This is a liquid-fuel rocket engine developed by the Aerojet-General Corporation to power the upper stages of launch vehicles.
In 1958, the U.S. Air Force's Thor intermediate range ballistic missile (IRBM) was modified to carry three upper stages: the Able, Able-Star, and the Agena. Increased mission requirements led to a new upper stage called the Delta. The first launch of the Delta in 1960 failed, but subsequent launches proved highly successful, so much so that the name "Delta" was soon applied to the entire vehicle. This nomenclature is misleading, however, because subsequent versions of the Delta vehicle used other upper stages.
The Delta engine, as shown here, evolved into several different models. The original engine burned nitrogen tetroxide and a hydrazine-based fuel and produced a thrust of 8,067 pounds. It was regeneratively-cooled and gimballed. Later versions burned other propellants and had higher performances.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.