In flames, turbulence can either limit or enhance combustion efficiency by means of strain and mixing. The interactions between turbulent motions and chemistry are crucial to the behaviour of combustion processes. In particular, it is essential to correctly capture non-equilibrium phenomena such as localised ignition and extinction to faithfully predict pollutant formation. Reactor-based combustion models — such as the Eddy Dissipation Concept (EDC) or Partially Stirred Reactor (PaSR) — may account for turbulence-chemistry interactions at an affordable computational cost by calculating combustion rates relying upon canonical reactors of small fluid size and timescale. The models may include multiscale mixing, detailed chemical kinetic schemes and high-fidelity multispecies diffusion treatments. Although originally derived for conventional, highly turbulent combustion, numerous recent efforts have sought to generalise beyond simple empirical correlations using more sophisticated relationships. More recent models incorporate the estimation of scales based on local variables such as turbulent Reynolds and Damköhler numbers, phenomenological descriptions of turbulence based on fractal theory or specific events such as extinction. These modifications significantly broaden the effective range of operating conditions and combustion regimes these models can be applied to, as in the particular case of Moderate or Intense Low-oxygen Dilution (MILD) combustion. MILD combustion is renown for its ability to deliver appealing features such as abated pollutant emissions, elevated thermal efficiency and fuel flexibility. This review describes the development and current state-of-the-art in finite-rate, reactor-based combustion approaches. Recently investigated model improvements and adaptations will be discussed, with specific focus on the MILD combustion regime. Finally, to bridge the gap between laboratory-scale canonical burners and industrial combustion systems, the current directions and the future outlook for development are discussed.
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