Harnessing Wave Energy: Breakwaters And Bearing Selection

1. Design a bearing assembly that minimises power loss.
2. Select bearing materials and coatings for minimum friction and wear.
3. Design a complete conditioning monitoring system for a machine to ISO standards.
 

Global Potential of Wave Energy

Recently governments all over the world, the United Kingdom included, have shifted their attention to clean and sustainable sources of energy. This is mainly due to the finite natural resources, the climate change threat and the increasing human population and industrialization (Ringwood, 2014). Governments have are finding efficient and convenient alternatives to the conventional fossil fuel energy. In the first century, renewable energy sources such as wind, solar and ocean energy have become so common in various countries. The potential of global wave energy stood at around 3.7 terawatts (TW) according to a research by Mork et al (Astariz, 2015). This is much greater than the current installed energy capacity all over the world.

The wave energy technology is in early development stages and several techniques have been developed to harness the wave energy from the oceans and convert it into electrical energy. The system generally consists of a collector that internments and transfer waves to air energy, the pneumatic energy are then converted to electricity by a power takeoff system (PTO) (Falcao, 2016).Wave action causes the pressure inside the collector to increase and decrease continuously. The wave technology system is comprised of several moving mechanical parts and therefore bearing plays a critical role in the operation of the system. The site selected and the water conditions highly determine the efficiency of the system and how long they can be operational.   

Breakwaters were mainly crated to produce safe havens for boats and ships in the rough oceans but they are nowadays a very critical component in wave energy harvesting (Daniel, 2016). The material selected for the bearing and the conditions determine the how long the bearing is going to last in proper condition.  The existing breakwater is a coastal structure constructed to avert the overwhelming effect of waves on the shoreline and marine vehicles. The breakwater should be erected vertically to the shoreline where they are normal or almost normal to the wave line (Uihleim, 2016). The expensive power generation components are placed onshore where they are protected from the harsh marine environment by the breakwater. The selected existing breakwater must be strong enough to withstand the pressure of the waves and the weight of the energy conversion systems. The breakthrough should be high than the maximum height reached by the waves.

According to Van der Meer, the maximum height the incident wave reaches (R us) is given as,

Technology Used to Harness Wave Energy

R _us = 1.5y_f y_b H_s (tanα /√5)

Where; y_{f is} a reduction factor for friction

           y_b is a reduction factor for existence of a berm

           H_s is the significant wave height

           Α is the wave steepness

In reality, monochromatic ocean waves do not occur but it is essential to investigate the operation of the WEC components in regular waves in UK. More realistic conditions will involve the incorporation of energy losses and eliminate assumptions as much as possible. The emblematic hydraulic PTO system behaves just like a Coulomb damper that produces a square wave force instead of a viscous sinusoidal damper. The PTO unit includes the power losses due to friction and the height of the wave slightly reduces the efficiency of the unit. The losses involved include friction in the pipework and cylinder, pressure losses across check valves and internal flow leakages in the motor.

Backwater is a water body caused by either a flood tide or held back by a constructed dam. The estimated maximum height of the waves should be used to determine how a wall can be constructed to establish a backwater. During stormy weather the equipment is designed to be raised outside the ocean to avoid damage. In the site selection process, a backwater should be considered as an essential part.

There is viscous drag offered by the ocean water therefore the lower part of the vertical cylindrical boy is an extended hemisphere to reduce the viscous drag. We assume that the fluid is incompressible and has zero viscous losses to use hydrodynamic equations to solve the forces involved and the motion.

The buoy motion is given by the equation; 

M=fh(t)+ fm(t)

Where; m - mass of the buoy              X – acceleration of the buoy               fh(t) – Vertical component of the total wave force                  fm(t)  - Vertical component of the mechanical force The force of the wave can further be simplified as; Fh(t)=fe(t) + fr(t) + fhs (t) Where; fe(t) – Excitation force                 fr(t) – force produced by an oscillating body               fhs(t) – linearized hydrostatic force The radiation force can be related to angular velocity and acceleration of the buoy as ;  Where; A(ω) – added mass coefficient             B(ω) – radiation damping coefficient The produced hydrostatic force is given by; Fhs= (t) = - pgsx Where; ρ – ocean water density             g – gravitation constant            S – cross-section area of the buoy in x-direction Angular Velocity Erotational =   0.5 I ω2 Where; ω- angular velocity              I – moment inertia              E – kinetic energy Assuming the buoy moves at an angle of 600 per unit time then the angular velocity can be calculated as shown below; ω = 60x (2 / 360 rad/s       = 1.047 rad/s The vertical force caused by the up and down movement of the piston is 4000 N  implying the float makes a 2000 N force in its up and down movement. The total mass of the system consisting of the lever, arm and the float is estimated to be 250 kg. The breakwater has a height of O.4 m and the interval between waves is estimated to 5 seconds. The hydraulic power can be calculated from the pressure exerted and the flow rate of the fluid in the hydraulic pipe work. Assume a piston of 0.5 m2 cross-sectional area and a flow rate of 150 l/s. Pressure= Force x Area                   =2000 x  0.5                    =1000 pa Hydraulic Power = (Flow rate x pressure) / 600                                 =(150 x 1000) / 600                                  =250 kw Assuming the hydraulic system and all the components are operating at an average of 85 percent. The electrical  power generated = 0.85 x s50                                                            = 212.5 KW At a wave interval of 5 second and assuming constant fair weather conditions; Daily energy produced = (24 x 60 /5) x 212.5                                            = 60.912Kw Given that the system consist of 5 units, Total Annual Energy produced= 60.912 x 365 x 5                                                         =111.16 Mega Watts Bearing Diameter/ Width Selection           The selected bearing diameter should sufficient enough to withstand all the opposing forces during the up and down movement of the lever (Babarit, 2015). The length of the lever is approximately 1.5 meter so we assume the weight of the system acts at the center of the arm, that is, 0.75 m. The bearing loads can be assigned as P1 and P2 for the arm and the buoy respectively. Taking moments about the breakwater, let say point A, P2= Force x Distance        =2000 N X 1.5 m      = 3000 NM P1 = p2 F X O.75 = 3000 F2= 3000 / 0.75       =4000N Pressure= Force x Area

