Abstract

The aim of this work is to examine the state-of-the-art turbulent flame speed (ST) correlations and optimize their adjustable parameters to best match a wide range experimental turbulent premixed combustion results. Based on previous work, four correlations have been selected for this study. Using a matlab-based Nelder–Mead simplex direct search method, each correlation's adjustable parameters are optimized such that their mean absolute percentage error (MAPE) is minimized. In addition to the literature correlations, a new empirical correlation is developed using the same search method to define constants and powers in the expression. Two sets of optimized parameters are proposed to account for atmospheric and elevated (0.2–3.0 MPa) pressure flames. Each correlation is tested further, examining their ability to match ST trends for varying equivalence ratio (φ) and turbulent velocity ratio (u′/SL)⁠. It was found that a minimum of two correlations and two sets of adjustable parameters are required to accurately account for the entire range of data, thus showing that there is currently no turbulent flame speed correlation that is applicable across all engine-relevant conditions.

Issue Section:
Research Papers
Keywords:
turbulent flame speed, C1–C3 fuels, mean absolute percentage error, engine-relevant conditions, correlation
Topics:
Flames, Turbulence, Fuels, Engines

References

1.
Peters
,
N.
,
1999
, “
The Turbulent Burning Velocity for Large-Scale and Small-Scale Turbulence
,”
J. Fluid Mech.
,
384
, pp.
107
–
132
.10.1017/S0022112098004212
2.
Zimont
,
V. L.
,
2000
, “
Gas Premixed Combustion at High Turbulence. Turbulent Flame Closure Combustion Model
,”
Exp. Therm. Fluid Sci.
,
21
(
1–3
), pp.
179
–
186
.10.1016/S0894-1777(99)00069-2
3.
Kobayashi
,
H.
,
Tamura
,
T.
,
Maruta
,
K.
,
Niioka
,
T.
, and
Williams
,
F. A.
,
1996
, “
Burning Velocity of Turbulent Premixed Flames in a High-Pressure Environment
,”
Symp. (Int.) Combust.
,
26
(
1
), pp.
389
–
396
.10.1016/S0082-0784(96)80240-2
4.
Ravi
,
S.
,
Morones
,
A.
, and
Petersen
,
E.
,
2013
, “
Evaluation of Numerical Turbulent Combustion Models Using Flame Speed Measurements From a Recently Developed Fan- Stirred Explosion Vessel
,”
Eighth U.S. National Combustion Meeting
, Park City, Utah, May 19–22, Paper No.
070LT-0096
.https://sutherland.che.utah.edu/USCI2013/PAPERS/1E06-070LT-0096.pdf
5.
Abdel-Gayed
,
R. G.
,
Bradley
,
D.
, and
Lawes
,
M.
,
1987
, “
Turbulent Burning Velocities: A General Correlation in Terms of Straining Rates
,”
Proc. R. Soc. A
,
414
(
1847
), pp.
389
–
413
.10.1098/rspa.1987.0150
6.
Bradley
,
D.
,
Lawes
,
M.
, and
Mansour
,
M. S.
,
2011
, “
Correlation of Turbulent Burning Velocities of Ethanol–Air, Measured in a Fan-Stirred Bomb Up to 1.2 MPa
,”
Combust. Flame
,
158
(
1
), pp.
123
–
138
.10.1016/j.combustflame.2010.08.001
7.
Kolla
,
H.
,
Rogerson
,
J. W.
,
Chakraborty
,
N.
, and
Swaminathan
,
N.
,
2009
, “
Scalar Dissipation Rate Modeling and Its Validation
,”
Combust. Sci. Technol.
,
181
(
3
), pp.
518
–
535
.10.1080/00102200802612419
8.
Kerstein
,
A. R.
,
1988
, “
Pair-Exchange Model of Turbulent Premixed Flame Propagation
,”
Symp. (Int.) Combust.
,
21
(
1
), pp.
1281
–
1289
.10.1016/S0082-0784(88)80359-X
9.
Ronney
,
P. D.
,
1995
, “
Some Open Issues in Premixed Turbulent Combustion,” Modeling in Combustion Science
,”
Lect. Notes Phys.
,
449
, pp.
1
–
22
.10.1007/3-540-59224-5_1
10.
Shy
,
S. S.
,
Lin
,
W. J.
, and
Wei
,
J. C.
,
2000
, “
An Experimental Correlation of Turbulent Burning Velocities for Premixed Turbulent Methane-Air Combustion
,”
Proc. R. Soc. A
,
456
(
2000
), pp.
1364
–
5021
.10.1098/rspa.2000.0599
11.
Venkateswaran
,
P.
,
Marshall
,
A.
,
Seitzman
,
J.
, and
Lieuwen
,
T.
,
2013
, “
Pressure and Fuel Effects on Turbulent Consumption Speeds of H2/CO Blends
,”
Proc. Combust. Inst.
,
34
(
1
), pp.
