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High-fidelity simulations of the mixing and combustion of a technically premixed
hydrogen flame
D.Miraa,∗, A. Botha, O. Lehmkuhla, S. Gomeza, J. Forckb, T. Tannebergerb, P. Stathopoulosb,c, C.O. Paschereitb
aBarcelona Supercomputing Center (BSC), Barcelona, Spain.
bTechnische Universität Berlin (TUB), Berlin, Germany.
cDeutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Berlin, Germany.
Abstract
Numerical simulations are used here to obtain further understanding on the flashback mechanism of a technically
premixed hydrogen flame operated in lean conditions. Recent work from the authors (Mira et al., 2020) showed that
the hydrogen momentum strongly influences the flame dynamics and plays a fundamental role on the stability limits
of the combustor. The axial injection influences the vortex breakdown position and therefore, the propensity of the
burner to produce flashback. This work is an extension of our previous work where we include a detailed description
of the mixing process and the influence of equivalence ratio fluctuations and heat loss on the flame dynamics.
Keywords:
hydrogen, turbulent flame, large-eddy simulations, flamelets
1. Introduction
The combustion of hydrogen-enrich fuels in gas tur-
bines is a highly investigated topic [1], with the potential
to contribute significantly to the decarbonization of a va-
riety of energy applications [2–4]. This potential comes
with the demand on future burner designs to accommo-
date a multitude of fuels with varying, but high, amounts
of hydrogen [5], while allowing for a wide stability range,
high efficiency and low NO𝑥emissions. From these
requirements, the investigation of burner designs to op-
erate on pure hydrogen can establish a benchmark for
many upcoming high-reactivity fuel combustors, lead-
ing to insights that can have a significant effect on a wide
variety of future energy applications.
Flame stabilization is one of the major factors to be
considered for the safe operation of hydrogen gas turbine
burners. A burner design to operate with hydrogen-
air mixtures building upon the concept of central non-
swirling axial air injection (AI) for Flashback (FB) pre-
vention was developed by Reichel et al. [6–9]. This
burner concept was introduced by Burmberger and Sat-
telmayer [10] and it is used in this burner to increase the
operational range when operated with hydrogen. This
∗Corresponding author: Daniel Mira, BSC.
Email address: daniel.mira@bsc.es (D.Mira)
Figure 1: Schematic of burner model, indicating different volume flow
pathways through swirl generator or axial injection.
burner design is particularly interesting for high reactiv-
ity fuels like hydrogen or syngas, which are prone to FB
in conventional swirl stabilized burners as reported by
Mayer et al. [5].
The burner geometry, see Fig. 1, was studied experi-
mentally by Reichel et al. [6–9] with the goal of finding a
configuration for extending stability limits set by FB. The
investigation was primary focused on driving mecha-
nisms influencing FB as well as their inter-dependencies.
In particular, the influence of fuel momentum and AI on
FB resistance were assessed. It was shown that without
AI, the central recirculation zone (CRZ) caused by the
vortex break down (VB), which is necessary for flame
Preprint submitted to Proceedings of the European Combustion Meeting 2021 March 15, 2021
anchoring, extends close or even into mixing tube for
some operating conditions, showcasing a deficit in axial
velocity on the central axis of the mixing tube. This
is typical for high swirl, low-reacting fuel combustors
[11, 12], but can lead to FB if high reacting fuels are
used [5]. Using different rates of AI, which can be
quantified by the ratio of axially injected, non-swirling
air flow to total air flow 𝜒=¤
𝑉ax/( ¤
𝑉ax +¤
𝑉swirl), it could
be shown for a medium AI rate (𝜒=7.5%) that it over-
comes the axial velocity deficit partially over the length
of the mixing tube, while not pushing the VB further
downstream. In contrast, a high rate of AI ( 𝜒=12.5%)
could overcome the axial velocity deficit over the whole
mixing tube pushing the VB downstream into the com-
bustion chamber. This strategy allows an increase in FB
resistance, as the flow profile at the mixing tube outlet
approaches the ideal plug-like flow shape [7], which was
also demonstrated by numerical simulations in the work
by Mira et al. [13]. Reichel et al. [7] have shown that the
AI reduces the initial swirl number. Note that high swirl
ensures a compact flame attached to the burner exit, but
lower swirl is favourable for FB resistance due to simpler
axial velocity deficit compensation.
