Düşey Bir Gözenekli Kanalda Yanmanın Sayısal İncelenmesi

Abstract

Gözenekli yakıcıların serbest alevli yakıcılara göre yüksek yanma verimi ve yüksek güç yoğunluğu sağlama ile daha düşük seviyede gaz salım oranına sahip olmak gibi üstün özellikleri vardır. Bu avantajları bulundurmasından dolayı hem sayısal hem deneysel birçok çalışma gözenekli yakıcıların gaz salımlarını, çalışma limitlerini ve ısıl verimlerini incelemek için gerçekleştirilmiştir. Bu çalışmanın amacı düşey iki boyutlu, eşdeğer gözenek çapları farklı üç bölgeden olu¸san, gözenekli bir kanalda yanmanın sayısal olarak ısıl dengesiz model ile incelenmesidir. Gözenekli yakıcı için yapılan çalışmalar ikiye ayrılmıştır. Bunların birincisi, gözenekli kanalın ısıl dengesiz enerji denklemleri ile incelenmesidir. Kanal ısıl dengesiz olarak kabul edilmiştir, çünkü yanma esnasında katı ve gaz fazları arasında yüksek sıcaklık farkı oluşacaktır. Gözenekli kanal içerisinde tüm hız, sıcaklık ve tür alanları SIMPLE algoritması tabanlı geliştirilen bilgisayar programı ile hesaplanmaktadır. Çalışmadaki ikinci bölüm ise gaz fazı içerisinde yanmanın Laminar Flamelet Yaklaşımı ve GRI 3:0 mekanizması (53 Tür, 325 Reaksiyon) ile modellendiği kısımdır. Kanal içerisinde katı fazı için silikon karbid (SiC) kullanmıştır. Problemimizde, düşey kanal farklı gözenek çaplarına sahip art arda sıralanmış üç bölümden olu¸surken, katı fazın ve gaz fazının öz ısı, ısıl iletkenlik ve viskozite gibi özellikleri sıcaklığa ba˘glı olarak kullanılmıştır. Çalışmamızda ilk adım olarak hesaplamalara başlamadan önce, laminar flamelet denklemlerinin adyabatik olmayan koşullarda hep pozitif hem negatif çeşitli entalpi noksanlıklarında çözülmesiyle modelimiz için gerekli flamelet çizelgeleri oluşturulmuştur. Bu çizelgelerde gaz sıcaklığı ve türlerin gaz karışımı içerisindeki kesirlerinin yanı sıra gaz karışımının yoğunluk ve öz ısı gibi bilgileri de yer almaktadır. Laminar flamelet yaklaşımında bahsedilen tüm bu bilgiler, karışım kesri ve gaz enerjisi denklemleri çözülerek, karışım kesri, skaler dağılım oranı ve entalpi noksanlığı değişkenlerinin hesaplanmasıyla ön işlemde hazırladığımız çizelgelerde üç boyutlu ara bulma yapılarak bulunur. Gözenekli yakıcıların gaz emisyonları ile ilgili avantajlarından sıkça söz edilmektedir, bu yüzden çalışmamızda kanal içerisinde NO ve CO salımlarının değişimine yer verilmiştir. Gözenekli yakıcıların bir diğer avantajı kanal içerisinde katı matris yardımı ile açığa çıkan tepkime enerjinin bir bölümünün yanmamış gazlara kazandırılması ile gaz karışımının sıcaklığının tepkime öncesi bir miktar yükselmesi ve bu sayede yanma limitlerinin arttırılmasıdır. Bu konu ile ilgili gözenekli yakıcıda farklı hava fazlalığı oranları için çözümler karşılaştırılmıştır. Sonuç olarak yakıcı kanal içerisinde hız, sıcaklık ve tür kesirlerinin dağılımları incelenmiştir. Elde edilen sonuçlar kararlı hal için verilmiş ve bu sonuçların çözüm ağından bağımsız olduğu gösterilmiştir. Gözenekli yakıcılarda Laminar flamelet yaklaşımı çok yeni bir konudur. Bu yaklaşım ile bulduğumuz sonuçlar literatürde farklı hem deneysel hem sayısal çalışmalar ile karşılaştırılmıştır. Bu çalışma ile bu yaklaşımın gözenekli yakıcılar için uygulanabileceği ve son derece verimli bir yanmanın elde edilebileceği gösterilmiştir.

