to meet the new condition.
There are generally two types of analysis that are used in industry: 2D modelling, and 3D modelling. While 2D modelling conserves simplicity and leads to a low computational demand for, it tends to yield less accurate results. 3D modelling, however, produces more accurate results while sacrificing computational efficiency. Within each of these modelling schemes, the programmer can insert numerous algorithms (functions) which may make the system behave linearly or non-linearly. Linear systems are far less complex and generally do not take into account plastic deformation. Non-linear systems do account for plastic deformation, and many also are capable of testing a material all the way to fracture.
3 Reactor Concept 1
3.1 General Design
The initial design concept for the Reactor frame was outlined by Marine Power Systems in the form of a basic conceptual CAD model. The initial design was to be a fabricated steel structure made from readily available steel sections which would also incorporate water tights chambers within the structure. Staged flooding of these chambers would then allow controlled submergence of the device.
As the first stage of this project, an initial frame was designed using mild steel channel, angle and ‘I’ beam sections along with mild steel flat plate to provide the walls for the separate chambers.
These flat steel plates required significant stiffening to withstand the internal and external pressures when in operation (see figure 8 below).
3.2 Computational Modelling & Analysis
3.2.1 3D Geometry
The reactor model was build up using Autodesk Inventor Professional. A basic skeletal frame was firstly put together to act as a foundation to the structure, starting with a top ‘H’ frame and main outer frame. This top frame provides the mounting interface for all other equipment such as the power take off system. This frame was then split into the chamber sections using standard steel plate sections. These separated chambers then had to be stiffened to provide rigidity and allow them to withstand internal and external pressures exerted on them.
3.2.2 Assumptions
It is extremely difficult to simulate real life operating conditions for something that is going to be positioned under the sea. Assumptions therefore had to be made to try and achieve this. With regard to the reactor, the following simplifications and assumptions were made:
- No welds are shown in any simulations. This allows simulations to run more smoothly and effectively.
- All faces within the structure will be treated as fully bonded faces.
- All corner PTO loads will act directly on the corner mounting plate. Detailed fixing design has not yet been finalised so whole mounting faces were used.
- Central PTO loads will act directly on the central mounting plate. Detailed fixing design has not yet been finalised so whole mounting faces were used.
- The reactor was appropriately constrained at the mooring attachment points to enable simulations to be run for operational and storm survival configurations.
- A gravitational load was applied in all simulations. Gravity taken as 9.81 m/s2.
3.2.3 Loadcase Summary
The Reactor Barge model was subjected to several load cases to simulate the following scenarios:
- External Pressure on Outer Chamber
- External Pressure on Inner Chamber
- Internal Pressure on Outer Chamber
- Internal Pressure on Inner Chamber
- PTO loads (Operational)
- Towing
- Lifting
- Mooring
- Central Tether (full load)
Each simulation was run and the results were evaluated to determine maximum stress, displacement and a minimum safety factor.
The safety factors below show an acceptable margin on peak loads and stress level for material endurance limits in fatigue (23). The localized peak stresses show a need for careful specification and inspection of welded joints in some locations.
| Simulation Title | Minimum Safety Factor |
| External Pressure on Outer Chamber | 2.1 |
| External Pressure on Inner Chamber | 2.3 |
| Internal Pressure on Outer Chamber | 2.2 |
| Internal Pressure on Inner Chamber | 5.5 |
| PTO Loads (Operational) | 5.68 |
| Towing | 7.9 |
| Lifting | 6 |
| Mooring | 1.14 |
| Central Tether (full load) | 2.37 |
Table 1 – Concept 1 Minimum Safety Factors
3.2.4 Mesh Settings
The following mesh settings were typical for each simulation (see below). All simulation mesh’s were refined accordingly and converged.
