# LES of a non-premixed hydrogen flame stabilized by bluff-bodies of various
shapes

Agnieszka Wawrzak1$\star$ 1 Czestochowa University of Technology, Faculty of
Mechanical Engineering and Computer Science, Al. Armii Krajowej 21, 42-201
Czestochowa, Poland  Robert Kantoch1 1 Czestochowa University of Technology,
Faculty of Mechanical Engineering and Computer Science, Al. Armii Krajowej 21,
42-201 Czestochowa, Poland  and Artur Tyliszczak1 1 Czestochowa University of
Technology, Faculty of Mechanical Engineering and Computer Science, Al. Armii
Krajowej 21, 42-201 Czestochowa, Poland  1 Czestochowa University of
Technology, Faculty of Mechanical Engineering and Computer Science, Al. Armii
Krajowej 21, 42-201 Czestochowa, Poland

##  1 Introduction

A better understanding of mutual interactions between turbulent flow and flame
occurring downstream the bluff-body geometries limit the further progress in
improvements in the efficiency and safety of various combustion applications
(burners, chambers, engines). Moreover, a suitable control of turbulent flames
dynamics is required for establishment of low-emissions devices according to
current international regulations. Such a control can be achieved by applying
passive and/or active flow control techniques. Both provide modulation of the
multi-scale mixing processes (enhancement/suppression) by the intensification
of interactions between large and small turbulent scales.

Using the bluff-body as a part of the injection system constitutes the
prominent example of the passive flame control. The bluff-body generates
recirculation zones improving the mixing and stabilizing the flame position
(Docquier and Candel, 2002). Tyliszczak et al. (2014) examined a non-premixed
flame stabilized in a central recirculation zone produced by a
conical/cylindrical bluff-body. They showed that the flame is approaching
extinction due to even small changes in simulation parameters. Combination of
the passive and active control methods can be applied for optimization of the
combustion process in bluff-body burner as it was shown by Kypraiou et al.
(2018). The researchers performed the experimental studies on the premixed,
partially-premixed and non-premixed methane flames showing that the impact of
acoustic oscillations on the bluff-body flames is directly related to the fuel
injection system.

The complexity of turbulent mixing and combustion processes raises many
important questions that still remain unanswered, despite the great interest
of the scientific community in this field. For instance, to what extend does
the mixing of the fuel and oxidizer downstream the bluff-body depend on the
shape and roughness of the bluff-body? As it was recently demonstrated by
Dróżdż et al. (2021), the wavy wall, with carefully selected waviness
parameters, can effectively enhance the effect of amplitude modulation and
hence increase wall shear stress and postpone turbulent separation.

Concerning the geometrical shaping, interesting findings were recently
reported by Tyliszczak et al. (2022). The authors showed a distinct trend
regarding the dynamics of the jets coming out from the shaped orifices. They
found a shorter potential core and faster velocity decay for a circular jet
compared to a non-circular one, e.g., issuing from a triangular nozzle. This
contradicted the common knowledge of the jets emenating from sharp-edged
orifices. In general, they are more energetic compared to jets generated by
smoothly profiled nozzles, therefore they are characterized by a faster decay
of the axial velocity (Mi and Nathan, 2010; Kuban et al., 2021). Nevertheless,
Tyliszczak et al. (2022) have shown that the level of control that can be
achieved by shaping the nozzle is higher than previously expected.

The present paper aims at numerical simulations of non-premixed hydrogen flame
stabilized by specially designed bluff-bodies with corrugated surfaces.
Computational fluid dynamics (CFD) tools have been widely used for the flame
control analyses providing the results related to both the global
characteristics as well as concerning deep insight into a flame structure and
its dynamics.

In this work we use the Large Eddy Simulation method and a ’no model’ approach
for the simulations of the combustion process where the chemical sources terms
are calculated directly using the filtered variables (Duwig et al., 2011). The
response of the flame to different wall topologies (flat or wavy, with the
waviness oriented streamwise) and complex shapes (hexagram, square) is
thoroughly discussed based on instantaneous and time averaged results.

