tidal-energy

name	tidal-energy
description	Tidal energy conversion — tidal stream (horizontal axis tidal turbine, HATT; Betz limit; thrust coefficient; tidal current resource), tidal range (barrage/lagoon; potential energy E = ρgAR²/2; sluicing strategy), tidal turbine blade design (NACA profiles; TSR; cavitation; marine growth), mooring and foundation loads (drag, lift), resource assessment (harmonic analysis, M2 constituent), environmental impact, and leading projects (MeyGen, SIMEC Atlantis, Orbital Marine).
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Tidal Energy Conversion — Complete Skill

Tidal Resource Fundamentals

Tidal Forcing

Tidal constituents: superposition of astronomical forcing M2 (principal lunar semidiurnal): period 12.42 h; dominant worldwide S2 (principal solar semidiurnal): period 12.00 h; 46% of M2 amplitude N2 (larger lunar elliptic): period 12.66 h K1, O1, P1: diurnal constituents; dominant where diurnal tides predominate (Gulf of Mexico, Pacific Coast)

Spring-neap cycle: M2 and S2 beat → spring tides (M2+S2, ~14-day peaks) and neap tides (M2−S2, half amplitude) Spring tidal range R_spring = 2 × (A_M2 + A_S2) [A = amplitude of constituent] Neap range R_neap = 2 × |A_M2 − A_S2|

Tidal current speed: u(t) = Σᵢ Uᵢ × cos(ωᵢt + φᵢ) [Uᵢ = amplitude; ωᵢ = angular frequency; φᵢ = phase] Annual mean spring peak u_s typically reported; resource characterized by u_s or power density

High-resource sites (>2 m/s spring current): Pentland Firth (Scotland): u_s = 3–5 m/s; MeyGen project Bay of Fundy (Canada): large range; u_s = 3–4 m/s Alderney Race (Channel Islands): u_s = 4–5 m/s

Tidal Stream Energy Conversion

Betz Theory for Tidal Turbines

Available power in tidal stream: P_available = 0.5 × ρ_water × A_rotor × u³ [ρ_water = 1,025 kg/m³; A = πD²/4; u = undisturbed current] Power density: P/A = 0.5 × 1,025 × u³ [W/m²] At u = 2 m/s: P/A = 4,100 W/m² = 4.1 kW/m² (much higher than wind at same speed due to density) At u = 3 m/s: P/A = 13.8 kW/m²

Betz limit: C_P,max = 16/27 = 0.593 [theoretical maximum power coefficient] P_max = C_P,max × 0.5 × ρ × A × u³ = 0.296 × ρ × A × u³

Thrust force on rotor: T = C_T × 0.5 × ρ × A × u² [C_T = thrust coefficient; C_T = 8/9 at Betz optimum] At u = 2 m/s; D = 20 m; C_T = 0.8: T = 0.8 × 0.5 × 1,025 × π(10)² × 4 = 0.8 × 0.5 × 1,025 × 314.2 × 4 = 514 kN

Typical C_P values: Modern HATT (Horizontal Axis Tidal Turbine): C_P = 0.40–0.45 at design TSR Variable pitch turbine: maintains C_P_max over wider u range; preferred for tidal

Tip Speed Ratio

TSR (Tip Speed Ratio): λ = ω × R / u [ω = rotor angular velocity; R = blade tip radius; u = inflow velocity] Design λ_optimal for HATT: λ = 5–7 (similar to wind turbines)

Rotational speed: n = λ × u / (π × D) [rev/s; or × 60 for RPM] Example: D = 18 m; u = 2.5 m/s; λ = 6: n = 6 × 2.5 / (π × 18) = 0.265 rev/s = 15.9 RPM

Torque: Q = P / ω = C_P × 0.5 × ρ × A × u³ / (λ × u / R) = C_P × 0.5 × ρ × A × u² × R / λ

Blade Design

NACA profiles for tidal blades: Typical: NACA 63-4xx or 65-4xx series; t/c = 18–25% at root; 12–18% at tip C_L/C_D_max: 60–100 (for clean marine profiles at Re = 10⁶–10⁷) Design lift coefficient: C_L = 0.8–1.2 at design angle of attack

BEM (Blade Element Momentum) design: c(r) = (8π × r × sin(2θ_p/3)) / (N_B × C_L × (1 + (4a/(1−a) × (r/R)²/λ² + ...)^0.5)) [local chord; Prandtl tip loss applied] a = 1/3 (induction factor at Betz optimum); N_B = 3 blades typical

Cavitation: Cavitation number: σ = (p_∞ − p_v) / (0.5 × ρ × v_rel²) p_∞ = p_atm + ρg × h_depth [at depth h; increased pressure delays cavitation] Critical: σ > σ_cr to avoid cavitation; low-pressure suction side at high TSR most susceptible Design: blade sections with σ_cr < σ at design TSR; deeper turbines more cavitation-safe

Marine growth: Barnacles, mussels, seaweed: increases blade roughness → earlier transition → higher drag; C_L/C_D reduces 20–40% Anti-fouling coatings or scheduled cleaning (dry dock or diver/ROV) Service interval: 6–12 months for inspection; 2–3 years for major maintenance

