## 2 Experimental Methods  
Ignition experiments of the n-butane/air mixture at \(\phi\) = 0.7 with \(Le\approx\) 2.1 >> 1 are conducted in the central uniform region of the large dual-chamber, constant-temperature/pressure, fan-stirred cruciform explosion facility using a pair of stainless-steel electrodes of 2 mm in diameter with sharp ends over a range of \(u^{\prime}\) = 0-2.1 m/s and at atmospheric pressure and room temperature conditions. The selection of lean n-C\({}_{4}\)H\({}_{10}\) at \(\phi\) = 0.7 as a fuel is because of its possible relevance to lean-burn combustion in SI engines having a sufficiently large \(Le\approx\) 2.1 >> 1, closely matching that of lean gasoline fuel. Such dual-chamber, fan-stirred cruciform burner has been used to measure laminar and turbulent burning velocities of expanding spherical flames at various gaseous and liquid fuel/air mixtures with different values of \(Le\) under high-temperature and high-pressure conditions [26; 27], as well as MIE\({}_{\rm L}\) and MIE\({}_{\rm T}\) of the lean iso-octane/air mixture [7] and the lean PRF95/air mixture [23]. Details of the explosion facility and its associated turbulence properties can be found in [21; 22; 24; 28] and references therein. For completeness, a simplified sketch version of the dual-chamber cruciform explosion facility is presented in Figure 1. Moreover, also plotted in Figure 1 is the ignition circuit for generating near-square voltage and current waveforms to measure E\({}_{\rm ig}\) of high accuracy [7], and the high-speed schlieren imaging arrangement for recording the early development of flame kernels over a range of \(u^{\prime}\) varying from 0 to 2.1 m/s. The experimental procedure used in the present work is the same as our previous studies; this will not be elaborated upon here, so the reader is directed to Refs. [23; 27; 28] for details. The outer safety chamber is pressurized with the dehumidified air at a pressure slightly higher than the initially selected pressure inside the inner cruciform burner. The inner cruciform burner is first vacuumed and then the appropriate mole fractions of n-butane and air are sequentially injected into the inner cruciform burner to 1 atm in this study using the partial pressure method. Next is the mixing of the lean n-butane/air mixture by counter-rotating two specially-designed fans and perforated plates (see Figure 1), where  
Figure 1: The simplified sketch of a dual-chamber, constant temperature/pressure, fan-stirred explosion facility capable of generating near-isotropic turbulence alongside the schlieren imaging arrangement and the schematic ignition circuit. A typical enlarged schlieren image of the turbulent expanding flame is inserted in the experimentation domain (the central quartz window) to show the electrodes and the successful ignition event. the two fans are rotated at a fixed fan frequency \(f\) = 30 Hz for at least 1.5 min to ensure the well mixing of fuel and air. For the laminar case, the two fans are turned off right after the mixing, and then we wait for about 10 s to let turbulence completely dissipate, allowing a quiescent mixture before ignition. As to turbulent cases, after the well mixing of fuel and air, the fan frequency is set to the desired value for the wanted \(u^{\prime}\approx 0.0462f\) (ms\({}^{-1}\)), measured by high-speed particle image velocimetry (PIV) [22; 26; 29]. Additionally, the integral length scale of turbulence \(L_{\rm I}\approx 10.7f^{0.34}\) (mm), leveled off to about 45 mm at high values of \(f\geq 70\) Hz [22; 26; 29]. A pair of 2-mm stainless-steel electrodes with sharp ends at a constant \(d_{\rm gap}\) = 2.0 mm are used to centrally ignite the lean n-butane/air mixture under quiescent and turbulent conditions at various values of E\({}_{\rm ig}\) controlled by the loading resistors (\(R_{\Omega}\)) in the ignition circuit (see the top left inset of Figure 1). The higher the value of \(R_{\Omega}\) is, the smaller the value of E\({}_{\rm ig}\) is.