Sürekli yanma odalarında alev cephesinin dinamik yapısına ait bir çalışma

Abstract

ÖZET Alev stabilizörünün bulunduğu sürekli yanma odalarındaki dö nel hareketli (recirculating) akışlarda, türbülanslı alevin yanma odası içerisindeki konumu ve alev cephesinin teorik olarak tesbiti bu çalışmanın konusunu teşkil etmektedir. Alevin oluşumu ve konumu nun belirlenmesinde parametreler olarak ana akım hızı, alev hızı, blokaj oranı ve stabilizerin koniklik açısı kullanılmışlardır. Problemin matematik modellendirilrresinde homojen karışım ve ön karışım alevli yanma kabul edilmiştir. Homojenliğin tutuşmadan sonra alevin yayılma alanı boyunca da var olduğu kabul edilerek sı caklık dağılımı bu yayılma alanı boyunca Uniform alınmıştır. Çalışmada akış alanına ait eliptik kısmî diferansiyel denk lemler silindirik koordinatlarda yazılıp sonlu fark denklemlerine dönüştürüldükten sonra ardışık ikameli iteratif metodla çözülmüşler dir. Muhtelif akış hızı, alev hızı, blokaj oranı ve koniklik açısı değerleri için sonuçlar bulunmuş ve literatürdeki deneysel sonuçlar la karşılaştırılmalardır. ıı

