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.327-334 (1990).

1.

Bilger, R.W., "Conditional Moment Closure for Turbulent Reacting Flow",

Phys Fluids A, 5 (2), 1993,

436-444.

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),

Springer-Verlag, Berlin Heidelberg, 1992, pp 3-16.

3.

Smith, N.S., Chen, J-Y. and Bilger, R.W., "Modelling of Nonpremixed Hydrogen Jet Flames Using a

Conditional Moment Method",

Twenty-fourth Symposium (International) on Combustion, The

Combustion Institute, 263-269, 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

267-285, 1993.

5.

A.Y.Klimenko, "Conditional moment closure and fluctuations of scalar dissipation",

Fluid Dynamics,

28, 630-637, (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, 3255-64, 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, 179-186, 1993.

8.

Montgomery, C.J., Kosaly, G. and Riley, J.J., "Direct Numerical Simulation of Turbulent Reacting Flow

Using a Reduced Hydrogen-Oxygen Mechanism",

Combust. Flame, 95: 247-260, 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, 6:1331-1356, 1994.

10.

Smith, N.S.A., Bilger, R.W., Carter, C.D., Barlow, R.S. and Chen, J-Y., "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, 357-375, 1995.

11.

Li, J.D. and Bilger, R.W., "A Simple Theory for the Conditional Mean Velocity in a Turbulent

Scalar-Mixing Layer",

Physics Fluids, 6, 605-610, 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, 173-197, 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, 775-783, 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, 1665-1673, 1995.

15.

A.Y.Klimenko, "Note on the conditional moment closure in turbulent shear flows",

Physics of Fluids, 7,

446-448, (1995)

16.

Lee, Y.Y. and Pope, S.B., "Nonpremixed Turbulent Reacting Flow Near Extinction",

Combust. Flame, 101,

501-528, 1995.

17.

Barlow, RS and Carter C D, “ Relationships among nitric oxide, temperature and mixture fraction in

hydrogen jet flames”,

Combust Flame, 104, 288-299, 1996.

18.

Desjardin, P E and Frankel, SH, “Assessment of turbulent combustion submodels using the linear eddy

model,

Combust Flame, 104, 343-357, 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, 393-417, 1995.

21.

Klimenko, A.Yu., Bilger, R.W. and Roomina, M.R., "Some PDF Integrals for Self-Similar Turbulent Flows",

Combustion Sci. and Technology, 107, 403-410, 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, 25-29, (1995)

23.

Brown, R.J. and Bilger, R.W., "Measurement and Modelling of Non-buoyant turbulent reacting plumes",

Twelfth Australasian Fluid Mechanics Conference, The University of Sydney, 621-624, 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, 625-628, 1995.

25.

Swaminathan, N and Mahalingham, S, “ Assessment of conditional moment closure for single and

multistep chemistry” Combust Sci Technol, 112, 301-326, 1996.

26.

Kronenburg, A. and Bilger, R.W., "Modelling of Differential Diffusion Effects in Nonpremixed

Nonreacting Flow",

Phys Fluids, 9, 1435-1447, 1997.

27.

O’Young, F. and Bilger, R.W., "Scalar Gradient and Related Quantities in Turbulent Premixed Flames",

Combustion and Flame, 109, 682-700, 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 Air-Diluted 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 Asia-Pacific Conference on Combustion, Osaka University, Japan, May 1997

pp 174-177.

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 263-275, 1997.

31.

Swaminathan, N. and Bilger, R.W., "Direct Numerical Simulation of Turbulent Nonpremixed Hydrocarbon

Flames Using a Two-step 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, 2621-2635, 1998.

33.

A.Y.Klimenko, "Conditional methods in application for Lagrangian modeling".

Phys.Fluids. 10, No 4,

922-927, 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, 2424-2426, 1998.

35.

Swaminathan, N. and Bilger, R.W., "Assessment of Combustion Sub-models for Turbulent Nonpremixed

Hydrocarbon Flames",

Combustion and Flame, 116, 519-545, 1999.

36.

Klimenko, A.Yu. and Bilger, R.W., "Conditional Moment Closure for Turbulent Combustion",

Progr.

Energy Combustion Sci., 25, 595-687, 1999.

37.

Barlow, R.S., Smith, N.S.A., Chen, J-Y., and Bilger, R.W., “Nitric Oxide Formation in Dilute Hydrogen Jet

Flames: Isolation of the Effects of Radiation and Turbulence-Chemistry Submodels”,

Combustion and

Flame, 117, 4-31,1999

38.

