Analysis of local bifurcations in a channel subjected to non-uniform axial heating

The effect of non-uniform axial heating on density wave oscillations of a two-phase flow channel is studied. This study becomes relevant in view of designing and modelling of nuclear reactor heat removal systems as several reactor fuel rods (Boiling Water Reactors) exhibit non-uniform axial heat flux profiles. In this work a Nodalized Reduced Order Model (NROM) has been developed The unique feature of the model is that, using this model the stability behaviour of two-phase flow systems with a wide range of axial heat flux variations (single humped and double humped) can be studied. In addition to these, the model behaves as an auto-adaptive scheme, where the mesh sizes between consecutive nodes automatically vary during the system evolution according to the provided shape of axial heat flux. This helps to minimize the computational effort required to achieve significant accuracy to capture the state variable variations. The effects of single humped and various double humped axial heating profiles on local bifurcation have been studied. It has been observed in this study that in addition to the linear stability characteristic the nonlinear stability behaviour (depicted by the position of generalized Hopf points and occurrences of limit cycles) also changes significantly as the axial heat flux changes from uniform to non-uniform even though the total heat rate provided remains same. Moreover, a generalized description of the cause due to which these changes occur in stability behaviour of the system is also presented.