在2012年，普林斯頓大學Law之研究團隊(Chaudhri et al.)首度提出一向外傳
播預混紊流球狀火焰具有自我相似之傳播特性，他們發現正規化紊流火焰傳播速率[(1/SbL)d<R>/dt]與一火焰紊流雷諾數(ReT,flame = u'<R>/DT < 2,500)呈現1/2冪次之自我相似傳播關係，其中SbL為未作密度校正之層流燃燒速率(生成物SL)，<R>為平均紊焰半徑，t為時間，u'為方均根紊流擾動速度，以及DT為熱擴散係數。我們特別用下標flame來清楚顯示ReT,flame與一般所認知之流場紊流雷諾數ReT,flow = u'LI/相當地不同，其中LI為積分長度尺度，而則為為運動黏滯係數。值得一提的是，Law團隊所量測紊流火焰速率(d<R>/dt)之方法，與傳統量測紊流火焰速率(SF)有所異同，相同之處為兩者均需先量測<R>與t之函數關係，並取中段<R>vs. t之資料作分析，以避開前段引燃和後段容器尺寸限制之影響；不同之處僅在傳統SF = <R>/t，是以線性耦合中段<R> vs. t之資料，而d<R>/dt是將中段所有<R>值對t作微分。事實上，由Law團隊和本實驗室所獲得之資料，均顯示d<R>/dt會隨t之增加而近似線性增加，故SF可看作d<R>/dt對時間之平均值。本研究主要回答下列兩大問題:(1)若使用SF數據，d<R>/dt與ReT,flame之自我相似傳播特性是否仍存在?(2)若是，此自我相似傳播特性是否仍適用於ReT,flame遠大於2,500?
為釐清前述之問題，本論文採用本實驗室已建立之大型高壓雙腔體設計之十字形預混紊流燃燒設備，其可產生可控制之近似等向性紊流並使燃燒實驗可在固定系統壓力條件下進行，實驗使用與Law團隊相同之當量比 = 0.9的甲烷/空氣燃氣，進行一系列不同固定系統壓力(p = 0.1 ~ 0.5 MPa)及不同u'值(u' = 1.43 ~ 5.60m/s)之燃燒實驗，使用Schlieren光學技術(100 × 100 mm2)和直接火焰拍攝法(170 × 170 mm2)，以擷取平均球狀紊焰半徑隨時間變化之資料，即找到<R>(t)。實驗結果顯示，在不同p及u'下，對ReT,flame關係之數據不僅仍具有自我相似傳播特性，且本研究所量得之(1/SbL)d<R>/dt資料與Law團隊之資料有高度重合性，我們並找到前述球狀紊焰之自我相似傳播特性於ReT,flame高達10,000時，仍存在之証據。此研究結果對預混紊流燃燒領域有重要之貢獻。

In 2012, Law and his co-workers at Princeton university (Chaudhri et al.) found that a constant-pressure, unity Lewis number expanding turbulent premixed flame has the self-similar propagation, in which the normalized turbulent flame speed [(1/SbL)d<R>/dt] as a function of the average flame radius (<R>) scales as a flame turbulent Reynolds number (ReT,flame = u'<R>/DT < 2,500) to the one-half power.
is laminar burning velocity before density correlation, and the superscript b indicates the burnt side, t is time, u' is the r.m.s. turbulent fluctuation velocity, and DT is the
thermal diffusivity. Here the subscript flame is used to clearly distinguish ReT,flame from the fenerally-used flow turbulent Reynolds number (ReT,flow = u'LI/ , where LI
is the integral length scale of turbulence and  is the kinematic viscosity of reactants. It is worthy of noting that there are similarity and difference on the determination of turbulent flame speed between d<R>/dt and SF (the tradition method). The similarity is that both methods need to measure <R> as a function of t first, and then analyze some middle part of <R> vs. t data in order to avoid the influence of ignition in the beginning of flame growth and circumvent the influence of the chamber walls in the latter flame propagation. The only one difference is that SF = <R>/t which is the slope of the traditional method uses the linear fitting to obtain middle part of <R> vs. t data and thus SF if an average turbulent flame speed, while d<R>/dt is to differentiate all available data within the middle part of <R> vs. t data that increases nearly linearly with time. Actually, SF can be viewed as the average value of d<R>/dt within the same time period of <R> vs. t data. We aim to address two key questions: (1)what happen if SF data are applied to replace d<R>/dt and whether does the self-similar propagation still exist?(2)Can aforesaid self-similar propagation, [(1/SbL)d<R>/dt] ~ ReT,flame 0.5, be valid for ReT,flame 2,500?
