Velocity dilatation and total, solenoidal, and dilatational dissipation rates of the total flow kinetic energy are extracted from three different direct numerical simulation databases obtained by three independent research groups using different numerical codes and methods (e.g., single-step chemistry and complex chemistry flames) from six different premixed turbulent flames associated with flamelet, thin reaction zone, and broken reaction zone regimes of turbulent burning. The results show that dilatational dissipation can be larger than solenoidal dissipation in the flamelet regime and is substantial in the thin reaction zone regime. Accordingly, the influence of combustion-induced thermal expansion on the dissipation rate is not reduced to an increase in the mixture viscosity by the temperature. A simple criterion for identifying conditions associated with significant dilatational dissipation is discussed, and dilatational dissipation due to the influence of turbulence on mixing in preheat zones is argued to play a role even at high Karlovitz numbers Ka. In particular, the magnitude of dilatation fluctuations and probability of finding negative local dilatation are increased by Ka, thus implying that the impact of molecular transport of species and heat on the dilatation increases with increasing Karlovitz number.

1.
A. N.
Kolmogorov
, “
The local structure of turbulence in incompressible viscous fluid for very large Reynolds number
,”
Dokl. Akad. Nauk SSSR
30
,
299
(
1941
).
2.
A. S.
Monin
and
A. M.
Yaglom
,
Statistical Fluid Mechanics: Mechanics of Turbulence
(
The MIT Press
,
Cambridge, Massachusetts
,
1975
),
Vol. 2
.
3.
L. D.
Landau
and
E. M.
Lifshitz
,
Fluid Mechanics
(
Pergamon Press
,
Oxford, UK
,
1987
).
4.
U.
Frisch
,
Turbulence: The Legacy of A. N. Kolmogorov
(
Cambridge University Press
,
Cambridge, UK
,
1995
).
5.
S. B.
Pope
,
Turbulent Flows
(
Cambridge University Press
,
Cambridge, UK
,
2000
).
6.
A.
Tsinober
,
An Informal Conceptual Introduction to Turbulence
(
Springer
,
Heidelberg, Germany
,
2009
).
7.
S. K.
Lele
, “
Compressibility effects on turbulence
,”
Annu. Rev. Fluid Mech.
26
,
211
(
1994
).
8.
P. G.
Huang
,
G. N.
Coleman
, and
P.
Bradshaw
, “
Compressible turbulent channel flows: DNS results and modelling
,”
J. Fluid Mech.
305
,
185
(
1995
).
9.
V. M.
Canuto
, “
Compressible turbulence
,”
Astrophys. J.
482
,
827
(
1997
).
10.
R.
Friedrich
and
F. P.
Bertolloti
, “
Compressibility effects due to turbulent fluctuations
,”
Appl. Sci. Res.
57
,
165
(
1997
).
11.
Y.
Andreopoulos
,
J. H.
Agui
, and
G.
Briassulis
, “
Shock wave-turbulence interactions
,”
Annu. Rev. Fluid Mech.
32
,
309
(
2000
).
12.
O.
Zeman
, “
Dilatation dissipation: The concept and application in modeling compressible mixing layers
,”
Phys. Fluids A
2
,
178
(
1990
).
13.
S.
Jagannathan
and
D. A.
Donzis
, “
Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations
,”
J. Fluid Mech.
789
,
669
(
2016
).
14.
J.
Wang
,
T.
Gotoh
, and
T.
Watanabe
, “
Spectra and statistics in compressible isotropic turbulence
,”
Phys. Rev. Fluids
2
,
013403
(
2017
).
15.
J. P.
John
,
D. A.
Donzis
, and
K. R.
Sreenivasan
, “
Solenoidal scaling laws for compressible mixing
,”
Phys. Rev. Lett.
123
,
224501
(
2019
).
16.
J.
Teng
,
J.
Wang
,
H.
Li
, and
S.
Chen
, “
Spectra and scaling in chemically reacting compressible isotropic turbulence
,”
Phys. Rev. Fluids
5
,
084601
(
2020
).
17.
D. A.
Donzis
and
J. P.
John
, “
Universality and scaling in homogeneous compressible turbulence
,”
Phys. Rev. Fluids
5
,
084609
(
2020
).
18.
J. P.
John
,
D. A.
Donzis
, and
K. R.
Sreenivasan
, “
Compressibility effects on the scalar dissipation rate
,”
Combust. Sci. Technol.