Another dominant parameter influencing the flame
stabilization in this burner is the fuel momentum that
is introduced by the high-speed injection of hydrogen.
Since hydrogen has a very low amount of energy density,
volume flow rates are very high compared to conven-
tional fuels like natural gas, to account for a similar ther-
mal power output. The momentum ratio 𝐽, as described
in Reichel et al. [9] can be used to quantify the amount of
axial injection featured in the burner. Note the momen-
tum ratio increases with increase in equivalence ratio 𝜙
for a constant air mass flow rate. If compared to natu-
ral gas, hydrogen yields a momentum ratio that is 37%
higher assuming the same combustor power and taking
differences in volumetric heating value and molecular
mass into account [9]. The hydrogen injection upstream
of the mixing tube also contributes to lowering the re-
sulting swirl number at the mixing tube outlet, though
it is not able to overcome the axial velocity deficit at
the center of the mixing tube without the AI (𝜒=0).
Only when including AI, an increase in FB resistance
is found. In fact, the experimental results showed that
higher equivalence ratios cause a downstream shift of the
stagnation point, therefore increasing FB resistance [9].
These observation were also confirmed by numerical
simulations using a perfectly premixed assumption in
a previous work from the same authors [13], where the
flow field and flame stabilization were well predicted im-
posing the same axial momentum as in the technically
premixed case. In this case, the additional fuel mo-
mentum gained by higher equivalence ratios has a more
significant impact on the flow field then the increased
reactivity. It can be summarized that AI and fuel mo-
mentum can promote the favourable plug-like flow shape
at the outlet of the mixing tube, while featuring a CRZ
and pushing the stagnation point into the combustion
chamber contributing to additional FB resistance.
This work is an extension of our previous work [13]
where the hydrogen-air mixing is accounted for and the
impact of fluctuations in equivalence ratio and fuel het-
erogeneity are analysed. The paper is structured as fol-
lows. A description of the modelling approach is pre-
sented in the next section and the computational cases
considered for the inert and reacting flow problems are
then described. The results section is followed by a de-
tailed description of the mixing process and preliminary
results of the reacting flow field for a stable operating
point is presented and discussed. Finally, some conclu-
sions and directions of future work are given.
2. Modelling approach
2.1. Governing equations
The equations describing the flow field correspond
to the low-Mach number approximation of the Navier-
Stokes equations with the energy equation represented
by the total enthalpy. The Favre-filtered governing equa-
tions for LES correspond to the continuity, momentum
and enthalpy and read as:
𝜕¯𝜌
𝜕𝑡 +∇·(¯𝜌˜u)=0,(1)
𝜕¯𝜌˜u
𝜕𝑡 +∇·(¯𝜌˜u˜u)=−∇·𝜏𝑀−∇¯𝑝+∇·(¯𝜇∇˜u),(2)
𝜕 𝜌 ˜
ℎ
𝜕𝑡 +∇·𝜌˜u˜
ℎ=−∇·𝜏ℎ+∇·¯𝜌¯
𝐷∇˜
ℎ,(3)
where standard notation is used for all the quantities with
¯𝜌,˜u,˜
ℎ,˜
𝐷,¯𝑝and ¯𝜇represent the density, velocity vector,
total enthalpy (sensible and chemical), diffusivity, pres-
sure and dynamic viscosity using filtered quantities. The
𝜏term stands for the unresolved or subgrid terms related
to the filtering operation and applies to the unresolved
momentum flux 𝜏𝑀and the unresolved enthalpy flux 𝜏ℎ.