In order to address the aforesaid questions, a series of lean methane/air mixtures, experiments at the equivalence ratio  = 0.9 and carried out in the large high-pressure,
dual-chamber turbulent premixed combustion facility which can produce controllable near-isotropic turbulence with u' varying from 1.43 m/s to 5.60 m/s at constant vessel
pressure conditions varying from 1atm to 5atm. Both the Schlieren optical imaging a view field of 100mm × 100mm and the direct flame imaging with a large view field of 170mm × 170mm are applied to measure the average flame radius as a function of time, that is <R>(t). Each of <R> data is ensemble averaged from six identical runs. Results show that at different p and u', the data of scale as ReT,flame
0.5, which is the same as that of (1/SbL)d<R>/dt, both showing self-similar propagation. Most importantly, such self-similar propagation is fund to be varied even at much higher values of ReT,flame up to 10,000.

[1]經濟部能源局，“中華民國100年能源統計手冊”，2011。
[2]陳幸中，“高壓預混甲烷燃燒：層焰與紊焰傳播速度量測”，國立中央大學機械工程研究所，碩士論文，2009年。
[3]彭明偉，“中央引燃往外傳播預混火焰在高壓條件下之層流和紊流燃燒速度量測”，國立中央大學機械工程研究所，碩士論文，2010年。
[4]林文基，“甲烷與丙烷預混紊流燃燒速度量測”，國立中央大學機械工程研究所，碩士論文，1999年。
[5]黃朝祺，“貧油甲烷預混紊流燃燒最小引燃能量定量量測”，國立中央大學機械工程研究所，碩士論文，2006年。
[6]許耀文，“高壓預混紊流燃燒最小引燃能量量測”，國立中央大學機械工程研究所，碩士論文，2012年。
[7]Chaudhuri, S., Wu, F., Zhu, D. and Law, C. K., “Flame Speed and Self-Similar Propagation of Expanding Turbulent Premixed Flames” Phys. Rev. Lett. 108, 044503 (2012).
[8]Huang, C. C., Shy, S. S., Liu, C. C., Yan, Y. Y., “A Transition on Minimum Ignition Energy for Lean Turbulent Methane Combustion in Flamelet and Distributed Regimes,” Proc. Combust. Inst. 31, 1401-1409 (2007).
[9]Damköhler, G., “The Effect of Turbulent on the Flame Velocity in Gas Mixtures”, Z. Elektrchem. 46, 601-652 (1940). (English translation NASA Tech. Mem. 1112, (1947).
[10]Pocheau, A., “Front Propagation in a Turbulent Medium”, Europhys. Lett. 20, 401-406 (1992).
[11]Williams, F. A., Combustion Theory, 2nd Ed., Addison-Wesley, Redwood City, (1985).
[12]Borghi, R., “On the Structure and Morphology of Turbulent Premixed Flames”, Recent Advances in the Aerospace Sciences, Ed. C. Casci, 117-138, New York, Plenum (1985).
[13]Bray, K. N. C., “Turbulent Flows with Premixed Reactants,” Turbulent Reacting Flows, Eds. Libby, P. A. & Williams, F. A., 115-183, New York, Springer-Verlag (1980).
[14]Peters, N., “Laminar Flamelet Concepts in Turbulent Combustion”, Proc. Combust. Inst. 21, 1231-1250 (1986).
[15]Peters, N., “The turbulent burning velocity for large-scale and small-scale turbulence”, J. Fluid Mech. 384, 107-132 (1999).
[16]Shy, S. S., Lin, W. J. and Wei, J. C., “An Experimental Correlation of Turbulent Burning Velocities for Premixed Turbulent Methane-Air Combustion,” Proc. R. Soc. Lond. A 456, 1997-2019 (2000).
[17]Kitagawa, T., Ogawa, T. and Nagano, Y., “The Effects of Pressure on Unstretched Laminar Burning Velocity, Markstein Length and Cellularity of Spherically Propagating Laminar Flames,” COMODIA, August 2-5, Japan (2004).
[18]Bradley, D., Haq, M. Z., Hicks, R. A., Kitagawa, T., Lawes, M., Sheppard, C. G. W. and Woolley, R., “Turbulent Burning Velocity, Burned Gas Distribution, and Associated Flame Surface Definition,” Combust. Flame 133, 415-430 (2003).
[19]Bradley, D., Gaskell, P. H. and Gu, X. J., “Burning Velocities, Markstein Lengths, and Flame Quenching for Spherical Methane-Air Flame: A Computational Study”, Combust. Flame 104, 176-198 (1996).
[20]Liu, C. C., Shy, S. S., Chen, H. C. and Peng, M. W., “On Interaction of Centrally-Ignited, Outwardly-Propagating Premixed Flames with Fully-Developed Isotropic Turbulence at Elevated Pressure” Proc. Combust. Inst. 33 , 1293-1299 (2011).
[21]Markstein, G. H., Nonsteady Flame Propagation, Pergamon (1964).
[22]Kelly, A. P. and Law, C. K., “Nonlinear effects in the extraction of laminar flame speed from expanding spherical flames,” Combust. Flame 156, 1844-1851 (2009).
[23]Liu, C. C., Shy, S. S., Peng, M. W., Chiu, C. W. and Dong, Y. C., “High-pressure burning velocities measurements for centrally-ignited premixed methane/air flames interacting with intense near-isotropic turbulence at constant Reynolds numbers,” Combust. Flame 159, 2608-2619 (2012).