Porous burners has superior technological features against free flame burners such as high combustion efficiency, providing high power density and low emission of pollutant gases. Due to these advantages, it is a popular topic among researchers nowadays. Many numerical and experimental studies are conducted to investigate pollutant emissions, operating limits and thermal efficiency of porous burners. Purpose of this study is to investigate combustion inside a porous channel that has three regions with different equivalent pore diameters in two dimension. Equivalent pore diameter should be chosen carefully because stability of combustion in porous media depends on the modified Peclet number. Stable combustion occurs only when modified Peclet number is over 65. Porous burners provides feedback of heat from burnt gases to unburned gases. First region of the channel is designed to have modified peclet number less than 65 so that flame cannot propagate here. Second regions is where the combustion occurs. Heat released from burnt gases transferred to solid matrix and by conduction, heat is diffusing to first region to increase unburned gas temperature. Increasing the temperature of unburnt gases allows ultra-lean combustion regimes. This is how feedback mechanism works in porous burners. In this study, Numerical analysis for porous burner are divided by two parts. First part is investigating the porous channel with non-equilibrium energy equations. Since temperature difference will be recognizably high during combustion, we can't assume that gas and solid temperatures will be the same. For this reason, two different energy equation is solved for gas and solid phase. While high temperature resistant ceramic foam inside the channel represents the porous burner, methane and air is used as fuel and oxidizer. Thermophysical properties of both solid and gas are not taken constant, they are all dependent on temperature. Heat capacity and density of gas mixture is found from flamelet tables and thermal conductivity and viscosity of gas mixture is calculated using Lennard-Jones parameters while heat capacity and thermal conductivity of solid is taken from an experimental study. Second part is to model combustion in porous media with flamelet approach using GRI 3:0 mechanism (53 species, 325 reactions). Before calculations, laminar flamelet tables are constructed by solving flamelet equations for non-adiabatic conditions as pre-process. In flamelet approach, gas temperature is determined by three-dimensional interpolation with mixture fraction, scalar dissipation rate and enthalpy defect values. This approach does not includes combustion chemistry to calculations. For complex combustion mechanisms, this is an great advantage for computation time. Governing equations are discretized with finite volume method and the computation is executed by SIMPLE Algorithm based in-house code written in FORTRAN language. Computational domain is divided into small control volumes, all with the same size. This is the basic outline of the code; After giving initial condition to all variables in the computation zone, first momentum and continuity equations for porous media are solved to obtain velocity field in the channel. Then Mixture fraction equation is solved to find gas temperature distrubiton and to calculate scalar dissipation rate. Later gas energy equation is solved to calculate entalphy defect. As the last equation solid energy is solved to obtain solid temperature distrubition in the channel and all thermophysical properties are updated according to temperature. That would be end of the loop for one time step, and this loop will continue until steady-state solution is found. It was mentioned that porous channel has three regions. As dimensions, First region (h1) is 5cm long, second region (h2) is 10cm long and third region (h3) is 15cm long, while width of the channel is 10cm. Three different mesh size is compared with each other to prove that code works independent of mesh size. These computational domains; 52x102, 104x204 and 156x306. Temperature distribution on a verticle line at the middle of the channel is compared relative to computational domain with smallest mesh size. Results shows us that error of domain with the largest mesh size to domain with the smallest mesh size is around 7:85 and error of the other domain to domain with smallest mesh size is around 2:5. As a result, mesh size of 104x204 domain found to be sufficient enough. At the middle point of the channel, both gas and solid temperature is observed during calculation. After program stops running, temperature values over time of that point shows us that this is the steady state solution since temperature values stay constant after a certain time. Velocity distribution is presented in results. Velocity profile differs from open channel flow, meaning that permeability plays dominant role in momentum equation. Temperature distributions shows us that feedback of heat is archived solving two different energy equation for flamelet approach. Temperature is diffused to first solid region from second with conduction term in solid energy equation and temperature of unburned gases are increased with convection term in gas energy equation. Temperature distribution on a verticle line at the middle of the channel is also compared with a similar study in literature conducted by Farzaneh in 2012. In this study, porous channel is also consist of three different regions. Porpuse of first two is same with ours; mixing region and combustion region. Third region of that study consist of heat exchangers. This explains the dramatic temperature drop in that region. Fractions of species can be found same as the gas temperature from flamelet table with three dimensional interpolation using mixture fraction, scalar dissipation rate and enthalpy defect. Major species fraction are found in each iteration since they are used to calculate thermal conductivity and viscosity of gas mixture. Rest of the species can be found in post-processing if those three necessary parameters are saved. Feedback of chemical reaction energy to unburnt gases via conduction in solid matrix, raises gas mixture temperature before combustion. This feedback mechanism increase flammability limits for lean mixture. In our study, results are presented for three different excess air ratios. Since the energy from chemical reaction is kept the same, exit temperature of the burner decreased with higher excess air ratio. Although exit temperature changes in burner for different excess air ratios, maximum temperature in the channel is not effected by the excess air ratio since our problem solves non-premixed combustion where combustion always occurs in stoichiometric conditions at the flame front. Gas emissions are said to be one of the advantages of porous burners. In this study, gas emission of NO and CO is also studied and production of these species are shown in the middle of the channel. Gas emission are compared with different excess air ratios as they are compared with a different study as well. After seeing results, it can be said that NO and CO emissions is highly related with temperature especially flame front temperature and exit temperature. Since increasing excess air ratio, decreases exit temperature, as expected NO emission is decreased with higher excess air ratio. In conclusion, combustion is modeled with flamelet approach in porous media. Mesh in dependency test is conducted and results are compared with a recent previous study. Velocity, mixture fraction, gas and solid temperature distribution are presented in results as well as some major species concentrations. In our literature survey, we haven't seen any study applying same approach before. With this approach, methane-air reaction is solved using GRI 3:0 mechanism but complexity of the chemical reactions wasn't involved in the computations since it was tabulated in the pre-processing process. Doing so, computational power and time is reduced comparing solving detailed chemistry with the same mechanism for the same problem.