Theory

A hot outlet radiating into cold air sees a larger radiation resistance than one radiating into gas of its own temperature: at low $ka$ it scales with $(\rho_o c_o)/(\rho c)$ times the same-gas value, the result of Hirschberg and Hoeijmakers (2014) for one ideal gas. The program evaluates the outside air at this temperature and the ambient pressure and re-applies the terminations to the stored scattering matrices.

Equations

\frac{R_{rad}}{R_{rad,same\ gas}} = \frac{\rho_o c_o}{\rho c} \qquad (ka \ll 1)

(1)

where	meaning	unit
$R_{rad}$	Radiation resistance of the outlet	Pa s/m
$\rho_o, c_o$	Density and speed of sound of the outside air	kg/m³, m/s
$\rho, c$	Density and speed of sound of the outlet gas	kg/m³, m/s

Default and rule

Default: the ambient air temperature of the Material step
Rule: The ambient air temperature of the Material step (Ambient air temperature).
Source: Hirschberg and Hoeijmakers (2014), for the low- $ka$ scaling; the termination formulas are those of Insertion loss: radiation impedance.

Valid range -40 to 60 °C

No solve

The insertion loss is re-evaluated from the stored matrices.

References 1

Hirschberg, A. and Hoeijmakers, M. (2014). Comments on the low frequency radiation impedance of a duct exhausting a hot gas. The Journal of the Acoustical Society of America, 136(2), EL84-EL89. DOI 10.1121/1.4885540

Theory

Equations

Default and rule

Valid range -40 to 60 °C

Related 3

References 1