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Show 1. The Arrhenius law nature of equation (26) accounts for the strong dependency of the reaction rates on temperatures. 2. When in scales - smaller than addressable by the EBU-model - high turbulent fluctuations act to increase the reaction rates in flames then a correction term like equation (25) may be introduced to account for this effect. However, it should be noted that Ronney and Yakhot found that at moderately high turbulence, the small scales act to increase the local reaction rates over a "thin" flame and that at very high turbulent fluctuations these scales may actually cause a decrease of the turbulent rates. It is not clear to the author whether the latter effect can be traced in computational cells of engineering length scales. In addition, it should be clearly noted that the derived model does not intend to cover the complexity and range of scales, which are covered by more detailed models (Ronney and Yakhot, (1992); Peters, (1986); Bray (1996)). The T K - model tries to present a simple and fast coupling of mean flow field properties to estimate local reaction rates at lower flame temperatures within an accuracy range required to obtain second-order information. Application of the TK-model to multi-step reaction schemes. The proposed function Ct (eq. (19)) depends only on local flow properties and on the "fuel" mass fraction of the reaction considered (see eq. (25)). Following the above argumentation on the physical meaning of the TK-model it is reasonable to propose that the same form and constants of eq. (25) may be applied to other quasi-global reaction schemes with one fuel and one oxidiser as educts of the reaction. In contrary to die activation energy, very fine scale turbulent structures will not be reaction scheme dependent. Hence, it is believed that the carbon monoxide disappearance rate expression of Howard et al. (1972) may as well be improved by the TK-model. However, future validation campaigns of natural gas flames against detailed in-flame measurements should carefully evaluate the model's performance to predict carbon monoxide and/or carbon dioxide concentrations. Results Finally the derived model is applied to the frozen-flow field data of the MFB-1 flame 258 prediction. Figure 12 plots the results for the term energy at local temperatures around 800K by ca. 2 5 % , at 1200K by 1 0 % and at 1800K by 5%. 1 - C, ft* CM, \\ (30) ff where CE a = 2.5, a = 0.25 and b =-0.75 Due to the high turbulence in the ignition zone, caused by the fast mixmg of natural gas and air, the TK-model reduces the activation 1 0.95 0.9 0.85 0.8 0.75 .'' *«. k * * * * * i.. 1 f f T ******/»* '* * * * T »/ ' * \ \ /' */$fdtX, il'jW'W :'. > ;.»:y •~ t ffl&ffi ^^^ 600 800 1000 1200 1400 1600 1800 2000 Figure 12: Correction factor eq. (30) [-] over local temperatures [K] Consequently, Equation (30) is applied to predict the reaction rates in all computational cells ranging from local stoichiometries of 0.01 to 20.0 (Figure 13). Reaction rates corresponding to the upper 3 0 % of total heat release and generated by means of the EBU-model are as well added to Figure 13 (see D-symbols). It can be seen that the TK-model predicts reaction rates within a difference of less than one order of magnitude when compared to the reaction rates of the EBU-model at temperatures between 1000K and 1200K 100-3 0 001 - 0.0001-s 00000 600 800 1000 1200 1400 1600 1800 2000 Figure 13: Predicted local reaction rates of CxFL[kg m"3 s"1] over local temperatures [K] calculated by the TK-model (eq.(26)) and based on the frozen flow field of the EBU-model predictions 11 |
