| OCR Text |
Show 7 sizes, f^ is dependent on the Knudsen number Kn{ = ^-2.) which is represented by a mean free path of gas i^and a particle diameter dp. In the case of transition regime (0.01 __ Kn __ 10), f is obtained by Eq. (13) [15]. In the present model, with including the specific /Iy = 27T(__>,• 4 Dj)(dpi + dpj) x -rt-r-d-j 8(A + -Pj) dpi 4- dpj 4 2^jj Cij(dPi 4 dPJ) (13) _Hi = W + « ) a 5 <14) 9ij ~ _d-AT dpi ( } A, = ^ (16) fractal dimension (Dpgf) of the four shapes in the coagulation rate equation between each particle as the shape factor, the influence of the shape of the soot is furthermore considered. According to the de Gennes' method [16], the diffusion coefficient of an aggregate (D) is expressed by Eq. (17) and (18) using the particle's diffusion coefficient (_?-) and the specific scales (s). D = D0st (17) 7 = ~ (18) uf Df is the fractal dimension and is assumed to be 1.78, which is the same as in the case of the three-dimensional diffusion limited aggregation. In this study, Df\s replaced to Dporjar\d s is defined as ^ , which is the parameter used to classify the aggregates into four kinds shapes. The 57 chemical species and 314 elementary equations are considered in the present model. Runge-Kutta method was used to solve the simultaneous ordinary differential equations. The temperature profile in the tube was approximated in the sixth order equation and taken into consideration. Results and Discussion The temperature and calculated concentration profiles of benzene and hydrogen under the residence time of 0.5 sec are shown in Fig. 4. The reaction kinetics model predicts the disappearance of benzene and the production of hydrogen at the beginning of the uniform temperature region. Variations of soot volume with residence time are shown in Fig. 5. The present model well predicts the soot volume change in any residence time. Fig. 6. shows the existence ratio of four kinds of the shapes at the residence time 0.5sec. Each calculated ratio is in good agreement with the experimental those, respectively. We |
