Zorlamalı akışta minimum entropi üretim için nükleer yakıt demeti geometrisi

Abstract

ÖZET Günümüzde enerji kaynaklarının sürekli azalması mevcut enerjinin daha verimli kullanılmasını kaçınılmaz hale getirmiştir. Tüm termodinamik sistemlerde olduğu gibi nükleer reaktörlerde de ısı transferi, akışkan sürtünmeleri ve kütle transferinden kaynaklanan tersinmezlikler meydana gelmekte ve bu durum sistemin verimim düşürmektedir. Bu nedenle bu çalışmada nükleer reaktörlerde fisyon sonucu açığa çıkan ismin çekilmesi sırasında oluşan tersinmezlikler termodinamiğin ikinci kanunundan faydalanılarak incelenmiştir. Çalışmanın başında yakıt demeti geometrisinin hız ve sıcaklık dağılımları incelenmiştir. İlerleyen bölümlerde yakıt demetleri arasında zorlamalı akış için laminar ve türbülanslı bölgelerde ısı transferi ve akışkan sürtünmelerinden kaynaklanan tersinmezlikler boyutsuz entropi üretim sayısı ile tanımlanmış ve deneysel olarak çıkarılan Reynolds sayısına bağlı Nusselt sayısı ile sürtünme faktörü korelasyonları da kullanılarak optimum yakıt geometrisi tespit edilmiştir. Bu şekilde güç reaktörlerinde farklı akış şekilleri için optimum Reynolds sayısı ile s/r0 (yakıt demeti geometrisi oranı) ve B0 (iş parametresi) boyutsuz sayılan bulunarak en uygun ve en verimli çalışma şartlan tespit edilmiştir. vıı

