Partikül yüklü, eş eksenli iki jet için karışma ve yanma modeli

Abstract

ÖZET Ufak parçacıkların hava akımları içinde dağılmaları ve bazı şart larda buharlaşma ve yanmaları ile ilgili problemlerle endüstride ve mü hendislik alanlarında son zamanlarda oldukça sık karşılaşılmaktadır. Bu çalışmada metal parçacıklarının bir ön yanma odası içinde belli bir sı caklığa kadar ısıtıldıktan sonra ana hava akımı içine sokulmaları olayı teorik açıdan incelenmiştir. Hava emmeli roketlerin yanma odaları için bir model oluşturan bu sistemde olayın aerodinamik durumunu idare eden akış denklemleri katı, sıvı, gaz fazdaki madde dağılımını ve sıcaklık ve basınç alanlarını veren denklemlerle birlikte eşzamanlı olarak mevcut, sınır şartları altında çözülmüşlerdir. Matematik modelin verdiği elip tik kısmi diferansiyel denklemler sonlu fark denklemleri olarak ifade edildikten sonra bir cebirsel denklem takımına indirgenmişlerdir. Bu denklem takımı iteratif bir metod ile nümerik olarak çözülmüştür. Akı şa, fazlara ve akışkana ait büyüklükler kaynak terimleri ile birbirine bağlanmışlardır. Bu kaynak terimleri ve basınç iterâsyon sürecinin bir evvelki adımındaki değerler kullanılarak hesaplanmış ve sonraki adıma dahil edilmişlerdir. Parçacıklar sıcaklık ve çap gruplarına ayrılmışlar ve akış alanı içinde buharlaşma veya yanma miktarları belirlenirken dağılım denklemi tek bir çap grubu için çözülmüştür. Bu denklemin sonlu farklarla yazıl mış şekline ait konveksîyon ve difüzyon terimleri kullanılarak tanecik lerin hareketleri bir kontrol hacminden diğerine takip edilmiş ve bun lara yolları üzerinde bir tutuşma ve yanma modeli uygulanarak sıcaklık veya çap değişimleri belirlenmiştir. Akış alanındaki viskozite dağılımı için k-c modeli kullanılmıştır. Sayısal çözümler sonucunda çeşitli parametrelerin tutuşma bölge sine, yanma verimine, oda sıcaklığına olan etkileri elde edilmiş ve so nuçların deneysel ölçümlerle iyi bir uyum içinde oldukları gösterilmiş tir.

