combustion model
In the previous topics, the greater discrepancies of results between the simulation and the experiment still exist in low opposed flow regime.
This may be attributed to the 3D effect is not included in the combustion model. Therefore, this topic utilizes the unsteady three-dimensional combustion model to study the influence of 3D effect on the flame behavior over a finite-length PMMA slab. The present three-dimensional unsteady combustion model is basically developed from the original two-dimensional one of part 1 of present work. In this problem, the governing equations and the assumptions are basically the same as these given in the previous description of chapter 2, except that the model is
developed from two-dimension to three-dimension. Therefore, the mathematical model and the assumptions are not represented here for brevity. The non-dimensional gas and solid governing equations are listed in Table 7. The discrepancies between the part 1 of present dissertation and present work are listed in the Table 8.
Figure 3.3.1 presents the configuration of three-dimensional ignition over a vertically oriented PMMA slab in a mixed convective environment.
The dimensions of wind tunnel and the solid fuel plates used in the present simulation are all the same as those of Pan’s experiment (1999).
Computations are carried out using a non-uniform mesh distribution as shown in the figure 3.3.2. The tests of the independence of the grid-size were conducted in advance and the results are shown in Table 9.
According to the grid-independence test, a non-dimensional time step of Δt
= 10 (equivalent to a real time of 0.02 s) and non-uniform grid dimensions of 290×95×50 were found to optimize the balance among resolution, computational time and memory space requirements. The prior numerous studies, such as those of Mell and Kashiwagi (2000), Nakamura et al.
(2002) and Shih and T’ien (2003), indicated that the 3D effect is dominated by the flow velocity. Therefore, the parametric study herein is conducted by changing the opposed flow velocity and its range is the same as used in the experiment of Pan (1999), to enable the results to be compared fairly with the prior predictions of Wu et al. (2003) and the part 1 of present dissertation. Remind that the solid fuel in present study is assumed to be homogeneous that its compositions are uniform and its thickness is remained constant by assuming the flame spreads relatively fast enough that the fuel surface near the flame base remains approximately flat.
Notably, both the computation domain utilized in these combustion models mentioned above are two-dimensional, whereas the one utilized in the present model is three-dimensional. The ambient oxygen concentration in
the present model is fixed at 0.233.
Figure 3.3.3 displays the three-dimensional flame spread over the solid fuel surface. The left hand side is the camera image observed by the Pan’s experiment (1999) and the right hand side demonstrates the simulated result in the present study. The opposed flow velocity and temperature are 40cm/s and 313K and the solid fuel thickness is 0.82cm.
The simulated flame profile is highly similar to the one of experiment. It can be found that both the flame tails of experimental observation and the simulation contract over the solid fuel surface. This is because the asbestos plates locates behind the origin ( ) and it does not continuously provide the fuel vapor to form the flammable mixture. This factor increases the formation time of flammable mixture and decreases the intensity of chemical reaction as well. Hence, the overall flame temperature is reduced, declining the downstream flame size. However, the flame tail of Wu et al. (2003) still grows (not shown here) because the solid fuel expends upstream and downstream infinite and the flame spreads in an open atmosphere. Furthermore, in this figure, it can be seem that the opposed flow is confined by the tunnel walls and the flame is pushed by the flow toward the solid fuel surface slightly.
Figure 3.3.4 displays the time history of the three-dimensional flame profiles and the flow velocity vector distributions from ignition to subsequent flame spread for the opposed flow velocity of 40cm/s and temperature of 313K and the solid fuel thickness of 0.82cm. The time history of ignition and subsequent flame spread is similar to that mentioned in the part 1 of present dissertation. The solid fuel receives the external heat flux to raise its temperature gradually and some part of the heat received by the solid fuel also heats the gas phase simultaneously, as shown by figure 3.3.4(a) and figure 3.3.4(b). The flame is ignited as gas
phase temperature raise high enough, resulting the drastic chemical reaction and thermal expansion, as demonstrated in figure 3.3.4(c).
Thereafter, the flame starts to spread downward and spreads with steady rate after several seconds, as shown in figure 3.3.4(d).
