Article

The Propagation Characteristics of Turbulent Expanding Flames

of Methane/Hydrogen Blending Gas
Haoran Zhao 1, * , Chunmiao Yuan 1 , Gang Li 1 and Fuchao Tian 2

1 Fire & Explosion Protection Laboratory, Northeastern University, Shenyang 110819, China;
yuanchunmiao@mail.neu.edu.cn (C.Y.); ligang@mail.neu.edu.cn (G.L.)
2 State Key Laboratory of Coal Mine Disaster Prevention and Control, China Coal Technology and Engineering
Group Shenyang Research Institute, Shenfu Demonstration Zone, Fushun 113122, China;
tianfuchao@cumt.edu.cn
* Correspondence: zhaohaoran@mail.neu.edu.cn

Abstract: In the present study, the effect of hydrogen addition on turbulent flame propagation
characteristics is investigated in a fan-stirred combustion chamber. The turbulent burning velocities
of methane/hydrogen mixture are determined over a wide range of hydrogen fractions, and four
classical unified scaling models (the Zimont model, Gulder model, Schmidt model, and Peters model)
are evaluated by the experimental data. The acceleration onset, cellular structure, and acceleration
exponent of turbulent expanding flames are determined, and an empirical model of turbulent flame
acceleration is proposed. The results indicate that turbulent burning velocity increases nonlinearly
with the hydrogen addition, which is similar to that of laminar burning velocity. Turbulent flame
acceleration weakens with the hydrogen addition, which is different from that of laminar flame
acceleration. Turbulent flame acceleration is dominated by turbulent stretch, and flame intrinsic
instability is negligible. Turbulent stretch reduces with hydrogen addition, because the interaction
duration between turbulent vortexes and flamelets is shortened. The relative data and conclusions
can provide useful reference for the model optimization and risk assessment of hydrogen-enriched
gas explosion.

Keywords: flame acceleration; turbulent burning velocity; unified scaling models; explosion;
hydrogen-enriched gas
Citation: Zhao, H.; Yuan, C.; Li, G.;
Tian, F. The Propagation
Characteristics of Turbulent
Expanding Flames of Methane/
Hydrogen Blending Gas. Energies 1. Introduction
2024, 17, 5997. https://doi.org/ Hydrogen-enriched fuels are expected to play a crucial role in reducing carbon emis-
10.3390/en17235997 sions and mitigating global warming in the 21st century. A methane/hydrogen mixture
Academic Editor: Toufik Boushaki
is thought to be typical hydrogen-enriched fuel that can be widely used in gas turbines,
internal combustion engines, and industrial burners [1,2]. However, adding hydrogen can
Received: 28 October 2024 evidently increase the risk of explosion, which can be further worsened by turbulent distur-
Revised: 22 November 2024 bance [3,4]. Flame propagation, as a key contributor to the explosion of methane/hydrogen
Accepted: 23 November 2024 mixtures, is usually examined in terms of turbulent burning velocity and flame acceler-
Published: 28 November 2024
ation. Previous studies [5–7] have indicated that turbulent burning velocity and flame
acceleration parameters (e.g., acceleration onset, fractal excess) are indispensable in the
explosion overpressure prediction model; otherwise, the explosion intensity would be
Copyright: © 2024 by the authors.
underestimated. Thus, a comprehensive understanding of the turbulent flame propagation
Licensee MDPI, Basel, Switzerland. characteristic of methane/hydrogen blending gas is essential for its safe utilization.
This article is an open access article The turbulent burning velocity of methane/hydrogen mixtures has been extensively
distributed under the terms and studied. Mandilas et al. [8] found that the hydrogen addition could promote the turbulent
conditions of the Creative Commons burning velocity of methane/hydrogen flames, which was attributed to the growth in lami-
Attribution (CC BY) license (https:// nar burning velocity, but this promotion was weakened with the increase in equivalence
creativecommons.org/licenses/by/ ratio. Muppala et al. [9] measured the turbulent burning velocity of lean methane/hydrogen
4.0/). flames, analyzed the effects of preferential diffusion, and validated the algebraic flame

Energies 2024, 17, 5997. https://doi.org/10.3390/en17235997 https://www.mdpi.com/journal/energies

Energies 2024, 17, 5997 2 of 14

surface wrinkling model. Fairweather et al. [10] measured the turbulent burning velocity
of methane/hydrogen flames over a wide range of turbulent intensities and equivalence
ratios. They found that this increase with hydrogen addition was evident under fuel-lean
conditions as well. Cai et al. [11] studied the self-similar propagation of methane/hydrogen
flames and explored the effects of Lewis number on turbulent burning velocity. In addition,
there have been other studies about the turbulent burning velocity of methane/hydrogen
flames [12–15]. Unlike laminar burning velocity, turbulent burning velocity is affected by
many factors, including chemical kinetics, flame intrinsic instability, and flame–turbulence
interaction. So far, it has been known that turbulent burning velocity can be increased by
hydrogen addition, usually due to increased laminar burning velocity and flame intrinsic
instability. Flame–turbulence interaction is determined by the timescale of chemical reac-
tion and turbulent disturbance, which can be characterized by dimensionless turbulent
intensity (u′ /SL ) or Karlovitz number (Ka). With the addition of hydrogen, the timescale of
chemical kinetics is shortened due to the high reactivity of hydrogen [16,17]; as a result, the
flame–turbulence interaction varies as well. Thus, the underlying mechanism of hydrogen
addition on turbulent burning velocity is still awaiting further clarification. Except for those,
a series of unified scaling models have been proposed in the past decades [18–21], to seek
a general correlation of turbulent burning velocity suitable for different conditions. The
unified scaling model of turbulent burning velocity is important for predicting explosion
overpressure, as it reflects the fuel consumption rate and heat release rate. Although these
models have been extensively validated by the experimental data of single-component
fuels, such as hydrogen [22], methane [23], and iso-octane [24], their performances on
multiple-component fuels are still waiting to be evaluated. It is unknown whether these
models can accurately estimate the effect of hydrogen addition.
Flame acceleration is another important aspect of turbulent flame propagation. Chaud-
huri et al. [25] derived that turbulent expanding flames followed a self-similar acceleration
law, and the dependence between flame propagation speed and flame radius could be
scaled as ST ∼ Pedt , where dt is a constant equal to approximately 0.5. Correspondingly, a
series of experimental data have been collected to validate this quantitative relationship,
although some scatters appeared between different conditions [26]. Yang et al. [27] re-
vealed that turbulent flame acceleration varied segmentally under different turbulent flame
regimes, and the dependence between flame propagation speed and flame radius could be
scaled as Pe0.30 , Pe0.43 , and Pe0.67 in the wrinkled flamelets, corrugated flamelets, and thin
reaction zone. Bauwens et al. [28] found that turbulent flame acceleration was continuously
intensified with increasing turbulence intensity. While the laminar flame acceleration of
hydrogen-enriched fuels is well understood thanks to the abundant experimental data
available to determine the underlying mechanisms [29–33], the turbulent flame acceleration
of these fuels is much less understood. Research findings are mainly concentrated on
the flame acceleration exponent dt , whereas the results of acceleration onset and cellular
morphology are rarely reported. The effect of hydrogen addition on turbulent flame ac-
celeration remains an open issue. The lack of experimental data and understanding of the
underlying mechanism has also prevented the development of a quantitative model for
turbulent flame acceleration.
The present study undertakes a comprehensive investigation into the turbulent flame
propagation of methane/hydrogen mixtures to clarify the effect of hydrogen addition
on turbulent flame propagation and explore related models. The turbulent burning ve-
locities of methane/hydrogen mixtures are determined over a wide range of hydrogen
fractions (0~100%H2 ), and the abilities of several unified scaling models are evaluated by
the experimental data of methane/hydrogen mixtures. The turbulent flame acceleration
onset, cellularity scale, and acceleration exponent of methane/hydrogen mixtures are de-
termined, and an empirical model of turbulent flame acceleration is proposed and verified.
Based on the experimental data and models, the dominant mechanism of turbulent flame
propagation is interpreted, which can provide useful reference for the safe utilization of
methane/hydrogen fuels.
Energies 2024, 17, x FOR PEER REVIEW 3 of 15

propagation is interpreted, which can provide useful reference for the safe utilization of
Energies 2024, 17, 5997 methane/hydrogen fuels. 3 of 14

