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Show heating furnaces, flares etc. Indeed, acid/alkali modelling can be used to model any process where fuel/air mixing dominates, table 1. Great care must be taken when scaling the resul ts from the cold, isothermal model condition, to the hot full scale plant, but providing this is done correctly the technique yields quantitative results of flame length against excess air. Physical modelling is usually supplemented by mathematical modelling to predict the temperature and heat flux profiles within the furnace enclosure. Such models are based on two or three-dimensional, steadystate, element calculations, which account for the interactive effects of convection, radiation and heat release throughout the defined enclosure. My own company, Fuel and Combustion Technology, has used acid/alkali modelling to investigate and solve problems with cement and lime kilns, alumina calciners, flash calciners, duct burners, reformer burners, etc. One of the major advantages of acid/alkali modelling is that it can take fully into account, the aerodynamics of the system and reveals any unstable transient responses. Furthermore, it is relatively inexpensive especially in relation to the savings which can be achieved, which on a large plant, can run into thousands of dollars per day. 2.1.3 Mathematical Modelling Mathematical modelling has come to the fore as a result of the development of the digital computer, prior to that anything beyond the simplest model, such as the "Well Stirred Furnace Model" (10), was impractical, since the time taken to do even a simple iterative calculation by hand is immense. I remember reading in Neville Shute's autobiography (11) that it took two man weeks to make one iteration of the stresses in a transverse frame of the RlDO Airship! There were so many iterations required that it took two to three months to calculate the forces in each frame. Such calcula tions now take only a few seconds or minutes wi th modern computers which have also opened the way to the solution of the much more complex fluid flow, mixing, heat transfer and chemical reaction problems, using these techniques. Indeed, the combustion process and its integration into energy transfer and associated equipment design, is the most complex of all processes engineering problems, requiring the simultaneous solution of heat, mass and momentum transfer equations under transient conditions. With the advent of zone models introduced by Hottel and Sarofim (12) in the 1960' s, computer solutions became imperative. These models cannot predict the aerodynamics for anything but simple systems but can take flow patterns into account and are frequently used (by FCT), in conjunction wi th physical modelling. Since the basic chemistry of the combustion process has been investigated and proven over many years, it is possible to calculate accurately the equilibrium conditions and predict transient effects in a flame, although we still do not fully understand the reactions of trace catalytic elements or water vapour, both of which modify the flame chemistry. In industrial combustion systems which use turbulent diffusion flames, the chemical effect~ of the combustion process are secondary, since the reaction time constants are orders of magnitude faster than the diffusion mixing constants. Thus, the combustion process can be reduced, with a "mixed is burnt" assumption controlling the rate of heat release. |