Nükleer yakıt soğutucu kanallarında birleşik taşınımla ısı transferinin sayıal çözümü

Abstract

ÖZET Birleşik taşınımla ısı transferi geniş kullanım alanı dolayısıyla endüstrinin bir çok alanında kullanılmaktadır. Özellikle nükleer reaktörlerin soğutma kanallarının ve nükleer mühendislikte kullanılan kanalların soğutulmasında, elektronik devrelerin monte edildiği kabinlerin soğutulmasında sık olarak kullanılmaktadır. Bu çalışmada düşey olarak konumlandırılmış paralel levha şeklindeki kanallarda birleşik taşınımla ısı transferi sayısal olarak incelenmiştir. Tüm korunum denklemleri fiziksel modele uygulanmış ve denklemler sonlu farklar metoduna göre ayrıklaştırılmıştır. Akışkan olarak su seçilmiş ve Prandtl sayısı 5.0 olarak alınmıştır. Çalışmanın sonucunda hız, sıcaklık, basınç ve Nusselt sayısının değişimi grafik olarak verilmiştir. vııı

SUMMARY NUMERICAL SOLUTION OF MIXED CONVECTION HEAT TRANSFER IN NUCLEAR REACTOR COOLANT CHANNELS Mixed convection heat transfer is of considerable interest to the technical field due to its frequent occurences in industrial, technological and natural surroundings. The nuclear reactor fuel assemblies, which are of various configurations and which generates heat by fission product decay. Much of the previously published work on this subject is concerned with either the effects of free convection, developed laminar forced convection for confined flows or purely free convection for unconfined flow situations such as a single vertical plate around vertical or horizontal cylinders. Notable exceptions of Elenbaas (1942) earned out analytical and experimental work on natural flow in such cross sectional geometries as the equilateral triangle, square, rectangle, circle and infinite paralel plates. Buoyancy effetcs on heat transfer in flow through a parallel-plate channel are relevant to solar energy collection, as in conventional flat plate collectors, and the cooling of modern electronic equipment and cooling of parallel plates of nuclear reactor. In this study, plate type fuel is used. The parallel plates are mounted vertically, forming vertical flat channels through which coolant passes. The coolant may be driven by natural convection, forced convection, or mixed convection depending on the power density of the parallel plates. In this study, transient heat transfer characteristics in laminar mixed convection through a parallel plate channels are investigated. A number of studies have been conducted on laminar steady or transient mixed convection. ixAn analytical method which was proposed by Tao (1966) to study fully developed mixed convection was approximately treated by Quintiere and Mueller (1973). The predicted Nusselt number was contrasted with the limiting cases of pure free and forced convection. In following years various axial length scales to distinguish regions of different convective mechanism from the developing state to the fully developed state were presented by Yao (1983). Further steady state laminar mixed convection in a short channel at low Peclet numbers including axial heat conduction in the flow was investigated by Chow et al. (1984) by solving the full Navier-Stokes equations. Heat transfer in steady mixed convection in vertical tubes was numerically and experimentally investigated by Scheele et al (1963). Scheele and Hanratty (1963), and Lawrence and Chato (1966) for buoyancy aiding and opposing flows. The effect of natural convection on instability and transition of the forced flow was experimentally examined. Similar study was performed by Zeldin and Schmidt (1972). This study, investigates transient thermal characteristics of internal mixed convection flow. The purpose of this study is to explore unsteady laminar mixed convection in a vertical plate channel under buoyancy aiding conditions. The study is started by giving flow and thermal characteristics in a vertical flat duct for two dimensions. The flat depth w is at least ten times the interplate spacing b so that w>10b. To facilitate the analysis, the Boussinesq appoximation is invoked. Besides this, only high Peclet number flow is treated here so that the longitudinal conduction in the flow is negligibly small. Also the plates are rather thin so that heat conduction in them can be neglected and only boundary layer flow is examined. The mixed convection problem can be presented using the Parabolized Navier Stokes equations (Asian, 1991).The non dimensional form of the governing equations are obtained for an incompressible flow and Boussinesq approximation. Under the above assumptions, the basic equations in dimensionless form describing the conversation of mass, momentum and energy for unsteady mixed convection in a vertical plane channel are defined as follows: ^+^ = 0 (1) dü rrdU rrcU dP â2Y Gr ` âz âX âY dX âY2 Re de TTâe m ı e2 e dr âX âY PrdY2 K ' In this study U is solved the finite difference form of equation (2) and V is solved numerically by using equation (4) V-/%iY (4) The initial and boundary conditions are as follows: r = 0, U = 6(Y-Y2), 0 = 0 t>0, x=0 U = 6(Y-Y2), 0 = 0 Y=1, u=0,,Pr§ +f.r. XIThe governing equations are solved using a finite difference method based on LSOR. To obtain enhanced accuracy, the gridlines were positioned nonuniformly and non-uniform grid which clustered toward the walls is employed to resolve the sharp gradients present near the walls. In order to test accuracy, four sets of grids were used (81x41,101x61, 101x81, 131x61). The nonuniformity of the grid is described by the relation in which *,+l=*i+«*A s, represents the spatial location of the grid line, A the step size and as the grid stretching parameter (Baytaş, 1996). During the program test, solution for a typical case with Pr=5.0, Gr/Re=1 000.0, A1=A2=10.0, and /h'0-5 were obtained using different space and time intervals to ensure that the solution is grid-independent. The code was checked for accuracy the earlier published experimental and numerical results of Lin, T.F., Yin, C.P., Yan, W.M., (1991). Equation (2) and (3) are expressed in terms of finite difference approximations by employing the upstream difference in convection terms and central difference in the diffusion terms. The unsteady terms are treated by the backward difference so that the scheme is fully implicit. The resulting system of the algeabric equations can be cast into a tridiagonal matrix equation, which can be solved by the Thomas Algorithm (Anderson at al., 1984). Heat transfer characteristics depend on the Prandtl number, ratio of the Grashof number to Reynolds number Gr/Re, degree of asymmetric heating yH, and wall-to-fluid heat capacity ratios A1 and A2. Computations can be performed for any combinations of these parameters. XIIThe effects of these parameters on the transient heat transfer characteristics presented with graphics. The effects of Gr/Re ratio on the velocity profile are given fig. 4.1. a, fig. 4.1.b, and fig. 4.1.C for a typical case with yH =1.0, A1=A2=1.0 at X=0.2 for aiding flow. For pure forced convection (Gr/Re=0.0), U does not change with time (Fig. 4.1. a), but when the buoyancy force is activated (Gr/Re > 0.0), flow near the channel walls is contionusly accelerated by the aiding buoyancy after the initiation of the transient by imposing heat fluxes to the flow. After a certain r, concavity in the velocity profile appears in the central portion, because to maintain the mass conservation, flow in the central portion of the channel is slowed down (Fig. 4.1. b, Fig. 4.1. c). The influences of Gr/Re on the time variation of the temperature profiles are less significant. The influences of the wall-to-fluid heat capacity ratios on the transient velocity and temperature profiles are illustrated in Figs. 4.2 and 4.3. The results indicate that the evolution of the flow and thermal fields becomes slower for larger A1 and A2. In this study the major results can be summarized as follows: Raising the buoyancy force in aiding flow increases the Nusselt number both in the transient process and at steady state. Dominant factor to determine the time rate of energy transfer into fluid is the wall-to-fluid heat capacity ratio, the effects of Gr/Re and yH are not so important. The distorted velocity profiles in mixed convection flow (Figs. 4.1 and 4.2) have inflection point at high Gr/Re. XIII