Convergent - Divergent Nozzle

Suppose a nozzle is used to obtain a supersonic stream starting from low speeds at the inlet (Fig. 40.3). Then the Mach number should increase from Ma=0 near the inlet to Ma>1 at the exit. It is clear that the nozzle must converge in the subsonic portion and diverge in the supersonic portion. Such a nozzle is called a convergent-divergent nozzle. A convergent-divergent nozzle is also called a de laval nozzle, after Carl G.P. de Laval who first used such a configuration in his steam turbines in late nineteenth century.

From Fig. 40.3 it is clear that the Mach number must be unity at the throat, where the area is neither increasing nor decreasing. This is consistent with Eq. (40.11) which shows that dV can be nonzero at the throat only if Ma =1. It also follows that the sonic velocity can be achieved only at the throat of a nozzle or a diffuser.

Fig 40.3 A Convergent-Divergent Nozzle

The condition, however, does not restrict that Ma must necessarily be unity at the throat. According to Eq. (40.11), a situation is possible where Ma ≠ 1 at the throat if dV = 0 there. For an example, the flow in a convergent-divergent duct may be subsonic everywhere with Ma increasing in the convergent portion and decreasing in the divergent portion with Ma ≠ 1 at the throat (see Fig. 40.4).

Fig 40.4 Convergent-Divergent duct with Ma ≠ 1 at throat

The first part of the duct is acting as a nozzle, whereas the second part is acting as a diffuser. Alternatively, we may have a convergent divergent duct in which the flow is supersonic everywhere with Ma decreasing in the convergent part and increasing in the divergent part and again Ma ≠ 1 at the throat (see Fig. 40.5)

Fig 40.5 Convergent-Divergent duct with Ma ≠ 1 at throat

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