SUMMARY A STUDY ON THE DYNAMIC STRUCTURE OF FLAME FRONT IN CONTINUOUS COMBUSTION CHAMBERS Experimental and theoretical combustion problems are of a great importance for that there is still a gap between these stud ies and relevant engineering applications. But, since researchers encounter considerable difficulties with combustion experiments due to expensive and time consuming character of them, they will. further demand the support of mathematical models. Today there are many technical and economical reasoning emphasizing the importance of the combustion chamber design consid erations. Since combustion processes involve many mechanical, chem ical and thermodynamic features all together, theoretical descrip tion of these processes constitute one of the most complex engi neering applications. Therefore any mathematical model, presenting the physical lay-out of the problem, should overcome many difficul ties in every respect without loosing simplicity. Such an important- problem is the stabilization of the flame in continuous combustion chambers of engineering equipment. This problem comes out to be very important especially in aircraft jet engines due to the fact that a stationary flame can not prevail anymore over the incoming mixture if any disturbance effects the flow conditions. In order to prevent this and assure stability for the flame, various types of bluff-bodies, set across the stream, are used. Such a geometric modification causes some of the hot. gases, which result from the chemical reaction, to flow back in an upstream direction; they can then ignite the incoming mixture of unburned fuel and air. Besides the well known mechanical complexities due to the- fluid flow, occurrance of combustion and dynamic character of the 1 flame front will contribute tp the 'number of theoretical consid erations. Although excluding a full detailed describtion of turbu- iiilent character of combustion problems in recirculating flows, the requirement for the first group, i.e. for mechanical considerations are met in a great extent. For the second, combustion processes are identified in two distinct groups. One is tha physically-controlled processes, in which the chemical reaction proceeds so rapidly that the the processes are entirely determined by the finite rates at. which mixing of the reactants takes place. Consideration of chemi cal kinetics is ignored in this case. Second group belongs those processes in which both the reaction and the mixing of the reac tants occur at finite rates. Then it is no longer valid to exclude the chemical-kinetic considerations from the analysis. In the literature, however, combustion problems are dealt with introduction of rather simple chemical reaction or combustion ki netic models. Most of these models are based on the account of ei ther of the above mentioned identifications for the sake of simplic ity. However such models are not representative for the illustration of the real processes and are valid only in the circumstances in cluding several restrictions. This means that the problem is seen in an insuefficient perspective. As a result of inadequate data supplied the discontinuity of flame region described by these models could not simulate the reality; there. are no reliable criterion for ap pearance, flashback and blow-off of the flame front. In an attempt to compensate for this deficiency to some extent a comprehensive parameter, burning velocity, is introduced in this study. This parameter makes us capable of dealing with the pure physical behaviour of the flame and impose no restriction in accounting the thermo-chemical çharasteristic view-points. Also in the model the other characteristic mechanical and geometrical para meters, such as fluid inlet velocity, blockage ratio and bluff-body approach angle, as well as the thermo-chemical ones, such as the chemical properties bf the fuel, inlet temperature and equivalence ratio, can be regarded easily in the calculations. These parameters accompanied with the flame velocity concept give the problem oppor- IVtunity in description of the extremes in flame motion and satisfac tion of combustion chamber design requirements. In geometrical modelling of the problem, we took the account of a combustion chamber of unconstructed apertures. At the inlet, a conic is set coaxially across the stream. In mathematical modelling. on the other hand, we considered the following assumptions: - The walls are at rest and they, are impermeable both to heat and matter. - The flow is axisymmetric with no swirl velocity. - Incoming fuel-air mixture is perfectly homogenous. - Homogenity prevails throughout the luminous region (i.e. the volume enclosed by the flame envelope is occupied by a ho mogenous mixture of combustion products). This assumption is also valid for the recirculating portion of the combustion gases. - Pressure changes are negligible compared to the temperature changes throughout the chamber so that pressure field need not to be calculated here. - Effective Prandtl and Schmidt numbers ara assumed to be equal to unity. This assumption shows conformity with the experi mental results obtained for recirculating flows. For the calculation of vorticity we should add the following as sumptions: - Gradients of fluid density and radial change of radius r are considered to be negligible at the immediate vicinity of the horizontal walls. - For near-wall regions, gradients of all dependent variables are negligible compared to their normal gradients; then we can eliminate them from the differential equations. In the study the elliptic partial differential equations defining the flow field, are expressed in cylindirical coordinates put into finite difference form and then solved by an iterativeprocedure of successive substitution technique. For various flame velocity, inlet velocity, conic approach angle and blockage ratio. the results are obtained and compared with their experimental al ternatives available in the literature. For a more inclusive com parison some calculations for isothermal case have been performed also. The results are presented briefly in the following paragraphs. (i) For either case,- isothermal or with flame, length1 of recircu lation zone increases with increasing conic approach angle. But in a wide range of domain this length is less in the case with flame in contrast to the experiments performed by Winter feld [2]. How ever this result is in agreement with that of obtained by Scurlock. He concluded that the difference in viscosity values of burned and unburned gases arising as a result of combustion will cause an increase in the momentum transfer from the second to the first. (ii) For isothermal cases length of recirculation zone found to be increasing as the inlet velocity increases. With flame, however, it decreases for low velocities (below 30 m/s), then remains con stant in a certain range and starts to decrease again at high ve locities (above 70 m/s). (iii) For the same inlet velocity, increasing turbulent flame ve_, locity causes the' same effect in the length of this zone in such a way that its value reaches to a certain limit and it is no more effected by the increaments in the flame velocity. Near the limi ting value of this length the corresponding value of flame velocity indicates flashback behaviour. While such a condition depends on the selection of the theoretical ignition startpoint, it is certain that there is a flame velocity which causes flashback for a given inlet velocity. (iv) The calculated maximum widths found to be almost the same as of found by the experiments. Very small differences may be attribu ted to again selection of ignition startpoint and number of grids used in the solution process. vi(v) Geometry of the recirculation zone is one of the determinative factors for exchange motions. We have found that this geometry is in a strict relation with flame velocity. This means that flame velocity has a direct influence on determination of the exchange motions. (vi) For the same increament in flame velocity, flame front has an increasing tendency to move back as the inlet velocity increases. (vii) On the same axial plane mass flow recirculation rate is higher at high flame velocities. But velocity gradients decreases with increasing flame velocity which results: in a rise in tendency of backward motion of flame front. At this point we should emphasize that, as its very nature, mass flow recirculation rate will change depending on the changes in temperature of the recirculation zone, so will the velocity gradients and tendency of the flame front to move in any direction. As a last attempt here we will present an important conclu sion led by the above results. That is; the behaviour of the flame front in the combustion space is not solely determined by the rela tion between the flame and inlet velocities, but it gains an activ ity as a result of thermodynamic conditions imposed by itself. This conclusion is supported by the results given in Figures 5.10-5.12. It is obvious from these figures that, as they do in several engi neering applications, velocity gradients take on a very important role in formation and behaviour of the flame front. But the posi tion of the flame front, so the space occupied by hot gases, deter mines the velocity profile in return which leads us to the conclu sion given at the beginning of this paragraph. This result is a well-expected reminder of Karlovitz number which explains the flame streching mechanism. Undoubtfully, some of the simplifying assumptions used in this study may be remarkable for a more realistic modelling of the problem. We should also state that the study marked some important vndetails subject to future studies. Some such details may be summa rized as follows: (i) We need further researches for a well representative turbulence model for recirculating flows with combustion. But in any case we may use different turbulence models for comparison, other assump tions remaining the same. Turbulence models of differential equa tion type, especially, should be preferred. (ii) We may attempt to solve the problem considering non-homogenous mixtures and permeable walls. Such a problem would yield conver gence problem and solution would not be economic with slow-running computer systems. This is because that turbulence differential equa tions would be non-linear and energy equation would have a very strong source term. (iii) In order to decrease the effect of exit boundary conditions (i.e. normal gradients of all dependent variables are zero at the exit) on the flow field we should choose length of the combustion chamber longer. Alternatively we can use more complicated exit conditions which would be undesirable for an easy solution proce dure. (iv) Some graphical results indicate the importance of working with more parametric values in the determined region of them. That is some curves tend to show critical extremes, possibly in dicating some physical points of interest. Therefore through these critical regions, we should take account of values differ ing less from each other. viia.