This is the Viking 5C engine. Four Viking 5C liquid-propellant rocket engines were used to propel the first stage of the Ariane 4 expendable launch vehicle used by the European Space Agency from 1990 to 2003.
A consortium of six countries, France, Germany, Spain, Belgium, Sweden, and Italy, designed and manufactured this engine. It uses a form of transpiration or "sweat cooling." In sweat cooling, a coolant (the fuel) is injected uniformly and continuously over the internal wall of the nozzle by using a porous wall material. The developer of this technique for the Viking was Heinz Bringer, who had worked on a similar system during the development of the German V-2 rocket of World War II. This object was donated to the Smithsonian in 2006 by SAFRAN.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.