wave energy

1- Introduction

Objective: discuss the potential contribution of ocean energy to overall energy supply and climate mitigation.
Renewable ocean energy originates from six distinct sources, each with different origins and requiring different conversion technologies:
- Waves: energy from the wind transferred to the upper ocean surface; stores as potential energy (mass displacement from mean sea level) and kinetic energy (motion of water particles).
- Tidal Range: rise and fall driven by Earth–Moon–Sun gravitation and rotational effects.
- Tidal Currents: water flow resulting from tidal range (filling/emptying of coastal regions).
- Ocean Currents: wind-driven and thermohaline circulation.
- Ocean Thermal Energy Conversion (OTEC): energy from temperature differences between surface (solar-heated) water and colder water below ~1000 m.
- Salinity Gradients (osmotic power): energy from salinity differences between freshwater and seawater at river mouths.

2- Ocean energy

A. Wave energy

Wave energy is the energy transferred from wind to the ocean.
Energy storage forms:
- Potential energy: due to water mass displaced from the mean sea level.
- Kinetic energy: due to motion of water particles.
Wave size and period depend on:
- Wind speed
- Duration of wind blowing (order of days)
- Fetch: distance over which the wind blows across the ocean.
Waves efficiently transfer energy and can travel long distances as swells beyond storm regions.
Most energetic waves are generated between 30° and 60° latitudes by extratropical storms.

B. Tidal range

Tides are regular, predictable changes in ocean height due to gravitational and rotational forces among Earth, Moon, and Sun, plus centrifugal and inertial effects.
Common tidal patterns:
- Semi-diurnal: roughly two high tides and two low tides per day.
- Diurnal: only one high and one low tide per day.
Tidal day (lunar day): 24 h 50 min; this shifts the timing of successive high/low tides daily.
Diurnal and semi-diurnal tides occur at different times in different locations.
Tides vary in amplitude over the year due to relative Earth–Moon–Sun positions.
Spring tides: maximum tidal range when Sun, Moon, and Earth align (full moon and new moon).
Neap tides: minimum tidal range when Earth–Moon axis is at 90° to Earth–Sun axis.
Tide timing and magnitude depend on: global position, ocean bed shape, shoreline geometry, and Coriolis acceleration.
Amphidromic points: locations where tidal range is nearly zero, yet tidal currents may remain high due to differences in water surface levels on either side.

C. Tidal currents

Tidal currents are the horizontal water movements within tidal systems, driven by the rise and fall of tides.
Currents are generated by horizontal water movement and modulated by seabed bathymetry, especially near coasts or constrictions (e.g., islands).
Timing and magnitude of tidal currents are highly predictable and largely insensitive to climate change.
Near-shore currents exist; significant currents also occur in open ocean, with some regions (e.g., western boundary currents) offering sufficient velocities (~2 m/s) to drive present-day technologies.

D. Ocean currents

Ocean currents are continuous, directed water movements driven by multiple forces: wind, Coriolis effect, breaking waves, and temperature/salinity differences.
About 15% of the total solar input to the ocean is retained as thermal energy, concentrated at the surface and decreasing with depth due to low thermal conductivity.
Surface water temperatures can exceed +25°C in the tropics, while temperatures ~1,000 m depth range from +5°C to +10°C.

E. Ocean Thermal Energy Conversion (OTEC)

OTEC relies on temperature differences between surface warm water and colder deep water to generate electricity.
A minimum temperature difference of oxed{ riangle T 1 20^
ing C } is generally required to operate an OTEC plant.
OTEC resources: an annual average temperature difference map shows tropical areas with potential greater than $20^ ing C$ .
Characteristics:
- OTEC provides continuously available (base-load) energy, albeit with low energy density compared with wave/tidal energy.
- Seasonal variation exists (slight between seasons).

