## 2 Experimental Setup and Methodology
Subsequently, a small amount of the blended fuel is introduced into the chamber from its storage tank, taking into consideration the partial  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Main Fuel \%**} & \multicolumn{1}{c}{**H\({}_{2}\)**} & **NH\({}_{3}\)** & **CH\({}_{4}\)** & \(T_{pred}\) & \(p_{u}/p_{b}\) & \(K_{R}\times\mathbf{10^{-2}}\) & \(C_{p,R}\) & \(\alpha_{R}\times\mathbf{10^{-5}}\) & \(v_{R}\times\mathbf{10^{-5}}\) \\ \hline \(\mathrm{H}_{2}\) & **NH\({}_{3}\)** & **CH\({}_{4}\)** & \(\gamma\) & \(\beta\) & \(\sigma\) & \(k\) & W/(m-k) & J/kg/K & m\({}^{2}\)/s & m\({}^{2}\)/s \\ \hline \multirow{8}{*}{**0**} & 0 & 100 & 0 & 0 & 1 & 2224 & 7.518 & 2.41 & 107.99 & 1.59 & 1.98 \\  & 20 & 80 & 0 & 0.2 & 0.8 & 2210 & 7.507 & 2.41 & 1085.84 & 1.58 & 1.98 \\  & 40 & 60 & 0 & 0.4 & 0.6 & 2192 & 7.491 & 2.41 & 1096.21 & 1.58 & 1.97 \\  & 60 & 40 & 0 & 0.6 & 0.4 & 2167 & 7.467 & 2.41 & 1110.33 & 1.57 & 1.96 \\  & 80 & 20 & 0 & 0.8 & 0.2 & 2130 & 7.427 & 2.41 & 1130.27 & 1.57 & 1.95 \\  & 100 & 0 & 0 & 1 & 0 & 2072 & 7.350 & 2.41 & 1162.7 & 1.56 & 1.93 \\ \hline \multirow{8}{*}{**20**} & 0 & 100 & 0.2 & 0 & 0.8 & 2234 & 7.471 & 2.60 & 1095.8 & 1.62 & 2.13 \\  & 20 & 80 & 0.2 & 0.16 & 0.64 & 2222 & 7.455 & 2.62 & 1105.46 & 1.621 & 2.15 \\  & 40 & 60 & 0.2 & 0.32 & 0.48 & 2208 & 7.435 & 2.64 & 1 pressure (according to the Gibbs-Dalton law). This step is repeated for all three fuels. Finally, the chamber is injected with air. Afterward, the initial pressure and temperature are measured, all valves are closed, and camera settings, ignition power, and ignition timing are set. The mixture is now prepared for ignition. Data are recorded, and photographs are taken with a single trigger. The procedure of the experiment is mentioned in detail [45]. LBV was evaluated using the same procedure as in our previous study [14]. The stretched flame speed, \(S_{N}\), was evaluated as follows  
\[S_{N}=\frac{\mathrm{d}r_{sch}}{\mathrm{d}t} \tag{4}\]  
where \(r_{sch}\) is the radius of the flame directly obtained from the schlieren photos and \(t\) is the progress time. The spherically propagating flame is influenced by the effects of flame stretch. In the present study, the flame stretch rate, \(\epsilon\), was evaluated using the following linear equation  
\[\epsilon=\frac{1}{A_{F}}\frac{\mathrm{d}A_{F}}{\mathrm{d}t}=\frac{2}{r_{sch}} \frac{\mathrm{d}r_{sch}}{\mathrm{d}t}=2\frac{S_{N}}{r} \tag{5}\]  
where (\(A=4\pi r_{sch}^{2}\)) is the area of the flame front. Regarding the asymptotic analysis, an unstretched flame speed can be estimated using the nonlinear relationship in Equation (6). \[\left(\frac{S_{N}}{S_{S}}\right)^{2}\ln\left(\frac{S_{N}}{S_{S}}\right)^{2}=- \frac{2L_{b}k}{S_{S}} \tag{6}\]  
where \(L_{b}\) is the burned gas Markstein length. Thus, \(S_{S}\) can be calculated by the non-linear extrapolation of \(\epsilon\to 0\) (or \(r_{sch}\rightarrow\infty\)). \(S_{l}\) can then be calculated by \(S_{L}=S_{S}\cdot\rho_{b}/\rho_{u}\)  
Here, \(\rho_{b}\) and \(\rho_{u}\) are the densities of the burnt gas and unburned mixture, respectively. Both densities were estimated from the thermal equilibrium, which was calculated by Chemkin-Pro. Using a centrally ignited constant volume chamber to establish a spherical flame to estimate the unstretched LBV during a constant pressure period is well-known, but it introduces some uncertainties. These uncertainties include initial pressure fluctuation during filling, temperature fluctuations, radiation heat loss, buoyancy, ignition energy, and confinement. The accuracy of the pressure transducer, with an error of less than \(\pm 0.1\) kPa, is relatively small and can be ignored. Similarly, the confinement effect can be neglected since the outer diameter is larger (305 mm) than the optical window (120 mm), as required. The flame propagating profile can be divided into three regions: the ignition-affected region, the quasi-steady region, and the high-pressure and buoyancy-influenced regions.