A numerical study of the diffusive-thermal instability of opposed nonpremixed tubular flames

Bak, Hyun Su; Lee, Su Ryong; Chen, Jacqueline H.; Yoo, Chun Sang

doi:10.1016/j.combustflame.2015.09.019

A numerical study of the diffusive-thermal instability of opposed nonpremixed tubular flames

Journal Article · Thu Oct 22 00:00:00 EDT 2015 · Combustion and Flame

DOI:https://doi.org/10.1016/j.combustflame.2015.09.019· OSTI ID:1497641

Bak, Hyun Su ^[1]; Lee, Su Ryong ^[2]; Chen, Jacqueline H. ^[3]; ^[4]

Ulsan National Inst. of Science and Technology (UNIST) (Korea, Republic of). Dept. of Mechanical Engineering
Seoul National Univ. of Science and Technology (Korea, Republic of). Dept. of Mechanical and Automotive Engineering
Sandia National Lab. (SNL-CA), Livermore, CA (United States). Combustion Research Facility
Ulsan National Inst. of Science and Technology (UNIST) (Korea, Republic of). Dept. of Mechanical Engineering. School of Mechanical and Nuclear Engineering

The diffusive-thermal (D-T) instability of opposed nonpremixed tubular flames near extinction is investigated here using two-dimensional (2-D) direct numerical simulations together with the linear stability analysis. Two different initial conditions (IC), i.e. the perturbed IC and the C-shaped IC are adopted to elucidate the effects of small and large amplitude disturbances on the formation of flame cells, similar to conditions found in linear stability analysis and experiments, respectively. The characteristics of the D-T instability of tubular flames are identified by a critical Damköhler number, Da_C, at which the D-T instability first occurs and the corresponding number of flame cells for three different tubular flames with different flame radii. It is found that Da_C predicted through linear stability analysis shows good agreement with that obtained from the 2-D simulations performed with two different ICs. The flame cell number, N_cell, from the 2-D simulations with the perturbed IC is also found to be equal to an integer close to the maximum wavenumber, k_max, obtained from the linear stability analysis. However, N_cell from the 2-D simulations with the C-shaped IC is smaller than k_max and N_cell found from the simulations with the perturbed IC. This is primarily because the strong reaction at the edges of the horseshoe-shaped cellular flame developed from the C-shaped IC is more likely to produce larger flame cells and reduce N_cell. It is also found that for cases with the C-shaped IC, once the cellular instability occurs, the number of flame cells remains constant until global extinction occurs by incomplete reaction manifested by small Da. It is also verified through the displacement speed, S_d, analysis that the two edges of the horseshoe-shaped cellular flame are stationary and therefore do not merge due to the diffusion–reaction balance at the edges. Moreover, large negative S_d is observed at the local extinction points while small positive or negative S_d features in the movement of flame cells as they adjust their location and size towards steady state.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Lab. (SNL-CA), Livermore, CA (United States); Ulsan National Inst. of Science and Technology (UNIST) (Korea, Republic of)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Research Foundation of Korea (NRF); Ministry of Science, ICT and Future Planning (MSIP) (Korea, Republic of)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1497641

Alternate ID(s):: OSTI ID: 1254880

Report Number(s):: SAND2015--10478J; 672293

Journal Information:: Combustion and Flame, Journal Name: Combustion and Flame Journal Issue: 12 Vol. 162; ISSN 0010-2180

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (35)

