Session: 11-18-01: Fundamental Issues in Fluid Mechanics/Rheology of Nonlinear Materials and Complex Fluids/Plasma Flow

Paper Number: 165694

Asymptotic Behavior of a Buoyant Jet Regime Inside a Carbon-Dioxide Ejector 

Ejectors are employed in different engineering processes, including steam cycles and vapor compression systems. To optimize ejectors, the complex multiphase flow topologies and turbulent structures within must be resolved, resulting in computationally costly simulation models. Lower fidelity models can be employed, but they often lack sufficient physics to capture the three-dimensional internal flow characteristics. The flow topology inside an ejector has four primary regimes, which differ from each other based on the dominant physical mechanism of the flow: compressibility, interface instability, buoyancy, or turbulent jet expansion. Coherence function analysis revealed that the flow can be treated as mostly incompressible. The third regime, i.e., the buoyancy-dominated regime inside an ejector, is the most complex and unusual in terms of flow characteristics. Understanding this regime requires a similarity transformation approach to complete the low-order model of an ejector.

To this end, a class of self-similar solutions is developed to describe the jet behavior inside the buoyancy-dominated regime. The mathematical formulation assumes an incompressible, steady, and isothermal flow, with density variation only due to mixing. The central jet expands due to momentum diffusivity, and the total momentum flux is affected by a constant streamwise pressure gradient. A counterflow annular wall jet develops at the location where the expanding central jet meets the cylindrical wall in a typical ejector configuration. This offset happens due to the wall effect and the local density gradient.

This work focuses on establishing the methodology for laminar or low Reynolds number flows, and it will be extended to turbulent or high Reynolds number flows. The initial estimation of the boundary conditions is obtained from a validated high-fidelity numerical simulation of a subcritical liquid carbon-dioxide (CO₂) ejector employed in a CO₂ multi-stage refrigeration cycle. The self-similar solution of the flow is derived by superimposing driving mechanism of an axisymmetric jet expansion and a counterflow wall jet in a quiescent environment. The solution for the interface between the two jets is developed using a similar approach to laminar mixing. These three coupled solutions provide three separate ordinary differential equations, which are an indirect function of the inlet Reynolds number and the pressure gradient. A linear perturbation is introduced with inlet Reynolds number and pressure gradient to estimate the solution for the flow with a varying pressure difference, inlet density, velocity, temperature, and density gradient across the two jets.

This self-similar solution and the understanding of the asymptotic behavior of the buoyancy-dominated regime will enable the development of a low-order model for fast assessment of jet interface characteristics, accelerating shape and flow optimization studies of ejectors coupled with cycle level operations.

Presenting Author: Sreetam Bhaduri Purdue University

Presenting Author Biography: Sreetam joined Purdue University in Spring 2022. Prior to coming to Purdue, he pursued a Master of Science (by Research) in Mechanical Engineering from the Indian Institute of Technology Madras, Chennai, India in Fall 2021. Previous to his master's degree, he pursued a Bachelor of Technology (B.Tech) in Mechanical Engineering from Vel Tech University, Chennai, India back in Fall 2018. During his undergraduate and graduate studies, he engaged himself researching internal combustion engines, with both experiments and numerical simulations. His primary research interests are in Computational Combustion Modeling and Computational Fluid Dynamics (CFD).

Authors:

Sreetam Bhaduri Purdue University
Ivan C. Christov Purdue University
Eckhard A. Groll Purdue University
Davide Ziviani Purdue University