Two mathematical models (a one-dimensional and a two-dimensional) were adopted to study, numerically, the thermal hydrodynamic characteristics of flow inside the cooling channels of a Nuclear Thermal Rocket (NTR) engine. In the present study, only a single one of the cooling channels of the reactor core is simulated. The one-dimensional model adopted here assumes the flow in this cooling channel to be steady, compressible, turbulent, and subsonic. The physics based mathematical model of the flow in the channel consists of conservation of mass, momentum, and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The working fluid (gaseous hydrogen) is assumed to be compressible through a simple ideal gas relation. The physical and transport properties of the hydrogen is assumed be temperature dependent. The governing equations of the compressible flow in cooling channels are discretized using the second order accurate MacCormack finite difference scheme. Convergence and grid independence studies were done to determine the optimum computational cell mesh size and computational time increment needed for the present simulations. The steady state results of the proposed model were compared to the predictions by a commercial CFD package (Fluent.) The two-dimensional CFD solution was obtained in two domains: the coolant (gaseous hydrogen) and the ZrC fuel cladding. The wall heat flux which varied along the channel length (as described by the nuclear variation in the nuclear power generation) was given as an input.
Numerical experiments were carried out to simulate the thermal and hydrodynamic characteristics of the flow inside a single cooling channel of the reactor for a typical NERVA type NTR engine where the inlet mass flow rate was given as an input. The time dependent heat generation and its distribution due to the nuclear reaction taking place in the fuel matrix surrounding the cooling channel. Numerical simulations of flow and heat transfer through the cooling channels were generated for steady state gaseous hydrogen flow. The temperature, pressure, density, and velocity distributions of the hydrogen gas inside the coolant channel are then predicted by both one-dimensional and two-dimensional model codes. The steady state predictions of both models were compared to the existing results and it is concluded that both models successfully predict the steady state fluid temperature and pressure distributions experienced in the NTR cooling channels. The two dimensional model also predicts, successfully, the temperature distribution inside the nuclear fuel cladding.
