Combustion and Flame 145 (2006) 415–434 www.elsevier.com/locate/combustﬂame Effects of strain rate and curvature on the propagation of a spherical ﬂame kernel in the thin-reaction-zones regime K.W. Jenkins a , M. Klein b , N. Chakraborty c , R.S. Cant c,∗ a School of Engineering, Cranﬁeld University, Bedford MK43 0AL, UK b Technische Universität Darmstadt, Institut für Energie- und Kraftwerkstechnik, Petersenstr. 30, D-64287 Darmstadt, Germany c Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK Received 3 March 2005; received in revised form 5 August 2005; accepted 4 October 2005 Available online 29 November 2005 Abstract Strain rate and curvature effects on the propagation of turbulent premixed ﬂame kernels have been investigated in the thin-reaction-zones regime using three-dimensional compressible direct numerical simulations (DNS) with single-step Arrhenius chemistry. An initially spherical laminar ﬂame kernel is allowed to interact with the sur- rounding turbulent ﬂuid motion to provide a propagating turbulent ﬂame with a strong mean spherical curvature. The statistical behavior of the local displacement speed in response to strain and curvature is investigated in detail. The results demonstrate clearly that the mean curvature inherent to the ﬂame kernel conﬁguration has a signiﬁcant inﬂuence on the propagation of the ﬂame. It has been found that the mean density-weighted displacement speed ρS d in the case of ﬂame kernels varies signiﬁcantly over the ﬂame brush and remains different from ρ 0 S L (where ρ 0 is the reactant density and S L is laminar ﬂame speed), unlike statistically planar ﬂames. It is also shown that the magnitude of reaction progress variable gradient |∇c| is negatively correlated with curvature in the case of ﬂame kernels, in contrast to the weak correlation between |∇c| and curvature in the case of planar ﬂames. This correlation induces a net positive correlation between the combined reaction and normal diffusion components of displacement speed (S r + S n ) and curvature in ﬂame kernels, whereas the previous studies based on statistically planar ﬂames did not observe any appreciable correlation between (S r + S n ) and curvature.  2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Direct numerical simulation; Turbulent premixed combustion; Flame kernel 1. Introduction Turbulent premixed combustion can be found in a wide variety of engineering devices, such as indus- trial gas turbines and spark ignition engines. Since * Corresponding author. Fax: +44 1223 332662. E-mail address: rsc10@eng.cam.ac.uk (R.S. Cant). the majority of practical combustion systems oper- ate in turbulent ﬂow environments, it is necessary to consider the turbulence and its interaction with the ﬂame. Direct numerical simulation (DNS) has be- come an established tool for understanding ﬂame– turbulence interaction [1]. Using DNS, it is now pos- sible to simulate a turbulent ﬂame without the need for turbulence modeling, and useful statistics can be extracted to support combustion modeling based on 0010-2180/$ – see front matter  2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustﬂame.2005.10.012