F. Salinity gradients (osmotic power)

Energy arises from mixing freshwater with seawater across a semi-permeable membrane, driven by chemical potential differences.
Two main concepts: Reversed Electro-Dialysis (RED) and Pressure-Retarded Osmosis (PRO).
RED: uses a stack of alternating anion and cation exchange membranes to generate voltage from chemical potential differences.
PRO: uses osmotic pressure difference as the driving force; seawater and freshwater have a tendency to mix; membranes permit selective water flow, generating pressure.
Osmotic pressure definition: oxed{ oxed{ 1 = i imes n imes R imes T } } where:
- $i$ is the Van 't Hoff index, representing the number of particles formed per dissolved substance.
- $n$ is molar concentration (mol/L).
- $R$ is the ideal gas constant.
- $T$ is temperature in Kelvin.
Typical osmotic pressure ranges for seawater vs freshwater: around $2.4-2.6 ext{ MPa}$ (24–26 bar).
Operational pre-pressurization: seawater is pressurized to about half the osmotic pressure, ~ $1.2-1.3 ext{ MPa}$ (12–13 bar).
In membrane modules, freshwater migrates through the membrane into pressurized seawater, producing brackish water that is split into two streams.
Power production distribution in PRO: roughly one-third goes to a hydropower turbine, while the remainder passes through a pressure exchanger to pressurize incoming seawater.
Brackish water can be returned to river or sea, with mixing of sources over time.

3- Technology and applications of wave energy

Numerous wave energy technologies exist, with demonstrations across operation principles to convert wave energy.
Major variables in wave energy systems:
- Mode of wave interaction with devices (heaving, surging, pitching).
- Water depth (deep, intermediate, shallow).
- Distance from shore (shoreline, nearshore, offshore).
A generic wave energy device scheme comprises three conversion stages:
- Primary interface: fluid-mechanical processes that feed mechanical power to the next stage.
- Secondary subsystem: can provide direct drive or short-term storage to facilitate power processing before electrical conversion.
- Tertiary conversion: electromechanical and electrical processes.
Wave energy converters are categorized by location, size, and operating principle:
- Location-based categories:
- Shoreline devices: attached to/embedded in boundary; easier maintenance; shorter offshore cables but potentially weaker wave regimes.
- Nearshore devices: suitable for moderate depths (10–25 m); example: a 2 MW device with a 1.5 MW wind turbine potential to be added; aims to maximize energy in close-to-shore areas; environmental considerations may limit large nearshore farms.
- Offshore devices: target high-power waves (> 40 m depth) before energy dissipation devices.
Wave energy converters (WECs) types by geometry/orientation:
- Point absorbers: small in diameter relative to wavelength; move to harvest energy from the wave motion in all directions, converting up/down pitching into rotary/oscillatory motion.
- Attenuators: elongated structures aligned with the wave direction; consist of multiple cylindrical sections connected by hinges; sections move relative to each other.
- Terminators: long devices perpendicular to the main wave direction; stationary or rotating to dissipate wave energy.
Other operating-principle categories:
- Pressure differential devices: oscillating water columns (OWC) and Archimedes principle converters; typically shoreline-adjacent.
- Overtopping devices: fluids collected above sea level and released through turbines; axial-flow turbines commonly used for low heads.
- Impact/surge devices: flexible/ articulated structures that move water mass within a constrained chamber.
Wells turbine (example of pressure differential concept):
- Self-rectifying air turbine with symmetric blades and no flow-direction-dependent twisting; rotates in the same direction regardless of airflow direction.
- Advantages: no guide vane is required; simplification of design.
- Drawbacks: noisy operation, narrow operating range, reduced torque at low flow; higher angle of attack causes flow separation and stall, reducing power extraction.
Wells turbine theory of operation and performance metrics (as given in the example):
- General coefficients:
- Torque coefficient: C_T = rac{T}{
 ho 1 ext{omega}^2 R^5}
- Stagnation pressure drop coefficient: C{po} = rac{ riangle Po}{
 ho 1 ext{omega}^2 R^2}
- Turbine efficiency: oxed{ oxed{ 1 = rac{T ext{omega} riangle P_o}{Q} } }
- Flow coefficient: oxed{ oxed{ 1 = rac{C_x}{U} } }
 where:
- $Cx$ = axial flow velocity, $U$ = rotor tip speed, $T$ = torque, $ho$ = density, $ext{omega}$ = angular velocity, $R$ = rotor tip radius, $riangle Po$ = total pressure drop, $ext{Q}$ = volume flow rate.
- Example values (Wells turbine):
- Tip diameter: $D_T = 588 ext{ mm} ightarrow R = 294 ext{ mm}$
- Hub diameter: $D_H = 400 ext{ mm}$
- Tip clearance: $t = 1 ext{ mm}$
- Rotational speed: N = 2000 ext{ rpm} \Rightarrow 1 = rac{2\u03c0 N}{60} = 209.33 ext{ rad/s}
- Flow velocity at inlet: $V = 12.31 ext{ m/s}$
- Torque: $T = 12.79 ext{ N·m}$
- Total pressure loss: $riangle P_o = 2476 ext{ Pa}$
- Air density: $ ho = 1.225 ext{ kg/m}^3$
- Derived quantities (from the example):
- Flow area: A = rac{1}{4}igl(DC^2 - DH^2igr) = rac{1}{4} igl( (DT + 2t)^2 - DH^2 igr) = 0.147 ext{ m}^2
- Volume flow rate: $Q = C_x A = 12.31 imes 0.147 = 1.81 ext{ m}^3/ ext{s}$
- Rotor tip speed: U = 1 imes R = 209.33 imes 0.294 = 61.54 ext{ m/s}
- Torque coefficient: C_T = rac{T}{
 ho 1^2 R^5} = rac{12.79}{1.225 imes 209.33^2 imes 0.294^5} \approx 0.1084
- Stagnation pressure drop coefficient: C{po} = rac{ riangle Po}{
 ho 1^2 R^2} = rac{2476}{1.225 imes 209.33^2 imes 0.294^2} \approx 0.053
- Efficiency: 1 = rac{T ext{omega} riangle P_o}{Q} = rac{12.79 imes 209.33 imes 2476}{1.81} \approx 60.24 ext{%}
- Flow coefficient: 1 = rac{C_x}{U} = rac{12.31}{61.54} \approx 0.20
Research trends in Wells turbine (examples and references): near blade tip and casing groove, near blade tip and casing endplate design, near blade trailing edge Gurney flap, static extended trailing edge, and radiused edge blade tips.
- References (examples):
- Halder et al. (2015): High-performance ocean energy harvesting turbine design – casing treatment scheme. Energy, 86, 219–231. doi:10.1016/j.energy.2015.03.131
- Madhan Kumar et al. (2021): Combined casing groove and blade tip treatment for wave energy harvesting turbine.
- Das et al. (2022): Performance improvement of a Wells turbine through automated optimization technique. Energy Conversion and Management: X, 16, 100285. doi:10.1016/j.ecmx.2022.100285
- Kotb et al. (2021): Potential of performance improvement of a modified Wells turbine using passive control for wave energy conversion. Ocean Engineering, 242, 110178. doi:10.1016/j.oceaneng.2021.110178
- Kumar et al. (2019): Performance enhancement of Wells turbine: Combined radiused edge blade tip, static extended trailing edge, and variable thickness modifications. Ocean Engineering, 185, 47–58. doi:10.1016/j.oceaneng.2019.05.041
Example recap: Wells turbine specs and computed performance metrics illustrate how design choices affect efficiency, pressure loss, and energy capture.

