Mixing of a passive scalar in a high-Schmidt turbulent round jet was studied using large-eddy simulation (LES) coupled to filtered density function (FDF). This coupled approach enabled the solution of the continuity, momentum, and scalar (concentration) transport equations when studying mixing in a confined turbulent liquid jet discharging a conserved scalar (rhodamine B) into a low-velocity water stream. The Monte Carlo method was used for solving the FDF transport equation and controlling the number of particles per cell (NPC) using a clustering and splitting algorithm. A sensibility analysis of the number of stochastic particles per cell as well as the influence of the subgrid-scale (SGS) mixing time constant were evaluated. The comparison of simulation results with experiments showed that LES/FDF satisfactorily reproduced the behavior observed in this flow configuration. At high radial distances, the developed superviscous layer generates an intermittency phenomenon leading to a complex, anisotropic behavior of the scalar field, which is difficult to simulate with the conventional and advanced SGS models required by LES. This work showed a close agreement with reported experimental data at this superviscous layer following the FDF approach.

References

References
1.
Mejía
,
J. M.
,
Sadiki
,
A.
,
Molina
,
A.
,
Chejne
,
F.
, and
Pantangi
,
P.
,
2015
, “
Large Eddy Simulation of the Mixing of a Passive Scalar in a High-Schmidt Turbulent Jet
,”
ASME J. Fluid Eng.
,
137
(
3
), p.
031301
.
2.
Eidson
,
T.
,
1985
, “
Numerical Simulation the Turbulent Rayleigh–Bénard Problem Using Subgrid Modeling
,”
J. Fluid Mech.
,
158
, pp.
245
268
.
3.
Germano
,
M.
,
Piomelli
,
U.
,
Moin
,
P.
, and
Cabot
,
W. H.
,
1991
, “
A Dynamic Subgrid-Scale Eddy Viscosity Model
,”
Phys. Fluids A
,
3
(
7
), pp.
1760
1765
.
4.
Moin
,
P.
,
Squires
,
K.
,
Cabot
,
W.
, and
Lee
,
S.
,
1991
, “
A Dynamic Subgrid-Scale Model for Compressible Turbulence and Scalar Transport
,”
Phys. Fluids A
,
3
(
11
), pp.
2746
2757
.
5.
Huai
,
Y.
,
2005
, “
Large Eddy Simulation in the Scalar Field
,” Ph.D. thesis, Technische Universität Darmstadt, Darmstadt, Germany.
6.
Huai
,
Y.
, and
Sadiki
,
A.
,
2007
, “
Large Eddy Simulation of Mixing Processes in Turbulent Liquid Flows With Chemical Reactions
,”
5th International Symposium on Turbulence and Shear Flow Phenomena
,
R.
Friedrich
,
N. A.
Adams
,
J. K.
Eaton
,
J. A. C.
Humphrey
,
N.
Kasagi
, and M. A. Leschziner, eds., Munich, Germany, pp.
1137
1142
.
7.
Colucci
,
P. J.
,
Jaberi
,
F. A.
,
Givi
,
P.
, and
Pope
,
S. B.
,
1998
, “
Filtered Density Function for Large Eddy Simulation Turbulent Reacting Flows
,”
Phys. Fluids
,
10
(
2
), pp.
499
516
.
8.
Jaberi
,
F. A.
,
Colucci
,
P. J.
,
James
,
S.
,
Givi
,
P.
, and
Pope
,
S. B.
,
1999
, “
Filtered Mass Density Function for Large Eddy Simulation Turbulent Reacting Flows
,”
J. Fluid Mech.
,
401
, pp.
85
121
.
9.
Riley
,
J. J.
,
2004
, “
Review of Large-Eddy Simulation of Non-Premixed Turbulent Combustion
,”
ASME J. Fluids Eng.
,
128
(
2
), pp.
209
215
.
10.
Wang
,
L.
,
2007
, “
On Discrete Representation Filtered Density Functions for Turbulent Combustion
,”
Annu. Res. Briefs Center Turbul. Res.
,
2007
, pp.
219
229
.
11.
Dopazo
,
C.
, and
O'Brien
,
E. E.
,
1976
, “
Statistical Treatment Non-Isothermal Chemical Reactions in Turbulence
,”
Combust. Sci. Tech.
,
13
(1–6), pp.
99
112
.
12.