Figure 3.3.5 displays the ignition delay time as a function of opposed flow velocity for 2D and 3D problems, respectively. The opposed flow temperature and solid fuel thickness are fixed at 313K and 0.82cm. As mentioned previously, the ignition delay time increases with an increase of opposed flow velocity. However, in this figure, it can be found that the ignition delay times of 3D problem are greater than ones of 2D problem and the discrepancies of ignition delay time between the 2D and 3D problems are decrease with an increase of opposed flow velocity. The difference of ignition delay time between 2D and 3D problems for opposed flow velocity of 40cm/s is 0.64s, whereas the one for opposed flow velocity of 100cm/s is 0.11s. In the lower opposed flow regime of 3D problem, the fuel vapor is carried downstream by the convection but some of the fuel vapor is diffused to the lateral sides of wind tunnel, hindering the accumulation of fuel vapor near the solid fuel surface, increasing the formation time of the flammable mixture, resulting the greater difference of ignition delay time between the 2D and 3D problems. However, in the higher opposed flow regime of 3D problem, the fuel vapor transferred to the lateral sides of wind tunnel by the diffusion becomes difficult. In other words, most of produced fuel vapor is carried downstream by convection. This phenomenon is similar to that of 2D problem.
Therefore, the influence of 3D effect on ignition delay time is reduced when the flame is ignited under the high speed flow regime.
Figure 3.3.6 presents the steady flame spread rate versus the opposed flow velocity at a fixed opposed flow temperature of 313K and a solid fuel thickness of 0.82 cm. The steady flame spread rate herein is determined
by the slope of a best fit line that passes through the pyrolysis front position which is defined as the first upstream position of ρs =0.99. The solid, dash and dash-dot lines in this figure indicate the simulated results of the present work, the part 1 of present dissertation and Wu et al. (2003), respectively. There are three results in each line. The circular symbols separately represent the data measured by Pan (1999). Notably, the conditions such as the opposed flow velocity and temperature and the solid fuel thickness used in these computations are all the same as those used in the experiment. This figure indicates that all the flame spread rates of experimental measurement and simulated results fall as the opposed flow velocity increases. Comparing with the results between the experiment and predictions in the figure 3.3.6, the results of present work are closer to those of experiment, especially in lower speed flow regime. In the investigation of part 1 of present dissertation, the enclosure effect and both gas and solid phase radiations are added to the combustion model. The enclosure effect confines the flow more parallel to the solid fuel surface and enhances the oxygen supply for combustion, increasing the flame spread rate. Additionally, the radiation effect plays a role of heat loss from the solid fuel and reduces the pyrolysis intensity, decreasing the flame spread rate. These two effects are competing with each other.
Obviously, the influence of enclosure on the flame spread rate overcomes the one of radiation in this flow speed regime. Hence, the flame spread rate of part 1 of present dissertation increases compared with the one of Wu et al. (2003).
In the present work, the 3D effect is considered in the combustion model. The 3D effect includes two mechanisms, such as the oxygen diffusion from the side walls of tunnel to the flame and the heat loss from the flame to the side walls of tunnel. The former one enhances the chemical reaction and the flame intensity as well, whereas the latter one
results in a lower flame temperature and reduces the corresponding spread rate. Figure 3.3.7 displays the temperature contours of gas phase and flow velocity vector distributions at a fixed opposed flow velocity of 40cm/s and temperature of 313K and solid fuel thickness of 0.82cm for 2D and 3D problems, respectively. In this figure, it can be seem that the flame profiles are almost the same between the 2D and 3D problems but the flame front for 3D problem is shift back to downstream slightly due to the slower flame spread rate, as shown in figure 3.3.6. Figures 3.3.8 illustrate the flame characteristics on X-Z plane for opposed flow velocity of 40cm/s and temperature of 313K and solid fuel thickness of 0.82cm at t = 25s.