##  2 Modelling

###  2.1 LES Approach

In the present study we use two different numerical LES solvers and apply a
two-stage computational approach. In the first stage (I), the second order
ANSYS Fluent LES solver is involved to model the flow inside the inlet section
of the bluff-body burner. The further calculations (stage II) are performed
using a in-house high-order numerical algorithm based on the projection
methods (Tyliszczak, 2016). It solves the Favre filtered set of the governing
equations assuming the low Mach number approximation (Geurts, 2004):

$\partial_{t}\bar{\rho}+\nabla\cdot(\bar{\rho}\widetilde{\mathbf{u}})=0$ (1)
$\bar{\rho}\partial_{t}\widetilde{\mathbf{u}}+(\bar{\rho}\widetilde{\mathbf{u}}\cdot\nabla)\widetilde{\mathbf{u}}+\nabla\bar{p}=\nabla\cdot\
(\boldsymbol{\tau}+\boldsymbol{\tau}^{\mathrm{SGS}})$ (2)
$\bar{\rho}\partial_{t}\widetilde{Y}_{\alpha}+(\bar{\rho}{\widetilde{\mathbf{u}}\cdot\nabla)\widetilde{Y}_{\alpha}}=\nabla\cdot\left({\bar{\rho}({D}_{\alpha}+{D}^{\mathrm{SGS}}_{\alpha}){\nabla\widetilde{Y}_{\alpha}}}\right)+\overline{\dot{w}}_{\alpha}$
(3)
$\bar{\rho}\partial_{t}\widetilde{{h}}+(\bar{\rho}{\widetilde{\mathbf{u}}\cdot\nabla)\widetilde{h}}=\nabla\cdot\left({\bar{\rho}({D}+{D}^{\mathrm{SGS}}){\nabla{h}}}\right)$
(4) $p_{0}=\overline{\rho}R\widetilde{T}$ (5)

where the bar and tilde symbols denote filtered quantities, ${u}_{i}$ are the
velocity components, $p$ is the hydrodynamic pressure, $\rho$ is the density
and $h$ stands for the total enthalpy. The symbols $p_{0}$ and $R$ are the
thermodynamic pressure and gas constant, respectively. The subscript $\alpha$
is the index of the species $\alpha=1,\dots,\textrm{N-species}$ whereas the
variables $Y_{\alpha}$ represent species mass fractions. An unresolved sub-
grid stress tensor, resulting from the filtering of the non-linear advection
terms is defined as
$\boldsymbol{\tau}^{\mathrm{SGS}}=2\mu_{\mathrm{t}}\mathbf{S}$, where
$\mathbf{S}$ is the rate of strain tensor of the resolved velocity field and
$\mu_{\mathrm{t}}$ is the sub-grid viscosity computed according to the model
proposed by Vreman (2004). The sub-grid diffusivities in Eqs. 3, 4 are
computed as ${D}^{\mathrm{SGS}}=\mu_{t}/(\bar{\rho}\sigma)$ where $\sigma$ is
the turbulent Schmidt/Prandtl number assumed equal to 0.7 (Jones and Navarro-
Martinez, 2007).

Figure 1: Schematic view on the computational configuration. Bluff-body
geometries and computational meshes.

The chemical sources terms $\overline{\dot{w}_{\alpha}}$ in Eq. 3 involve the
filtered reaction rates of species $\alpha$, which are strongly non-linear
functions of the species mass fractions and enthalpy:

$\overline{\dot{w}_{\alpha}(\mathbf{Y},h)}={\dot{w}_{\alpha}(\widetilde{\mathbf{Y}},\widetilde{h})}+\mathcal{F}(\widetilde{Y_{\alpha}{Y_{\alpha}}^{{}^{\prime\prime}}},\widetilde{{Y_{\alpha}}^{{}^{\prime\prime}}T},\dots)$
(6)

They are computed applying the ’no model’ approach and are calculated directly
using the filtered variables
$\overline{\dot{w}_{\alpha}(\mathbf{Y},h)}={\dot{w}_{\alpha}(\widetilde{\mathbf{Y}},\widetilde{h})}$
(Duwig et al., 2011).

Figure 2: Axial velocity profiles at three different heights above the bluff-
body obtained using Fluent and SAILOR codes.

(a) cylindrical bluff-body with the flat wall

(b) square bluff-body

(c) star bluff-body

(d) cylindrical bluff-body with the wavy wall

Figure 3: Instantaneous $Q$-parameter isosurfaces and vorticity modulus
contours in the central cross-section shown at the boundaries. The partially
translucent blue cylindrical surfaces denote a border of subdomain used for
the calculation of the entrainment.

Figure 4: Instantaneous distributions of the OH mass fraction, temperature,
heat release rate (HRR), scalar dissipation rate (SDR), and the axial
velocity. The black line represents its zero level. The results obtained for
the various bluff-bodies are shown in the rows.

