Lif esaslı yalıtım malzemelerinde ısı geçişinin incelenmesi
Investigation of heat transfer in fibrous insulation materials
Yazar: ALİ CAN GÜÇLÜ
Danışman: PROF. DR. SEYHAN UYGUR ONBAŞIOĞLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Isı-Akışkan Bilim Dalı
Derece: Yüksek Lisans, 2012
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Isı geçişi = Heat transfer ; Isı iletimi = Heat conduction ; Monte Carlo Yöntemi = Monte Carlo Method ; Radyatif ısı geçişi = Radiative heat transfer ; Yalıtım malzemeleri = Insulating materials

Özet:
Yalıtım malzemeleri farklı sıcaklıktaki iki ortam arasındaki ısı geçişini azaltmak için kullanılan, endüstriyel ve domestik çok geniş bir uygulama alanında, konfor, enerji verimliliği ve kimi malzemelerin korunması gibi kaygılar nedeniyle kullanımı zorunlu olan malzemelerdir. Lif esaslı yalıtım malzemeleri ise çeşitli maddelerden üretilen liflerden oluşmakta ve tüm yalıtım malzemelerinin büyük çoğunluğunu oluşturmaktadır.Bu çalışmada, lif esaslı yalıtım malzemelerinin ısı geçişi özellikleri incelenmiştir. Bu incelemede, malzemenin ısıl özelliğinin bir göstergesi olan Eşdeğer Toplam Isı İletim Katsayısı (W/m.K) terimi, genelde kullanılan deneysel yığın yöntem ile değil, ışınım, gaz iletimi, katı iletimi gibi ısı geçişi mekanizmalarının ayrı ayrı incelenmesi ile teorik olarak elde edilmiştir.Literatürde, fiber bazlı yalıtım malzemeleri, geniş kullanım alanı nedeniyle bir çok çalışmaya konu olmuştur. Bu çalışmaların genel bir sonucu, fiber bazlı yalıtım malzemelerinde ısı geçişinin ışınım, gaz iletimi ve katı iletimi ile meydana geldiğidir. Diğer taraftan, fiberler arası sıkışan havanın oldukça küçük miktarda ve durgun olması, taşınım ve doğal taşınım mekanizmalarının oluşmasını engellemektedir.Araştırmacılar, fiber bazlı yalıtım malzemelerinin incelenmesinde katı ve gaz iletimi terimleri için genel olarak ampirik formüllerden yararlanmışlardır. Işınımın çözümlenmesinde ise ampirik formüllerin yanısıra İki Akı Yöntemi de yaygın olarak kullanılmaktadır. Bu çalışmada ise, katı ve gaz iletimi, diğer araştırmacılar gibi ampirik formüllerle incelenmiş, yüksek sıcaklık ya da düşük basınç gibi durumlarda baskın mekanizma olan ışınım ise sayılan iki yöntemle değil, bilgisayar programlanmasına daha uygun olan ve bir Monte Carlo (MC) yöntemi olan, Monte Carlo Işın İzleme (MCIİ) yöntemiyle incelenmiştir.Monte Carlo yöntemi bir stokastik çözüm yöntemi sınıfını ifade eder. Bu yöntem rasgele sayıların kullanımı ve olayların olasılık dağılımları üzerine kuruludur ve ışınım problemlerinde sıklıkla kullanılmaktadır. Öte yandan, lif esaslı yalıtım malzemelerinde ise şimdiye kadar sadece birkaç çalışmada kullanılmıştır. Yöntemin ışınım problemleri için faydası karmaşık geometrilerde kolaylıkla uygulanabilmesidir.MCIİ yönteminde ısı kaynağı ile ısı alıcı arasına yerleştirilmiş lif esaslı yalıtım malzemesine, ısı kaynağından yeri ve yönü kümülatif olasılık dağılımına göre rasgele sayılar ilişkisi ile belirlenmiş ışın demetleri gönderilir. İç yapısı modellenen yalıtım malzemesi içinde bu ışın demetleri izlenerek ısı alıcıya ulaşan ışın demetleri sayılır. Isı alıcıya ulaşan toplam ışın demeti sayısının, ısı kaynağından gönderilen toplam ışın demeti sayısına oranı yardımıyla ışınımla ısı geçişi miktarı elde edilir. Bu değer ampirik olarak hesaplanan iletim terimlerine eklenerek toplam ısı geçişi bulunur. Burada önemli olan nokta, malzeme iç yapısının ve ışın demetlerinin izolasyon malzemelerini oluşturan liflere çarptıktan sonraki hareketinin doğru modellenmesidir. Bunun için çalışmada, ışın demeti dalga boyuna ve fiber çaplarına bağlı yöntemler önerilmiştir.Çalışmada, literatürden seçilmiş bazı deneysel ve teorik çalışmalar incelenmiş ve MCIİ yöntemiyle alınan sonuçlar, ilgili çalışmalarla karşılaştırılmıştır. Çalışma sonuçları MCIİ yönteminin lif esaslı yalıtım malzemelerinin ısıl incelenmesinde etkili bir şekilde kullanılabileceğini göstermiştir.