Nilsen, V and Kosaly, G, “Differential diffusion in turbulent reacting flows”, Combust Flame, 117,

493-513, 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, 145-159, 2000.

40.

Kronenburg, A., Bilger, R.W. and Kent, J.H., “Second Order Conditional Moment Closure for Turbulent Jet

Diffusion Flames”,

Twenty-seventh Symposium (International) on Combustion, The Combustion

Institute, Pittsburgh, PA ,1097-1104, 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., “Second-order conditional moment closure for the auto-ignition of

turbulent flows”,

Physics of Fluids, 10, 1246-8,1998.

43.

Gough, A.J., Mobini, K., Chen, Y.-C. and Bilger, R.W., “Measurements and predictions in a confined44.

3 of 5

bluff-body burner modelled as an imperfectly stirred reactor”,

Twenty-seventh Symposium

(International) on Combustion, The Combustion Institute, Pittsburgh, PA , 3181-3188, 1998.

Swaminathan, N. and Bilger R.W., “Conditional variance equation and its analysis”,

Twenty-seventh

Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1191-1198,

1998.

45.

Kronenburg, A. and Bilger, R.W., “Modelling differential diffusion in nonpremixed reacting turbulent

flow: model development",

Combustion Sci. Technol. , 166, 195-227, 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, 175-194, 2001.

47.

Kronenburg, A., Bilger, R.W. and Kent, J.H., “Modelling soot formation in turbulent methane-air 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, 1896-1906, 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, 689-708, 1999.

50.

Roomina, M.R. and Bilger, R.W.,” Conditional Moment Closure (CMC) Predictions of a Turbulent

Methane-Air Jet Flame”,

Combustion and Flame, 125, 1176-1195, 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

, 2679-2695, 1999.

52.

Bilger, R.W., “Recent progress in CMC methods for the prediction of pollutant species in non-premixed

combustion”,

5th International Conference on Technologies and Combustion for a Clean Environment,

Lisbon, Portugal, pp 167-176, July 1999.

53.

Kim, S. H., Huh, K. Y. and Liu, T., "Implementation of the Conditional Moment Closure Model to a

Turbulent Nonpremixed H2/CO-Air Stabilized on a Bluff-Body Flame,"

Transactions of the Canadian

Society of Mechanical Engineers,

23, No.3&4, pp.425-434, 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.76-80 (1999)

55.

Bushe, W. K., Bilger, R. W. and Ruetsch, G. R., “Direct numerical simulation of turbulent non-premixed

combustion with realistic chemistry”,

J. Fluid Mech., (submitted).

56.

Bilger, R.W., "Future progress in turbulent combustion research",

Progr. Energy Combust. Sci., 26,

367-380, 2000.

57.

Kim, S.H., Tao, L. and Huh, K.Y., "Application of the Elliptic Conditional Moment Closure Model to a

Two-dimensional Nonpremixed Methanol Bluff-Body Flame",

Combust. Flame, 120:75-90, 2000.

58.

Haworth, D C, Blint, R J, Cuenot, B and Poinsot, T, “Numerical simulation of turbulent propane-air

combustion with nonhomogeneous reactants”, Combust Flame, 121, 395-417, 2000.

59.

Overholt, M R and Pope, S B, “Direct numerical simulation of a statistically stationary, turbulent

reacting flow”,

Combust Theor Model, 3, 371-408, 1999.

60.

Cuenot, B, Egofolfopolous, FN and Poinsot, T, “An unsteady flamelet model for non-premixed

combustion”,

Combust Theory Model, 4, 77-97, 2000.

61.

Kim, S.H., Huh, K.Y. and Fraser, R.A., "Numerical Prediction of the Autoignition Delay in a Diesel-like

Environment by the Conditional Moment Closure Model," SAE2000-01-0200.

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, 185-193, 2000.

63.

Cha, CM and Kosaly, G, “ Quasi-steady modelling of turbulent nonpremixed combustion”,

Combust

Flame, 122, 400-421, 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, 275-294, 2001

66.

Sreedhara, S. and Lakshmisha, K. N., "Direct Numerical Simulation of Autoignition in a Nonpremixed,

Turbulent Medium"

Proceedings of the Combustion Institute, 28, 25-34, 2000.

67.

Brizuela, E. A., "Three-dimensional Conditional Moment Closure Modeling of the BERL 300kW Burner",

Abstracts of Work-in-Progress 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 H2-air

premixed flames with complex chemistry",

Combustion Theory and Modelling, 5, 429-446,2001.

