Consider the flow in a convergent-divergent nozzle (Fig. 40.9). The upstream stagnation conditions are assumed constant; the pressure in the exit plane of the nozzle is denoted by PE ; the nozzle discharges to the back pressure, PB .
With the valve initially closed, there is no flow through the nozzle; the pressure is constant at P0. Opening the valve slightly produces the pressure distribution shown by curve (i). Completely subsonic flow is discerned.
Then PB is lowered in such a way that sonic condition is reached at the throat (ii). The flow rate becomes maximum for a given nozzle and the stagnation conditions.
On further reduction of the back pressure, the flow upstream of the throat does not respond. However, if the back pressure is reduced further (cases (iii) and (iv)), the flow initially becomes supersonic in the diverging section, but then adjusts to the back pressure by means of a normal shock standing inside the nozzle. In such cases, the position of the shock moves downstream as PB is decreased, and for curve (iv) the normal shock stands right at the exit plane.
The flow in the entire divergent portion up to the exit plane is now supersonic. When the back pressure is reduced even further (v), there is no normal shock anywhere within the nozzle, and the jet pressure adjusts to PB by means of oblique shock waves outside the exit plane. A converging diverging nozzle is generally intended to produce supersonic flow near the exit plane.
If the back pressure is set at (vi), the flow will be isentropic throughout the nozzle, and supersonic at nozzle exit. Nozzles operating at PB (corresponding to curve (vi) in Fig. 40.8) are said to be at design conditions. Rocket-propelled vehicles use converging-diverging nozzles to accelerate the exhaust gases to the maximum possible velocity to produce high thrust.
