The different flame structures and stabilization mechanisms discussed above can be ex- pressed in terms of two dimensionless parameters, U0/SR,0|st, and Da(=τres/τig,st). Here, Da represents the Damköhler number, SR,0|st and τig,st are the 1-D unstrained laminar flame speed and 0-D ignition delay of a stoichiometric n-heptane/air mixture at given T0, respectively. τres is the flow residence time within the domain, defined by Lz/U0. Figure 5.14 shows the regime diagram for n-heptane jet flame in the U0/SR,0|st − Da space. Several points are noted from the figure.
First,Damainly determines the location of thermal ignition zone relative toξstisoline.
Thus, lifted flames exhibit the MILD combustion mode at relatively-low Da, while they can be stabilized as a tetrabrachial edge flame at relatively-high Da. On the other hand, U0/SR,0|st is related to the axial position of the flamebase relative to ξst isoline.
Therefore, at the sameDa, lifted flames can exhibit either tribrachial edge flame or MILD combustion mode depending on U0/SR,0|st.
Second, there are two ‘Fail to autoignite’ regimes where an autoignition kernel fails to develop within the computational domain. The first one is where Da is less than its critical value, Dac, for which the flow residence time scale within the burner becomes less than the corresponding ignition delay time scale. The second one is where U0 is smaller than its critical value, Uc. If the flow rate of the fuel jet is too low, the mixture equivalence ratio within the mixing layer becomes too lean to autoignite. In such case, Da cannot be defined.
Third, the variation in U0 affects both Da and U0/SR,0|st. For instance, the increase of U0 contributes not only to the increase of U0/SR,0|st but also to the decrease of τres
inDa. Therefore, Da (U0/SR,0|st) decreases (increases) with the increase ofU0, which is delineated by the line with an arrow in Fig. 5.14. In the similar manner, the increase of T0 leads to the increase (decrease) of Da (U0/SR,0|st).
Based on the above, the results of the present study with four differentT0 ranges can be effectively illustrated by four different paths shown in Fig. 5.14.
• Path I (T0 = 1010 K):Da in this path is relatively-low, indicating that the ignition
Figure 5.14: A flame regime diagram for laminarn-heptane jet flame in theU0/SR,0|st−Da space.
delay atT0= 1010 K is long enough for the fuel and oxidizer to be well mixed before they approach the lifted flame. Thus, its HL becomes larger than those for high T0, and consequently, the lifted flame exhibits the MILD combustion characteristics within the whole range of U0. Since the flame front of the lifted flame is fuel-lean, the flame stabilization is highly affected by autoignition. OnceU0 decreases beyond Uc, any nozzle-attached or lifted flame cannot exist because the mixture is too lean to form even an ignition kernel. Note that an ignition kernel also fails to be formed at higherU0when the flow residence time within the burner is less than the ignition delay.
• Path II (T0 = 1025 K): A distinct transition from the tribrachial edge flame to the MILD combustion mode occurs, featuring a significant variation in HL. At relatively-low U0, the lifted flame is stabilized as a tribrachial edge flame with negligible temperature increase upstream of the flamebase. At relatively-high U0, however, thermal ignition process occurs further downstream of zξst such that the MILD combustion mode appears. The contribution of autoignition to the flame stabilization gradually increases withU0.
• Path III (T0 = 1050 K): Since the ignition delay is relatively short, a partially- premixed edge flame rather than a MILD combustion mode appears near zξst at
relatively-high U0, which leads to a smooth variation in HL at the transition from the tribrachial edge flame to the partially-premixed edge flame.
• Path IV (T0 = 1080 K): The ignition delay is short enough for the fuel/air mixture to autoignite even near the fuel/oxidizer nozzle outlets. When U0 is large enough to lift off an autoignited flame, another lean flame branch develops upstream of the main tribrachial edge flame. Consequently, the lifted flame is stabilized as a tetrabrachial edge flame. The lifted flame shows a transition to a turbulent flame at higher U0, but this is beyond the scope of this thesis and is not discussed.
