OCR Text |
Show cm3/mole/s. After convergence was achieved with the single-step reaction, another attempt was made to proceed to Bilger's detailed mechanism using the resulting converged solution fields for temperature, carbon dioxide and water, again without success. It seems that reasonable starting solution fields for C O and H 2 is also needed to initiate the detailed mechanism. In an attempt to obtain these additional species concentration fields for the initiation of the detailed chemistry mechanism, the single-step solution was used as a starting solution for the composition dependent 4- step mechanism of Jones and Lindstedt (1988). CH4 CH4 H2 CO + |o2 + H20 + \o2 + H20 => => <==> <==> CO + 2H2 CO + 3H2 H20 C02 + H2 Using this mechanism involved some additional coding of the composition dependent reactions (See Jones and Lindstedt, 1988). Note that two of these reactions proceed in the forward direction only. The resulting solution for the 4-step mechanism was then used successfully as an initial solution for the detailed 17 species/58 step mechanism of Bilger. The solution was obtained using a multi-level grid procedure whereby iterations were performed on a coarser subset of the grid (employing every other grid point) and then interpolating the results onto the finer grid. Iterations would then proceed on the finer grid, applying 3-sweeps with the solution-adaptive grid algorithm every 10 iterations of the implicit solver. All the components of the dependent variable vector of Eq. (11) were considered as adaptation variables (0's of Eq. 27 with a = 1,0 = 0). Discussion The predicted centerline temperature is compared with the experiments of Mitchell (1975) in Fig. 2. The experimental flame height of 6 cm (location of maxim u m temperature) is overpredicted by the calculations. The calculated value is approximately 9 cm. This disagreement can possibly be attributed to the constant Schmidt and Prandtl number assumptions. The computational grid is shown in Fig. 3. The left-half of the figure is the initial grid and the right-half is the final solution-adapted computational grid. Grid clustering regions mark locations of high gradients of the dependent variables. Multiple grid clustering is observed due to the consideration of all the dependent variables in the weighting function selection procedure. Profiles of axial temperature distribution are compared with the experimental measurements of Mitchell (1975) at 3 different axial locations in Fig. 4. Results compare well at z = 1.2 cm. The radial location of peak temperature is overpredicted at z = 2.4 and z = 5 cm. Thus the flame shape is wider at these locations compared with the experiments, due probably to the overprediction of the flame height. Computed axial velocity profiles are compared with the experiments in Fig 5. Again, results compare very well at z = 1.2 c m near the base of the flame but the axial velocity is overpredicted slightly at the other locations where the temperature is overpredicted. This overprediction at z = 2.4 and 5 c m was also observed in the results of X u et al. (1993). Figures 6-9 show computed profiles of all major species molar concentration compared with the experiments. In general, agreement is good where the temperature is predicted accurately. The rate of consumption of methane in the axial direction is not predicted well as shown in the centerline profiles of Fig. 9. In addition to this, the increase in oxygen concentration along the centerline is not well predicted. These two factors, probably attributed to the use of the constant Schmidt number, may be the root cause of the overprediction in the flame height. The presence of fuel farther away from the inlet as predicted in the computations would explain the overprediction in the flame height. One peculiarity in the results is the presence of water and carbon dioxide near the walls at z = 2.4, even more so at z = 5. This can be seen in the plots of Figs. 7&8 and in the contour plot of C O o of Fig. 11. Conclusions A solution-adaptive, preconditioned Navier-Stokes procedure for reacting flows is presented. The technique was used to compute the flow and chemistry in a diffusion flame using a 58-step reaction mechanism. Computational results agree with the experimental data quite well despite the overprediction in the overall flame height. Better agreement could perhaps be achieved using a more accurate model of the species and thermal transport coefficients. present computations experiment (Mitchell, 1975) 10 15 1m] Fig. 2: Centerline temperature distribution. 7 |