solar-thermal-systems

name	solar-thermal-systems
description	Solar thermal systems — flat plate collector (Hottel-Whillier model, FR, UL, FRUL), evacuated tube collectors, concentrating solar power (parabolic trough, Fresnel, heliostat/tower, dish-Stirling), optical efficiency, concentration ratio, working fluids (water, glycol, thermal oil, molten salt), solar fraction, storage sizing, TRNSYS simulation, ASHRAE 93 collector test, and net metering for solar thermal.
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Solar Thermal Systems — Complete Skill

Solar Resource

Irradiance Definitions

Global Horizontal Irradiance (GHI): total solar radiation on horizontal surface GHI = DNI × cos(θ_z) + DHI [θ_z = solar zenith angle; DNI = Direct Normal Irradiance; DHI = Diffuse]

Direct Normal Irradiance (DNI): beam radiation perpendicular to sun ray (used for concentrators) Typical: DNI = 700–1,000 W/m² peak; annual average 4–7 kWh/m²/day (good solar sites)

Air mass: AM = 1/cos(θ_z); AM 1.0 = sun at zenith; AM 1.5 = standard test (θ_z = 48.2°) Extraterrestrial irradiance: G_0 = 1,361 W/m² (solar constant at AM 0)

Solar angle equations: Hour angle ω = 15° × (t_solar - 12) [t_solar = solar time; ω = 0 at noon; ±15°/hr] Declination δ = 23.45° × sin(360° × (284 + DOY)/365) [DOY = day of year] cos(θ_z) = sin(φ)×sin(δ) + cos(φ)×cos(δ)×cos(ω) [φ = latitude]

Flat Plate Collectors

Hottel-Whillier-Bliss (HWB) Model

Useful heat collected: Q_u = A_c × F_R × [G_T × (τα) - U_L × (T_fi - T_a)] [W; key collector equation]

Variables: A_c = collector aperture area [m²] G_T = total irradiance on tilted collector surface [W/m²] (τα) = transmittance-absorptance product (optical efficiency); typical τα = 0.75–0.90 U_L = overall heat loss coefficient [W/m²·K]; typical 3–8 W/m²·K (flat plate) T_fi = fluid inlet temperature [°C] T_a = ambient temperature [°C] F_R = collector heat removal factor

Collector heat removal factor F_R: F_R = (ṁ × c_p) / (A_c × U_L) × [1 - exp(-A_c × U_L × F' / (ṁ × c_p))] F' = collector efficiency factor (accounts for fin efficiency between tubes) F' = W/(U_L × [1/(U_L × (W-D)) × (1/F_fin) + 1/(π×D_i×h_fi)])^(-1) [W = tube pitch; D = tube OD; h_fi = internal conv. coeff.] For well-designed collector: F_R = 0.70–0.92; F' = 0.85–0.97

Collector efficiency (instantaneous): η = Q_u / (A_c × G_T) = F_R × [(τα) - U_L × (T_fi - T_a)/G_T] η = η₀ - a₁ × X - a₂ × G_T × X² [ASHRAE 93 / ISO 9806 form; X = (T_fi - T_a)/G_T; η₀ = F_R(τα); a₁ = F_R U_L; a₂ = F_R U_L2]

Example flat plate collector: F_R(τα) = 0.72; F_R U_L = 4.5 W/m²·K; G_T = 800 W/m²; T_fi = 60°C; T_a = 20°C η = 0.72 - 4.5 × (60-20)/800 = 0.72 - 0.225 = 0.495 (49.5%) Q_u = 0.495 × 800 = 396 W/m²

Heat Loss Coefficient U_L Components

U_L = U_top + U_bottom + U_edge: U_top (through cover glass) dominates: U_top = [hc_conv + h_r_plate-cover + ...]^(-1) + 1/h_wind U_bottom (through insulation): U_bottom = k_insul / t_insul ≈ 0.04/0.05 = 0.8 W/m²·K (50mm mineral wool) For single-glass flat plate: U_top ≈ 4–6 W/m²·K; for double-glass: U_top ≈ 2–3 W/m²·K

Evacuated tube collectors: U_L = 0.5–1.5 W/m²·K (very low; vacuum eliminates convective loss) η₀ = 0.65–0.78; better at high T (swimming pool heating 50°C+ benefits significantly)

Concentrating Solar Power (CSP)

Concentration Ratio and Optical Efficiency

Concentration ratio C: C = A_aperture / A_receiver [geometric; ratio of intercepted area to absorber area] Parabolic trough: C = 15–80; linear Fresnel: C = 10–40; tower/heliostat: C = 300–1,000; dish: C = 500–3,000

Optical efficiency η_opt: η_opt = ρ_mirror × (τα)_receiver × γ × cos(θ) [ρ = mirror reflectivity; γ = intercept factor; θ = incidence angle] ρ = 0.92–0.94 (high-quality silver mirror); γ = 0.95–0.99 (intercept factor from ray tracing) θ = angle of incidence on aperture; IAM (Incidence Angle Modifier) corrects for off-normal incidence

Receiver heat gain: Q_u_receiver = η_opt × C × A_aperture × G_DNI - A_receiver × U_receiver × (T_receiver - T_a) [U_receiver = 0.05–0.15 W/m²·K for evacuated receiver tube (parabolic trough)]

Maximum concentration (thermodynamic limit): C_max = (sin²θ_sun) → for sunlight θ_sun = 4.65 mrad → C_max = 46,200 (geometric maximum)