O'Brien
,
E. E.
,
1980
, “
The Probability Density Function (PDF) Approach to Reacting Turbulent Flows
,”
Turbulent Reacting Flows
,
P. A.
Libby
, and
F. A.
Williams
, eds.,
Springer-Verlag, Berlin
, Heidelberg, pp.
185
218
.
13.
Pope
,
S. B.
,
1985
, “
PDF Methods for Turbulent Reactive Flow
,”
Prog. Energy Combust. Sci.
,
11
(
2
), pp.
119
192
.
14.
Shetty
,
D. A.
,
Chandy
,
A. J.
, and
Frankel
,
S. H.
,
2010
, “
A New Fractal Interaction by Exchange With the Mean Mixing Model for Large Eddy Simulation/Filtered Mass Density Function Applied to a Multiscalar Three-Stream Turbulent Jet
,”
Phys. Fluids
,
22
(
2
), p.
025102
.
15.
Mitarai
,
S.
,
Riley
,
J. J.
, and
Kosály
,
G.
,
2005
, “
Testing Mixing Models for Monte Carlo Probability Density Function Simulations
,”
Phys. Fluids
,
17
(
4
), p.
047101
.
16.
Meyer
,
D. W.
, and
Jenny
,
P.
,
2009
, “
Micromixing Models for Turbulent Flows
,”
J. Comput. Phys.
,
228
(
4
), pp.
1275
1293
.
17.
van Vliet
,
E.
,
Derksen
,
J. J.
, and
van den Akker
,
H. E. A.
,
2005
, “
Turbulent Mixing in a Tubular Reactor: Assessment an FDF/LES Approach
,”
AIChE J.
,
51
(
3
), pp.
725
739
.
18.
Mustata
,
R.
,
Valiño
,
L.
,
Jiménez
,
C.
,
Jones
,
W. P.
, and
Bondi
,
S.
,
2006
, “
A Probability Density Function Eulerian Monte Carlo Field Method for Large Eddy Simulations: Application to a Turbulent Piloted Methane/Air Diffusion Flame (Sandia D)
,”
Combust. Flame
,
145
(1–2), pp.
88
104
.
19.
Olbricht
,
C.
,
Hahn
,
F.
,
Sadiki
,
A.
, and
Janicka
,
J.
,
2007
, “
Analysis Subgrid Scale Mixing Using a Hybrid LES-Monte-Carlo PDF Method
,”
Int. J. Heat Fluid Flow
,
28
(
6
), pp.
1215
1226
.
20.
Yaldizli
,
M.
,
Mehravaran
,
K.
, and
Jaberi
,
F. A.
,
2010
, “
Large-Eddy Simulations Turbulent Methane Jet Flames With Filtered Mass Density Function
,”
Int. J. Heat Mass Transfer
,
53
(11–12), pp.
2551
2562
.
21.
Zhao
,
W.
,
Zhang
,
C.
, and
Chen
,
C.
,
2011
, “
Large Eddy Simulation of Bluff-Body Stabilized Flames Using a Multi-Environment Filtered Density Function Model
,”
Proc. Combust. Inst.
,
33
(
1
), pp.
1347
1353
.
22.
McDermott
,
R.
, and
Pope
,
S. B.
,
2007
, “
A Particle Formulation for Treating Differential Diffusion in Filtered Density Function Methods
,”
J. Comput. Phys.
,
226
(
1
), pp.
947
993
.
23.
van Vliet
,
E.
,
Derksen
,
J. J.
,
van den Akker
,
H. E. A.
, and
Fox
,
R. O.
,
2007
, “
Numerical Study on the Turbulent Reacting Flow in the Vicinity the Injector an LDPE Tubular Reactor
,”
Chem. Eng. Sci.
,
62
(
9
), pp.
2435
2444
.
24.
Schwertfirm
,
F.
, and
Manhart
,
M.
,
2009
, “
A-Priori Analysis the LMSE Micromixing Model for Filtered-Density Function Simulation in High Schmidt Number Flows
,”
High Performance Computing in Science Engineering, Garching/Munich 2007
,
S.
Wagner
, M. Steinmetz, A. Bode, and E. Brehm, eds.,
Springer-Verlag, Berlin, Heidelberg
, pp.
303
314
.
25.
Schwertfirm
,
F.
, and
Manhart
,
M.
,
2010
, “
Development a DNS–FDF Approach to Inhomogeneous Non-Equilibrium Mixing for High Schmidt Number Flows
,”
Direct and Large-Eddy Simulation VII
,
V.