Abstract:
Insulation materials are the materials used for decreasing the heat transfer rate between two mediums or surfaces. In buildings, furnaces, boilers, reactors or any other applications, right use of these materials is very important in terms of energy efficiency and protection of materials. Besides, in manned space vehicle application, which is one of an important application area, right usage is even vital.Fibrous insulation materials, comprise the majority of insulation materials. Rockwool and glasswool insulations are the most known examples of fibrous insulation materials. They decrease the heat transfer due to their low Equivalent Total Thermal Conductivity (K) property. This term can be defined as the thermal conductivity of the materials which allow more than one heat transfer mechanisms like radiation and conduction etc. or which compose of different mediums like gas and a solid or two different kind of solids etc., considered as a pure solid material. In fibrous insulation materials, the fibers and the squeezed gas between the fibers, allow solid conduction, gas conduction, radiation etc. heat transfer mechanisms. That makes necessary to use of the term Equivalent Total Thermal Conductivity.It is generally acknowledged that for insulation materials, Equivalent Total Thermal Conductivity value must be lower than 0.1 W/m.K. Thermal conductivity value of air is lower than any other solid material. Dry air which has a small quantity so as to disallow the natural convection provides best heat insulation. In fibrous insulation materials, the air between fibers provides that feature and those materials owe their low total thermal conductivity value to this air mass.In conventional techniques, heat transfer rate of insulation materials is found by using an experimental bulk method. In this method, the insulation material is put between two plates whose temperatures are known and a heat flux is created. By measuring this heat flux and thickness of the material, the Equivalent Total Thermal Conductivity can be calculated by Fourier Law.In this study, instead of experimental bulk model, a theoretical model is suggested to calculate the heat flux to use it in the Fourier Law formula.In literature, since fibrous insulation materials has an extensive application area, there is a lot of research to increase the understanding of heat transfer mechanisms in that kind of materials. Previous research indicates that radiation, solid conduction and gas conduction occur as heat transfer mechanisms in fibrous insulation materials. On the other hand, convection and natural convection are negligible in that kind of materials. In addition to that, since radiation heat transfer depends on the fourth power of the temperature, but conduction is not, at high temperatures (~above 500 K) radiation heat transfer becomes most dominant heat transfer mechanism in fibrous insulation materials.In general, researchers investigate solid and gas conduction mechanisms with empirical formulations. But for radiation heat transfer term, a method called Two Flux Method is used conventionally. Some researchers, however, use empirical formulations as well.In this study, instead of those heat flux and empirical techniques, for the analysis of radiation heat transfer, a Monte Carlo (MC) Method, called Monte Carlo Ray Tracing (MCRT) Method, is used because of its advantages in terms of computer programming. Although this method is commonly used for radiation problems, till now it has been used rarely for radiation heat transfer analysis of fibrous insulation materials.MC methods are a class of stochastic techniques. These methods are based on usage of random numbers and probability distributions of events. In the analysis of radiation heat transfer, these methods become very advantageous when the geometry of heat transfer surfaces is very complicated to reach a solution analytically.In this study, conduction mechanisms are investigated with empirical formulations as in literature. By these formulations the sum of gas conduction and solid conduction thermal conductivity values are calculated and added to equivalent radiation thermal conductivity value, which is calculated with Fourier Law after finding radiation heat flux with MCRT Method. This summation of thermal conductivity values gives the Total Equivalent Thermal Conductivity of insulation material, what this study aims.In MCRT method, in general, a bundle of rays is emitted from a randomly selected point with regard to its probability distribution from a heat source surface to the direction that is again chosen randomly according to its probability distribution and then it is traced until it is absorbed by an element in the domain. Because the study is done under the steady state conditions and considering the conservation of energy, if the ray bundle is absorbed by fiber then it is emitted again isotropically. If the heat source or the heat sink, however, absorbs the ray bundle then the process is terminated and then restarts with a new bundle emission from the heat source until adequate number of ray bundles are emitted. When the heat sink absorbs a bundle, it is registered. Then, by considering