Stability analysis of a natural circulation lead-cooled fast reactor

This dissertation is aimed at nuclear-coupled thermal hydraulics stability analysis of a natural circulation lead cooled fast reactor design. The stability concerns arise from the fact that natural circulation operation makes the system susceptible to flow instabilities similar to those observed in boiling water reactors. In order to capture the regional effects, modal expansion method which incorporates higher azimuthal modes is used to model the neutronics part of the system. A reduced order model is used in this work for the thermal-hydraulics. Consistent with the number of heat exchangers (HXs), the reactor core is divided into four equal quadrants. Each quadrant has its corresponding external segments such as riser, plenum, pipes and HX forming an equivalent 1-D closed loop. The local pressure loss along the loop is represented by a lumped friction factor. The heat transfer process in the HX is represented by a model for the coolant temperature at the core inlet that depends on the coolant temperature at the core outlet and the coolant velocity. Additionally, time lag effects are incorporated into this HX model due to the finite coolant speed. A conventional model is used for the fuel pin heat conduction to couple the neutronics and thermal-hydraulics. The feedback mechanisms include Doppler, axial/radial thermal expansion and coolant density effects. These effects are represented by a linear variation of the macroscopic cross sections with the fuel temperature. The weighted residual method is used to convert the governing PDEs to ODEs. Retaining the first and second modes, leads to six ODEs for neutronics, and five ODEs for the thermal-hydraulics in each quadrant. Three models are developed. These are: 1) natural circulation model with a closed coolant flow path but without coupled neutronics, 2) forced circulation model with constant external pressure drop across the heated channels but without coupled neutronics, 3) coupled system including neutronics with higher modes and thermal-hydraulics. In the second model, the HX and the external flow path are not incorporated and therefore no time delays are considered, and a constant heat source term is assumed. There is no difference among four equivalent loops, and the system is finally described by a set of ODEs. The thermal hydraulics in the first and third models is represented by sets of ODEs with time lags, namely, DDEs, due to external pipes and the HX model. Models 1 and 2 use a constant heat source term rather than coupled neutronics as is the case in model 3. In model 3, the four equivalent loops are linked via modal neutronics. They are represented by twenty-six (six for neutronics; twenty for thermal-hydraulics / five for each loop) equations. Two approaches, one in time domain and the other in frequency domain, are used for stability analyses. For model number 1, based on the characteristic of DDEs, a MATLAB package is used to carry out the stability analysis. Results of the frequency domain anal- ysis are presented in core-height—friction-factor space, dividing the space into stable and unstable regions. Results are also verified in time-domain. For model number 2, eigenvalues of the Jacobian matrix are evaluated for the frequency domain stability analysis. Scenarios including pulse stimulation on coolant velocity, and different friction factors are simulated in the time domain. The third model is studied only in the time domain. Eight different scenarios are simulated. These include system response after different perturbations such as positive or negative reactivity insertion in one or more quadrants. Results show that SUPERSTAR design is very robust, and that the nominal operation points have considerable safety margins. Results also identify regions in design and operation parameter spaces where the reactor becomes less stable or even unstable