1000= 4000 x A

A= 1000 / 4000

   = 0.25 m²

A=

 r   = √ (0.25/3.14)

      = 0.28 

The maximum load is 4000 N which lies between 1000 and 1000 in the graph. The waves are estimated to be occurring once after 5 seconds therefore the revolution per second stands at around 0.2. Using the above graph the selected diameter of the bearing should be 5mm to accommodate any energy losses and fluctuations in the force generated by the waves. 

Calculation of Maximum Allowable Tear and the PV limit

Wear Volume, Q = KWL and k= Q /WL

Where

v = volume of worn material (m³)

W = normal applied load (N)

L = total sliding distance (m)

k = is the “specific wear rate” also known as wear coefficient.  The standard units are m² N^-1.   Values of 10^-16 or lower are indicative of mild wear, and values greater than 10^-14 represent severe wear.

Critical Roles of Breakwaters and Bearings

Most material wear rates lie within the 10^-17 and 10^-12.

Estimating the volume of worn material = maximum wear depth x worn area

                                                                   = 0.001 x 0.25 = 0.00005 m³.

Specific wear rate, k = Q /WL

                               k =0.00005 / 2000 x 0.4

                                   = 6.25 x 10^-08 m²N^-1

Since the value is greater than 10^-14 it implies a great wear

PV factor;

Average interface pressure, P = W/A

Volume removed,   Q = A?h

Distance of sliding, L = V?t, where V is velocity, t is time

Therefore, Q =K WL / H becomes A?h = K (P?A) (V?t)/H, or

                           h/t = K (PV) / H

h/t is the wear rate (m/s) and PV is known as the ‘PV’ factor.

PV ê  wear rate  ê     H é wear rate  ê 

The maximum PV factor is = 6.25 x 10^-08 / 0.4

                                             = 1.56 x 10^-07

Increasing PV increases both wear rate and interface temperature.  For polymers, this will soften them and further increase wear rate.  

The estimated values above have been calculating assuming zero viscous drag and friction. However in the ideal working operations of the system there is friction force in the bearing as well as viscous drag that leads to energy losses (Veigas, 2014). It is hard to estimate the energy losses due to viscous drag and we will assume they are negligible.

The power loss due to friction in the bearing can however be calculated using the friction coefficient. Assuming the friction coefficient of the bearing material is 03

Friction force, F = μW     = 2000 x 0.3 = 600

 Power = F?V = μWV = 600 x 15 = 9.000 Kw

Thus heat generated is equal to the energy loss = μWV   

Now Heat loss from contact α 1/A (and will also depend on thermal conductivity, heat paths etc.) 

The k value of the system is 6.25 x 10^-08 m²N^-1 and this is greater than the k values of group 3 and group 4 materials. For optimum operation of the system the final design should be made of group 4 material. The bearing design should be hydrodynamic bearings. Carbon graphite should be used due to its high mechanical strength and its low chemical reaction will make it suitable for the harsh ocean environment.  

The completed sustainable wave energy converter technology will require an efficient real-time monitoring system to ensure the technology operates at its maximum efficiency.  There are so many interrelated factors involved and automation of the system is necessary. Real-Time Integrated Monitoring and Control Systems (RTIMCS) have been developed mainly in the generator control and power take-off (PTO) (Greaves, 2015). The supervisory monitoring of these systems is very important and will help improve the efficiency of wave energy converter systems. 

Calculation of Maximum Allowable Tear and the PV Limit in Bearing Selection

Condition monitoring is significant in ensuring that the operation and maintenance costs are reduced because of the environment the ocean energy devices operate in. The various subsystems of the wave energy converter have to be monitored in the harsh environmental conditions they operate in. The condition monitoring mechanism should consist of the latest sensors that will help regulate and detect faults efficiently.

Vibration sensors are important in velocity sensors for mid frequencies and position transducers in the system. Discrete Wavelet Transform (DWT) can also be applied to the appropriate vibration sensors. Gearbox and bearing monitoring techniques that are used in wind energy can both be applied in ocean energy sector.

Acoustic sensors can also be used in the system. Crack propagation, slipping of grain boundaries, as well as plastic deformation, may generate elastic waves and hence acoustic sensors will detect these waves. Temperature sensors must be part of the monitoring system considering the fact that there is friction between moving parts of the bearing. The heat generated contributes to a significant loss of energy; therefore, the temperature should be maintained at the optimum range. Current, power and flux sensors should be installed to regulate the speed of the motor according to the values of these variables. 

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