Modelling of Spray Combustion with Doubly Conditional Moment Closure

Turbulent spray combustion is characterised by a strong coupling of evaporation, mixing and chemical reaction. This leads to a wide spectrum of combustion regimes, where self-propagating premixed flames and diffusion-controlled non-premixed flames may occur simultaneously within the same flame. The physical processes involved in spray combustion and their interaction take place over a broad range of scales, which makes their modelling in numerical simulations challenging. This thesis presents the development of Doubly Conditional Moment Closure (DCMC) for the modelling of turbulent spray combustion. This modelling approach allows us to consider the effects of finite-rate chemistry and spray evaporation on the flame. Using a parametrisation of the flame structure, based on mixture fraction and reaction progress variable permits us to resolve premixed, non-premixed and intermediate combustion modes. In the first part of this thesis, the model development is presented. With its foundation as a statistical model, DCMC does not require any strong assumption in terms of the combustion mode or regime. The DCMC equation is derived in a general form, which involves only a minimum number of modelling assumptions about the physical processes involved. Closure for the DCMC equation is discussed and a complete set of models is suggested. Since little experience exists in the modelling of doubly-conditional terms, the closure models were generalised from conventional Conditional Moment Closure (CMC) or adapted from other combustion models with similar parametrisation. In the second part, the DCMC model is validated for two test flames. The DCMC model was first applied to the Cambridge spray jet flame using the Reynolds-Averaged Navier-Stokes (RANS) approach. This flame is characterised by significant pre-vaporisation and behaves as a propagating spray flame, with similarities to premixed flames, but with small-scale inhomogeneity in the gaseous mixture and the presence of liquid droplet interacting with the flame – a problem which requires the doubly-conditional description of the flame structure employed in the DCMC model. The role of the spray terms on the flame structure and mixing field were assessed using RANS and promising results were obtained. Finally, a Large-Eddy Simulation (LES) with DCMC acting as sub-grid scale combustion model was applied to the Rouen spray jet flame. LES-DCMC was found to accurately predict the spray statistics, lift-off height and flame shape. Small-scale effects of the spray on the flame could be resolved thanks to the doubly-conditional parametrisation of the flame structure. Temporal fluctuations and spatial variations of the flame structure were investigated. Spatial gradients of the doubly-conditional flame structure were small and convective transport was found to play a minor role on the flame structure compared to the effects of micro-mixing and chemical reaction in the DCMC equation. The findings of this work suggest that, besides spray combustion, DCMC shows great potential for the modelling of partially premixed flames and extinction.PhD scholarship by the Gates Cambridge Trust. High-performance computing resources provided by the UK Consortium on Turbulent Reacting Flows (UKCTRF)