Laminer metan hava difüzyon alevinin modellenmesi

Abstract

Metan yanmasında seçilen reaksiyon mekanizma sayısının olabildiğince çok olması gerekir. Ancak bilgisayarla hesaplama zamanını oldukça arttıran bu saymın, etkili reaksiyon mekanizma sayısının azaltılabilmesi için önemlidir. Birinci bölümde kısaca temel reaksiyon tiplerinden bahsedildikten sonra metan hava difüzyon alevinde metan yanması için akış diyagramı verilmiştir. Ayrıca kimyasal kinetik modellemelerde farklı araştırmacıların kullandıkları mekanizmalardan bahsedilmiştir. İkinci bölümde metan hava yanmasının sayısal çözümleri incelenerek, metanın yanması sırasında gerçekleşen önemi yüksek olan reaksiyon adımları incelenmiştir. Sonuçlar üzerinde etkisi az olan mekanizmalar ihmal edilerek, metan yanmasını karakterize eden reaksiyonların en az sayısı bulunmaya çalışılmıştır. Kararlı hal ve kısmi denge yaklaşımları yapılarak elde edilen bağıntılar kullanılarak reaksiyon hızları bulunmuştur. Üçüncü bölümde difüzyon alevine dört adımlı mekanizmanın uygulanması için etkili denklemler tanımlanmıştır. Süreklilik, Momentum, Bileşenler ve Enerjinin korunumu denklemleri yazılarak, bu denklemlerin hangi yöntemlerle çözüleceğine dair bilgi verilmiştir. Dördüncü bölümde ise korunum denklemlerinin çözülmesi neticesinde, sıcaklığa ve hız gradyenine bağlı olarak bileşenlerin mol oranlan değişimi, kimyasal üretim hızlan, üretilen enerji miktan ile difüzyon hız katsayılarının değişimi irdelenmiştir.

