Unexpected Propagation of Ultra-Lean Hydrogen Flames in Narrow Gaps

Abstract

Very lean hydrogen flames were thought to quench in narrow confined geometries. We show for the first time how flames with very low fuel concentration undergo an unprecedented propagation in narrow gaps: H2-air flames can survive very adverse conditions by breaking the reaction front into isolated flame cells that travel steadily in straight lines or split to perform a fractal-like propagation that resembles the pathway of starving fungi or bacteria. The combined effect of hydrogen mass diffusivity and intense heat losses act as the two main mechanisms that explain the experimental observations.

Full text

Unexpected propagation of ultra-lean hydrogen flames in narrow gaps
Fernando Veiga-L´opez1,∗Mike Kuznetsov2, Daniel Mart´ınez-Ruiz3,
Eduardo Fern´andez-Tarrazo1, Joachim Grune4, and Mario S´anchez-Sanz1†
1Dpto. de Ing. T´ermica y de Fluidos, Universidad Carlos III de Madrid, 28911, Legan´es, Madrid, Espa˜na
2Institut f¨ur Kern- und Energietechnick, Karlsruhe Institut f¨ur Technologie, 76344, Eggenstein-Leopoldshafen, Deutschland
3ETSIAE., Universidad Polit´ecnica de Madrid, Plaza del Cardenal Cisneros 3, 28040, Madrid, Espa˜na and
4Pro-Science GmbH, Parkstrasse 9, 76275, Ettlingen, Deutschland
(Dated: May 2, 2020)
Very lean hydrogen flames were thought to quench in narrow confined geometries. We show for
the first time how flames with very low fuel concentration undergo an unprecedented propagation in
narrow gaps: H2-air flames can survive very adverse conditions by breaking the reaction front into
isolated flame cells that travel steadily in straight lines or split to perform a fractal-like propagation
that resembles the pathway of starving fungi or bacteria. The combined effect of hydrogen mass
diffusivity and intense heat losses act as the two main mechanisms that explain the experimental
observations.
Hydrogen is one of the preferred fuel options because
of its high energy density, versatility and null-CO2emis-
sions when it is oxidized to produce energy either in fuel
cells or in combustion systems. One of the main concerns
of hydrogen-based power generation technology in com-
parison to conventional hydrocarbons are the potential
safety issues associated with the storage, use and han-
dling of hydrogen [1–3].
The small size of the H2molecule brings along a higher
permeation of hydrogen through solid walls, especially in
non-metallic containers [4], what significantly increases
the risk of undesired leaks [5]. On top of this, its high
reactivity, with a lean flammability limit around %H2=
4 at Earth’s gravity [3, 6], and ignition energy as low
as 0.02 mJ, ten times lower than other hydrocarbons
[7, 8], makes hydrogen more prone to undesired deflagra-
tions and explosions when the leak takes place in confined
spaces with no ventilation [9]. Furthermore, the dim visi-
ble emissions and weak heat radiated from lean hydrogen
flames makes their detection extremely difficult [10].
Combustion is a complex exothermic chemical pro-
cess formed by a sequence of elementary reactions involv-
ing intermediate species that are created and consumed
during the oxidation of the fuel. Conventional hydrogen
premixed flames propagate ideally as a continuous front
that advances burning the fresh mixture of fuel and ox-
idizer and leaves hot combustion products behind (ide-
ally, only water vapor) [11]. However, premixed flames
are inherently unstable. The viscosity and thermal ex-
pansion gradient across the flame front, the competition
between heat conduction and mass diffusion in the fluid,
the effect of gravity, the interaction with acoustic waves
[12, 13] and the heat losses [14], fold and stretch the flame
altering some of its dynamic and morphological proper-
ties [15].
To further investigate the morphology, stability
and safety issues of ultra-lean confined hydrogen-air
∗fveiga@ing.uc3m.es
†mssanz@ing.uc3m.es
High-speed
camera
Pressure
sensor
Mixer
MFC
Gas
analyzer
Light
source
Spark
plug
L
h
W
Injection
port
m
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Mirror
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Venting
valve
Feeding
valve
FIG. 1. Schematic of the experimental setup. Z-shape
Schlieren system used for image acquisition. The dimensions
of the cell are 950×200×6−1 mm (L×W×h). The black ar-
rows at the top end of the chamber represent the unobstructed
release of the combustion products.
flames, we modified a previously-used experimental setup
(Fig. 1) [16], formed by two parallel flat plates disposed
vertically and separated a small distance hapart. Previ-
ous combustion studies have made use of similar narrow-
channel geometries to investigate the onset and develop-
ment of premixed flame instabilities[17–19]. Here, the
faint emissions of fast hydrogen flames require the uti-
lization of Schlieren techniques and high-speed imaging
to track the reaction front. The path followed by the
flames can be outlined by trailing the condensed water
streaks formed just behind them [20] (Figs. 2 and 3). The
small value of the Reynolds number found in our experi-
ments (Re '33) anticipates a premixed hydrogen flame
that remains in the laminar regime and propagates as a
continuous wrinkled front [21]. The high mass diffusivity
of hydrogen outlines a reactive front characterized by the
formation of small wrinkles related to the development