###  2.2 Test case

In the present work we consider a typical combustion chamber with a conical
bluff-body similar to the one studied experimentally by Kypraiou et al.
(2018). We replace the methane by the hydrogen diluted with nitrogen, which is
an alternative zero-carbon fuel. The hydrogen mass fraction in the fuel stream
is equal to 0.05. A schematic view of the analysed configuration is presented
in Fig. 1. The cold fuel (300 K) is injected to the chamber through the 4 mm
slot in a fuel pipe ended with a bluff-body surface. The bulk axial velocity
of the fuel is assumed equal to $10$ m/s. Inside the chamber the fuel ignites
in a co-flowing air heated to 1000 K. A global equivalence ratio is equal to
0.047 and the theoretical power generated by the combustion process is 0.5 kW.
Unlike in the original configuration of Kypraiou et al. (2018) we do not add
the swirl to the oxidizer stream and the dominant effect on the flame is due
to the changing geometry of the bluff-body.

Concerning the dynamics of the bluff-body stabilized flames, directly above
the bluff-body a central recirculation zone (CRZ in Fig. 1) is formed. Its
dimensions and inner structure depend on the bluff-body size and flow
parameters. Inside CRZ a smaller inner recirculation zones (IRZs) may exist.
The bluff-bodies investigated in this paper are characterised by the
equivalent diameter $D_{b}=2\,\sqrt[]{S/\pi}$=25 mm ($S$ \- actual area of
bluff body) and they are placed in a circular duct of diameter $D$=37 mm. Four
different bluff-bodies are considered, the cylindrical with a flat and wavy
wall (waviness oriented streamwise), square, and hexagram (star) one. All
geometries are displayed in Fig. 1 along with the computational meshes
prepared in the ANSYS Meshing module.

###  2.3 Numerical details

As mentioned before, the simulations are performed using a two-stage approach
schematically presented in Fig. 1. In the first stage (I) the ANSYS Fluent
solver is used to model the flow through the entrance duct and around the
bluff-bodies. During these calculations we acquire unsteady velocity signals
at the end of the inlet section for a period of 150$D_{b}/U_{b}$ ($U_{b}$\-
bulk velocity of the co-flow). The computational grids for all bluff-bodies
generated in ANSYS Meshing module are shown in the central cross-section in
Fig. 1. They are block-structured and precisely fitted to the shape of each
bluff-body. All geometries are discretised in this way that a near-wall cell
size allows for a proper resolution of the turbulent boundary layers
($y+\approx 1$). The minimum element size is assumed at the level of 0.5 mm
for the bluff-body with the flat wall, whereas in the case of the wavy-wall a
finer mesh in the near-wall region is used with the cell height 0.25 mm. The
overall numbers of cells in the inlet duct are equal to 3.6$\times 10^{5}$ and
3.7$\times 10^{5}$ for the cylindrical bluff-body with the smooth and wavy
wall, respectively.

In the second part of the calculations (stage II) the SAILOR code is applied,
which so far has been used in a number of studies devoted to combustion
problems in jet type flames (Tyliszczak, 2015; Rosiak and Tyliszczak, 2016)
and mixing layers (Wawrzak and Tyliszczak, 2019, 2020). The extracted velocity
fields from the stage I of the simulations are imposed onto the inlet plane of
the computational domain involving only the outer section of the burner (see
Fig. 1). There is no heat transfer between the flame and the bluff-body, since
the bluff-body is only embedded in the preliminary Fluent simulations. In a
real situation, a flame attached to a bluff-body would certainly lose heat
toward it. However, we neglected this effect and conducted comparative studies
focusing on flow structure affected by different bluff-bodies. One would
expect that the possible errors resulting from the applied procedure would be
similar in all cases.

In stage II, the computational domain extends 6$D_{b}$ in the axial direction
and 4$D_{b}$ in the radial and tangential directions. A grid independent
solution is obtained at a grid size $N_{x}\times N_{z}\times N_{y}=144\times
144\times 192$ nodes. The nodes are compacted axially and radially but almost
a uniform mesh is constructed close to the inlet section. The maximum cell
volume is equal to $1.7\times 10^{-9}$ m3, that corresponds to the minimum
cell volume of the computational meshes used in the ANSYS software. The time-
step is computed according to the Courant-Friedrichs-Lewy (CFL) condition with
the CFL number assumed equal to 0.25.