Figures 3.3.9 and 3.3.10 separately display the flame characteristics on Y-Z plane for opposed flow velocity of 40cm/s and 100cm/s at t = 25s and the opposed flow temperature and solid fuel thickness are fixed at 313K and 0.82cm. The right half displays the gas phase temperature contours and flow velocity vector distributions, whereas the left half presents the fuel and oxidizer mass fractions, respectively. In the figure 3.3.8, it can be seem that the solid fuel pyrolyze the fuel vapor mixing the air to form the flammable mixture in the flame front region. The ambient oxygen concentration is fixed at 0.233 in the present study and the oxygen supply rate from side to the flame center by diffusion will be decreased with an increase of flow convective velocity, as shown in figures 3.3.9 and 3.3.10.
Comparing with the magnitude of oxygen supply by convection, the oxygen side diffusion can be neglected due to the flame spread in high speed flow regime. Therefore, the influence of oxygen side diffusion on the flame spread rate is insignificant in the present study. This phenomenon mentioned above has been confirmed by the prior studies of Mell and Kashiwagi (2000), and Shih and T’ien (2003). In the other hand, the cold tunnel walls conduct heat away from the flame which introduces the heat loss. In these figures, it can be seem that the higher gas phase
temperature contours are clustered at the flame leading edge and then drop gradually from the flame center to the side walls. Moreover, it can also be pointed out that the influences of lateral walls are more significant than that of the top wall. For example, in the figure 3.3.9, the distance (0.85cm) from the origin to the joint of the isothermal of 1.17 on the z axis is shorter than that (1.02cm) on the y axis. It indicates that the heat loss from the flame to the lateral walls of wind tunnel is greater than that to the top wall of wind tunnel because the distance (5cm) between the origin and lateral wall of wind tunnel is shorter than one (10cm) between the origin and top wall of wind tunnel. Summarized the factors discussed above, the overall 3D effect on the flame spread behavior in this work is to decrease the flame spread rate and it can be seem that the flame spread rate of present work compared with the results of part 1 of present dissertation is slightly reduced from the figure 3.3.6. Hence, the flame spread rates predicted in the present work are closer to the ones measured by the experiment of Pan (1999), especially in lower speed flow regime.
Chapter 4 Conclusions
This work numerically investigates the flame ignition and subsequent flame spread characteristics over a finite-length PMMA slab under mixed convection conditions in a wind tunnel using an unsteady combustion model. The modified combustion model of present study, included finite-length solid fuel, enclosure effect, gas and solid phase radiations and 3D effect, is expected to be more completeness and accuracy to predict the ignition delay time and flame spread rate. The previous studies mostly are addressed either thermally thick or thin materials, whereas the present work is emphasized on intermediate-thickness materials.
The first part of this study utilizes an unsteady combustion model, with opposed flow velocity and temperature and solid fuel thickness as parameters, to investigate the effects of these factors on the ignition delay and the subsequent downward flame spread over a PMMA slab of finite length under mixed convection conditions in a two-dimensional wind tunnel. The results obtained by simulation herein are compared with the corresponding predictions and experimental measurements. The ignition delay time increases as the opposed flow velocity or the solid fuel thickness increases and the flow temperature falls. Additionally, the steady flame spread rate increases as the opposed flow velocity or the solid fuel thickness declines and the flow temperature increases. The gas phase radiation effect can be neglected because the flame spreads in the high speed flow regime. On the other hand, the solid phase radiation affects the ignition delay time and flame spread rate significantly. It increases the ignition delay time and reduces the flame spread rate. Moreover, the
downstream flame size grows over an infinite length fuel plate, whereas that herein contracts slightly over a finite length fuel plate, resulting in the lower flame spread rate. The factors, such as radiation and finite fuel length mentioned above, reduce the flame spread rate and thus mitigate the discrepancies between the predicted results of present work and the corresponding experimental measurements. However, the discrepancies remained in the low flow velocity regime, because the three-dimensional effect is neglected in the present two-dimensional model. Also, the enclosure effect is insignificant in the high flow velocity regime and in the two-dimensional model.