The asymptotic structure of counterflow diffusion flames for large activation energies Liñán, Amable Acta Astronautica, Vol. 1, Issue 7-8 https://doi.org/10.1016/0094-5765(74)90066-6	journal	July 1974
Several new numerical methods for compressible shear-layer simulations Kennedy, Christopher A.; Carpenter, Mark H. Applied Numerical Mathematics, Vol. 14, Issue 4 https://doi.org/10.1016/0168-9274(94)00004-2	journal	June 1994
Edge-flames and sublimit hydrogen combustion Short, M.; Buckmaster, J.; Kochevets, S. Combustion and Flame, Vol. 125, Issue 1-2 https://doi.org/10.1016/S0010-2180(00)00246-7	journal	April 2001
Structure and Propagation of Methanol–Air Triple Flames Echekki, Tarek; Chen, Jacqueline H. Combustion and Flame, Vol. 114, Issue 1-2 https://doi.org/10.1016/S0010-2180(97)00287-3	journal	July 1998
Structure and propagation of triple flames in partially premixed hydrogen–air mixtures Im, H. G.; Chen, J. H. Combustion and Flame, Vol. 119, Issue 4 https://doi.org/10.1016/S0010-2180(99)00073-5	journal	December 1999
Diffusive-thermal instability and flame extinction in nonpremixed combustion Chen, Ruey-Hung; Mitchell, G. Bradley; Ronney, Paul D. Symposium (International) on Combustion, Vol. 24, Issue 1 https://doi.org/10.1016/S0082-0784(06)80030-5	journal	January 1992
Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations Kennedy, Christopher A.; Carpenter, Mark H.; Lewis, R. Michael Applied Numerical Mathematics, Vol. 35, Issue 3 https://doi.org/10.1016/S0168-9274(99)00141-5	journal	November 2000
Structure, aerodynamics, and geometry of premixed flamelets Law, C. K.; Sung, C. J. Progress in Energy and Combustion Science, Vol. 26, Issue 4-6 https://doi.org/10.1016/S0360-1285(00)00018-6	journal	August 2000
Edge-flames Buckmaster, J. Progress in Energy and Combustion Science, Vol. 28, Issue 5 https://doi.org/10.1016/S0360-1285(02)00008-4	journal	January 2002
Stretch rate of tubular premixed flames Wang, Peiyong; Wehrmeyer, Joseph A.; Pitz, Robert W. Combustion and Flame, Vol. 145, Issue 1-2 https://doi.org/10.1016/j.combustflame.2005.09.015	journal	April 2006
A numerical study of transient ignition and flame characteristics of diluted hydrogen versus heated air in counterflow Yoo, Chun Sang; Chen, Jacqueline H.; Frank, Jonathan H. Combustion and Flame, Vol. 156, Issue 1 https://doi.org/10.1016/j.combustflame.2008.07.012	journal	January 2009
Structural study of non-premixed tubular hydrocarbon flames Hu, Shengteng; Pitz, Robert W. Combustion and Flame, Vol. 156, Issue 1 https://doi.org/10.1016/j.combustflame.2008.07.017	journal	January 2009
Extinction and near-extinction instability of non-premixed tubular flames Hu, Shengteng; Pitz, Robert W.; Wang, Yu Combustion and Flame, Vol. 156, Issue 1 https://doi.org/10.1016/j.combustflame.2008.09.004	journal	January 2009
Diffusive-thermal instability of premixed tubular flames Kurdyumov, Vadim N. Combustion and Flame, Vol. 158, Issue 9 https://doi.org/10.1016/j.combustflame.2011.01.012	journal	September 2011
The effect of stretch on cellular formation in non-premixed opposed-flow tubular flames Shopoff, S. W.; Wang, P.; Pitz, R. W. Combustion and Flame, Vol. 158, Issue 5 https://doi.org/10.1016/j.combustflame.2011.01.016	journal	May 2011
Direct numerical simulations of ignition of a lean n-heptane/air mixture with temperature inhomogeneities at constant volume: Parametric study Yoo, Chun Sang; Lu, Tianfeng; Chen, Jacqueline H. Combustion and Flame, Vol. 158, Issue 9 https://doi.org/10.1016/j.combustflame.2011.01.025	journal	September 2011
Experimental study of cellular instability and extinction of non-premixed opposed-flow tubular flames Shopoff, S. W.; Wang, P.; Pitz, R. W. Combustion and Flame, Vol. 158, Issue 11 https://doi.org/10.1016/j.combustflame.2011.04.007	journal	November 2011
Direct numerical simulations of the ignition of lean primary reference fuel/air mixtures with temperature inhomogeneities Luong, Minh Bau; Luo, Zhaoyu; Lu, Tianfeng Combustion and Flame, Vol. 160, Issue 10 https://doi.org/10.1016/j.combustflame.2013.04.012	journal	October 2013
Quantitative atomic hydrogen measurements in premixed hydrogen tubular flames Hall, Carl A.; Kulatilaka, Waruna D.; Gord, James R. Combustion and Flame, Vol. 161, Issue 11 https://doi.org/10.1016/j.combustflame.2014.05.015	journal	November 2014
A DNS study of the ignition of lean PRF/air mixtures with temperature inhomogeneities under high pressure and intermediate temperature Kim, Seung Ook; Luong, Minh Bau; Chen, Jacqueline H. Combustion and Flame, Vol. 162, Issue 3 https://doi.org/10.1016/j.combustflame.2014.09.001	journal	March 2015
