A new methodology is developed for local entropy generation analysis of turbulent flows using large eddy simulation (LES). The entropy transport equation is considered in LES and is solved along with continuity, momentum, and scalar transport equations. The filtered entropy equation includes several unclosed source terms that contribute to entropy generation. The closure is based on the filtered density function (FDF) methodology, extended to include the transport of entropy. An exact transport equation is derived for the FDF. The unclosed terms in this equation are modeled by considering a system of stochastic differential equations (SDEs). The methodology is employed for LES of a turbulent shear layer involving transport of passive chemical species, energy, and entropy. The local entropy generation effects are obtained from the FDF and are analyzed. It is shown that the dominant contribution to entropy generation in this flow is due to combined effects of energy transfer by heat and mass diffusion. The FDF results are assessed by comparing with those obtained by direct numerical simulation (DNS) of the same layer. The FDF predictions show favorable agreements with the DNS data.

References

References
1.
Herwig
,
H.
, and
Kock
,
F.
,
2006
, “
Local Entropy Production in Turbulent Shear Flows: A Tool for Evaluating Heat Transfer Performance
,”
J. Therm. Sci.
,
15
(
2
), pp.
159
167
.10.1007/s11630-006-0159-7
2.
Adeyinka
,
O. B.
, and
Naterer
,
G. F.
,
2004
, “
Modeling of Entropy Production in Turbulent Flows
,”
ASME J. Fluids Eng.
,
126
, pp.
893
899
.10.1115/1.1845551
3.
Rezac
,
P.
, and
Metghalchi
,
H.
,
2004
, “
A Brief Note on the Historical Evolution and Present State of Exergy Analysis
,”
Int. J. Exergy
,
1
(
4
), pp.
426
437
.10.1504/IJEX.2004.005787
4.
Nishida
,
K. T. T.
, and
Kinoshita
,
S.
,
2002
, “
Analysis of Entropy Generation and Exergy Loss During Combustion
,”
Proc. Combust. Inst.
,
29
(
1
), pp.
869
874
.10.1016/S1540-7489(02)80111-0
5.
Sezer
,
I.
,
Altin
,
I.
, and
Bilgin
,
A.
,
2009
, “
Exergetic Analysis of Using Oxygenated Fuels in Spark-Ignition (SI) Engines
,”
Energy Fuels
,
23
(
4
), pp.
1801
1807
.10.1021/ef8002608
6.
Datta
,
A.
,
2005
, “
Effects of Gravity on Structure and Entropy Generation of Confined Laminar Diffusion Flames
,”
Int. J. Therm. Sci.
,
44
(
5
), pp.
429
440
.10.1016/j.ijthermalsci.2004.10.003
7.
Stanciu
,
D.
,
Isvoranu
,
D.
,
Marinescu
,
M.
, and
Gogus
,
Y.
,
2001
, “
Second Law Analysis of Diffusion Flames
,”
Int. J. Appl. Thermodynamics
,
4
(
1
), pp.
1
18
.
8.
Li
,
Z. W.
,
Chou
,
S. K.
,
Shu
,
C.
, and
Yang
,
W. M.
,
2005
, “
Entropy Generation During Microcombustion
,”
J. Appl. Phys.
,
97
(
8
), p.
084914
.10.1063/1.1876573
9.
Raghavan
,
V.
,
Gogos
,
G.
,
Babu
,
V.
, and
Sundararajan
,
T.
,
2007
, “
Entropy Generation During the Quasi-Steady Burning of Spherical Fuel Particles
,”
Int. J. Therm. Sci.
,
46
(
6
), pp.
589
604
.10.1016/j.ijthermalsci.2006.07.006
10.
Hutchins
,
T. E.
, and
Metghalchi
,
M.
,
2003
, “
Energy and Exergy Analyses of the Pulse Detonation Engine
,”
ASME J. Eng. Gas Turbines Power
,
125
(
4
), pp.
1075
1080
.10.1115/1.1610015
11.
Datta
,
A.
, and
Som
,
S.
,
1999
, “
Energy and Exergy Balance in a Gas Turbine Combustor
,”
Proc. Inst. Mech. Eng. Part A
,
213
(
1
), pp.
23
32
.10.1243/0957650991537400
12.
Rakopoulos
,
C. D.
, and
Giakoumis
,
E. G.
,
2006
, “
Second-Law Analyses Applied to Internal Combustion Engines Operation
,”
Prog. Energy Combust.
,
32
(
1
), pp.
2
47
.10.1016/j.pecs.2005.10.001
13.
Yapici
,
H.
,
Kayataş
,
N.
,
Albayrak
,
B.
, and
Baştürk
,
G.
,
2005
, “
Numerical Calculation of Local Entropy Generation in a Methane-Air Burner
,”
Energy Convers. Manage.