| Avg. Element Size (fraction of model diameter) | 0.1 |
| Min. Element Size (fraction of avg. size) | 0.2 |
| Grading Factor | 1.5 |
| Max. Turn Angle | 60 |
| Create Curved Mesh Elements | No |
| Use part based measure for Assembly mesh | Yes |
Table 2- Concept 1 Simulation Mesh Settings
3.2.5 Mechanical Properties
Mild steel grade 275 & 355 was used throughout the reactor barge and the following properties were used in the simulations (see below).
| Name | Steel, Mild_275 | |
| General | Mass Density | 7.85 g/cm^3 |
| Yield Strength | 275 MPa | |
| Ultimate Tensile Strength | 410 MPa | |
| Stress | Young’s Modulus | 220 GPa |
| Poisson’s Ratio | 0.275 ul | |
| Shear Modulus | 86.2745 GPa | |
Table 3 – Simulation Material Properties for Mild Steel Grade 275
| Name | Steel, Mild_355 | |
| General | Mass Density | 7.85 g/cm^3 |
| Yield Strength | 355 MPa | |
| Ultimate Tensile Strength | 490 MPa | |
| Stress | Young’s Modulus | 220 GPa |
| Poisson’s Ratio | 0.275 ul | |
| Shear Modulus | 86.2745 GPa | |
Table 4 – Simulation Material Properties for Mild Steel Grade 355
3.3 Simulation Results – Concept 1
3.3.1 Simulation 1 – External Pressure On Outer Chambers
For the external pressure simulation, the full assembly was taken and split into a quarter section to speed up simulation run times. Additional fixed constraints were added accordingly (see figure 11 below).
Pressure loads of 20.15 KPa were added in conjunction with the load case document and applied to the model as shown in figure 12 below.
In general the stresses in the outer chambers were very low with some local high points of between 110 MPa and 130 MPa around lateral bracing and plate interfaces, this is compared to the material yield strength of 275MPa. There were also some very high stress concentrations picked up at beam joint locations but from experience these in reality would not be of concern, this may be an area where inspections should be focused once in operation. Maximum displacement of 12.82mm occurred in the corner baffle plate where expected and a minimum safety factor of around 2.1 (see figures 13, 14 & 15 below).
3.3.2 Simulation 2 – External Pressure On Inner Chambers
For the internal pressure simulation, the full assembly was taken and split into a quarter section to speed up simulation run times. Additional fixed constraints were added accordingly (see figure 16).
Pressure loads of 60.45 KPa were added in conjunction with the load case document and applied to the model as shown below.
The stresses in the inner chambers were very low with some local high points of between 100 MPa and 120 MPa around lateral bracing and plate interfaces (there were also some very high stress concentrations picked up but from experience these in reality would not be of concern but may be an area where inspections should be focused once in operation). Maximum displacement of 10mm occurred in the top deck plate where expected and a minimum safety factor of around 2.3 was seen (see figures 18, 19 & 20 below).
3.3.3 Simulation 3 – Internal Pressure on Outer Chambers
For the internal pressure simulation, the full assembly was taken and split into a quarter section to speed up simulation run times. Additional fixed constraints were added accordingly (see figure 21 below).
Pressure loads of 19.6 KPa were added in conjunction with the load case document and applied to the model as shown in figure 22 below.
The stresses in the outer chambers were very low with some local high points of between 105 MPa and 125 MPa around lateral bracing and plate interfaces, this is compared to the material yield strength of 275MPa. There were also some very high stress concentrations picked up at beam joint locations but from experience these in reality would not be of concern, this may be an area where inspections should be focused once in operation. Maximum displacement of 12.47mm occurred in the corner baffle plate where expected and a minimum safety factor of around 2.2 (see figures 23, 24 & 25 below)
.
3.3.4 Simulation 4 – Internal Pressure on Inner Chamber
For the internal pressure simulation, the full assembly was taken and split into a quarter section to speed up simulation run times. Additional fixed constraints were added accordingly (see figure 26 below).
Pressure loads of 19.6 KPa were added in conjunction with the load case document and applied to the model as shown in figure 27 below.
