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Show series of resistors (eddy-break-up and chemical kinetics) and calculates the effective rate as (Re1f4f ) ~ 1 1 REBU + RArrl For a combustion reaction where one fuel reacts with one oxidising species, the expression for a quasi-global Arrhenius law can be written as 'Arrh.f d\X dt = A Arrh E^ RT X a( r la„i \X„\ (15) Commonly eq. (15) yields a rate which is given in mole cm"3 s"1. The conversion of the above form into kg m 3 s'1 for usage m C F D applications reads: R Arrh.f d\Y dt = A Arrh 10 3 \la,+an, -1 .-fefeHfeC (16) w/ -K" •vfWf Currently detailed chemical kinetics mechanisms cannot be included in most C F D combustion models because the cost and time requirements of such a treatment would be too great. Westbrook and Dryer (1984) argued that there are many occasions where the great amount of chemical information provided by a detailed mechanism is unnecessary and a much simpler reaction scheme like (eq, (1) and eq. (2)) will suffice. Philipp (1991) stated that a 2- step mechanism for methane combustion yields good results when the attention of the engineer is focussed on the rate of local heat release rather than on detailed chemistry information. Finite rate for methane combustion. Dryer and Glassman (1972) derived a two-reaction model for methane oxidation in a turbulent flow reactor, where the reaction scheme (eq. (l)and eq. (2)) is applied replacing x=l and y=4 in the hydrocarbon species CxHy. This reaction of methane was studied at atmospheric pressure, over the temperature range H O O K to H O O K and a stoichiometry range of 2.0 to 20.0. The over-all methane disappearance rate was found to be RArrh.CHA ~ i( 13.2±0.20 •10 •I 5 2.025010'±5.020 10° RT I 5 'CHt 0.7 08 (17) »SJ4-' 0.8 O, WC,H , where the activation energy Ea is given in J kmol"1, respectively the rate in kg m"3 s"1. Although the above methane disappearance rate is only adequately correlated over the temperature range H O O K to H O O K it is believed that the global equation may be applied to lower temperature regions and stoichiometry factors below 1.0. The latter assumption can lead to overpredictions in the order of 2 5 % to 5 0 % of measured flame speeds m sub-stoichiometnc regions (Westbrook and Dryer, 1984). However, this error lies within die given accuracy of eq.(17) itself. At temperatures below H O O K the error range of the activation energy ( ± 5.020 • IO6 in eq. (17)) leads to ca. 7 5 % deviation of the predicted reaction rate, regardless to the stoichiometric regime. Since the purpose of this study is to investigate natural gas flames, it is assumed that the above rate expression for methane may be applied to the disappearance rate of the hydrocarbon species C xHy (see eq. (1)) under the assumption that neither x nor y/4 differ too much from unity. Finite rate for carbon monoxide combustion. Howard et al. (1972) determined the rates of carbon monoxide oxidation in after-flame gases at atmospheric pressure and correlated the experimental results with previous data to obtain a rate expression for practical purposes over the temperature range 840K to 2360K. Dryer and Glassman (1972) proposed a similar expression for the carbon monoxide disappearance rate. However their data was only correlated over a temperature range of 1030K to 1230K. Therefore the expression by Howard et al. is preferred 1.2552 io8 14 R Arrh. CO = 1.310" 10 -3.^-0 [yco] 10 [ft 0 5 RT 'H-,0 0 5 (18) rl.O r'VCO^ W^rV, 0.5 ,0.5 'H,0 wc,o With Ea given in J kmol"1, respectively the rate in kg m"3 s"1. Kjaldman (1993) applied this global C O combustion rate sucessfully to multi-dimensional C F D calculations of light and heavy fuel oil flames. Analysis of Predicted Local Turbulent Reaction Rates In the following the local turbulent reaction rates of the hydrocarbon species CxHy will be analysed. In die absence of carbon monoxide (CO) in die fuel, reaction (eq. (1)) is the preceding path to the combustion of C O . Moreover, when local heat releases of natural gas flames are considered and the lower calorific values (LCV) of natural gas and C O are compared the contribution to the local heat release of CxHy and CO, when equal magnitudes of reaction rates are assumed, yields ratios in between 3:1 to 4:1. As stated earlier it is known that areas of high heat release are the driving force behind the flame structure of type-2 swirl-stabilised flames. Since the combustion of the hydrocarbon species CxHy contributes at least 3 times more to this force it is reasonable to base the analysis on the C xHy species only. Index of combustion models. In the following this study uses the abbreviation EBU, when the pure eddy-break-up combustion model is used, with no limitation by finite reaction rates. The index KIN will classify the fmite rate results only. T K stands for the improved combustion model presented later in this study. In addition the indices of the 5 |
