Development of flow and heat transfer models for the carbon fiber rope in nozzle joints of the space Shuttle Reusable Solid Rocket Motor

Qunzhen Wang*, Mark Ewing +, Ed Mathias ÷,Cory Smith §and Joe Heman +ATK Thiokol Propulsion Company, Brigham City, UTMethodologies have been developed for modeling both gas dynamics and heat transfer inside thecarbon fiber rope (CFR) for applications in the space shuttle reusable solid rocket motor joints.Specifically, the CFR is modeled using an equivalent rectangular duct with a cross-section area,friction factor and heat transfer coefficient such that this duct has the same amount of mass flow rate,pressure drop, and heat transfer rate as the CFR. An equation for the friction factor is derived basedon the Darcy-Forschheimer law and the heat transfer coefficient is obtained from pipe flowcorrelations. The pressure, temperature and velocity of the gas inside the CFR are calculated using theone-dimensional Navier-Stokes equations. Various subscale tests, both cold flow and hot flow, havebeen carried out to validate and refine this CFR model. In particular, the following three types oftesting were used: (1) cold flow in a RSRM nozzle-to-case joint geometry, (2) cold flow in a RSRMnozzle joint No. 2 geometry, and (3) hot flow in a RSRM nozzle joint environment simulator. Thepredicted pressure and temperature history are compared with experimental measurements. Theeffects of various input parameters for the model are discussed in detail.