This is a Lunar Module Ascent Engine (LMAE). The LMAE was part of the Lunar Module (LM), the spaecraft that landed Apollo astronauts on the moon. The LMAE was a curcial component of the spacecraft. It powered the LM ascent stage, carrying the astronauts off the surface of the moon and back to the Command Module spacecraft.
This engine was one of the test engines for the LMAE program. It was fired in 1964 at White Sands Test Facility, New Mexico for a total of 380 seconds. It was later used during LM thermal tests at Grumman Aerospace, which was the prime contractor for the LM.
This engine was donated to the Smithsonian in 1972 by the Grumman Aerospace Co.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.