Dynamics of bluff-body-stabilized premixed hydrogen/air flames in a narrow channel Lee, Bok Jik; Yoo, Chun Sang; Im, Hong G. Combustion and Flame, Vol. 162, Issue 6 https://doi.org/10.1016/j.combustflame.2015.03.009	journal	June 2015
Tubular premixed and diffusion flames: Effect of stretch and curvature Pitz, Robert W.; Hu, Shengteng; Wang, Peiyong Progress in Energy and Combustion Science, Vol. 42 https://doi.org/10.1016/j.pecs.2014.01.003	journal	June 2014
Numerical investigation of the curvature effects on diffusion flames Wang, Peiyong; Hu, Shengteng; Pitz, Robert W. Proceedings of the Combustion Institute, Vol. 31, Issue 1 https://doi.org/10.1016/j.proci.2006.07.223	journal	January 2007
Flame dynamics Matalon, Moshe Proceedings of the Combustion Institute, Vol. 32, Issue 1 https://doi.org/10.1016/j.proci.2008.08.002	journal	January 2009
A DNS study on the stabilization mechanism of a turbulent lifted ethylene jet flame in highly-heated coflow Yoo, Chun Sang; Richardson, Edward S.; Sankaran, Ramanan Proceedings of the Combustion Institute, Vol. 33, Issue 1 https://doi.org/10.1016/j.proci.2010.06.147	journal	January 2011
A DNS study of ignition characteristics of a lean iso-octane/air mixture under HCCI and SACI conditions Yoo, Chun Sang; Luo, Zhaoyu; Lu, Tianfeng Proceedings of the Combustion Institute, Vol. 34, Issue 2 https://doi.org/10.1016/j.proci.2012.05.019	journal	January 2013
Minor-species structure of premixed cellular tubular flames Hall, Carl A.; Kulatilaka, Waruna D.; Jiang, Naibo Proceedings of the Combustion Institute, Vol. 35, Issue 1 https://doi.org/10.1016/j.proci.2014.05.108	journal	January 2015
A DNS study of self-accelerating cylindrical hydrogen–air flames with detailed chemistry Xin, Y. X.; Yoo, C. S.; Chen, J. H. Proceedings of the Combustion Institute, Vol. 35, Issue 1 https://doi.org/10.1016/j.proci.2014.06.076	journal	January 2015
Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: flame stabilization and structure Yoo, C. S.; Sankaran, R.; Chen, J. H. Journal of Fluid Mechanics, Vol. 640 https://doi.org/10.1017/S0022112009991388	journal	December 2009
The effect of thermal expansion on diffusion flame instabilities Matalon, M.; Metzener, P. Journal of Fluid Mechanics, Vol. 647 https://doi.org/10.1017/S0022112009993016	journal	March 2010
Fine Structure of Scalar Fields Mixed by Turbulence. I. Zero-Gradient Points and Minimal Gradient Surfaces Gibson, Carl H. Physics of Fluids, Vol. 11, Issue 11 https://doi.org/10.1063/1.1691820	journal	January 1968
Diffusive-thermal instabilities of diffusion flames: onset of cells and oscillations Metzener, Philippe; Matalon, Moshe Combustion Theory and Modelling, Vol. 10, Issue 4 https://doi.org/10.1080/13647830600719894	journal	August 2006
Linear analysis of diffusional-thermal instability in diffusion flames with Lewis numbers close to unity Kim, J. S. Combustion Theory and Modelling, Vol. 1, Issue 1 https://doi.org/10.1080/713665228	journal	January 1997
Diffusional-thermal instability in strained diffusion flames with unequal Lewis numbers Kim, J. S.; Lee, S. R. Combustion Theory and Modelling, Vol. 3, Issue 1 https://doi.org/10.1088/1364-7830/3/1/007	journal	March 1999
Cellular instabilities, sublimit structures and edge-flames in premixed counterflows Buckmaster, John D.; Short, Mark Combustion Theory and Modelling, Vol. 3, Issue 1 https://doi.org/10.1088/1364-7830/3/1/011	journal	March 1999

Cited By (1)

Numerical investigation of non-premixed and premixed rotational tubular flame: a study of flame structure and instability Bordbar, Mehdi; Motaghian, Shahrooz; Pasdarshahri, Hadi Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 42, Issue 1 https://doi.org/10.1007/s40430-019-2134-8	journal	December 2019

Similar Records

Extinction and near-extinction instability of non-premixed tubular flames

Journal Article · Wed Jan 14 23:00:00 EST 2009 · Combustion and Flame · OSTI ID:21227377

Scaling of cell size in cellular instabilities of nonpremixed jet flames

Journal Article · Mon Oct 15 00:00:00 EDT 2007 · Combustion and Flame · OSTI ID:20961973

Steady periodic structure of a flame with a finite cell amplitude

Journal Article · Tue Sep 01 00:00:00 EDT 1987 · Combust., Explos. Shock Waves (Engl. Transl.); (United States) · OSTI ID:6960716

Related Subjects

42 ENGINEERING
diffusive-thermal instability
displacement speed
hydrogen
linear stability analysis
nonpremixed tubular flame

A numerical study of the diffusive-thermal instability of opposed nonpremixed tubular flames

Citation Formats

References (35)

Cited By (1)

Similar Records

Related Subjects