12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

NUMERICAL ANALYSIS OF THE FLOW DYNAMICS BEHIND
NON-CIRCULAR BLUFF-BODIES

Agnieszka Wawrzak
Robert Kantoch
Department of Thermal Machinery
Department of Thermal Machinery
Czestochowa University of Technology
Czestochowa University of Technology
Al. Armii Krajowej 21, 42-201 Czestochowa, Poland Al. Armii Krajowej 21, 42-201 Czestochowa, Poland
agnieszka.wawrzak@pcz.pl
robert.kantoch@pcz.pl

Artur Tyliszczak
Bernard J. Geurts
Department of Thermal Machinery
University of Twente
Czestochowa University of Technology
P.O. Box 217
Al. Armii Krajowej 21, 42-201 Czestochowa, Poland 7500 AE Enschede, The Netherlands
artur.tyliszczak@pcz.plb.j.geurts@utwente.nl

ABSTRACTsive flame control often relies on a trial-and-error approach
because of the largely unknown response of the flow dynamics
to changes in the inlet parameters. It turns out that even smallchanges may drastically alter the combustion regimes. For instance, Tyliszczak et al. (2014) showed that a non-premixed
flame stabilized in a central recirculation zone produced bya conical/circular bluff-body may extinguish following even asmall change of the system parameters. Passive and active control techniques may also be combined as shown by Kypraiou
et al. (2018). These experimental investigations focused on
the impact of acoustic oscillations on bluff-body flame andtheir connection to a fuel injection system. Despite huge interest of the research community in the combustion instabilities, numerous questions still remain unanswered, e.g., to what
extent the mixing of fuel and oxidizer downstream the bluffbody depend on the shape and roughness of the bluff-body?
As it was recently found by Kuban et al. (2021) for jet type
flows, the level of control that can be achieved in flames by
nozzle shaping is higher than previously expected. Numerous
works devoted to the jet configurations have been performed
regarding these issues. It turns out that the jets issuing fromsharp-edged orifices are more energetic compared to the jetsgenerated by smoothly contoured nozzles, and therefore they
characterise a faster axial velocity decay (Mi & Nathan, 2010;
Azad et al., 2012). Recent research performed by Tyliszczak
et al. (2022) showed a different trend concerning the dynamics
of the jets issuing from shaped orifices. It was presented thatthe shorter potential core and the faster velocity decay occur
rather for a circular jet than for a non-circular one, e.g., issuingfrom a triangular nozzle. Similar observations were also madeby Aleyasin et al. (2018). The discrepancies between findings
reported in Tyliszczak et al. (2022); Aleyasin et al. (2018) and
Mi & Nathan (2010); Azad et al. (2012) are attributed to differences in the constructions of nozzle ends (smooth, sharp,
contraction type).
The aim of this paper is to better understand multi-scale
mixing processes occurring downstream shaped bluff-body geometries. Particular attention is put on the mixing modulation,i.e., its enhancement or suppression compared to a circularshape. The mixing efficiency is crucial for flame initiation (ig-

The dynamics of passively controlled turbulent flow
around different bluff-bodies used in the injection system of
a combustion chamber is studied using large-eddy simulation(LES). The influence of three bluff-body geometries (cylindrical, square, star) is analyzed using an in-house high-orderacademic code. The inlet boundary conditions are generated
separately using the ANSYS Fluent software in a precursor
simulation. The paper focuses on the structure of the wake,the size and shape of turbulent vortices, the size and locationof the recirculation zones and the impact of these parameters
on a passive scalar mixing. The performed simulations allow
identification of large vortical structures formed downstream
the bluff-bodies. Their topology and dynamics strongly depend on the bluff-bodies shape but the mixing intensity is notnecessarily amplified when non-circular bluff-bodies are used.
In the presence of sharp corners (square and star bluff-body)the small-scale vortices generated in their vicinity cause a deformation of large vortical structures and this effect leads to aless intense entrainment of the flow to the recirculation region.

INTRODUCTION
A suitable control of turbulent flow dynamics is required
for establishing low-emissions and safe industrial devices (engines, burners, combustion chambers, etc.). Therefore, flow
control constitutes a very important field of research both experimentally and numerically. Such control can be achieved byapplying passive and/or active flow control techniques. Passive control involves manipulation of the flow field without
adding any external energy. It is based on geometric shaping or adding fixed elements. Active methods involve energy
input whose type and level may be fixed or vary depending
on instantaneous flow behaviour. In the field of combustion, aprominent example of passive control is the use of bluff-bodies
as parts of the injection systems in the combustion chambers.
The bluff-body generates recirculation zones improving themixing and stabilizing the flame position (Docquier & Candel, 2002). Their dimensions and inner structures depend on
the bluff-body shape and flow parameters. Research on pas-1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

(a)

(b)

Figure 1. Sketch of the bluff-body combustion chamber (a) and the bluff-body geometries (b) with the view of the computational
meshes in the inlet sections for the computations performed using the ANSYS Fluent code.
z=18mm
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Figure 2. Axial velocity profiles downstream the circular bluff-body at various distances from the inlet plane. The symbols refer tothe experimental data (Kypraiou et al., 2018).

