Asymptotic Behavior of a Buoyant Jet Regime inside a Carbon-dioxide Ejector

Ejectors are used in various engineering systems, including steam and vapor compression cycles. Optimizing the performance of ejectors requires understanding and analysis of multiphase and turbulent flow structures associated with their internal flow fields. This approach yields higher fidelity but at a high computational cost. Lower-fidelity one-dimensional (1D) models offer lower computational costs; however, 1D models are often empirical and provide limited understanding of the internal flow fields, overlooking possibilities of optimization. Ejector flows can be categorized into four regimes: Regime 1 (R1), which is compressibility dominated; Regime 2 (R2), which is interface instability driven; Regime 3 (R3), which is buoyancy dominated; and Regime 4 (R4), which is a wall-bounded turbulent jet expansion. Among these, the buoyancy-dominated regime is the most complex and least understood. This work discusses an approach to develop a reduced-order model utilizing a self-similarity framework to capture the internal flow field of the jet within the buoyancy-dominated regime under quasi-steady, compressible, and isothermal flow conditions, where density variations arise only from mixing. The density variation is captured through the Favre-averaging approach. The model captures the expansion of a central jet influenced by momentum diffusivity and a constant streamwise pressure gradient. Interaction of the central jet with the cylindrical wall induces a counterflow annular wall jet due to the combined effects of negative radial density gradients and shear stress imposed by the wall. Initially, the discussion focuses on flow topology inside the ejector, followed by the self-similarity methodology and implementation of asymptotic analysis. Finally, the resemblance...