| name | jet-engine-thermodynamics |
| description | Jet engine thermodynamics — turbojet/turbofan Brayton cycle, SFC, overall efficiency, fan/compressor/turbine work, bypass ratio, component efficiencies, inlet recovery, afterburner. |
| metadata | {"priority":7,"promptSignals":{"phrases":["jet engine thermodynamics","turbojet","turbofan","bypass ratio","specific fuel consumption","SFC","Brayton cycle aircraft"],"minScore":3}} |
Jet Engine Thermodynamics — Complete Skill
Brayton Cycle (Ideal)
States: 0-inlet, 1-compressor inlet, 2-compressor exit, 3-combustor exit, 4-turbine exit, 9-nozzle exit
Thermal efficiency (ideal):
η_th = 1 - T₁/T₂ = 1 - 1/PR^((γ-1)/γ)
PR = Overall Pressure Ratio = P₂/P₁
γ = 1.4 (air); γ_hot ≈ 1.33 (exhaust gases)
Modern turbofans: OPR = 40–50 (Trent XWB, GE9X); η_th,ideal ≈ 50%
Turbojet Analysis
Component Equations (Actual with efficiency)
Inlet: P₁₃ = π_d × P₀ (π_d ≈ 0.95–0.99 subsonic; less at supersonic)
Compressor: T₃ = T₁ + T₁ × (PR_c^((γ-1)/γ) - 1) / η_c
W_c = c_p × (T₃ - T₁) per unit mass
η_c = isentropic efficiency of compressor (0.85–0.92 modern)
Combustor: T₄ = T₃ + Q_fuel × η_b / (c_pg × ṁ) [turbine inlet temperature TIT or T₄]
η_b = combustion efficiency (0.99–0.999)
Modern TIT: 1600–1900 K (cooled blades); uncooled limit: ~1400 K
Turbine: T₅ = T₄ - η_t × T₄ × (1 - PR_t^(-(γ_g-1)/γ_g))
Power balance: W_turbine = W_compressor → T₄ - T₅ = c_p/c_pg × (T₃ - T₂)
Nozzle exit velocity:
V₉ = √(2 c_pg η_n T₅ (1 - (P₀/P₅)^((γ_g-1)/γ_g)))
Thrust: F = ṁ × (V₉ - V₀) [for simple turbojet; no bypass]
Turbofan (High Bypass)
Bypass ratio (BPR): BPR = ṁ_fan_bypass / ṁ_core
Modern large turbofans: BPR = 10–15 (GE9X: BPR = 9.9; Trent XWB: BPR ≈ 9.3)
Military turbofans: BPR = 0.2–5
Thrust contributions:
F_core = ṁ_core (V_core - V₀) (hot nozzle)
F_fan = ṁ_fan (V_fan - V₀) (cold nozzle)
F_total = F_core + F_fan
Why high BPR? Moving more air slowly (fan) more efficient than accelerating less air fast
Propulsive efficiency: η_p = 2V₀ / (V₉ + V₀) → maximize by V₉ → V₀ (more air, lower velocity)
Turbofan Efficiency Components
Core thermal efficiency: η_th = W_net / Q_in = work extracted / fuel energy
Fan transfer efficiency: η_fan = work to fan / shaft power; fan η_c ≈ 0.88–0.93
Propulsive efficiency: η_p = F V₀ / (F V₀ + kinetic energy residual)
Overall efficiency: η_0 = η_th × η_prop = F V₀ / (ṁ_f × Q_LHV)
Specific fuel consumption (SFC):
TSFC = ṁ_f / F [kg/N·s or lb/lbf·hr]
Modern turbofan: TSFC ≈ 0.5–0.6 lb/lbf·hr at cruise; 14–17 mg/N·s SI
TSFC ≈ 1/(η₀ × Q_LHV / V₀) → decreases with altitude (as η_p improves)
Specific Thrust and Work
Specific thrust: F/ṁ₀ [N·s/kg]
High BPR: F/ṁ₀ ≈ 200–300 N·s/kg (low V₉-V₀); military: 500–700+
Specific work: W_net / ṁ = F × V₀ / ṁ
Design Point Optimization
Maximizing thrust per unit airflow:
Set OPR to match T₄ (temperature-limited): OPR_opt = (T₄/T₁)^(γ/(γ-1)) × η_c × η_t × (γ_g/(γ_g-1)) × ...
Maximizing overall efficiency:
Increase BPR → better η_p; increase OPR → better η_th; increase T₄ → more specific work
T₄/T₁ ratio: determines specific thrust; limited by material (Ni superalloys, TBC, cooling)
T₄ increase of 100K → ~4% more specific thrust; requires improved cooling (cooling air penalty)
Afterburner (Reheat)
Additional fuel burned in jetpipe between turbine exit and nozzle
T_afterburner ≈ 2000–2200 K (stoichiometric possible)
Thrust increase: 50–70% with afterburner (reheat) at significant fuel penalty
SFC with afterburner: 2.0–2.5× dry SFC → used only for takeoff and combat
Low bypass turbofan with afterburner: F-22, F-35, Eurofighter
Key Performance Numbers
| Engine | BPR | OPR | T₄ [K] | TSFC cruise |
|---|
| GE90-115B | 8.4 | 42 | ~1750 | 0.536 lb/lbf·hr |
| Trent XWB | ~9.3 | 52 | ~1800 | ~0.52 |
| LEAP-1A | ~11 | 40 | ~1750 | ~0.51 |
| CFM56-7 (737NG) | 5.1 | 32.8 | ~1660 | 0.545 |
| F135 (F-35, dry) | 0.57 | 35 | ~1950 | ~0.80 |
Output
Provide: OPR, BPR, T₄ [K], V₉_core and V₉_fan [m/s], F_total [kN], TSFC [mg/N·s], η_th [%], η_p [%], η_overall [%], component efficiency summary (η_c, η_t, η_fan), cooling flow fraction estimate.