In general the stresses in the outer chambers were very low with some local high points of between 40 MPa and 50 MPa around lateral bracing and plate interfaces, this is compared to the material yield strength of 275MPa. There were also some very high stress concentrations picked up at beam joint locations but from experience these in reality would not be of concern, this may be an area where inspections should be focused once in operation. Maximum displacement of 8.5mm occurred in the corner baffle plate where expected and a minimum safety factor of around 5.5 (see figures 28, 29 & 30 below).
3.3.5 Simulation 5 – Power Take Off Loads (Operational)
For the PTO simulation, 4 corner loads were applied to the top frame using a dummy PTO block along with a central load added to the central mounting pad. Constraints were added accordingly (see figure 31 below). This simulation should be re-run once a detailed corner PTO sub assembly is available.
Forces of 43.93 kN were added for the corner PTO loads as well as a central load of 185.82 kN in conjunction with the load case document and applied to the model as shown in figure 32 below.
The stresses in the PTO loads were very low with a maximum stress of 48.39 MPa (see figure 33 below). We are well below the fatigue limit of the steel based on a fatigue strength/endurance limit of 205 MPa (half the ultimate tensile strength of 410 MPa). Maximum displacement was 2.2mm but this was found at the unsupported end of the “dummy PTO block” which in reality would not be the case. Ignoring this, the maximum deflection elsewhere in the model was around 0.5mm (see figure 34 below). A minimum safety factor of 5.68 was achieved (see figure 35 below).
3.3.6 Simulation 6 – Towing
For the towing simulation, 2 loads were applied to the tow eye mounting plate and constrained as shown in figure 36 below
Loads of 2385.982 N were added to each face at set angles in conjunction with the load case document as shown in figure 37 below
The maximum stresses were very local to the mounting pad itself with the highest value of 34.79 MPa (see figure 37). Maximum displacement was 3.4mm at the outer extremities of the assembly (see figure 39) with a minimum safety factor of 7.9 (see figure 40).
3.3.7 Simulation 7 – Lifting
For the lifting point simulation the whole barge fabrication was suspended from the lifting lug mounting plates which are incorporated into the barge fabrication (see below). This represents a direct vertical lift.
Forces of 29.4kN were also added to each corner of the assembly to represent the additional weight of the corner PTO assemblies. This simulation should be re-run once a detailed corner PTO sub assembly is available along with all other top deck furniture/components (see figure 42 below).
The maximum stresses were very local to the lifting lug mounting plate itself with the highest value of 45.75 MPa (see figure 43). Maximum displacement was 0.43mm at the outer extremities of the assembly (see figure 44) with a minimum safety factor of 6 (see figure 45).
3.3.8 Simulation 8 – Mooring
For the mooring point simulation, the full assembly was taken and split into a quarter section to speed up simulation run times. Additional constraints were added accordingly (see figure 46).
A force of 98.1 kN was attached to the top beam end plate as shown in figure 47.
The maximum stresses was very local to where the cross brace meets the top frame member with the highest value of 240.7 MPa (see figure 48). Maximum displacement was 5.12 mm (see figure 49) with a minimum safety factor of 1.14 (see figure 50). Further work is required here but more detailed information is needed with regard to the mooring design.
3.3.9 Simulation 9 – Central Tether
For the central tether simulation, the whole barge fabrication was suspended from the central mounting pad to simulate a direct pull in excess of 20 tons (figure 51 below).
The maximum stresses were very local to the mounting pad itself with the highest value of 116.022 MPa (see figure 52). Maximum displacement was 0.7mm at the outer extremities of the assembly with a minimum safety factor of 2.37 (see figures 53 & 54).
4 System Design Change
Updated computational modelling Highlighted an increased efficiency in power capture with no additional depth setting floats to provide the net positive buoyancy as well as changing from a slack mooring system to a taught mooring system.
Although this system design change showed a big increase in power capture efficiency, it made the overall device increasingly weight sensitive due to the loss of the additional Buoyancy in the depth setting floats. The new approach was fully reliant on the Power capturing float to provide the positive net buoyancy.