,
46
(
11–12
), pp.
1885
1919
.10.1016/j.enconman.2004.09.007
14.
Lior
,
N.
,
Sarmiento-Darkin
,
W.
, and
Al-Sharqawi
,
H. S.
,
2006
, “
The Exergy Fields in Transport Processes: Their Calculation and Use
,”
Energy
,
31
(
5
), pp.
553
578
.10.1016/j.energy.2005.05.009
15.
Ugarte
,
S.
, and
Metghalchi
,
M.
,
2005
, “
Evolution of Adiabatic Availability and Its Depletion Through Irreversible Processes
,”
Int. J. Exergy
,
2
(
2
), pp.
3
13
.10.1504/IJEX.2005.006983
16.
Chavannavar
,
P.
, and
Caton
,
J.
,
2006
, “
Destruction of Availability (Exergy) Due to Combustion Processes: A Parametric Study
,”
Proc. Inst. Mech. Eng. Part A
,
220
(
7
), pp.
655
668
.10.1243/09576509JPE267
17.
Som
,
S. K.
, and
Datta
,
A.
,
2008
, “
Thermodynamic Irreversibilities and Exergy Balance in Combustion Processes
,”
Prog. Energy Combust. Sci.
,
34
(
3
), pp.
351
376
.10.1016/j.pecs.2007.09.001
18.
Klausner
,
J. F.
,
Li
,
Y.
,
Darwish
,
M.
, and
Mei
,
R.
,
2004
, “
Innovative Diffusion Driven Desalination Process
,”
ASME J. Energy Resour. Technol.
,
126
, pp.
219
225
.10.1115/1.1786927
19.
Yilbas
,
B. S.
,
2002
, “
Entropy Production During Laser Picosecond Heating of Copper
,”
ASME J. Energy Resour. Technol.
,
124
, pp.
204
213
.10.1115/1.1488173
20.
Sciacovelli
,
A.
, and
Verda
,
V.
,
2010
, “
Entropy Generation Minimization in a Tubular Solid Oxide Fuel Cell
,”
ASME J. Energy Resour. Technol.
,
132
, p.
012601
.10.1115/1.4001063
21.
Teng
,
H.
,
Kinoshita
,
C. M.
,
Masutani
,
S. M.
, and
Zhou
,
J.
,
1998
, “
Entropy Generation in Multicomponent Reacting Flows
,”
ASME J. Energy Resour. Technol.
,
120
(
3
), pp.
226
232
.10.1115/1.2795040
22.
Call
,
F. W.
,
1998
, “
Dispersion—An Entropy Generator of Diffusion
,”
ASME J. Energy Resour. Technol.
,
120
, pp.
149
153
.10.1115/1.2795026
23.
Gyftopoulos
,
E. P.
, and
Beretta
,
G. P.
,
1993
, “
Entropy Generation Rate in a Chemically Reacting System
,”
ASME J. Energy Resour. Technol.
,
115
, pp.
208
212
.10.1115/1.2905995
24.
Datta
,
A.
,
2000
, “
Entropy Generation in a Confined Laminar Diffusion Flame
,”
Combust. Sci. Technol.
,
159
(
1
), pp.
39
56
.10.1080/00102200008935776
25.
Briones
,
A. M.
,
Mukhopadhyay
,
A.
, and
Aggarwal
,
S. K.
,
2009
, “
Analysis of Entropy Generation in Hydrogen-Enriched Methane-Air Propagating Triple Flames
,”
Int. J. Hydrogen Energy
,
34
(
2
), pp.
1074
1083
.10.1016/j.ijhydene.2008.09.103
26.
Shuja
,
S. Z.
,
Yilbas
,
B. S.
, and
Khan
,
M.
,
2006
, “
Entropy Generation in Laminar Jet: Effect of Velocity Profiles at Nozzle Exit
,”
Heat Mass Transfer
,
42
(
9
), pp.
771
777
.10.1007/s00231-005-0056-8
27.
Walsh
,
E. J.
, and
Hernon
,
D.
,
2006
, “
Unsteady Volumetric Entropy Generation Rate in Laminar Boundary Layers
,”
Entropy
,
8
(
1
), pp.
25
30
.10.3390/e8010025
28.
Walsh
,
E. J.
,
Mc Eligot
,
D. M.
,
Brandt
,
L.
, and
Schlatter
,
P.
,
2011
, “
Entropy Generation in a Boundary Layer Transitioning Under the Influence of Free-Stream Turbulence
,”
ASME J. Fluids Eng.
,
133
, p.
061203
.10.1115/1.4004093
29.
