Bir Basınçlı Su Reaktöründe Kaza Sırasında Reaktör Kabında Oluşan Kalp Enkazının Soğumasının Sayısal Olarak İncelenmesi

Abstract

Bir nükleer reaktörde, kalp içinde açığa çıkan yüksek ısı soğutma suyu devresi ile dışarı çekilir. Soğutma suyu devresinde meydana gelen bir arıza kalbin soğutulma işlemini tehlikeye sokar. Kalp içinde su seviyesi düşer ve açığa çıkan yüksek ısının dışarı çekilememesi sonucunda kalp malzemesi ergir ve reaktör kabının alt kısmına yığılır. Bu tür bir kaza sırasında, içerisinde yüksek sıcaklıktaki ergimiş kalp malzemesi bulunan çelik reaktör kabı, dış yüzeyinden uygun bir şekilde soğutulmazsa delinme tehlikesi ile karşı karşıya kalınır. Yapılan bu çalışmada, bir PWR tipi reaktörde meydana gelen bu tarz bir kaza şifâsında yarıküresel çelik reaktör kabının dış yüzeyinden soğutulmasının, çelik kapta oluşacak sıcaklık dağılımım nasıl etkilediği incelenmiştir. Bunun için, ergimiş malzeme ve çelik reaktör kabından oluşan fiziksel sistemin matematiksel modellemesi yapılmıştır. Yarıküresel çelik kaptaki sıcaklık dağılımım veren iki boyutlu diferansiyel denklem ve sımr koşulları sonlu farklar yöntemine göre ayrıklaştınlarak çözülmüştür. Sonuçlar, Mayinger (1976) ve Gabor (1980)'a ait ısı taşınımmı ifade eden iki ayrı eşilişkiden yararlanılarak elde edilmiştir. Elde edilen sonuçlardan, içerisinde ergimiş kalp malzemesi bulunan çelik kabın dış yüzeyinden soğutulmasının, çelik kabın delinmesini engellemede büyük önem taşıdığı gözlenmiştir. Kalp malzemesinin ergime sıcaklığı 2500 K, çeliğin ergime sıcaklığı ise 1700 K'dir. Yapılan hesaplamalarda ısı iletimi, ısı taşımmı, ısıl ışınım ile ısı transferi, soğuma sonucu oluşan faz değişimi (katılaşma) ve bozunum ısısı gibi konular gözönünde bulundurulmuştur. Yapılan çalışma sonucu, ergimiş malzemeden oluşan havuz yüzeyinden üst yapıya ışınımla olan ısı transferinin de çelik reaktör kabındaki sıcaklık dağılımını önemli oranda etkilediği gözlenmiştir.

