A Fully Implicit, Back-Substituted Algorithm for Thermalhydraulic Networks

Abstract

The principles of applying the fundamental conservation equations to create a mathematical model of a thermalhydraulic system are relatively uncomplicated but the resulting manipulation of the equations is not. The mathematics involved in developing an efficient numerical algorithm can become quite onerous. This paper describes the ongoing development of an algorithm which is quite general yet does not involve any forbidding mathematics. The scheme involves adding extra coefficients to some of the terms in the conservation equations which act as switches. All terms and switches are carried through to the final set of equations so the user can tailor the scheme for a particular requirement. The general procedure starts with the substitution of the mass equation into the energy equation and then obtaining the change in enthalpy in terms of the fluid flow. Next the mass and energy equations are substituted into the equation of state, the result is combined with the momentum equation to finally yield a single equation in terms of the change in fluid flow. The benefits of this method are that the system stability can be determined from the eigenvalues directly and the method is a more immediately comprehended because it has a more intuitive approach to developing the system of equations. In addition the method provides a convenient test-bed where the same computer code can be used for a wide variety of situations.