BgNS TRANSACTIONS volume 20 number 2 (2015) pp. 140–142 Simplified Model of VVER–1000 Thermal Hydraulic Process G.G. Gerova Technical University of Sofia, Department of Thermal and Nuclear Power Engineering, 8 Kliment Ohridski Blvd., 1000 Sofia, Bulgaria Abstract. 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 = cv T , 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 +Δt]. 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. Keywords: finite volumes method, RELAP5, thermal hydraulics 1 Introduction It is known that there are a number of computer codes which are carrying out calculations of thermal-hydraulic processes occurring in nuclear reactors. One of these codes is RELAP5 which is developed for best estimate simulation of light water reactor cooling system during postulated ac- cidents [2]. The programs’ main issue is that they are with closed source and the user can’t make any changes in mod- els and computation procedures. Therefore sometimes it is useful to develop one’s own code. That report considers the development of such code in MATLAB environment. It presents one dimensional flow of water coolant at WWER – 1000 nuclear reactor’s core. As a basis for creating the model is used Navier-Stokes dif- ferential equation system, namely – conservation of mass equation, momentum and energy conservation equations with two additional thermodynamic algebraic equations. Following the approach which is used in RELAP5 [2] some terms are neglected: in equation of momentum – Reynolds term and in equation of energy – diffusion term. The sys- tem that governs the process is ∂ρ ∂t + ∂ ∂x (ρu)=0 ∂ (ρu) ∂t + ∂ (ρu.u) ∂x = - ∂P ∂x ∂ (ρi) ∂t + ∂ (ρi.u) ∂x = -P ∂u ∂x + Q (1) P = P (ρ, T ) and i = c v T. (2) The system can be split into two and be resolved in two parts: • solving first two equation regarding velocity and pressure distribution; • solving energy equation regarding temperature. In this report the second part is taken into account, namely – solving energy equation regarding temperature distribu- tion at given values of velocity and pressure. By using the second equation of state from Eq. (2) energy conservation equation can be written regarding only the unknown T ∂ ∂t (ρc v T )+ ∂ ∂x (ρc v Tu)= -P ∂u ∂x + Q, (3) where c v is thermal conductivity at constant volume. This equation should be solved at some initial and bound- ary conditions • initial condition T (x, 0) = T 0 (x) corresponds to core temperature at initial moment t =0; • boundary conditions T (0,t)= T b and ∂T ∂n (L, t)=0 correspond to the inlet temperature of the fluid at the beginning of the core and lack of heat flux at the end of the core. 140 1310–8727 © 2015 Bulgarian Nuclear Society