Khan
,
W. A.
, and
Gorla
,
R. S. R.
,
2011
, “
Second Law Analysis for Free Convection in Non-Newtonian Fluids Over a Horizontal Plate Embedded in a Porous Medium: Prescribed Surface Temperature
,”
ASME J. Heat Transfer
,
133
, p.
052601
.10.1115/1.4003045
30.
Okong'o
,
N. A.
, and
Bellan
,
J.
,
2010
, “
Small-Scale Dissipation in Binary-Species, Thermodynamically Supercritical, Transitional Mixing Layers
,”
Comput. Fluids
,
39
(
7
), pp.
1112
1124
.10.1016/j.compfluid.2010.02.001
31.
Shuja
,
S. Z.
,
Yilbas
,
B. S.
, and
Budair
,
M. O.
,
2001
, “
Local Entropy Generation in an Impinging Jet: Minimum Entropy Concept Evaluating Various Turbulence Models
,”
Comput. Meth. Appl. Mech. Eng.
,
190
(
28
), pp.
3623
3644
.10.1016/S0045-7825(00)00291-7
32.
Stanciu
,
D.
,
Marinescu
,
M.
, and
Dobrovicescu
,
A.
,
2007
, “
The Influence of Swirl Angle on the Irreversibilities in Turbulent Diffusion Flames
,”
Int. J. Thermodyn.
,
10
(
4
), pp.
143
153
.
33.
Pope
,
S. B.
,
2000
,
Turbulent Flows
,
Cambridge University Press
,
Cambridge, UK
.
34.
Poinsot
,
T.
, and
Veynante
,
D.
,
2005
,
Theoretical and Numerical Combustion
,
2nd ed.
,
R. T. Edwards, Inc.
,
Philadelphia, PA
.
35.
Janicka
,
J.
, and
Sadiki
,
A.
,
2005
, “
Large Eddy Simulation of Turbulent Combustion Systems
,”
Proc. Combust. Inst.
,
30
, pp.
537
547
.10.1016/j.proci.2004.08.279
36.
Peters
,
N.
,
2000
,
Turbulent Combustion
,
Cambridge University Press
,
Cambridge, UK.
37.
Menon
,
S.
,
2000
, “
Subgrid Combustion Modelling for Large-Eddy Simulations
,”
Int. J. Engine Res.
,
1
(
2
), pp.
209
227
.10.1243/1468087001545146
38.
Pitsch
,
H.
,
2006
, “
Large-Eddy Simulation of Turbulent Combustion
,”
Annu. Rev. Fluid Mech.
,
38
, pp.
453
482
.10.1146/annurev.fluid.38.050304.092133
39.
Piomelli
,
U.
,
1999
, “
Large-Eddy Simulation: Achievements and Challenges
,”
Prog. Aerosp. Sci.
,
35
, pp.
335
362
.10.1016/S0376-0421(98)00014-1
40.
Givi
,
P.
,
2006
, “
Filtered Density Function for Subgrid Scale Modeling of Turbulent Combustion
,”
AIAA J.
,
44
(
1
), pp.
16
23
.10.2514/1.15514
41.
Ansari
,
N.
,
Jaberi
,
F. A.
,
Sheikhi
,
M. R. H.
, and
Givi
,
P.
,
2011
, “
Filtered Density Function as a Modern CFD Tool
,”
Engineering Applications of CFD
, Vol. 1,
M. A. R. S.
Al-Baghdadi
, ed.,
International Energy and Environment Foundation
,
Al-Najaf, Iraq
, Chap. 1, pp.
1
22
.
42.
Williams
,
F. A.
,
1985
,
Combustion Theory
,
2nd ed.
,
The Benjamin/Cummings Publishing Company
,
Menlo Park, CA
.
43.
Safari
,
M.
,
Sheikhi
,
M. R. H.
,
Janbozorgi
,
M.
, and
Metghalchi
,
H.
,
2010
, “
Entropy Transport Equation in Large Eddy Simulation for Exergy Analysis of Turbulent Combustion Systems
,”
Entropy
,
12
(
3
), pp.
434
444
.10.3390/e12030434
44.
Sagaut
,
P.
,
2005
,
Large Eddy Simulation for Incompressible Flows
,
Springer-Verlag
,
New York, NY
.
45.
Sheikhi
,
M. R. H.
,
Givi
,
P.
, and
Pope
,
S. B.
,
2007
, “
Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Turbulent Reacting Flows
,”
Phys. Fluids
,
19
(
9
), p.
095106
.10.1063/1.2768953
46.
Sheikhi
,
M. R. H.
,
Givi
,
P.
, and
Pope
,
S. B.
,
2009
, “
Frequency-Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Turbulent Flows
,”
Phys. Fluids
,
21
(
7
), p.
075102
.10.1063/1.3153907
47.
