Industrial CFD and Fluid Modeling in Engineering—2nd Edition

Following the success of the first edition of “Industrial CFD and Fluid Modeling in Engineering”, this second edition continues to showcase cutting-edge research that pushes the boundaries of computational fluid dynamics (CFD) in addressing complex industrial flow problems. In recent decades, advances in CFD algorithms and computing power have enabled simulations that were previously infeasible. Yet, applying CFD to realistic industrial scenarios remains challenging due to complex geometries, multiphysics couplings, and the need for validated modeling assumptions. The first edition laid a strong foundation by bringing together leading ideas in industrial flow modeling, with a particular emphasis on RANS validation in practical geometries and emerging CFD strategies. In this second edition, we build upon that foundation with 13 new contributions that highlight innovative methodologies and diverse applications—from improved turbulence models and optimization techniques to multiphase flow simulations—reflecting both continuity with the prior collection and significant new advancements. Each paper in this Special Issue illustrates how researchers are addressing challenges in industrial fluid mechanics through novel CFD approaches, collectively advancing the state of the art in the field.

We begin with a comprehensive review that bridges past and present modeling techniques, illustrating the continuity of research in industrial CFD. Delvar et al. present an extensive literature review on single- and twin-screw extruders for polymerization processes, tracing the evolution from early analytical models to modern CFD-based simulations. This review highlights progress in reactive extrusion modeling while underscoring the current challenges and future directions for CFD in this domain. The authors particularly emphasize that reactive extrusion poses unique difficulties due to the interplay of mixing, heat transfer, chemical reactions, and non-Newtonian fluid behavior under high shear, which is further complicated by multiphase flows and complex extruder geometries.

Notably, the themes identified in the review—such as multiphase flow management, turbulence modeling, and the need for efficient computation—resonate throughout many papers in this edition. The continuity between editions is evident: while the first edition emphasized foundational CFD approaches and their applicability, this second edition expands into innovative hybrid methods, design optimization, and cross-disciplinary techniques (including machine learning integration) to address industrial challenges. Collectively, these works maintain a scholarly dialogue with earlier studies, extending their scope into new industries and increasingly complex phenomena. In doing so, this Special Issue reaffirms the transformative role of CFD in engineering while pushing it into new and dynamic arenas.

Several contributions in this edition focus on multiphase flows and mixing processes, which are critical in various industries, from construction to aquaculture. Ferrari et al. [1] introduce a new numerical mixing index designed to quantify mixing efficiency in concrete production. By applying a statistical methodology to a transient Eulerian–Eulerian CFD simulation of a concrete truck mixer, they assess how aggregate particles and cement paste homogenize during the initial revolutions of the mixer. The proposed cell-based mixing index, defined using statistical measures of concentration, allows for a quantitative evaluation of distribution uniformity as mixing progresses. Their results show that as the drum rotates, material distribution improves and vortical structures enhance mixing, with the computed index increasing accordingly. This method offers a practical tool for the predictive evaluation of new mixer designs, enabling engineers to estimate how design parameters—such as internal geometry, rotation speed, and mixture composition—affect mixing outcomes prior to prototype construction. This capability streamlines the development of more efficient concrete mixers and is also applicable to other types of mixing equipment.

In the context of viscoplastic fluids, Benmoussa and Páscoa explore how impeller geometry can improve mixing performance. Their study examines a chamfered anchor impeller design for agitating non-Newtonian (yield-stress) fluids, comparing various chamfer angles to a standard design. Through CFD simulations conducted in an unbaffled mixing vessel, they evaluate each impeller’s ability to overcome yield stress, enhance flow circulation, and improve thermal homogeneity. The findings reveal that a 67.5° chamfered impeller significantly enhances flow distribution and reduces dead zones, particularly near vessel walls where stagnant regions often occur. Additionally, it promotes stronger vertical mixing and a more uniform temperature field, demonstrating that subtle geometric modifications at the blade tip can meaningfully impact the mixing of highly viscous fluids. These insights provide valuable guidance for designing more efficient mixers in industries such as food processing, polymer production, and chemical manufacturing, where handling viscoplastic fluids is common.

