OCR Text |
Show 6 The computational geometry consists of 99 x 35 nodes in axial and radial directions respectively. The fuel jet was assumed to be fully developed at the burner outlet. The mean reacting flowfield is computed by solving the transport equation for all species on a 2-D elliptic finite volume grid. A twostep global kinetic model was used to model the combustion chemistry. The average source terms of the main reacting species have been found from the Eddy Dissipation Concept (EDC). The mean radiation flux is calculated by the 6-Flux equation model. The mean temperature is calculated using the enthalpy equation which in turn, is used in calculating the mean concentrations of a11 species and, more importantly here the mean soot mass fraction, Y s' In order to account for the temperature fluctuations on the average soot formation rate, the local temperature state relationships are obtained b) modifying the adiabatic temperature profiles in a manner similar to (17). In this approach the instantaneous temperature can be found by T(~) = Tad ( ~)[l -Xr( Tad ( ~) )4] (17) Tad,max In this relation T(~) and T ad(~) are the local instantaneous and the local adiabatic temperatures respectively. Also Tad, max. is the maximum adiabatic temperature. The radiant fraction Xr' is being experimentally measured as explained previously. By integrating the net laminar soot source term over the pdf of the mixture fraction, the average soot source term is obtained. The mean mixture fraction is computed according to Eqn. 18 derived from that given by Masri and Bilger (18) and the variance is found by assuming a steady state assumption. (gy +gy +~y ) 16 CH 4 28 co 44 cO2 c;= 0.75 (18) In the present model a composite pdf function is used. The pdf, P(~) , consists of a turbulent part, Pt(~ ) represented by a Gaussian distribution and a non-turbulent part represented by a Delta function. The use of the composite pdf in this manner alleviates most of the problems associated with numerical singularities which result from unphysical combinations of the mean and variance values. The first part is the original continuous probability distribution (Clipped Gaussian) which is assumed to hold inside the turbulent jet boundary. Outside this boundary the continuous distribution is replaced by a Delta function evaluated at the undistributed conditions (~ = 0). The location of the turbulent jet boundary is then determined by the intermittency factor. Therefore the composite pdf may be written as P(;) = (1- 1')0(0) + YFr(;) where y is the intermittency factor ( 1 > y > 0 ), _ {l. - 0 for g < 0.25 (2 Y = 1. 25/ (g / ~ + 1) - for g ~ 0.25 (2 where g is the variance and Pt(~) is given by, for a Clipped Gaussian distribution (19) (20) p,(~) = J21ng exp{ ~~ (~- d} (21) The fully coupled soot/radiation calculation was attempted for the first time in a recent paper by Sivathanu & Gore (19). The mean mass fraction of NO (Y NO) is obtained by solving a transport equation. The source of NO formation dealt with in the current model is that of Zel'dovich (20). N2 +O~NO+N (22) N+02~NO+0 (23) As the second step is fast the molar production rate of thermal NO may be written as; WNO = 2k] [N2 ][ 0] (24) where k 1 is the specific reaction rate constant for the first step ( k 1 = 1. 36 x 1011 exp( -37,7 50rr) m 3 Ikmol/s). The NO mass fraction equation is solved by post processing I.e. after a converged solution of the above soot/radiation coupling has been achieved. |