The subgrid viscous stress tensor is determined based on
the Stoke’s assumption and the turbulence contribution
is obtained by the use of the Boussinesq approxima-
tion [14]. A unity Lewis number assumption has been
made to simplify the scalar transport in the governing
equations. Heating due to viscous forces is neglected
in the enthalpy equation and the unresolved heat flux is
modelled using a gradient diffusion approach [15]. The
2
modelling framework is closed by an appropriate expres-
sion for the subgrid-scale viscosity. The eddy-viscosity
is obtained from the Vreman [16] model using a constant
𝑐𝑘=0.1. The same single-value constant has been used
in previous studies and it is also retained here [13, 17].
The flame structure of this non-premixed flame is de-
termined by the flamelet method [13]. Based on the
characteristics of the mixing field, a comparison of the
tabulation of premixed laminar flames and counterflow
diffusion flames for the construction of the thermochem-
ical database is undertaken, though the results presented
here will only include those based on diffusion flamelets.
An unsteady extinguishing flamelet is used as a natu-
ral continuation of this two-dimensional manifold [18].
The flamelet database uses the chemistry from the full
San Diego mechanism (Chemical-Kinetic Mechanisms
for Combustion Applications [19]), which demonstrated
excellent performance for predicting hydrogen flames in
a variety of flow conditions [13, 15, 20] and is also re-
tained here. The effects of heat loss on the flamelet
database are considered by the tabulation of strained
diffusion flames at different enthalpy levels. Three con-
trolling variables are used to characterize the thermo-
chemical state of the flamelets composing the manifold:
mixture fraction 𝑍, progress variable 𝑌𝑐, and normalized
enthalpy 𝑖. In order to account for turbulent/chemistry
interactions at the subgrid scale, the tabulated properties
from the manifold are integrated with a presumed-shape
probability density function (PDF) that describes the sta-
tistical effect of turbulence on the flame structure [21].
The systems of equations read:
𝜕𝜌 ˜
𝑍
𝜕𝑡 +∇·𝜌˜u˜
𝑍=−∇·𝜏𝑍+∇·¯𝜌¯
𝐷∇˜
𝑍,(4)
𝜕𝜌 ˜
𝑌𝑐
𝜕𝑡 +∇·𝜌˜u˜
𝑌𝑐=−∇·𝜏𝑌𝑐+∇·¯𝜌¯
𝐷∇˜
𝑌𝑐+ ¤𝜔𝑌𝑐,
(5)
𝜕𝜌𝑍𝑣
𝜕𝑡 +∇·(𝜌˜u𝑍𝑣)=−∇·𝜏𝑍𝑣+∇·¯𝜌¯
𝐷∇𝑍𝑣(6)
−2𝜏𝑍·∇˜
𝑍−2𝑠𝜒𝑍.
The unresolved terms 𝜏𝑍and 𝜏𝑌𝑐are closed using a
gradient diffusion approach [21]. The term ¤𝜔𝑌𝑐is the
filtered progress variable source term and 𝑠𝜒𝑍is the
unresolved part of the scalar dissipation rate, which is
modeled assuming a linear relaxation of the variance
within the subgrid [21].
3. Computational cases
The operating conditions considered in this study cor-
respond to a lean point at equivalence ratio 𝜙=0.6
during stable operation. The burner operates with a
Reynolds number Re =75000 based on the mixing tube
diameter with pre-heated air at Tair =453K and hydro-
gen coming at TH2 =320K. Geometrical details of the
burner and additional parameters describing the operat-
ing point can be found in the experimental papers [6–9]
and our previous numerical work [11–13].
For the mixing analysis, an evaluation of different
aspects going from the resolution of the mesh, a simpli-
fication of the fuel injection and including Lewis number
effects using constant Lewis number (𝐿𝑒) in the mixture
fraction and subgrid variance transport equation are con-
sidered. The baseline case (BL) corresponds to the case
with unity Lewis number, the fuel injection directly on
the boundary patch with 16 holes, and the reference mesh
with resolution of 0.4 mm in the mixing tube, see[13] for
further information about this mesh. The rest of cases
includes variation in these parameters and the fine mesh
includes a resolution in the upstream part of the mixing
tube of 0.1 mm to better resolve the mixing process. A
summary of the test cases is given in Table 1. The react-
ing cases include two cases considering the full domain,
the reference mesh and unity Lewis number including
an adiabatic and non-adiabatic case respectively.