192
,
1320
(
2020
).
19.
F. A.
Jaberi
and
C. K.
Madnia
, “
Effects of heat of reaction on homogeneous compressible turbulence
,”
J. Sci. Comput.
13
,
201
(
1998
).
20.
M. P.
Martín
and
G.
Candler
, “
Effect of chemical reactions on decaying isotropic turbulence
,”
Phys. Fluids
10
,
1715
(
1998
).
21.
F. A.
Jaberi
,
D.
Livescu
, and
C. K.
Madnia
, “
Characteristics of chemically reacting compressible homogeneous turbulence
,”
Phys. Fluids
12
,
1189
(
2000
).
22.
D.
Livescu
,
F. A.
Jaberi
, and
C. K.
Madnia
, “
The effects of heat release on the energy exchange in reacting turbulent shear flow
,”
J. Fluid Mech.
450
,
35
(
2002
).
23.
S. D.
Mason
and
C. J.
Rutland
, “
Turbulent transport in spatially developing reacting shear layers
,”
Proc. Combust. Inst.
28
,
505
(
2000
).
24.
B.
Bobbitt
and
G.
Blanquart
, “
Vorticity isotropy in high Karlovitz number premixed flames
,”
Phys. Fluids
28
,
105101
(
2016
).
25.
B.
Bobbitt
,
S.
Lapointe
, and
G.
Blanquart
, “
Vorticity transformation in high Karlovitz number premixed flames
,”
Phys. Fluids
28
,
015101
(
2016
).
26.
A. N.
Lipatnikov
and
J.
Chomiak
, “
Effects of premixed flames on turbulence and turbulent scalar transport
,”
Prog. Energy Combust. Sci.
36
,
1
(
2010
).
27.
V. A.
Sabelnikov
and
A. N.
Lipatnikov
, “
Recent advances in understanding of thermal expansion effects in premixed turbulent flames
,”
Annu. Rev. Fluid Mech.
49
,
91
(
2017
).
28.
S.
Nishiki
,
T.
Hasegawa
,
R.
Borghi
, and
R.
Himeno
, “
Modeling of flame-generated turbulence based on direct numerical simulation databases
,”
Proc. Combust. Inst.
29
,
2017
(
2002
).
29.
S.
Nishiki
,
T.
Hasegawa
,
R.
Borghi
, and
R.
Himeno
, “
Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases
,”
Combust. Theory Modell.
10
,
39
(
2006
).
30.
Y-H.
Im
,
K. Y.
Huh
,
S.
Nishiki
, and
T.
Hasegawa
, “
Zone conditional assessment of flame-generated turbulence with DNS database of a turbulent premixed flame
,”
Combust. Flame
137
,
478
(
2004
).
31.
A.
Mura
,
K.
Tsuboi
, and
T.
Hasegawa
, “
Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data
,”
Combust. Theory Modell.
12
,
671
(
2008
).
32.
A.
Mura
,
V.
Robin
,
M.
Champion
, and
T.
Hasegawa
, “
Small scale features of velocity and scalar fields in turbulent premixed flames
,”
Flow, Turbul. Combust.
82
,
339
(
2009
).
33.
V.
Robin
,
A.
Mura
,
M.
Champion
, and
T.
Hasegawa
, “
Modeling the effects of thermal expansion on scalar turbulent fluxes in turbulent premixed flames
,”
Combust. Sci. Technol.
182
,
449
(
2010
).
34.
V.
Robin
,
A.
Mura
, and
M.
Champion
, “
Direct and indirect thermal expansion effects in turbulent premixed flames
,”
J. Fluid Mech.
689
,
149
(
2011
).
35.
K.
Bray
,
M.
Champion
,
P. A.
Libby
, and
N.
Swaminathan
, “
Scalar dissipation and mean reaction rates in premixed turbulent combustion
,”
Combust. Flame
158
,
2017
(
2011
).
36.
A. N.
Lipatnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames
,”
Phys. Fluids
26
,
105104
(
2014
).
37.
A. N.
Lipatnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
DNS assessment of relation between mean reaction and scalar dissipation rates in the flamelet regime of premixed turbulent combustion
,”
Combust. Theory Modell.
19
,
309
(
2015
).
38.
A. N.
Lipatnikov
,
J.
Chomiak
,
V. A.
Sabelnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
Unburned mixture fingers in premixed turbulent flames
,”
Proc. Combust. Inst.