2
b h = 2 mm; 10.5% H2
a h = 3 mm; 10.5% H2
Continuous front (A)
a.1
Two-headed steady cells (C'')Splitting cells (B)
c.1
Flame Flame path (condensed water) Unburned mixture
b.1
c h = 2 mm; 10.25% H2
30 mm
Ignition
Flame
g
FIG. 2. Downward-propagating hydrogen flames and their different propagation modes. Image and scheme of a-a.1 continuous
flame front propagation, b-b.1 splitting cells that propagate forming fractal patterns and c-c.1 several two-headed isolated
steady flame cells. The Supplementary Material includes a video illustrating the three propagation regimes described in the
figure.
of thermodiffusive instabilities (Fig. 2aand 3a). In gaps
narrower than h < 6 mm, the expected continuous flame
front breaks into a set of small flame cells separated by
cold, unburned gas, unveiling two unprecedented propa-
gation modes that only emerge in flames with low enough
hydrogen concentration. In the first one, the flame front
breaks into several unstable flame cells (Fig. 2band 3b)
that split continuously and propagate leaving a path that
conforms a fractal-like pattern that reminds of ferns and
tree leaves. This propagation mode evokes the way starv-
ing fungi or bacteria colonies [22, 23] spread, with lack of
nutrients being analogous to fuel scarcity. Also, diffusion-
limited aggregation phenomena reveal similar fractal pat-
terns [24]. In the second regime, the flame front breaks
into a few isolated stable flame cells (Fig. 2cand 3c)
that move steadily delineating an almost straight trajec-
tory that reminds of the fingering patterns found during
smoldering combustion of thin solid materials [25].
From the experimental results it is unclear both how
the flame cells are formed and why hydrogen flames with-
stand more adverse conditions than heavier hydrocarbon
fuels [12]. To investigate the causes that lead to the new
propagation regimes identified experimentally, we mod-
eled the propagation of the H2-air flame using an in-house
finite-element code [14]. Since the flow is laminar and the
flame thickness δT∼(0.5−1) mm is comparable to the
gap size h, the propagation problem of the flame can be
treated as quasi two-dimensional, considerably simplify-
ing the simulations.
The computations are carried out using an in-house
finite elements Freefem++ code that uses a self-adaptive
mesh that clusters elements near the reactive front where
the maximum gradients of temperature, reaction rate and
velocity are found. The minimum element size used in
the calculations is about 1 µm. The results (Fig. 4)
show that increasing the heat losses at the plates leads
to a broken reactive front that evolves to form two- or
single-headed flame cells, as observed in the experiments
for decreasing gap thickness h. The characteristic cell
size ranges from 5 to 10 mm for lean hydrogen mixtures
(Fig. 4), very similar to the size found in the experi-
mental results (Figs. 2 and 3). Analogous simulations
performed for heavier hydrocarbons with less mass diffu-
sivity extinguished at relatively low heat losses forming a
continuous reactive front. Our computations, therefore,
identified the intense heat losses at the walls and the high
mass diffusivity of the fuel as the two main mechanisms
controlling the emergence of the newly-discovered prop-
agation modes (see Supplementary Material).
Experimentally, the relative importance of heat losses
is measured using the Peclet number [16] P e =h/δT, a
non-dimensional parameter that compares the character-
istic diffusive and residence times. Lower values of P e in-
dicates more relevant heat conduction and, therefore, the
effect of heat losses can be stimulated by increasing the
wall surface area-to-volume ratio reducing the gap size h