Table 1: Computational cases for the mixing analysis
Case 𝐿𝑒 Domain Mesh
BL 1.0 Simple Regular
C1D 1.0 Full Regular
C1M 1.0 Simple Fine
C1L 0.5 Simple Regular
4. Results
In this section, results of the mixing analysis and the
reacting flow field are presented. The study of mixing
aims to evaluate the impact of modelling and numerical
parameters on the development of the axial velocity pro-
files and mixture fraction distribution across the mixing
tube. The reacting case describes the preliminary results
of the flame comparing adiabatic and non-adiabatic cal-
culations.
4.1. Mixing
As the fuel-air mixing plays an important role in flame
dynamics and flashback resistance, a dedicated analysis
of the mixing process is presented. Firstly, an study
of the interaction between the fuel jets and the swirling
3
Figure 2: Time-averaged axial velocity (left) and mixture fraction
(right) of BL-case in central plane.
air is conducted to evaluate the impact of the fuel mo-
mentum and fuel-air mixing on the velocity profiles and
mixture fraction field across the mixing tube. The com-
plete domain (Case C1D) is compared to a simplified
configuration in which the fuel is directly injected into
the boundary patches at constant flow rate. The fuel is
injected in the upstream part of the mixing tube through
16 injection holes and the hydrogen is mixed with the
swirling air. This partially premixed mixture forms a
rich ring surrounding the AI. This interaction results in
a region with high axial velocity that is attenuated as
the flow develops downstream. The hydrogen concen-
tration is shifted to the centerline of the mixing tube
developing a partially premixed mixture that is richer
on the central part, which is consistent with the experi-
mental and numerical findings [8, 12]. The mixing field
suggests the flame can exhibit equivalence ratio fluctua-
tions, which do not introduce instabilities as found in the
experiments [9] and numerical simulations[13]), but can
influence the flame stabilization mechanisms. Looking
at the axial velocity distribution at the mixing tube outlet
it can be seen that the flow does not overcome the central
axial velocity deficit over the whole length of the mixing
tube. Therefore, the VB stabilizes just at the outlet of
the mixing tube. Further analysis is devoted in the next
subsection to this effect.
Considering the differences in magnitude of the trans-
port properties for hydrogen and air, an assessment of the
influence of diffusivity and viscosity on the mixing pro-
cess was conducted. Preferential diffusion effects might
influence the mixing and combustion process in turbu-
lent flames [22], so this is examined here. The unity
Lewis number approach is compared with a constant ef-
fective Lewis number 𝐿 𝑒 =0.5. As mentioned in Tab.
1), case C1L had the Lewis number set to 𝐿 𝑒 =0.5,
while the species diffusion in case C1 was set to half
the species diffusivity with 𝐿 𝑒 =1. Figure 3 shows
the development of axial momentum in the mixing tube
considering the 4 different cases.
Figure 3 exhibits few characteristics that illustrate the
aforementioned descriptions. At the beginning of the
mixing tube, the axial momentum of the case C1D is
clearly higher than the rest of cases. This is due to
the higher but unevenly distributed injection velocities,
which differ from the BL-case in not being forced uni-
formly onto the boundary condition of the mixing tube.
At approximately 𝑧=0.056 [𝑚]the axial momentum
reaches its maximum, which can be attributed to the
flow adapting to the end of the swirler veins. The spa-
tial variations in axial momentum along the mixing tube
correspond to variations in the velocity field across the
mixing tube, see Fig. 2.
The swirl number is reduced as the flow approaches
the combustion chamber. As discussed by Burmberger
and Sattelmayer [10], a decline in swirl number is caused
by a negative gradient of azimuthal velocity along the
Figure 3: Comparison of axial momentum averagedover cross sections
of the mixing tube (orange lines mark coordinates of specified cross
section, see Fig. 5).