Concerning the boundary conditions, at the side boundaries the velocity is set
to zero and the species and enthalpy are computed form the Neumann condition,
i.e., $\partial{Y}_{\alpha}/\partial n=0$ and $\partial h/\partial n=0$. The
pressure is computed from the Neumann condition ($\partial p/\partial n=0$)
both at the side boundaries as well as at the inlet plane. At the outlet
boundary, all velocity components, species and enthalpy are computed from the
convective boundary condition $\partial C/\partial t+V_{c}\partial C/\partial
y=0$, where $C$ represents a general variable and $V_{c}$ is the convection
velocity calculated as the mean velocity in the outlet plane. To avoid back-
flow the velocity $V_{c}$ is limited such that $V_{c}=\max(V_{c},0)$. The
pressure at the outflow is assumed constant and equal to $p=101325$ Pa.

The SAILOR code uses the projection method for pressure-velocity coupling
(Tyliszczak, 2016) combined with a predictor-corrector method (Adams-Bashforth
/ Adams-Moulton) applied for the time integration. The spatial discretization
is performed on half-staggered meshes applying the 6th order compact finite
difference approximation for the momentum and continuity equations. The
second-order TVD (Total Variation Diminishing) scheme with Koren limiter is
used for the transport equations for chemical species and enthalpy. The time
integration of the chemical source is performed with the help of the VODPK
(Variable-coefficient Ordinary Differential equation solver with the
Preconditioned Krylov method) solver (P. N. Brown and A.C. Hindmarsh, 1989)
that is well suited for stiff systems. The chemical reaction terms are
calculated using the CHEMKIN interpreter and the chemical reactions are
computed using detailed mechanism of Mueller et al. (Mueller et al., 1999)
involving 9 species and 21 reactions.

Preliminary simulations performed using ANSYS Fluent and the SAILOR code for
the air stream flowing in the duct around the cylindrical bluff-body were
conducted to verify the solution strategy. The comparison of the velocity
profiles behind the bluff-body revealed that an interpolation of the velocity
components required for the two-stage computational procedure does not
introduce significant errors. As can be seen in Fig. 2 both solvers provided
similar velocity evolution downstream of the bluff-body. However, the results
obtained using the SAILOR code seem to be more accurate, at least
qualitatively, as they reflect the symmetric shape of the bluff-body. The
applied two-stage approach was also proven to yield the correct results in
previous studies devoted to passively controlled jet flames issuing from
polygonal nozzles (Kuban et al., 2021).

(a) cylindrical bluff-body with the flat wall

(b) square bluff-body

(c) star bluff-body

(d) cylindrical bluff-body with the wavy wall

Figure 5: Time-averaged axial velocity contours (mean-left, r.m.s-right) and
isolines of the zero axial velocity ($\left<U_{y}\right>=0$).

##  3 Results

###  3.1 Instantaneous flame dynamics

As the streams of the fuel and oxidizer are injected from the inlet plane into
a quiescent ambient fluid the flow undergoes the Kelvin-Helmholtz instability
due to velocity gradients in the shear layers. The vortex rings are generated
and detached from the bluff body edge. Their shape is respective to the bluff-
body shape that can be deduced based on the $Q$-parameter isosurfaces
presented in Fig. 3. In this figure, the blue cylinders denote the control
surface used to predict the entrainment rate, which will be discussed later.
Additionally, the vorticity magnitude plotted on the central cross-section is
shown at the sides. Depending on the bluff-body, the flow fields differ and it
can be seen that with increasing bluff-body complexity the flow patterns
become more complex. Since the initial vortices are considerably dependent on
the shape and wall topology of the bluff-body, their distortion changes as
they travel downstream. Regarding the circular bluff-body, an earlier
formation of streamwise vortical structures takes place for the case with the
flat wall, whereas stronger vortex rings are observed when the wall is wavy.
The results obtained for the cases with the square and star bluff-bodies
reveal very complex flow structure. The presence of small-scale vortices
generated behind the sharp corners causes a deformation of large vortical
structures closer to the inlet compared to the case with the circular bluff-
body. Comparison of the vorticity contours reveals that flow inside CRZ is the
most energetic for the cases with the non-circular shapes, consistently with
the findings for non-reacting jet flows (e.g. Tyliszczak et al. (2022)). For
the cases with the square and star bluff-bodies the vorticity contours seem to
be more wrinkled, especially in the region closer to the inlet in the outer
shear layer. Keeping in mind that the flames reflect the shapes of the bluff-
bodies close to the inlet plane, it is expected that the impact of large-scale
intense vortices on the flame structure and its shape is prominent.

(a) mean axial velocity

(b) rms axial velocity

(c) entrainment rate

Figure 6: Centerline profiles of the time-averaged axial velocity (a) and its
fluctuations (b) and the profiles of the entrainment (c).

