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Show also that quantitative comparison is also good. The maximum heat release predicted by our calculations reachs the value of 2.7 108 W / m 3 against 2.5 108 for experimental measurements of Maistret [10]. Case 3 : Cylindrical rod stabilizer This case deals with a horizontal two-dimensional V-flame. The combustion chamber is quite similar to the one described in case 2. The height, depth and lenght of the combustion chamber are respectively 50, 80 and 330 m m (Figure 7). The V-flame is stabilized by a small cylindrical rod of 3 m m diameter (blockage ratio of 6 %) which gives a short hot gas recirculating zone and permits to reveal phenomena due to the turbulent combustion. The computational grid used in the present calculations has 80 x 30 nodes in the longitudinal and transversal directions, respectively. The domain is filled with a propane-air mixture with an equivalence ratio of 0.7. The inlet velocity V 0 is equal to 8 m/s and the fresh gas temperature T 0 is 300 K. Figure 8 is qualitative comparison between flame surface density fields (Figure 8.a) from the present work and the C H emission field (Figure 8.b) from Maistret [10]. The V-shaped flame is well predicted and flame propagation compares well with measurements. Compared to case 2, the principal interest of this configuration is an easier measurement of the V-flame angle which is not much influenced by the small hot gas recirculating zone. The half-angle measured experimentally by Maistret [10] is 5 degrees against 6 degrees for our calculations. Case 4 : Backward-facing-step This configuration preserves the essential features of premixed combustion with stabilization achieved by recirculation of hot products and is at the same time a simpler case to observe and model. The height and length of the combustion chamber used for this case (Figure 9) are respectively 100 and 300 m m . The computational grid used in the present calculations has 60 x 30 nodes in the longitudinal and transversal directions, respectively. The domain is filled with a propane-air mixture with an equivalence ratio of 0.7. The inlet velocity V 0 is equal to 20 m/s and the fresh gas temperature To is 300 K. The entrance Reynolds number ReH = ^r~ is based on step height H (50 m m ) , average inlet velocity Vo and kinematic viscosity v. The value of ReH is equal to 66 103. Figure lO.a shows the calculated flame surface density field. The reaction zone between the main fresh mixture flow and the hot gas recirculating zone (behind the step) is clearly seen. The model predicts well the recirculation zone behind the step and gives also and idea about the width of the reactive layer and its growth. Schlieren visualizations (Figures lO.b and lO.c) of Pitz and Daily [16], show that the reaction takes place largely in the two-dimensional eddies which are not confined to the velocity gradient region. The reattachement length, defined as the point in the separation region where there is no net flow reversal, corresponds in the present case to -g- = 4.9. This value of the reattachement length explains the curvature of the reaction zone at the combustor exit. Case 5 : Single injector furnace This case corresponds to a sudden-expansion or "dump" combustor geometry. The height and length of the combustion chamber (Figure 11) are respectively 100 and 220 m m . The computational grid used in the present calculations has 75 x 25 nodes in the longitudinal and transversal directions, respectively. The domain is filled with a propane-air mixture with an equivalence ratio of 0.75. The inlet velocity Vo is equal to 100 m/s and the fresh gas temperature T 0 is 300 K. Flame surface density field is displayed in Figure 12. The interesting observation in this figure is that concerning the immediate region following the exit injector in which the predicted flame surface presents the classical cone shape where fuel is not consummed yet. Note that in this configuration, large hot gas recirculating zones are observed in both sides of the predicted reaction zone. The influence of the presence of other injectors in the same furnace will be presented in the next case. Case 6 : Multi-injector furnace The geometry studied in this case is a two-dimensional furnace equipped with five slots feeded with propane-air mixture. The height and length of the combustion chamber (Figure 13) are respectively 100 and 220 m m . The computational grid used in the present calculations has 75 x 55 nodes in the longitudinal and transversal directions, 6 |
