7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Unsteady turbulent twophase flow using Euler/Lagrange approach devoted to twoway
coupling conditions
Mouldi Chrigui*, Amsini Sadiki* and Guyh Dituba Ngoma**
*Technische Universitiit Darmstadt, Dept. of Mechanical Engineering, Institute for Energy and Powerplant Technology ,
Petersenstr.30, 64287 Darmstadt, Germany
** UQAT 445 boul. de l'Universit6 RouynNoranda (Qu~bec) J9X 5E4, Canada
mchrigui~ekt.tudarmstadt.de
Keywords: EulerLagrange method, unsteady coupling, dispersion, URANS
Abstract
While performance comparisons between LES and URANS for single phase flows of technical importance have been provided
in the literature, efforts have been put recently in reporting prediction comparisons between Euler/Euler and Euler/Lagrange
LES approaches for twophase flows, especially for confined bluffbody gassolid flow as experimentally investigated by
Borde et al. [1].
In the present work we focus on URANS in the frame of a Eulerian/Lagrangian approach in order to achieve a performance
comparison between the LES already reported in the literature and the URANS. So, a timedependent solid particle and gas
phase flow, including twoway coupling effects is evaluated through comparison with experiments by Borde et al.. Thereby a
thermodynamically consistent turbulence modulation approach for the determination of the source terms that induce the effect
of the particles on the turbulence level of the carrier phase is included. The dispersion of particles is modeled by the Markov
sequence approach ameliorated with the drift factor by remodeling the pressure gradient. A particular emphasis is put on the
disperse phase feedback on the carrier phase and coupling procedure within each Eulerian time step along with an unsteady
coupling of both codes applied, the FASTEST3D code for the gas phase description based on the kEpsilon turbulence model
and the LAG3Dsolver for tracking particles.
The polydispersed configuration under investigation features an important recirculation zone and has a mass loading of 22%
where the disperse phase consists of glass beads.
Quantitative results of the disperse phase as well as those of the carrier phase are presented at different stations around the
recirculation zone. They agree favorably well with experimental data and with the LES results in [6] assessing positively the
accuracy of the numerical method implemented.
Introduction
Today, almost every industry that applies advanced design
engineering uses CFD to predict and to optimize flow
processes. To achieve this task, with respect to combustion
for instance, a design tool that allows to directly take into
account unsteady effects inherent to combustion systems is
highly demanded [25, 9, 1113, 19, 20].
Although a rapid development of computers and
applicationoriented numerical methods is notable, Direct
Numerical Simulations (DNS) cannot and will not be able to
meet the urgent need of economical and reliable predictive
methods to aid combustion safety studies and the design of
practical high Reynolds number combustion systems in the
near future [1113, 19, 20]. It is worth mentioning that the
above underlined unsteady effects remain inaccessible to
today's RANS (here Reynolds Averaged based Numerical
Simulations) methods widely used in 3D CFD industrial
simulation tools [10]. To face the pressing economy and
prescribed design requirement, unsteady techniques, like
Unsteady RANS and Large Eddy Simulation (LES) that
have demonstrated their potential in reasonably simple
systems (laboratory flames) are valuable candidates. In such
configurations LES provides excellent evaluations of mean
and fluctuation fields of temperature, species and velocities.
It also allows to gain early insights on unsteady structures,
especially on aero/hydrodynamics and combustion
generated instabilities [14, 19, 20]. Despite these LES
successes, its path to become a validated production tool in
the industry is still open [19, 20]. In general, experience
reveals that LES is expected to be very good for flows,
where the flow is governed by large, turbulent structures,
which can be captured by a fairly coarse mesh. If attached
boundary layers play a role, LES may give very poor
predictions in these regions, unless very fine grids are used
with correspondingly increasing computational costs [7, 10].
In LES of twophase flows, physics and numerics also
interact strongly and numerous issues with respect to
computational cost, among others, are still open [6, 13, 14,
1720].
The question is now how to use the advanced considerations
in costsaving computations for calculations of complex
configurations with common, computational capacities. In
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
carrier gas flow which is captured by an Eulerian approach.