2. Methodology
2. Methodology
2.1. Experimental Setup
2.1. Turbulent
Experimental Setup
flame propagation experiments of methane/hydrogen mixtures are con-
ductedTurbulent flame propagation
in the turbulent combustion experiments
chamber of Xi’an of methane/hydrogen
Jiaotong University. mixtures are con-
The schematic
ducted in theof
configuration turbulent combustion
the chamber is shown chamber
in Figure of 1.
Xi’an
TheJiaotong
chamberUniversity.
volume is 22.6The L, schematic
with a
configuration
305 of the chamber
mm inner diameter and 310ismmshowninner in length.
Figure 1.Two The chamber
quartz volume
windows areisfixed
22.6 L, onwith
botha
305 mm inner diameter and 310 mm inner length. Two quartz windows
sides of the chamber, with an optical diameter of 150 mm to allow for schlieren imaging. are fixed on both
sidesimpellers
Four of the chamber, with an
are mounted optical diameter
diagonally to induceofa 150 mm to allow
quasi-uniform andforisotropic
schlieren imaging.
turbulent
FourThe
field. impellers are characteristics
turbulent mounted diagonally
such astoturbulent
induce a intensity
quasi-uniform and isotropic
and integral turbulent
length scale are
field. Theby
measured turbulent
PIV. Thecharacteristics
original images such as turbulent
of spherically intensity flames
expanding and integral
(as shownlength scale
in Fig-
are2)measured
ure are capturedby PIV.
by aThe original images
high-speed digital of spherically
camera expanding
(Phantom flames
V611), with the(as shown in
resolution
Figure 2) are captured by a high-speed digital camera (Phantom V611),
of 750 × 750 and the frequency of 10,000 fps. Considering the size of quartz window, the with the resolution
of 750 ×of
accuracy 750 and can
image the frequency
be up to 0.22of 10,000
mm/pixel. fps. Further
Considering the
details ofsize
the of quartz window,
combustion chamber the
accuracy of image can be up to 0.22 mm/pixel. Further details of
and turbulent characteristics can be referred in the authors’ previous study [34]. the combustion chamber
and turbulent characteristics can be referred in the authors’ previous study [34].

Energies 2024, 17, x FOR PEER REVIEW

Figure 1. Schematic configuration of the turbulent combustion chamber.

Figure 1. Schematic configuration of the turbulent combustion chamber.

As turbulent expanding flames are not smooth but wrinkled, the flame radius is ob-
tained by area method. By writing codes and adjusting thresholds, the original images are
processed through grayscale, binarization, filling, and noise reduction. The inside of the
flame boundary is filled with white pixels and the outside is filled with black pixels. Ac-
cording to the calibration of the window space, flame area (A) can be calculated according
to the number of white pixels, and flame radius is estimated by R = (A/π)0.5.
After that, the varying flame propagation speed (SF) is obtained by the differential
between flame radius and flame propagation time. To obtain a specific value of turbulent
burning velocity, the average method is adapted in the present study. The turbulent burn-
ing velocity is defined as the average value of the flame propagation speed over a flame
1
radius range of 10~45 mm. That is, ST = ⋅ ∑n1 SF ⁄σ, where σ is the thermal expansion
n
ratio of unburned gas to burned gas.

Figure
Figure 2. Original 2. Original
images images expanding
of spherically of spherically expanding
flames flames (top:
(top: laminar laminar
flames; flames;
bottom: bottom: tur
turbu-
lent flames). flames).

As turbulent expanding flames

2.2. Experimental are not smooth but wrinkled, the flame radius is
Conditions
obtained by area method.
In the present study, theand
By writing codes adjusting
premixed gasthresholds, the original images
is a methane/hydrogen/air mixture. Th
VolH₂
ume fraction of hydrogen (H2 %= ) spans from 0 to 100%. The initial press
VolH₂ +VolCH₄
0.1 MPa and 0.3 MPa, respectively. The rotational speed of turbulent impellers i
trolled at 500 r/min and 1500 r/min, which corresponds to a turbulent intensity of 0.8
and 2.66 m/s, and an integral length scale of 7.44 mm and 11.25 mm, respectively
equivalence ratio of premixed gas is kept at ϕ = 1.0, and the initial temperature is k
Energies 2024, 17, 5997 4 of 14

are processed through grayscale, binarization, filling, and noise reduction. The inside of
the flame boundary is filled with white pixels and the outside is filled with black pixels.
According to the calibration of the window space, flame area (A) can be calculated according
to the number of white pixels, and flame radius is estimated by R = (A/π)0.5 .
After that, the varying flame propagation speed (SF ) is obtained by the differential
between flame radius and flame propagation time. To obtain a specific value of turbulent
burning velocity, the average method is adapted in the present study. The turbulent burning
velocity is defined as the average value
 of the
 flame propagation speed over a flame radius
1 n
range of 10~45 mm. That is, ST = n · ∑1 S F /σ, where σ is the thermal expansion ratio of
unburned gas to burned gas.

2.2. Experimental Conditions

In the present study, the premixed gas is a methane/hydrogen/air mixture. The
Vol H2
volume fraction of hydrogen (H2 % = Vol H2 +Vol CH4 ) spans from 0 to 100%. The initial
pressure is 0.1 MPa and 0.3 MPa, respectively. The rotational speed of turbulent impellers
is controlled at 500 r/min and 1500 r/min, which corresponds to a turbulent intensity of
0.89 m/s and 2.66 m/s, and an integral length scale of 7.44 mm and 11.25 mm, respectively.
The equivalence ratio of premixed gas is kept at ϕ = 1.0, and the initial temperature is kept
at 300 K. In addition to turbulent flame experiments, the laminar flame experiments are also
conducted for comparison. The uncertainty of laminar and turbulent flame experiments is
about 5% and 10%, respectively, which is used as the basis for estimating the error bars.
Detailed information on the experimental conditions and other flame parameters are shown
in Table 1.

Table 1. Experimental conditions and relative flame parameters.

