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This question is prompted by the problem on page 350 of the fluid mechanics book by Landau and Lifshitz. The problem states, "A small amount of heat is supplied over a short segment of a tube in a perfect gas in steady flow in the tube. Determine the change in the gas velocity when it passes through the segment." This seems to me to be applicable to an afterburner. The solution is obtained by using conservation of mass flux and momentum flux and then increasing the energy flux by the heat added. The change in velocity turns out to be given by, \begin{equation} dv=\frac{(\gamma-1)q}{\rho(c^{2}-v^{2})} \end{equation} where $\gamma$ is the ratio of specific heats, $q$ is heat added per unit cross-section per unit time, $\rho$ is density, $v$ is velocity and $c$ is the local speed of sound. This formula says that if the flow is supersonic $v>c$ then $dv<0$ and the gas velocity slows down. The addition of heat only increases the gas velocity if the flow is subsonic. So, my question is, "Does this result imply that the flow in an afterburner is subsonic?"

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Afterburners are subsonic but not because of that equation.

Afterburners are typically subsonic for a couple of reasons. First combustion is easier at low speeds. While supersonic combustion is possible (see scramjets), most times the combustion areas of a jet are the points where some of the slowest flow through the engine occurs. Secondly, the goal of the afterburner is not to increase velocity or pressure (in fact ideal combustion is isobaric, and real combustion features a pressure loss) but to increase temperature. The reason behind this is that high temperature gas releases more energy for the same decrease in pressure than low pressure gas. This is how turbine engines are able to operate, and why combustion occurs at the highest possible pressure. After the afterburner the flow becomes supersonic traveling through the nozzle, which in an engine equipped with an afterburner is almost always variable geometry.

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