In this study, the generality and prediction accuracy of a generalised series model for the large eddy simulation of premixed and non-premixed turbulent combustion is explored. The model is based on the Taylor series expansion of the chemical source term in scalar space and implemented into OpenFOAM. The mathematical model does not depend on combustion regimes and has the correct limiting behaviour. The numerical error sources are also outlined and analysed. The model is first applied to a piloted methane/air non-premixed jet flame (Sandia Flame D). The statistical (time-averaged and RMS) results agree well with the experimental measurements, particularly with regard to the mixture fraction, velocity, temperature, and concentrations of major species CH4, CO2, H2O, and O2. However, the concentrations of the intermediates CO and H2 are over-predicted, due to the limitations of the reduced reaction mechanism employed. Then, a Bunsen-piloted flame is simulated. Most of the statistical properties of both the reactive species and progress variables are well reproduced. The only major discrepancy evident is in the temperature, which is probably attributed to the experimental uncertainties of temperature fields in the pilot stream. These findings demonstrate the model’s generality for both a premixed and non-premixed combustion simulation, as well as the accuracy of prediction of reactive species distribution.