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Aircraft Propulsion, 2nd Edition by Saeed Farokhi

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6.28 Overexpanded Nozzle Flow—Shock Losses

There is an aspect of nozzle performance that is hampered by the presence of shocks inside the nozzle. This behavior, which is represented by a severe case of overexpansion, is not readily apparent from Equation 6.66. An overexpanded nozzle has an area expansion ratio A9/A8 in excess of that needed for a perfect expansion. This results in an exit static pressure, which falls below the ambient pressure p9/p0 < 1. The need for an abrupt adjustment of the static pressure in the emerging supersonic flow causes a shock formation on the nozzle lip. The mild cases of overexpansion are resolved through oblique shock waves on the nozzle lip. A greater mismatch between the static pressures of the jet and ambient calls for a stronger shock, which in essence increases the wave angle with respect to stream. Eventually, a normal shock is formed at the nozzle lip. In case the normal shock at the nozzle lip is found incapable of satisfying static pressure continuity across the jet slipstream, the normal shock is then brought inside the nozzle. At this time, the exit flow is subsonic and a potential boundary layer separation needs to be investigated. Let us first examine the flow environment near the exit of an overexpanded nozzle in supersonic flight. Figure 6.62 shows the external flow around a nozzle boattail and the jet geometry dominated by wave formations. The shear layer separating the inner and outer flowfields is labeled as the jet slipstream. ...

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