The turbulent fluid phase is described following a
URANSmodeling approach. The unsteady, general fonn of
the transport equation needed emerges as:
this respect it appears that for many industrial and
engineering purposes statistical modeling will continue to
be the main approach to representing the effects of turbulent
processes in CFD for technical flows regardless of recent
progress in Large Eddy Simulation (LES) and novel
development of statistical closures at a level higher than the
first order [3, 7, 9]. An alternative to LES in this case may
be URANS. A comparison review is given in [8, 9]. Since,
in URANS, part of the turbulence (incoherent random
fluctuations) is modeled and another part deterministicc or
very large coherent structures) is resolved, the conunon
question is what type of turbulence model should be useful
in URANS. While, in LES, nondissipative discretization
schemes should be used in order not to dampen out resolved,
turbulent fluctuations, this is to some extent also true for
URANS. In general, a discretization scheme that has little
numerical dissipation should be used. But how dissipative a
scheme needs to be in order to be stable is flowdependent.
If the flow has strong vortex shedding, the standard
kEpsilon model can do a good job, as pointed out in [9, 10].
Othenvise both the discretization and the turbulence model
have high dissipation and the unsteadiness in computations
will be dampened out.
Regarding twophase flows, most codes apply RANS based
methods and use Eulerian/Lagrangian (EL) technique in
which the flow is solved following an Eulerian method and
the particles are tracked according to a Lagrangian approach.
In unsteady cases, the numerical coupling between the
Eulerian flow solver and the Lagragian particle tracking
code needs new considerations as for LES.
Alternative method is naturally to use twofluid or
multifluid method in which both the gas and disperse
phases are solved using an Eulerian method (Euler/Euler or
EE) [5, 6].
While Sadiki et al. [3, 9] compared the performances of
LES and URANS for single phase flows of technical
importance, Garcia et al.[6] reported a prediction
comparison between EE and EL LES approaches for
confined bluffbody gassolid flow as experimentally
investigated in [1].
In the present work we restrict ourself to URANS in the
frame of an Eulerian/Lagrangian approach so as to provide a
comparison between the LES results in [6] and URANS
predictions.
The paper is organized as follows. In the next section we
give an overview of the governing equations along with the
details of the submodels used and the numerical procedure.
To evaluate the potential of the models proposed, the
configuration by Borde et al [1] will be introduced and
simulated. In the next section, results obtained are presented
and discussed. The last section is devoted to conclusions.
Modelling and Numerics
Gas phase, droplet description and Twoway
Coupling
To account for the instantaneous flow properties
encountered by the particles, involving each particle history
starting from the injection into the flow, an
EulerLangrangian approach is adopted. The particles are
described by a Lagrangian transport through a continuous
a(p/) aJPero) aJPV o) aJPWo) a/ ao a c
at a or 0= ax aye, =
Sm+Sm (1)
in which may represent the mean value of mass density p,
velocity components (u, v. w), turbulent kinetic energy and
turbulent dissipation rate, respectively. JF represents an
effective diffusion coefficient and So the well known
turbulence source tenns in single phase flows.
To better capture streamline curvature effects in turbulent
flows, it is well known that models of second order level,
nonlinear or algebraic kEpsilon models are very
appropriate. We apply therefore the nonlinear kEpsilon
(see in [11]) modified for twophase flow description by
including source tenns for phase exchange, S Op This
additional source tenns in (1) characterizes the direct
interaction of mass, momentum and turbulent quantities
between the two phases and account for the twoway
coupling between the fluid turbulence and the particles.
Details about these tenns can be found in [2, 11].
With respect to twoway coupling in multiphase flows, only
models accounting for the induced turbulence attenuation or
augmentation separately are available [6, 1116, 17], as
reviewed by Crowe [16] who used the energy balance to
attempt a first consistent description. Since all the
phenomena involved are thennodynamic processes, we
therefore include and exploit the second law of
thennodynamics which governs every plwsical process.
This yields a model that accounts in a physically consistent
Tray for a fully twoway coupling [11]: this model captures
well both the enhancement and the diminution of the
turbulence of the gas phase due to the presence of both big
and small particles in polydispersed flows as it is the case in
the configuration under study. For details about this model,
please refer to [2, 11, 12].
To compute the properties of particles moving in turbulent
flow, the Lagrangian approach is employed. The trajectories
of individual particles are obtained from motion equations,
where all external effects, except drag force and gravity, are
neglected [2, 6, 11, 14, 15, 17, 18].
Numerical procedure
The computational method is based on an EulerLagrangian
coupling approach. For the Lagrangian phase a 3D
Lagrangian LAG3D code for particle tracking has been
extended. To simulate the dispersion of particles and their
interaction with the turbulent flow, the Markovsequence
model based on the calculation of Lagrangian and Eulerian
correlations factors [2, 11] is applied.
