🔥 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

Compressible Rayleigh Flow (Heat Addition)

Cfd

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👁️ Views 44

⚡ Solves 35

💾 Downloads 354 📦 Fortran Code 4.4 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

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🔥 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 = 0.208

Max Heat Limit: q_max = 2655.5 kJ/kg | Applied: 250.0 kJ/kg

✅ Sub-Choking Heat

Exit Total Temperature (T₀₂) 548.8 K 275.6 °C

Exit Stagnation Pressure (P₀₂) 1.97 bar Loss: 1.3 %

Exit Static Temperature (T₂) 544.0 K Static P₂: 1.91 bar

Entropy Generation (Δs) 610.7 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                 : Industrial Process Air Burner & Furnace Preheater
Inlet Conditions           : M1 = 0.150, T01 = 300.0 K, P01 = 2.00 bar, gamma = 1.40
Heat Applied / Max Choking : q = 250.0 kJ/kg (q_max = 2655.5 kJ/kg, cp = 1.005 kJ/kg.K)
-----------------------------------------------------------------
EXIT MACH NUMBER (M2)      : 0.2082
Total Temperature T01->T02 : 300.0 K -> 548.8 K (Increase = +248.8 K)
Total Pressure P01 -> P02  : 2.000 bar -> 1.973 bar (Combustion Loss = 1.3%)
Static Temp T1 -> T2       : 298.7 K -> 544.0 K
Static Pressure P1 -> P2   : 1.969 bar -> 1.915 bar
Entropy Generation Delta s : 610.74 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