SUMMARY NUCLEAR FUEL BUNDLE GEOMETRY FOR MINIMUM ENTROPY GENERATION IN FORCED CONVECTION In this study, it has been focused on the design of the rod bundles for minimum entropy generation in forced, convection heat transfer. The need for the utilization of the second law of thermodynamics in thermal design decisions has been advocated by several investigators. A well documented justification of this viewpoint was published by Bejan (1987) in a monograph and was updated in 1994 by the same author. In the investigation of Bejan (1987), the basic principles of the second law of the thermodynamics has been presented and a series of heat transfer engineering applications have been optimized in such a manner that they operate while producing minimum entropy. It has been shown for many cases that the major contributors to entropy generation are heat transfer irreversibilities and flow friction irreversibilities. The paramount effect, which use of the second law of thermodynamics has on efficient use of available energy, is also apparent in this study. In another investigation presented by Poulikakos (1982), a theoretical framework for the minimization of entropy generation (the waste energy, or useful energy) was established in extended surfaces (fins) and it was focused on the design of fins for minimum entropy generation in forced convection heat transfer. This design philosophy allows us to properly account for the fact that, in addition to enhancing heat transfer, extended surfaces increase fluid friction. In that investigation, the competition between enhanced thermal contact and fluid friction is settled when the heat transfer irreversibility and the fluid friction irreversibility add to yield a minimum rate of entropy generation for the fin. Until recently, only heat transfer and fluid friction irreversibilities were considered in convection applications irreversibilities associated with mass transfer were largely ignored. This fact was recognised by San (1987 a,b) who proposed an approach in a sequence of two interesting papers for the study of internal forced convection applications in which mass transfer irreversibilities are important. More specifically, these authors first derived expressions for entropy generation in two limiting cases of combined forced convection heat and mass transfer in a two- dimensional channel. The two limiting cases were pure heat transfer and pure mass transfer. Expressions for optimum plate spacing and optimum Reynolds number were reported for both laminar and turbulent flows. The analysis was generalized later to account for the simultaneous existence of heat and mass transfer irreversibilities during forced convection in a paralel plate channel. vuiThe investigation of Poulikakos (1988) was focused on the problem of entropy generation by heat transfer, mass transfer and flow friction irreversibilities in external laminar and turbulent forced convection. After deriving general expression for entropy generation, which accounts for the combined action of the specified irreversibilities, two fundamental applications were presented of the expression. To this end, optimum operating conditions were define for forced convection heat and mass transfer from a flat plate and from a cylinder. In this work, before investigating the second law of thermodynamics, longitudinal laminar flow between cylinders arranged in triangular array was studied. The aim of this analysis is to determine the pressure drop, shear stress and velocity distribution characteristic of the system. The starting point of this study is the basic law of momentum conservation. The resulting differantial equation has been solved analytically and results were obtained over a wide range of porosity values for the triangular array. In the second part of this study, consideration was given to the fully devoloped heat transfer characteristics for longitudional laminar flow between cylinders arranged in an equilateral triangular array. The analysis was carried out for the condition of uniform heat transfer per unit length using the fundamental principle of energy conservation. Solution were obtained for the temperature distribution, and from these, Nusselt number were derived for a wide range of spacing-to-diameter ratios as below Nv!±m)a!m (1) ' * UJr.-r, ( where h is the heat transfer cofficient which is defined as *- İ- *22 (2) *d£Tw-TJ (ic dJ12)(Tw-T^ If the derivation of wall-to-bulk temperature is made, the following functional relation is revealed, 1^BW (3) This is an interesting result in that the dependence on geometry enters only as the ratio s/r0, rather than s and r` seperately. It may be seen that the Nusselt number is essentially the reciprocal of the dimensionless bulk temperature parameter which has been displayed in Eq.(3). From this, it follow that the Nusselt number depends only on the spacing ratio s/r0. If the IXgraph of Nusselt number as a function of s/r0 has been prepared, it can be seen from this figure that Nusselt number monotically increases as s/r0 decreases; and with this it follows from Eq.(l) that the wall-to-bulk temperature difference is smaller at smaller spacing for a fixed heat input. This trend is in accord with physical reasoning. The objective of this study is to outline an entirely different approach to the optimization of the rod bundles geometry. This approach consist of calculating the entropy generation rate of one typical element of the flow area and minimizing it systematicly. The first and second law of thermodynamics, taken together, state that the entropy generated by any engineering system is proportional to the work lost (destroyed) irreversibly by the system. This truth is expressed concisely as the Gouy- Stodola Theorem (Szargut (1980)). W^T £ Sa (4) all system component where Wlost is the lost available work (lost availability, or lost energy), T is the absolute temperature of the enviroment and Sa is the entropy generated in each compartment of the system. This equation implies that the thermodynamic irreversibility (entropy generation) of each system component contributes to the aggregate loss of available work in the system (Wlost). An important observation concerns the order of magnitude of the viscous term relative to the heat transfer term in the makeup of Sa. This issue requires some care because in a large number of convective heat transfer problems the viscous dissipation term pt$ is routinely neglected in the first law of thermodynamics. If in an actual problem the characteristic dimension (scales) for velocity gradient and temperature gradient are v7L* and AT*/L/ then the size of the viscous term /* $ relative to the conduction term kV.(VT) in the energy equation is (fluid friction/ _ n(v*)2 _ [heat transfer )Xstlaw kLT On the other hand the size of fluid friction irreversibility relative to heat transfer irreversibility is (fluid friction/ _ T n(v*)2 (6) [heat transfer j^ ^ Ar kAT It is clear now that although /n(v*)2/kAT* may be much smaller than unity in many applications, the fluid friction irreversibility term is not necessarily negligible in the volumetric rate of entropy generaiton which isS.=- (V7)2 +-Ü * (7) ` jn T As is shown in Eq.(6), the size of the viscous term depends also on the ratio of the characteristic absolute temperature divided by the characteristic temperature difference, T7AT*. In many heat transfer applications this ratio is considerably greater than unity, as it will be discovered in subsequent examples and problems. In view of this discussion we recognize two dimensionless parameters in the entropy generation analysis of convective heat transfer problems. These parameters are dimensionless temperature difference *`=f 00 and the irreversibility distribution ratio, 5- (fluid friction) <j)=_2L^ i i (9) Iff Sa (heat transfer) where the entropy generation expression Eq.(7) has the basic form: s'l'=S'î'(heat transfer) +S% '(fluid friction) ( 1 0) Entropy generation profiles and maps may be constructed using Eq.(7) so long as the velocity and temperature gradients are known at each point in the convective medium. The backbone of this construction can be outlined writing second law of thermodynamics for an open system. In large number of convective heat transfer situations the velocity and temperature graident are not known at each point in the medium. This is the case when the flow regime is turbulent or when the flow geometry is so complicated that an exact description of velocity and temperature is not available in analitical and numerical form. However, most of these heat transfer arrangements are documented in the heat transfer archives on the basis of heat transfer and fluid friction data measured along the solid boundaries surrounding the flow. Therefore the corelations, which describes the heat transfer and fluid friction rate, have been used to obtain the optimum geometrical design of the rod bundles in this study. Consider the flow passage of arbitrary cross-section A2. The bulk properties of the stream m are T, p, q/P,h. Focusing on a slice of thickness dz as a system, the rate of entropy generation is given by the second law XI*».-**-3s? (11) Using the defination of the first law of thermodynamics, average heat transfer coefficient, friction factor, Reynolds number, Stanton number and hydraulic diameter, entropy generation rate per unit length is obtained as below <£_*!_£?**-£- di) ` 4T*mc, St p'r d A Rearranging the Eq.(12) the entropy generation number Ns is defined as *.--^-?r*£4 (13) q'jkl* nNu 32 tf' where B0 is _M!p_ (14) 0 («y/V2 If the pipe flow type is known the Nusselt number and friction factor are given by the well-known corelations (Kim (1988) and Kakaç (1987)). Using this corelations and setting 5N8/3Re=0 Re^ is obtained for the minimum entropy generation. xu