MODELLING

nition), propagation, or extinction. In this paper, the researchis carried out using large eddy simulation (LES), which in thepast has been proven to correctly capture the dynamics of thistype of turbulent flow while keeping computational costs at
a reasonable level. To examine and understand the responseof the flow to changes of various inlet parameters associatedwith particular bluff-body shapes we perform the simulationsfor ‘cold’ flow conditions (no chemical reactions). The flow
structure in the vicinity of bluff-bodies is analysed in detail.
The ultimate aim is to answer whether it is possible to findthe shape, which for a given inlet flow parameters would provide the most favourable conditions for a stable combustion
process, e.g., the homogeneity of the flow and low strain rate.
We examine whether using the rectangular or star shape bluffbody improves the turbulent mixing intensity with respect tothe case with the circular bluff-body.

A schematic view of a typical combustion chamber witha conical bluff-body is shown in Fig. 1. It consists of a fuelpipe in the center and an outer section where from the bottom a co-flowing stream is provided through an inlet section
with a cylindrical duct (D=37 mm). An analogous configuration has been used in experimental (Kypraiou et al., 2018) andnumerical (Tyliszczak et al., 2014) investigations of the combustion process stability. In this paper, we modify the shape ofthe bluff-body assuming it as the circular, square or hexagram(star). All bluff-bodies are characterised by the same equivalent diameter Db =25 mm (see Fig. 1), which corresponds to acircle with the√ surface area A the same as a given bluff-body,i.e., Db = 2 Aπ). The research is performed for non-reacting
cases focusing on changes in mixing due to changes in bluffbody shape. To mimic a situation in which both the fuel andoxidizer are provided to an injector system we introduce a mixture of hydrogen and nitrogen (5% H2 /95% N2 ) that is injected
into the combustion chamber through the central pipe (D f =4

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022(a) circular(b) square(c) star

Figure 3. Isosrfaces of instantaneous Q-parameter with the view of the computational meshes for the computations performed using
the SAILOR code.
mm). The co-flowing oxidiser stream is air. Both, the fueland oxidiser, have a temperature of 300 K. The stoichiometricvalue of the mixture fraction is ξST = 0.335. Following the
Bilger’s definition, the mixture fraction is computed as:ξ=(YH −YH,o )/2WH − (YO −YO,o )WO(YH,f −YH,o )/2WH − (YO,f −YO,o )WO

the burner (see Fig. 1). It is a rectangular domain of the length
6Db in the axial direction (‘y’) and the width 4Db × 4Db in the‘x-z’ plane. The sub-grid viscosity is computed according to amodel proposed by Vreman (2004).
The numerical code SAILOR is based on the projection
method for pressure-velocity coupling Tyliszczak (2014) combined with a predictor-corrector method (Adams-Bashforth /Adams-Moulton) for the time integration. The spatial discretization is performed on half-staggered meshes by the 6thorder compact difference approximation for the Navier-Stokes
and continuity equations. The second-order TVD (Total Variation Diminishing) scheme with Koren limiter is used for theconvective terms of the species mass fraction and enthalpy
transport equations. The accuracy of the SAILOR code isdemonstrated in Fig. 2 showing the radial profiles of the mean
axial velocity obtained for the flow configuration analysedby (Kypraiou et al., 2018). In this case, an even more complicated problem than the present one was considered, it included the swirl of the incoming oxidizer stream. The velocity profiles in Fig. 2 are compared at three different axial
distances from the bluff-body. A very good agreement is observed both close to the bluff-body plane (z=8 mm) as well as
further downstream at z=28 mm.

(1)

where Y ’s are the elemental mass fractions, W ’s are atomic
weights and the subscripts, f and o, correspond to the fuel andoxidizer stream, respectively.
The simulations are performed using a two-stage approach. In the first stage, we involve the ANSYS Fluent LES
solver to model the flow inside the cylindrical inlet section,i.e., in the entrance duct and around the bluff-bodies. In theseprecursor calculations, we acquire unsteady velocity signals
at the end of the inlet section for a period of 150Db /Ub (Ub bulk velocity of the oxidiser). In the second part, the simulations are performed using a high-order low Mach number
LES solver SAILOR (Tyliszczak, 2014). The acquired velocity components are superimposed onto the inlet plane of themain computational domain involving only the outer section of3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022(a) y/Db =0.35(b) y/Db =0.6(c) y/Db =0.7(d) y/Db =0.1.5

Figure 4. Contours of the instantaneous vorticity along with isolines of the instantaneous mixture fraction (red colour - ξST = 0.335)
on the ‘x-z’ planes depicted in Fig. 3(b).