H2 (%) P (MPa) u′ (m/s) LT (mm) 1 SL (cm/s) 2 lf (mm) 3 s 4 Ka

0 0.1, 0.3 0.89 7.44 37.6, 24.6 0.060, 0.031 7.47 0.33, 0.44
20 0.1, 0.3 0.89 7.44 43.1, 28.3 0.056, 0.028 7.42 0.26, 0.34
40 0.1, 03 0.89 7.44 52.3, 34.7 0.049, 0.025 7.36 0.18, 0.24
60 0.1, 0.3 0.89 7.44 69.5, 46.9 0.041, 0.020 7.26 0.11, 0.14
70 0.1, 0.3 0.89 7.44 84.6, 58.0 0.036, 0.018 7.20 0.08, 0.09
80 0.1, 0.3 0.89 7.44 107.9, 77.2 0.031, 0.015 7.11 0.05, 0.05
90 0.1, 0.3 0.89 7.44 146.4, 114.6 0.026, 0.011 7.00 0.03, 0.03
100 0.1, 0.3 0.89 7.44 213.5, 199.7 0.021, 0.007 6.84 0.01, 0.01
0 0.1, 0.3 2.66 11.25 37.6, 24.6 0.060, 0.031 7.47 1.37, 1.85
20 0.1, 0.3 2.66 11.25 43.1, 28.3 0.056, 0.028 7.42 1.08, 1.44
40 0.1, 0.3 2.66 11.25 52.3, 34.7 0.049, 0.025 7.36 0.76, 1.00
60 0.1, 0.3 2.66 11.25 69.5, 46.9 0.041, 0.020 7.26 0.45, 0.58
70 0.1, 0.3 2.66 11.25 84.6, 58.0 0.036, 0.018 7.20 0.32, 0.39
80 0.1, 0.3 2.66 11.25 107.9, 77.2 0.031, 0.015 7.11 0.20, 0.23
90 0.1, 0.3 2.66 11.25 146.4, 114.6 0.026, 0.011 7.00 0.12, 0.11
100 0.1, 0.3 2.66 11.25 213.5, 199.7 0.021, 0.007 6.84 0.06, 0.04
1 SL is calculated using Chemkin Pro with GRI3.0 Mech. 2 Laminar flame thickness is evaluated by l f = DT /S L ;
DT —thermal diffusivity. 3 Thermal expansion ratio is defined as the density ratio of unburned gas to burned gas,
which is evaluated by σ = ρu /ρb . 4 Karlovitz number is defined as the timescale ratio of chemical reaction to small
 ′ 3/2  −1/2
turbulent eddies, which is evaluated by Ka = Su
L
· Ll T .
f

2.3. Validation of the Experimental Apparatus

Before the study of turbulent flame propagation, it is essential to assess the reliability
of current experimental apparatus. The laminar burning velocities of methane/hydrogen
flames were measured to compare with the results in the literature [35–37], as shown in
Figure 3. It should be mentioned that the effect of thermal radiation is not considered
here. According to the study of Santner et al. [38], the thermal radiation usually contributes
significantly to uncertainty for extreme conditions, such as low flame temperature and high
 Before the study of turbulent flame propagation, it is essential to assess the reliability
of current experimental apparatus. The laminar burning velocities of methane/hydrogen
flames were measured to compare with the results in the literature [35–37], as shown in
Energies 2024, 17, 5997 Figure 3. It should be mentioned that the effect of thermal radiation is not considered here.
5 of 14
According to the study of Santner et al. [38], the thermal radiation usually contributes
significantly to uncertainty for extreme conditions, such as low flame temperature and
high pressure. In the present study, the effect of thermal radiation is neglected due to the
pressure. In the present study, the effect of thermal radiation is neglected due to the high
high flame temperature. Aditionally, the effect of buoyancy is also neglected due to the
flame temperature. Aditionally, the effect of buoyancy is also neglected due to the high
high flame
flame propagation
propagation speed.
speed. As we Ascan
wesee,
canthe
see,present
the present results
results are inare in good
good agreement
agreement with
with the experimental results in the literature and the prediction of GRI3.0 Mech
the experimental results in the literature and the prediction of GRI3.0 Mech [39]. Laminar [39].
Laminar burning velocity increases nonlinearly with increasing hydrogen fraction,
burning velocity increases nonlinearly with increasing hydrogen fraction, confirming con-
firming that the current experimental apparatus is reliable and can be further used
that the current experimental apparatus is reliable and can be further used to investigate to in-
vestigate turbulent
turbulent flame propagation.
flame propagation.

250
CH4/H2/air T=300 K, P=0.1 MPa, φ=1.0
Present data
200 Hu et al. data Law et al. data
Halter et al. data GRI3.0 Mech
150
SL (cm/s)

100

50

0
0 20 40 60 80 100
H2%
Figure 3.
Figure 3. Laminar
Laminar burning
burningvelocity
velocityvalidation
validationofofCH
CH4 /H
4/H2/air
2 /airmixtures
mixtures (Hu
(Hu et
et al. [33], Law et al. [34],
[34], Halter
Halter et al. et al. [32]).
[32]).

3. Results and
3. Results and Discussion
Discussion
3.1.
3.1. Turbulent Burning Velocity
Turbulent Burning Velocity
The
The turbulent
turbulentburning
burningvelocities
velocitiesofofmethane/hydrogen
methane/hydrogenmixtures
mixturesare
areshown
showninin
Figure 4,
Figure
and
4, andthethe
detailed values
detailed valuesare
arelisted
listedininTable
Table2.2.Turbulent
Turbulent burning
burning velocity increases non-
velocity increases non-
linearly with hydrogen fraction, and this increase is more pronounced at high hydrogen
linearly with hydrogen fraction, and this increase is more pronounced at high hydrogen
fractions, which is similar to the results of laminar burning velocity. Obviously, adding a
fractions, which is similar to the results of laminar burning velocity. Obviously, adding a
small amount of hydrogen to pure methane does not significantly enhance turbulent burn-
small amount of hydrogen to pure methane does not significantly enhance turbulent burn-
ing velocity, but adding a small amount of methane to pure hydrogen can greatly inhibit
ing velocity, but adding a small amount of methane to pure hydrogen can greatly inhibit
turbulent burning velocity. Furthermore, the sensitivity of turbulent burning velocity to
turbulent burning velocity. Furthermore, the sensitivity of turbulent burning velocity to
hydrogen faction is affected by turbulence intensity and pressure. By comparing the results
hydrogen faction is affected by turbulence intensity and pressure. By comparing the re-
of u′ = 0.89 m/s and 2.66 m/s, it is clear that the dependence between turbulent burning
sults of u′ = 0.89 m/s and 2.66 m/s, it is clear that the dependence between turbulent burn-
velocity and hydrogen fraction becomes more sensitive with the increase in turbulent inten-
ing velocity and hydrogen fraction becomes more sensitive with the increase in turbulent
sity. Additionally, the dependence becomes more sensitive at elevated pressure than under
intensity. Additionally, the dependence becomes more sensitive at elevated pressure than
atmospheric conditions. Except for those, by comparing the present data with the results
under atmospheric conditions. Except for those, by comparing the present data with the
of Zheng et al. [40], it implies that the turbulent burning velocity of methane/hydrogen
results ofisZheng
blending et al.higher
obviously [40], itthan
implies
thatthat the turbulent
of natural gas. burning velocity of methane/hy-
drogen blending is obviously higher than that of
According to the flamelets theory of Damkohler [41], natural gas. turbulent burning velocity
depends on laminar burning velocity and flame surface area. Turbulent flame area is
primarily influenced by the wrinkling caused by turbulent stretch and flame intrinsic
instability. From this point, the effect of hydrogen addition on turbulent burning velocity
should not be attributed to a single factor (e.g., increased laminar burning velocity) alone.
The variation in turbulent stretch and flame intrinsic instability should also be considered.
To eliminate the role of laminar burning velocity and emphasize the role of the other two
factors, the normalized turbulent burning velocities ST /SL are shown in Figure 5. As we can
see, the variation in ST /SL with hydrogen fraction can be divided into two stages. When the
hydrogen fraction is lower than 40%, the value of ST /SL remains almost unchanged, which
is consistent with the observation of Fairweather et al. [7]. However, when the hydrogen
fraction is over 40%, the value of ST /SL declines sharply, attributable to the variation in
turbulent stretch and flame intrinsic instability with hydrogen addition.
Energies 2024,
Energies 2024, 17,
17, 5997
x FOR PEER REVIEW 66 of 15
of 14

500
CH4/H2/air Τ=300 Κ, φ=1.0
400 u'=0.89 m/s solid: 0.1 MPa
u'=2.66 m/s hollow: 0.3 MPa

300

ST (cm/s) 200

100

0
0 20 40 60 80 100
H2%
4. Turbulent burning velocity
Figure 4. velocity of
of CH
CH44/H
/H2/air mixtures.
2 /air mixtures.