Figure 4 illustrates the instantaneous distributions of OH species mass
fraction, temperature, heat release rate (HRR), scalar dissipation rate (SDR),
and the axial velocity. It can be observed that the flames are stabilized by
the reversed flow (see the black isolines indicating the recirculation zones)
that also manifests by a large level of OH species in the inner shear layer.
The heat release rate is found to be the strongest near the flame edge where
also the OH species is abundantly produced. Both the OH and HRR distributions
indicate relatively low reactive regions inside the recirculation zones within
the axial distance $y/D=0.4-0.8$. Here, the fuel is rapidly mixed with the
recirculating hot air and combustion products promoting the partial oxidation
accompanied by a small amount of heat release. The scalar dissipation rate is
low in these regions, contrary to the vicinity of the bluff-body flame and
downstream axial locations. Finally, it can be seen that the recirculation
zone, which have the shape depending on bluff-body, controls the shape of the
flame.

###  3.2 Statistical properties

Detailed analysis of the flame dynamics in CRZ has been carried out based on
the time-averaged results presented in Figs. 5-7. The time-averaging procedure
started after the flames fully developed in the domain and was continued for
250$D_{b}/U_{b}$ time units resulting in well-converged statistical results.
Figure 5 presents the contours of the time-averaged axial velocity and its
fluctuations (r.m.s) for all cases considered. The location of the
recirculation zone is represented by the isolines of $\left<U_{y}\right>=0$.
As can be seen, the narrowing of the central recirculation zones is caused by
the the oxidizer stream. This is accompanied by a significant increase of the
axial velocity fluctuations due to a strong shear forces. It is evident that
the location, size and shape of the recirculation zones are only slightly
affected by the wall topology compared to the changes caused by the bluff-body
shape. However, there are noticeable differences regarding the cases with the
flat and wavy walls. Unlike as in the case with the flat wall, the isoline of
the zero axial velocity in the case with the wavy wall is nearly parallel to
the fuel stream. It results in an enhanced mixing that manifests by a more
uniform velocity field inside CRZ. It is also clearly seen that the
recirculation zone shrinks radially in the case with star bluff-body. It
significantly changes the shape also when the square bluff-body is used. In
this case, the fluctuation maximum is shifted beyond the recirculation zone.

Centerline profiles of the mean and r.m.s axial velocity normalized by $U_{b}$
are presented in Figs. 6(a) and 6(b). In the initial part of the flow they
represent mainly the velocity of the fuel. It can be seen that in all the
cases it starts to decay almost in the same axial locations. The smallest drop
is found for the case with the square bluff-body. In this case, the axial
velocity minimum is about $U_{y}/U_{b}$=0.1 larger and is shifted $15\%D_{b}$
towards the bluff-body. Concerning the differences in the fluctuations
profiles it can be seen that for the case with the square bluff-body the
fluctuations maximum occurs earlier (0.1$D_{b}$) and reaches approximately 5%
lower level compared to the remaining cases. The shift and smaller value of
the velocity minimum are the result of intensified mixing caused by the small
vortices generated at the sharp corners. This suggests that the square bluff-
body can ensure the most intensified fuel/oxidizer mixing.

The entrainment is calculated following Wygnanski and Fiedler (1969) as:

$\frac{d\dot{Q}}{dy}=\ointop_{c}\mathbf{U}\cdot\mathbf{n}dc=\int_{0}^{2\pi}\left\langle
V_{r}\right\rangle rd\theta$ (7)

where $\dot{Q}$ is the volume flux, $c$ is a path outside a given region,
$\mathbf{U}$ and $\mathbf{n}$ are the velocity and normal vectors, $V_{r}$ is
the radial velocity component. In this work we calculate the entrainment over
a surface of a cylindrical domain with the radius 1.5$D_{b}$ that was shown in
Fig. 3. This cylinder encloses the flow region in which the majority large
vortical structures fits.

