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Show The strong effects of the temperature dependency of Arrhenius laws is shifted to temperatures lower than 900K. The final result of this study is shown in Figure 14. The calculated effective rate (the LIM-rate) based on the frozen-flow- field is written as: 1 R LIM.CMX (31) ff 1 1 R EBU.CM^ R TK.CM^ ff This effective reaction rate model is derived from eq. (14) by replacing the "chemical kinetic" finite rate results with the "turbulent kinetic" reaction rates. The maximum effective reaction rate predicted is 2.5 kg m 3 s"1 and does not change significantly between local temperatures ranging from 1000K to HOOK. It is believed that the calculated effective rates represent the "main-flame-zone" with good accuracy. At temperatures higher than H O O K the eddy-break- up rates are getting substantially slower and becoming the significant term m eq. (31). O n the other hand the nature of the Arrhenius type "turbulent kinetic" formulation of the TK-model decrease the effective rates below local temperatures of 900K. 100-a 0.00001 0.01-• 0.001 -= 0.0001---ji 600 800 1000 1200 1400 1600 1800 2000 Figure 14: Effective local reaction rates of C xHy [kg m 3 s"'] of the L I M model over local temperatures [K] based on the frozen flow field of the EBU-model predictions Conclusions A classification of accuracy levels for CFD-predictions by Weber et al. (1993) is applied to evaluate the results from C F D predictions of a 2 M W t natural gas turbulent diffusion flame. The type-2 swirling natural gas flame was computed by means of an eddy-break-up model (EBU). A consistent theory to apply the EBU-model to multi-steps reaction schemes is presented. It has been demonstrated that the good accuracy of the EBU-predictions is deemed satisfactory for prediction of local turbulent reaction rates. The analysis is focused on the near burner zone and covers all computational nodes where the local stoichiometry ranges from 0.01 to 20.0. A n area of intense high heat release is located just downstream the quarl outlet and is defined as the "main-flame-zone". The analysis of local heat releases highlighted the importance of this "main-flame- zone" for the flame structure, which is considered to be mainly controlled by the driving forces generated in the "mam-flame-zone". The results of the analysis explain die strength of the widely-used E B U combustion model to match accuracy levels needed for engineering purposes by its ability to predict the "mam-flame-zone" reaction rates reasonably well. However, modern gas-firing combustion systems try to avoid high heat releases in flames with the objectives to generate homogeneous temperature distributions and to reduce pollutant formation. Hence, distinct "mam-flame-zone" will occur at lower temperatures and over a wider volume. A comparison of reaction rates obtained by means of the E B U combustion model and by means of a quasi-global Arrhenius rate expression for the combustion of methane shows that neither the EBU-, nor the finite rate-, nor a coupling of both combustion models by a limitation law can be applied to model reaction rates in high turbulent flows at temperatures lower than 1200K with reasonable accuracy. A statistical analysis of the predicted reaction rates yields a formulation for an improved Arrhenius law-type model, called "turbulent-kinetic" (TK) combustion model. The proposed model accounts not only for the strong temperature dependency of chemical reactions at lower flame temperatures but as well for small scale turbulent fluctuations within the chemical reaction zone. At this stage, 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 (1992)). 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 which delivers reasonable good results required for engineering purposes. In addition, the model stays attractive for use in C FD applications where computational speed is a critical consideration. Future works will focus on an intensive validation of the proposed "novel" engineering combustion model against detailed in-flame measurements from a number of semi-industrial- scale natural-gas flames. The main objective of these works will be to examine whether the functional relationship and the constants of the TK-model found in this study are applicable to flames of different flow and heat-release pattern. 12 |