RESULTSThis could be already noticed by analysing the Q-parameterin Fig. 3. This is due to the non-circular sections that produce
the stagnation regions and rib vortices right after the cornersof the duct providing the oxidizer. As a result, the flow field is
deformed significantly. The evidence of that are the contoursof the instantaneous distribution of the mixture fraction. As
can be seen in Fig. 4(c), they are concentrated mainly on thelower left side of the bluff-body wake.
The differences between the flows downstream of thebluff-bodies can be quantified by the comparison of the timeaveraged results. Figures 5-6 show the centreline profiles of
the time-averaged axial velocity and its fluctuations as well as
the mixture fraction in all analysed cases. First, we focus on
the profiles of the mean axial velocity component presented
in Fig. 5. The results obtained using different computational
grids for circular and square shapes are also included for thecomparison. The labels of particular lines in the legend correspond to the number of nodes in the radial and axial directions, respectively. The use of the grid counting of 144×192
nodes provides a nearly grid-independent solution at a reasonable computational cost. It can be seen that the velocity in thenear and far flow field regions is calculated with a similar accuracy on all the meshes. The results obtained using the denser
mesh reveal only small differences in the axial locations where
the recirculation zone ends (y/Db ≈ 1.1). In this paper, how-

The structure of the flow behind the bluff-bodies is shownin Fig. 3 presenting iso-surfaces of a constant value of the Qparameter representing the vortical structures. Additionally,
the computational mesh is presented at the sides. It is compacted towards the inlet plane and the axis. One can see in
Fig. 3 that the vortices generated in the close vicinity of theinlet plane reflect the bluff-body shape. Large toroidal structures resulting from the Kelvin-Helmholtz instability, and also
the accompanying smaller longitudinal vortices undergo timespace evolution. In the case of non-circular shapes, the vortices
reflect the shapes of the bluff-bodies even further downstream.
On the other hand, they become smaller and more irregular.
The presence of small-scale vortices generated in the vicinity of sharp corners causes the deformation of large vorticalstructures and increases the axial velocity fluctuations that amplify the mixing process. One can expect that compared to thecircular bluff-body configuration the flame structure would be
different in these cases.
Figure 4 displays the vorticity contours and the mixture
fraction isolines in the ‘x-z’ planes at different axial distancesfrom the inlet plane of the square bluff-body. The red lines indicate the instantaneous position of the stoichiometric mixture
fraction ξST = 0.335. One can observe that the flow structure becomes highly irregular at the axial location 0.75Db .

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
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Figure 5. Profiles of the time averaged axial velocity (mean)
along the axis obtained for different meshes and different
bluff-bodies (black lines - circular, red lines - square, blue line
- star).

Figure 6. Profiles of the time-averaged axial velocity fluctuations and the mixture fraction along the axis.

there are noticeable differences right above the bluff-bodies(y/Db = 0.5) and they persist further downstream. When thesquare bluff-body is used the radial size of the recirculation
zone is larger than in the two remaining cases. For instance,
the profiles at y/Db = 0.5 reveal that the recirculation zone is
0.1Db wider in the location where the axial velocity is equal
Uy /Ub = 0.5 (see the dashed line in Fig. 7(a)). In contrast
to the velocity profiles the differences in the mixture fraction
profiles are less pronounced and observed only in the near field(up to y/Db = 0.7). One can see in Fig. 6 that the profiles diverge from each other in a near-axis region and inside the outer
shear layer and overlap inside the recirculation zone where themixing intensity is the largest. It can be concluded that the
time-averaged results do not reveal such strong dependence on
the bluff-body geometry as the the instantaneous solutions (seeFig. 4).