3
b h = 4 mm; 7% H2
a h = 5 mm; 8% H2
Flame Flame path (condensed water) Unburned mixture
Splitting cells (B)
Continuous front (A)
b.1a.1
One-headed steady cells (C')
c.1
c h = 3 mm; 7.5% H2
30 mm
Ignition
Flame
g
FIG. 3. Upward-propagating hydrogen flames and their different propagation modes. Image and scheme of a-a.1 continuous
flame front propagation, b-b.1 fractal-like propagation mode and c-c.1 several one-headed isolated steady flame cells. The
Supplementary Material includes a video illustrating the three propagation regimes described in the figures
or thickening the flame by reducing the concentration of
hydrogen in the mixture [12, 26] (Table S1). For suffi-
ciently narrow chambers (h < 6 mm) and lean mixtures
(%H2<16 -hdependent-), conductive heat losses be-
come decisive [12] and the flame front breaks into pieces.
It is under these conditions when the two unprecedented
propagation regimes appear. Starting with a constant
gap size h, we increase the relative importance of heat
losses by reducing the concentration of hydrogen. In
mixtures leaner than a critical value, the flame evolves
from a continuous front to a group of isolated flame cells
that propagate as a fractal. Such transition arises soon
after ignition and the few cells so formed do propagate
until they reach the end of the chamber. During this
time, the flame cells split and bifurcate cyclically, with
newborn flame cells branching off, almost perpendicu-
larly, from the main path to quench or to later repeat the
splitting cycle (Fig. 2band 3b). The paths followed by
the flame cells are approximately 5-mm wide and form
a unique fractal pattern of fractal dimension df'1.7
(Supplementary Material), that suggests a non-chaotic
behaviour of the propagation, similar to the fractal di-
mension df'1.65 observed in the propagation of starv-
ing bacteria and electrochemical depositions [23, 27].
Further reduction in hydrogen concentration triggers a
second transition that stops the flame cell splitting mech-
anism. After ignition, now only a few stable isolated cells
travel steadily at an almost constant velocity of around
30 cm/s –case dependent–, keeping their size also con-
stant (Supplementary Material) until they reach the end
wall of the chamber or extinguish as they collide with the
water trail left by other flame cell, where no more fuel
is available (Fig. 2cand 3c). Conductive heat losses to
the walls of the chamber offset heat production to keep
the size of the flame cell constant. The unbalance be-
tween heat production and heat losses would explain the
splitting mechanism observed in richer flames. An anal-
ogous behavior is observed in unconfined environments,
when radiative heat losses were found to be key for the
stabilization of three-dimensional hydrogen flames balls
at micro-gravity [28–30].
The relative importance of heat losses was also mod-
ified keeping a constant hydrogen concentration and
changing the gap size. Qualitatively, the results are sim-
ilar regarding the emergence of the two above-described
regimes and are used to delineate a stability map in the
h–%H2parametric space (Fig. 4). The criteria used to
define the different regions traced in Fig. 4 is based on
the fractal dimension of the condensed water path formed
during the flame propagation, that evolves from df'2
(continuous front Fig. 2aand 3a), df'1.7 (splitting
cells Fig. 2band 3b) to df'1 (steady traveling cells
Fig. 2cand 3c). Also, the fractal dimension provides in-
formation about the degree of utilization of the available
fuel, with df= 2 indicating total fuel consumption and
df= 1 showing that most of the fresh mixture remains
unburned (Supplementary Material).
The effect of mass diffusivity was explored by test-