Ill A MIXING AND COMBUSTION MODEL FOR PART I CLE-L ADEH CONFINED COAXIAL JETS S U M M A R Y Turbulent mixing and combustion of particle-laden jets in an ax isymmetric-cwaxial flow field are of considerable importance in many engineering applications including air breathing propulsion systems. One of these systems, the gas-generator ramjet, involves the flow of fluids, which contain gaseous and solid fuels such as metal particles. Interactions between the particles and the gas phase as well as homogeneous and heterogeneous chemical reactions result in a complex phenomena. Many physical and chemical parameters, which are dependent on each other, effect the system simultaneously. However, the under standing of this fuel-rich particle-laden jet ignition £ffid combustion process in a ducted air flow is important for improving combustion efficiency and widening the operational limits of a gas-generator ramjet. Experiments for obtaining information on real systems or on models are necessary, but often are uneconomical and time consuming. It is therefore unavoidable to deve lope a mathematical model of the system, which can predict the system performance in a quick and reliable way. Thus it will be possible to predict the behaviour of theI iv ?? system for various parameters limiting the amount of experimental work. In this theoretical study a mathematical model including ignition and combustion of particulate fuel is presented for steady, two-dimensional, axisymmetrical gas-particle flow. Eoron is selected as solid fuel due to its applications in ramjets, because of its high energy density. The governing equations of the fluid, turbulent diffusion of gaseous and solid phases and temparature field are solved simultaneously by numerical methods. Equations are coupled through source terms and thermodynamical relations. Instead of the equations for primitive variables, equations for vorticity and stream- function are used, then obtaining the pressure field from integration of momentum equations when necessary. A source term is included to the continuity equation because of the- mass addition to the gas phase and the stream function at the wall boundary of the combustion chamber does not maintain a constant value anymore. The elliptic partial differential equations for the dependent variables are transformed into finite difference form by Taylor series expansion. Upwind differencing is used for the convection terms to provide stability at high Reynolds number, where as the diffusion terms are replaced by their central difference analogues. There is one finite difference equation at each grid point on the domain of solution. The set of algebraic equations resulting from difference equations aresuplemented with boundary conditions for every dependent variable and then solved with an iterative method. The turbulent mixing is based on k-e model. Infinite rate kinetic model is utilized for the reactions between gaseous fuel and air. This model does not represent the real case, but is simple and seems to be adequate for understanding the effect of mass-fuel rate on system performance. The particles, divided into temperature and diameter groups, are followed from one control volume to the other. An ignition and combustion model based on King { 26 ) is applied during the travel time of the particles. SoV it is possible to determine heating up or mass decrease of a particle. Depending on its new temperature or diameter, the particle may change its temperature or diameter group as it is arrives to the next grid point. The number of particles in each group travelling from one grid point to the other in both directions is determined from the convection and the diffusion terms of a single particle diffusion equation in finite difference form. Boron oxide, particle temperature and diameter fields and the boundary on which the ignition occurs are then obtained. It is assumed, that the particles are in dynamical equilibrium with the carrier gas, which is relevant for most of the flow fields but not in the regions near the primary nozzle. Because of elliptic character of the fluid equations, recirculation is permitted and obeying of the particles to recirculations is also taken into account. A staggered grid is employed for the calculation of boron oxide formation rate due to boron combustion. Limited quantitative experimental data is available for the ignition characteristics of the described particle-gaş flow» ?_1 though a systematical comparison with experiments is not possible for every parameter, partly qualitative, partly quantitative agreement with data of the previous authors is achived. For the purpose of comparison with experimental results present in literature, main parameters, which effect the performance, are selected. These can be outlined as follows: 1. Gas phase fuel rate (mfn) : This parameter together with the ratio of secondary air mass to primary jet mass determines the temperature near the primary nozle. It can be concluded from the experimental and theoretical studies on ignition of single boron particle, that the temparature of surrounding oxidizer plays a significant role on ignition time. Experiments in combustion chambers indicate the requirement of a minimum temperature level of 2400 K at the fore-end, if sufficient boron combustionVI is to be achieved. As well as the temperature leye} the length and the position of this high temperature region is also important. Solutions are presented for various fuel rates. With decreasing air-fuel ratio i.e. increasing fuel rates the percentage of particles which ignite also increases. Ignition limits and the position of the ignition line are in good agreement with experiments of Schadow(19,20,21) 2. Initial particle temperature {T Q) : This temperature is determined by the primary chamber outlet temperature assuming, that the gas and the solid phase are in thermal' equilibrium at the exit. Experiments with boron showed, that an initial particle temperature of approximately 1850-1950 K is required for rapid boron combustion. Higher fuel rates are necessary for lower initial temperature to compansate the decreasing percentage of boron ignition. At initial temperature below 1750 K ignition is seriously dangered.The present study has also satisfactory results compared with experiments '.' 3. Loading factor (tc) : This is defined as the ratio of the mass of particulate phase to the mass of gas phase in primary jet. The overall air to solid fuel ratio is determined by this factor» The choice of this factor rather than the air mass / primary jet mass ratio is due to the purpose of eliminating the changes in mixing pattern or in gas phase reaction rate with this ratio. With decreasing loading factor better combustion efficiencies are possible, but at very low values the chamber temperature sinks, creating the danger of an instable ignition. Good results are obtained with varying loading factors when compared with experiments. 4. Initial particle diameter (D Q) : Particles used in experiments are of 1-3 ym in diameter. With increasing initial diameter the applied ignition model shows little >. differences in the position of ignition in the combustion chamber, at higher fuel mass rates. Differences are greater if the fore-endvıı temperature in the chamber is low. The combustion rate will decrease with increasing initial diameter. 5. Primary chamber exit velocity (V.) :, Both the flow/ pattern and the temperature field in the region near the primary exit are affected by this velocity. At near sonic exit velocities the mixing is slower after the primary nozzle: and: a near s tochiometric ratio, is held for. longer.distances. As the velocity Increases primary gas fuel mixes with secondary air further downstream where the stochiometric ratio can not be held any more. The resulting low reaction temperature causes an increase of the ignition time. At.: lower velocities also the combustion efficiency decreases because of the mismatch between the high temperature region and the mass rate field of particles. Because of a better mixing in the chamber and of higher energy density of the whole system sonic velocities are proved to be optimum. In this model hydrogen is used as gas phase fuel. Solutions are also obtained with ethylene (C-H.) as fuel using the combustion chamber shape and dimensions and other parameters of Schadow(19,38). The results obtained from solutions for the mass ratio of boron oxide to total boron (mass of boron + mass of boron oxide) and the temperature distributions in the chamber are in very good agreement with measurements (19,38). Some lower temperatures are obtained than the experimental data far from the symmetry axis. This result/can be explained by the effect of B20_ condensation in real system giving back the latent heat of vaporization. A model for the condensation of boron oxide is not included in the present study, although it is possible to include it in future works. As a results of this study, it can be concluded that the theoretical * model presented is capable of predicting the system performance depending on various parameters of the flow and the geometry and is open to further applications including vaporization, he teregeneous reactions and recondensation of reaction products.