We examined the impact of the cut/sweep ratio of a “Lily” impeller on the distribution of dissolved oxygen in shrimp cultivation ponds. Aeration and oxygenation are crucial in aquaculture for maintaining water quality; in this case, five impeller designs with varying blade cut percentages were analyzed using CFD with a user-defined oxygen transport model. The simulations demonstrate that modifying the cut/sweep ratio substantially affects the pond’s flow patterns and oxygen dispersion. Specifically, variations in the impeller’s cut significantly influenced dissolved oxygen levels, dynamic pressure, and flow velocity throughout the pond. The “no-cut” impeller variant produced the highest average oxygen concentration and the strongest circulation, indicating superior aeration performance. However, the study also found that only the region immediately surrounding the aerator achieved sufficiently high oxygenation to sustain aquatic life, leaving distant areas under-oxygenated. These findings suggest that additional aerators or improved impeller designs are necessary to ensure a uniform oxygen distribution across large ponds. By quantifying how design modifications influence oxygen transfer efficiency, this work offers practical insights for developing better aeration systems in sustainable aquaculture.

Another key theme in this edition is the application of CFD for design optimization in aerodynamic and turbomachinery systems [2,3]. Yun et al. present a two-stage multi-objective optimization of a high-speed train’s nose shape, aimed at improving performance across multiple criteria. In the first stage, CFD-based shape optimization yields a more pointed nose that reduces aerodynamic drag by approximately 8.7% relative to the baseline model. Building on this, the second stage introduces additional objectives: minimizing tunnel micro-pressure waves (to reduce pressure transients when entering tunnels) and enhancing stability under crosswinds, while ensuring that drag remains near its minimized value. By applying constraints from stage one, the authors obtain a Pareto-optimal set of nose geometries that simultaneously reduce micro-pressure wave intensity and improve crosswind safety, with only a minimal (<1.5%) trade-off in drag relative to the single-objective optimum. This two-stage CFD optimization strategy exemplifies an effective balance between competing aerodynamic considerations. It provides railway engineers with a refined design that meets the stringent requirements of next-generation high-speed trains—reducing drag to enhance energy efficiency while mitigating tunnel pressure effects and stability risks. This study underscores how CFD-based multi-objective design can deliver innovative and practical solutions in vehicle aerodynamics.

In the realm of fluid machinery, Avanzi et al. [4] introduce ARES, a novel mean-line design and analysis code for axial-flow pumps, specifically developed for an “Outboard Dynamic-Inlet Waterjet”—a marine pump system inspired by aero-engine technology. The solver enforces radial equilibrium through streamlines along the pump’s meridional flow path, using empirical correlations to account for complex effects such as secondary flows, tip leakage, and end-wall losses. By comparing ARES predictions with experimental data from several test cases, including single-stage rotors and rotor–stator configurations, the authors assess the code’s accuracy across a range of operating conditions. At design point flow rates, ARES closely predicts hydraulic efficiency compared to measurements. Minor discrepancies emerge at off-design conditions, where loss models are less accurate, leading to increased errors in efficiency predictions. Nonetheless, ARES effectively captures radial distributions of pressure and velocity, particularly at midspan, though some complex end-wall boundary layer effects remain difficult to reproduce. This work demonstrates that simplified 1D/2D CFD approaches, like ARES, can provide fast and reliable tools for preliminary waterjet pump design, enabling engineers to rapidly evaluate design iterations with reasonable accuracy.

Holtmann and Key [5] focus on enhancing turbulence modeling fidelity for unsteady diffuser flows in centrifugal compressors. Building upon an “isolated diffuser” CFD methodology—which models the diffuser passage with an unsteady inlet boundary condition abstracted from the impeller to reduce computational cost—they address discrepancies from full-stage simulations caused by oversimplified inlet turbulence assumptions. To improve accuracy, the authors introduce a non-uniform turbulence inflow model for the isolated diffuser and assess its impact across multiple operating conditions, from choke to near-surge. This enhanced approach prescribes realistic spatial variations in turbulence at the diffuser inlet, resulting in significantly better agreement with full-stage results. Across four loading conditions, the isolated diffuser with non-uniform inlet turbulence yields much closer predictions of flow structures and one-dimensional performance parameters, matching full 3D simulations far better than the uniform-turbulence model. Importantly, this improvement comes without additional computational costs, preserving the efficiency advantage of the isolated model. By refining turbulence modeling in reduced-order simulations, this work offers more reliable and efficient design evaluations for vaned diffuser compressors, benefiting turbomachinery designers seeking faster turnaround times without sacrificing accuracy [6,7].

