1 of 5
References on Conditional Moment Closure
for Turbulent Combustion Modelling
(Updated April, 2005)
Klimenko, A. Yu., “Multicomponent diffusion of various admixtures in turbulent flow”,
Fluid Dynamics,
25, pp.327334 (1990).
1.
Bilger, R.W., "Conditional Moment Closure for Turbulent Reacting Flow",
Phys Fluids A, 5 (2), 1993,
436444.
2.
Bilger, R.W., “Advanced Laser Diagnostics: Implications of Recent Results for Advanced Combustor
Models”,
Aerothermodynamics in Combustors, R S L Lee, J H Whitelaw, amd T S Wung (Eds),
SpringerVerlag, Berlin Heidelberg, 1992, pp 316.
3.
Smith, N.S., Chen, JY. and Bilger, R.W., "Modelling of Nonpremixed Hydrogen Jet Flames Using a
Conditional Moment Method",
Twentyfourth Symposium (International) on Combustion, The
Combustion Institute, 263269, 1993.
4.
Bilger, R.W., "Conditional Moment Closure Modelling and Advanced Laser Measurements" in
Turbulence
and Molecular Processes in Combustion (Sixth Toyota Conference) T. Takeno, ed., Elsevier, Amsterdam
267285, 1993.
5.
A.Y.Klimenko, "Conditional moment closure and fluctuations of scalar dissipation",
Fluid Dynamics,
28, 630637, (1993)
6.
Li, J.D., and Bilger, R.W., "Measurement and Prediction of the Conditional Variance in a Turbulent
Reactive Scalar Mixing Layer",
Physics Fluids A, 5, 325564, 1993.
7.
Mell, W.E., Nilsen, V., Kosaly, G. and Riley, J.J., "Direct Numerical Simulation Investigation of the
Conditional Moment Closure Model for Nonpremixed turbulent reacting flows",
Combust. Sci. Technol.,
91, 179186, 1993.
8.
Montgomery, C.J., Kosaly, G. and Riley, J.J., "Direct Numerical Simulation of Turbulent Reacting Flow
Using a Reduced HydrogenOxygen Mechanism",
Combust. Flame, 95: 247260, 1993.
9.
Mell, W.E., Nilsen, V., Kosaly, G. and Riley, J.J., "Investigation of Closure Models for Nonpremixed
Turbulent Reacting Flows",
Physics of Fluids, 6:13311356, 1994.
10.
Smith, N.S.A., Bilger, R.W., Carter, C.D., Barlow, R.S. and Chen, JY., "A Comparison of CMC and PDF
Modelling Predictions with Experimental Nitric Oxide LIF/Raman Measurements in a Turbulent H2 Jet
Flame",
Combustion Sci. and Technology, 105, 357375, 1995.
11.
Li, J.D. and Bilger, R.W., "A Simple Theory for the Conditional Mean Velocity in a Turbulent
ScalarMixing Layer",
Physics Fluids, 6, 605610, 1994.
12.
Anselmet, F, Djeridi, H and Fulachier, L, “Joint statistics of a passive scalar and its dissipation in
turbulent flows”,
J Fluid Mech, 280, 173197, 1994.
13.
Nandula, S P, Brown, T M and Pitz, R W, “Measurements of scalar dissipation in the reaction zones of
turbulent nonpremixed H2 air flames”,
Combust Flame, 99, 775783, 1994.
14.
Mi, J, Antonia, R A and Anselmet, F, “ Joint statistics between temperature and its dissipation rate
components in a round jet”,
Phys Fluids, 7, 16651673, 1995.
15.
A.Y.Klimenko, "Note on the conditional moment closure in turbulent shear flows",
Physics of Fluids, 7,
446448, (1995)
16.
Lee, Y.Y. and Pope, S.B., "Nonpremixed Turbulent Reacting Flow Near Extinction",
Combust. Flame, 101,
501528, 1995.
17.