Tidal Range Devices

Tidal Barrage

Principle: dam across tidal estuary; water level difference H drives turbines during ebb/flood cycle Available energy per cycle: E = 0.5 × ρ × g × A_basin × R² [R = tidal range; A_basin = basin area] Example: La Rance (France): A = 22 km² = 22×10⁶ m²; R = 8 m E_cycle = 0.5 × 1,025 × 9.81 × 22×10⁶ × 64 = 7.14×10¹² J = 7.14 TWh per semi-diurnal cycle But two cycles per day (M2); actual energy yield accounting for variable R and efficiency: P_avg = 240 MW (La Rance actual)

Sluicing strategy: Ebb generation only: sluice fills on flood; generates on ebb (most common) Two-way generation: generates on both ebb and flood; more complex hydraulic turbines Pumping: pump water into basin near high tide → raise effective head → more energy

Bulb turbine: horizontal axis; low head (H = 2–10 m); large diameter (5–8 m); reversible for two-way Capacity factor: 25–35% (limited by tidal timing)

Tidal Lagoon

Offshore lagoon: semi-circular impoundment in open sea; no estuary required No complete estuary blockage → less environmental impact than barrage Swansea Bay tidal lagoon concept: A = 11.5 km²; R = 4.5 m; installed capacity 320 MW

Multiple lagoons: phase-shifted lagoons → more consistent output; compensate for slack water

Structural and Foundation Design

Gravity Base Foundation

Overturning from thrust: M_overturning = T × H_hub [T = rotor thrust; H_hub = height above mudline] Self-weight restoring: M_restoring = W_structure × B/2 [B = base width] Safety factor: M_restoring / M_overturning ≥ 1.5

Scour protection: Near-bed current velocity accelerates around structure → sediment erosion Rock armor filter layers extend 3–5× D from foundation perimeter Design: d_50 = 0.036 × (u_scour² / Δg) [van Rijn; Δ = 1.65 for rock]

Mooring (Floating/Semi-submersible Turbines)

Catenary mooring: Restoring force F_moor = f(horizontal displacement) from catenary geometry Steel chain or synthetic (polyester) tethers; anchor types: drag embedment, suction caisson, driven pile Fatigue from tidal current fluctuations → mooring line cyclic tension; assess with T-N curves

Resource Assessment

Harmonic analysis: fit tidal gauge or ADCP (Acoustic Doppler Current Profiler) data to tidal constituents Least-squares fit: η(t) = Σᵢ [aᵢcos(ωᵢt) + bᵢsin(ωᵢt)] [η = water level or velocity] Outputs: amplitudes and phases of all significant constituents

Power density distribution: Annual power density map: P/A = 0.5 × ρ × <u³> [cube of mean-cubed speed] Resource grade: Excellent > 5 kW/m²; Good 2–5; Marginal < 2

Array effects: tidal turbine farms reduce flow → downstream turbines see lower u → spacing optimization Allowable extraction: up to ~20–30% of natural flux without significant tidal regime change

Leading Projects

MeyGen (Pentland Firth, Scotland): 6 MW (Phase 1A); 4 × 1.5 MW Andritz Hydro Hammerfest turbines; fully operational; Cf ≈ 40% SIMEC Atlantis AR2000: 2 MW; largest single turbine; 24 m diameter; ebb and flood Orbital Marine O2: 2 MW floating tidal turbine; 74 m long; twin 1 MW rotors; off Orkney

Standards and References

Standard	Scope
IEC 62600-200	Tidal energy — Power performance assessment
IEC 62600-201	Tidal energy — Reliability, availability, and maintenance
DNV-ST-0164	Tidal turbines — structural and marine systems
EMEC	European Marine Energy Centre — testing and protocols
Cornett (2006)	Global tidal resource inventory

Output

Provide: site data (location; tidal constituent A_M2 [m/s]; u_spring_peak [m/s]; u_neap [m/s]; water depth [m]; duration data: % exceedance above 1/2/3 m/s), power available (P/A = 0.5×ρ×u³ [kW/m²] at spring; annual mean P [kW/m²] from probability distribution), rotor design (HATT: D [m]; N_B = 3; TSR λ; n_rated [RPM]; C_P at rated u; P_rated [kW]; C_T; thrust T [kN]), blade profile (NACA series; t/c at root/tip [%]; chord c(r) from BEM; pitch angle; cavitation number σ at tip; σ > σ_cr confirmed), turbine specifications (generator: rated P [kW]; rated speed; gearbox ratio; overall η including generator ×0.90), foundation (gravity base: dimensions; mass [t]; overturning check SF; scour protection r_armor [mm] D_50), annual energy (AEP = P_rated × Cf [MWh]; Cf = 30–40%; capacity factor based on u distribution), environmental (marine growth plan; environmental impact: fish passage; noise <160 dBre1μPa at 500m), comparison (vs. offshore wind: $/MWh; capacity factor; predictability advantage), and applicable standard (IEC 62600-200 for performance; DNV-ST-0164 for structure; EMEC test protocol).