1527
–
1535
.10.1016/j.proci.2012.06.077
12.
Siewert
,
P.
,
Griebel
,
P.
, and
Jansohn
,
P.
,
2007
, “
Influence of Pressure on Flame Front Corrugation and Turbulent Flame Speed: Fractal Analysis of Lean Premixed Methane/Air Flames
,”
Third European Combustion Meeting
,
Chania, Crete
, Apr. 11–13.
13.
Muppala
,
S.
,
Manickam
,
B.
, and
Dinkelacker
,
F.
,
2015
, “
A Comparative Study of the Different Reaction Models for Turbulent Methane/Hydrogen/Air
,”
J. Therm. Eng.
,
1
(
5
), pp.
367
–
380
.10.18186/jte.60394
14.
Driscoll
,
J. F.
,
2008
, “
Turbulent Premixed Combustion: Flamelet Structure and Its Effect on Turbulent Burning Velocities
,”
Prog. Energy Combust. Sci.
,
34
(
1
), pp.
91
–
134
.10.1016/j.pecs.2007.04.002
15.
Lipatnikov
,
N.
, and
Chomiak
,
J.
,
2002
, “
Turbulent Flame Speed and Thickness: Phenomenology, Evaluation, and Application in Multi-Dimensional Simulations
,”
Prog. Energy Combust. Sci.
,
28
(
1
), pp.
1
–
74
.10.1016/S0360-1285(01)00007-7
16.
Peters
,
N.
,
2000
,
Turbulent Combustion
,
Cambridge University Press
,
Cambridge, UK
.
17.
Kobayashi
,
H.
,
2002
, “
Experimental Study of High-Pressure Turbulent Premixed Flames
,”
Exp. Therm. Fluid Sci.
,
26
(
2–4
), pp.
375
–
387
.10.1016/S0894-1777(02)00149-8
18.
Gulder
,
O. L.
,
1991
, “
Turbulent Premixed Flame Propagation Models for Different Combustion Regimes
,”
Symp. (Int.) Combust.
,
23
(
1
), pp.
743
–
750
.10.1016/S0082-0784(06)80325-5
19.
Burke
,
E. M.
,
Guthe
,
F.
, and
Monaghan
,
R. F. D.
,
2016
, “
A Comparison of Turbulent Flame Speed Correlations for Hydrocarbon Fuels at Elevated Pressures
,”
ASME Paper No. GT2016-57804
.10.1115/GT2016-57804
20.
Muppala
,
S. P.
,
Aluri
,
N. K.
,
Dinkelacker
,
F.
, and
Leipertz
,
A.
,
2005
, “
Development of an Algebraic Reaction Rate Closure for the Numerical Calculation of Turbulent Premixed Methane, Ethylene, and Propane/Air Flames for Pressures Up to 1.0 MPa
,”
Combust. Flame
,
140
(
4
), pp.
257
–
266
.10.1016/j.combustflame.2004.11.005
21.
N. J
,
A.
, and
Mead
,
R.
,
1965
, “
A Simplex Method for Function Minimizatio
,”
Comput. J.
,
7
(
4
), pp.
308
–
313
.10.1093/comjnl/7.4.308
22.
Liu
,
C. C.
,
Shy
,
S. S.
,
Peng
,
M. W.
,
Chiu
,
C. W.
, and
Dong
,
Y. C.
,
2012
, “
High-Pressure Burning Velocities Measurements for Centrally-Ignited Pre- Mixed Methane/Air Flames Interacting With Intense Near- Isotropic Turbulence at Constant Reynolds Numbers
,”
Combust. Flame
,
159
(
8
), pp.
2608
–
2619
.10.1016/j.combustflame.2012.04.006
23.
Nakahara
,
M.
, and
Kido
,
H.
,
2008
, “
Study on the Turbulent Burning Velocity of Hydrogen Mixtures Including Hydrocarbons
,”
AIAA J.
,
46
(
7
), pp.
1569
–
1575
.10.2514/1.23560
24.
Tamadonfar
,
P.
, and
Gulder
,
O. L.
,
2015
, “
Effects of Mixture Composition and Turbulence Intensity on Flame Front Structure and Burning Velocities of Premixed Turbulent Hydrocarbon/Air Bunsen Flames
,”
Combust. Flame
,
162
(
12
), pp.
4417
–
4441
.10.1016/j.combustflame.2015.08.009
25.
Mandilas
,
C.
,
Ormsby
,
M. P.
,
Sheppard
,
C. G. W.
, and
Woolley
,
R.
,
2007
, “
Effects of Hydrogen Addition on Laminar and Turbulent Premixed Methane and Iso- Octane-Air Flames
,”
Proc. Combust. Inst.
,
31
(
1
), pp.
1443
–
1450
.10.1016/j.proci.2006.07.157
26.
Fairweather
,
M.
,
Ormsby
,
M. P.
,
Sheppard
,
C. G. W.
, and
Woolley
,
R.
