Impact of CONVERGE CFD Software on Refrigeration Technology

The Challenge

The investigation of near-critical state fluid jets is an important problem for various engineering applications such as propulsion and thermal systems. In these contexts, ejectors are used to convert flow work into kinetic energy and, ultimately, into a pressure lift in various systems, including gas turbines, liquid propulsion systems, and refrigeration systems. The ejector operating principle relies on a high-speed jet in single- or multi-phase conditions. The efficiency of ejector devices depends on the physics of the jet, especially under multi-phase operations.

Ejector components are used in various engineering applications as expansion recovery devices. Specifically, ejectors are flow devices that convert kinetic energy into pressure recovery. Different types of ejectors exist based on the application. For example, ejectors used for gas turbine cooling expand high-pressure gas with mixing gas-phase fluid, which increases volumetric efficiency of the combustor; ejectors used in refrigeration systems expand the liquid-phase of fluid with mixing gas-phase fluid, developing a two-phase fluid and decreasing compressor work input. Figure 1 presents a schematic diagram of a multi-phase ejector. The inlet of an ejector, often known as “motive”, contains liquid at high pressure, and the suction contains vapor phase of the same or a different fluid. High-pressure liquid that flows out of the motive throat induces a negative pressure gradient in the suction throat by increasing kinetic energy, which develops a suction effect on the vapor flowing through the suction inlet. These distinct vapor and liquid flows mix downstream through the mixing zone and expand in the following diffuser zone, increasing the pressure.

Ejectors are not only used in refrigeration systems, but they are also widely applied in oil and natural gas systems for waste gas recovery processes and in gas turbines to enhance cooling performance by improving compressor entrainment efficiency.

Improving the design and operational performance of ejectors in a refrigeration system is linked to reduction of entropy generation. Entropy production restricts the coefficient of performance (COP) of the system from further improvement. Local exergy analysis of an ejector operating with carbon dioxide (CO2) as the fluid in a two-phase regime shows that entropy generation in the mixing zone is 2.92 times higher than in the diffuser zone. High entropy generation in the mixing zone is linked to a turbulence evolution mechanism at the shear layer of the jet, where entropy generation is related to turbulence length scales. The operation of ejectors relies on the physics and control strategy of the shear layer (for single phase) and the liquid-gas interface (for multi-phase), putting restrictions on improving the COP of the system. Therefore, understanding the evolution of shear layer turbulence and the mechanism of liquid-gas interface instabilities on the jet inside ejectors could provide new insights to decrease entropy generation and maximize the COP of the system.

This current research, in collaboration with a technical team from Bechtel, aims to understand the various stages inside the ejector to identify pathways to improve the ejector efficiency. The ejector of interest is a liquid-vapor variable-geometry CO2 ejector, as shown in Figure 1. The flow inside the ejector comprises a subcooled jet, which is the primary energy input to the ejector; a gaseous suction flow, which increases the cooling capacity of the ejector cycle through work recovery; a mixing zone, where entrainment of the suction flow into the motive flow occurs; and a diffuser, which increases pressure and reduces the work required by a compressor. To conduct the analyses, a high-fidelity computational fluid dynamics (CFD) model is needed to resolve the boundary layers and interphase phenomena.

Case Study: Large Eddy Simulation of the Multi-Phase Jet Inside an Ejector

Problem Description

The computational domain of the ejector, shown in Figure 2,^1,2,3,4 is modeled in cylindrical coordinates with axial (x), radial (r), and azimuthal (θ) directions. The domain includes the motive inlet (x/d = −13), suction inlet (−11 ≤ x/d ≤ −8), diffuser outlet (x/d = 23), and adiabatic no-slip walls. Boundary conditions are assigned based on experimental data. At the motive inlet, pressure, temperature, and CO₂ mass fraction are prescribed, and the inlet gap is tuned to match the measured mass flow rate. The suction inlet is defined by its mass flow rate, temperature, and CO₂ composition. The outlet pressure is fixed, with no backflow allowed, and all the walls are treated as adiabatic with a no-slip boundary condition.

Computational Modeling Using CONVERGE CFD Software

CONVERGE CFD software provides a robust platform for simulating complex, unsteady, multi-phase flows with minimal manual meshing. In this study, CONVERGE is used to solve the three-dimensional compressible Navier-Stokes equations coupled with phase transport and large eddy simulations (LES) for CO₂ ejector flows. Thermophysical and transport properties are sourced directly from the NIST database, enabling accurate modeling of real-fluid behavior across a wide range of thermodynamic states.

A key advantage of CONVERGE is its automatic cut-cell meshing, which accurately resolves complex geometries without requiring a user-generated mesh. This feature also enables box filtering for LES, ensuring that a large portion (≥80%) of turbulent kinetic energy is resolved. Furthermore, CONVERGE provides full control over subgrid-scale (SGS) models and constants, offering users flexibility comparable to that of in-house CFD codes.

Advanced grid control features include region-based embedding and Adaptive Mesh Refinement (AMR). Embedding refines the mesh locally (down to 0.125 mm), while AMR dynamically adapts grid resolution during the simulation (as fine as 0.0156 mm) based on gradients in velocity, temperature, and phase fraction. This results in a highly detailed, physics-driven mesh (60 million cells) that adapts to flow evolution without remeshing.