Table 2.
2. Detailed
Detailed values
values of
of turbulent
turbulent burning
burning velocity
velocity of
of CH
CH4/H
/H2/air mixtures.
Table 4 2 /air mixtures.

H2 (%) P (MPa) H (%) u′ (m/s)

P (MPa) L′T(m/s)
u (mm) LT (mm) ST (cm/s)ST (cm/s)
2
0 0.1, 0.3 0.89 7.44 55.50, 51.14
0 0.1, 0.3 0.89 7.44 55.50, 51.14
20 0.1, 0.3 20 0.890.1, 0.3 7.44
0.89 7.44 55.88, 57.34
55.88, 57.34
40 0.1, 03 40 0.890.1, 03 7.44
0.89 7.44 71.71, 71.59
71.71, 71.59
60 0.1, 0.3 60 0.890.1, 0.3 0.89
7.44 7.44 94.51, 88.47
94.51, 88.47
70 0.1, 0.3 70 0.890.1, 0.3 0.89
7.44 7.44 112.40, 119.00 119.00
112.40,
80 0.1, 0.3 0.89 7.44 136.41, 148.09
80 0.1, 0.3 90 0.890.1, 0.3 7.44
0.89 7.44 136.41, 148.09
179.96, 207.17
90 0.1, 0.3 100 0.890.1, 0.3 7.44
0.89 7.44 179.96, 207.17
235.91, 316.58
100 0.1, 0.3 0 0.890.1, 0.3 2.66
7.44 11.25 83.43, 106.68
235.91, 316.58
0 0.1, 0.3 20 2.660.1, 0.3 2.66
11.25 11.25 100.10, 124.84
83.43, 106.68
40 0.1, 0.3 2.66 11.25 122.14, 145.02
20 0.1, 0.3 60
2.660.1, 0.3 11.25
2.66 11.25
100.10, 124.84
149.20, 164.04
40 0.1, 0.3 70 2.660.1, 0.3 11.25
2.66 11.25 122.14, 145.02
181.93, 199.19
60 0.1, 0.3 80 2.660.1, 0.3 11.25
2.66 11.25 149.20, 164.04
209.83, 244.16
Energies 2024,
70 17, x FOR PEER REVIEW
0.1, 0.3 90 2.660.1, 0.3 2.66
11.25 11.25 267.26, 333.48
181.93, 199.19 7 of 15
100 0.1, 0.3 2.66 11.25 325.32, 426.19
80 0.1, 0.3 2.66 11.25 209.83, 244.16
90 0.1, 0.3 2.66 11.25 267.26, 333.48
100 0.1, 0.3 6 2.66 11.25 325.32, 426.19
CH4/H2/air φ=1.0
nearly unchanged u’=0.89 m/s
5According to the flamelets theory of m/s
u’=2.66 Damkohler [41], turbulent burning velocity de-
pends on laminar burning velocity and flame surface area. Turbulent flame area is primar-
declined
4
ily influenced by the wrinkling caused by turbulent stretch and flame intrinsic instability.
From this point, the effect of hydrogen addition on turbulent burning velocity should not
ST/SL

3
be attributed to a single factor (e.g., increased laminar burning velocity) alone. The varia-
tion in turbulent stretch and flame intrinsic instability should also be considered. To elim-
inate2 the role of laminar burning velocity and emphasize the role of the other two factors,
the normalized turbulent burning velocities ST/SL are shown in Figure 5. As we can see,
the variation
1 in ST/SL with hydrogen fraction can be divided into two stages. When the
hydrogen 0 fraction
20 is lower
40 60 40%,
than 80the value
100 of ST/SL remains almost unchanged, which
H2%
is consistent with the observation of Fairweather et al. [7]. However, when the hydrogen
fraction is over 40%, the value of ST/SL declines sharply, attributable to the variation in
Figure 5.
5. Normalized
Normalized turbulent
Figure
turbulent stretch andturbulent burning velocity
burning
flame intrinsic velocity SSTT/S
instability /SLL versus
with versus hydrogen
hydrogen
hydrogen fraction
fraction (solid:
addition. (solid: 0.1 MPa;
0.1 MPa;
hollow: 0.3
hollow: 0.3 MPa).
MPa).

turbulent stretch
The turbulent stretch and
and flame
flame intrinsic
intrinsic instability
instability versus
versus different
different hydrogen
hydrogen fractions
fractions
are evaluated
evaluatedquantitatively,
quantitatively, as shown
as shownin Figure 6. Here,
in Figure 6. the turbulent
Here, stretch is the
the turbulent interaction
stretch is the
between turbulent
interaction between eddies and flamelets,
turbulent eddies andwhich is parameterized
flamelets, which is by Karlovitz number,
parameterized defined
by Karlovitz
as the timescale ratio of chemical reaction to small turbulent eddies. For stoichiometric mix-
tures, flame intrinsic instability is mainly induced by hydrodynamic instability, and thermal–
diffusive instability is neglected. The hydrodynamic instability is mainly caused by the density
gradient between the burned and unburned zone, which is affected by the thermal expansion
ratio and flame thickness. Here, the hydrodynamic instability is parameterized by the ratio of
 H2%
Figure 5. Normalized turbulent burning velocity ST/SL versus hydrogen fraction (solid: 0.1 MPa;
hollow: 0.3 MPa).
Energies 2024, 17, 5997 7 of 14
The turbulent stretch and flame intrinsic instability versus different hydrogen fractions
are evaluated quantitatively, as shown in Figure 6. Here, the turbulent stretch is the interaction
betweendefined
number, turbulent aseddies and flamelets,
the timescale ratio ofwhich is parameterized
chemical reaction to smallby Karlovitz number,
turbulent eddies. definedFor
as the timescale
stoichiometric ratio of chemical
mixtures, reactioninstability
flame intrinsic to small turbulent
is mainlyeddies.
induced Forbystoichiometric
hydrodynamic mix-
tures, flame
instability, andintrinsic instability is mainly
thermal–diffusive induced
instability by hydrodynamic
is neglected. instability, and
The hydrodynamic thermal–
instability
isdiffusive instability
mainly caused by isthe
neglected.
density The hydrodynamic
gradient between the instability
burnedisand mainly caused zone,
unburned by thewhich
density
isgradient
affectedbetween the burned
by the thermal and unburned
expansion ratio andzone, which
flame is affected
thickness. by the
Here, thethermal expansion
hydrodynamic
instability
ratio and flameis parameterized
thickness. Here, by the
thehydrodynamic
ratio of thermal expansion
instability ratio to flame
is parameterized bythickness.
the ratio of
Karlovitz number appears
thermal expansion ratio toto reduce
flame with hydrogen
thickness. Karlovitzfraction,
numberand this reduction
appears intensifies
to reduce with hydro-
when the hydrogen
gen fraction, and thisfraction
reduction is intensifies
over 40%,when indicating that the
the hydrogen stretchis effect
fraction of turbulent
over 40%, indicating
eddies
that the onstretch
flamelets effectweakens witheddies
of turbulent the increasing
on flamelets of hydrogen
weakens with addition. When hydrogen
the increasing of hydro-
isgen
added to methane,
addition. When hydrogen the concentration of H radical
is added to methane, is increased,of
the concentration promoting
H radical isthe chain
increased,
branch reactions and total chemical reaction rate. At this time,
promoting the chain branch reactions and total chemical reaction rate. At this time, the stretch the stretch of turbulent
vortexes on local
of turbulent vortexes flamelets
on localisflamelets
weakened, because the
is weakened, interaction
because duration
the interaction is shortened.
duration is short-
Reversely,
ened. Reversely,
σ/l f is increased with hydrogen fraction, implying that
σ/lf is increased with hydrogen fraction, implying that hydrodynamic hydrodynamic instability
insta-
isbility
promoted by hydrogen
is promoted by hydrogen addition. By comparing
addition. By comparing the the
results
resultsin Figures
in Figures 5 and
5 and 6,6,it itcan
can
bebefound
found thatthat thethevariation
variationofof STS /STL/S L is nearly
is nearly consistent
consistent with
with that of that of Karlovitz
Karlovitz number,number,
although
although hydrodynamic
hydrodynamic instability instability
exhibits the exhibits
oppositethe trend.
oppositeThus,trend.
it can Thus, it can be
be inferred inferred
that that
the increase
the increase in turbulent burning velocity with hydrogen addition
in turbulent burning velocity with hydrogen addition is primarily due to the growth in lami- is primarily due to the
growth in laminar burning velocity, with the turbulent stretch acting
nar burning velocity, with the turbulent stretch acting as an “amplification” factor. When the as an “amplification”
factor. When
hydrogen the hydrogen
fraction is high, thefraction is high, therole
“amplification” “amplification”
of the turbulent rolestretch
of theisturbulent
weakened. stretch
is weakened.

