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A simplified two-mixture-fraction-based flamelet model is proposed in this work for a non-premixed staged combustion mode in which three feeds are introduced into the flow field. As the third stream is injected downstream of the main port, the system can be considered a special case of the two-mixture-fraction-based systems. It is considered that if a well-mixing is achieved in the upper stream prior to the third-stream injection, the simplification of the two-mixture-fraction-based flamelet model is feasible. In this work, a simplified model is proposed which can greatly reduce the library size compared to the complete two-mixture-fraction-based flamelet library providing identical resolutions for the fuel stream mixture fraction and the progress variable, respectively. Analysis associated with the interpolation strategy has been implemented. Extension of the current model for the cases in which the well-mixing state is not attained is also analysed, as well as the consideration of heat loss. To validate the model, two adiabatic cases of two-dimensional (2D) direct numerical simulations (DNS) have been performed in this work. To describe the chemical events, one is using finite-rate chemistry (FRC), while the other one is realised by means of the current flamelet model (FLM). An  a priori  test case that directly looks up the libraries by using the tracking parameters obtained from the FRC case is also considered. It is observed that the interpolation along the primary oxidiser mixture fraction direction outperforms that along directions for both fuel and primary oxidiser mixture fractions. It is also found that three one-mixture-fraction-based flamelet libraries which form the current model are sufficient for simulation of the non-premixed staged combustion, while the extended one which composes five libraries is expected to gain higher accurateness. In the FLM case, although the distributions of tracking parameters deviate from the FRC case slightly, good agreements can be obtained in terms of temperature and species mass fractions. The  a priori  test shows that the current model can reproduce the reacting flow accurately when the tracking parameters are identical to the FRC case. It is confirmed that the current model can be used to predict the characteristics of the reacting flow in the non-premixed staged combustion.

A simplified two-mixture-fraction-based flamelet modelling and its validation on a non-premixed staged combustion system