6.2 Numerical applications and validation
6.2.2 Complex configurations
6.2.2.4 Flame/vortex interaction
6.2. Numerical applications and validation
p=patm
O2/N2
O2/N2 CH4/N2
Figure 6.13: Geometrical configuration of the 2-D coflow Methane/air flame.
Parameter central inlet left/right inlets
T[K] 950 950
u0[m/s] 0.8 0.5
YCH4 0.1 0
YO2 0 0.224
YH2O 0 0
YCO2 0 0
YCO 0 0
YN2 0.9 0.776
Table 6.5: 2-D Methane/air coflow burner boundary conditions data.
velocity profiles near the top outlet. These discrepancies can be attributed, at least partly, to the different treatment of outlet boundaries in the LB solver and Fluent simulations.
thick-6.2. Numerical applications and validation
0.0172
0
YCO YCO2
0.1
0
YO2
0.224
0
u[m/s]
1.3
0.487
T[K]
2220
950
Figure 6.14: Steady-state species, velocity and temperature fields for the Methane/air coflow diffusion flame.
0 2 4 6 8
0.8 0.9 1 1.1 1.2 1.3
0 2 4 6 8
0 0.05 0.1 0.15
H2O O2
CH4
CO
Figure 6.15: (left) velocity and (right) species mass fraction profiles along the vertical cen-terline as obtained from (red plain line) Fluent and (black symbols) the LB solver.
is smaller than the flame front speed, consuming the fresh gas before it can form a pocket,
• Corrugated flamelet: As for the previous regime, the flow structure is bigger than the flame thickness. Here the flow structure is able to stretch the flame front and eventually create small pockets with sizes comparable to that of the fluid structure,
• Thin reaction zones: The flow structure is smaller than or comparable to the flame
thickness, however it is still bigger than the thickness of the inner layer (typically one-tenth of the flame thickness). While not able to penetrate into the inner layer, the flow structure enhances energy and mass transfer in the pre-heat zone,
• Broken reaction zone: Mixing due to small turbulent structure becomes faster than the chemistry, and can lead to local extinction.
Indeed, it has been observed that flow structure size (as compared to the flame thickness) and energy (or velocity) are two parameters determining the effect of the flow structure on the flame front. To mimic flow/flame interactions, a number of studies have focused
-0.1 1 10 102 103 104
-0.1 1 10 102 103
broken reaction zone
thin reaction zones
corrugated flamelets wrinkled flamelets laminar
flame
Figure 6.16: Regime diagram for premixed turbulent combustion [10].
on direct numerical simulations of the interaction between a pair of vortices and a flame front [219, 220]. As such, following those studies, the interaction of a Methane/air premixed flame front with two counter-rotating Lamb-Oseen vortices [221] is considered in a 2-D configuration. The overall configuration is illustrated in Fig. 6.17. Such a configuration, among other sources, was also studied with details in [222, 223, 2]. The simulations consist of a rectangular domain of size Lx×Ly, with the flame front initially placed at x = Lx/2.
A fresh gas mixture at equivalence ratio of 0.7 and temperature of 800K fills the left-hand side of the domain while the right-hand side is filled with burnt gas. Two counter-rotating Lamb-Oseen vortices of radius rc are then placed at a horizontal distance d from the flame front. While top and bottom boundaries are periodic, at the inlet (on the left) constant temperature, composition and flow-rates are enforced. The outlet (on the left) is modeled using zero-gradient boundary conditions. The Lamb-Oseen vortices are initialized as:
Γ
−
r2
Figure 6.17: Overall configuration of the 2-D premixed flame/vortex interaction case.
where Γ is the vortex strength (also called vortex circulation) expressed in m2/s and r the radial distance from the vortex center. For all cases studied here, the BFER chemical scheme is used to model the flame [218],δx is set to 4.26×10−5m andδt= 6×10−8s. Furthermore, Lx is set to 42.6mm andLy to 17.04mm. The species and temperature profiles are initialized using the solution of a 1-D freely-propagating flame at φ = 0.7. The vortices are then initialized at a distance of 8rc from the flame front.