Beyond specific design studies, several papers in this issue contribute to enhanced CFD methodologies and the integration of CFD with other modeling approaches, expanding the tools available for industrial fluid dynamics. McConnell et al. [8] examine the performance of an advanced turbulence simulation technique—an Improved Delayed Detached-Eddy Simulation (IDDES)—in predicting unsteady aerodynamic flows. Using the canonical case of turbulent vortex shedding behind a triangular bluff body, they assess IDDES against both experiments and a traditional Delayed Detached-Eddy Simulation (DDES). The IDDES model captures key flow features with high fidelity, including recirculation length, velocity profiles, and Reynolds stress distributions, all of which align well with experimental data. However, compared to the simpler DDES, the IDDES exhibits a slight overprediction (about 4%) of recirculation zone length and a modest (about 3%) increase in the computational cost. Encouragingly, the IDDES maintains good accuracy even on coarser meshes, demonstrating its robustness. The study offers valuable guidance on the trade-offs of using the IDDES in industrial applications: while more complex, it can adaptively transition between RANS and LES modes to handle a wide range of flow regimes, providing improved predictive power for challenging cases such as bluff body flows, with only a minor increase in cost. This work contributes to the ongoing refinement of hybrid RANS–LES techniques for industrial CFD applications.

A notable cross-disciplinary innovation is presented by Santos et al., who develop a framework that integrates conventional simulations with machine learning (ML) to predict structural damage in subsea structures exposed to ocean wave conditions. The authors train an ML model on a dataset generated from a combination of analytical formulations (Morison’s equations for wave loading), finite-element structural analysis, and 2D/3D CFD simulations of wave–structure interactions [9,10,11,12]. This streamlined data generation strategy—combining fast analytical and reduced models with high-fidelity CFD—provides the ML model with diverse scenarios of wave parameters and corresponding structural responses. The resulting model can quickly predict key metrics of structural stress and damage under various ocean conditions. Validation against a six-month field experiment involving a benthic lander equipped with strain gauges confirms the accuracy of the predictions. The study demonstrates the feasibility of using trained ML surrogates to anticipate structural loads and potential damage in a fraction of the time required for full FSI simulations. This work exemplifies the potential of integrating CFD with machine learning and real-world data, signaling a future where AI-assisted CFD models support decision making in offshore engineering and other fields by delivering fast, reliable estimates of complex fluid–structure phenomena.

Ajmani et al. [13] address an important problem in public health and building engineering by developing an efficient co-simulation strategy for indoor airflow and pollutant dispersion. Focusing on a mechanically ventilated lecture hall, they combine a 1D fluid network model of the ventilation system with detailed 3D CFD and discrete particle modeling (DPM) to simulate the dispersion of exhaled aerosol particles representing respiratory droplets. This hybrid modeling approach significantly reduces computational costs by coupling a simpler network flow solver for ducts with high-fidelity CFD for room airflow. The study demonstrates that such a workflow can reliably predict local aerosol concentrations and identify poorly ventilated zones. The authors find that the existing ventilation system was imbalanced and inefficient at managing the aerosol distribution: despite a high overall air exchange rate, certain areas experienced prolonged aerosol residence and elevated concentrations. Through integrated 1D–3D simulations, they propose practical modifications (such as altering flow circulation paths via diffuser adjustments or adding fans) and show how these changes can be efficiently implemented within the co-simulation framework to markedly improve air quality. The findings underscore the value of CFD-based analysis in designing healthier indoor environments and highlight the benefits of coupling multi-scale models (network models for quick global insights with CFD for detailed local predictions) to optimize ventilation performance in large occupied spaces.