the total number of those, the heat flux from heat source to heat sink can be calculated.As stated before, in MCRT method, true determination of probability distribution of the event is vital and there are two important probability distributions to be known: probability distribution of the emission point and probability distribution of direction of rays. It is generally easy to find probability distribution of emission point of ray bundles because of constant temperature distribution assumption of heat sources. But when deciding the directional probability distribution of ray bundles, the number of parameters to be known is greater. First of all it is important to know whether the event is emission or scattering. For emission from surfaces, both from source or fibers, all surfaces assumed as Lambertian surface and the probability distribution is reached according to that. For scattering conditions, first we must determine the scattering type: Geometric Scattering (mirror like reflection), Mie scattering or Rayleigh Scattering. Scattering type is determined with the help of Size Parameter, which depends on radiation wavelength and particle size (fiber diameter).In this study it is shown that Rayleigh Scattering does not occur in insulation materials. On the other hand Geometric Scattering can be seen especially when the fiber diameters are bigger than 30 µm and the temperature of heat source is more than 1000 K. In general, fiber diameters change between 3-15 µm that means the mostly seen phenomena in fibrous insulation materials is Mie Scattering.In this study both Mie scattering and Geometric scattering cases are analyzed. Firstly, in Mie scattering conditions, scattering behavior of rays is determined with Legendre Polynomials. To do this three different models created with three different Legendre coefficients, which are formed with the help of Mie equations for different forward Mie scattering conditions, are taken from literature. Results revealed that Linear Anisotropic Scattering (LAS) Model, that is one of those mentioned three models, best describes the scattering phenomena for fibrous insulations.Secondly, for geometric scattering conditions, mirror like reflection assumption is used.For each Mie scattering and Geometric scattering condition, problems selected from literature are solved with MCRT method and results are compared with the results of earlier experimental and theoretical works.The most important result of this study is that it is proven that MC method can be effectively used for radiation heat transfer analysis of fibrous insulation materials. Besides, this study presents that increasing fiber absorptivity value of fibrous insulation materials causes an increase on radiation heat transfer under Geometric Scattering conditions. On the contrary, under Mie scattering conditions, radiation heat transfer rate decreases if fiber absorptivity value increases. So, roughly, to provide a better insulation, it is suggested that for fibrous insulation materials, low absorptivity fibers should be used when fiber diameter is bigger than 30 µm and high absorptivity fibers should be used for lower fiber diameters.In this study it is also shown that while the rate of radiation heat transfer is about 25% for 100 K temperature difference between heat source and heat sink, the rate increases to 75% when difference is 900 K. So, it is confirmed that radiation heat transfer is the dominant mechanism especially at high temperatures. Besides, it is shown that since the gas conduction terms are negligible in the vacuum conditions, the dominant heat transfer mechanism is radiation even at low temperature difference intervals.It is observed that, for geometric scattering cases, fiber diameter of the insulation material has no effect on radiation heat transfer, on the other hand, it is known that under Mie scattering cases, fiber diameter of the insulation material affects radiation heat transfer rate. Because fiber diameter size is one of a parameter of Mie equations and Legendre Polynomial solution that is used for this study is formed with Mie Equations.Another hypothesis that is presented with this study is that the Hanyey-Greenstein equation (an equation that can be used for modeling scattering behavior in Mie scattering conditions but mostly used for radiation in tissues in literature) with the HG coefficient of 0.35 can be used for fibrous insulation materials as well. The benefit of using HG equation is to decrease computer process time to 1/3 of the processing time spent for the LAS model.As future works, this research can be validated experimentally for different insulation materials and some studies can be done for extending the usage area of this method, like taking into account the wavelength distribution of scattered rays for non-grey fiber materials. In addition to that, there can be done some studies on extinction coefficient value, which is a very important parameter in the solution of Mie Scattering case radiation heat transfer problem. If a trustable empirical formulation can be reached that depends on fiber diameter and insulation material?s density, then application of MCRT method become easier.?