Barlow, RS and Carter C D, “ Relationships among nitric oxide, temperature and mixture fraction in
hydrogen jet flames”,
Combust Flame, 104, 288299, 1996.
18.
Desjardin, P E and Frankel, SH, “Assessment of turbulent combustion submodels using the linear eddy
model,
Combust Flame, 104, 343357, 1996.
19.
Brown, R.J. and Bilger, R.W., "Experimental Study of a Turbulent Reacting Plume: Part II  Conditional
Concentration Statistics,
Atmospheric Environment, 32, 629 – 646, 1998.
20.
2 of 5
Mantel, T. and Bilger, R.W., "Conditional Statistics in a Turbulent Premixed Flame Derived from Direct
Numerical Simulation",
Combustion Sci. and Technology, 110, 393417, 1995.
21.
Klimenko, A.Yu., Bilger, R.W. and Roomina, M.R., "Some PDF Integrals for SelfSimilar Turbulent Flows",
Combustion Sci. and Technology, 107, 403410, 1995,
22.
A.Y.Klimenko and R.W.Bilger, "Some analytical and asymptotic results for pdfs and conditional
expectations in turbulent shear flows", 10th Symposium on Turbulent Shear Flows, Pennsylvania State
University, USA, v.3, Sess.31, 2529, (1995)
23.
Brown, R.J. and Bilger, R.W., "Measurement and Modelling of Nonbuoyant turbulent reacting plumes",
Twelfth Australasian Fluid Mechanics Conference, The University of Sydney, 621624, 1995.
24.
Li, J.D. and Bilger, R.W., "Conditional Moment Closure of Reactive Plumes in Homogeneous Turbulence",
Twelfth Australasian Fluid Mechanics Conference, The University of Sydney, 625628, 1995.
25.
Swaminathan, N and Mahalingham, S, “ Assessment of conditional moment closure for single and
multistep chemistry” Combust Sci Technol, 112, 301326, 1996.
26.
Kronenburg, A. and Bilger, R.W., "Modelling of Differential Diffusion Effects in Nonpremixed
Nonreacting Flow",
Phys Fluids, 9, 14351447, 1997.
27.
O’Young, F. and Bilger, R.W., "Scalar Gradient and Related Quantities in Turbulent Premixed Flames",
Combustion and Flame, 109, 682700, 1997.
28.
Stårner, S.H., Bilger, R.W., Long, M.B., Frank, J.H. and Marran, D.H., "Scalar Dissipation Measurements in
Turbulent Jet Diffusion Flames of AirDiluted Methane and Hydrogen",
Combustion Sci. and
Technology, 129
, 141 163, 1997.
29.
Mobini, K., Bilger, R.W., Smith, N.S.A. and Brizuela, E.A., "Imperfectly Stirred Reactor Modelling of a Gas
Turbine Combustor"
First AsiaPacific Conference on Combustion, Osaka University, Japan, May 1997
pp 174177.
30.
Bilger, R.W., "Combustion Theory and Conditional Moment Closure Modelling", in
Advances in
Combustion Science: In Honor of Ya. B. Zel’dovich, (W.A. Sirignano, A.G. Merzhanov, and L. DeLuca, Eds)
Progress in Aeronautics and Astronautics, vol 173, AIAA, pp 263275, 1997.
31.
Swaminathan, N. and Bilger, R.W., "Direct Numerical Simulation of Turbulent Nonpremixed Hydrocarbon
Flames Using a Twostep Reduced Mechanism,
Combustion Sci. and Technology, 127
, 167  196,
1997.
32.
Yeung, P K, “Correlations and conditional statistics in differential diffusion: scalars with uniform mean
gradients”,
Phys Fluids, 10, 26212635, 1998.
33.
A.Y.Klimenko, "Conditional methods in application for Lagrangian modeling".
Phys.Fluids. 10, No 4,
922927, 1998.
34.