It is worth mentioning that the regime diagram in Fig. 5.14 is valid only for highly- diluted n-heptane or iso-octane laminar jet flames under autoignitive condition because it can significantly be changed depending on the fuel characteristics such as fuel type and fuel mole fraction in the fuel jet. For instance, lifted jet flames with ScF < 1 (e.g., methane, ethane, and ethylene jet flames) do not exist in the form of a tribrachial edge flame without the assistance of autoignition [23], and thus, cannot have the ‘tri- brachial’ edge flame regime in their regime diagram. On the contrary, for autoignited lifted methane/hydrogen or DME jet flames, their flame structure changes from ‘MILD’
to ‘tetrabrachial’ edge flame with increasing U0 under specific conditions, leading to a decreasing liftoff height trend due to the differential diffusion effect of H2 [7, 65, 96, 110].
Therefore, their flame stabilization characteristics should be distinguished from those of n-heptane jet flames in Fig. 5.14. It is also of importance to note that the ‘MILD’ and
‘partially-premixed’ edge flame regimes in Fig. 5.14 would readily disappear with the increase of XF,0 because the lifted flames with relatively-large XF,0 are strong enough to keep attaching to ξst isoline even at high U0.
Chapter 6
Flame stabilization of turbulent
lifted hydrogen jet flames in heated
coflows near the autoignition limit
The objective of the present study is to investigate the ignition dynamics and flame stabilization characteristics of turbulent lifted hydrogen jet flames in heated coflowing air near the autoignition limit by performing 3-D DNS at several coflow air temperatures.
Both instantaneous and time-averaged flame/flow characteristics are examined and the ignition characteristics upstream of turbulent lifted jet flames are investigated by per- forming the displacement speed and combustion mode analyses [34, 112]. Furthermore, we examine the effect of mixing between the cold fuel and heated coflow air by rolled-up vortices in the shear layer on the ignition kernel development in the near field of the jet.
6.1 Stabilization of turbulent lifted flames
6.1.1 0-D ignition characteristics
Prior to discussing the details of the turbulent lifted H2 jet flames, we first examine the fundamental thermochemical characteristics of the H2/air mixture. Figure 6.1 shows the 0-D ignition delay, τig,0D, of the stoichiometric H2/air mixture at atmospheric pressure as a function of temperature, T, with the initial fuel mole fraction, XF,0, of 0.65. As shown in Fig. 6.1, τig,0D spans several orders of magnitude in the T space, and the variation in τig,0D shows the steepest slope at T ≈ 930 K. Moreover, considering that the coflow residence time within the present 3-D DNS domain, τc, is 15 ms (see the horizontal line in Fig. 6.1), T of 930 K is approximated as the temperature near the autoignition limit.
Note that in the present study, ‘autoignition limit’ refers to the minimum temperature at which H2/air mixture can autoignite within the 3-D domain. In this context, T of 950 K slightly exceeds the autoignition limit, and hence, we adopt Case H as the baseline case for the present study. Note thatτig,0Dfor T = 750 and 850 K are orders of magnitude higher than τc such that autoignition is not expected to occur for Cases L and M. Therefore, both cases represent turbulent lifted jet flames under non-autoignitive condition. On the other hand, it has been demonstrated that autoignition plays an important role in the flame stabilization of the lifted flame with Tc = 1100 K (Case Ig) [34]. Thus, Case Ig serves as a reference case for the stabilization of turbulent lifted flames assisted by
T [K]
τig,0D [ms]
750 800 850 900 950 1000 1050 1100 10-1
100 101 102 103 104 105
φ = 1 X = 0.65F,0
τc = 15 ms
Figure 6.1: Variation in 0-D ignition delay, τig,0D, of the stoichiometric H2/air mixture as a function of temperature with a fuel mole fraction,XF,0, of 0.65.
autoignition.
