Yanma odalarının modellenmesi
Modelling of combustion chambers
- Tez No: 21719
- Danışmanlar: PROF. DR. OSMAN F. GENCELİ
- Tez Türü: Doktora
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Matematiksel modelleme, Yanma modelleri, Yanma odası, Mathematical modelling, Combustion models, Combustion chamber
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Sürekli rejimde iki boyutlu reaktif türbülanslı akışlara ait matematik bir yanma odası modeli geliştirilmiştir. Değişken hız ve sıcaklık alanlarında aynı anda gerçekleşen bir dizi olayın bir sonucu olarak ortaya çıkan yanma işleminin karmaşık yapısı üç alt modelin toplamı şeklinde düşünülmüştür. Alt modelleri sırasıyla hidrodinamik akış, yanma ve ışınım modelleri oluşturmaktadır. Hidrodinamik akış modeli özellikle türbülansın etkilediği konvektif ve difüzif akışkan hareketlerini, yanma modeli kimyasal reaksiyonları ve ışınım modeli ışınımla olan ısı geçişini kapsamaktadır. Hidrodinamik akış için k-e türbülans modeli kullanılmıştır. Bu alt modelde momentum denklemleri türbülansın kinetik enerjisi (k) ve disipasyon hızı (e) ile birlikte çözülmektedir. Yanma modeli ise gaz fazında gelişen reaksiyonların hem Gibbs fonksiyonunun minimizasyonu prensibine dayanan denge kabulü, hem de reaksiyon hızlarının dikkate alındığı kinetik yaklaşım için ayrıntılı çözüm verebilmektedir. Sunulan çalışmada metan gazının yanması ile ilgili 19 bileşen ve 34 adet ileri-geri reaksiyon çiftini içeren bir reaksiyon mekanizması kullanılmıştır. Yanma odasında ışınımla olan ısı geçişi 4-Akı (Flux) modeliyle karakterize edilmiştir. Bu yöntemin esası ışınım akısının radyal ve eksenel doğrultularda gerçekleştiği kabulüne dayanmaktadır. Alt modeller benzer kısmi diferansiyel denklemler ile ifade edilebilmektedir. Bu nedenle sayısal çözümde ortak bir algoritma kullanılmıştır. Alt modellerin performansları gerek sunulan çalışma kapsamında gerçekleştirilen bir dizi deneye ait bulgularla, gerekse literatürden alınan verilerle karşılaştırılarak ayrı ayrı irdelenmiştir. Yanma odası modelinin çözüm stratejisini alt modeller arasında gerçekleştirilen bir“süper-iterasyon”işlemi oluşturmaktadır. Yanma odası modeli reaktör içindeki akım fonksiyonu, hız, sıcaklık ve aralarında bazı radikallerin de bulunduğu yanma ürünlerinin dağılımlarını verebilmektedir. Modelin sonuçları IFRF* m M-2 deney serisinden olan 29 no. l'u difüzyon alevine ait bulgularla ve sunulan çalışma kapsamında gerçekleştirilen deneysel çalışmaya ait verilerle karşılaştırılmıştır. Bu amaçla tasarlanan küçük ölçekli, ön karışımlı bir reaktörde sıcaklık ve birtakım kararlı yanma ürünlerin derişiklikleri ölçülmüştür. Yapılan karşılaştırmalar sonucu geliştirilen yanma odası modelinin gerçekçi sonuçlar verdiği belirlenmiştir. xiv
Özet (Çeviri)
MODELLING OF COMBUSTION CHAMBERS SUMMARY The object of this PhD thesis is to develop an efficient mathematical model of turbulent, chemically reacting gas phase flows. The solution of the Navier-Stokes equations incorporating physical modelling for turbulence, combustion and thermal radiation has been obtained by combining several computer codes that had previously been developed. Numerical results, for quantities such as temperature, stream function and species mole number distributions within the flow field have been obtained. The performance of the model has been tested using the experimental data from the M-2 trials of the IFRF (International Flame Research Foundation) and carrying out an experimental study within the framework of the presented thesis. Computer simulation and prediction of turbulent, chemically reacting flows is known as an extremely difficult problem due to the complex interactions of many reacting chemical species with continuously changing temperature and velocity fields. However, the problem has attracted increasing interest in recent years. The requirements for greater combustion efficiency and decreased pollutant emissions from a variety of devices, from power plants to jet engines, and the introduction of new devices have led to the need for improved methods of prediction and calculation for turbulent flows involving chemical reactions [7]. In general there exist two types of approach to reacting, turbulent flows. One is the chemical equilibrium approach with infinite reaction rate assumption. The other is the well-stirred reactor model, which considers finite-rate reactions with infinite-rate mixing. The model presented employs both the equilibrium and the non-equilibrium (kinetic) chemistry approach. For the solution of chemical and of energy conservation equations the computer code CREK [16] has been used. The hydrodynamic solution of the flow field has been obtained by the computer code TEACH which uses the k-e method for turbulence modelling [9,28]. Radiant energy transfer has been simulated by the 4-Flux method [3,4]. xvTHE PREDICTION PROCEDURE The Governing Equations The governing partial differential equations for the conservation of mass, momentum, energy and chemical species in