35
,
1401
(
2015
).
39.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
S.
Nishiki
,
T.
Hasegawa
, and
N.
Chakraborty
, “
DNS assessment of a simple model for evaluating velocity conditioned to unburned gas in premixed turbulent flames
,”
Flow, Turbul. Combust.
94
,
513
(
2015
).
40.
V. A.
Sabelnikov
,
A. N.
Lipatnikov
,
N.
Chakraborty
,
S.
Nishiki
, and
T.
Hasegawa
, “
A transport equation for reaction rate in turbulent flows
,”
Phys. Fluids
28
,
081701
(
2016
).
41.
V. A.
Sabelnikov
,
A. N.
Lipatnikov
,
N.
Chakraborty
,
S.
Nishiki
, and
T.
Hasegawa
, “
A balance equation for the mean rate of product creation in premixed turbulent flames
,”
Proc. Combust. Inst.
36
,
1893
(
2017
).
42.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
Flamelet perturbations and flame surface density transport in weakly turbulent premixed combustion
,”
Combust. Theory Modell.
21
,
205
(
2017
).
43.
A. N.
Lipatnikov
,
J.
Chomiak
,
V. A.
Sabelnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
A DNS study of the physical mechanisms associated with density ratio influence on turbulent burning velocity in premixed flames
,”
Combust. Theory Modell.
22
,
131
(
2018
).
44.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
N.
Chakraborty
,
S.
Nishiki
, and
T.
Hasegawa
, “
A DNS study of closure relations for convection flux term in transport equation for mean reaction rate in turbulent flow
,”
Flow, Turbul. Combust.
100
,
75
(
2018
).
45.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
Combustion-induced local shear layers within premixed flamelets in weakly turbulent flows
,”
Phys. Fluids
30
,
085101
(
2018
).
46.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
Letter: Does flame-generated vorticity increase turbulent burning velocity?
,”
Phys. Fluids
30
,
081702
(
2018
).
47.
A. N.
Lipatnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
A DNS assessment of linear relations between filtered reaction rate, flame surface density, and scalar dissipation rate in a weakly turbulent premixed flame
,”
Combust. Theory Modell.
23
,
245
(
2019
).
48.
A.
Lipatnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
Closure relations for fluxes of flame surface density and scalar dissipation rate in turbulent premixed flames
,”
Fluids
4
,
43
(
2019
).
49.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
A direct numerical simulation study of the influence of flame-generated vorticity on reaction-zone-surface area in weakly turbulent premixed combustion
,”
Phys. Fluids
31
,
055101
(
2019
).
50.
V. A.
Sabelnikov
,
A. N.
Lipatnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
Application of conditioned structure functions to exploring influence of premixed combustion on two-point turbulence statistics
,”
Proc. Combust. Inst.
37
,
2433
(
2019
).
51.
V. A.
Sabelnikov
,
A. N.
Lipatnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
Investigation of the influence of combustion-induced thermal expansion on two-point turbulence statistics using conditioned structure functions
,”
J. Fluid Mech.
867
,
45
(
2019
).
52.
V. A.
Sabelnikov
,
A. N.
Lipatnikov
,
N.
Nikitin
,
S.
Nishiki
, and
T.
Hasegawa
, “
Application of Helmholtz-Hodge decomposition and conditioned structure functions to exploring influence of premixed combustion on turbulence upstream of the flame
,”
Proc. Combust. Inst.
(published online) (
2021
).
53.
V. A.
Sabelnikov
,
A. N.
Lipatnikov
,
N.
Nikitin
,
S.
Nishiki
, and
T.
Hasegawa
, “
Solenoidal and potential velocity fields in weakly turbulent premixed flames
,”
Proc. Combust. Inst.
(published online) (
2021
).
54.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
S.
Nishiki
, and
T.
Hasegawa
, “
Influence of thermal expansion on potential and rotational components of turbulent velocity field within and upstream of premixed flame brush
,”
Flow, Turbul. Combust.
(published online) (
2021
).
55.
H. L.
Dave
and
S.
Chaudhuri
, “
Evolution of local flame displacement speeds in turbulence
,”
J. Fluid Mech.
884
,
A46
(
2020
).
56.