4- Technology and applications of tidal range

Tidal range development has historically focused on estuarine sites using a barrage to enclose an estuary and drive conventional low-head hydro turbines; a barrage can operate in both directions to generate electricity from incoming and outgoing tides.
Barrages create a reservoir (basin) with turbines between the inlet and the basin.
Alternative barrage configurations include multi-basin operations where basins fill and empty at different times; turbines are located between basins; such schemes can provide more flexible, near-continuous power generation.
The latest advances focus on offshore basins, i.e., tidal lagoons—single or multiple lagoons located away from estuaries.
A tidal lagoon is formed by installing a retaining wall across a bay or extending from the coast, creating ponds of water that are discharged through turbines at low tide.
The conversion mechanism most widely used for tidal range electricity is the bulb-turbine.
Typical capacity factor for tidal power stations is estimated to vary from 25 ext{% to }35 ext{%}.

5- Technology and applications of tidal and ocean currents

Technologies to extract kinetic energy from tidal, river, and ocean currents are under development; tidal energy converters are the most mature to date.
Key difference: river/ocean currents are generally unidirectional, while tidal currents reverse between ebb and flood; thus tidal turbines are designed to generate in both directions.
Turbines are classified by principle of operation: axial-flow, cross-flow, and reciprocating devices.
On a single device, multiple turbines may be used (examples often show multiple rotors).
Design considerations include:
- Reversing flow (tidal) needs bidirectional or reversible designs.
- Cavitation and harsh underwater conditions (salt water, debris, fouling).
- Axial-flow turbines can reverse nacelle direction with each tide or use fixed nacelle with blades that tolerate bidirectional flow.
- Rotor shrouds (cowlings/ducts) can improve hydrodynamic performance by increasing rotor velocity and reducing tip losses.
- Economic balance: the energy gained by shrouds must offset the additional cost over the device life.
- Turbine siting is crucial due to wake effects and to optimize array deployments (akin to wind farms).