The particle injection is based on a stochastic approach by
considering the particle mass flux and the particle size
distributions obtained at the inlet far off the nozzle exit from
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure 1: The configuration of Borde et al. [1]
Results and Discussion
As pointed out Sadiki et al. [3, 9] compared the
performances of LES and URANS for single phase flows of
technical importance. Garcia et al. [6] reported a prediction
comparison between EE and EL LES approaches for
confined bluffbody gassolid flow as experimentally
investigated in [1]. Even though the codes used are different,
attempt is made to provide URANS results for this
configuration in order to allow a first step comparison
between LES results and URANS predictions. Here,
URANS results are compared to exactly the same
experimental data set used for the LES results in [6].
Prior to any computations with twophase flows, the
accuracy of the URANS solver for the turbulent gas phase
was first evaluated. The single phase has been computed
and favorably compared to experimental data provided by
Borde et al. (see in [6]). A computational grid with 1,2
million grid points was found sufficient.
With respect to tivophase flows let us first focus on the
carrier gas phase. In Figures 2 radial profiles of mean axial
gas velocities at different stations (z=3, 80, 160, 240 and
320 mm) along zaxis are shown in comparison to
experimental data. Together with Figures 34 that display
radial profiles of mean radial gas velocities and of turbulent
kinetic energy of the gas phase at the same stations along
zaxis show a fair agreement with experimental data. The
numerical model retrieves well the most properties of the
flow, especially the length of the recirculation zone is
surprisingly well captured. However, the turbulent kinetic
energy is predicted too low, essentially at two positions
(z=80 and 160mm). LES results in [6] also predicted all
these quantities in the same order of magnitude.
experimental measurements [11]. The particles sizes are
sampled from the particles distribution functions obtained
experimentally. The total number of parcels injected in the
flow field was about 400000 for all calculations. Average
values and variances of particles characteristic variables are
evaluated in each cell.
For the Eulerian description of the turbulent gas phase far
from the droplet, the simulation is performed using the three
dimensional CFDcode FASTEST in which the equations
are solved by finite volume method. The time integration is
achieved implicitly with the CrankNicholson method while
the diffusion terms are discretized with central schemes on a
non orthogonal block structured grid. The velocitypressure
coupling is accomplished by a SIMPLE algorithm. The
whole system is solved by the SIPsolver.
Numerically, the interaction between the continuous and the
dispersed phases consists in a coupling between the two
codes involved following an unsteady method. Since the
used criteria for the time step determination of the disperse
phase outline very restrictive and limited flying track for
individual particle, the time step marching algorithm for the
coupling is controlled by the continuous phase, therein at
least two internal interactions between both phases during a
coupling evolution ivere asserted.
Experimental Configuration
The configuration consists in a confined bluffbody
gassolid flow, as experimentally investigated by Borde et al.
[1], where a jet of air and solid particles are injected in a
coflory of air. It is represented in Figure 1, while the flow
parameters used are listed in Table 1. It features an
important recirculation zone and has a mass loading of 22%
where the disperse phase consists of solid particles (glass
beads with diameter ranging from 20 to 100 microns with a
mean value of 60 microns). Therefore breakup, evaporation
coalescence do not have to be considered. Particle
combustion process is out of study. The disperse phase
displays a global volume fraction of 1.052x104, however
the local values for the volume fraction at the region closed
to the injection zone is much more important, inducing
thereby a considerable effect of the disperse phase on the
flow characteristics of the continuous phase. Since the solid
volume fraction is about 104 collision effects are assumed
to be negligible.
Borde et al. provided measurements data performed by
means of a twocomponent phaseDoppler anemometer
(PDA): single phase data at different crosssections within
the jet, in the annular direction and along the zaxis as well
as the mean and RMS particles velocities for each size
classes.
Ucenter 4m/s
Uconlow 6m/s (Re=30000)
Mass lodn 22%; Ve>104 (innerjet
Denst of pricles 2470 k/m
Table 1: The flow parameters used
Coflory (air)
Air + solid particles
Outlet
Wall
2024602~024602460202 602
Mean axfal Ras vlocities [m/s]
Figure 2: Radial profiles of mean axial gas velocities at
different stations along zaxis: red: experiment; blue:
simulation
I =.tmm z=lomm zL6omm r=240mm z=320mm I
I s .~ i .~r . I r I . i . r . .
