# Development of a Reduced Order Model and its application to the Forsmark-1 Instability Event of 1996/1997

[Rapport]

This report describes the development of a reduced order model (ROM) which is then used to analyze a specific instability event . The ROM consists of three sub-models: a neutron-kinetic (NK) model (describing neutron transport), a thermal hydraulic (TH) model (HT) (describing the coolant flow ) and a heat transfer model (describing heat transfer between the fuel and the coolant). All these three models are coupled to each other, using two feedback mechanisms: void fraction feedback and doppler feedback. Each of the sub-models is described by a set of reduced ordinary differential equations, derived from the corresponding time-space dependent partial differential equations by using different types of approximations and mathematical methods. The neutron kinetic model is derived from the two-group time-space-dependent diffusion equations with one effective group of delayed neutrons by using eigenmode expansion. In the NK model, only the effect of the first three modes, namely the fundamental the first and the second azimuthal modes are taken into account. The thermal hydraulic model is derived from the space-time dependent mass, momentum and enthalpy local conservation equations, using spatial quadratic approximation for both the enthalpy and the quality distributions, after applying the weighted residual procedure. The equations are written for the single and for the two phase regions, separately. For the sake of simplicity, in the latter case the HEM is used. The heat transfer model is derived from an energy balance equation written for one fuel rod with three radial regions. The reduction of the (HT) equations is performed by assuming a piece-wise quadratic approximation for the fuel pellet temperature and using a weighted residual procedure (WRP). In order to have proper representation of both azimuthal modes, a four heated channels model was constructed. The recirculation loop model was also introduced into the ROM. The coupling reactivity coefficients for both void fraction and fuel temperature were calculated explicitly, evaluating the cross section perturbations with the help of the SIMULATE-3 system code and the CORE SIM simulator. As an event of interest for the application of the ROM, the instability event that happened in 1996/1997 at the Swedish Power Plant Forsmark-1, was chosen. The ROM input data were adjusted in order to represent the proper operational conditions. As a reference for benchmarking the ROM, the system code output data were used. The time signal for each of the modes were then calculated and some considerations about their stability were made

**Nyckelord: **boiling water reactor stability,decay ratio, space-dependent neutron noise, reduced order models,density wave oscillations

Denna post skapades 2010-08-31. Senast ändrad 2015-03-30.

CPL Pubid: 125475