NATRAN-2, LMFBR Piping System Pressure Transients, Fluid Hammer and Na H2O Reaction

1 - Description of problem or function: NATRAN2 analyzes short-term pressure-pulse transients in a closed hydraulic system consisting of a two-dimensional axisymmetric domain connected to a one- dimensional piping network. The one-dimensional network may consist of series or parallel piping, pipe junctions, diameter discontinuities, junctions of three to six branches, closed ends, surge tanks, far ends, dummy junctions, acoustic impedance discontinuities, and rupture disks. By default, the working fluid is assumed to be liquid sodium without cavitation; but another working fluid can be specified in terms of its density, sonic speed, and viscosity. The source pressure pulse can arise from one of the following: a pressure-time function specified at some point in the two-dimensional domain, a pressure-time function or a sodium-water reaction specified at some point in the one- dimensional domain. The pressure pulse from a sodium-water reaction is assumed to be generated according to the dynamic model of Zaker and Salmon. 2 - Method of solution: For the two-dimensional region, NATRAN2 uses a numerical integration technique, based on the method of characteristics and formulated for the system of quasi-linear hyperbolic equations describing fluid-hammer phenomena in a closed two-dimensional axisymmetric domain. The set of nonlinear partial differential equations is first converted to a system of integral equations written along bi-characteristics. The solution is constructed in a step-by-step procedure by approximating the integral equations by the trapezoidal formula and using the resulting difference relations along four bi-characteristics and one streamline through each point. Spatial derivatives of the dependent variables are eliminated from the difference relations. The solution at any point then is obtained explicitly by a linear combination of the remaining difference relations. 3 - Restrictions on the complexity of the problem: The program currently provides for maxima of: 1 two-dimensional cylindrical region, 30 grid points in the r-direction, 60 grid points in the z-direction, 50 one-dimensional pipe branches, 120 nodes per pipe branch, 50 junctions, 10 surge tanks. Cavitation is assumed to be absent. In the two-dimensional analysis, viscosity effects are neglected. A sufficiently large length-to-diameter ratio must be allowed for extended regions both upstream and downstream of the two-dimensional domain, since the matching of the boundary conditions at the interfaces neglects any two-dimensionality close to the interface