10 1000
CH4/H2/air φ=1.0 P=0.1 MPa
CH4/H2/air φ=1.0
P=0.3 MPa
800
1
600
σ/lf (mm-1)
Ka

0.1 400
u'=0.89 m/s P=0.1 MPa
u'=2.66 m/s P=0.1 MPa
u'=0.89 m/s P=0.3 MPa 200
0.01 u'=2.66 m/s P=0.3 MPa
(a) (b)
0
0 20 40 60 80 100 0 20 40 60 80 100
H2% H2 %

Figure6.6.Turbulent
Figure Turbulentstretch
stretchand
andhydrodynamic
hydrodynamicinstability
instability versus
versus hydrogen
hydrogen fraction
fraction ((a): turbulent
((a): turbulent
stretch;
stretch;(b):
(b):hydrodynamic
hydrodynamicinstability).
instability).

As a classic issue of premixed turbulent combustion, numerous unified scaling models

of turbulent burning velocity have been developed in the past decades. Although these
models have been extensively discussed in previous studies [23,24,42,43], they have not
been comprehensively evaluated by the data of hydrogen-enriched fuels. Below are four
topical models:
1/2
Zimont model [44] ST = S L + 0.4(u′ ·S L ) Re1/4
−1/4
Schmidt model [45] ST = S L + u′ · (1 + Da−2
20.5 1/2
Peters model [46] ST = S L ·(1 + 0.195· LδLT ·((1 + Da ) − 1))
1/2
Gulder model [47] ST = S L + 0.62(u′ ·S L ) Re1/4

The models are evaluated by the experimental data of methane/hydrogen mixtures,

as shown in Figure 7. Turbulent burning velocity is converted into values of the progress
variable c = 0.5, and the relative method can be referred in the study of Bradley [48]. As we
can see, all the models can capture the promotion effect of turbulence intensity on turbulent
burning velocity. The Zimont model and Gulder model are able to reasonably predict the
enhancement effect of initial pressure, but the Schmidt model and Peters model fail to
predict the pressure effect. Regarding the impact of hydrogen addition, the Zimont model
and Gulder model can accurately capture the nonlinear dependence between turbulent
 The models are evaluated by the experimental data of methane/hydrogen mixtures, as
shown in Figure 7. Turbulent burning velocity is converted into values of the progress variable
shown in Figure 7. Turbulent burning velocity is converted into values of the progress variable
c = 0.5, and the relative method can be referred in the study of Bradley [48]. As we can see, all
c = 0.5, and the relative method can be referred in the study of Bradley [48]. As we can see, all
the models can capture the promotion effect of turbulence intensity on turbulent burning ve-
the models can capture the promotion effect of turbulence intensity on turbulent burning ve-
locity. The Zimont model and Gulder model are able to reasonably predict the enhancement
Energies 2024, 17, 5997 locity. The Zimont model and Gulder model are able to reasonably predict the enhancement
effect of initial pressure, but the Schmidt model and Peters model fail to predict the pressure 8 of 14
effect of initial pressure, but the Schmidt model and Peters model fail to predict the pressure
effect. Regarding the impact of hydrogen addition, the Zimont model and Gulder model can
effect. Regarding the impact of hydrogen addition, the Zimont model and Gulder model can
accurately capture the nonlinear dependence between turbulent burning velocity and hydro-
accurately capture the nonlinear dependence between turbulent burning velocity and hydro-
burning
gen velocity
fraction, but the and hydrogen
other two models fraction, but the other
underestimate two models
this nonlinear trend.underestimate
Quantitatively,this the
gen fraction, but the other two models underestimate this nonlinear trend. Quantitatively, the
nonlinear trend.
prediction Quantitatively,
of the Gulder model is the prediction
obviously of than
higher the Gulder model is obviously
the experimental higher
results, primarily
prediction of the Gulder model is obviously higher than the experimental results, primarily
thantothe
due anexperimental
overestimatedresults,
pre-factorprimarily
of 0.62. due
The to an overestimated
Zimont pre-factor
model’s prediction is theofclose
0.62.toThe
the
due to anmodel’s
Zimont overestimated pre-factor
prediction the of 0.62.toThe
theZimont model’sresults
prediction is the close to the
experimental results at weaklyisturbulent closeconditions,experimental
while at highly at weakly
turbulent turbulent
conditions, the
experimental
conditions, resultsatathighly
while weaklyturbulent
turbulentconditions,
conditions, while at highly
the Zimont turbulent
model’s conditions, the
Zimont model’s prediction is still slightly higher. The present Zimont modelprediction is still
prediction results
Zimont
slightly model’s
higher.withprediction
Thethepresent is still slightly higher. The present Zimont model prediction results
are consistent resultsZimont
of Sadeq model
et al.prediction results
[49], and the latterare consistent on
concentrates with the results
gas-to-liquid
are consistent
of Sadeq with the results of Sadeq et al. [49], and the latter concentrates on gas-to-liquid
(GTL) fuel.etOverall,
al. [49],the
and the latter
Zimont model concentrates
provides the onmost
gas-to-liquid (GTL) fuel.
accurate prediction Overall,
of the the
turbulent
(GTL)
Zimont fuel.
modelOverall, the Zimont model provides the mostofaccurate prediction of thevelocity
turbulent
burning velocityprovides the most
of methane/hydrogen accurate
flames. prediction the turbulent burning of
burning velocity of methane/hydrogen
methane/hydrogen flames. flames.

