Bir Nükleer Kaza Sonrası Doğal Taşınım İle Isı Çekiminin Sayısal Olarak İncelenmesi

Abstract

Geniş kullanım alanları dolayısıyla, içinde enerji kaynağı bulunduran veya dışardan ısıtılan kapalı kaplardaki doğal taşınım problemleri üzerine yapılan çalışmalar çok önem kazanmıştır. Bu çalışmaların ilginç ve önemli odak noktalarından biri de nükleer kazalarda kalp malzemesinin eriyerek meydana getirdiği enkazın şiddetli bir ısı kaynağı gibi ve reaktör kabının da kapalı bir kap gibi davranarak oluşturduktan modeldir. Bu çalışmada başlangıç noktası olan bu model, kapalı bir kap İçersinde, bir ısı kaynağı içeren akışkan için doğal taşınım problemi olarak ele alınmaktadır. Bütün temel korunum denklemleri söz konusu fiziksel modele uyarlanmış ve sonlu farklar metoduna göre sayısal olarak çözülmüştür. Akışkan olarak ergimiş kalp malzemesi seçilmiş ve buna bağlı olarak da Pradtl sayısı 0.73 olarak alınmıştır. Tüm sonuçlar 0-106 arasında değişen farklı Rayleigh sayılan için incelenmiştir. Ayrıca ısı transferi hesabı yapılarak yerel ve ortalama Nusselt sayıları hesaplanmış, yerel Nu sayılarının duvarlar boyunca değişimi ve ortalama Nu sayılarının da, sistemin sürekli rejime ulaşmasının incelenmesi açısından, zamana göre değişimleri belirlenmiştir. Ayrıca, tüm sonuçlar sıcaklık ve hız alanları şeklinde sunulmuştur.

Natural convection in enclosures has received increasing attention in recent years. The attention is due in part to recognition of the importance of this process in many diverse applications such as home heating, solar collectors, crygenic storage, thermal insulation, crystal growth, furnace and nuclear reactor safety. In addition, engineering processes in fluids with chemical reactions or microwave heating are common today. Another example is geophysical problems (Runcorn, 1962) associated with the under ground storage of nuclear water, among other. In this study it was thought that heat generation in the core debris as a result of a post-accident. A severe nuclear reactor accident involving the melting of the reactor core, dominate the residual risk associated with the use of nuclear power (Powers, 1990). Many safety-significant phenomena may be hypothesized to occur when core debris is expelled from the reactor coolant system. In recent years, the most important post-accident is that at Three Mile Island Unit 2 (TMI-2) reactor, now 14 years old, remains as the United States' worst commercial nuclear reactor accident. 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 plenum of the reactor vessel (DJ.Osetek, 1990). The high temperature core material when released into the reactor cavity is composed of an oxidic and a metalic melt. The interaction with the structural concrete is driven by the sensible and latent heat from the initial debris, by the decay heat power from the fission products which are partly in the metal phase but mainly in the oxide phase and by the chemical reaction enthalpies which are releasing a considerable amount of energy mainly from the zirkonium oxidation in the early interaction process. Vll The liquid products of concrete decomposition, mainly Si02 and CaO, are soluble in the oxidic fuel melt. This leads to an increase of the melt mass as the erosion of the concrete propageles and to a substantial change of the oxidic properties: Densities, viscosities and freezing temperature are in the long term dominated by the concrete material. The mixture of this material lowers the densities of the decay heat source in the oxidic melt, while however the integral decay heat remains uneffected and follows the slowly decreasing decay heat level. In this work, an square enclosure was thought with a uniform heat source distrubition in it. As in a post-accident which includes heat that is produced in the core debris directly as result of radioactive decay and chemical reactions. A numbers of studies have been conducted on convection in fluids with internal energy sources. Kulacki and Goldstein (1972) measured heat transfer from a plane layer containing internal energy source with equal boundary temperatures. John and Reineke (1974) reported the characteristics of flow and heat transfer within a horizontal semicircular enclosure and a horizontal rectengular enclosure. Beukema and Bruin (1983) developed a model of three dimensional natural convection in a confined porous medium with internal heat generation and applied theory to the storage process of agricultural products. Ozoe and Churchill (1983) computed the three-dimensional velocity and temperature fields for a cellular element with aspect ratio of seven in a rectangular enclosure heated from below. Recently Acharya' and Goldstein (1985) gave a numerical solution of natural convection in an externally heated square box containing uniformly distributed internal energy sources. Lee and Goldstein (1988) experimantally analyzed the temperature distribution and heat transfer rate for an inclined square geometry with uniform energy sources within it. They used as converting fluid distilled water with NaCl added to raise the electrical conductivity and Mach-Zehnder interforameter to measure the temperature distribution within the water bounded by four rigid isothermal planes maintained at the same temperature. vm A 60 Hz. a.c. was passed from one silver-plated copper plate to the opposing one through the water to provide a relatively uniform internal heat source. The purpose of this work is the numerical study of the flow in a confined vertical square enclosure which its walls mainted at the constant temperature being driven by uniform heat source within and examination of the temperature field and heat transfer to the walls. We started from the conservation equations of mass, momentum and energy for the motion of which is laminar using the Boussinesq approximation. The square enclosure is assumed to be very long in the third dimension. The flow is also assumed to be laminer, steady and two dimensional with the axes of the flow parellel to the third dimension. Using the dimensionless variables, the governing equations are non- dimensionalzed. The dimensionless parameters characterizing the system are defined, as Rayleigh number; Ra- 9&D3 m qllxDz vet ' Jc and Prandtl number Pr=± In this study the governing equations are discretizated by control volume approach as discretization equations. One of the discritizeted governing equations is Poisson equation, which is an elyptic equation was solved with Successive Overrelaxation Method (SOR). According to the SOR a relaxation factor (X) which is defined by trying IX is used and it was defined as A, =1. 8. Dimensionless vorticity transport and energy equations 3x dX dY dY -u"> ru-> r*\ 3x dX dY are solved by using the two-dimensional Alteernating-Direction-Implicit (ADI) method. The relationships between veloticity and stream function are as follows dY dx The first and second derivatives in space are approximated by central differences. Each time step is divided into two halves. For the first half time step *n to tn+i/2 derivatives with respect to one space direction are represented by finite- difference analogues evaluated at t,,.,.,^ where those with respect to the other direction are evaluated at t" and are already known. In the next half time-step from tn+i/2 t0 tn+i me reverse procedure is used. And forward differences are used for aproximating the time derivatives. The boundary condition for the vorticity is calculated by a three-point forward or backward scheme for the stream function. A Prandtl number of 0.73 has been used in this study and while this choice corresponds to air it also approximates the Prandtl number value for molten mixed- oxide nuclear fuel, (Acharya, 1985). The Rayleigh numbers are chosen as different values, from 0 to 106. Also local and average Nusselt numbers are calculeted separetly for four walls of square enclosure. Finally conduction, transition and laminar boundary layer regions are determinated by computing average Nu number for different Rayleigh numbers.