Sıkıştırılmış sıvı kaynaması

Abstract

Sıkıştırılmış sıvı kaynaması, (subcooled flow boiling) teknolojinin birçok alanı için önemlidir. Su soğutmalı nükleer reaktör teknolojisinde, hem soğutucu hem de yavaşlatıcı olarak kullanılan suyun buharlaşması ile oluşan buhar boşluk oranının doğru hesaplanması ayrı bir önem kazanmaktadır. Bunun nedeni oluşan boşlukların yakıtın yanma hızını, kalp basınç düşüşünü, ısıl sınırlan, nükleer reaktörün kararlı (steady-state) ve geçiş (transient) hallerindeki cevabım etkilemesidir. Isıtılan bir kanal boyunca oluşan gaz ve sıvı faz, kanal içinde farklı akış rejimlerinde bulunabilir. Bu rejimin anlaşılması akışın analizini kolaylaştırır. Isıtılan bir kanalda kabarcık oluşumu sıvı fazın ortalama sıcaklığı doyma sıcaklığına gelmeden başlayabilir. Bu durum, kanal içinde oluşan radyal sıcaklık dağılımının kanal duvarında kaynama için gerekli şartlan sağlaması ile olur. Duvar yüzeyinde meydana gelen kabarcıklara! oluşumunu, büyümesini ve sıvı faz içinde yükselişini analitik olarak tanımlamak çok zordur. Bu yüzden, büyük ölçüde deneysel çalışmalardan da faydalanılmaktadır. Buhar kabarcıkları ısıtılan yüzey üzerindeki pürüzlerde sıkışan gaz veya buharın genleşmesi ile meydana gelir. Genellikle, yüzeydeki pürüzler yüzey gerilim kuvvetleri sebebi ile bütün olarak sıvı faz ile doldurulamazlar. Tamamıyla sıvı faz ile doldurulan pürüzler kaynama bölgesi olarak rol oynamazlar. Yüzeyde oluşan kabarcığın şekli ve büyüklüğü oluştuğu pürüzün sağladığı şartların bir fonksiyonudur. Isıtılan yüzeyde oluşan kabarcıkların yüzeyden ayrılmaya başladığı nokta net buhar üretim noktası (the point of net vapor generation) olarak adlandırılır Bu noktanın doğru tahmini, buhar boşluk oranının doğru hesaplanmasına önemli bir şekilde bağlıdır. Kurulan modellerde buhar boşluk oranının ve net buhar üretim noktasının bulunması için elde edilen bağıntılar büyük farklılık gösteren sonuçlar vermektedir. Bu çalışmada farklı araştırmacılar tarafından konu ile ilgili kurulan modeller incelenmiştir. İncelenen modellerin her biri için buhar boşluk oranlan ve net buhar üretim noktalan hesaplanmış, birbirleri ile karşılaştırılmıştır Ayrıca Kanada'da Ecole Polytecnique de Montreal, Institut Genie Energetique'de yapılan deney sonuçlan ile de karşılaştırma yapılmıştır. Buhar boşluk oranlarının çeşitli modeller tarafından hesaplanmasında farklılık, dolayısıyla deney sonuçlan ile uyumlarında yetersizlik görülmüştür. Bu yetersizliğin nedenlerinden biri de net buhar üretim noktasının modeller tarafından doğru saptanmasından zorluktur. Bunu gidermek için söz konusu deney sonuçlarından, net buhar üretim noktasını veren yeni bir bağıntı (correlation) türetilmiştir. S.Y. Ahmad tarafından geliştirilen modele bir çarpan ilave edilerek modelin hesapladığı boşluk oranlarının düzeltilmesine çalışılmıştır. Bu çarpan ve net buhar üretim noktasını veren yeni bağıntı ile desteklenen S.Y. Ahmad modelinin verdiği sonuçların, orjinal modelin verdiği sonuçlara oranla, deney sonuçlan ile çok daha uyumlu olduğu gösterilmiştir.