Swaminathan, N and Dally, B B, “Cross stream dependence of conditional averages in elliptic region of
flows behind a bluff body”,
Phys Fluids, 10, 24242426, 1998.
35.
Swaminathan, N. and Bilger, R.W., "Assessment of Combustion Submodels for Turbulent Nonpremixed
Hydrocarbon Flames",
Combustion and Flame, 116, 519545, 1999.
36.
Klimenko, A.Yu. and Bilger, R.W., "Conditional Moment Closure for Turbulent Combustion",
Progr.
Energy Combustion Sci., 25, 595687, 1999.
37.
Barlow, R.S., Smith, N.S.A., Chen, JY., and Bilger, R.W., “Nitric Oxide Formation in Dilute Hydrogen Jet
Flames: Isolation of the Effects of Radiation and TurbulenceChemistry Submodels”,
Combustion and
Flame, 117, 431,1999
38.
Nilsen, V and Kosaly, G, “Differential diffusion in turbulent reacting flows”, Combust Flame, 117,
493513, 1999.
39.
Kronenburg, A., Bilger, R.W. and Kent, J.H., "Computation of Conditional Average Scalar Dissipation in
Turbulent Jet Diffusion Flames",
Flow,Turbulence and Combustion, 64, 145159, 2000.
40.
Kronenburg, A., Bilger, R.W. and Kent, J.H., “Second Order Conditional Moment Closure for Turbulent Jet
Diffusion Flames”,
Twentyseventh Symposium (International) on Combustion, The Combustion
Institute, Pittsburgh, PA ,10971104, 1998.
41.
Swaminathan, N. and Bilger, R.W., “Authors’ Reply to Comments by N. Peters”,
Combustion and Flame,
116, 677, 1999.
42.
Mastorakos, E. and Bilger, R.W., “Secondorder conditional moment closure for the autoignition of
turbulent flows”,
Physics of Fluids, 10, 12468,1998.
43.
Gough, A.J., Mobini, K., Chen, Y.C. and Bilger, R.W., “Measurements and predictions in a confined44.
3 of 5
bluffbody burner modelled as an imperfectly stirred reactor”,
Twentyseventh Symposium
(International) on Combustion, The Combustion Institute, Pittsburgh, PA , 31813188, 1998.
Swaminathan, N. and Bilger R.W., “Conditional variance equation and its analysis”,
Twentyseventh
Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 11911198,
1998.
45.
Kronenburg, A. and Bilger, R.W., “Modelling differential diffusion in nonpremixed reacting turbulent
flow: model development",
Combustion Sci. Technol. , 166, 195227, 2001.
46.
Kronenburg, A. and Bilger, R.W., “Modelling differential diffusion in nonpremixed reacting turbulent
flow: application to turbulent jet flames”,
Combustion Sci. Technol. , 166, 175194, 2001.
47.
Kronenburg, A., Bilger, R.W. and Kent, J.H., “Modelling soot formation in turbulent methaneair jet
diffusion flames”,
Combustion and Flame, 121, 24 40, 2000.
48.
Bushe, W K and Steiner, H, “Conditional moment closure for large eddy simulation of nonpremixed
turbulent reacting flows’,
Phys Fluids, 11, 18961906, 1999.
49.
Roomina, M.R. and Bilger, R.W.,” Conditional Moment Closure (CMC) Modelling of a Turbulent Methanol
Jet Flame”,
Combustion Theory and Modelling, 3, 689708, 1999.
50.
Roomina, M.R. and Bilger, R.W.,” Conditional Moment Closure (CMC) Predictions of a Turbulent
MethaneAir Jet Flame”,
Combustion and Flame, 125, 11761195, 2001.
51.
Swaminathan, N. and Bilger, R.W., “Study of the conditional variance and covariance equations for
second order CMC closure”,
Physics of Fluids, 11
, 26792695, 1999.
52.
