🔥 Compressible Rayleigh Flow (Heat Addition)

Evaluate 1D compressible flow with heat addition or combustion, computing exit Mach (M2), thermal choking limit (q_max), stagnation pressure loss, and entropy generation.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 44

⚡ Calculs faits 35

💾 Téléchargements 241 📦 Code Fortran 4.4 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

🔥 Combustor Duct Thermal Expansion & Thermal Choking (M = 1.0)

Real-time visual simulation of flame heat zone, thermal acceleration & Rayleigh entropy increase

📝 Configuration & Presets

⚡ Gas Turbine Combustor 🚀 Ramjet Afterburner ✈️ Scramjet (M = 2.4) 🏭 Furnace Burner Duct

🔥 Thermal Heat Addition & Gas

Heat Added Δq [kJ/kg]:

Specific Heat c_p [kJ/(kg·K)]: Air: 1.005, Combustion Gas: 1.15–1.25

Specific Heat Ratio γ:

🚀 Inlet Flow & Stagnation State

Inlet Mach Number M₁:

Inlet Total Temperature T₀₁ [K]:

Inlet Total Pressure P₀₁ [bar]:

Rayleigh Flow Formulations:
• Stagnation Temp Ratio: T₀/T₀* = 2(γ+1)M² (1 + ½(γ−1)M²) / (1 + γM²)²
• Max Heat Addition: q_max = c_p (T₀* − T₀₁) [kJ/kg]
• Heat addition accelerates subsonic flow toward M=1 and decelerates supersonic flow.
• Total Pressure Loss: ΔP₀ is unavoidable during heat addition at high speed.

📊 Rayleigh Flow Results

📊 Output Summary
💾 Fortran Source

Exit Mach Number (M₂)

M₂ = 0.895

Max Heat Limit: q_max = 609.8 kJ/kg | Applied: 600.0 kJ/kg

✅ Sub-Choking Heat

Exit Total Temperature (T₀₂) 1021.4 K 748.3 °C

Exit Stagnation Pressure (P₀₂) 2.99 bar Loss: 14.6 %

Exit Static Temperature (T₂) 886.6 K Static P₂: 1.79 bar

Entropy Generation (Δs) 906.2 J/(kg·K) Irreversible heat addition

📈 Exit Mach Number M₂ vs Heat Added Δq (kJ/kg)

📉 Exit Stagnation Pressure P₀₂ (bar) vs Heat Added

=================================================================
 THERMOFLUIDCALC — COMPRESSIBLE RAYLEIGH HEAT ADDITION REPORT
=================================================================
Case Title                 : Turbojet Afterburner / Ramjet Heat Addition
Inlet Conditions           : M1 = 0.350, T01 = 450.0 K, P01 = 3.50 bar, gamma = 1.38
Heat Applied / Max Choking : q = 600.0 kJ/kg (q_max = 609.8 kJ/kg, cp = 1.050 kJ/kg.K)
-----------------------------------------------------------------
EXIT MACH NUMBER (M2)      : 0.8945
Total Temperature T01->T02 : 450.0 K -> 1021.4 K (Increase = +571.4 K)
Total Pressure P01 -> P02  : 3.500 bar -> 2.990 bar (Combustion Loss = 14.6%)
Static Temp T1 -> T2       : 439.8 K -> 886.6 K
Static Pressure P1 -> P2   : 3.219 bar -> 1.789 bar
Entropy Generation Delta s : 906.19 J/(kg.K)
=================================================================

📘 Calculation Methodology & Rayleigh Flow Standards

Thermal Choking Limit

Adding heat to a subsonic compressible flow increases Mach number and entropy up to the sonic point $M=1$. Exceeding $q_{max}$ causes thermal choking:

                    qmax = cp (T₀* − T₀₁)
                

Combustion Total Pressure Loss

Fundamental momentum conservation dictates that adding thermal energy to a high-speed gas creates an unavoidable fundamental total pressure drop $\Delta P_0$.

Key Engineering Assumptions

1D steady frictionless flow in constant cross-sectional area duct.
Uniform thermal energy addition across the stream.
Ideal gas with constant average $c_p$ and $\gamma$.

ThermoFluidCalc Engineering Report