Armenio
, B. Guerts, and J. Froehlich, eds.,
Springer
,
The Netherlands
, pp.
153
159
.
26.
Schwertfirm
,
F.
, and
Manhart
,
M.
,
2010
, “
A Numerical Approach for Simulation Turbulent Mixing and Chemical Reaction at High Schmidt Numbers
,”
Micro and Macro Mixing: Analysis, Simulation and Numerical Calculation
,
H.
Bockhorn
, D. Mewes, W. Peukert, and H. J. Warnecke, eds.,
Springer-Verlag, Berlin, Heidelberg
, pp.
305
324
.
27.
Pope
,
S. B.
,
1990
, “
Computations of Turbulent Combustion: Progress and Challenges
,”
Proc. Combust. Inst.
,
23
(1), pp.
591
612
.
28.
Heinz
,
S.
,
2003
, “
On Fokker–Planck Equations for Turbulent Reacting Flows. Part 2. Filter Density Function for Large Eddy Simulation
,”
Flow, Turbul. Combust.
,
70
(1), pp.
153
181
.
29.
Klimenko
,
A. Y.
,
2007
, “
On Simulating Scalar Transport by Mixing Between Lagrangian Particles
,”
Phys. Fluids
,
19
(
3
), pp.
31702
31704
.
30.
Haworth
,
D. C.
,
2010
, “
Progress in Probability Density Function Methods for Turbulent Reacting Flows
,”
Prog. Energy Combust. Sci.
,
36
(
2
), pp.
168
259
.
31.
Haworth
,
D. C.
, and
Pope
,
S. B.
,
2011
, “
Transported Probability Density Function Methods for Reynolds-Averaged and Large-Eddy Simulations
,”
Turbulent Combustion Modeling: Advances, New Trends and Perspectives
,
T.
Echekki
and
E.
Mastorakos
, eds.,
Springer
,
The Netherlands
, pp.
119
142
.
32.
Ottinger
,
H. C.
,
1996
,
Stochastic Processes in Polymeric Fluids: Tools Examples for Developing Simulation Algorithms
,
Springer-Verlag, Berlin
, Heidelberg.
33.
Antoine
,
Y.
,
Lemoine
,
F.
, and
Lebouché
,
M.
,
2001
, “
Turbulent Transport a Passive Scalar in a Round Jet Discharging Into a Co-Flowing Stream
,”
Eur. J. Mech. B
,
20
(
2
), pp.
275
301
.
34.
Durst
,
F.
, and
Schäfer
,
M.
,
1996
, “
A Parallel Blockstructured Multigrid Method for the Prediction Incompressible Flow
,”
Int. J. Numer. Methods Fluids
,
22
(
6
), pp.
549
565
.
35.
Löhner
,
R.
,
1995
, “
Robust, Vectorized Search Algorithms for Interpolation on Unstructured Grids
,”
J. Comput. Phys.
,
118
(2), pp.
307
313
.
36.
Lubbers
,
C. L.
,
Brethouwer
,
G.
, and
Boersma
,
B. J.
,
2001
, “
Simulation the Mixing a Passive Scalar in a Round Turbulent Jet
,”
Fluid Dyn. Res.
,
28
(
3
), pp.
189
208
.
37.
Babu
,
P. C.
,
2007
, “
Simulation & Modeling Three Turbulent Flow Problems
,” Ph.D. thesis, University Minnesota, Minneapolis, MN.
38.
Sheikhi
,
M. R. H.
,
Drozda
,
T. G.
,
Givi
,
P.
,
Jaberi
,
F. A.
, and
Pope
,
S. B.
,
2005
, “
Large Eddy Simulation a Turbulent Nonpremixed Piloted Methane Jet Flame (Sandia Flame D)
,”
Proc. Combust. Inst.
,
30
(
1
), pp.
549
556
.
39.
Townsend
,
A. A.
,
1976
,
The Structure Turbulent Shear Flow
,
2nd ed.
,
Cambridge University Press
,
Cambridge, UK
.
40.
Dowling
,
D. R.
, and
Dimotakis
,
P. E.
,
1990
, “
Similarity on the Concentration Field Gas-Phase Turbulent Jets
,”
J. Fluid Mech.
,
218
, pp.
109
141
.
41.
Dahm
,
W. J. A.
,
1985
, “
Experiments on Entrainment, Mixing and Reaction in Turbulent Jets at Large Schmidt Number
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
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