Three-dimensional Voronoï analysis is performed to quantify both global and local aspects of clustering of inertial spheroidal particles in wall turbulence using data sets from a direct numerical simulation coupled with a Lagrangian point-particle approach. We consider oblate and prolate spheroids and characterize their inertia and shape by means of the Stokes number St and aspect ratio λ, respectively. It is observed that particles tend to drift toward the wall, and this tendency is most prominent for St = 30. Although inertia dominates over shape on the particle clustering, intermediate asphericity (λ = 0.33 and 3) is found to promote spheroids’ flux to the wall for St ≤ 30, while heavy spheroids (St = 100) with greater departure from spheres (λ = 0.1 and 10) distribute more evenly across the channel. The tendency of inertial spheroids to concentrate locally in preferred turbulence structures decreases with the distance from the walls. Owing to the particles’ preferential distribution in lower-than-mean fluid velocity regions, the local clustering of spheroidal particles decreases with the increasing asphericity. Particles with large inertia (St ≥ 30), especially spheres and prolate spheroids, are more likely to cluster in the viscous sublayer.

The wide use of pumps and turbines has significant value in energy conservation and utilization. In this work, a three-dimensional Computational Fluid Dynamics (CFD) model and a one-dimensional theoretical model of a Pump as Turbine (PAT) were established. On this basis, the correlation between pressure and velocity was quantitatively investigated by a proposed sensitivity index (SPV). A synergy field analysis was then applied to evaluate the flow characteristics of a pump and PAT, providing a perspective from the mechanism of the energy transfer enhancement for hydraulic devices. Moreover, the hydraulic and synergy performances of PAT were studied under various operating conditions. The results show that the minimum SPV is obtained in the impeller. With increasing flow rate, the SPV of the PAT generally increases, and the synergy angle of the impeller surface increases as well. A strong disordered synergy field is observed in regions of the blade leading edge, trailing edge, and volute tongue. The variations in efficiency and head with flow rate showed similar trends, respectively, with the synergy angle of the outlet and the mid-plane. This study provides an analytical method for quantitative evaluation of flow synergy characteristics, and it supplies a basis for further design improvement of the pump and PAT.

CO₂ is regarded as an effective and environmentally friendly refrigerant. Using a CO₂ ejector is a proven method for enhancing the effectiveness of a transcritical CO₂ refrigerant system. However, the complex internal flow of a CO₂ ejector, involving supersonic effects, phase change effects, metastable effects, and so on, makes it difficult to understand. In order to summarize the current state of the technology and knowledge gaps, this work provides a comprehensive literature review on CO₂ ejectors. In the first part, mathematical modelling and simulation calculations of CO₂ ejectors are presented, and an overview and classification of ejector models are given. In the second part, the structural optimization part of the ejector is described in detail, and the nozzle structure, the mixing chamber length, improvements to multi-jet systems, and the impact of these factors on the system performance are analyzed. In the third part, flow visualization is used to study the complex flow phenomenon, and the effect of the shock wave on the entrained rate of the ejector is discussed. Finally, the paper outlines the relationship between all ejector technologies, working fluids, and ejector performance and makes valid recommendations for further research and development of CO₂ ejectors.