Fluid

The gas that flows through the muffler: dry air, humid air (dry air with water vapour, Relative humidity), the exhaust gas of an engine (the products of complete combustion of a hydrocarbon fuel with air), one of the standard gases (argon, carbon dioxide, nitrogen, oxygen, water vapour), or a custom gas of the user's material library.

Last updated 2026-11-11

Theory

The two gases differ in molar mass and heat capacity. Dry air is a fixed mixture of N₂, O₂, Ar and CO₂ (mole fractions 0.78084, 0.20946, 0.00934, 0.00036). Exhaust gas contains CO₂ and H₂O from the fuel and less O₂; its composition follows from the fuel's hydrogen-to-carbon ratio (H/C atom ratio) and the excess-air ratio (Excess-air ratio), see Fuel.

The choice acts through the molar mass $M$ and the heat capacity $c_p(T)$ of the mixture, which set:

the density of every run, $\rho = p M/(\mathcal{R} T)$ ;
the heat capacity and the ratio $\gamma$ of compressible and heat-transfer runs;
the speed of sound $c = \sqrt{\gamma \mathcal{R} T/M}$ of the acoustics.

With the constant-heat-capacity model (Heat capacity model) the typed molar mass and $c_p$ are used for either choice, so the choice then has no effect.

The standard gases come with the program; their values are derived from NASA data (see Material (custom gas) for how). Choosing one stores a copy of its values in the case file, exactly as for a library gas, and a project whose stored copy equals a standard gas shows that gas again when it is opened. A custom gas (Material (custom gas), Tools > Material library) brings its own molar mass, heat capacity, viscosity and Prandtl number; for a standard gas and a custom gas, the gas-constant fields of this step are not used.

The viscosity is air's Sutherland law for air and exhaust gas: the viscosity of exhaust gas is within a few per cent of air's at the same temperature, and the pressure drop of a muffler hardly depends on the Reynolds number at these Reynolds numbers.

Equations

M = \sum_i x_i M_i, \qquad \frac{c_p(T)\,M}{\mathcal{R}} = \sum_i x_i\,\frac{c_{p,i}(T)\,M_i}{\mathcal{R}}

(1)

where	meaning	unit
$x_i$	Mole fraction of species $i$ (N₂, O₂, Ar, CO₂, H₂O)	-
$M_i$	Molar mass of species $i$	kg/kmol
$M$	Molar mass of the mixture	kg/kmol
$c_{p,i}$	Specific heat capacity of species $i$ (temperature polynomial)	J/(kg K)
$\mathcal{R}$	Universal gas constant, 8314.47	J/(kmol K)

Default and rule

Default

air

Rule

Air.

Source

Mixture properties at 700 °C and 1 atm, as computed by the program:

dry air: $M$ 28.965 kg/kmol, $c_p$ 1136 J/(kg K), $\gamma$ 1.338, $\rho$ 0.3627 kg/m³;
diesel exhaust at $\lambda = 1.5$ : $M$ 29.04 (+0.3 % density), $c_p$ 1215 (+7 %), $\gamma$ 1.308;
natural-gas exhaust at $\lambda = 1$ : $M$ 27.74 (-4 % density), $c_p$ 1301.

The species polynomials are the program's fits to the NASA Glenn data (see Heat capacity model); the solver receives the mixture coefficients in OpenFOAM's janaf form (OpenFOAM user guide, 2026). The air composition is that of the standard atmosphere (U.S. Standard Atmosphere, 1976), with CO₂ rounded to close the four-species sum.

Valid range air | argon | carbon dioxide | exhaust gas | humid air | nitrogen | oxygen | water vapour | custom gas

Choices

Air (the default), argon, carbon dioxide, exhaust gas, humid air, nitrogen, oxygen and water vapour, in alphabetical order, then custom gas. Humid air shows the relative humidity or the water-vapour mole fraction; Exhaust gas shows the fuel, H/C ratio and excess-air ratio; custom gas the list of the material library.

Composition

Complete combustion only: CO, unburnt hydrocarbons, NOₓ, soot and the humidity of the intake air are neglected (each well below 1 % of the moles for a running engine).

Theory

Equations

Default and rule

Valid range air | argon | carbon dioxide | exhaust gas | humid air | nitrogen | oxygen | water vapour | custom gas

Related 9

References 2