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Rayleigh Line Flow Heat Addition Calculator

Rayleigh flow describes 1D compressible flow in a constant-area frictionless duct with heat transfer.

Flow Mach number entering the heating section.

Total stagnation temperature at duct entrance.

Enthalpy addition per unit mass (e.g. from fuel combustion).

Fluid ratio of specific heats (1.4 for air).

Specific gas constant (287 J/kg·K for air).

Calculated Result
0.835

Exit Mach Number (M₂)

Thermal Choking Status

Normal Flow (Subcritical)

Max Allowable Heat (q_max)

449.4 kJ/kg

Exit Stagnation Temp (T₀₂)

598.9 K

Sonic Stagnation Temp (T₀*)

797.4 K

Specific Heat Cp

1004.5 J/(kg·K)

Calculation Breakdown

  1. Rayleigh Sonic Reference StateT₀₁/T₀* = [2(γ+1)M₁²(1 + (γ-1)M₁²/2)] / (1 + γM₁²)² => T₀* = 797.4 K
  2. Maximum Thermal Additionq_max = Cp · (T₀* - T₀₁) = 449.4 kJ/kg
  3. Exit Conditionsq = 250.0 kJ/kg, T₀₂ = 598.9 K, M₂ = 0.835

What Is the Rayleigh Line Flow Heat Addition Calculator?

Rayleigh flow models compressible flow inside constant-area ducts undergoing heat addition or rejection without friction.

It governs afterburner combustion, ramjet burners, and heat exchangers operating at high Mach numbers.

How Does the Rayleigh Line Flow Heat Addition Calculator Work?

Adding heat pushes the Mach number toward unity from either direction (subsonic accelerates, supersonic decelerates).

If heat added exceeds q_max, the flow thermally chokes at the duct exit, forcing an upstream reduction in mass flow rate.

Rayleigh Line Flow Heat Addition Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\frac{T_0}{T_0^*} = \frac{2(\gamma+1)M^2\left(1 + \frac{\gamma-1}{2}M^2\right)}{(1+\gamma M^2)^2}, \quad q_{max} = C_p(T_0^* - T_{01})

Rayleigh line stagnation temperature ratio and maximum permissible heat addition.

How to Use the Rayleigh Line Flow Heat Addition Calculator

  1. Enter inlet Mach number, inlet stagnation temperature, and heat addition.
  2. Check exit Mach number and verify thermal choking status.

Step-by-Step Example Calculation

Ramjet Combustor Heat Addition

Input Values:

inletMachNumber:0.3
inletTotalTemperatureKelvin:400
heatAddedJoulesPerKg:300000
specificHeatRatio:1.4
gasConstantJPerKgK:287
Worked Steps: Verifies whether fuel combustion causes thermal choking.

Understanding Your Result

Exit Mach of 1.0 indicates maximum sonic throughput has been achieved.

Stagnation pressure always drops during subsonic heat addition due to momentum drag.

Factors That Affect the Result

  • Higher inlet Mach numbers drastically lower the maximum allowable heat addition before choking.

When Should You Use This Calculator?

  • Gas turbine afterburner sizing, scramjet/ramjet isolator design, and supersonic combustors.

Assumptions & Limitations

  • Assumes 1D steady flow of an ideal gas with constant specific heat and negligible wall friction.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard gas dynamics analytical Rayleigh equations.

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