[24]Darrieus, G., “Propagation D’Un Front de Flamme: Assai de Théorie des Vitesses Anomales de Déflagration par Developpement Spontané de la turbulence”, Presented at 6th Int. Cong. Appl. Mech., Paris (1938).
[25]Landau, L. D. and Lifshitz, E. M., Fluid Mechanics, Pergamon, Oxford (1987).
[26]Law, C. K. and Sung, C. J., “Structure, Aerodynamics, and Geometry of Premixed Flamelet”, Prog. Energy Combust. Sci., 26, 459-505 (2000).
[27]Daniele S., Jansohn P., Mantzaras J. and Boulouchos K., “Turbulent flame speed for syngas at gas turbine relevant conditions”, Proc. Combust. Inst., 33, 2937-2944 (2011).
[28]Lipatnikov, A. N., and Chomiak, J., “Turbulent flame speed and thickness: Phenomenology, evaluation, and application in multi-dimensional simulations” Prog Energy Combust Sci, 28, 1-74 (2002).
[29]Bradley, D., Lawes, M., and Mansour, M. S., “Correlation of turbulent burning velcities of ethanol-air, measured in a fan-stirred bomb up to 1.2MPa” Combust. Flame 158, 123-158 (2011).
[30]Peters, N., “Turbulent Combustion” Cambridge University Press (2000).
[31]Shy, S. S., Lin, W. J., Peng, K. Z., “High-Intensity Turbulent Premixed Combustion: General Correlations of Turbulent Burning Velocities in a New Cruciform Burner,” Proc. Combust. Inst. 28, 561-568 (2000).
[32]Shy, S. S., I, W. K., Lin, M. L., “A New Cruciform Burner and its Turbulence Measurements for Premixed Turbulent Combustion Study,” Exp. Therm. Fluid Sci. 20, 105-114 (2000).
[33]Yang, T. S., Shy, S. S., Chyou, Y. P., “Spatiotemporal Intermittency Measurements in a Gas-Phase Near-Isotropic Turbulence Using High-Speed DPIV and Wavelet Analysis,” J. Mech. 21, 157-169 (2005).
[34]Yang, T. S., Shy, S. S., “Two-Way Interaction between Solid Particles and Homogeneous Air Turbulence: Particle Settling Rate and Turbulence Modification Measurements,” J. Fluid Mech. 526, 171-216 (2005).
[35]Liu, C. C., Shy, S. S., Chiu, C. W., Peng, M. W., Chung, H. J., “Hydrogen/Carbon Monoxide Syngas Burning Rates Measurements in High-Pressure Quiescent and Turbulent Environment,” Int. J. Hydrogen Energy 36, 8595-8603 (2011).
[36]Shapiro, A. H., The Dynamics and Thermodynamics of Compressible Fluid Flow 1, Ronald Press (1953).
[37]Chaudhuri, S., Wu, F., Zhu, D. and Law, C. K., “Flame Speed and Self-Similar Propagation of Expanding Turbulent Premixed Flames” Phys. Rev. Lett. 108, 044503 (2012).
[38]董益銍，“淨煤氣化合成氣貧油可燃極限與速度量測:壓力和紊流效應”，國立中央大學機械工程研究所，碩士論文，2012年。
[39]Kobayashi, H., Nakashima, T., Tamura, T., Maruta, K and Niioka, T., “Turbulence Measurements and Observations of Turbulent Premixed Flames at Elevated Pressures up to 3.0 MPa” Combust. Flame 108, 104-117 (1997).
[40]Rozenchan, G., Zhu, D. L., Law, C. K. and Tse, S. D., “Outward Propagation, Burning Velocities, and Chemical Effects of Methane Flames up to 60 atm”, Proc. Combust. Inst., 29, 1461-1469 (2002).
[41]Lipatinikovi, A. N., private communication.
[42]Andrews, G. E., and Bradley, D., “The Burning Velocity of Methane-Air Mixtures,” Combust. Flame 19, 275-288 (1972).
[43]Smallwood, G. J., Gulder, O. L., Snelling, D. R. and Deschamps, B. M., “Characterization of Flame Front Surfaces in Turbulent Premixed Methane/Air Combustion” Combust. Flame 101, 461-470 (1995).
[44]Kobayashi, H., Tamura, T., Maruta, K. and Niioka, T., “Burning velocity of Turbulent Premixed Flames in a High-Pressure Environment”, in: Twenty-Sixth Symposium (international) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 389-396.
[45]Kobayashi, H., Seyama, K., Hagiwara, H. and Ogami, Y., “Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature”, Proc. Combust. Inst., 30, 827-834 (2005).
[46]Wang, H., You, X. Q., Joshi, A. V., Davis, S. G., Laskin, A., Egolfopoulos, F., Law, C. K., USC Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1–C4 Compounds, May 2007. <http://ignis.usc.edu/USC_Mech_II.htm>.