4.1 Reactor Design Change
Investigations were carried out and concluded that a significant amount of weights was taken up purely by the stiffening required for the flat steel plates used to create the reactors chambers. It was now critical to look at alternative methods of constructing these chambers and incorporating them into a new reactor design. Several alternatives were considered and marked accordingly (see table 5)
4.2 Alternative Concept
Based on the analysis of the alternative options as presented in section 4.1, it was decided that a mild steel skeletal frame with separate composite flotation/ballast chambers was going to be the best alternative solution. The key advantages of this concept were potential significant reductions in submerged weight, efficient pressure vessel shape and constructability. As an additional benefit, separating the flotation/ballast chambers from the frame enabled the central Power Take Off (PTO) assembly to be dropped lower into the structure instead of sitting on the top deck (see figure 55 below). This allowed the main power capturing float position to be lowered dramatically which meant that the overall height of the device decreased and improved the whole centre of gravity for transportation and deployment.
5 Reactor Concept 2
5.1 General Design
The updated reactor design was constructed from a mild steel frame as discussed in section 5.2 above. The new frame had removable GRP floatation /ballast tanks fitted into the frame with an adjustable rubber mounting block interface. These tanks were secured in place with separate steel ‘J’ frames which bolted to the outside of the main reactor frame.
5.2 Computational Modelling & Analysis
5.2.1 3D Geometry
The updated reactor design was again constructed as a 3d model using Autodesk Inventor Professional. A basic skeletal frame was constructed in a similar way to the original design. Firstly, a top frame was constructed to provide the mounting intercace for all other top deck equipment. The frame was then build on to incorporate structure to provide the mounting interface for the separate tanks. Finally a skid section was added.
5.2.2 Assumptions
As stated in section 4.2.2 above, it is very difficult to simulate real life operating conditions and certain estimates and assumptions have to be made. These includes:
- No welds shown in any simulations to help simplify the model and speed up simulation run times.
- All faces set to fully bonded with a 3mm tolerance to take into account any gaps to be filled with weld in the manufacturing process
- All loads applied to whole mounting plate faces.
- Central PTO loads act vertically on the central mounting plate.
- All PTO load path do not take any misalignment into account.
- The reactor was appropriately constrained at the mooring attachment points to enable simulations to be run for operational and storm survival configurations.
- A gravitational load was applied in all simulations. Gravity taken as 9.81 m/s2.
- Flotation/ballast tanks and ‘J’ frames not included in any simulations.
5.2.3 Loadcase Summary
The Reactor Barge model was subjected to several load cases to simulate the following scenarios:
- Float in Cradle, Storm
- PTO Storm Loads
- PTO Operational Loads
- Lifting Points
- Towing
Each simulation was run and the results were evaluated to determine maximum stress, displacement and a minimum safety factor.
Simulation Title |
Minimum Safety Factor |
| Storm Loads With Float in Cradle | 2.1 |
| PTO Storm Loads | 2.5 |
| PTO Operational Loads | 2 |
| Lifting Point Loads | 2.4 |
| Towing Loads | 5 |
Table 6 – Concept 2 Minimum Safety Factors
5.2.4 Mesh Settings
The same mechanical properties were used for the updated reactors design as those shown in section 4.2.4.
5.2.5 Mechanical Properties
The same mechanical properties were used for the updated reactors design as those shown in section 4.2.5.
5.3 Simulation Results
5.3.1 Simulation 1 – Storm Loads with Float in Cradle
The full assembly model was taken and appropriate constraints applied to simulate the storm loads with float in cradle (see figure 58 Below).
Mooring loads of 229 kN were applied to the model along with corner PTO loads of 18.93 kN and a central PTO load of 134.6 kN all in conjunction with the loadcase document.
