Sonlu eleman yöntemiyle ısı ışınımı problemlerinin çözümü
Solution of radiation heat transfer problems with finite element method
- Tez No: 66487
- Danışmanlar: DOÇ. DR. CEM PARMAKSIZOĞLU
- Tez Türü: Yüksek Lisans
- Konular: Enerji, Energy
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1997
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Makine Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Enerji Bilim Dalı
- Sayfa Sayısı: 49
Özet
ÖZET Bütün cisimler sıcaklıklarından dolayı elektromagnetik dalgalar şeklinde ışınım yayarlar. Yayılan ışınım maddesel ortam olmaksızın her yönde yayılır. Işınım enerjinin bir kısmı diğer bir cisme geldiğinde cisim tarafından yutulur. Net ısı akısı yüksek sıcaklıktaki cisimden düşük sıcaklıktaki cisme doğru olur. Enerjinin bu şekilde geçişi ısıl ışınım olarak adlandırılır. Bu çalışmada ısı ışınımı problemlerini çözmek için sonlu elemanlarla çözüm yapan ANSYS yazılım programı kullanılmıştır. Ele alınan problemlerin sonlu eleman modeli oluşturulmuş, gerekli olan sınır şartlan uygulanarak ısı akısı ve sıcaklık dağılımı hesaplanmıştır. İlk örnekte sıcaklıkları bilinen iki nokta arasında geçen ısı akısı hesaplanmıştır. Son iki örnek gerek yüzeyler arasında ve yüzeylerden çevreye ışınımla ısı geçişinin olduğu gerekse de ısı akısının olduğu farklı geometrilerde genel ısı ışınımı problemleri için sıcaklık değişimleri hesaplanmıştır. vıı
Özet (Çeviri)
SUMMARY Thermal radiation is one of basic mechanisms for the transfer of energy between two bodies or regions at different temperatures, the energy being conveyed by electromagnetic waves. Therefore, radiation does not require an intervening medium for the transfer of energy, as is needed for conduction and convection. A portion of this energy flux when impinging other bodies is absorbed. As a result, net energy flow occurs from a body of bigger temperature to a body having lower temperature. This mode of energy transfer is termed heatradiation[13,14]. Espanding the Stefan- Boltzmann Law to two- surface radiation equation, the heat transfer rate between two surfaces I and J is : Ql = a.el.cl}.Fl.(0l4-0s4) (1) This equation is not linear and cannot be solved using the linear equation solver. Therefore the equation is expanded as: Q!=ö:£1.ç),j.Fi.(Öi2+Öj2).(Öi+Öj).(ö,-Öj) or (2) 01=1^.(0,-0,) (3) K1 = asl.n).ct.04 (5) S,, = Kronecker delta JI 0, when J*I This equation can be used to construct a single row in the following matrix equation: such that: [C]{Q} = [D]{04} (6) each row J in \C] = cp“ - 1 J Ul *I J ^,1=1,2, N (7) Fi each row J in [D] = (ân-¥n)a,I=1,2,....N (8) solving for {q} : {qMk*]^4} (9) [K* ] = [C ?>] [D] (10) IXEquation (9) is analogous to equation (1) and can be set up for sandard matrix equation solution by the process similar to the steps shown in equation (l)tru (3). {qJ-PC'Kt} (11) [K ] now includes T terms and is calculated iteratively. To be able to include radiationeffects in elements other than LINK31, The ANSYS Program uses MATRIX50 (the substructure elements) to bring in the radiation matrix. MATRIX50 has an option that instructs yhe solution phase to calculate [K1]. The AUX12 utility is used to create the substructure matrix. AUX12 calculate the effective conductivity matrix [Kte]. The view factor, Fu, is defined as the fraction of total radiant energy that leaves surface I which arrives directly on surface J. It can be expressedby the following equation: 1,, cos/?/. cos/?,,.”. __,_..,_. ^J FiFj TC.t Two methods are available to calculate the view factors: the hidden procedure and the non - hidden procedure. The non- hidden procedure calculates a view factor for every surface to every other surface whether the view is blocked by an element or not, the following equation is used and the integration is performed adaptively. 