6- Technology and applications of ocean thermal energy conversion (OTEC)

OTEC plants can use three conversion schemes: open cycle, closed cycle, and hybrid.
Open cycle: water serves as the working fluid.
- Surface seawater is pumped into a low-pressure chamber where evaporation occurs.
- The low-pressure steam drives a turbine; evaporated steam can be discharged into the ocean or condensed with seawater to produce desalinated water.
Closed cycle: uses a working fluid such as ammonia or freon in a low-temperature Rankine cycle.
- Surface seawater passes through an evaporator to vaporize the working fluid.
- The vapor drives a turbine; the vapor is condensed by cold seawater typically from depths below 1000 m.
Hybrid cycle: combines attributes of closed and open cycles; after heating, seawater enters a flash evaporator, with partial desalination.
Challenges of OTEC include maintaining vacuums, biofouling and corrosion in heat exchangers, and reliable long-term operation.

7- Technology and applications of salinity gradients

Energy arises from mixing freshwater and seawater; the heat effect is small.
RED and PRO are the main concepts for converting this chemical potential into electricity.
Reversed electro dialysis (RED): uses an array of anion/cation exchange membranes to generate a voltage from chemical potential differences between concentrated salt solutions and freshwater.
- The chemical potential difference generates voltage across membranes; the total system potential is the sum of membrane voltages.
Pressure-retarded osmosis (PRO): uses osmosis (osmotic pressure difference) as the driving force; the difference in salt concentration creates a driving force for water flux through semipermeable membranes.
Osmotic pressure formula (Van 't Hoff): oxed{ 1 = i imes n imes R imes T }
- i = Van 't Hoff index (number of particles per dissolved substance).
- n = molar concentration (mol/L).
- R = 0.08206 L·atm·mol⁻¹·K⁻¹.
- T = temperature in Kelvin.
For seawater and freshwater, typical osmotic pressure differences are about $2.4-2.6 ext{ MPa}$ (24–26 bar).
Pre-pressurization: seawater is pressurized to about half the osmotic pressure, approx. $1.2-1.3 ext{ MPa}$ (12–13 bar).
In PRO membranes, freshwater migrates into pressurized seawater, producing a brackish stream; the brackish water can be split into streams for power generation and pressurization.

8- Summary of practical considerations and connections

Ocean energy sources offer complementary options for a diversified renewable energy portfolio: waves provide high energy density but spatially variable; tides and currents offer predictable resources; OTEC and salinity gradient technologies provide base-load potential in suitable regions.
Technological maturity varies by resource: tidal range and salinity gradients have seen practical deployments, while many ocean current and osmotic concepts are still under development.
Environmental, economic, and grid integration considerations drive device siting, scale, and combination with other renewables.
Research and development focus areas include: improving device efficiency, reducing costs (e.g., through loss reduction, array optimization, and passive flow-control strategies), and addressing reliability and maintenance challenges underwater.

9- Quick reference: Key values and concepts from the material

Global theoretical wave energy potential: $32{,}000 ext{ TWh/yr}$ (roughly twice the 2008 global electricity supply of $16{,}800 ext{ TWh/yr}$ ).
Latitude range associated with the most energetic ocean winds (30°–60°).
Open-cycle OTEC concept uses surface water as working fluid; closed-cycle uses ammonia or Freon; hybrid combines both.
Tidal lagoon capacity factor: 25 ext{%}–35 ext{%}.
Shallow to intermediate water depths (10–25 m) are typical for nearshore wave devices; offshore devices target deeper waters (>40 m).
Tidal current speeds around $2 ext{ m/s}$ in favorable regions.
Example Wells turbine (numerical):
- Tip diameter: $DT = 588 ext{ mm}$ ; hub diameter: $DH = 400 ext{ mm}$ ; tip clearance: $t = 1 ext{ mm}$ .
- Rotation: $N = 2000 ext{ rpm}$ ; wind speed: $V = 12.31 ext{ m/s}$ ; torque: $T = 12.79 ext{ N·m}$ ;
- Pressure loss: $riangle P_o = 2476 ext{ Pa}$ ; density: $ ho = 1.225 ext{ kg/m}^3$ .
Wells turbine derived coefficients (example):
- $C_T ext{ (torque coefficient)} \approx 0.1084$
- $C_{po} ext{ (stagnation pressure drop coefficient)} \approx 0.053$
- 1 ext{ (efficiency)} \approx 60.24 ext{%}
- 1 ext{ (flow coefficient)} \approx 0.20
Osmotic pressure example: for a 2.0 M NaCl solution at 30°C and 200 L water, 1 \approx 0.497 ext{ atm} (illustrative calculation shown in the source).