External cooling of the reactor vessel lower head is a way of mitigation and termination of a severe accident in light water reactors. Effects of external cooling of the reactor vessel lower head on the temperature distribution, has numerically been investigated using a two-dimensional steady-state differential heat transfer equation. Under severe accident conditions, the most important action to terminate the accident state is to cool molten core material within the reactor vessel lower head. The heat generated in reactor core is removed outside of the core by primary and secondry coolant system. Any problem in these coolant systems may result in the absence of water in core. This loss of water in reactor core endangers the critical core cooling function. Because of the inability of removing the heat generated in the core to the outside, the temperature of the core increases to the melting point (2500K). Consequently, the core material melts and relocates into the vessel lower head. If the steel reactor vessel can not be cooled sufficiently, it may loose its geometry and the failure of the reactor vessel may occur. This result threatens the reactor containment and the environment. In this study, it was seen that the external cooling of the reactor vessel lower head is very effective to retain the molten core material within the reactor vessel lower head. One of the most important nuclear reactor accident has occured in Three Mile Island Unit 2 (TMI-2) reactor which is now 17 years old. It is the worst commercial nuclear reactor accident in United States. The TMI-2 accident resulted in extensive oxidation and melting of the reactor core and significant release of fission products from the fuel. At least 45% (62 metric tons) of the core melted and about 20 metric tons of molten core material relocated into the lower head of the reactor vessel (DJ.Osetek, 1990). Many studies have been conducted on external cooling of a reactor vessel lower head containing melted core material within. The earliest study was performed by Candon (1982). He investigated the effectiveness of cooling of the outer wall of the reactor vessel containing melted core material within. In this study, a one-dimensional steady-state analysis was conducted for the vessel outer wall. As a result, it was shown that for real decay heat generation rates, the external cooling of the vessel presents the vessel melt-through. O'Brien and Hawkes (1991), performed a thermal analysis on the effectiveness of the external cooling of a PWR cavity during a severe accident, containing partial core melting and relocated core material into the reactor vessel lower head. For a certain range of decay heat, vessel wall temperatures and heat fluxes were obtained using one-dimensional heat transfer equation. It was resulted that the thermal failure of the vessel wall should occur, if the natural-convection heat transfer coefficients predicted from the numerical solutions are correct. Hodge (1991) investigated the external cooling of a BWR vessel. The thermal behavior of the melted core material and the effects of this material to the steel reactor vessel were considered in this study. Mayinger (1976) has performed a numerical study of laminar natural convection with internal heat sources in two-dimensional enclosures. In this study, he has obtained a correlation for heat convection. Gabor (1980) has performed an experimental study in a hemispherical enclosure containing a heat source within. In this study, he has obtained another correlation for heat convection. These two correlations are used to investigate the temperature distribution through the reactor vessel in this study. The physical system which contains the melted core material and the steel reactor vessel is used to build up mathematical model. The steady-state two- dimensional differential heat conduction equation in the hemi-spherical shell of the reactor vessel is determined as ; r2 dr drJ r2SinQ dQK 59 ' The solve this equation the boundary conditions should also be determined. Using the physical system the boundary conditions can be written as : ~Ki*=k?k °-0-e° r=*" z=0 or 2 -K^- = K(TW-TL) r = R2 xi dT w o 0=0," 2 The determined two-dimensional heat conduction equation and the boundry conditions are solved numerically using finite difference method. Successive Overrelaxation Method (SOR) is used to solve the discreted two dimensional heat conduction equation. According to the SOR, a relaxation factor (X) is defined by trying and determined as X = 135. The crust thickness which occurs as a result of solidification of melted core material along the wetted vessel wall is determined by using one-dimensional steady state heat conduction equation. The used differential equation and its boundary conditions can be written as : d2T, a | Qu.a _ q dz* T=T" z = 0 R, T =T z = 8, After the relocation of the core material into the vessel lower plenum, the corium in the vessel lower head can have both liquid and solid phases. Therefore, the moving boundary problem is considered to solve the one - dimensional steady state heat conduction equation. The steady state equation which can be written for moving boundary is: t*' dz z=8, = hd(Tp-Te) Using these two equations, the equation which gives the steady state crust thickness is determined as: 2 Sa = -\tdÇp-Te^r (hdfTp-T^ +2q'£aka(Te-Twi) a"' The radiative heat fluxes from the upper surface of the pool to the unwetted vessel wall and the upper structure are determined by using the enclosure theory of the radiation heat transfer. This theory can be written as: N r m ^ İV,4 Qi - Z FiÂ-zA^-J- QJ=siAia T? - I FtJTJ for i,j = u,w,s. Using this theory, the desired radiation heat transfer rates can be determined as: ' _(/s+f6)fs+(L-f2)fy Ju A _(/2+l)/7-(/6-/4)/3 Ju The heat conduction, heat convection, radiative heat loss to the upper regions of the reactor vessel and the unwetted portion of the vessel lower head, crust thickness occured as a result of solidification and decay heat generation are considered in calculations. The components of the core material are assumed to be mixed homogeneously. The PWR cavity is assumed to be cooled prior to slumping. The temperature of the cooling water is choosen as 323 K. There is assumed to be no water in the reactor vessel lower head and so there occurs no fuel/coolant interactions at the time of core slumping. The initial temperature of the vessel is taken to be 420 K at each position. The temperature of upper surface of molten core material is uniform and the temperature of upper structure is taken to be 800 K or 1600 K. The results are obtained by changing the emmisivities of reactor vessel, upper structure and the surface of the molten core material between 0.1 and 0.8. The effects of change on the temperature of the upper structure (Ts) and the volume of the molten core material were investigated in this study. The crust thickness which occurs as a result of solidification along the vessel inner wall was obtained using two different heat convection correlations. The maximum crust thickness was 4.7 cm when Mayinger (1976)'s correlation is used. However, it increases to 12.8 cm when Gabor (1980)'s correlation is used. According to these correlations, the inner wall temperatures and the temperature distributions in reactor vessel lower head were obtained. Because of the radiative heat transfer considered in Gabor (1980)'s correlation, the inner wall temperature doesn't increase to the melting point of the steel (1700 K). But, when Mayinger 1976)' s correlation is used, the temperature of the inner vessel wall goes over the Melting point in some portion of the vessel. The results showed that the effect of emmisivities of molten core material surface, reactor vessel and upper structure and the upper structure temperature on the vessel inner wall temperature is small but, emmisivity of unwetted portion of the vessel has a very important effect on the temperature of the unwetted wall. Consequently, a partial melting region may occur in reactor vessel lower head but, complete failure of vessel can be prevented by external cooling during a severe accident in a PWR.