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Show 1. From these data a correction factor f was introduced into the equation 3 applicable for all hydrocarbon fuels, i.e.: d[NO]p = f kpr [O]a [N21 [FUEL] exp (Ea/RT) dt and f = 4.75 + C1 n - C2 8 + C3 82 - C4 83 (4) where C1-C4 are constants, n is the number · of carbon atoms of hydrocarbon fuel, and 8 is the equivalence ratio. In this study values used for C1 to C4 were 8.19 x 10- 2, 23.2, 32, 12.2 respectively. These values are valid for aliphatic alkane hydrocarbon fuels and for air/fuel ratio of 0.6-1.6. 4. TURBULENCE/CHEMISTRY INTERACTION MODELLING 4.1 Role of turbulent fluctuation on NO formation: The kinetic mechanism of NO format i on and destruct ion descri bed in the above sect i on all have been obtained from laboratory experiments using either a laminar premixed flame or shock-tube studies where molecular diffusion conditions are well defi ned. However the flow in any pract i ca 1 combust i on system ish i gh 1 y turbulent, which implies that temporal fluctuations in temperature and speci es concentrat ions wi 11 i nf1 uence the characteri st i cs of the f1 arne. Therefore the calculation of mean reaction rates purely in terms of time mean temperature and species concentration can result in substantial errors. 4.2 The treatment of NO formation in a turbulent diffusion flame using a joint pdf: To predict NO levels equations 1-4 must be time integrated along the stream lines in the solutions which means extraction of Lagrangian information from an Eulerian solution. This requires a highly resolved Eulerian solution for reasonable accuracy, which is computationally expensive. Instead an extra partial differential equation for the conservat i on of the mass fract i on of NO, (mNO) was cons i dered in tensor form: (6) where i = 1, 2, 3, p is the average density, Uis are average velocities in three directions, ~eff is the effective viscosity which is combined from the laminar and turou ent viscosities, Gi NO is the Prandt1 number in the three di rect ions for turbu1 ent di ffus i'on of NO based on the eddy diffusivity assumption, SNO is the mean turbulent net rate of chemical production of NO and WNO is the molecular weight of NO. Methods of modelling mean turbulent reaction rate can be based on either (i) moment methods (14), or (ii) probability density function (pdf) techniques (15). The pdf method has proven very useful in the theoretical description of turbulent flow (16). In previous studies by us (17) a single variable pdf in terms of a normalised temperature representing the react i on progress was used to predi ct the NOx emi ss ion ina cyl i ndri ca 1 furnace. Despite the encouraging results obtained using single-point pdf method, the closure of the molecular mixing has been a problem in turbulent combustion modelling. This problem is aggravated by an increased number of fluctuating field variables involved in the prediction 6 |
