Effect of Low Temporal Resolution on the Uncertainty of Resolving Flame Speed of Moving Flames

Dong Hyuk Shin

doi:10.15231/jksc.2020.25.4.037

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2020 Vol.25, Issue 4 Preview Page Next Page

Research Article

Effect of Low Temporal Resolution on the Uncertainty of Resolving Flame Speed of Moving Flames 저시간 분해능으로 인한 화염 속도 분석의 불확실성

31 December 2020. pp. 37-46

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Abstract

This paper analyzes the effect of low temporal resolution on the accuracy of determining the local flame speed for experimental measurements and simulations. Flame speed measurement of moving flames requires the evaluation of a temporal derivative of flame front motion. Measurements have limited temporal resolution, which can lead to a bias error in the calculation of flame speed. The error associated with the temporal resolution was derived in the leading order effect on sampling time. In order to demonstrate the error term, we employed numerical examples. Artificial flame solutions are generated by solving the G-equation with prescribed flow fields and fine spatial/temporal resolutions. By varying the sampling time step, we demonstrated the error can lead to negative values of the measured flame speed. Furthermore, when coarse sampling time steps are used, the calculated flame speed also exhibits a spurious curvature dependency. Lastly, the associated error can be estimated by spatial gradients of the flame front for convection dominated flows.

Keywords

Flame speed

Temporal resolution

Negative flame speed

References

J.F. Driscoll, Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities, Prog. Energy Combust. Sci., 34 (2008) 91-134. 10.1016/j.pecs.2007.04.002

I.B. Zeldovich, G.I. Barenblatt, V.B. Librovich, G.M. Makhviladze, Mathematical theory of combustion and explosions, Plenum Press, New York, 1985. 10.1007/978-1-4613-2349-5

D.G. Goodwin, H.K. Moffat, R.L. Speth, Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes, Caltech Pasadena CA, 2009.

R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-Ⅱ: A Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics, Sandia National Labs., Livermore, CA(USA), 1989. 10.2172/5681118PMC2448549

J.H. Chen, H.G. Im, Correlation of flame speed with stretch in turbulent premixed methane/air flames, Symp. Int. Combust., 27 (1998) 819-826. 10.1016/S0082-0784(98)80477-3

J.H. Chen, H.G. Im, Stretch effects on the burning velocity of turbulent premixed hydrogen/air flames, Proc. Combust. Inst., 28 (2000) 211-218. 10.1016/S0082-0784(00)80213-1

E.R. Hawkes, J.H. Chen, Comparison of direct numerical simulation of lean premixed methane-air flames with strained laminar flame calculations, Combust. Flame, 144 (2006) 112-125. 10.1016/j.combustflame.2005.07.002

G. Hartung, J. Hult, R. Balachandran, M. R. Mackley, C. F. Kaminski, Flame front tracking in turbulent lean premixed flames using stereo PIV and time- sequenced planar LIF of OH, Appl. Phys. B, 96 (2009) 843-862. 10.1007/s00340-009-3647-0

L.J. Humphrey, B. Emerson, T.C. Lieuwen, Premixed turbulent flame speed in an oscillating disturbance field, J. Fluid Mech., 835 (2018) 102-130. 10.1017/jfm.2017.728

P.J. Trunk, I. Boxx, C. Heeger, W. Meier, B. Bohm, A. Dreizler, Premixed flame propagation in turbulent flow by means of stereoscopic PIV and dual-plane OH-PLIF at sustained kHz repetition rates, Proc. Combust. Inst., 34 (2013) 3565-3572. 10.1016/j.proci.2012.06.025

J. Kerl, C. Lawn, F. Beyrau, Three-dimensional flame displacement speed and flame front curvature measurements using quad-plane PIV, Combust. Flame, 160 (2013) 2757-2769. 10.1016/j.combustflame.2013.07.002

J.R. Osborne, S.A. Ramji, C.D. Carter, A.M. Steinberg, Relationship between local reaction rate and flame structure in turbulent premixed flames from simultaneous 10 kHz TPIV, OH PLIF, and CH2O PLIF, Proc. Combust. Inst., 36 (2017) 1835-1841. 10.1016/j.proci.2016.07.124

B. Peterson, E. Baum, B. Bohm, A. Dreizler, Early flame propagation in a spark-ignition engine measured with quasi 4D-diagnostics, Proc. Combust. Inst., 35 (2015) 3829-3837. 10.1016/j.proci.2014.05.131

B. Peterson, E. Baum, A. Dreizler, B. Bohm, An experimental study of the detailed flame transport in a SI engine using simultaneous dual-plane OH-LIF and stereoscopic PIV, Combust. Flame, 202 (2019) 16-32. 10.1016/j.combustflame.2018.12.024

N. Chakraborty, Comparison of displacement speed statistics of turbulent premixed flames in the regimes representing combustion in corrugated flamelets and thin reaction zones, Phys. Fluids, 19 (2007) 105109. 10.1063/1.2784947

I.R. Gran, T. Echekki, J.H. Chen, Negative flame speed in an unsteady 2-D premixed flame: A computational study, Symp. Int. Combust., 26 (1996) 323-329. 10.1016/S0082-0784(96)80232-3

Y.-C. Chen, R.W. Bilger, Experimental investigation of three-dimensional flame-front structure in premixed turbulent combustion-I: hydrocarbon/air bunsen flames, Combust. Flame, 131 (2002) 400-435. 10.1016/S0010-2180(02)00418-2

N. Peters, Turbulent Combustion, Cambridge University Press, Cambridge, 2000. 10.1017/CBO9780511612701

F.A. Williams, Combustion Theory, CRC Press, Florida, 1985.

G. Jiang, D. Peng, Weighted ENO Schemes for Hamilton-Jacobi Equations, SIAM J. Sci. Comput., 21 (2000) 2126-2143. 10.1137/S106482759732455X

S. Gottlieb, C.-W. Shu, Total variation diminishing Runge-Kutta schemes, Math. Comput. Am. Math. Soc., 67 (1998) 73-85. 10.1090/S0025-5718-98-00913-2

Information

Publisher :The Korean Society Combustion
Publisher(Ko) :한국연소학회
Journal Title :Journal of The Korean Society Combustion
Journal Title(Ko) :한국연소학회지
Volume : 25
No :4
Pages :37-46
Received Date : 2020-10-19
Revised Date : 2020-10-25
Accepted Date : 2020-12-12
DOI :https://doi.org/10.15231/jksc.2020.25.4.037

Journal of The Korean Society Combustion ISSN:1226-0959(Print) 2466-2089(Online) 한국연소학회지

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