Improved semi-theoretical correlation to predict the Sauter mean diameter of swirl cups

The spray downstream of swirl cups involves complex two-phase flow. Comprehensively, understanding the flow physics of the spray to accurately predict the characteristics of the swirl spray is crucial for developing next-generation low-emission gas turbine combustors. The Sauter mean diameter (SMD) of the spray is an important design parameter in a gas turbine combustor, and the semi-theoretical method is among the most widely used approaches for predicting the SMD of atomizers. Of the available semi-theoretical models for predicting the SMD of prefilming-type atomizers, Shin's phenomenological three-step atomization (PTSA) model is a physics-based correlation. The PTSA model comprises three submodels: those of the pressure-swirl spray, impingement and film formation, and aerodynamic breakup. Based on similar physical mechanisms, the PTSA model can effectively predict the SMD for the spray shear layer of swirl cups. In this study, a new model, called the PTSA-V model, is proposed by introducing the viscosity of the liquid to the three submodels of PTSA. Additionally, the submodel of impingement and film formation was reconstructed, using a simplified model of a round water jet impinging on a cylindrical wall to predict the thickness of the liquid film on the Venturi surface. Experiments were carried out on a swirl cup under different pressures and temperatures of fuel as well as varying pressure drops in the air by using a two-component phase Doppler particle analyzer. The resulting uncertainty in predictions of the PTSA-V model was lower than ± 7.4 % under the 26 operating conditions considered here, compared with an uncertainty of ± 20 % in the outcomes of PTSA. Uncertainty in predictions of PTSA-V was lower than ± 15 % when it was applied to SMD data downstream of the swirl cup from the literature.