Theory

An incompressible run assumes one uniform temperature: the density follows the ideal-gas law at the ambient (or mean) pressure, equation (1), and the viscosity Sutherland's law, equation (2), which depends on the temperature only. A hot exhaust gas is much less dense and more viscous than cold air: at 700 °C and 1 atm air has a density of about 0.36 kg/m³ against 1.20 kg/m³ at 20 °C, so the same mass flow is more than three times faster.

For the compressible solver the temperature is the starting value of the temperature field and the inlet temperature, unless an inlet sets its own (Inlet temperature, which follows this value when left empty). The solver then computes the temperature everywhere, so it may differ from this value inside the muffler.

The acoustics use the speed of sound $c = \sqrt{\gamma R_s T}$ at this temperature when the acoustic medium is uniform; with the medium mapped from a compressible CFD run they use the solved temperature field instead.

Equations

\rho = \frac{(p_{atm} + p_g)\,M}{\mathcal{R}\,T}, \qquad T = T_{\mathrm{°C}} + 273.15

(1)

\mu = \frac{A_s\,T^{3/2}}{T + T_s}

(2)

where	meaning	unit
$T$	Gas temperature	K
$\rho$	Density	kg/m³
$p_{atm}$	Ambient pressure	Pa
$p_g$	Gauge reference pressure (0, or half the previous static pressure drop, see the density reference)	Pa
$M$	Molar mass of the gas	kg/kmol
$\mathcal{R}$	Universal gas constant, 8314.47	J/(kmol K)
$\mu$	Dynamic viscosity	Pa s
$A_s$	Sutherland coefficient	kg/(m s K^0.5)
$T_s$	Sutherland temperature	K

c = \sqrt{\gamma(T)\,\frac{\mathcal{R}}{M}\,T}, \qquad \gamma = \frac{c_p}{c_p - \mathcal{R}/M}

(3)

where	meaning	unit
$c$	Speed of sound	m/s
$\gamma$	Ratio of heat capacities	-
$c_p$	Specific heat capacity at constant pressure	J/(kg K)

Default and rule

Default: 20 °C
Rule: 20 °C.
Source: The ideal-gas law and the ideal-gas speed of sound; Sutherland's law (Sutherland, 1893).

Valid range above -273.15 °C; the temperature-dependent heat capacity covers 200-3000 K

Values

Above -273.15 °C. Older case files that stored the temperature in kelvin are converted on loading.

One temperature

An incompressible run has no energy equation: a muffler that cools the gas noticeably needs the compressible solver with heat transfer for a temperature that changes along the flow.

References 1

Sutherland, W. (1893). The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 36(223), 507-531. DOI 10.1080/14786449308620508

Theory

Equations

Default and rule

Valid range above -273.15 °C; the temperature-dependent heat capacity covers 200-3000 K

Related 6

References 1