In this study, the generality and prediction accuracy of a generalised series model for large eddy simulation of premixed and non-premixed turbulent combustion is explored. The model is based on Taylor series expansion of the chemical source term in scalar space and implemented into OpenFOAM. The mathematical model does not depend on the combustion regimes, and has the correct limiting behaviour. The numerical error sources are 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 experimental measurements, particularly with regard to the mixture fraction, velocity, temperature, and concentrations of major species CH4, CO2, H2O, and O2. The concentrations of 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 reactive species and progress variable are well reproduced. The only major discrepancy evident is in the temperature, which is attributed to the experimental uncertainties of temperature fields in the pilot stream. These findings have demonstrated the model`s generality for both premixed and non-premixed combustion simulation, as well as the accuracy of prediction of reactive species distribution.