Twelve different combinations of vortex strength and core radius are considered here.
They are listed in Table 6.6. Before going into simulation of the different configurations and case Γ[m2/s] rc[m] umax[m/s]
1 6.71×10−2 3.43×10−4 22.27 2 3.355×10−2 3.43×10−4 11.14 3 1.6775×10−2 3.43×10−4 5.57 4 8.3875×10−3 3.43×10−4 2.78 5 6.71×10−2 1.715×10−4 44.54 6 3.355×10−2 1.715×10−4 22.27 7 1.6775×10−2 1.715×10−4 11.14 8 8.3875×10−3 1.715×10−4 5.57 9 6.71×10−2 8.575×10−5 89.08 10 3.355×10−2 8.575×10−5 44.54 11 1.6775×10−2 8.575×10−5 22.27 12 8.3875×10−3 8.575×10−5 11.14
Table 6.6: Characteristics of considered configurations for the vortex/flame interaction study.
sets of parameters, a first simulation (corresponding to case number 1) was performed. The
resulting iso-temperature contours at different stages of the interaction were then extracted and compared to simulations reported in [2], performed with AVBP. Given that there were minor differences between the present study and that reported in [2], such as initial distance between the vortex pair and flame front, the comparison is only intended as a qualitative validation of the solver. Given that the study presented here does not make use of grid refinement, resolving the flame front and using the same domain size as that in [2] would have been time-consuming. Temperature fields at three stages of the pocket formation process as obtained from LB simulations and results from [2] are shown in Fig. 6.18. A good agreement, in terms of pocket size and shape, can be observed here. The different stages
Figure 6.18: Snapshots of iso-temperature contours (from 1000 to 2000K withδT = 200K) at three stages of the pocket formation process as obtained (bottom halves) from LB simulations and (top halves) from [2] using AVBP.
of the pocket formation process are further illustrated in Fig. 6.19 via snapshots of the fuel mass fraction field at four different times. In the first three snapshots, the flame is stretched around the pair of vortices. Given that the rotation velocity of the vortices is larger than the flame speed they take a pocket of fresh gas into the burnt gas area. After entering the burnt gas area, as the vortices move, the pocket of fresh gas gets smaller due to consumption by the flame around the vortices. Finally, approximately 0.3ms after the initial interaction between the flame and the vortices, the pocket of fresh air disappears.
The simulations were then repeated for all sets of parameters in Table 6.6. The interac-tions between the vortices and flame front are illustrated in Fig. 6.20 through the temperature fields. Having in mind that at the fresh gas temperature and equivalence ratio considered here the flame front speed isSL = 1.79m/s while the thickness isδF = 3.43×10−4m, it can be seen that for the largest vortices, atumax = 2.78m/s, the flame propagation dominates over the convective flux induced by the vortex and the fresh gas pocket is not formed. Although the initial maximal velocity in the vortex is larger than the flame front speed, one must also take into account dissipative losses before the vortex pair gets to the flame front. At higher velocities, it can be observed that the vortex pair is able to form a pocket of fresh gas in the burnt gas region. Looking at simulations with smaller vortices, it can also be seen that the size of the pocket, as expected, is proportional to the size of the vortices. Furthermore, as the size of the perturbation gets smaller, and closer to the flame thickness, δ = 3.43×10−4m,
Figure 6.19: Fuel mass fraction fields at three different times, i.e. (from left to right): 0, 0.08, 0.16, 0.24 and 0.32ms for case 1.
Simulations performed in this section showed that the LB-based numerical schemes con-sidered in the present manuscript can be used to model low Mach number combustion in multi-dimensional configurations, for both premixed and diffusion flames, and can correctly capture flame/flow interaction.