Water and vapor have the widest application as a working fluid in heat engineering and technology \vhich is explained by the following: (1) water is the most widely abundant substance in nature, (2) water and vapor possess relatively good thermodynamic properties, (3) water and vapor do not have harmful effect on metals and living organism. Nucleus formation is öne of the essential processes in boiling heat transfer. Exact analytical description of this process is not yet possible but using experimental results and making simplifications some analytical models may be obtained. it is well known experimental result that vapor bubbles form at distinct sites on the heated surface. Bubble formation starts from small amount of gas ör vapor entrapped in small cavities on a heated surface. This cavities are called nucleation sites. Cavities entrain vapor and seldom be completely filled with Hquid because of surface tension effects. A cavity that is completely filled with liquîd cannot act as a nucleation site. When vapor bubbles are growing, the size and shape of vapor bubbles departing from the heated surface are a strong fimction of the conditions where they are formed. While buoyancy and hydrodynamic drag forces attempting to detach the bubble from the heated surface, surface tension and liquid inertia forces acting to prevent detachment. The liquid inertia force is a dynamic force resulting from the displacement of liquid during bubble growth. During the growth of bubbles the temperature near the cavity firstly decreases, then after passing through a minimum it increases slightly until the bubble departs, then temperature continues to increase until the cavity and its surrounding become so superheated that the next bubble can be bora. During departure and rise, bubbles transfer their interaal energy from the heated surface to the liquid. Moreover, the rising bubble activates a drift flow in its wake, thus it induces a suction effect near the wall. This suction effect deforms the temperature profile mixing cold water and höt water. The axial void fraction profile for a heated channel with inlet subcooling depends upon the distribution of bulk liquid temperature. Experiments have shown that the boiling subcooled liquid gives rise to a two-phase flow where vapor and subcooled liquid exist simultaneously at a given cross section in the channel. This indicates that for these cases the assumption of thermal equilibrium in calculating void fraction is not applicable. Void profiles in such channels are a complicated fiınction of mass flux, heat flux, inlet subcooling and channel geometry. xii Because of the obvious relationship between void and reactivity it ıs important to calculate its distribution in liquid-cooled nuclear reactors. Several attempts have been made to determine the axial distribution of void fraction. On the basış of photographic study GrifEth, Clark and Rohsenow[18] were first to propose two separate regions in subcooled boiling. This fundamental investigation has been the basis of most later work. For the first region they suggested that heat was removed simultaneously by single-phase heat transfer mechanism and by condensation of vapor bubbles. By assuming that bubbles ahvays remain in the vicinity of the wall, GrifBth, et al. proposed that in the second region the condensing area and therefore the condensing coefficient remained constant. However, recent flow regime studies show that the bubbles do migrate into the main flow stream for the second subcooled region and the area of vapor condensation does not necessarily remain constant. Later Maurer[19] suggested a linear interpolation betvveen the end of the wall voidage region defined by GrifBth, et al. and the point of 40 percent void fraction on the modified Martinelli-Nelson void curve, this arbitrarily chosen boundary was based on experimental observations. Houghton[20], by neglecting slip velocity, solved the coupled nonlinear differential equations representing the void fraction and the liquid temperature in a heated channel. The solution obtained was a complicated implicit function, and in some cases it predicted that the liquid phase was superheated by as much as 10 deg°C, no experimental evidence of such superheating has yet been found. Bowring[21] subsequentiy presented a very reasonable physical model to calculate void fraction in subcooled boiling region. He also showed that for most of the experimental data then available the efFect of bubble condensation was negligible, a finding contrary to Houghton's model. Bowring' finding that e, the ratio of agitative heat flux to the evaporative, remains constant does not satisfy the boundary conditions of the subcooled region (because at the bulk boiling boundary s=0); it thus gives a discontinuity in the void profile. Lavigne[22] developed a Riccati-type differential equation for the distribution of quality in the subcooled boiling by assuming that (a) the mass of vapor formed per unit length is a function of local subcooling, and (b) the rate of condensation of vapor is proportional to the product of its mass and local subcooling. The solution yielded a functional relationship betvveen true quality and thermodynamic quality. He briefly treated the problem of calculating void fractions, suggesting that the slip ratio can be taken equal to öne. The condensation coefficient was simply assumed to be constant for given geometry and pressure. Brief explanations of some other important subcooled boiling models are given below. Xİİİ S. Levy Model : A model is developed to predict the vapor volumetric fraction during forced convection subcooled boiling. The proposed method of calculations consists of three steps: 1. The point of bubble departure from the heated surface (i. e. the location of vapor volumetric fractions significantly higher than zero) is determined from a bubble force balance and the single-phase liquid turbulent temperature distribution away from the heated wall. 2. A relation is postulated between the true local vapor weight fraction and the corresponding thermal equilibrium value. 