Caccavaro et al. [14] provide a valuable methodology-focused contribution by comparing mesh-based and meshless CFD approaches for simulating ship hydrodynamics. They examine a classic test case (a Wigley hull) and a full-scale 30 m ship hull using two open-source codes: OpenFOAM (an Eulerian, grid-based finite volume solver) and DualSPHysics (a Lagrangian, meshless smoothed particle hydrodynamic solver). Each approach is paired with an appropriate turbulence modeling strategy—RANS k–$ϵ$ in OpenFOAM and a particle viscosity model in SPH—and validated against experimental data. The comparative study reveals that mesh-based simulations (OpenFOAM) provide more compact resistance predictions with shorter computational times, while the meshless SPH approach excels in capturing free-surface deformations, such as wave profiles around the hull, with comparable accuracy. In practice, OpenFOAM delivers reliable drag force estimates rapidly, making it advantageous for iterative design processes, whereas DualSPHysics offers a better resolution of complex free-surface phenomena, like bow and stern waves, making it particularly valuable when detailed surface behavior is of interest. The authors discuss the trade-offs: the efficiency and robustness of the Eulerian approach versus the strengths of the Lagrangian method in handling complex interfaces and large deformations. By outlining the benefits and limitations of each, this work guides naval architects in selecting suitable CFD tools or combining them (e.g., applying SPH for specific components) to achieve a comprehensive assessment of a vessel’s hydrodynamic performance.

Taken together, the papers in this Special Issue underscore the diverse applications of CFD in contemporary engineering, demonstrating its remarkable versatility in tackling challenges across numerous sectors. From indoor air quality management to marine and agricultural engineering, CFD has become an indispensable tool for both analysis and innovation. For example, Hanspal and Cryer illustrate the widespread adoption of CFD within the agricultural industry, showcasing how a major agrochemical company employs CFD to address a broad spectrum of manufacturing and environmental challenges. Their article presents case studies ranging from optimizing pesticide production equipment to simulating pollutant dispersion in environmental scenarios—situations where experimental testing would be prohibitively costly, hazardous, or impractical. By digitally evaluating “what-if” scenarios—such as chemical plant explosion aftermaths or river contamination events—CFD enables engineers to predict outcomes and plan mitigation strategies in cases that would be impossible to fully test empirically. The inclusion of this study highlights CFD’s expanding role beyond traditional industries and underscores its critical importance in both process optimization and risk assessment. Similarly, the role of CFD in process safety and loss prevention highlights its critical contribution to hazard mitigation in industrial settings [15].

A particularly noteworthy addition to this collection is the contribution by Gutiérrez et al. [16], which explores the temperature effects on fluid dynamics inside a continuous casting tundish. Their study rigorously compares isothermal and non-isothermal CFD simulations, challenging long-standing assumptions. Through detailed analysis of buoyancy and inertial forces, as well as inclusion removal rates, the authors demonstrate that temperature gradients induce substantial changes in flow patterns, particularly in zones where buoyancy forces dominate. The findings reveal that while isothermal models may suffice under certain conditions—especially when flow control devices are present—non-isothermal simulations become essential when these controls are absent or weak, as temperature gradients significantly affect flow behavior and inclusion removal efficiency. This nuanced understanding of tundish hydrodynamics not only enhances process control but also informs more precise design and operational strategies in steelmaking.

In conclusion, this second edition of "Industrial CFD and Fluid Modelling in Engineering" exemplifies how cutting-edge CFD research is advancing both the accuracy and the scope of fluid flow simulations in industry. The collected studies explore new turbulence modeling techniques, propose efficient co-simulation and optimization frameworks, validate CFD approaches through novel experimental comparisons, and integrate CFD with other disciplines such as structural mechanics and machine learning. Collectively, these works aim to make CFD more reliable and impactful for addressing real-world engineering challenges [17]. By improving modeling fidelity and computational efficiency, these studies collectively push the boundaries of what CFD can achieve, while also paving the way for future innovations in industrial fluid mechanics. As the Guest Editor of this Special Issue, I would like to extend my sincere gratitude to all the authors for their high-quality contributions and to the reviewers for their rigorous and constructive feedback. I also wish to thank the editorial team for their invaluable support in bringing this second edition to fruition. Together, these efforts have produced a rich and insightful collection of papers that will undoubtedly stimulate further research and development in industrial CFD and fluid modeling.