Aqueous redox flow batteries (ARFBs) have attracted significant attention in the field of electrochemical energy storage due to their high intrinsic safety, low cost, and flexible system configuration. However, the advancement of this technology is still hindered by several critical challenges, including capacity decay, structural optimization, and the design and application of key materials as well as their performance within battery systems. Addressing these issues requires systematic theoretical foundations and scientific guidance. Numerical modeling has emerged as a powerful tool for investigating the complex physical and electrochemical processes within flow batteries across multiple spatial and temporal scales. It also enables predictive performance analysis and cost-effective optimization at both the component and system levels, thus accelerating research and development. This review provides a comprehensive overview of recent progress in the modeling of ARFBs. Taking the all-vanadium redox flow battery as a representative example, we summarize the key multiphysics phenomena involved and introduce corresponding multi-scale modeling strategies. Furthermore, specific modeling considerations are discussed for phase-change ARFBs, such as zinc-based ones involving solid–liquid phase transition, and hydrogen–bromine systems characterized by gas–liquid two-phase flow, highlighting their distinctive features compared to vanadium systems. Finally, this paper explores the major challenges and potential opportunities in the modeling of representative ARFB systems, aiming to provide theoretical guidance and technical support for the continued development and practical application of ARFB technology.

Proton exchange membrane water electrolysis is a promising technology for large-scale green hydrogen production due to its high efficiency, compact design, and rapid dynamic response. However, its commercialization is strictly limited by high material costs, durability issues, and complex multiphysics coupling within the membrane electrode assembly. This work provides a comprehensive and critical review of key physicochemical processes and advanced predictive modeling approaches for PEMWEs. To capture recent paradigm shifts, we introduce an innovative multi-dimensional classification framework—incorporating spatial resolution, temporal dynamics, and methodological paradigms—to critically evaluate lumped-parameter, continuum, microscale, and multiscale models, explicitly defining their applicability bounds and inherent limitations. The fundamental mechanisms governing electrode kinetics, membrane water transport, and gas–liquid two-phase flow are analyzed, establishing state-of-the-art quantitative benchmarks for microstructural parameters and advanced 3D flow field topologies under high-current-density and high-pressure regimes. Furthermore, we systematically examine model validation rigor, typical prediction errors, and the critical failure of static models in capturing dynamic property shifts during extreme bubble breakthrough. Recent breakthroughs integrating in situ diagnostics, pore-scale simulations, density functional theory, and Physics-Informed Neural Networks are extensively discussed. Future efforts must prioritize mechanical–electrochemical–thermal coupling, transient degradation prognostics, and machine learning-driven predictive digital twin technologies to overcome current empirical limitations and accelerate the gigawatt-scale deployment of PEMWE systems.

The application of liquid lithium as a coolant for the forthcoming era of space nuclear reactors exhibits significant potential, and spiral tube heat exchanger components are commonly used in steam generators for reactors. However, the heat transfer characteristics of liquid lithium in spiral tubes are not yet fully understood. This research establishes a non-isothermal heat transfer model incorporating a modified turbulent Prandtl number to analyze the flow of liquid lithium through spiral tubes with varying geometries. Numerical analysis is carried out focusing on the influence of inlet velocity, the distribution of related parameters, and the geometry of spiral tubes. The results demonstrate that in the range of the dimensionless Dean number 8165–13,063, the Nusselt number and the pressure drop present approximately linear relations with the Dean number. For the distribution law of relevant physical quantities, the inner side of the tube displays an eye-anatomy low-flowrate area and a high-temperature area, while a low-pressure area forms on the inner pipe wall. Finally, the pitch and spiral radius are found to be reduced as much as possible to ensure high liquid lithium-based heat transfer performance with a small pressure drop. The optimized design parameters reveal that within the actual design range of non-dimensional pitch of 0.667–10.667 and curvature of 0.0556–0.1667, the non-dimensional pitch and curvature are 0.667–2.667 and 0.1667, respectively. This study offers valuable insights into the heat transfer properties of liquid lithium within heat exchangers of the spiral tube design, promoting its application in space nuclear reactor power supply.

Liquid lithium is expected to be the promising coolant for the next generation of space nuclear reactor power sources, and pipe structures have critical impacts on the flow and heat transfer characteristics, whereas related studies are still incomplete. In this work, a steady-state non-isothermal heat transfer model with modified turbulent Prandtl number is developed for the turbulent flow of liquid lithium in elbows with different bends. The results demonstrate that liquid lithium has best performance in a 90 deg bend in the Pe range of 320–955, which has the highest heat transfer performance per unit pressure drop and exhibits the lowest entropy generation. Due to the difference in flow velocity between the inner and outer sides of the pipe, a high-temperature region exists in the inner-wall area from the pipe bend and migrates from the wall side to the center area in the exit area. When decreasing the flow velocity and increasing the wall heat flow density, a more significant increase in the percentage of the high-temperature region is demonstrated on the inner wall side of the pipe in the exit area of the bend. Under a given total length of L, the inlet length H with the H/L ratio of 0.025 has the minimum entropy generation within the unit pressure drop, and is the best U-tube structure. This work provides comprehensive investigations on flow and heat transfer characteristics of liquid lithium in bends and U-tubes and inspires practical applications.

Liquid lithium is widely regarded as an optimal cooling medium for space nuclear reactors due to its exceptional heat transfer properties and low density. However, the helium bubbles generated by liquid lithium under space irradiation pose significant hazards to the safe and stable operation of nuclear reactions. This study employs the COMSOL finite element software to construct the level-set two-phase flow models and bubble stream model separately to investigate the local accumulation of helium bubbles and the overall flow of low-concentration gas–liquid mixtures. The main focus is on examining the different distributions of multiple helium bubbles randomly generated in local liquid lithium and the influence of boundary conditions on their accumulation morphology, as well as the impact of low-concentration bubble stream on their overall heat transfer performance. Agglomerated bubbles with radii between 5 μm and 150 μm are classified into three categories based on local concentrations: circular (≤20.37%), irregular elongated (up to 30.44%), and banded (up to 36.31%).The interconnected banded bubbles can be up to 8 times larger than irregularly elongated ones, and they have a positive effect on the distribution of physical quantities and wall temperature perturbations in the pipeline. The increase in inlet velocity triggers bubble impacts and fragmentation, further reducing thermal resistance and enhancing heat transfer performance. When the bubble diameter is less than 15 μm and the bubble concentration is within 1%, the influence of the mixed flow on overall heat transfer is not significant. This study provides insights for manipulating bubble structure and guiding localized and comprehensive thermal analyses.