Pasif sistemlerde türbülanslı doğal taşınım

Turbulent naturel convection in passive systems

Tez No: 39139
Yazar: SEYHAN UYGUR
Danışmanlar: PROF.DR. A. NİLÜFER EĞRİCAN
Tez Türü: Doktora
Konular: Enerji, Makine Mühendisliği, Energy, Mechanical Engineering
Anahtar Kelimeler: Belirtilmemiş.
Yıl: 1993
Dil: Türkçe
Üniversite: İstanbul Teknik Üniversitesi
Enstitü: Fen Bilimleri Enstitüsü
Ana Bilim Dalı: Belirtilmemiş.
Bilim Dalı: Belirtilmemiş.
Sayfa Sayısı: 77

Özet

ÖZET Bu çalışmada, Trombe duvarlı bir pasif sistem ile ısıtılan odanın içindeki türbülanslı doğal taşınım incelenmiştir. Odanın geometrisi ve sınır koşulları; incelenen olayı, kenar oranı bire eşit, aynı duvar üzerinde, yukarıdan hava girişi, aşağıdan hava çıkışı olan kapalı bir hacim içerisindeki türbülanslı doğal taşınım problemi durumuna getirmektedir. Literatürdeki türbülans modelleri böyle bir problem için uygun değildir. Bu nedenle, çalışmada, bu geometriye uyum sağlayacak, düşük Reynolds sayılarına uygun, buoyant etkiyi içeren yeni bir türbülans modeli geliştirilmiş; bu modelle çözüm yapılabilmesi için yeni bir yöntem sunulmuş ve bir bilgisayar programı oluşturulmuştur. Bölüm l.'de; pasif sistemler, bu sistemlerdeki türbülans, türbülansm genel özellikleri, kapalı hacım ve buoyant etki ile ilgili özel durumlar ve literatürde bu konulardaki boşluklar özetlenerek çalışmanın amacı belirtilmiştir. Bölüm 2. 'de; türbülanslı olayların modellenmelerinin neden gerektiği ve bu modellemenin nasıl yapıldığı anlatılarak türbülanslı akıştaki yönetici denklemlerin genel yapıları verilmiştir. Bölüm 3. 'de; literatürde kullanılan standart k-E modeli ve bu modelin düşük Reynolds sayılarına sahip akışlardaki yetersizliği, sayısal olarak yarattığı yanılgılar ve çözüm yolları tartışılmıştır. Bölüm 4. 'de; ısıtılan odanın geometrisi ve çözümün genel aşamaları verilmiş; geliştirilen türbülans modeli anlatılmıştır. Geliştirilen modelde, skaler galkantı terimleri için iki seçenek kullanılmıştır: F unlardan birincisi standart gerilme/akı yaklaşımı, ikincisi ise Daly Harlow yaklaşımıdır. Modelin denklemleri hareketin yönetici denklemleri ile birlikte sonlu farklar yöntenine göre ayrıklaştırılarak çözülmüştür. Programın akış diyagramı ve sayısal yöntemin ayrıntıları bu bölümde verilmiş; model, çok sık incelenen boyut ve parametrelere sahip sistemlere uygulanmış ve literatürdeki çalışmalarla uyunı sağladığı görülmüştür. Bölüm 5. 'de; modelin her iki seçeneği büyük kenar oranlarına sahip kapalı hacimlere uyarlar jmış; her iki seçenekten de aynı sonuç elde edilmiştir. T?.ombe duvarlı pasif sistemle ısıtılan oda geometrisinde ise, Daly Harlow seçeneğinin, dengesiz katmanlaşmayı, viskoz sınır tabakanın değişimini ve ikincil akışları daha iyi yansıttığı sonucuna varılmıştır. Duvarlar arasındaki sıcaklık farkları ve ventilasyon delikleri arasındaki mesafe deriştirilerek, bu parametrelerin oda içindeki türbülanslı sıcaklık ve hız alanlarına etkileri tartışılmıştır. Ayraca; aynı yöntem, cam yüzey ile duvar arasında kalan bokluktaki ve poroz malzemeden yapılmış Trombe duvarı' ıdaki akışa da uygulanmıştır. vııı

Özet (Çeviri)