,
2009
, “
Turbulent Burning Rates of Methane and Methane-Hydrogen Mixtures
,”
Combust. Flame
,
156
(
4
), pp.
780
–
790
.10.1016/j.combustflame.2009.02.001
27.
Smallwood
,
G.
,
1995
, “
Characterization of Flame Front Surfaces in Turbulent Premixed Methane/Air Combustion
,”
Combust. Flame
,
101
(
4
), pp.
461
–
470
.10.1016/0010-2180(94)00226-I
28.
Nakahara
,
M.
,
Kido
,
H.
, and
Nakashima
,
K.
,
2005
, “
A Study on the Local Flame Displacement Velocity of Premixed Turbulent Flames
,”
JSME Int. J. Ser. B
,
48
(
1
), pp.
164
–
171
.10.1299/jsmeb.48.164
29.
Brutscher
,
T.
,
Zarzalis
,
N.
, and
Bockhorn
,
H.
,
2002
, “
An Experimentally Based Approach for the Space- Averaged Laminar Burning Velocity Used for Modeling Premixed Turbulent Combustion
,”
Proc. Combust. Inst.
,
29
(
2
), pp.
1825
–
1832
.10.1016/S1540-7489(02)80221-8
30.
Savarianandam
,
V. R.
, and
Lawn
,
C. J.
,
2006
, “
Burning Velocity of Premixed Turbulent Flames in the Weakly Wrinkled Regime
,”
Combust. Flame
,
146
(
1–2
), pp.
1
–
18
.10.1016/j.combustflame.2006.05.002
31.
Cintosun
,
E.
,
Smallwood
,
G. J.
, and
Gulder
,
O. L.
,
2007
, “
Flame Surface Fractal Characteristics in Pre- Mixed Turbulent Combustion at High Turbulence Intensities
,”
AIAA J.
,
45
(
11
), pp.
2785
–
2789
.10.2514/1.29533
32.
Vukadinovic
,
V.
,
Habisreuther
,
P.
,
Suntz
,
R.
, and
Zarzalis
,
N.
,
2013
, “
Influence of Pressure on Markstein Number Effect in Turbulent
,”
ASME Paper No. GT2013-94307
.10.1115/GT2013-94307
33.
Kobayashi
,
H.
,
Kawabata
,
Y.
, and
Maruta
,
K.
,
1998
, “
Experimental Study on General Correlation of Turbulent Burning Velocity at High Pressure
,”
Symp. (Int.) Combust.
,
27
(
1
), pp.
941
–
948
.10.1016/S0082-0784(98)80492-X
34.
Tamadonfar
,
P.
, and
Gulder
,
O. L.
,
2014
, “
Flame Brush Characteristics and Burning Velocities of Premixed Turbulent Methane/Air Bunsen Flames
,”
Combust. Flame
,
161
(
12
), pp.
3154
–
3165
.10.1016/j.combustflame.2014.06.014
35.
CHEMKIN-PRO
,
2011
, “
Reaction Design
,” CHEMKIN-PRO 15112,
San Diego, CA
.
36.
Metcalfe
,
W. K.
,
Burke
,
S. M.
,
Ahmed
,
S. S.
, and
Curran
,
H. J.
,
2013
, “
A Hierarchical and Comparative Kinetic Modeling Study of C1 C2 Hydrocarbon and Oxygenated Fuels
,”
Int. J. Chem. Kinet.
,
45
(
10
), pp.
638
–
675
.10.1002/kin.20802
37.
Raymond
,
D. G. G.
,
Moffat
,
H. K.
, and
Speth
,
L.
,
2017
, “
Cantera: An Object-Oriented Software Toolkit for Chemical Kinetics, Thermodynamics, and Transport Processes
,” Version 2.3.0.10.5281/zenodo.170284
38.
Muppala
,
S.
, and
Dinkelacker
,
F.
,
2004
, “
Numerical Modelling of the Pressure Dependent Reaction Source Term for Premixed Turbulent Methane/Air Flames
,”
Prog. Comput. Fluid Dyn. Int. J.
,
4
(
6
), pp.
328
–
336
.10.1504/PCFD.2004.004605
39.
Burke
,
E. M.
,
Singlitico
,
A.
,
Morones
,
A. E.
,
P.
L
,
Guthe
,
F.
,
Speth
,
L.
, and
Monaghan
,
R. F. D.
,
2015
, “
Progress Towards a Validated Cantera-Based Turbulent Flame Speed Solver
,”
Seventh European Combustion Meeting
, Budapest, Hungary, Mar. 30–Apr. 2.https://www.researchgate.net/profile/Alessandro_Singlitico/publication/283350945_Progress_Towards_a_Validated_Cantera-based_Turbulent_Flame_Speed_Solver/links/563652e208aeb786b703f081/Progress-Towards-a-Validated-Cantera-based-Turbulent-Flame-Speed-Solver.pdf
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