Bilger, R.W., “Recent progress in CMC methods for the prediction of pollutant species in nonpremixed
combustion”,
5th International Conference on Technologies and Combustion for a Clean Environment,
Lisbon, Portugal, pp 167176, July 1999.
53.
Kim, S. H., Huh, K. Y. and Liu, T., "Implementation of the Conditional Moment Closure Model to a
Turbulent Nonpremixed H2/COAir Stabilized on a BluffBody Flame,"
Transactions of the Canadian
Society of Mechanical Engineers,
23, No.3&4, pp.425434, 1999.
54.
A.P.Wandel, K.A.Weinman and A.Y.Klimenko, Diffusion in Conserved Scalar Space: Direct Validation by
DNS. Aust. Comb. Symp. Pp.7680 (1999)
55.
Bushe, W. K., Bilger, R. W. and Ruetsch, G. R., “Direct numerical simulation of turbulent nonpremixed
combustion with realistic chemistry”,
J. Fluid Mech., (submitted).
56.
Bilger, R.W., "Future progress in turbulent combustion research",
Progr. Energy Combust. Sci., 26,
367380, 2000.
57.
Kim, S.H., Tao, L. and Huh, K.Y., "Application of the Elliptic Conditional Moment Closure Model to a
Twodimensional Nonpremixed Methanol BluffBody Flame",
Combust. Flame, 120:7590, 2000.
58.
Haworth, D C, Blint, R J, Cuenot, B and Poinsot, T, “Numerical simulation of turbulent propaneair
combustion with nonhomogeneous reactants”, Combust Flame, 121, 395417, 2000.
59.
Overholt, M R and Pope, S B, “Direct numerical simulation of a statistically stationary, turbulent
reacting flow”,
Combust Theor Model, 3, 371408, 1999.
60.
Cuenot, B, Egofolfopolous, FN and Poinsot, T, “An unsteady flamelet model for nonpremixed
combustion”,
Combust Theory Model, 4, 7797, 2000.
61.
Kim, S.H., Huh, K.Y. and Fraser, R.A., "Numerical Prediction of the Autoignition Delay in a Diesellike
Environment by the Conditional Moment Closure Model," SAE2000010200.
62.
Kim, S. H., Huh, K. Y. and Fraser, R. A., "Modeling Autoignition of a Turbulent Methane Jet by the
Conditional Moment Closure Model,"
Proceedings of the Combustion Institute,
28, 185193, 2000.
63.
Cha, CM and Kosaly, G, “ Quasisteady modelling of turbulent nonpremixed combustion”,
Combust
Flame, 122, 400421, 2000.
64.
K.A.Weinman.and A.Y.Klimenko Estimation of the Kolmogorov constant (Co) for the Lagrangian
structure function using Direct Numerical Simulation for a continuous Scalar,
Physics of Fluids, to
appear
65.
Klimenko, A. Y. "On the Relation of the Conditional Moment Closure and Unsteady Flamelets",
Combust
Theory Model, 5, 275294, 2001
66.
Sreedhara, S. and Lakshmisha, K. N., "Direct Numerical Simulation of Autoignition in a Nonpremixed,
Turbulent Medium"
Proceedings of the Combustion Institute, 28, 2534, 2000.
67.
Brizuela, E. A., "Threedimensional Conditional Moment Closure Modeling of the BERL 300kW Burner",
Abstracts of WorkinProgress Poster Presentations, 28th International Symposium on Combustion,
The Combustion Institute, Pittsburgh, PA, p 334, 2000.
68.
4 of 5
Swaminathan, N. and Bilger R.W., "Scalar dissipation, diffusion and dilatation in turbulent H2air
premixed flames with complex chemistry",
Combustion Theory and Modelling, 5, 429446,2001.
69.
Swaminathan, N. and Bilger R.W., "Analyses of conditional moment closure for turbulent premixed
flames",
Combustion Theory and Modelling, 5, 241260, 2001
70.