Although CONVERGE does not include built-in verification tools, the simulation results have been rigorously validated following the ASME V&V 20 standard. Grid convergence studies reveal negligible numerical uncertainty (≤0.13%), and a comparison with experimental data confirms the model’s predictive capability, with model error bounds of 2.5% ±2.66% for mass flow rate and 0.72% ±1.09% for suction pressure.

Lastly, spectral analysis of turbulent kinetic energy shows a clear inertial subrange with κ^−5/3 scaling, confirming that the LES approach and discretization schemes successfully capture the dominant energy transfer mechanisms. Overall, CONVERGE enables high-fidelity simulations of multi-phase, turbulent flows with exceptional automation and accuracy.

Different Regimes of Motive Jet in an Ejector

The behavior of the motive jet in an ejector is governed by the turbulent structures that develop along the liquid-gas interface, directly influencing flow entrainment. Four distinct regimes are identified based on dominant physical mechanisms:

• R1: Compressibility effects
• R2: Interface instability
• R3: Core flow destabilization
• R4: Fully developed turbulent flow

These regimes coexist and interact within the ejector. The instantaneous jet morphology, shown in Figure 7, is visualized using the spatial distribution of the density ratio ρ_CO2(g)/ρCO₂(l). Grayscale shading ranges from dark (low gas-liquid density ratio) to white (high ratio), indicating interface transitions. The evolution of turbulent coherent structures at the interface is crucial for entrainment performance (m˙ _s/m˙ _m). The motive jet, an annular co-axial flow, is wall-bounded and subject to a streamwise adverse pressure gradient. Vorticity dynamics drive interface deformation:

• Azimuthal vorticity (ω_θ) initiates the process,
• which stretches and tilts into axial vorticity (ω_x),
• while generating weaker radial vorticity (ω_r) that realigns with ω_x.

In regime R2, Kelvin–Helmholtz instability (KHI) leads to the formation of ring vortices, supported by ω_θ from regime R1. Azimuthal instabilities induce periodic bulges in these rings, forming counter-rotating vortex pairs around the jet shear layer. These ω_x structures continue to stretch and intensify due to angular momentum conservation, leading to thinner, more energetic vortex formations (Figure 8).¹

Summary and Future Work

A detailed understanding of jet morphology within the mixing zone of an ejector is essential for the development of next-generation ejector designs. From a thermodynamic perspective, this region is the primary source of exergy destruction, and its optimization presents an opportunity for significant performance improvements. In this study, the jet morphology has been categorized into distinct flow regimes based on the dominant underlying physics. This regime-based classification lays the groundwork for the development of low-order models that capture only the most relevant physical phenomena, thereby enabling faster and more efficient computational strategies.

Ultimately, this physics-informed modeling approach is expected to accelerate the shape optimization of ejectors across a wide range of applications. The use of CONVERGE CFD software has significantly streamlined this process through its advanced features, particularly automatic meshing and granular numerical control, which align with the company’s guiding principle: “Never Make a Mesh Again.”

For an in-depth discussion of the methodologies and findings, please refer to the following articles:

1. Bhaduri, S., Christov, I.C., Groll, E.A., and Ziviani, D., “Asymptotic Behavior of a Buoyant Jet Regime inside a Carbon-dioxide Ejector,” arXiv Preprint, 2025. DOI: 10.48550/arXiv.2507.01992
2. Bhaduri, S., Peltier, L.J., Ladd, D., Groll, E.A., and Ziviani, D., “Regimes of a Decelerating Wall-Bounded Multiphase Jet Inside Ejectors,” Physics of Fluids, 37, 2025. DOI: 10.1063/5.0278015
3. Bhaduri, S., Ren, J., Peltier, L.J., Ladd, D., Groll, E.A., and Ziviani, D., “Flow Physics of a Subcritical Carbon Dioxide Jet in a Multiphase Ejector,” Applied Thermal Engineering, 256, 2024. DOI: 10.1016/j.applthermaleng.2024.124043

Acknowledgments

This research has been funded by the National Bechtel Corporation, USA. We would like to acknowledge the continued support from Mr. David Ladd, Dr. Leonard J. Peltier, and Prof. Ivan C. Christov. The authors would also like to thank Convergent Science Inc. for providing an academic license and technical support through their CONVERGE Academic Program.

References

1. Bhaduri, S., Ren, J., Peltier, L.J., Ladd, D., Groll, E.A., and Ziviani, D., “Flow Physics of a Subcritical Carbon Dioxide Jet in a Multiphase Ejector,” Applied Thermal Engineering, 256, 2024. DOI: 10.1016/j.applthermaleng.2024.124043
2. Bhaduri, S., et al., “Investigation of Characteristic Turbulent Coherent Structures in a Subcritical Carbon Dioxide Jet in a Multiphase Ejector,” Bulletin of the American Physical Society, 2024.
3. Bhaduri, S., et al., “Numerical Investigation of Cavitation Shedding in a Multiphase Flow with Sharp Density Gradient,” Bulletin of the American Physical Society, 2023.

Bhaduri, S., Peltier, L.J., Ladd, D., Groll, E.A., and Ziviani, D., “Regimes of a Decelerating Wall-Bounded Multiphase Jet Inside Ejectors,” Physics of Fluids, 37, 2025. DOI: 10.1063/5.0278015