Parabolic Trough

Most deployed CSP technology: Width: 5–9 m aperture; focal length 1.7–3.0 m; receiver tube (HCE) at focal line HTF (Heat Transfer Fluid): Therminol VP-1 or Hitec XL or synthetic thermal oil; T_max ≈ 400°C Annual capacity factor: 20–40% without storage; 40–50% with 6–15 h thermal storage

Steam conditions for power block: Typical: Rankine cycle; T_HTF = 390°C → T_steam ≈ 370°C; P_steam = 100 bar; η_Rankine ≈ 37% Overall solar-to-electric: η_CSP = η_opt × η_receiver × η_HX × η_Rankine ≈ 0.93×0.95×0.97×0.37 ≈ 32%

Linear Fresnel: Lower cost (flat mirrors); lower efficiency (larger cosine losses, blocking/shading); easier to maintain η_opt ≈ 0.55–0.70 (vs. 0.70–0.80 for parabolic trough)

Central Receiver (Tower + Heliostat Field)

Solar field: Heliostats (flat or slightly curved mirrors): 50–150 m² each; motorized tracking (2-axis) Field efficiency: weighted average cos(θ) × atmospheric attenuation × blocking/shadowing ≈ 0.55–0.75

Receiver types: External receiver (Gemasolar/SolarTwo): molten salt falls over external tubes Volumetric air receiver: open porous surface; T_air = 700–1,000°C; for Brayton/combined cycle Cavity receiver: windowless; better optical efficiency; direction-specific field layout

Molten salt storage: 2-tank (cold 290°C + hot 565°C) nitrate salt (NaNO₃/KNO₃ 60/40): E_storage = ρ×Cp×ΔT×Volume ρ = 1,860 kg/m³; Cp = 1.5 kJ/kg·K; ΔT = 275°C E_per_m³ = 1860 × 1.5 × 275 = 768 MJ/m³ = 213 kWh/m³ (thermal) For 6 h × 100 MW_thermal: V = 6×3600×10⁸ / (768×10⁶) = 2,812 m³ total salt

Dish-Stirling System

Highest solar-to-electric conversion (28–32% peak): Parabolic dish D = 5–25 m; Stirling engine at focal point; T_max = 700–900°C C = 500–3,000; small scale (3–50 kW per dish) No thermal storage (direct power generation only)

Thermal Storage

Sensible Heat Storage

Sizing: E_storage = ρ × Cp × ΔT × V [J; V = storage volume] ΔT = T_hot - T_cold (temperature swing of storage)

Materials: Water: ρ=1,000 kg/m³; Cp=4.18 kJ/kg·K; ΔT=60°C → 69 kWh/m³ Molten salt: see above (213 kWh/m³); requires insulation and freeze protection Concrete/rock (solid sensible): ρ=2,200 kg/m³; Cp=0.9 kJ/kg·K; ΔT=200°C → 110 kWh/m³

Solar Fraction and System Sizing

f-Chart Method (ASHRAE)

Solar fraction f: fraction of load met by solar system f = Solar energy contributed / Total heating load

Simplified approach: Q_solar_annual = A_c × η_annual × H_T_annual [kWh; H_T = annual irradiance on collector plane [kWh/m²]] f = Q_solar / Q_load [verify Q_solar ≤ Q_load; no dump allowed without proper design]

Optimal sizing: f = 0.5–0.70 for domestic hot water (higher f → diminishing returns; larger storage) Storage-to-collector ratio: V_storage/A_c = 50–75 L/m² for domestic hot water systems

ASHRAE 93 Collector Testing

Standard collector test conditions: G_T = 790–1,000 W/m² (constant within ±15 W/m²) Steady state: T_in, T_out constant within ±0.1°C for 15 min 4 test points: X = (T_fi - T_a)/G_T = 0; 0.05; 0.10; 0.15 m²·K/W

Test data reduction: Fit: η = η₀ - a₁ × X (linear); plot η vs. X; η-intercept = η₀; slope = -a₁ = F_R U_L Report F_R(τα) = η₀; F_R U_L = a₁ [ASHRAE 93 parameters for collector selection]

Standards and References

Standard	Scope
ASHRAE 93	Methods of testing to determine the thermal performance of solar collectors
ISO 9806	Solar energy — solar thermal collectors — test methods
ASTM E891	Standard tables for terrestrial solar spectral irradiance
IEA SHC Task 26	Solar water heating systems (f-chart and f-frame methods)
NREL SAM	System Advisor Model for CSP and flat plate simulation

Output

Provide: application (domestic hot water/industrial process heat/CSP power; load profile Q_load [kW]; temperature requirement T_supply [°C]; location and annual DNI [kWh/m²/day]), collector selection (flat plate/evacuated tube/parabolic trough/tower; F_R(τα) and F_R U_L or η₀/a₁ from ASHRAE 93; aperture area A_c [m²]), instantaneous efficiency (η [%] at G_T [W/m²]; T_fi [°C]; T_a [°C]; X value), annual yield (Q_solar [kWh/yr]; H_T_annual [kWh/m²/yr]; η_annual [%]; solar fraction f [%]), storage sizing (V_storage [m³]; storage material; ΔT [°C]; E_stored [kWh]; hours of autonomy [h]), CSP specific (if applicable: C [dimensionless]; η_opt [%]; receiver U_L [W/m²·K]; DNI threshold for operation [W/m²]; annual capacity factor [%]), HTF selection (fluid type; T_max [°C]; freeze protection strategy), economics (collector cost [$/m²]; system cost [$]; payback [yr]; levelized cost of heat [$/kWh]), and applicable standard (ASHRAE 93 test; ISO 9806; NREL SAM simulation).