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Three formulations of quasi-two-dimensional flamelet (Q2DF) models are derived from the two-dimensional flamelet formulation on the basis of assumptions regarding the third stream (diluent), and these models are validated by means of a two-dimensional direct numerical simulation (DNS) of a three-feed non-premixed combustion system into which the diluent is injected as the third stream. DNS combined with the Arrhenius formation (ARF) together with a detailed mechanism is also performed as a reference case and compared with the present models. The characteristics of the flamelets in three-feed non-premixed combustion are discussed in detail for ARF in terms of the three mixture fractions, temperature, and major and minor species. Some discrepancies appeared between the ARF and the Q2DF models. The difference in the cross-scalar dissipation rates between Q2DF and the two-dimensional flamelet model is considered the major reason for the deviations. The cross-scalar dissipation rates for the reactor streams and the diluent are expected to be either positive or negative values in the two-dimensional flamelet model, whereas only positive numbers resulted in the Q2DF cases. And the cross-scalar dissipation rate for the fuel and the oxidizer in the Q2DF models are always negative which is also varied from that in the two-dimensional flamelet model. As the results are not determined solely by a single mixture fraction, one scalar dissipation rate is insufficient for establishing a complete database, and it is considered that an additional scalar dissipation rate is needed to improve the model. Overall, it is confirmed that the three Q2DF models presented in this study capture the fundamental characteristics of flamelets in the three-feed non-premixed combustion system, although further improvement is required.

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The development of turbulent combustion models for a threefeed non-premixed flame is essential for the research of gas-turbine in the oxy-fuel integrated coal gasification combined cycle (IGCC) system. The quasi-two-dimensional flamelet models are considered effective and accurate substitutes for the two-dimensional flamelet model, however, there are still many aspects worth further investigations in terms of each dimension in the flamelet library. The considerations of heat loss, the presumed probability density function (PDF), and the resolution of the diluent fraction in largeeddy simulation (LES) should be attached importance to. In this paper, heat loss, diluent fraction PDF, and resolution of the diluent fraction have been investigated. It has been shown that the current heat loss model in the flamelet equation can correctly interpret the reactions which are facilitated by high temperature. The beta-PDF used for diluent fraction results in a lower temperature in the flame zone than that of the delta-PDF as the diluent fraction fluctuation cannot be overlooked. And also, coarse resolution in terms of the diluent fraction gives interpolation error and shoud be paid attention to.