## 2 LBV Test Methods  
The LBV is an intrinsic fuel parameter controlled by pressure, temperature, and equivalence ratio. For premixed fuel-air combustion, the prevalent LBV testing methods include the Bunsen burner method, spherical flame method, stagnation flame method, heat flux method, annular stepwise diverging tube, and externally heated diverging channel method [22]. The characteristics, advantages, and disadvantages of each LBV testing method are summarized in Table 1.  
The spherical flame method entails confining a premixed fuel/air mixture within a sealed spherical chamber and igniting it at the center of the chamber under a known equivalence ratio and initial temperature and known pressure conditions [23]. The spherical flame propagates outward into the unburned mixture while the LBV is measured. Flame stretch, arising from phenomena such as unsteady flame propagation, non-uniform flow fields, flame curvature variations, and diffusion effects, significantly influences LBV measurements. The stagnation flame method involves supplying identical premixed gases into two nozzles placed at a certain distance apart to achieve uniform velocities at the nozzle exits [24]. Igniting the ejected mixture leads to the formation of a stable stagnation flame at a fixed position after collision, allowing for the measurement of the radial propagation velocity of the laminar flame. This approach partially mitigates the influence of flame stretch on the measured flame propagation speed. In the heat flux method, the flow of unburned mixture is directed orthogonal to a stationary flame front at the burner exit plane, enabling direct measurement of the unburned fuel/air mixture velocity and thus obtaining the LBV of the fuel [25]. The Bunsen burner method is the conventional approach for measuring the LBV of various fuel/air mixtures [26]. The LBV is defined as the normal \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Earliest Year** & **Characteristic** & **Advantage** & **Disadvantage** \\ \hline Spherical flame method & 1934 & Plotting p-t curves or r-t curves & Controllable initial temperature and pressure conditions & Significantly affected by flame stretch \\ Stagnation flame method & 1985 & Fixes the effect of flame stretch on LBV & No downstream conductive heat losses & Extrapolation required; complex for liquid fuel \\  & & Direct measurement & Direct measurement & Failure under both high pressure (\textgreater{}10 atm) and high temperature \\ Heat flux method & 1994 & of adiabatic flame speed & liquid fuel & Effective when \\  & & Introduces tracer & Traditional method with the simplest structure & Inaccurate due to boundary layer near burner rim, difficulties in flame \\ Annular stepwise diverging tube & 2011 & Introduces tracer & Capable of the measurement of high-LBV fuels & Further investigation in both experiments and simulations needed \\  & & Direct measurement & Investigation of the condition \\  & & Introduces tracer & of burning velocities under a large range of temperature & high-LBV fuels needed \\  & & & Direct measurement & \\  & & & of burning velocities & Investigation of the condition of higher pressures and \\  & & & & of temperature \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Six LBV testing methods and information. component of the unburned gas velocity along the flame front and is calculated according to the following formula:  
\[S_{L}=u_{g}sina \tag{1}\]  
where S\({}_{L}\) represents LBV, u\({}_{g}\) denotes the velocity of the unburned gas, and \(\alpha\) represents the half-cone angle of the conical flame, shown in Figure 1d. One approach to testing the LBV of a Bunsen burner involves the utilization of the conservation of mass principle:  
\[S_{L}=\frac{\dot{Q}}{A_{f}} \tag{2}\]  
where \(\dot{Q}\) and \(A_{f}\) are the volumetric flow rate and average flame area, respectively. The use of tracer particle methods enables a clearer determination of the flame edge position, facilitating a more precise calculation of the flame area.