Turningpointsandsub-andsupercriticalbifurcationsinasimpleBWRmodelOriginalResearchArticle

Stabilityandsemi-analyticalbifurcationanalysesofBWRshavebeenperformedusingadynamicalsystemapproach.AreducedordermodelofaBWRthatincludessimpleneutronicsaswellasthermalhydraulicshasbeenused.Analyseshavebeencarriedoutusingabifurcationanalysiscode,BIFDD,thatcarriesoutanalytic–numericstabilityandbifurcationanalysesofsetofordinarydifferentialequationsandODEswithdelays.Alargesegmentoftheparameterspacehasbeeninvestigatedusingthisveryefficienttool.Stabilityboundariesareobtainedinseveraltwo-dimensionalparameterspaces.Inaddition,thenatureofbifurcationalongthesestabilityboundarieshasalsobeendetermined.ResultsindicatethatbothsubcriticalaswellassupercriticalPoincaré–Andronov–Hopfbifurcationsarelikelytooccurinregionsofinterestinparameterspace. Inadditiontothesemi-analyticalbifurcationstudies,thegoverningequationshavealsobeenintegratednumerically.Resultsconfirmthefindingsofthestabilityandbifurcationanalyses.Numericalintegrations,carriedoutforparametervaluesawayfromthestabilityboundary,furthershowthatthebifurcationcurves,inmanycasesofsubcriticalbifurcations,haveaturningpoint.Thebifurcationcurveinthesecasesextendsbackintotheunstableregion.Theseresultsshowthatitispossibletoexperiencelargeamplitudestableoscillationsintheunstableregioninfinitesimallyclosetothestabilityboundary.Moreover,largeamplitudestableoscillationsarealsopossible,followinglargebutfiniteperturbations,inthestableregionoftheparameterspacenearthestabilityboundary.ThesefindingsprovidealternateexplanationfortheexperimentalandoperationalobservationsinBWRsthatindicatetheexistenceofstablelimitcycleoscillationsandthepossibilityofgrowingamplitudeoscillations. Resultsobtainedhereusingasimplemodelsuggestthatfurtherworkalongtheselines,withmoredetailedmodels,isneededtoidentifyoperatingconditionsandperturbationamplitudesthatmightleadtostablelimitcyclesorgrowingamplitudeoscillationsincurrentandnextgenerationofBWRs.