ever, we are particularly interested in the region y/Db < 1.1,
as downstream of the distance y/Db > 1.1 the mixture fractionlevel is very low, and hence, the mixing process in this part of
the flow is not so important. Hence, the mesh consisting of
144×192 nodes was chosen for comparative studies.
A comparison of the velocity profiles obtained for different shapes reveals a slightly slower velocity decay in the nearfield region (up to 0.6Db ) when the square bluff-body is used.
Moreover, in this case the minimum velocity value is shifted
towards the inlet plane by 0.1Db compared to the configurations with the circular and star bluff-bodies. Worth noticing isthat in the former case, the velocity drops down the fastest. Regarding the profiles of the velocity fluctuations, it can be seenthat the flow behind the circular bluff-body manifests a significantly faster fluctuations increase along the axis. On the other
hand, using the square bluff-body leads to the largest fluctuations maximum. The differences are at the level of 3%Ub ,however, they become less pronounced when the flow leaves
the recirculation zone.
Depending on the bluff-body shape the mixture fraction
decreases slower or faster, see Figure 6. When the circularbluff-body is used the mixing is the most intense, i.e., initially large mixture fraction values drop significantly faster,compared to the two remaining cases. These results suggestthat the observed flow behaviour for the bluff-bodies has somesimilarities with the one reported for jet flows by Tyliszczak
et al. (2022) and Aleyasin et al. (2018). There, contrary to anumber of investigations, the circular nozzle also turned out
to be the most effective taking into account the mixing enhancement. In the present configuration, it has been found thata large amount of the oxidiser stream is taken from the surroundings and transported towards the flow axis. This effectis the most pronounced in the case of the circular bluff-bodywhere large vortical structures seem to be the best formed. Itturns out that the corners of the square and star bluff bodies
make the vortical structures weaker, and thus, not so effectivein transporting the oxidizer to the recirculation region. Apparently, the complex nozzle shape does not necessarily ensure abetter mixing intensity.
A radial flow characteristics gives a deeper insight into theflow dynamics. The time-averaged axial velocity and mixture
fraction values along the radial direction at various axial distances are presented in Fig. 7. Concerning the axial velocity,

CONCLUSIONSThe paper focused on the dynamics of the flow downstream of the bluff-bodies with the aim of better understanding the scalar mixing in bluff-body stabilized burners. Threedifferent conical bluff-body geometries were considered, i.e.,the circular, rectangular and star. The research has been performed using the LES approach and two numerical codes, the
ANSYS Fluent for the precursor simulations to generate theinlet boundary conditions and the high-order SAILOR codefor the analysis of the scalar mixing. The performed computations revealed a smaller than expected dependence of the flow
behaviour on the bluff-body shape. Instantaneous solutions
showed that in the close vicinity of the bluff-body surface thelarge vortical structures exist and their shapes follow the onesof the bluff-bodies. This, however, did not translate on the
mixing process intensity or significant changes of the velocity field in the bluff-body wake. The differences between thetime-averaged solutions were less pronounced. To some extent surprising is the fact that the sharp corners of the squareand star shape bluff-bodies have only a moderate impact on
the flow dynamics. However, it was found that the decay of
the axial velocity as well as the mixture fraction is the fastest
behind the circular bluff-body. On the other hand, the use of
the square bluff-body leads to the shortest but the widest recirculation zone region.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

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Figure 7.

Radial profiles of the time averaged mean axial velocity (a) and mixture fraction (b).

ACKNOWLEDGMENTS

issuing from polygonal nozzles. Energies 14 (3), 554.
Kypraiou, A.M., Allison, P.M., Giusti, A. & Mastorakos, E.
2018 Response of flames with different degrees of premixedness to acoustic oscillations. Combustion Science andTechnology 190 (8), 1426–1441.
Mi, J. & Nathan, G.J. 2010 Statistical properties of turbulent
free jets issuing from nine differently-shaped nozzles. Flow,
Turbulence and Combustion 84 (4), 583–606.
Tyliszczak, A. 2014 A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows. Journal of Computational Physics 276,
438–467.
Tyliszczak, A., Cavaliere, D.E. & Mastorakos, E. 2014
LES/CMC of blow-off in a liquid fueled swirl burner. Flow,
Turbulence and Combustion 92 (1-2), 237–267.
Tyliszczak, A., Kuban, L. & Stempka, J. 2022 Numericalanalysis of non-excited and excited jets issuing from noncircular nozzles. International Journal of Heat and Fluid
Flow 94, 108944.
Vreman, A.W. 2004 An eddy-viscosity subgrid-scale modelfor turbulent shear flow: Algebraic theory and applications.
Physics of Fluids (1994-present) 16 (10), 3670–3681.

This work was supported by National Science Centerin Poland (Grant 2020/39/B/ST8/02802) and the National
Agency for Academic Exchange (NAWA) (Research project
ANIMATE No. PPI/APM/2019/1/00062). The computations
were carried out using PL-Grid Infrastructure.

REFERENCES
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Azad, M., Quinn, W.R. & Groulx, D. 2012 Mixing in turbulent free jets issuing from isosceles triangular orifices withdifferent apex angles. Experimental Thermal and Fluid Science 39, 237–251.
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Kuban, L., Stempka, J. & Tyliszczak, A. 2021 Numerical analysis of the combustion dynamics of passively controlled jets

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