Brown, R J and Sawford, B L, “Probability density function integrals and smallscale mixing in turbulent
plumes”,
BoundaryLayer Meteorol, 97, 219249, 2000.
71.
Coelho, P J and Peters, N, “ Unsteady modelling of a piloted methane/air jet flame based on the Eulerian
particle flamelet model”,
Combust Flame, 124, 444465, 2001.
72.
Brethouwer, G. and Nieuwstadt, F.T.M., "DNS of mixing and reaction of two species in a turbulent
channel flow: a validation of Conditional Moment Closure",
Flow, Turbulence and Combustion, 66, 209
239, 2001.
73.
Steiner, H. and Bushe, W K, “Large eddy simulation of a turbulent reacting jet with conditional source
term estimation”,
Phys Fluids, 13, 754769, 2001.
74.
Steiner, H. and Bushe, W K, “Large eddy simulation of a turbulent reacting jetflame”,
Z. Agnew Math
Mech, 81, S563S564, 2001.
75.
Cha, C.M., Kosaly, G and Pitsch, H., “ Modeling extinction and reignition in turbulent nonpremixed
combustion using a doublyconditional moment closure approach”,
Phys Fluids, 13, 38243834,
2001.
76.
Cleary, M J, Kent, J H and Bilger, R W, “Prediction of Carbon Monoxide in Fires by Conditional Moment
Closure”,
Proceedings of the Combustion Institute,
29, Part 1, 273279. 2002 .
77.
Kim, S.H., Huh, K Y and Bilger, R W, “Secondorder conditional moment closure modelling of local
extinction and reignition in turbulent nonpremixed hydrocarbon flames,
Proceedings of the Combustion
Institute,
29, Part 2, 21312137 ,2002.
78.
Pitsch, H, “Improved Pollutant Predictions in LargeEddy Simulation of Turbulent Nonpremixed
Combustion by Considering Scalar Dissipation Fluctuations”,
Proceedings of the Combustion Institute,
29, .
79.
Sreedhara, S. and Laksmisha, K.N., “Assessment of Conditional Moment Closure Models of Turbulent
Autoignition Using DNS Data”,
Proceedings of the Combustion Institute,
29, (to appear).
80.
Kim, W.T. and Huh, K.Y., “Numerical Simulation of Spray Autoignition by the FirstOrder Conditional
Moment Closure Model” ,
Proceedings of the Combustion Institute,
29, 569576.
81.
Bradley, D., Emerson, D.R., Gaskell, P.H. and Gu, X. J., “Mathematical Modelling of Turbulent
NonPremixed Piloted Jet Flames with Local Extinctions”,
Proceedings of the Combustion Institute,
29,
21552162 (2003).
82.
Karpetis, A.N. and Barlow R.S., “Measurements of Scalar Dissipation in a Turbulent Piloted Methane/Air
Jet Flame”,
Proceedings of the Combustion Institute,
29, 19261936 (2003).
83.
Cleary, M J, Kent, J H and Bilger, R W, “A computational method for combustion using conditional
moment closure”,
Computational Fluid Dynamics 2002, S Armfield, P Morgan and K Srinivas (Eds),
SpringerVerlag, 2003, pp 7176.
84.
Devaud, C. B., Kent, J H and Bilger, R W “Conditional Moment Closure Modelling of Lifted Diffusion
Flames”, Work in Progress Poster, 29th Symposium (International) on Combustion, Sapporo, Japan, July
2002 (submitted).
85.
Mueller, C. “Nonpremixed Turbulent Flame Modelling using an Elliptic Conditional Moment Closure
Approach” Work in Progress Poster, 29th Symposium (International) on Combustion, Sapporo, Japan,
July 2002 (submitted).
86.
Kim, S H and Huh, K Y, “Use of the Conditional Moment Closure Model to Predict NO formation in a
Turbulent CH4/H2 Flame over a Bluff Body”,
Combust. Flame,
130, 94111, 2002.