Figure 4: Comparison of swirl number averaged over cross sections
of the mixing tube (orange lines mark coordinates of specified cross
section, see Fig. 5).
4
Figure 5: Velocity profiles along the mixing tube for BL-case.
mixing tube axis. The distribution of the swirl number
for the different computational cases is shown in Fig.
4. To better understand this effect, the velocity profiles
at different cross sections along the mixing tube are
shown in Fig. 5. A velocity deficit along the center
line is developed, which is partially influenced by the
high hydrogen content in the central part that reduces
the density. The description of the reacting flow fields
for this flame is given in the next section.
4.2. Reacting flow
This section describes some preliminary results of the
reacting flow field of the hydrogen flame. The flame can
be distinguished in Fig. 6 by a contour plot of the ve-
locity and progress variable fields at the middle plane of
the burner during stable operation. A partially premixed
mixture is exiting the mixing tube and a flame is stabi-
lized by vortex breakdown in the combustion chamber.
The flame is anchored by the central and corner recir-
culation zones and it is stabilized partially inside the
mixing tube.
The proximity of the flame tip to the entrance of the
combustion chamber develops an increase in axial ve-
locity that provides resistance to flashback. The flame is
burning around the global mixture fraction 𝑍𝑔=0.017,
though it extends from 𝑝 ℎ𝑖 =0.45 to near stoichiomet-
ric conditions. The values of temperature conditioned to
the mixture fraction can be used to identify the burning
conditions, and this is shown in Fig. 7. The addition of
heat loss has influenced the burning characteristics of
the flame and more departure from equilibrium.
A comparison of the computed velocity field with
the PIV data from Reichel et al., (2015) [8] along the
centerline is shown in Fig. 8. It shows the simulations
overpredict the maximum axial velocity at the mixing
tube, which can be caused by a stabilization of the flame
partially inside the mixing tube. After the flow expan-
sion, the LES can capture the position of the VB and
the size of the recirculation for the non-adiabatic case.
The results show an improvement on the prediction of
the flow field by adding heat loss to the combustion
model. The maximum axial velocity after the expansion
is reduced due to heat loss and the size of the central
recirculation is also improved. The heat loss simulation
is still unfinished and it is expected to further influence
the velocity field. The mean velocity fields for the two
cases at the middle plane is shown in Fig. 9. Further
analysis and validation are currently performed.
Figure 6: Axial velocity (left) and progress variable (right) fields of
the flame including heat loss during stable burning.
Figure 7: Conditioned temperature to the mixture fraction coloured
by the progress variable. Adiabatic case (upper) and heat loss case
(lower).
5
5. Conclusions
This study presents some preliminary results of the
large-eddy simulations of a technically premixed swirl
stabilized hydrogen burner with axial air injection. The
burner was designed by Reichel et al. [6–9] to operate
with fuel flexibility under lean conditions. The main
outcomes of the experimental investigation show the ax-
ial air injection and fuel momentum contribute to FB
resistance by displacing the VB further downstream. To
model this behaviour, LES in the low Mach number limit
with flamelet methods are used to study the main driving
mechanisms leading to flame stabilization in this burner.
The mixing analysis show that the central axial velocity
deficit could not be overcome over the whole length of
the mixing tube, leading to VB very close to the mix-
ing tube outlet, probably promoted by a fuel-rich central
zone. Regarding the influence of transport properties,
different Lewis numbers did not show an effect on the
iso-thermal flow. Preliminary results of the reactive flow
show the flame stabilizes partially inside the mixing tube
developing an increase in axial velocity along the cen-
terline that overpredicts the experimental values. This
overprediction is reduced by including heat loss and cur-
rent effort is dedicated to perform further analysis and
validation in this operating point considering different
tabulation strategies.
Acknowledgments
The research activities conducted here have been fi-
nanced by the CoEC project from the European Union’s
Horizon 2020 research and innovation programme under
grant agreement No 952181.
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