The research targets a specific energy-system problem. At city gate stations, high-pressure natural gas is expanded before entering lower-pressure distribution networks, and the associated temperature reduction can encourage hydrate formation and the freezing of suspended water droplets. Conventional indirect gas heaters burn additional natural gas to preheat the incoming stream, typically to 55–85 °C. Because flat-plate collectors can provide low-temperature heat, the researchers modeled a collector comprising a glass cover, air gap, absorber plate, nine parallel copper riser tubes and insulated boundaries. Water, rather than natural gas, served as the working fluid, entering at 31 °C at flow rates from 0.02 to 0.05 kg/s under solar irradiance ranging from 200 to 1,200 W/m².

The three-dimensional conjugate heat-transfer model was implemented in ANSYS Fluent 17.0 with the finite-volume method. Continuity, momentum and energy equations were solved using Reynolds-averaged Navier–Stokes calculations and the standard k-epsilon turbulence closure, while the Boussinesq approximation represented buoyancy in the air gap. The simulations assumed steady operation, uniform flow through all nine tubes, fully developed flow inside the tubes, negligible solar-radiation loss from collector boundaries and temperature-dependent properties for water and air. Symmetry conditions allowed one tube and its adjoining collector section to be represented rather than the complete assembly. Solar input was estimated with an isotropic diffuse-radiation model, and collector efficiency was defined as the water’s useful enthalpy gain divided by incident solar energy on the aperture.

Numerical accuracy was assessed through mesh refinement, turbulence-model comparison, experimental measurements and an established analytical collector model. Three grids containing 1.2 million, 2.4 million and 4.8 million cells were tested. The apparent order of convergence was 2.12, and the Grid Convergence Index for thermal efficiency was 0.82%, below the researchers’ 2% acceptance threshold, so the 2.4-million-cell mesh was used for the parametric runs. Predicted tube temperatures agreed with measurements from a collector operated at 928 W/m², a 310 K inlet-water temperature, a 303 K ambient temperature and a 36-degree tilt; the average deviation was about 3.2%, with a maximum near the outlet of 4.8%. At baseline, CFD predicted 23.1% efficiency, compared with 22.8% from the analytical model and 22.4% experimentally.

Mass flow produced the clearest operational response. Increasing the water flow from 0.02 to 0.05 kg/s raised thermal efficiency from 21.6% to 24.6%, a relative improvement of about 14%. The modeled mechanism was stronger convective heat transfer at the tube walls: higher flow reduced boundary-layer resistance, lowered the average absorber temperature and consequently reduced radiative and convective losses from the collector’s upper surface. Useful heat gain rose from 401 to 457 W, while outlet-water temperature declined from 35.8 to 32.4 °C as the same heat was distributed over a larger flow. In the proposed application, heated water could be stored for later use rather than consumed immediately, allowing an array to favor heat collection through higher circulation rates.

Absorber construction was the second major lever. At the stated baseline, copper produced 24.6% efficiency, aluminum 22.8% and steel 18.2%, making copper 35% more efficient than steel. The absorber also acts as a fin, transferring heat laterally from the plate between tubes to the bonded contact points. Copper’s high thermal conductivity maintained a more uniform plate temperature and moved more absorbed solar energy into the water, whereas steel created larger temperature gradients and greater fin resistance. Increasing plate thickness from 0.1 to 0.6 mm raised efficiency from 19.8% to 22.8%, a 15.2% improvement associated with lower through-thickness resistance. Aluminum nevertheless delivered about 92.7% of copper’s performance in the model, although the study did not establish its economic advantage experimentally.

Geometry produced additional differences that would be concealed by treating the collector as a uniform system. At an equivalent 25 mm hydraulic diameter, circular tubes delivered 22.6% efficiency, compared with 21.2% for hexagonal, 19.8% for square and 18.4% for triangular tubes. The sharp corners of polygonal sections promoted flow separation and recirculation regions with weaker local heat transfer. Absorber placement proved similarly consequential: configurations with the plate below the tubes reached 24.2% and 24.0% efficiency, a mid-height arrangement produced 21.6%, and above-tube configurations yielded 19.2% and 18.8%. The estimated constriction resistance at the plate–tube interface fell from roughly 0.25 K/W for narrow line contact to about 0.04 K/W when broader area contact reduced the thermal bottleneck.

