Heat release parameter

In combustion, heat release parameter (or gas expansion parameter) is a dimensionless parameter which measures the amount of heat released by an adibatic combustion process. It is defined as


 * $$q = \frac{T_{ad}-T_u}{T_u}$$

where
 * $$T_{ad}$$ is the adiabatic flame temperature
 * $$T_u$$ is the unburnt mixture temperature.

In typical combustion process, $$q\approx 2-7$$. For isobaric combustion, using ideal gas law, the parameter can be expressed in terms of density, i.e.,


 * $$q = \frac{T_{ad}-T_u}{T_u} = \frac{\rho_u-\rho_{ad}}{\rho_u}.$$

The ratio of burnt gas to unburnt gas temperature is


 * $$\frac{T_{ad}}{T_u} =1+q.$$

Gas expansion ratio
The gas expansion ratio is simply defined by


 * $$r = \frac{\rho_u}{\rho_b}$$

which is related to $$\alpha$$ by $$r=1+q.$$