1000 1000
1000 Zimont model 1000
Schmidt model
Zimont model Schmidt model
800 P=0.1 MPa u'=0.89 m/s 800
'
800 P=0.1
P=0.1 MPa
MPa uu'=0.89
=2.66 m/s
m/s 800
'
P=0.1
P=0.3 MPa
MPa uu'=2.66
=0.89 m/s
m/s
/cm·s-1

/cm·s-1
600 P=0.3
P=0.3 MPa
'
MPa uu'=0.89
=2.66 m/s
m/s 600
-1

-1
600 P=0.3 MPa u'=2.66 m/s 600

/cm·s
/cm·s

400 400

ST,c=0.5
ST,c=0.5

400 400

ST,c=0.5
ST,c=0.5

200 200
200 200
(a) (b)
0 (a) 0 (b)
0 0.0 0.2 0.4 0.6 0.8 1.0 0 0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
H% H%
H22% H22%
1000 1000
1000 1000 Gulder model
Peters model
Peters model Gulder model
800 800
800 800
/cm·s-1

/cm·s-1

600 600
-1

-1

600 600
/cm·s

/cm·s

400 400
ST,c=0.5

ST,c=0.5

400 400
ST,c=0.5

ST,c=0.5

200 200
200 200
(c) (d)
0 (c) 0 (d)
0 0.0 0.2 0.4 0.6 0.8 1.0 0 0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
H% H%
H22% H22%
Figure 7. Evaluation results of four topical unified scaling models ((a): Zimont model; (b): Schmidt
model; (c): Peters model; (d): Gulder model).

3.2. Turbulent Flame Acceleration

Similarly to laminar flames, the propagation of turbulent expanding flames can be ac-
celerated, and this acceleration can be further intensified by increased turbulent disturbance.
Plenty of studies [32] have indicated that the laminar flame acceleration does not occur at
the beginning of ignition because of the inhibition of flame positive stretch, but occurs when
the flame radius reaches a critical value, namely, the flame acceleration onset. Bauwens
et al. [28] found that flame acceleration onset existed in the weakly turbulent expanding
flames as well, and it occurred earlier than that of laminar flames. In the present study, the
critical flame radii of both laminar and turbulent expanding flames of methane/hydrogen
mixtures are determined, as shown in Figure 8a. The critical radii of most laminar flames at
P = 0.1 MPa are larger than the observation window (Rcr > 75 mm) and are not captured,
while all the critical radii of weakly turbulent flames at P = 0.1 MPa fall within the obser-
vation window. This indicates that weakly turbulent disturbance can indeed promote the
occurrence of flame acceleration. More importantly, the effect of hydrogen addition on the
onset of laminar and weakly turbulent flame acceleration is completely different. With the
increase in hydrogen fraction, the critical radii of laminar flame acceleration are decreased,
 To interpret the unusual phenomenon above, the relationship between flame accel-
eration onset and dimensionless turbulence intensity u′/SL is shown in Figure 8b. As we
can see, the critical radii of flame acceleration reduce with u′/SL, indicating the promotion
effect of turbulent disturbance. With hydrogen addition, laminar burning velocity is in-
Energies 2024, 17, 5997 creased, leading to a decline in u′/SL. As a result, flame acceleration onset is delayed, and
9 of 14
the critical flame radii are increased during this period. It should be mentioned that the
turbulent flame acceleration onset is determined under weakly turbulent conditions (u′ =
0.89 m/s, P = 0.1 MPa). Under moderate to intense turbulence and elevated pressures, due
mainly due strengthened hydrodynamic instability. Oppositely, the critical radii of weakly
to an increase
turbulent flamein acceleration
turbulent disturbance and with
are increased flamehydrogen
intrinsic instability, the flame aisdelay
addition, indicating acceler-in
ated at the beginning of ignition
flame acceleration at this time. and no onset is captured.

100 30
(a) P=0.1 MPa, laminar (b) CH4/H2/air φ=1.0
CH4/H2/air φ=1.0
P=0.3 MPa, laminar 25
80 P=0.1 MPa, u'=0.89 m/s
20
60

Rcr/mm
Rcr/mm

15
40
10

20 5

0 0
0 20 40 60 80 100 0.0 0.5 1.0 1.5 2.0 2.5
'
H2% u /SL

Figure 8. The critical

critical radii
radii of
oflaminar
laminarand
andturbulent
turbulentCH
CH4 /H /airflames
4/H22/air flames ((a):
((a): hydrogen
hydrogen fraction effect;
ef-
fect; (b): turbulent
(b): turbulent intensity
intensity effect).
effect).

To interpret
Flame the unusual
acceleration phenomenon
is essentially inducedabove, theevolution
by the relationship between
of flame flame accelera-
morphology. The
tion onset and surface
dimensionless turbulence ′ /S is shown in Figure 8b. As we can
intensity uthe
smooth flame becomes cellular, enlarging Lflame area and accelerating flame
see, the criticalHence,
propagation. radii ofthe
flame
flameacceleration
morphology reduce with u′ /SL , indicating
is quantitatively the promotion
characterized effect
in the present
of turbulent disturbance. With hydrogen addition, laminar burning velocity
study. The morphology of turbulent expanding flames is quantitatively characterized in is increased,
leading
two to aFirst,
steps: decline u′ /SL . Asis
theincellularity a result, flame
identified byacceleration onsetlearning
U-net machine is delayed, and the critical
algorithm, which
flame radii are increased during this period. It should be mentioned that the turbulent
flame acceleration onset is determined under weakly turbulent conditions (u′ = 0.89 m/s,
P = 0.1 MPa). Under moderate to intense turbulence and elevated pressures, due to an
increase in turbulent disturbance and flame intrinsic instability, the flame is accelerated at
the beginning of ignition and no onset is captured.
Flame acceleration is essentially induced by the evolution of flame morphology. The
smooth flame surface becomes cellular, enlarging the flame area and accelerating flame
propagation. Hence, the flame morphology is quantitatively characterized in the present
study. The morphology of turbulent expanding flames is quantitatively characterized in
two steps: First, the cellularity is identified by U-net machine learning algorithm, which
estimates the total length of cracks over the flame surface. Second, geometric conversion
is conducted using the method of Huang et al. [50], which estimates the cell size and cell
number according to the flame area and crack length. Figure 9 shows the topical evolution
process of spherically expanding flames. As we can see, the flame morphology evolution
can be divided into three stages. Initially, the cell size increases with flame expansion,
and the cell number remains almost unchanged. In this stage, the whole flame ball can be
thought as a large cell, and the flame surface has not broken into cells. Then, the cell size
reduces with flame expansion, meaning that the cells keep splitting and the cell number
keeps increasing. Correspondingly, the flame propagation speed begins to increase as well
due to enlarged flame area. Finally, the cell size reaches the cut-off scale and the cells
on flame surface begin to saturate. In the saturated cellularity stage, the cell number is
proportional to the square of flame radius.
As the cell size remains almost constant in the saturated stage, the saturated cell
sizes of turbulent expanding flames are obtained, as shown in Figure 10. The results of
laminar flames are also shown for comparison. The saturated cell scales of both laminar
and turbulent flames are smaller than 1 mm, yet the effects of hydrogen addition on
saturated cell size are different. At a constant turbulent intensity, the saturated laminar
flame cell size reduces with hydrogen fraction, but that of the turbulent flame remains
almost unchanged. This difference in saturated cell size variation can be attributed to the
different control mechanisms. It is known that the cellularity of laminar flames is induced
Energies 2024, 17, x FOR PEER REVIEW 10 of 15
Energies 2024, 17, 5997 10 of 14