In general the stresses in the frame were relatively low with the exception of one area showing some stress concentrations of 1514 MPa. Further inspections of the model highlighted that these high stresses were at a single element and would not be of concern. Maximum Displacement of 11.07mm occurred in the centre of the reactor frame directly under the power capturing float, where expected and showed a minimum safety factor of around 2 (see figures 59, 60 & 61 below)
5.3.2 Simulation 2 – PTO Storm Loads
For the PTO Storm Load simulation, the full assembly was taken and appropriate constraints added to simulate the Wavesub being pulled down onto the seabed via the mooring winches. PTO loads and a central tether load were applied accordingly. A force of 134.6 kN to the central mounting plate as well as corner PTO loads of 18.93 kN to each corner as shown in figure 62 below.
Again, stresses in the majority of the Frame were very low, below 110 MPa with the exception of a single high stress point. Further inspections of the model highlighted that these high stresses were at a single node and would not be of concern. Maximum displacement of 9.784mm was again seen in the centre of the frame where expected and a minimum safety factor of around 2.5 (see figures 63, 64 & 65 below)
5.3.3 Simulation 3 – PTO Operational Loads
For the PTO Storm Load simulation, the full assembly was taken and appropriate constraints added to simulate the Wavesub being pulled down onto the seabed via the mooring winches. PTO loads and a central teather load were applied accordingly. A force of 134.6 kN to the central mounting plate as well as corner PTO loads of 18.93 kN to each corner as shown in figure 66 below.
Stresses in the majority of the Frame were very low, below 110 MPa with the exception of a single high stress point, identical to those in the PTO storm loadcase. Maximum displacement of 11.71mm was again seen in the centre of the frame where expected and a minimum safety factor of around 2 (see figures 67, 68 & 69 below)
5.3.4 Simulation 4 – Lifting Points
For the lifting point simulation, the whole barge fabrication was suspended from the lifting lug mounting plates which are incorporated into the barge fabrication (see below). This represents a direct vertical lift. Forces of 29.4kN were also added to each corner of the assembly to represent the additional weight of the corner PTO assemblies.
The maximum stresses were very local to the lifting lug mounting plate itself with the highest value of 114MPa (see figure 71). Maximum displacement was 0.43mm at the outer extremities of the assembly (see figure 72) with a minimum safety factor of 2 (see figure 73).
5.3.5 Simulation 5 – Towing
For the towing simulation, 2 loads were applied to the tow eye mounting plate and constrained accordingly. Loads of 2385.982 N were added to each face at set angles in conjunction with the load case document as shown in figure 74 below
The maximum stresses were very local to the mounting pad itself with the highest value of 84.84 MPa (see figure 75). Maximum displacement was 1.189mm at the outer extremities of the assembly (see figure 76) with a minimum safety factor of 5 (see figure 77).
6 Manufacturing Cost Comparison
It was critical that any design for the reactor had to be cost effective. It can be seen in figure 77 below how these costs directly feed into the Levelised Cost of Energy Equation.
Due to its complex design with chambers incorporated into it, concept 1 became increasingly heavy purely because of the sheer amount of material required to stiffen the frame and plate structure. The final design weight of concept 1 was over 32 tonnes. A basic cost breakdown for concept 1 can be seen below (see appendix 4 for full cost breakdown).
| Weight | 32 Tonnes |
| Raw Material Cost | £27,000 |
| Labour Cost | £168,000 |
| Paint Protection Cost | £25,000 |
| Total Cost | £292,000 |
Table 7 – Concept 1 Cost Breakdown
It’s easy to see by looking at the figures in table 6 above that the majority of cost does not come from the amount of raw material. The complexity of the design and amount of man hours required to fabricate a structure of such as this is clearly the main area where cost is incurred.