0u=^SI v-2 Fip-Fjq (13) F! P=lq=l n.x The hidden procedure is a simplified method which uses below equation and assumes that all the variables are costant, so that the equation becomes[9]: 7ZT~ Ç'U = -J2-COSy!?I.COSyffJ (14)A space node may be defined to absorb all energy not radiated to other elements. If the model is not closed system then the user must define a space node with its appropriate boundary conditions. The ANSYS program provides three methods for radiation analysis. A brief description of two method is given below[8,10]: 1. LINK31, the radiation link element, is useful for simple problems involving radiation between two points or several pairs of points. LINK3 1 calculates heat flow caused by radiation between two points. The element requires you to specify in the form of real costant:. An effective radiation surface area. Form factor. Emissivity. The Stefan- Bolzmann constant. 2. The AUX12 radiation matrix generator is meant for more generalized radiation problems involving two or more surfaces. The method involves generating a matrix of form factors (view factors ) between radiating surfaces and using the matrix as a superelement in the thermal analysis. You also can include hidden or non- hidden surfaces, as well as a space node that can absorb radiation energy. The AUX12 analysis method consist of three steps[8]:. Define the radiating surfaces. To define the radiating surfaces, you create a superimposed mesh of LINK32 alements in 2-D (2- Dimensional) and SHELL57 elements in 3-D (3- Dimensional ) models. The orientation of the superimposed elements is important: AUX12 assumes that the viewing direction (i.e., the direction of radiation is along +Ze for SHELL57 lements and along +Ye for LINK32 elements. Therefore, you must mesh the superimposed elements in such a way that the radiation occurs from (or to) the proper face. The element orientation is controlled by the order in which the elements nodes are defined (based on the rigt- hand rule ), as shown below: XIThe findings were compared with the analitical solution for heat flow rate and temperature distribution. The error was less than 0.4 %. The comparisons of temperature distributions and heat fluxes have all shown good agreement. XlllThe findings were compared with the analitical solution for heat flow rate and temperature distribution. The error was less than 0.4 %. The comparisons of temperature distributions and heat fluxes have all shown good agreement. Xlll
Benzer Tezler
- Buğday muhafazasında silolardaki sıcaklık dağılımının modellenmesi
Modeling of temperature distribution stored wheat in bins
ERSİN VELİ VOLKAN
Doktora
Türkçe
2000
ZiraatAnkara ÜniversitesiTarım Makineleri Ana Bilim Dalı
PROF. DR. BAHA GALİP TUNALIGİL
- Çift kabuklu cephelerin ısı kayıplarının hesaplanmasında kullanılabilecek yeni bir yaklaşım
A new approach for double skin envelope's heat loss calculation
KEMAL FERİT ÇETİNTAŞ
Yüksek Lisans
Türkçe
2004
Mimarlıkİstanbul Teknik ÜniversitesiMimarlık Ana Bilim Dalı
PROF. DR. ZERRİN YILMAZ
- Burgers tipi denklemlerin trigonometrik B-spline kollokasyon sonlu eleman yöntemiyle nümerik çözümleri
Numerical solutions of burgers type equations using trigonometric B-spline collocation finite element method
İMRAN DİKEN
- Finite element modelling and measurement of stress evoluation in quenching processes
Su verme işlemlerinde oluşan gerilmelerin sonlu eleman yöntemiyle modellenmesi ve ölçülmesi
CEMİL HAKAN GÜR
Doktora
İngilizce
1995
Metalurji MühendisliğiOrta Doğu Teknik ÜniversitesiPROF.DR. A. ERMAN TEKKAYA
PROF.DR. TAYFUR ÖZTÜRK
PROF.DR. ŞAKİR BOR
- Sualtı araçlarından yayılan titreşim kaynaklı gürültünün sonlu eleman-sınır eleman metoduyla analizi
Vibro-acoustic analysis of underwater structures using finite and boundary element methods
BURAK ÜSTÜNDAĞ
Doktora
Türkçe
2024
Gemi Mühendisliğiİstanbul Teknik ÜniversitesiGemi İnşaatı ve Gemi Makineleri Mühendisliği Ana Bilim Dalı
PROF. DR. AHMET ERGİN
PROF. DR. BAHADIR UĞURLU