estimates the total length of cracks over the flame surface. Second, geometric conversion
by flame intrinsic instability. According to the theory of Matalon et al. [51], maximum
is conducted using the method of Huang et al. [50], which estimates the cell size and cell
disturbance wavenumber is proportional to Peclet number, denoted as nmax ~Pe~R/lf ,
number according to between
and the relationship the flamethe area and crack
lower length.
limit of Figure 9and
wavelength shows the topical
maximum evolution
wavenumber
process of spherically expanding flames. As we can see, the flame
is λmin ~2π·R/nmax . Hence, the saturated cell size of laminar flames is proportional morphology evolution to
can be divided into three stages. Initially, the cell size increases
flame thickness. With the increase of hydrogen fraction, the laminar flame thickness with flame expansion, andis
the cell number
decreased, leading remains almost in
to a reduction unchanged. In this
saturated cell size.stage, the whole
Nevertheless, forflame ball can
turbulent be
flames,
thought as a large
the cellularity cell, and
is mainly causedthe by
flame surfacestretch.
turbulent has notThebroken into cells.
saturated Then,
cell size theturbulent
of the cell size
reduces with flame expansion, meaning that the cells keep splitting
flame is dependent on the lower limit of turbulent vortexes, namely, the Kolmogorov length and the cell number
keeps
scale. increasing.
According Correspondingly, the flame propagation
to the turbulent characteristics reportedspeed
in thebegins
previousto increase as well
study [34], the
due to enlarged flame area. Finally, the cell size reaches the cut-off
Kolmogorov length scale is decreased with the growth in turbulent intensity. As a result, scale and the cells on
flame surface begin to saturate.
′ In the saturated cellularity ′ stage, the cell
the saturated cell size of u = 2.66 m/s is lower than that of u = 0.89 m/s, while the effect of number is pro-
portional
hydrogento the square
addition of flame
on the radius.
saturated cell size of turbulent expanding flames is negligible.

5 2.5x104
cell size
cell number
4 2.0x104

3 1.5x104
rcell/mm

Ncell
2 1.0x104
saturated cellularity
1 5.0x103

0 0.0
0 10 20 30 40 50 60 70
Energies 2024, 17, x FOR PEER REVIEW R/mm 11 of 15

Figure 9. The
The cellularity
cellularity evolution of spherically expanding flames.

1.5
As the cell size remains almost constant in the saturated stage, the saturated cell sizes
CH4/H2/air φ=1.0 P=0.3 MPa, laminar
of turbulent expanding flamesP=0.1 are MPa,
obtained, as shown in Figure 10. The results of laminar
u'=0.89 m/s
flames1.2 are also shown for comparison. The m/s
P=0.1 MPa, u'=2.66 saturated cell scales of both laminar and tur-
bulent flames are smaller than 1 mm, yet the effects of hydrogen addition on saturated cell
size 0.9
are different. At a constant turbulent intensity, the saturated laminar flame cell size
rscell/mm

reduces with hydrogen fraction, but that of the turbulent flame remains almost un-
0.6 This difference in saturated cell size variation can be attributed to the different
changed.
control mechanisms. It is known that the cellularity of laminar flames is induced by flame
0.3 instability. According to the theory of Matalon et al. [51], maximum disturbance
intrinsic
wavenumber is proportional to Peclet number, denoted as nmax~Pe~R/lf, and the relation-
ship 0.0
between the lower limit of wavelength and maximum wavenumber is λmin~2π·R/nmax.
0 20 40 60 80 100
Hence, the saturated cell size of laminar flames is proportional to flame thickness. With
the increase of hydrogen H %
fraction,
2 the laminar flame thickness is decreased, leading to a
reduction in saturated cell size. Nevertheless, for turbulent flames, the cellularity is mainly
Figure
Figure 10.
10. The saturated
saturated cell
cell size
size of
of spherically
spherically expanding
expanding flames.
caused byTheturbulent stretch. The saturated cell size of the turbulent flame is dependent on
the lower limit of turbulent
Once flame acceleration vortexes, namely, the Kolmogorov length scale. According to
Once acceleration occurs,occurs,the theevolution
evolutionofofflame flameradius
radiuswithwithpropagation
propagation time
timeis
the
no turbulent
longer linear,characteristics
but reported
approximately in
followsthe previous
a power study
law as [34],
R~t α the
(α >Kolmogorov
1). length
Simultaneously,
is no longer linear, but approximately follows a power law as R~t α > 1). Simultaneously,
scale is decreased
the flame
flame propagation withspeedthe growth in turbulent
continuously intensity.
increases theAs
asthe a result,
flame the saturated
propagates cell
outwardly.
the propagation speed continuously increases as flame propagates outwardly.
size of u′
To quantify = 2.66 m/s is lower than that of u′ = 0.89 m/s, while the effect of hydrogen addition
exponent ddtt is
To quantify the the acceleration
acceleration intensity
intensity of of turbulent flames, the
turbulent flames, the acceleration
acceleration exponent is
on the
taken as saturated
dR/dt
⁄
as σ·SL ==A⋅Pe
dR dt cell size
d
dt of turbulent
A· Pet . Here, dR/dt
⁄
. Here, σ·SLis isthe
dR dt expanding
thenormalized flames
normalizedflame is negligible.
flamepropagation
propagationspeed,speed,and Pe is
and Pe is
taken
σ⋅SL
the normalized flame radius defined σ⋅SL as Pe = R/lf . The acceleration exponents of turbulent
the normalized flame
methane/hydrogen radius
flames aredefined
shown as in Pe
Figure f. The acceleration exponents of turbulent
= R/l11. In general, turbulent flame acceleration
methane/hydrogen flames are shown
exponents reduce with increasing hydrogen fraction, in Figure 11. In general,
meaning turbulent flame acceleration
that acceleration intensity
exponents reduce with increasing hydrogen fraction, meaning
weakens at high hydrogen fractions. Combining the results of flame acceleration onset that acceleration intensity
and
weakens at high hydrogen
flame morphology, it can befractions.
concluded Combining
that the effect the results of flame
of hydrogen acceleration
addition onset
on turbulent
and flame morphology, it can be concluded that the effect of hydrogen addition on turbu-
lent flame acceleration is essentially different from that of laminar flame. Turbulent flame
acceleration is dominated by turbulent stretch, and the effect of flame intrinsic instability
can be negligible. Turbulent flame acceleration weakens with increasing hydrogen addi-
tion, because the stretch effect of turbulent eddies on flamelets is weakened with the ad-
dition of hydrogen.
 taken as = A⋅Pe t . Here, is the normalized flame propagation speed, and Pe is
σ⋅SL σ⋅SL
the normalized flame radius defined as Pe = R/lf. The acceleration exponents of turbulent
methane/hydrogen flames are shown in Figure 11. In general, turbulent flame acceleration
exponents reduce with increasing hydrogen fraction, meaning that acceleration intensity
Energies 2024, 17, 5997 11 of 14
weakens at high hydrogen fractions. Combining the results of flame acceleration onset
and flame morphology, it can be concluded that the effect of hydrogen addition on turbu-
lent flame acceleration is essentially different from that of laminar flame. Turbulent flame
flame acceleration is essentially different from that of laminar flame. Turbulent flame
acceleration is dominated by turbulent stretch, and the effect of flame intrinsic instability
acceleration is dominated by turbulent stretch, and the effect of flame intrinsic instability
can be negligible. Turbulent flame acceleration weakens with increasing hydrogen addi-
can be negligible. Turbulent flame acceleration weakens with increasing hydrogen addition,
tion, because the stretch effect of turbulent eddies on flamelets is weakened with the ad-
because the stretch effect of turbulent eddies on flamelets is weakened with the addition
dition of hydrogen.
of hydrogen.