the gaseous phase under steady state conditions can be rearranged into a general form which can be written as: a a a 0 (p u 0 ) - ( r ) + s (D ax J ax ax j j j where p is density, u is the velocity component, 0 is the dependent variable, T is the“effective”diffusion coefficient for that 0 quantity and S is the source term. The dependent variable 0 may stand for a variety of different quantities such as the mass fraction of chemical species, the enthalpy, a velocity component, the kinetic energy of turbulence, or dissipation. The transport equations in the form of (1) are reduced to their finite-difference form by integrating over the computational cells into which the domain is divided. The resulting algebraic equations can be written in the following form [9]: £ A 0 = E K 0 + sCT (2)“dp ”d d 0 d * d where the subscript d (“direction”) refers to the adjacent nodes N,S,E, W. A 's are the convection and diffusion coefficients. The d exact form of the A ' s depends on the nature of the governing d equations (elliptic, parabolic or hyperbolic) and on the form of finite-difference approximation used (upwind, central, etc...). The Turbulent Model The computer code TEACH which uses the usual two-equation model of turbulence has been employed in this study. Hydrodynamic equations have been solved for the turbulence kinetic energy k and its dissipation rate e. In order to validate the model results the performance of the k-e model has been tested by using experimental data for different reactor configurations [14,34]. The results show fairly good agreement with the data both taken from literature and obtained within the framework of the presented study. A comparison between xvithe k-e model and a zero-equation model has also been made and the advantage of the two-equation (k-e) model has been analyzed. The Combustion Model Combustion model enables the calculation of chemically complex equilibrium or non-equilibrium (kinetic) stationary states. In such cases where the chemical kinetic rates are known to be so fast compared to the turbulent mixing rates, the chemical equilibrium approach may be used. The Gibbs function minimization method has been used for the equilibrium solution. For a mixture of reacting gases at prescribed temperature and pressure, chemical equilibrium is obtained when the Gibbs function of the mixture is a minimum. For a mixture of ideal gases, the partial molar Gibbs function of species-k is given by, *k - \“ Tsk - K ~ Tsk + RT 1o*[^t] + RT lQs[-iH (3) u m J L o J where h is enthalpy (J/kmole), T is temperature (T), s is entropy (J/kmole K), R is universal gas constant (8314.3 J/kmole K), <r is mole number of species-k in mixture (kmole/kg), <r is mixture mole m number (kmole/kg), P is pressure (N/m ) and subscript ”o“ refers to the standart conditions. The mass-specific Gibbs function for the mixture which is composed of ns number of species is given by, ns G= I °k*k (4> k=l and the requirement for chemical equilibrium is, ”rîC, dG = V do-, = 0, (d2G) > 0 (5) A1 8V For the kinetic solution, the chemical kinetic source term for conservation of chemical species-i is, JJ \“ ”I <«ii“ «ij> <Rj ”R-j> «» where R. and R, are the rates of forward and reverse reactions j, ^ 3 respectively (kmole/m s). a.' and a.“ are the stoichiometric xviicoefficients for species-i. R. may be expressed in a modified Arrhenius form: B N a ns a R = X2 10 J T J exp (-T. /T) (p<r_) J n (pO (7) I, = X, 10 J T J exp (-T /T) {pc ) J fl {per ) J J J T ]-_< K where X, is contact index for reaction j, which is assumed to contain the effects of turbulence. It is not as yet possible to compute the contact indicies exactly, therefore by equating the contact indicies to unity, turbulent micromixing was taken to proceed at an infinite-rate. B and N are exponent factors. T is j J j the activation temperature (K), p is the mixture ideal -gas mass 3 - density (kg/m ). a is the third-body stoichiometric coefficient in reaction j. Mole number of species-i at a point P in the flow domain ar. p depends more strongly on the mole numbers of all species and the temperature at point P than on the values of <r,, at adjacent nodes. Therefore, energy and n number of conservation of chemical species equations should be solved simultaneously. Due to the non-linearities, the use of derivative information will be appropriate to achieve rapid convergence. As a result of these factors, the form of conservation of species, that is given by equation (1) has been written in CREK code as follows [IB]: £ Ad °”i d ?VRp-[ ' rA' ]}“ S. l-1'”<3> u d d Equations (8) are ns in number, where ns is the number of chemical species being considered. The thermal energy equation is also in the form of equation (8). Rewriting equations (8) in the functional form, E Ad °*i d fi= ŞA*Re-[ ' ' \}-\ ? 