O'Brien
, E. E.,
1980
, “
The Probability Density Function (PDF) Approach to Reacting Turbulent Flows
,”
Turbulent Reacting Flows
, Vol. 44,
P. A.
Libby
and
F. A.
Williams
, eds.,
Springer-Verlag
,
Heidelberg
, Chap. 5, pp.
185
218
.
48.
Lundgren
,
T. S.
,
1967
, “
Distribution Functions in the Statistical Theory of Turbulence
,”
Phys. Fluids
,
10
(
5
), pp.
969
975
.10.1063/1.1762249
49.
Sheikhi
,
M. R. H.
,
Drozda
,
T. G.
,
Givi
,
P.
, and
Pope
,
S. B.
,
2003
, “
Velocity-Scalar Filtered Density Function for Large Eddy Simulation of Turbulent Flows
,”
Phys. Fluids
,
15
(
8
), pp.
2321
2337
.10.1063/1.1584678
50.
Karlin
,
S.
, and
Taylor
,
H. M.
,
1981
,
A Second Course in Stochastic Processes
,
Academic Press
,
New York, NY
.
51.
Dopazo
, C.,
1994
, “
Recent Developments in PDF Methods
,”
Turbulent Reacting Flows
,
P. A.
Libby
and
F. A.
Williams
,
eds.
,
Academic Press
,
London, England
, Chap. 7, pp.
375
474
.
52.
Kloeden
,
P. E.
,
Platen
,
E.
, and
Schurz
,
H.
,
1997
,
Numerical Solution of Stochastic Differential Equations Through Computer Experiments
, Corrected Second Printing Edition,
Springer-Verlag
,
New York, NY
.
53.
Colucci
,
P. J.
,
Jaberi
,
F. A.
,
Givi
,
P.
, and
Pope
,
S. B.
,
1998
, “
Filtered Density Function for Large Eddy Simulation of Turbulent Reacting Flows
,”
Phys. Fluids
,
10
(
2
), pp.
499
515
.10.1063/1.869537
54.
Jaberi
,
F. A.
,
Colucci
,
P. J.
,
James
,
S.
,
Givi
,
P.
, and
Pope
,
S. B.
,
1999
, “
Filtered Mass Density Function for Large Eddy Simulation of Turbulent Reacting Flows
,”
J. Fluid Mech.
,
401
, pp.
85
121
.10.1017/S0022112099006643
55.
Drummond
,
J. P.
,
Carpenter
,
M. H.
, and
Riggins
,
D. W.
,
1991
, “
Mixing and Mixing Enhancement in Supersonic Reacting Flow Fields
,”
High Speed Propulsion Systems (Progress in Astronautics and Aeronautics)
, Vol. 137,
S. N. B.
Murthy
and
E. T.
Curran
, eds.,
American Institute of Aeronautics and Astronautics
, Chap. 7, pp.
383
455
.
56.
Kennedy
,
C. A.
, and
Carpenter
,
M. H.
,
1994
, “
Several New Numerical Methods for Compressible Shear-Layer Simulations
,”
Appl. Num. Math.
,
14
, pp.
397
433
.10.1016/0168-9274(94)00004-2
57.
Rogers
,
M. M.
, and
Moser
,
R. D.
,
1989
, “
The Development of Three-Dimensional Temporally-Evolving Mixing Layers
,”
7th Symposium on Turbulent Shear Flows
,
Stanford, CA
, pp.
1
6
.
58.
Sandham
,
N. D.
, and
Reynolds
,
W. C.
,
1991
, “
Three-Dimensional Simulations of Large Eddies in the Compressible Mixing Layer
,”
J. Fluid Mech.
,
224
, pp.
133
158
.10.1017/S0022112091001684
59.
Moser
,
R. D.
, and
Rogers
,
M. M.
,
1993
, “
The Three-Dimensional Evolution of a Plane Mixing Layer: Pairing and Transition to Turbulence
,”
J. Fluid Mech.
,
247
, pp.
275
320
.10.1017/S0022112093000473
60.
Gicquel
,
L. Y. M.
,
Givi
,
P.
,
Jaberi
,
F. A.
, and
Pope
,
S. B.
,
2001
, “
Velocity Filtered Density Function for Large Eddy Simulation of a Turbulent Mixing Layer
,”
DNS/LES-Progress and Challenges
,
C.
Liu
,
L.
Sakell
, and
R.
Herklotz
, eds.,
Greyden Press
,
Columbus, OH
, pp.
327
334
.
61.
Vreman
,
B.
,
Geurts
,
B.
, and
Kuerten
,
H.
,
1997
, “
Large-Eddy Simulation of the Turbulent Mixing Layer
,”
J. Fluid Mech.
,
339
, pp.
357
390
.10.1017/S0022112097005429
You do not currently have access to this content.