Optical properties had smaller but still measurable effects. Raising absorber absorptivity from 0.80 to 0.98 increased efficiency from 22.4% to 23.8%, a 6.3% relative gain. Increasing glass-cover transmissivity from 0.82 to 0.96 raised efficiency from 20.1% to 23.8%, or 18.4%. Irradiance behaved differently. Efficiency climbed from 18.2% at 200 W/m² to 23.1% at 928 W/m², but approached an asymptote of approximately 23.3% above 800 W/m². At high input levels, the hotter absorber increased radiative losses along with useful heat collection, leaving the efficiency ratio nearly unchanged. The authors interpret this saturation as a reason to size collectors and thermal storage around the full daily radiation profile rather than peak sunlight alone.

Two complementary sensitivity methods established the hierarchy behind these modeled trends. Morris screening used 50 trajectories with eight levels per parameter, while Sobol variance decomposition used 10,000 quasi-Monte Carlo model evaluations. For mass flow, the Sobol first-order index was 0.35 and the total-order index 0.41, indicating dominant influence with some interaction effects. Absorber conductivity followed at 0.22 and 0.29, while plate thickness produced 0.15 and 0.20. Tube geometry had a larger gap between its first-order and total-order indices, 0.11 and 0.16, indicating that its best choice depends partly on other settings. A quadratic response-surface model fitted to 50 central-composite design points had an R² above 0.95 and an adjusted R² above 0.92, providing the statistical basis for identifying parameter combinations within the modeled range.

The study converts the component results into a cautious system-level illustration rather than a demonstration at a gas station. For a representative station processing 100,000 standard cubic meters of natural gas per day and requiring a 45 K temperature rise, the authors estimated a continuous heating duty of 82.5 kW. Under their assumed irradiance and sunshine conditions, a 100 m² collector array operating at baseline efficiency was estimated to provide 13.1 GJ of heat annually, equivalent to about 0.5% of that duty and associated with 735 kg less carbon dioxide emissions. A larger array using the modeled high-performing settings was estimated to collect 73 GJ, or 2.8% of annual demand, and avoid about 4.1 tonnes of carbon dioxide. These projections depend on representative assumptions; the research did not perform a full techno-economic or life-cycle assessment.

Several limitations constrain direct transfer of the results to field installations. The steady-state model does not reproduce diurnal, seasonal or rapid cloud-driven changes, and its uniform-flow assumption may overstate real efficiency by an estimated 5–10% when headers distribute water unevenly. Headers, supports and fittings were omitted, water was the only working fluid, and wind speed and ambient temperature were fixed. Spectral optical effects were also neglected, although the authors estimate that they would generally alter performance by 1–2%. Most importantly, the optimized combination—higher flow, copper absorber, thicker plate, circular tubes and a below-tube absorber configuration—was not tested experimentally. The defensible conclusion is therefore that the validated numerical model identifies promising design priorities for solar-assisted natural gas preheating, while site-specific testing, transient modeling, flow-distribution analysis and full system optimization remain necessary before field benefits can be claimed.

Subject of Research: Computational optimization of flat-plate solar collectors for natural gas preheating applications

Article Title: CFD-based parametric analysis and design optimization of flat-plate collector geometry for low-carbon natural gas preheating in pressure regulating stations

Article References: Moondanizadeh, M., & Kianoush, P. (2026). CFD-based parametric analysis and design optimization of flat-plate collector geometry for low-carbon natural gas preheating in pressure regulating stations. Results in Engineering, 32, Article 113507. https://doi.org/10.1016/j.rineng.2026.113507

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113507

Keywords: flat-plate solar collectors, natural gas preheating, computational fluid dynamics, thermal efficiency, sensitivity analysis, absorber plate, tube geometry, thermal storage, city gate stations, solar thermal energy, CFD-based, parametric

The evaluation includes classical neural operators, geometric deep-learning methods, transformer-based neural solvers and implicit-field networks that use triplane representations. Specifically, the benchmark assesses the Fourier Neural Operator, PointNet, RegDGCNN, PointMAE, PointTransformer, Transolver, Transolver++, AB-UPT and TripNet, with 11 configurations evaluated in total. By placing these approaches within one standardized framework, CarBench is designed to support systematic comparisons between different ways of representing and modeling aerodynamic fields over three-dimensional vehicle geometries.