69.

Swaminathan, N. and Bilger R.W., "Analyses of conditional moment closure for turbulent premixed

flames",

Combustion Theory and Modelling, 5, 241-260, 2001

70.

Brown, R J and Sawford, B L, “Probability density function integrals and small-scale mixing in turbulent

plumes”,

Boundary-Layer Meteorol, 97, 219-249, 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, 444-465, 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, 754-769, 2001.

74.

Steiner, H. and Bushe, W K, “Large eddy simulation of a turbulent reacting jet-flame”,

Z. Agnew Math

Mech, 81, S563-S564, 2001.

75.

Cha, C.M., Kosaly, G and Pitsch, H., “ Modeling extinction and reignition in turbulent non-premixed

combustion using a doubly-conditional moment closure approach”,

Phys Fluids, 13, 3824-3834,

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, 273-279. 2002 .

77.

Kim, S.H., Huh, K Y and Bilger, R W, “Second-order conditional moment closure modelling of local

extinction and reignition in turbulent nonpremixed hydrocarbon flames,

Proceedings of the Combustion

Institute,

29, Part 2, 2131-2137 ,2002.

78.

Pitsch, H, “Improved Pollutant Predictions in Large-Eddy 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

Auto-ignition 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 First-Order Conditional

Moment Closure Model” ,

Proceedings of the Combustion Institute,

29, 569-576.

81.

Bradley, D., Emerson, D.R., Gaskell, P.H. and Gu, X. J., “Mathematical Modelling of Turbulent

Non-Premixed Piloted Jet Flames with Local Extinctions”,

Proceedings of the Combustion Institute,

29,

2155-2162 (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, 1926-1936 (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),

Springer-Verlag, 2003, pp 71-76.

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, 94-111, 2002.

87.

Kim, S H, ‘On the conditional variance and covariance equations for second-order conditional moment

closure”,

Phys Fluids, 14, 2011-2014, 2002.

88.

Devaud, C B , Kent J H and Bilger, R W, “Conditional moment closure applied to a lifted turbulent

methane-air flame”, Third Mediterranean Combustion Symposium, Marrakech, Morocco, 8-13 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), 45-70, 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, 93-114, 2004.93.

S. H Kim, K. Y. Huh, “Second-order conditional moment closure modelling of turbulent piloted jet

diffusion flames”,

Combust. Flame, 336-352 (2004).

94.

Kronenburg, A. “Double conditioning of reactive scalar transport equations in turbulent non-premixed

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, 2004-2011 (2004).

96.

Kronenburg, A. and Papoutsakis, A. E. “Conditional moment closure modelling of extinction and

reignition in turbulent non-premixed flames”, Proc. Combust. Inst., 30 , 735-742 (2005).

97.

Mortensen, M. “Consistent modelling of scalar mixing for presumed multi-parameter probability

density functions”,

Phys. Fluids 17, 018106 (2005).

98.

Kim, S. H., Choi, C. H. and Huh, K. Y., “Second-order conditional moment closure modelling of a turbulent

CH4/H2/N2 jet diffusion flame”,

Proc. Combust. Inst.

, 30, 735-742 (2005).

99.

Kim, I.S. and Mastorakos, E. ‘Simulations of turbulent lifted flames with two-dimensional conditional

moment closure”,

Proc. Combust. Inst.

, 30, 911-918 (2005).

100.

Mortensen, M. “Implementation of a conditional moment closure for mixing sensitive reactions”,

Chem.

Eng. Sci., 59, 24, 5709-5723 (2004).

1.

Bilger, R. W. “Marker fields for turbulent premixed combustion”,

Combust. Flame

138, 188-194, 20042.

deBruynKops, S. M. and Mortensen, M. “Conditional Mixing statistics in a self-similar scalar mixing

layer” Physics Fluids , 95-107 (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

bagasse-fired boiler”, 5th Asia-Pacific Conference on Combustion, The University of Adelaide,

Adelaide, Australia, 17-20 July, 2005 (submitted)

5.

Wandel,A. P. and Klimenko, A.Y. “Testing MMC mixing for Monte-Carlo simulations”, Physics Fluids

(submitted)

6.

Fairweather, M. and Woolley, R. M. “First-order conditional moment closure modelling of turbulent,

nonpremixed methane flames” Combust. Flame, 138, 3-19, 2004.

7.

Sawford, B. L. “Conditional scalar mixing statistics in homogeneous isotropic turbulence”, New J.

Physics, 6, 55, 2004.

8.

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