1 = I'ns (9) d d a set of Newton-Raphson correction equations may be obtained: xviiins Öf (o) (o) (o) E [ - ] A<r, = - f, i = l.ns (10) k=l do-, k k i where (o*., i = l.ns and T ) are the initial estimates of mole number of chemical species and temperature. Equations (10) may be solved iteratively, together with a similar correction equation for the temperature from equation (8), until the corrections (Ao-,, k = l,ns and AT) vanish. For the combustion of methane a reaction mechanism consisting of 19 species and 34 pairs of reactions (forward and reverse rates both considered) was utilized [41]. The performance of the combustion model has been tested by using relevant existing experimental data [46,47,48,49]. Mass fractions of major gas species (N2,02,CH4,C02,H20, CO and H2) and temperature as functions of local fuel -equivalence ratios have been analyzed for methane-air diffusion flames. Satisfactory agreement between the experimental data and both the equilibrium and kinetic predictions has been obtained for fuel-lean conditions. On the other hand, equilibrium predictions have been seen departed from kinetic and experimental values for stoichiometric and fuel-rich conditions whereas, a good agreement between the last two has been observed. The Radiation Model In this study a 4-flux model has been used to simulate radiative heat transfer in the model combustion chamber [3]. The basis of the method is to replace the continuous variation of radiant intensity with direction by mean values representing various angle ranges [40]. 4-flux model considers the radiation flux in both radial and axial directions. The solid angle at a point P is divided into four angular divisions as to satisfy the radiant intensity balance in considered directions. A comparison between the 4-flux model, 2-flux model and zone method has been given in a model reactor. It has been seen that the 4-flux model used in the presented study yields reasonable results. The Solution Strategy The structure of the model has been based on a“super- i t erat i on”process between hydrodynamic field solution and combustion model. The overall strategy applied to the combustion chamber model can be outlined in four steps: xix1. The solution of hydrodynamic equations for conservation of mass and momentum is first obtained by means of hydrodynamic model. 2. With the convective-diffusive values obtained in step (1), repeated visits are made to each node by means of combustion and radiation models to obtain the temperature and species mole number distributions. 3- The solution of the hydrodynamic field is repeated with the updated nodal values of density obtained in step (2). 4-“Super-iteration”process between the 1st and 3rd steps was carried out until no changes were noted in the density and velocity fields and the energy balance is satisfied. THE PERFORMANCE OF THE MODEL Description of the model reactor of IFRF In this study, it was intended to use the experimental data for Flame 29 of the IFRF M-2 trials in order to test the predictions of the presented model [10]. Flame 29 which has 3 MW thermal input is a non-swirling natural gas flame with axial fuel and coaxial air inlet. The combustion chamber is cylindrical and axially symmetric. The length and the radius of the reactor are given as L = 6250 mm, r = 1130 mm, respectively. Description of the experimental model reactor An experimental study has also been performed in order to validate the model results within the scope of the presented study. Experimental model which has 2 kW thermal input is a small scale premixed natural gas reactor. As experimental set up a combustion chamber with 150 x 150 mm in cross section and 195 mm in length was used. The flammable natural gas-air mixture ascends uniformly distributed in y direction and a secondary air jet is sent to the chamber in x direction from a hole at the foremost face. Burned gases leave the chamber through the rear face. Concentrations of some of the combustion products (C0,C02,02) and temperatures at various points have been measured by Kromschroder Type RGA 33 Flue Gas Analyzer. Comparison of prediction with reference measurements and experiments Results of the model for quantities such as velocity, stream function, equivalance ratio and species mole number distributions within the flow field have been compared with the experimental data of IFRF and the experimental data of the presented study. The agreement between the predictions and the experimental data is seen to be satisfactory. xxThe model presented gives also the distributions in the combustion chamber for the 19 considered species. Besides the stable species, it should be possible to observe the formation, variation and mutual interaction of a number of ions and radicals. A practical and reliable mathematical model for turbulent reacting flows whose performance is tested by comparison with experimental data has been developed. Application of such a complete model to some combustion problems which are encountered in practice will enhance the understanding of the flow, mixing, heat transfer and pollutant formation in furnaces and combustion chambers. xxi
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