3. The vapor volumetric fraction is obtained from the true local vapor weight fraction and an accepted relationship between vapor weight and volumetric fractions. N. Zuber, F.W. Staub and G. Bijwaard Model : The result of an analysis for predicting the vapor void fraction in boiling systems are presented. For two phase systems in thermodynamic equilibrium three efFects; i.e., of flow profile, vapor concentration profile across the düet and of relative velocity must be taken into account. it is shown here that when the bulk liquid is either subcooled ör superheated a fourth effect, that of the non-uniform liquid temperature distribution, must be considered. These four effects are included in an analytical expression for predicting the void fraction in saturated ör subcooled boiling. A method for also taking into account the nucleating characteristic of the heated surface is given since this effect also influences the non-equilibrium void prediction. Satisfactory agreement is shown between the analytical results and experimental data. F. W. Staub Model : The satisfactory prediction of the vapor volume fraction in subcooled boiling depends in large part on the ability to predict the point where a significant amount of net vapor is first formed. A method for the prediction of this point is derived here and compared with experimental measurements at both low and high fluid velocities. The derived relationship for this point include the effect of fluid properties, geometry and the liquid velocity. S.Z. Rouhani, E. Axelsson Model : The complex problem of void calculation in the different regions of flow boüing is divided in two parts. The first part includes only the description of the mechanisms and the calculations of the rates of heat transfer for vapor and liquid. it is assumed that heat is removed by vapor generation, heating of the liquid that replaces the detached bubbles, and in some parts, by single phase heat transfer. By considering the rate of vapor condensation in Iiquid, an equation for the difFerential changes in the true steam quality throughout the boüing regions is obtained. Integration of this equation yields the vapor weight fraction at any position. The second part of the problem concerns the determination of the void fractions corresponding to the calculated steam qualities. For this purpose we use derivations of Zuber and Findlay.This model is compared with data from different geometries including small rectangular channels and large rod bundles. The data XİV covered pressures from 19 to 138 bars, heat flux from 18 to 120 W/cm2 with many different subcoolings and mass velocities. The agreement is generally very good. P. Saha, N. Zuber Model : An analysis is presented directed at predicting the point of net vapor generation and vapor void fraction in subcooled boiling. It is shown that the point of net vapor generation depends upon local conditions-thermal and fluid dynamic. Thus, at low mass flow rates the net vapor generation is determined by thermal conditions, whereas at high mass flow rates the phenomenon is hydrodynamically controlled. Simple criteria are derived which can be used to predict these local conditions for net vapor generation. These criteria are used then to determine the vapor void fraction in subcooled boiling. Comparison between the results predicted by this analysis and experimental data presently available,show good agreement for wide range of operating conditions, fluids and geometries. R.T. Lahey Model : This model presents a phenomenologically based model for subcooled nucleate boiling. It is shown that the current state of understanding is such that mechanistic models cannot be uniquely determined; however, comparisons of the mechanistic model presented here in with existing data indicates good agreement. S.Y. Ahmad Model : A theoretical model is developed to determine the axial temperature distribution of subcooled liquid. It is a simple function of a heat transfer and a condensation parameter. The proposed model satisfactorily correlates the measured bulk temperature profiles. The corresponding void fraction is computed by using a new empirical slip correlation, valid in both subcooled and bulk boiling regions. The resulting axial void profile has been compared (over the entire heated length) with steam and water data from six different sources, covering a wide range of pressure, mass flux, surface heat flux, inlet subcooling and channel geometry. The method gives satisfactory agreement with experimental data. As it is understood there are lots of models which have been developed to investigate the subcooled boiling region and to understand subcooling phenomena. In this study, we examined subcooled boiling models by comparing them with each other and found a correlation to predict the point of net vapor generation using experimental results which were obtained at Ecole Polytecnique de Montreal Institut Genie Energetique in Canada. A correlation factor is also found for better agreement between calculations and experimental results. The correlation which gives the point of net vapor generation is obtained by fitting the experimental data to log-normal distribution. The availability of more data points will help build more accurate correlation. This correlation is used with S.Y. Ahmad model to increase the agreement between the results of calculation and experimental points. The corrections on calculated void fraction is also found XV necessary and a corrections factor in the form A1/z is calculated for each experimental conditions and applied to the same model for the calculation of void fraction. Then, the agreement with the experimental data is found much better than the agreement which was obtained using the original model.