Unterexpansion

Unterexpansion, in the context of gas dynamics and propulsion, refers to a nozzle flow condition in which the pressure of the exhaust at the nozzle exit is higher than the surrounding ambient pressure (P_e > P_a). In this situation the jet has not expanded to ambient pressure within the nozzle and continues to expand after leaving the nozzle, producing external shock structures and a characteristic plume that broadens with distance. The term Unterexpansion is the German equivalent; in English-language texts the term underexpansion is used. It is contrasted with ideal expansion (P_e ≈ P_a) and overexpansion (P_e < P_a), each affecting thrust and plume behavior.

Unterexpansion occurs when the nozzle expansion ratio is insufficient for the ambient pressure, or when a nozzle designed for higher ambient pressure is used in a lower-pressure environment. It is commonly observed in rocket engines or jet propulsion systems where ambient pressure is lower than the exit pressure, leading to external expansion and the formation of expansion fans and external shock cells outside the nozzle.

The practical implications include reduced thrust efficiency, since part of the exhaust energy expands outside the nozzle rather than contributing to momentum transfer. It also produces a broader plume and visible shock structures, which can aid in diagnostic testing. In design, engineers select an expansion ratio intended to approach ideal expansion over the mission’s altitude range; deviations from this can lead to underexpansion or overexpansion, each with distinct performance and plume characteristics. See also overexpansion, ideally expanded nozzle, and thrust coefficient.