A. N.
Lipatnikov
and
V. A.
Sabelnikov
, “
An extended flamelet-based presumed probability density function for predicting mean concentrations of various species in premixed turbulent flames
,”
Int. J. Hydrogen Energy
45
,
31162
(
2020
).
57.
A. N.
Lipatnikov
and
V. A.
Sabelnikov
, “
Evaluation of mean species mass fractions in premixed turbulent flames: A DNS study
,”
Proc. Combust. Inst.
(published online) (
2021
).
58.
H. G.
Im
,
P. G.
Arias
,
S.
Chaudhuri
, and
H. A.
Uranakara
, “
Direct numerical simulations of statistically stationary turbulent premixed flames
,”
Combust. Sci. Technol.
188
,
1182
(
2016
).
59.
H. A.
Uranakara
,
S.
Chaudhuri
,
H. L.
Dave
,
P. G.
Arias
, and
H. G.
Im
, “
A flame particle tracking analysis of turbulence-chemistry interaction in hydrogen-air premixed flames
,”
Combust. Flame
163
,
220
(
2016
).
60.
D. H.
Wacks
,
N.
Chakraborty
,
M.
Klein
,
P. G.
Arias
, and
H. G.
Im
, “
Flow topologies in different regimes of premixed turbulent combustion: A direct numerical simulation analysis
,”
Phys. Rev. Fluids
1
,
083401
(
2016
).
61.
M.
Klein
,
A.
Herbert
,
H.
Kosaka
,
B.
Böhm
,
A.
Dreizler
,
N.
Chakraborty
,
V.
Papapostolou
,
H. G.
Im
, and
J.
Hasslberger
, “
Evaluation of flame area based on detailed chemistry DNS of premixed turbulent hydrogen-air flames in different regimes of combustion
,”
Flow, Turbul. Combust.
104
,
403
(
2020
).
62.
D. M.
Manias
,
E.-A.
Tingas
,
F. E.
Hernández Pérez
,
R.
Malpica Galassi
,
P.
Paolo Ciottoli
,
M.
Valorani
, and
H. G.
Im
, “
Investigation of the turbulent flame structure and topology at different Karlovitz numbers using the tangential stretching rate index
,”
Combust. Flame
200
,
155
(
2019
).
63.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
F. E.
Hernández-Pérez
,
W.
Song
, and
H. G.
Im
, “
A priori DNS study of applicability of flamelet concept to predicting mean concentrations of species in turbulent premixed flames at various Karlovitz numbers
,”
Combust. Flame
222
,
370
(
2020
).
64.
A. N.
Lipatnikov
,
V. A.
Sabelnikov
,
F. E.
Hernández-Pérez
,
W.
Song
, and
H. G.
Im
, “
Prediction of mean radical concentrations in lean hydrogen-air turbulent flames at different Karlovitz numbers adopting a newly extended flamelet-based presumed PDF
,”
Combust. Flame
226
,
248
(
2021
).
65.
N.
Peters
, “
The turbulent burning velocity for large-scale and small-scale turbulence
,”
J. Fluid Mech.
384
,
107
(
1999
).
66.
N.
Babkovskaia
,
N. E. L.
Haugen
, and
A.
Brandenburg
, “
A high-order public domain code for direct numerical simulations of turbulent combustion
,”
J. Comput. Phys.
230
,
1
(
2011
).
67.
J.
Li
,
Z.
Zhao
,
A.
Kazakov
, and
F. L.
Dryer
, “
An updated comprehensive kinetic model of hydrogen combustion
,”
Int. J. Chem. Kinet.
36
,
566
(
2004
).
68.
M. P.
Burke
,
M.
Chaos
,
Y.
Ju
,
F. L.
Dryer
, and
S. J.
Klippenstein
, “
Comprehensive H2/O2 kinetic model for high-pressure combustion
,”
Int. J. Chem. Kinet.
44
,
444
(
2012
).
69.
V. R.
Kuznetsov
and
V. A.
Sabelnikov
,
Turbulence and Combustion
(
Hemisphere Publishing Corporation
,
New York
,
1990
).
70.
A. N.
Lipatnikov
and
J.
Chomiak
, “
Molecular transport effects on turbulent flame propagation and structure
,”
Prog. Energy Combust. Sci.
31
,
1
(
2005
).
71.
A.
Lipatnikov
,
Fundamentals of Premixed Turbulent Combustion
(
CRC Press
,
Boca Raton, FL
,
2012
).
72.
