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Show 100-3 10-. 0 1- 0.01 -5 0001 0 0001 0.00001 1 rf)D : t itr •jt: if. JU I ft; 1 * r b^^l «W JWPi |P v^m 600 800 1000 1200 1400 1600 1800 2000 Figure 11: Predicted local reaction rates of CxHy [kg m"3 s'1] over local temperatures [K] calculated by the finite rate (eq.(17)) and based on the frozen flow field of the EBU-model predictions permitted under the condition that the EBU -predictions fulfil the requirement of reasonable accuracy (at least second-order information level). As expected the finite rate model presents increasing reaction rates with increasmg local temperatures. However, the finite rate model does not match 50%o of the area of highest heat release on the low temperature side. Considered that the predicted values of reaction rates lower than 1000K from the EBU-model are unrealistic high, still a significant zone of ca. 4 0 % of the highest 3 0 % of heat release is underpredicted in between 1 and 3 orders of magnitude. Hence, the finite rate model is not able to ignite the flame early enough to deliver reasonable good accuracy. On the other hand the results explain the strength of the EBU-concept to match an accuracy of second-order information by its ability to predict the "mam-flame-zone" reaction rates reasonably well. The "mistakes" of predicting either too high or probably too low reaction rates at lower temperatures than 1200K, respectively higher than 1600K are of less importance to the overall accuracy, because the corresponding local heat releases are of minor influence to the flame structure. However, this analysis is based on predictions from a swirl-stabilised natural gas flame where a distinct "mam-flame-zone" can be localised. As highlighted in the introduction of this study improvements to the E B U model will be necessary when distinct "main-flame-zone" will be observed at lower temperatures and over wider volumes in the reaction chamber, as it is realised in modern gas-firing combustion systems when flue gases are entrained into the fuel and/or the oxidiser jet before combustion occur. In the following a "novel" engineering combustion model is proposed to improve the finite rate predictions. The aim is to deduce a finite rate model which calculates reaction rates of the same orders of magnitude than the EBU-model does at flame temperatures between 1000K and 1200K to sustain the "main-flame-zone". Towards lower flame temperatures than 1000K the new combustion model should emphasis the decreased reactivity of the fuel-au-flue-gas mixtures as Arrhenius laws postulate. "Novel" Combustion Model Using the frozen flow field predictions of the EBU-model parameter study on the Arrhenius law of the methane disappearance rate (eq. (17)) was conducted. The pre-exponential constant A, the activation energy Ea and the exponents of the species concentrations are varied. Small changes of the activation energy turned out to be most sensitive to mcrease the calculated reaction rates of the KIN-model at lower temperatures. Obviously, to increase the calculated reaction rate the activation energy has to be decreased. A model to define a corrected activation energy can be written m the following form as: Ea,eff=Ea{\-C,{<px,<t>2...)) (19) where Eieff, , called the effective activation energy, denotes the decreased result of the activation energy Ea multiplied by 1 - C, \<t>x, $2,...), which is a function based on local flow properties. When a certain flow characteristics, namely Ct\f>Xl(f>2,...), exists, the chosen form allows a correction to the finite rate Arrhenius law. O n the other hand it leaves the original activation energy unchanged if there is no evidence inside the function C, \<f>x, <j>2,...) for a correction. To obtain an algebraic solution for the function C, an array of reaction rates generated by means of the EBU-model and the KIN-model is compiled using die following condition: Arrh.CM. <R IT EBU.C H > sample data (20) where the index "ff' refers to results obtained by usmg the "frozen-flow"-field properties of the EBU-predictions. This condition extracted all data points at lower temperatures where the KIN-model calculates lower reaction rates then the EBU-model (see Fig. 11). In total 640 points are found. The data array sampled contained all major local flow properties, such like temperature, species concentration, turbulent kinetic energy and its dissipation rate, turbulent and laminar viscosities, density and the two reaction rates of the EBU-model, respectively the KIN-model. To simplify the following notations of formulae we define c -A .io~3i'a'+a-H.>/+a~) ^•Arrh.f ~ AArrh ^ ' P M* feT (21) rf'.wzr vfWf 9 |