This is a Torpedo, Type 21, Mod 2, for the Petrel anti-ship missile. The Petrel could be fitted with either this torpedo or the Navy Mk 13 type. When fully loaded, the Type 21(or Mr. 13) was a 2,000 pound airborne torpedo (i.e. carried and deployed by aircraft).
The Petrel missile was designed by the National Bureau of Standards during 1952-1954, then transferred to the Fairchild Company. The Petrel had a brief operational life, becoming operational in 1958 but was cancelled in the same year. The Type 21 torpedo was transferred to the NASM from the now defunct National Armed Forces Advisory Board in 1984.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.