Combustion can occur in either a flame or nonflame mode, and flames in turn are categorized as being either premixed flaines or nonpremixed ( diffasion ) flames. The two classes of flaines, premixed and nonpremixed are related to the state of mixedness of the reactants, as suggested by their names, In a premixed flame, the fuel and the oxidizer are mixed at the moleculer level prior to the occurrence of any significant chemical reaction. Contrarily, in a diffusion flame, the reactant are initially separaten, and reaction occurs only at the interface between the fuel and oxidazor where mixing and reaction both take place. The term "Diffusion " applies strictly to the molecular diffusion of chemical species, fuel molecules diffuse toward the flame from one direction while oxidazor molecules diffuse toward the flame from the opposite direction. The elementary reactions are classified as Bimolecülar, Termolecular, Recombinations and Chain reactions. The collection of elementary reactions necessary to describe on overall reaction is called a reaction mechanism. Reaction mechanism may involve only a few steps (i.e., elementary reactions ) or as many as several hundred. A field of active research involves selecting the minumum number of elmentary steps necessary to describe a particular global reaction. By examining numerical solutions of methane flames, it is possible to see major steps by which the methane is oxidized. The result of this analysis may be summarized as follows: CH4+H^CH3+H2 CH4 + OH -+CH3 +H20 CH3+0-*CH20+H CH20 + H^CH0 + H2 CH20 + OH -+CHO + H20 CHO + H-+CO+H2 CHO + M^CO + H + M CHO +02 -> CO + H02 CO + OH ^ C02 + H H + 02i? OH + O 0 + H2 t» OH + H 0H + H2^H20 + H OH + OH^H20 + 0 H + 02+M^H02 + M H + OH + M-»H20 + M H + H02^OH + OH H + H02 - H2 + 02 OH + H02-»H20 + 02 The general balance equation for a reactive species may be written in terms of ; Yi =Yi/Mias L(Yi) = Wi=£ (Vi,k" -vi;k>k where the operator L is defined as L(Yi)=p5yi/8t + pvj5yi/5xj + 8/8^(^/141) The " steady state " assumption is valid if the reactions by which an intermediate species is formed are slower than those by which it is consumed. Eliminating the reaction R3, R4, R7, Rll, R12, and R17, we find the following combinations, where the terms in square brackets can be neglected; L(tH) + [ L(f oh) + 2L(t0) -L(?ch3) + L(tcHo) - L(?H2o) = -2wr2w2 -2w5 -2w8 + 2w10 -2wM -2w15 +2w16 L(Yh2) + [ -L(Y0H) -2L(t0) + 3L(Ych3) +L(f ch2o) +L(tH02)]= 4w,+ 4w2+w6+w8+w9 -3w10+w14+Wi5-3w16 L(Y02) +[L(YH02)] = -Wio - Wi6 L(Yh2o) + |L(Yoh)+L(Yo)-L(Yh3)] = -wi -w2 -w9 +2wio +2wi6 L(Yco) +[L(Ych3)+L(Ych2)+L(Ycho)] = Wi + w2 - w9 L(Yco2) = w9 L(YcH4) = -Wi-W2 It is interesting to note that only 9 of the original 18 elementary reactions remain in this scheme, the reactions R5, R13 and R18 having the same effect as the corresponding parallel reactions R14, R12, R17, which eliminated. The stoichometric coefficient lead to the following set of global reactions: CH4 + H20 +2H -> CO + 4H2 CO + H2O^C02+H2 2H + M->H2 + M 3H2 + 02 s? 2H20 + 2H The rates of the global reactions are given in terms of the rates of the elemantary reactions by the following expressions: Wi=Wi +w2 wn=w9 Win = W6 + W8 + W14 + W15 Wiv = Wio + Wi6 XI The incompressible, inviscid flow in the vicinity of a Stagnation point (x=0, y=0 ) on a porous cylinder is described by, ue =ax, ve = -ay, where x and y are the coordinates parallel and perpendicular to the burner surface respectively, ue and ve are the corresponding velocity components ( the index e indicates the edge of the boundary layer ) and a is the velocity gradient. From Bernoulli's equation the local streamwise pressure gradient can be written as 8p/8x =-peuea The flowfield described above is impressed upon the viscous chemically reacting boundery layer near the stagnation point; u - > ue as y - * oo and the pressure gradient in the boundary layer is given by Bernoulli's equation. The equations describing the boundary layer flow are given below. Continuity : Spu / 8x + 8pv / 8y = 0 Momentum : pu ( 8u / 8x ) + pv( 8u / 8y ) - pe ue a = 8 / Sy ( \i&u I Sy ) Species : pu ( 8Yi / 8x ) + pv ( dY{ 1 8y ) = -8 / Sy ( pY; Viy ) + mi Mi Energy : pucp ( 8T / 8x ) +pvcp ( 8T / 8y ) = 8 / 8y ( X8T / 8y ) - 1 mi Mihi -Epcpi Yi Viy8T / 8y It is convenient to introduce dimensionless velocities f ' and V and the density- weighted coordinate n: f = u/ue V =. pv I PeHe<* TJ = a y- AA jpdy 'e 0 Replacing u and v by f and V, and making the coordinate transformation (x,y) to (x,n), we obtain the following set of ordinary differential equations for the flow in the vicinity of the stagnation-point streamline (x=0) dV Contmuity : f + = 0 drj o.. ır&ı P2 r, d2Xt mMi n Speıcıes : V - '- - - -Dt =*-,-L = 0 drj pejue drf pa x.dT X d2T 1 A _., p2 A ^dX;dT Energy : V - = V mJA^ + - V c D; - l- - *1 PeVec dn app tf cpeneM£TPl dn dn xu Momentum : / + V#- - ^ = -(C^-) drj pe drj drj where C=pu/ peu* For the present calculations we approximate the multi-component diffusion velocities as; Vp V, +Vc where Vi is computed from Curtiss-Hirschfelder approximation; 1 dX, Vt=-D, X, dy Vc is a correction term and neglected. Diffusion coefficients for mixture and binary diffusion coefficents; -ör l-Y, T,Xj*j 10-7rl,75 Dj,= MjM{ 1,013 p&r+Tvr} Mixture conductivities are computed using the simple ampirical mixture formula; 2 IM ?i+- i=\ '=1 Mixture viscocities are computed by Wilke's formula;,-t-^- ;=1 xm f 1 + M,.,-1/2 V M i J 1 + 1/4 Y After the solving conservation equations by using methods of Runge-Kutta, find the mole fraction of species depend on temperature for CHU, CH3, CO, H2, O2 and H2O species obtained data about mole fraction, diffusion coefficient and produced energy, investigated effects on results changing the initial values for species except CH4 and O2 in rate gradient and initial cases.