03 0 0.9 1 4)5 $ 0 03 I 0. 0 05 I 0.5 01 OS I 05 0 5 1
Mean radinI gas velocities [mis]
Figure 3: Radial profiles of mean radial gas velocities at
different stations along zaxis: red: experiment; blue:
simulation
z=3mm za 3mm z=160mm z=4mm =
0 0 5 1 1.5 0 0 5 I1 5 0 0 5 I1 5 0 0 5 I 0 05 115
Gas phase turb. kineic energ (m / ].
Figure 4: Radial profiles of turbulent kinetic energy of gas
phase at different stations along zaxis: red: experiment:
blue: simulation
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
200 loo loo 00 30 40
~ 'F~~ 9 "s~: Z'rmm
Fiue5 xa roie fma a veoite:smos
intaizued5 wxith predfined fma a velocities: givn fom th
experimental mea:siurement, whinlete injseto puositioni
dleterimind atindol writ h as noma ditrbtinarudh
eaxi o teinj tectionrs hole.h nme o njce
pachnel whn o thme patices eqare incte. These effects are
limitiaed winthe prange fromd z=7 toe z=200 mm. Deptheo
sihdeitotoexperimental datamnswhl th is resutio coionfirsa
cotrriet beavioury ofthea numeial mdelruto applied piting
out thatthe interctions boetwe ohpaesrslsi
mdficatio sofs the flow even ait riegison thaviga lowolue
fractio ofe the particles. The lnevtel ofthes turbuence is
reihtduedaccordng to experimental (nota tshw hre)ul aondm th
anisotropy is affected. The origin of such a modification
mainly lays on the heterogeneity of the particle
concentration field.
Mcan axial particle yclocilics [m/is]
Figure 6: Radial profiles of mean axial particle velocities
at different stations along zaxis. Red: experiments; blue:
simulation.
1 0.5 0 0.5 1 4.5 0 0.5 1 4.5 0 0.5 1 4.5 0 0.5 1 4.5 0 0.5
Mean radial particle velocities [m/s]
Figure 7: Radial profiles of mean radial particle velocities
at different stations along zaxis. red: experiments; blue:
simulation.
Figure 10: Axial profiles of mean axial particle velocities.
Symbol: experiment; red: simulation
0 .5
20 00 0 100 200 30 400
z [mm1
Figure 11: Axial profiles of RMS particle axial velocities.
Symbols: experiment; solid line: simulation
"rsp I I 1
200 loo too oo 30 40
z (mm
Figure 12: Axial profiles of RMS particle radial
velocities. Symbols: experiment; solid line: simulation
Conclusions
This paper aimed at demonstrating the feasability of
URANS based computations to twophase flows of
moderate complexity. The results demonstrate that URANS
is able to capture favorably well most properties of the flow
in a comparable way to LES, once intrinsincally unsteady
effects are not involved. Furthermore the results
demonstrate that thermodynamically consistent model
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
velocities, respectively. They show that the position where
the maximum levels of particle turbulence are found on the
axis is shifted towards the jet inlet according to the LES
results reported in [6].
r=3mm =somm z=uohmm 2=240mm
z=320km
1oo
z immi
/I mm zaumum z= mumm z= .um. z=Jrumm
a >1 1.5 o 0.5 1.5 5 o0.5 11.5 o 0.5 1 5 0.51 1 5
RMS axial particle velocities [m/s]
Figure 8: Radial profiles of RMS axial particle velocities
at different stations along zaxis. Red: experiments; blue:
simulation
I 2 3mm wo reom z.'m i '2m i
RMS radial particle velocities [m/s]
Figure 9: Radial profiles of RMS radial particle velocities
at different stations along zaxis. Red: experiments; blue:
simulation.
The quantitative results of the disperse phase, like those of
of the carrier phase, plotted at five different axial cross
sections around the recirculation zone in Figures 612, are
shown to agree favorably with the experimental data.
In particular Figure 610 show velocity fields for particles
for which a good agreement is achieved. The radial RMS
profiles of particles are especially good predicted. Figures
1112 display axial profiles of RMS particle axial and radial
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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Acknowledgements
For financial support we gratefully acknowledge the
Deutsche Forschungsgemeinschaft (DFG) through the
Sonderforschungsbereich 568 (project A4) and the
Graduiertenkolleg GKl344.
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