Since Cases H and Ig are under autoignitive conditions, their thermochemical con- ditions at the inlet are further examined. Figure 6.2 shows the profiles of τig,0D at the inlet stream for both cases. Note that both temperature and mixture composition are stratified at the inlet such that τig,0D is a function of T and ξ. Then, the variation in τig,0D, dτig,0D, can be expressed by:
dτig,0D(T, ξ) = ∂τig,0D
∂T
ξ
dT +∂τig,0D
∂ξ
T
dξ, (6.1)
where T and ξ are temperature and mixture fraction, respectively, of the local mixture.
The first and second terms in the right hand side of Eq. 6.1 denote the variation in τig,0D caused by the change of temperature and mixture composition, respectively [113].
Therefore, we can evaluate the sensitivity of dτig,0D to T and ξ by comparing the two terms as shown in Fig. 6.2. Note that the terms in Eq. 6.1 are plotted as dlog10(τig,0D), (∂log10(τig,0D)/∂T)|ξdT, and (∂log10(τig,0D)/∂ξ)|Tdξ to consider the broad range of vari- ations. Several points are noted from Fig. 6.2.
First, the most reactive mixture fraction, ξMR, with the minimum τig,0D for both cases is much leaner than ξst of 0.199. Here, ξMR for Cases H and Ig is 0.03 and 0.05, respectively, and correspondingly, the shortest 0-D ignition delay, τMR, for both cases is 1.5 ms and 0.14 ms, respectively.
Second, τig,0D on a logarithmic scale exhibits a ‘U-shaped’ profile for both cases. At ξ < ξMR, the change ofτig,0D, expressed bydlog10(τig,0D), is mainly caused by the variation
ξ T [K]
τig,0D (ξ, T) [ms] dlog10(τig,0D)
0.0 0.1 0.2 0.3 0.4 0.5
675 730 785 840 895 950
100 101 102 103 104
-0.15 0.00 0.15
(a)
Case H
dlog10(τig,0D) (∂log10(τig,0D)/∂ξ)
Tdξ
ξdT (∂log10(τig,0D)/∂T)
ξ T [K]
τig,0D (ξ, T) [ms] dlog10(τig,0D)
0.0 0.1 0.2 0.3 0.4 0.5
750 820 890 960 1030 1100
10-1 100 101 102
-0.30 0.00
(b) 0.30
Case Ig
Figure 6.2: Profiles of τig,0D, dlog10(τig,0D), (∂log10(τig,0D)/∂T)|ξdT, and (∂log10(τig,0D)/∂ξ)|Tdξ as a function of ξ and T at the inlet stream for (a) Case H and (b) Case Ig. The vertical solid line represents ξMR. The values of dlog10(τig,0D), (∂log10(τig,0D)/∂T)|ξdT, and (∂log10(τig,0D)/∂ξ)|Tdξ are numerically evaluated by adopting the first-order finite difference approximation.
in ξ rather than by T (i.e. dlog10(τig,0D) ≈ (∂log10(τig,0D)/∂ξ)|Tdξ). This is simply because the mixture under this condition is near its lean flammability limit such that the ignition of the mixture is more sensitive to the ξ variation. At ξ > ξMR, on the other hand, the change ofτig,0D is mainly attributed to the decrease ofT whereas the variation inξ shows a negligible impact on τig,0D (i.e. dlog10(τig,0D)≈(∂log10(τig,0D)/∂T)|ξdT).
Third, for Case H τig,0D increases significantly from τMR even with a small decrease of T. This trend is clearly different from that for Case Ig, whereτig,0D exhibits the same order of magnitude with τMR over a wide range of T (or ξ). This is because for Case H, Tc is slightly greater than the autoignition limit such that the reactivity of the mixture significantly decreases with the decrease of T (see Fig. 6.1), implying that the ignition process of a turbulent lifted flame in heated coflows near the autoignition limit (i.e. Case H) can be highly sensitive to temperature variation by turbulent mixing. The effects of turbulent mixing on the ignition of a turbulent lifted jet flame will be discussed later.