Kaynar sulu reaktörlerdeki kaynama olayı bu sistemlerin, kararlılık açısından zayıf noktasını oluşturur. Nötronik ile kuple olan termalhidrolik olaylar problemi daha karmaşık yapar. Genelde BWR (kaynar sulu reaktör) kararsızlıkları güç salınımlarının şekline göre global ve yerel (zıt-fazlı) olarak sınıflandırılırlar. Global salınımlarda bütün bölgesel güç monitörlerinden alınan sinyaller hep birlikte salınım yapmaktadırlar; halbuki zıt-fazlı güç kararsızlıklarında monitörlerin kaydettiği sinyaller birbirilerine göre belirli bir faz ilişkisi içinde iken; ortalama güç monitörleri büyük boyutlardaki bu sapma olaylarını tespit edemezler. Reakör akısının temel mod dışındaki tüm uzaysal harmonikleri kritik altıdır. Temel prensiplerden başlayarak modal nokta kinetik denklemleri türetilebilir. Bu denklemler termalhidrolik pertürbasyonların bölgesel veya üniform olmayan davranışları nedeniyle kupledir. Reaktör operatörleri tarafından rapor edilen, çok sayıda beklenmedik güç salınım olayı vardır. Güncel reaktör kodları ile kararsızlıkların benzeşimleri iyi bir şekilde yapılmaktadır; ancak analitik modeller olayın fiziksel yorumunda daha yararlı olmaktadır. Reaktör kararlılık analizi için önerilen en eski modellerden biri paralel kanal kararsızlığıdır; bu isim uygulanan hidrolik sınır koşullarından kaynaklanır ve global kararsızlık analizinde kullanılabilir. Bu çalışmada sözü edilen model, temel akı moduna birinci eksenel harmoniği de ilave ederek geliştirilmiş, böylece yeni bir kararsızlık modu önerilmiş ve analizi yapılmıştır. Analiz lineer denklemlerle frekans domeninde gerçekleştirilmiştir. Kaynama sınırının hareketi, modal nokta kinetik denklemler üzerinden reaktivite geri besleme etkisi yaratmaktadır. Sonuçlar, net bir şekilde, akının doğal birinci eksenel harmoniğinin reaktör kararlılığını etkilediğini göstermiştir.Anahtar Kelimeler: BWR kararlılığı, zıt fazlı güç salınımları, modal kinetik denklemler.Thermalhydraulic stability is one of the major and extensively studied problems of systems operating under two-phase flow conditions; especially BWRs, steam generators and drum boilers are of concern due to safety issues involved. In BWRs there is an additional fact that complicates the problem: thermalhydraulic and neutronic instabilities are strongly coupled and feed each other. Existence of nonuniform boiling phenomenon in boiling water reactors makes these systems susceptible to instabilities. Customarily, BWR instabilities are classified as global (in-phase) and local (out-of-phase) according to the spatial dependency of the power fluctuations. In global oscillations, the output signals from all local power range monitors fluctuate in unison; whereas in out of phase power oscillations they record signals which are in a certain phase relation to each other while the average power range monitors maybe missing to detect any such anomaly of gross dimensions. There are several unexpected power oscillation events reported by the operators. Present numerical codes can simulate these instabilities rather well on event basis; but more general physical insight can be gained readily through analytical modeling. Two-phase flow is inherently unstable due to its thermal-hydrauIic nature. In BWR such instability is expected to be modified for the worse by the void feedback to reactivity mechanism. One of the earliest models applied to the problem is the parallel channel instability so called because of the applied hydraulic boundary conditions, which is used to account for global instability. In this case, the boiling boundary of a single hot channel begins to move, as affected by any perturbation. This action in turn will modify the reactor power which further provides the system with a feedback of reactivity. Under certain circumstances, if overlooked, this chain of events may lead towards an episode of growing instability resulting in a scram. On the other hand out-of-phase oscillations are usually thought to be linked with the spatial harmonics of the fundamental flux mode and can easily pass undetected. All spatial harmonics save the fundamental mode are subcritical. Starting from basic principles modal point kinetics equations can be derived. These equations are coupled due to the local or nonuni-form behavior of the thermal-hydraulic perturbations. When the diameter of the core is close to its height, the first azimuthal mode is the least subcritical flux harmonic, whereas in a slender core the first axial mode dominates the first azimutal mode with respect to criticality. The motion of the boiling boundary is quite likely to trigger the axial mode in any case. In this work parallel channel model is extended by including the effect of the first axial harmonic of the fundamental flux mode, and hence a new type of instability is proposed and studied. In other words this study constitutes a second order perturbation analysis of the parallel channel model. Thermal-hydraulics is represented with two-phase homogeneous equilibrium model equations. Modal point kinetics equations are derived allowing for modal interactions through the motion of the boiling boundary which in fact separates the core into two nodes, one being single phase subcooled region and the other the two-phase region where nucleate boiling takes place. In this way the modal point kinetics equations attain a nodal character as well. Analysis is performed with linearized equations in frequency domain. The motion of the boiling boundary explicitly feeds back to the modal point kinetics equations. The Froude number Fr and fuel-time constant are important parameters that strongly affect the density-wave instability. The Froude number effect is stronger in the case of with boiling boundary feedback than in the case of without the feedback The Ledinegg instability is not likely to occur due to the coupling of the boiling boundary feedback and the thermalhydraulic feedback. In general, a positive boiling boundary feedback coefficient yields a less stable system to the density-wave instability and vice versa. For a very small fuel-time constant, however a positive boiling boundary feedback coefficient would stabilize the system. This is explained by the fact that an increase in void fraction would cause a decrease in power that would suppress further increase in void fraction. Results clearly indicate that the inclusion of the axial flux harmonic narrows the region of stability on the appropriate parameter space, therefore our approach results in more conservative prediction regarding the core stability.Keywords: BWR stability, out-of-phase power oscillations,modal kinetics equations