4
D
C'
B
A
D
C''
BA
Ignition
A. Continuous front
B. Splitting cells
C'. One-headed steady cells
C''. Two-headed steady cells
D. No ignition
Representative experiments
shown in Figs. 1 and 2
Ignition
Flame
Simulated one-headed cells
Simulated two-headed cells
h h
a
b
c
d
Flame
FIG. 4. Flame propagation modes in the h-%H2parametric space for both adownward- and bupward-propagating flames. The
solid lines separate the different propagation modes and the symbols represent the cases actually measured. Every experiment
is repeated at least 3 times to reduce the uncertainty of the measurements. The mixture composition was obtained with an
approximate error of ±0.04 %H2and the gap thickness hhas an average error of ±0.114 mm. cand ddetail the single and
double-headed flame cells Ω and the dimensionless temperature field T= (T0−Tu)/(Tb−Tu) obtained from our non-buoyant
numerical computations in the limit of very narrow channels. T0is the local temperature and Tbrepresents the adiabatic
(equilibrium) flame temperature of the simulated mixtures (Supplementary Material) with Tu= 298 K being the ambient
temperature.
ing experimentally methane and dymethilether (DME)
flames, fuels with much lower mass diffusivity. The rel-
evant parameter here is the Lewis number Le, a non-
dimensional number defined as the thermal-to-mass dif-
fusivity ratio that takes the value Le ≈0.3,1,1.75 in
lean hydrogen, methane and DME flames, respectively.
For methane and DME (Le ≥1), the flame does not
withstand the heat losses that increase as the gap size
his reduced and extinguishes from a continuous reac-
tive front. This result then identifies mass diffusivity
as the mechanism that counteracts heat losses [14] and
thermodiffusive instabilities, triggered by the high diffu-
sivity of hydrogen, become the survival mechanism that
enables local flame quenching under non-adiabatic con-
ditions and gives birth to flame cells within which the
temperature is high enough to sustain combustion [31].
The instantaneous high concentration gradient across the
front triggers the fast diffusion of hydrogen from the un-
burned region towards the surroundings of the flame, in-
creasing the local availability of H2and keeping the gas
above the crossover temperature ∼1000 K, temperature
below which the chemical reaction cannot proceed [32–
34]. The additional energy released by the burning of this
extra fuel is used to counteract conductive heat losses,
extending hydrogen combustion towards ultra-lean mix-
tures below %H2<5.
Considering safety-related real-life scenarios, Gravity
also plays an important role in stabilizing or destabi-
lizing flames in vertical channels [15]. To analyse to
a greater extent how gravity intervenes in the develop-
ment of the described propagation modes, we tested ex-
perimentally both upward- and downward-propagating
flames to expand our stability map (Fig. 4). Similarly to
methane and DME flames, in the downwards propagating
case, extinction takes place with the H2flames forming
a continuous reactive front for fuel concentrations below
%H2<9 in channels wider than 6 mm, approximately.
Surprisingly, leaner mixtures can be found in narrower
gaps once the reactive front of the H2flame is broken
into small separated cells that show, mainly, a double-
headed structure similar to that obtained numerically in
our computations (Fig. 4c). Simultaneously, the reduc-
tion in the gap size increases the relative importance of
the gas viscosity, reducing the buoyant velocity induced

5
by gravity and facilitating the propagation of the flame.
The minimum fuel concentration %H2= 8.5 was found
for h= 4 mm (Fig. 4a).
In upward-propagating flames, buoyancy accelerates
the flames and dilates the flammability limits to mix-
tures significantly leaner than in downward-propagating
flames (Fig. 4). As in downward-propagating flames, ex-
tinction takes place for richer mixtures in channels wider
than h > 5 mm. The minimum fuel concentration was
found for h= 5 mm when a fuel concentration as lean
as %H2'4.5 was capable of sustaining a solitary one-
headed flame cell (Fig. 4d) steadily traveling along the
combustion chamber. In narrower channels, conductive
heat losses shift the extinction limit towards richer H2
mixtures (Fig. 4). The influence of gravity diminishes in
very narrow channels, with both upward and downward
propagating flames presenting an almost coincident ex-
tinction limit when h= 1 mm (Fig. 4b). From the ex-
periments, one can conclude that one and two-headed
flames mainly appear when propagating up and down-
wards, respectively. However, we found both structures
for gravity-free conditions in our simplified numerical
model [14], result that leaves the influence of gravity on
the shape of these isolated traveling flames as an open
question.
The discovery of the propagation regimes described
above opens new research lines regarding near-limit hy-
drogen combustion in narrow geometries. Based on the
experimental results and in the mathematical modelling
of the problem carried out in this paper, we appoint the
conductive heat losses to the surrounding walls and the
high diffusivity of hydrogen flames as the two physical
mechanisms governing the onset of the two propagation
regimes unveiled in our paper. As the use of hydrogen
in the near future is expected to increase [1, 3], we an-
ticipate a raising concern about the safety of hydrogen-
powered devices [16] that will motivate the exploration
of interactions between different phenomena. That inter-
est may uncover unknown flame behaviours relevant in
the development of safety measures for intentional release
or unintentional leakage of hydrogen in narrow gaps and
confined environments.
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