Simplified model of VVER–1000 thermal hydraulic process

This report introduce developed mathematical model of thermal hydraulic process which occurs in the core of VVER – 1000 type of nuclear reactor and the coolant flow is considered in one dimension. Navier – Stokes differential equations system is taken like basis – namely continuity equation and momentum and energy conservation equations with two algebraic equations of state by which closure relationship is done. Following the approach of simplifying the model in momentum and energy equations some simplifying assumptions is made like Reynolds term in momentum equation is neglected and diffusion term – in energy equation. The differential equations system can be split into two parts: at one hand continuity equation and momentum equation are solved regarding velocity and pressure distribution and at another – solving energy equation. This report is considering the second case – solving the unsteady energy equation at prescribed distributions of velocity and pressure. By using one of the algebraic state equation, i=c_vT, the energy equation is written regarding the temperature. Velocity and pressure given in the model are estimated by the thermal hydraulics means. The energy equation is solved by finite volumes method at which considered region is divided by N finite volumes, scalar values T and P are represented at central points at volumes and the velocity – at borders of these volumes by so called staggered grid. The equation is integrated at the boundaries of every finite volume and in time at the interval [t; t+ t]. For results obtained by integration is applied Crank-Nicolson semi-implicit scheme. As a result this gives an algebraic system with three diagonal matrix which can be solved with Crout effective algorithm.