R. W.
Bilger
, “
Some aspects of scalar dissipation
,”
Flow, Turbul. Combust.
72
,
93
(
2004
).
73.
J. F.
MacArt
,
T.
Grenga
, and
M. E.
Mueller
, “
Effects of combustion heat release on velocity and scalar statistics in turbulent premixed jet flames at low and high Karlovitz numbers
,”
Combust. Flame
191
,
468
(
2018
).
74.
J. F.
MacArt
,
T.
Grenga
, and
M. E.
Mueller
, “
Evolution of flame-conditioned velocity statistics in turbulent premixed jet flames at low and high Karlovitz numbers
,”
Proc. Combust. Inst.
37
,
2503
(
2019
).
75.
V. A.
Sabelnikov
,
R.
Yu
, and
A. N.
Lipatnikov
, “
Thin reaction zones in constant-density turbulent flows at low Damköhler numbers: Theory and simulations
,”
Phys. Fluids
31
,
055104
(
2019
).
76.
B.
Ya Zel'dovich
,
G. I.
Barenblatt
,
V. B.
Librovich
, and
G. M.
Makhviladze
,
The Mathematical Theory of Combustion and Explosions
(
Consultants Burea
,
New York
,
1985
).
77.
N.
Peters
,
Turbulent Combustion
(
Cambridge University Press
,
Cambridge, UK
,
2000
).
78.
T.
Poinsot
and
D.
Veynante
,
Theoretical and Numerical Combustion
, 2nd ed. (
Edwards
,
Philadelphia
,
2005
).
79.
A. G.
Prudnikov
, “
Burning of homogeneous fuel-air mixtures in a turbulent flow
,” in
Physica Principles of the Working Process in Combustion Chambers of Jet Engines
, edited by
B. V.
Raushenbakh
(
Clearing House for Federal Scientific and Technical Information
,
Springfield
,
1967
), pp.
244
336
.
80.
N.
Chakraborty
and
R. S.
Cant
, “
Influence of Lewis number on curvature effects in turbulent premixed flame propagation in the thin reaction zones regime
,”
Phys. Fluids
17
,
105105
(
2005
).
81.
G.
Troiani
,
F.
Battista
, and
F.
Picano
, “
Turbulent consumption speed via local dilatation rate measurements in a premixed Bunsen jet
,”
Combust. Flame
160
,
2029
(
2013
).
82.
I. R.
Gran
,
T.
Echekki
, and
J. H.
Chen
, “
Negative flame speed in an unsteady 2-D premixed flame: A computational study
,”
Proc. Combust. Inst.
26
,
323
(
1996
).
83.
N.
Peters
,
P.
Terhoeven
,
J. H.
Chen
, and
T.
Echekki
, “
Statistics of flame displacement speeds from computations of 2-D unsteady methane-air flames
,”
Proc. Combust. Inst.
27
,
833
(
1998
).
84.
N.
Chakraborty
,
M.
Klein
, and
R. S.
Cant
, “
Stretch rate effects on displacement speed in turbulent premixed flame kernels in the thin reaction zones regime
,”
Proc. Combust. Inst.
31
,
1385
(
2007
).
85.
H.
Wang
,
E. R.
Hawkes
, and
J. H.
Chen
, “
A direct numerical simulation study of flame structure and stabilization of an experimental high Ka CH4/air premixed jet flame
,”
Combust. Flame
180
,
110
(
2017
).
86.
S.
Luca
,
A.
Attili
,
E.
Lo Schiavo
,
F.
Creta
, and
F.
Bisetti
, “
On the statistics of flame stretch in turbulent premixed jet flames in the thin reaction zone regime at varying Reynolds number
,”
Proc. Combust. Inst.
37
,
2451
(
2019
).
87.
R.
Yu
,
T.
Nilsson
,
C.
Fureby
, and
A.
Lipatnikov
, “
Evolution equations for the decomposed components of displacement speed in a reactive scalar field
,”
J. Fluid Mech.
911
,
A38
(
2021
).
88.
P.
Clavin
, “
Dynamic behavior of premixed flame fronts in laminar and turbulent flows
,”
Prog. Energy Combust. Sci.
11
,
1
(
1985
).
89.
A. M.
Klimov
, “
Laminar flame in a turbulent flow
,”
Zh. Prikl. Mekhaniki Tekhnicheskoy Fiz.
4
(
3
),
49
(
1963
).
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