In almost all the combustion problems studied so far, the flows are sufficiently subsonic such that M ≪ 1, where M is the Mach number. There are, however, situations in which reactions take place in flows whose velocities can be sufficiently high such that they either are close to sonic or are supersonic. Examples are combustion within supersonic ramjet (scramjet) engines and the initiation and propagation of blast waves.

In nonreactive fluid mechanics such high-speed flows are called compressible flows because density now varies appreciably with the flow velocity. Such a density variation is to be distinguished from that caused by the large amount of heat release in reactive, low subsonic flows studied in previous chapters. It is therefore important to recognize that density can still vary significantly in an aerodynamically incompressible, low subsonic flow due to heat release. When it is actually assumed to be constant for such a flow, either due to the smallness of the heat release or for analytical expediency, then the flow is said to be one of constant density.

There are several fundamental differences between high-speed flows and low subsonic flows. First, the isobaric assumption of Section 5.2.4 ceases to hold. Second, the kinetic energy of the flow is now appreciable as compared to the chemical energy and frequently needs to be considered. Indeed, we have already encountered this issue in Section 12.5 on supersonic boundary-layer flows. Third, while diffusion is an essential process in low subsonic flows, convection frequently dominates over diffusion in high-speed flows except for situations involving steep gradients such as those within boundary layers.