The second part of this study utilizes an unsteady combustion model with variable opposed flow velocity as parameters to investigate the flame ignition and subsequent downward flame spread over a finite-length PMMA slab with mixed convection conditions in a two-dimensional wind tunnel. The gas and solid phase temperatures, preheat length of solid fuel and the heat flux received by the solid fuel are used to examine flame ignition and spread characteristics. The numerical results show that the ignition delay time increases with the opposed flow velocity and it increases when radiation is considered. Additionally, the flame spread behaviors can be divided into two regimes based on the opposed flow velocity: one is the oxygen transport control regime for u∞ <32cm/s and the other one is the chemical kinetic control regime u∞ >32cm/s. The steady flame spread rate firstly increases and then declines as the opposed flow velocity is increased continuously. Furthermore, the results demonstrate that radiation weakens the flame and always reduces the corresponding spread rate. When compared with the radiation heat loss from the solid to the ambient, the gas phase radiation feedback is insignificant and can be neglected. This work also discusses the influences of the opposed flow temperature and solid fuel thickness on the
flame spread behavior. The predictions indicate that the hotter opposed flow temperature facilitates ignition and enhances the flame strength as defined by an increase in the corresponding spread rate. The ignition delay time becomes longer and the flame spread rate is reduced as the solid fuel thickness is increased. The comparison of ignition delay time and flame spread rate between several opposed flow velocities and temperatures demonstrates that the influence of the opposed flow temperature on the flame becomes inconspicuous as the opposed flow velocity is increased further. All of these results should be of assistance and guidance to the development of the models that seek to incorporate additional physical processes.
The third part of this study utilizes a three-dimensional unsteady combustion model with opposed flow velocity as parameters to investigate the influences of 3D effect on the ignition and subsequent downward flame spread over a finite-length PMMA slab under mixed convection conditions in the wind tunnel. The results obtained by simulation herein are compared with the corresponding experimental measurements of Pan (1999) and predictions of Wu et al. (2003) and the part 1 of present dissertation. The simulated flame profile in this part is similar to that observed by the experiment. The ignition delay time increases with an increase of opposed flow velocity. However, the ignition delay times of 3D problem are greater than ones of 2D problem and the discrepancies of ignition delay time between the 2D and 3D problems are decrease with an increase of opposed flow velocity. This is because the fuel vapor transferred to the lateral sides of wind tunnel by the diffusion becomes difficult when the flame is ignited under a high speed flow regime. The simulated results indicate that the flame spread rate decreases with an increase of opposed flow velocity. The flame is stretched by the high speed flow and most of the fuel vapors are carried downstream, reducing
the intensity of chemical reaction and the strength of flame as well.
Hence, the corresponding flame spread rate is decreased with opposed flow velocity. A comparison is made between the earlier experiment and simulations. The results indicate that the predicted values of present work are similar to the ones of experiment, especially in the lower speed flow regime. This is because the 3D effect is added in the present combustion model. The 3D effect has two mechanisms to influence the flame behaviors. One is the oxygen side diffusion and the other one is the heat losses to the side walls. The simulated results of present work demonstrate that the former effect influences the flame spread insignificant because the flame spreads under a high convective flow, whereas the latter one reduces the flame temperature slightly as well as the flame spread rate.
Therefore, the overall 3D effect on the flame behaviors in the present study is to reduce the spread rate of flame. Additionally, the simulated results show that the influence of lateral walls of wind tunnel are greater than that of top wall of wind tunnel due to the shorter distance between the flame and lateral walls of wind tunnel.
References
Aynai, M. B., Esfahani, J. A. and Mehrabian, R., Downward Flame Spread over PMMA Sheets in Quiescent Air: Experimental and Theoretical Studies, Fire
Safety Journal, 41, 164 (2006).
Bhattacharjee, S. and Grosshandler, W., Effect of Radiative Heat Transfer on Combustion Chamber Flows, Combustion and Flame, 77, 347 (1989)
Bhattacharjee, S. and Altenkirch, R. A., The Effect of Radiation on Flame Spread in a Quiescent, Microgravity Environment, Combustion and Flame, 84, 160 (1991).
Bhattacharjee, S., King, M., Takahashi, S., Nagumo, T. and Wakai, K., Downward Flame Spread over Poly(Methyl)Methacrylate, Proceedings of the
Bhattacharjee, S., King, M., Takahashi, S., Nagumo, T. and Wakai, K., Downward Flame Spread over Poly(Methyl)Methacrylate, Proceedings of the