The entrainment rate profiles presented in Fig. 6(c) shows that starting from
$y/D>0.2$ the volume flux linearly increases up to $y/D\approx 1.5$ that is
approximately the distance where the recirculation zones end. It drops further
downstream and reaches the local minimum at $y/D\approx 3$. Concerning the
impact of the bluff-body geometry on the entrainment, it can be seen that only
minor differences between the cases with the flat and wavy exist. The most
pronounced one seems to be the faster entrainment growth immediately above the
bluff-body surface for the case with the flat wall. The situation changes when
the star bluff-body is used. In this case, starting from approximately
$y/D=0.1$ the entrainment increases the fastest. This is caused by the
vortices generated in the acute corners and their quicker break-up. They also
alter the central flow downstream and therefore the maximum occurred at
$y/D\approx 1.5$ is lower than in the remaining cases. Regarding the region
above the recirculation zones, i.e., $y/D>2$, the solution obtained for the
configuration with the square bluff-body differs the most. In this case,
rather than the local minimum the profile reveals a plateau at relatively high
level. A similar shape of the entrainment in this region is observed for the
star bluff-body, yet, in this case the values of the entrainment are more or
less the same as in the cases with the cylindrical bluff-bodies.

(a) mean H2 (b) mean temperature

(c) rms temperature

Figure 7: Radial profiles of the time averaged H2 species mass fraction and
temperature (mean and rms) at different axial locations.

The increase of the entrainment in the configurations with the star and square
bluff-bodies influences the radial distribution of the hydrogen mass fraction
and temperature. Their profiles in three different axial distances inside the
recirculation zone ($x/D_{b}$=1, $y/D_{b}$=1.25, $y/D_{b}$=1.5) are presented
in Fig. 7. The enhancement of the mixing for the case with the square bluff-
body is manifested by a reduced fuel mass fraction in the axis at the distance
$y/D_{b}$=1.5 (see also Fig. 7(a)). Moreover, for this case the temperature at
$y/D_{b}$=1.5 is approximately 200 K higher compared to the remaining cases.
This means a more intense combustion process in the central part of the flow.
On the other hand, in the region of the shear layer $x/D_{b}$=0.5 the lowest
temperature is found in the configuration with the star bluff-body, especially
at $y/D_{b}$=1.25 and $y/D_{b}$= 1.5. Apparently, in the configuration with
the star shape bluff-body the flame is noticeably shifted towards the axis,
whereas in the case with the square bluff body it seems compacted towards the
inlet plane. This is in line with the observation made for the velocity field
and CRZ structure.

Radial profiles of the temperature fluctuations presented in Fig. 7(c) also
show important differences between particular solutions. Initially
($y/D_{b}$=1-1.25), the local maximum of the temperature fluctuations persists
in the inner shear layer at $x/D_{b}$=0.1 for all the cases. Then, the
fluctuations consistently rise and the maximum shifts towards the axis. It
appears first on the axis at $y/D_{b}$=1.5 when the square bluff-body is used.
In this case, the contribution of the fluctuating component is considerably
higher close to the inlet plane and is transferred further downstream with 40
K higher values than for the cylindrical bluff-body with flat wall. Such
increase in the fluctuating quantities consistently affects the mean
component. Moreover, it can be seen that there are no substantial differences
in the profiles obtained for different wall topologies.

##  4 Summary

The paper presented the analysis of flame structures behind a conical bluff-
body burner having different wall topologies and shapes. The research was
performed using the LES method and two numerical tools, ANSYS Fluent code and
in-house code SAILOR. The former allowed for accurate simulations of the flow
around the complex shape bluff-bodies and the latter for precise modelling of
the combustion process. It has been shown that in the vicinity of the bluff-
body its shape has a strong influence on vortices induced in the shear layer
formed between the central recirculation zone and the oxidizer stream.
Compared to the conventional circular shape, the acute corners caused the
enhancement of the mixing processes in the central recirculation zone. The
impact of change in geometry shape and wall topology observed in instantaneous
results were quantified based on the time-averaged plots of mean and
fluctuating velocity, fuel mass fraction and temperature. In general, it has
been observed that in the configurations with the star and square bluff-bodies
the flame in the recirculation zone is shifted towards the injected fuel
stream. A faster oxidizer entrainment observed in these cases caused an
enhanced mixing process. The analysis of the velocity distributions revealed a
shortened recirculation zone by 15% of the equivalent bluff-body diameter and
the smallest axial velocity drop for the configuration with the square bluff-
body. This resulted in a significantly larger temperature in the centerline of
the flame and higher temperature fluctuations. The influence of the wall
topology (flat vs. wavy) in the configuration with the classical conical
bluff-body turned out to be very small. It resulted only in minor
modifications of the flow structures in the direct vicinity of the inlet plane
but this had practically no impact on the flame formed downstream.

## Acknowledgment

This work was supported by the National Science Center in Poland (Grant
2020/39/B/ST8/02802) and statutory founds (BS/PB-1-100-3011/2022/P). The
computations were carried out using the PL-Grid Infrastructure.

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