OCR Text |
Show 5 gases. These measurements enabled the an emissions index value for nitrogen oxides (EINOx) to be derived (Eqn.(6) . (6) Theoretical Modelling The origin of the present model of soot formation is in the work of Gilyazetdinov (11) on carbon black formation . This model has been modified to be used within the frame work of laminar flamelet modelling of turbulent combustion (12-14). The effect of the different formation/destruction processes on soot mass fraction, Y s and particle number density, N, are represented by equations for the transport of these scalars. The volumetric source terms for number density, N, and soot mass fraction, Y s can be written as (12) ~ (7) (8) Where the respective rates a, ~ , y 8 are explicit functions of local mixture fraction, S density, p. temperature, T, and parent fuel concentration, Xc' The constant, No is Avogadro's number (= 6 x 1026), ' a = CaP- J'Txe exp( - Ta / T) (9) P = CfJ.fi (10) r = c yp-/T Xc exp( - Ty / T ) (11) (12) The symbols Co., ~ , y, 8 are fuel-type dependent constants and To. , Ty are activation temperatures, while the Xc is the fuel fraction. Soxid is the oxidation source term in kglm3/s and Sth is the source term due to the thermophoretic radial velocity component, Vth, which can be expressed as: V. = -0.55L or (13) th pT a- 1 f} Sth = -,a-(-'PYch~) (14) The oxidation source term is due to molecular oxygen (02) ' The most common model for treating soot oxidation by 02 is the Nagel and Strickland-Constable expression (NSC) (15). The computations performed by Moss and co-workers (12-14) showed that the above model can be used satisfactorily for different fuel types provided that the appropriate set of constants of those fuels are used. The set of constants used in the present implementation are those for methane (14). The model is sensitive to these constants due to the high temperature dependence of the rate constants. Instead of solving a separate transport equation for particle number density an alternative approach is to assume a local balance between the inception and coagulation rates. In other words the particle number density will reach a steady state value at each point in the flowfield depending on the local mixing state. This simplification enables the calculation of a local particle number density without having to solve a corresponding transport equation, thus from Eqn. 7, N=NJaw (15) o P(;) Because of the vital importance of linking the soot volume fraction calculation to the temperature field a radiation sink term has been added to radiation model. This sink term is in the form of an absorption coefficient for the solid phase. Following the work of Honnery et al (16) this absorption coefficient could be written as (16) where Kab is the absorptivity coefficient in 11m, fv is the soot volume fraction, and T is the local temperature. The gas phase radiation is not taken into account at this stage but it can be added in a future improvement of the model. |