| name | ic-engine-thermodynamics |
| description | IC engine thermodynamics — Otto/Diesel/dual cycle analysis, thermal efficiency, MEP, volumetric efficiency, heat release, knock, emissions, performance maps. |
| metadata | {"priority":7,"promptSignals":{"phrases":["IC engine","Otto cycle","Diesel cycle","engine thermodynamics","compression ratio","thermal efficiency engine","BMEP","volumetric efficiency"],"minScore":3}} |
IC Engine Thermodynamics — Complete Skill
Otto Cycle (Spark Ignition)
Ideal 4-stroke SI engine cycle (isochoric heat addition)
Thermal efficiency:
η_th = 1 - 1/r^(γ-1)
r = compression ratio V_BDC/V_TDC; γ = ratio of specific heats (1.4 for air)
Typical r = 8–13 (SI); higher → better η but knock limit
η_th at r=8: η = 1 - 1/8^0.4 = 56.5% (ideal); actual ≈ 25–40%
Mean Effective Pressure:
MEP = W_net / (V_BDC - V_TDC) = W_net / V_d
W_net = heat addition × η_th
Indicated MEP (IMEP): from P-V diagram
Brake MEP (BMEP): from dynamometer; accounts for friction
BMEP = 2πT / V_d [Pa; T in N·m per cylinder per rev × n_cylinders / z_cycles]
Typical SI BMEP: 800–1200 kPa (NA); 1400–2000 kPa (turbocharged)
Diesel Cycle (Compression Ignition)
Isobaric heat addition; higher compression ratio (16–24)
Cutoff ratio: r_c = V_3/V_2 (ratio of volumes at end/start of combustion)
Thermal efficiency:
η_th,Diesel = 1 - (1/r^(γ-1)) × (r_c^γ - 1)/(γ(r_c - 1))
At r=16, r_c=2: η ≈ 60% (ideal); actual diesel ≈ 35–45%
Diesel always higher η than Otto for same compression ratio
Dual Cycle
Partial constant-volume + partial constant-pressure; real engines closer to this
η_th,dual = complex expression involving both r_p (pressure ratio) and r_c
Real Engine Indicated Efficiency
η_indicated = IMEP × V_d / Q_in = ∫P dV / Q_fuel
Heat release rate: dQ/dθ from pressure trace analysis
Woschni correlation for heat transfer loss:
q_wall = h_c × A × (T_gas - T_wall)
h_c = C₁ × B^(-0.2) × P^(0.8) × T^(-0.55) × w^(0.8)
Volumetric Efficiency
η_v = m_actual / m_ideal = (actual air inducted) / (ρ_ambient × V_d)
Typical naturally aspirated: η_v = 0.80–0.90
Turbocharged: η_v > 1.0 possible (supercharging)
Effects:
- Intake manifold tuning: ram effect → η_v > 1.0 at specific RPM
- Temperature: hot intake reduces η_v
- Residual gas: dilutes charge → reduces η_v
Knock (Detonation) — SI Engines
End-gas autoignition before flame front arrives
Octane requirement index (ORI): engine octane need
RON (Research Octane Number): measured at low speed
MON (Motor Octane Number): measured at higher speed, higher temp
AKI (Anti-Knock Index) = (RON + MON)/2 (US pump rating)
Knock-limited compression ratio:
Higher octane → higher allowable r → better efficiency
Knock suppression: retard ignition timing (η penalty 2–5%), reduce charge temp, enrich mixture
Engine Performance Parameters
Power: P = BMEP × V_d × n / (2 for 4-stroke) [W; V_d in m³; n in rev/s]
Torque: T = P / (2π n)
BSFC (Brake Specific Fuel Consumption):
BSFC = ṁ_fuel / P [g/kW·h or lb/hp·h]
Best BSFC: ~230–250 g/kW·h (modern diesel); ~280–350 g/kW·h (SI)
Fuel conversion efficiency: η_f = 1 / (BSFC × Q_LHV) (SI consistent units)
Emissions
CO: incomplete combustion (rich mixture, λ < 1)
HC: unburned fuel (quench layers, crevices, oil films)
NOx: high temp + O₂ → N₂ + O → NO (Zeldovich mechanism)
Peak NOx: λ ≈ 1.05–1.10 (slightly lean, high temp)
PM (soot, diesel): rich zones → carbon particles
Three-way catalyst (TWC, SI): CO+HC+NOx reduction when λ ≈ 1.0 ±0.002
Euro 6 limits (SI, passenger car, cold WLTC):
NOx: 60 mg/km; HC+NOx: 100 mg/km; CO: 1000 mg/km; PM: 4.5 mg/km
Turbocharging
Compressor pressure ratio: P₃/P₁ = PR_c
Turbine expands exhaust to power compressor
Boost pressure: typically 1.5–2.5 bar absolute for SI; up to 4 bar for diesel
Intercooler: cools compressed air → increases density → more fuel → more power
Turbo lag: spool-up time 0.5–2 s; mitigated by twin-scroll, electric assist
Output
Provide: compression ratio, η_th,ideal [%], η_th,actual [%] (with losses), BMEP [kPa], P [kW], T [N·m], BSFC [g/kW·h], volumetric efficiency, knock risk assessment, emissions compliance check.