Concept 2 enables the structure to be simplifies for manufacture by not incorporating the chambers into the main frame. Instead relying on an alternative manufacturing process with a material with a significant reduction in mass. A basic cost breakdown for concept 2 can be seen below.
| Weight | 10.5 Tonnes |
| Raw Material cost | £17,000 |
| Flotation/Ballast Tank Cost | £32,000 |
| Labour Cost | £95,000 |
| Paint Protection Cost | £18,000 |
| Total Cost | £253,000 |
Table 8 – Concept 2 Cost Breakdown
Because the updated design did not have the tanks incorporated into the reactor structure, the cost for the separate tanks must be included in the raw material cost for a fair comparison. It’s clear that there is a saving of £10,000 with labour also greatly reduced as well as paint protection required. Overall there is a cost saving of £39,000 compared to the original reactor concept.
The biggest thing to take note of is both the reduction in raw material and the reduction in labour. One of the key aims of this project was to keep manufacturability of the reactor in mind and his shows a much leaner design concept with far less labour required.
7 Conclusion
The background research in this project takes a broad look at ocean energy, focussing specifically on wave energy. The research looks at the main classifications of wave energy converters, the general principles and current devices using them as well as alternative materials used to construct these devises.
The project aim was to create an optimised ¼ scale reactor design and carry out detailed analysis to determine in maximum stress, stress distribution, displacement and generally produce a design fit for purpose.
It is easy to see by looking at the reactor 1 concept simulations that there was the need for a large amount of additional steelwork to brace the flat panel sections creating the separate chambers. It was because of this additional material that the overall weight of the concept increased dramatically to over 32 tonnes. This also had an impact on the manufacturability of the reactor. By adding this amount of additional material, the complexity of the frame also increased and therefore had a direct impact of labour costs as seen in section 6.
There was then a system design change which required a complete design change to meet new requirements. The alternative design needed to be at least half the weight of the original design and therefore alternative construction methods were considered with the final decision of a mild steel construction with GRP tanks. Looking back at cost breakdowns in section 6 its clear to see that the updated concept 2 is a much better design solution. This design meets all the requirements set out in the original design specification and dramatically lowers overall weights and cost of manufacture. It is also easy to see that this design method would be easily scalable for a full-scale device.
With regards to the design and computational modelling of the reactor,
success can be measured in terms of the optimisation of a structure that does not yield under prescribed conditions. Under these criteria, the modelling was successful for both concepts. Loads such as the PTO operational loads are going to be occurring frequently and fatigue needs to be considered. Concept simulation results show a maximum stress of approximately 90 MPa which is less than a half of the fatigue strength/endurance limit of 205 MPa (half the ultimate tensile strength of 410 MPa). This gives a fatigue/endurance safety factor of 2.3. In a storm condition the results show a maximum stress of 165 MPa. This gives a fatigue/endurance safety factor of 1.3. This is deemed to be acceptable for a prototype device given that the storm load is based in a worst-case loading scenario with 25-year storm conditions.
7.1 Future Work
The modelling and analysis in this project is based on preliminary loading conditions. Once these conditions have been finalised and more accurate loading conditions are achieved, it is suggested that a final assembly model is created. This model should include all welded joints to try and reduce the number of high stress concentration points in the simulations. Adding welds and ensuring a smooth transition between the joints in the model should resolve this.
This model will also need to include detailed interface design between the reactor structure and any other load bearing auxiliary equipment. These interfaces should have the appropriate contacts applied to them and not rely on automatic contacts added by the Autodesk Invertor software. Faces should be split and corresponding faces should have contacts applied between them to achieve a more realistic simulation.
If the above is carried out and the results show that the material yield is exceeded, further design will need to be carried out. There may be a need to add additional structure locally to specific load paths or there may be a need to look at using alternative size steel sections and steel grades. This would then also have a direct impact of manufacturing costs and overall weight, something that is critical to the overall success of the WaveSub project and Marine Power Systems’ long-term aims.
References
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Appendix 1 – WaveSub Specification
Appendix 2 – Computational Loadcases
Appendix 3 –Operational Requirements
Appendix 4 – Reactor Concept 1 Cost Breakdown
Appendix 5 – Reactor Concept 2 Cost Breakdown
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