87.
Kim, S H, ‘On the conditional variance and covariance equations for secondorder conditional moment
closure”,
Phys Fluids, 14, 20112014, 2002.
88.
Devaud, C B , Kent J H and Bilger, R W, “Conditional moment closure applied to a lifted turbulent
methaneair flame”, Third Mediterranean Combustion Symposium, Marrakech, Morocco, 813 June,
2003.
89.
Devaud, C. B. and Bray, K. N. C. “Assessment of the applicability of conditional moment closure to a
lifted turbulent flame: first order model”,
Combust. Flame, 131, 102 114 (2003).
90.
Mobini, K and Bilger, R W, “Imperfectly Stirred Reactor Model of Reaction in a Burner with Strong
Recirculation”,
Combust Sci Technol, 174(1), 4570, 2004
91.
5 of 5
Cleary, M. J. and Kent, J.H., “A numerical method for conditional moment closure”,
2003 Australian
Combustion Symposium and 8th Australian Flame Days, Monash University, December 2003.
92.
Bilger, R W, “Some aspects of scalar dissipation”,
Flow, Turbul Combust,
72, 93114, 2004.93.
S. H Kim, K. Y. Huh, “Secondorder conditional moment closure modelling of turbulent piloted jet
diffusion flames”,
Combust. Flame, 336352 (2004).
94.
Kronenburg, A. “Double conditioning of reactive scalar transport equations in turbulent nonpremixed
flames”,
Phys. Fluids 16,2640 (2004).
95.
Devaud, C. B., Bilger, R. W. and Liu, T., “A new method of modelling the conditional scalar dissipation
rate”
Phys. Fluids 16, 20042011 (2004).
96.
Kronenburg, A. and Papoutsakis, A. E. “Conditional moment closure modelling of extinction and
reignition in turbulent nonpremixed flames”, Proc. Combust. Inst., 30 , 735742 (2005).
97.
Mortensen, M. “Consistent modelling of scalar mixing for presumed multiparameter probability
density functions”,
Phys. Fluids 17, 018106 (2005).
98.
Kim, S. H., Choi, C. H. and Huh, K. Y., “Secondorder conditional moment closure modelling of a turbulent
CH4/H2/N2 jet diffusion flame”,
Proc. Combust. Inst.
, 30, 735742 (2005).
99.
Kim, I.S. and Mastorakos, E. ‘Simulations of turbulent lifted flames with twodimensional conditional
moment closure”,
Proc. Combust. Inst.
, 30, 911918 (2005).
100.
Mortensen, M. “Implementation of a conditional moment closure for mixing sensitive reactions”,
Chem.
Eng. Sci., 59, 24, 57095723 (2004).
1.
Bilger, R. W. “Marker fields for turbulent premixed combustion”,
Combust. Flame
138, 188194, 20042.
deBruynKops, S. M. and Mortensen, M. “Conditional Mixing statistics in a selfsimilar scalar mixing
layer” Physics Fluids , 95107 (2005).
3.
Mortensen, M. and Andersson, B. “Presumed mapping functions for Eulerian modelling of turbulent
mixing”, Physics Fluids (submitted)
4.
Rogerson, J. Mann, A. and Bilger, R.W. “Application of conditional moment closure model to a
bagassefired boiler”, 5th AsiaPacific Conference on Combustion, The University of Adelaide,
Adelaide, Australia, 1720 July, 2005 (submitted)
5.
Wandel,A. P. and Klimenko, A.Y. “Testing MMC mixing for MonteCarlo simulations”, Physics Fluids
(submitted)
6.
Fairweather, M. and Woolley, R. M. “Firstorder conditional moment closure modelling of turbulent,
nonpremixed methane flames” Combust. Flame, 138, 319, 2004.
7.
Sawford, B. L. “Conditional scalar mixing statistics in homogeneous isotropic turbulence”, New J.
Physics, 6, 55, 2004.
8.
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