TURBULENT NATURAL CONVECTION IN PASSIVE SYSTEMS SUMMARY In this study a single-zone passive heating system with a Trombe Wall has been investigated by the fluid mechanics point of the view. The aim of the study was to design a passive system in the most comfortable and efficient form taking the turbulent air motion into account. Introduction Chapter of this thesis includes the main heat transfer concepts of a passive system and the goals in such a design. In fact, these systems are widely designed and constructed in United States and mid- European countries. But like other solar energy applications, turbulence occurring in passively heated zones has not been studied even roughly. In literature it is agreed that exceeding a critical Rayleigh number based on the height of the zone, the laminar flow assumption is invalid. Features of turbulent motion are discussed briefly in Introduction Chapter. Unstable stratification of temperature, separation, and secondary flows are symptoms of turbulence. In addition to these features, two important characteristics of the flow in a passively heated room, which make the turbulence solution harder to be executed are, firstly, that it is an enclosure, which makes the flow bounded; and secondly that convection heat transfer in the system is natural, so that the buoyancy force is dominant. In enclosures the boundary layers are affected greatly by the core region. Turbulence being stronger and more complicated by the effect of enclosure geometry and buoyancy force is in fact, a phenomenon, which is very familiar to us in our daily life. Turbulence doesn't have an exact definition but it exists everywhere in the universe. For example, the meteorological events, diffusion of smoke from a chimney into atmosphere, mixing processes are turbulent events. Randomness is the most explicit property of turbulence. By the means of this brief discussion about the passive heating systems, the turbulent motion occurring in them, the characteristic difficulties of the turbulent and natural convective flow, and the structure of turbulence, the aim of the thesis have been explained IXat the end of Introduction Chapter. The aim of the thesis is to model the turbulent natural convection in an enclosure in general, and to solve the turbulence equations together with the governing equations in a passively heated room with a Trombe Wall, in particular. A code has been developed for this aim. In Chapter 2, one of the solution alternatives to overcome the randomness is explained. It is called modelling of turbulence. A dependent variable in a turbulent motion has two parts, one is the mean and other is the fluctuation value. Even if the motion is steady, dependent variables fluctuate within very small time intervals. These fluctuations are random and their determination needs statistical knowledge and methods. If all these fluctuations were included by the governing equations, the computer storage to solve them would be incredibly big. So, instead of including and storing these fluctuation values, they are averaged over the time, and sometimes over the density, especially in combustion processes. The time interval is very long compared to the fluctuation interval and very short comparing with the time interval making the flow unsteady. Averaging the dependent variables creates additional terms which makes the number of unknown values more than the number of governing equations. Hence, additional equations are needed. This situation is called“closure problem of turbulence”in literature. The structure of the solution to this closure problem is called“modelling of the turbulence”. These models have various hypothesis for the turbulent motion and need empirical constants and coefficients. Equations formed by the model are solved with different numerical solutions. If the numerical solution is efficient enough, the investigation of the motion depends on the model's ability to represent the real flow. Modelling turbulence is a widely investigated subject especially in the last two decades, as a result of rapid developments in computers and numerical methods. One of these models, called“k-6”model, is very common and also forms the fundamentals of the model developed in this thesis. Before discussion of this model in the third chapter, the turbulent governing equations and Boussinessque eddy viscosity/dif fusivity approximation is explained briefly in Chapter 2. The governing equations written for an incompressible fluid for unsteady motion are continuity, momentum equations in x and y directions, energy equation and mass conservation equation which uses the vapor concentration in the air as the dependent variable in this study. Additional terms in these equations are Reynolds stresses and turbulent fluxes. In Chapter 2, their definitions and turbulent diffusion coefficients which are very similar to the laminar ones are introduced. In Chapter 3, fundamentals of k-6 model areexplained. First, the Prandtl mixing length model and its inefficiency have been mentioned. Then the reason for accepting turbulent kinetic energy as the velocity scale and the definition of turbulent kinetic energy is given. With such a scale the inheritance and transport of turbulence is represented more realistically. Two additional transport equations for turbulent kinetic energy k, and the dissipation of turbulent kinetic energy are solved together with the governing equations. These equations and empirical constants and coefficients are presented in the third chapter. Then the insufficiency of this model in flows with low Reynolds numbers are described. In k-G model, logarithmic law near the wall is combined with the model but usually, making turbulent solution in viscous sublayer and forming unmatched grid points with the velocity profile are common difficulties when the model is put into code for the numerical solution. Since the analytical solution is impossible, these difficulties should be overcome. For that reason modified models developed by various researches since 1970' s have been summarized in Chapter 3. These developed models are called“low Reynolds number models”. New coefficients are imported into the equations, and the resulting equations become appropriate to be put into numerical code. General structure of these equations are given in this chapter. In the fourth chapter, the procedure of the general calculation is summarized. This procedure consists of the meteorological data for the location of the passively heated zone to obtain the radiation and temperature on the glass plates. Then, the turbulent flow field in the gap between the glass plate and the wall and, the wall boundary conditions are predicted. The flow in the Trombe Wall which is made of a porous material, is also modelled and the boundary conditions of the zone heated passively are obtained. These boundary conditions are used to execute the main part of the work, modelling of the turbulent natural convection in an enclosure having the aspect ratio of one which has an air inlet upside and