1.0
CH4/H2/air φ=1.0 P=0.1 MPa u'=0.89 m/s
P=0.1 MPa u'=2.66 m/s
0.8 P=0.3 MPa u'=0.89 m/s
P=0.3 MPa u'=2.66 m/s
0.6
Energies 2024, 17, x FOR PEER REVIEW 12 of 15
dt

0.4

turbulent
0.2 flame regime, the enhancement in flame acceleration becomes smooth. In the
flamelet regime, turbulence mainly acts as a physical stretch to flame surface, which en-
larges
0.0the flame area and flame propagation speed. As a result, flame acceleration inten-
sity is always0 promoted
20 40by turbulent
60 80stretch,
100while in the highly turbulent flame regime,
the smallest eddies of turbulence H2% can penetrate into the preheating zone and even the re-
action zone. At this time, molecular transport and chemical reaction are affected by turbu-
Figure
Figure
lent 11. The
11. Theacceleration
disturbance, acceleration
meaning exponents
exponents ofof
turbulent
turbulent
that turbulence canCHCH4 /H
not 2 /air
4/H 2/airflames.
only flames. flame area, but also cause
enlarge
a change
Now inthat
local combustion
turbulent flame rate. Even under
acceleration is some extreme conditions, localitquenching
could Now
occur that
due turbulent
to the flame
heat acceleration
dissipation of is dominated
highlydominated
turbulent
by turbulent
turbulentstretch,
bydisturbance. stretch, it is
is′ rea-
reason-
sonable
able The to
to deducededucethat that
therethere
existsexists
a a quantitative
quantitative dependence
dependence between
between d d t and u /SL .
t and u′/SL. To clarify
To clarifyempirical model of the
this dependence, acceleration
accelerationexponent
exponents proposed by the authors [52]
of hydrogen-enriched gasis are
shown
this dependence,
here. The empirical themodel
acceleration
exhibits
′ exponents
good of hydrogen-enriched
agreement with the gas are shown
experimental results in
of Fig-
hy-
shown in Figure 12, covering a u /SL range of 0~12. Here, the results include present
ure 12, covering
drogen-enriched a u′/S
fuels.L range of 0~12. Here, the results include present methane/hydrogen
Additionally, the model is consistent with the experimental results
methane/hydrogen data and other hydrogen-enriched fuel data [52]. As we can see, the
data
of and other
Bauwens
enhancement hydrogen-enriched
etinal. [28] andflame
turbulent et al.fuel
Yangacceleration data
[27]. The [52].
effect Asofwe
is pronounced can
thesee,
turbulent
in the enhancement
stretch
flamelet on flame
regime, in tur-
acceler-
whereas
bulent flame
in theintensity
ation acceleration
highly turbulent is pronounced
flame regime,expressed
can be approximately in the
the enhancement flamelet
by a power regime,
in flame whereas in
law: acceleration becomes the highly
smooth. In the flamelet regime, turbulence mainly acts as a physical stretch to flame surface,
0.4
which enlarges the flame area anddflame t = 0.19⋅ uʹ ⁄SL speed.
propagation + 0.17
As a result, flame acceleration (1)
intensity is always promoted by turbulent stretch, while in the highly turbulent flame
Thethe
regime, present
smallest model
eddiesisofapplicable
turbulencetocan
laminar
penetrateflameintoacceleration
the preheatingas zone
well. and
For even
laminar
flames (u′/S = 0), the predicted value of laminar flame fractal excess is
the reaction zone. At this time, molecular transport and chemical reaction are affected
L 0.17, which is con-
sistent
by turbulent disturbance, meaning that turbulence can not only enlarge flame area, but is a
with results in the previous literature. It is emphasized that the present model
pure empirical
also cause one, in
a change whose
local accuracy
combustion is acceptable
rate. Even within
under somethe verified
extremerange (u′/SL <local
conditions, 12). For
the flame acceleration
quenching could occur in a more
due to the intense turbulent
heat dissipation offield,
highlythe presentdisturbance.
turbulent model is not suitable.

1.0
CH4/H2/Air CO/H2/Air H2/Air
dt=0.19·(u'/SL)0.4+0.17
0.8
Bauwens et al. Yang et al. dt=0.3, 0.43, 0.67

0.6
u'/SL=11.23
dt

0.4
u'/SL=2.19

0.2 u'/SL=0.39

0.0
0 2 4 6 8 10 12

u'/SL
Figure 12. The
Figure 12. The dependence
dependencebetween
betweenflame
flame acceleration
acceleration exponents
exponents u′ /S
andand u′/SL [27,28].
L [27,28].

4. Conclusions
In the present study, the turbulent burning velocity and flame acceleration of me-
thane/hydrogen mixtures are determined in a fan-stirred combustion chamber. The effect
of hydrogen addition on turbulent flame propagation is comprehensively investigated.
Energies 2024, 17, 5997 12 of 14

The empirical model of acceleration exponent proposed by the authors [52] is shown
here. The empirical model exhibits good agreement with the experimental results of
hydrogen-enriched fuels. Additionally, the model is consistent with the experimental
results of Bauwens et al. [28] and Yang et al. [27]. The effect of turbulent stretch on flame
acceleration intensity can be approximately expressed by a power law:

0.4
dt = 0.19· u′ /S L + 0.17 (1)

The present model is applicable to laminar flame acceleration as well. For laminar
flames (u′ /SL = 0), the predicted value of laminar flame fractal excess is 0.17, which is
consistent with results in the previous literature. It is emphasized that the present model is a
pure empirical one, whose accuracy is acceptable within the verified range (u′ /SL < 12). For
the flame acceleration in a more intense turbulent field, the present model is not suitable.

4. Conclusions
In the present study, the turbulent burning velocity and flame acceleration of methane/
hydrogen mixtures are determined in a fan-stirred combustion chamber. The effect of
hydrogen addition on turbulent flame propagation is comprehensively investigated. The
main conclusions are summarized as follows:
1. Turbulent burning velocity increases nonlinearly with hydrogen fraction, which is
similar to that of laminar burning velocity. The underlying mechanism of hydrogen
addition effects on turbulent burning velocity involves the growth of laminar burning
velocity and the weakening of turbulent stretch. The Zimont model and Gulder model
can accurately capture the nonlinear dependence between turbulent burning velocity
and hydrogen fraction, but the Schmidt model and Peters model underestimate
this trend.
2. Turbulent flame acceleration onset is delayed with hydrogen addition. The flame
morphology evolution of turbulent flame can be divided into three stages, and the
saturated cell size of turbulent flame is dependent on the Kolmogorov scale. The
acceleration exponent dt reduces with increasing hydrogen fraction, and an empirical
0.4
model dt = 0.19·(u′ /S L ) + 0.17 is proposed to quantify turbulent flame accelera-
tion. The results indicate that turbulent flame acceleration weakens with hydrogen
addition due to the weakening of turbulent stretch. Turbulent flame acceleration is
dominated by turbulent stretch, while the effect of hydrodynamic instability is slight
and negligible.

Author Contributions: Conceptualization, H.Z.; Methodology, H.Z.; Software, H.Z.; Validation,

H.Z.; Formal analysis, H.Z.; Investigation, H.Z.; Data curation, H.Z.; Writing—original draft, H.Z.;
Writing—review & editing, C.Y. and G.L.; Supervision, C.Y. and G.L.; Funding acquisition, H.Z., C.Y.,
G.L. and F.T. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by [National Natural Science Foundation of China] grant number
[52406126, 52274180, 52374187, 52174230], [Natural Science Foundation of Liaoning Province] grant
number [2024-BSBA-25], [Fundamental Research Funds for the Central Universities] grant number
[2301024], [Opening Fund of State Key Laboratory of Fire Science] grant number [HZ2024-KF09].
Data Availability Statement: The original contributions presented in the study are included in the
article, further inquiries can be directed to the corresponding author.
Conflicts of Interest: Author F.T. was employed by the company State Key Laboratory of Coal
Mine Disaster Prevention and Control, China Coal Technology and Engineering Group Shenyang
Research Institute, Shenfu Demonstration Zone. The remaining authors declare that the research was
conducted in the absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
Energies 2024, 17, 5997 13 of 14

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