Low-Order Predictions of Spatial Distributions of Conserved Scalars in Swirl Combustors Based on the Gaussian Plume Function

The mixture fraction is a conserved scalar characterizing the fuel-air mixing. As a key reference scalar for turbulent combustion modelling, its spatial distribution is usually obtained through 3D numerical simulation, which are, however, time-consuming and costly for combustors with complex geometries. To overcome such low efficiency in the iterative designing process, a low-order model was developed based on the Gaussian plume function to compute the mixture fraction field in the swirl combustor to accelerate the evaluation of the fuel-air mixing strategy and the parameterized design process. Compared with the conventional formulation, the derived new Gaussian plume function includes the effects of convection and corrections due to swirl flows. A mirror image reflection model was further developed to simulate the wall-plume interactions, together with the relevant corrections to ensure mass conservation. This newly derived Gaussian plume model was applied to the low-older prediction of the mixture fraction field in a methane swirl combustor. Based on the database generated through 3D numerical simulations, the model parameters were optimized with the least square method first. The prediction accuracy under broad working conditions was demonstrated. This study not only provides a novel approach for quick predictions of mixture fractions in swirl combustors, but also sets an instance for further development and application of the Gaussian plume model.