an outlet downside that is the exact condition of the passively heated single zone with a Trombe wall. Schematic diagramme and the geometry of this zone are present in this chapter together with the general algorithm of the solution procedure. Flow field in the Trombe wall is solved for the laminar flow. The governing equations of laminar flow combined with Darcy's Law in literature are solved by the means of the code developed for this thesis, cancelling the terms related to turbulence. The subsection of Chapter 4 entitled“Modified Turbulence Model”is the core of the study. It includes the essence of the model developed for the turbulent natural convection in an enclosure having the aspect ratio of one which has an air inlet upside and an outlet downside. Most of the turbulence models in literature XIare for the solution of isothermal forced flows. As the flows representing atmospheric events, diffusion of the pollutants etc. became popular in last decade, developments in modelling of the natural turbulent convection have been accelerated. Unfortunately, these models are not universal and it is almost decided that a turbulence model should be problem dependent and is valid for only similar geometries. For this reason, none of the models for turbulent natural convection are appropriate for the passively heated zone, and a modified turbulence model has been developed having the goals of representing the dominant buoyancy effect, the viscous effects in the vicinity of the wall and also the low turbulence due to buoyancy. Improvement of the computational convergence and decrease of the computer time were also among the aims of the work. The most important modification of the model is on the definition of scaler fluctuation variables. Instead of standard turbulent flux approximation, Daly Harlow approximation is used for the definition of the fluctuation parts of the temperature and concentration. Thus, turbulent parts of temperature and concentration are defined also in terms of velocity gradients. This new definition is imported into the buoyancy production / destruction term. It should be noted that both production and destruction are used for buoyancy term; because if stratification is unstable turbulence increases and if it is stable turbulence decreases. In the modified model, extra source terms in the differential equations of turbulent kinetic energy and dissipation of turbulent kinetic energy of the low Reynolds number models are omitted because they have no physical meaning and just imported for numerical tricks. Instead, the wall boundary conditions and low Reynolds number model coefficients damping the turbulent viscosity in the vicinity of the wall are updated to the system. These new boundary conditions and coefficients are listed in a table. Using Daly Harlow approximation for temperature and concentration fluctuations forms source terms in the differential equations of these dependent variables, so that the convergence accelerates in the numerical solution. The constant of the Daly Harlow approximation is given in a form matching with the standard turbulent fluctuation Then, all the equations of the modified model are written in two dimensional cartesian system and the numerical procedure has been described. Numerical solution consists of discretization by finite difference method and an iterative solution by the means of the code developed in this study. The general form of the dicretized differential equations, variable dependent and variable independent sources, the flow diagram of the code and the grid distribution are present in the third subsection of Chapter 4. Grids are generated in such a way that dimensions of the control XXIvolumes are very tiny near the walls and they become coarser towards the core region. The grid field is a staggered one that means vectorial dependent variables have been defined at the control faces while the scaler dependent variables have been defined at the grid points. In the code, the Power Law Differencing Scheme method, PLDS, for the convection terms, and Semi-implicit pressure Lainkage method, SIMPLE, for the pressure correction have been used. Both of these methods are described briefly. Also, underrelaxation equations and factors for every variable, and the convergence criteria are the subjects discussed in this subsection. General boundary conditions are given at the end of Chapter 4. At the walls, velocity, pressure and turbulent kinetic energy equal to zero; dissipation of kinetic energy, temperature at the horizontal walls and concentration have zero gradients, while the temperature values at the vertical walls are taken as constant. At inlet, velocity, temperature and concentration variables are constant, turbulent kinetic energy is a function of inlet velocity and dissipation of turbulent kinetic energy isa function of the turbulent kinetic energy at the inlet, while the pressure gradient equals to zero. At outlet section all the dependent variables, except pressure, equal to constant fluxes while the pressure has zero gradient. Based on the turbulence model and numerical code developed in this study, results of the investigation on a passively heated single zone with a Trombe wall are given in Chapter 5 entitled Conclusions and Suggestions. In this conclusion chapter, first of all, the two alternatives in the new modified model; one is the standard stress/flux approximation, and other is the Daly Harlow approximation to the temperature and concentration fluctuations are compared. It is shown that these two alternatives match for the tall enclosure geometries without any inlet or outlet. However they do differ for an enclosure having aspect ratio as one with an inlet upside and an outlet downside on the same wall. In this enclosure turbulent natural convection occurs. Daly Harlow approximation gives more realistic results for representing the unstable stratification, secondary flows and viscous sublayers near the walls. Concentration distribution in such a geometry has also been illustrated. Then, the effect of temperature differences between the walls and the distance between the inlet and outlet sections that means the distance between the ventilation holes, on the turbulence inside the enclosure are shown. It is concluded that temperature difference is proportional to the intensity of turbulence. However, if the inlet and outlet of the air are very near to each other turbulence intensity is high even at small temperature differences. In addition to the illustrations for the turbulent air motion in the room, the velocity and temperature fields between the glass xxiiplates and the wall having a big aspect ratio and in the Trombe wall have also been shown by the contours. The calculation field inside the Trombe wall which is made of a porous material is accepted to be laminar according to the criteria imported from the Darcy's Law. In the appendix chapter, the laminar calculation procedure for the Trombe wall is summarized. xiv

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