CarBench goes beyond standard interpolation tasks by including cross-category experiments. In these tests, representative transformer-based solvers are trained on a single car archetype and then evaluated on vehicle categories not represented in their training data. The purpose of this setup is to measure performance under changes in the distribution of test geometries, providing a direct assessment of cross-category generalization. The reported analysis covers both interpolation and cross-category evaluation, although the supplied research summary does not provide model-by-model numerical results or identify a single configuration as the overall winner.

Uncertainty is treated as part of the benchmark rather than as an afterthought. The framework includes metric-level uncertainty-estimation routines based on bootstrap resampling, allowing evaluation metrics to be reported with statistical variability. This is particularly important for a benchmark intended to make close comparisons among models, because apparent performance differences can be evaluated in relation to uncertainty in the measured metrics. The study’s comparison also includes computational efficiency, extending the analysis beyond conventional prediction error and pressure-field agreement.

The authors are releasing CarBench as an open-source framework, including the training pipelines, bootstrap-based uncertainty-estimation routines and pretrained model weights. The public repository is intended to give researchers a common basis for training and evaluating models on high-fidelity external automotive-aerodynamics simulations. CarBench does not establish that any tested surrogate can replace computational fluid dynamics or produce validated engineering benefits; its reported contribution is a reproducible benchmark for comparing model accuracy, pressure-field fidelity, efficiency, metric uncertainty and robustness when test geometries differ from those used for training.

Subject of Research: Benchmarking neural surrogates for high-fidelity three-dimensional automotive aerodynamics

Article Title: CarBench: A comprehensive benchmark for neural surrogates on high-fidelity 3D car aerodynamics

Article References: Elrefaie, M., Shu, D., Klenk, M., & Ahmed, F. (2026). CarBench: A comprehensive benchmark for neural surrogates on high-fidelity 3D car aerodynamics. Communications Engineering. https://doi.org/10.1038/s44172-026-00805-2

Image Credits: AI Generated

DOI: 10.1038/s44172-026-00805-2

Keywords: CarBench, neural surrogates, automotive aerodynamics, machine learning, computational fluid dynamics, DrivAerNet++, transformer models, geometric deep learning, pressure fields, model generalization, comprehensive, benchmark

The work is significant because it places five related profiles within one computational framework rather than drawing together results obtained under different domains, meshes, boundary conditions or flow settings. The investigators used identical computational domains, mesh characteristics, turbulence modelling, boundary conditions, inlet velocity and angle of attack for all five airfoils. The simulations treated the flow as steady, incompressible and turbulent, with the standard k–ε turbulence model, a uniform velocity inlet, a pressure outlet and a no-slip wall at the stationary airfoil surface. This common setup was intended to make geometry, rather than numerical methodology, the main source of variation in the comparison.

The computational model used a 100-millimetre chord and operated at a Reynolds number of approximately 2.2 × 10⁵. The researchers described this as a low-speed aerodynamic regime relevant to applications such as small aircraft and unmanned aerial vehicles. They generated the airfoil geometries with the standard NACA four-digit formulation and applied local mesh refinement around each airfoil to resolve near-wall flow and steep velocity gradients. A structured hybrid mesh dominated by eight-node hexahedral elements was used for the three-dimensional domains, whose outer boundaries were placed sufficiently far from the airfoils to reduce blockage effects.

Before comparing the five configurations, the team conducted a five-level mesh sensitivity test on the NACA 2408. The grids ranged from 84,620 cells with 20-millimetre elements to 417,380 cells with 8-millimetre elements. The predicted lift-to-drag ratio rose as the mesh was refined but approached a stable value: increasing the grid from 286,740 to 417,380 cells changed the ratio by only 0.10 percent. The researchers consequently selected the 286,740-cell mesh as a compromise between numerical resolution and computational cost, then applied it consistently to all five airfoils. The reported primary outputs were dimensional lift and drag forces, with L/D calculated directly from those forces rather than from lift and drag coefficients.

The results showed that the balance between lift and drag differed markedly across the family. NACA 2408 produced a reported lift force of 7,369.2 newtons, drag of 338.2 newtons and L/D of 21.79. NACA 2415 generated slightly less lift than NACA 2412, at 8,524.8 newtons, but substantially more drag, at 448.1 newtons, giving it a much lower L/D of 19.02. NACA 2418 and 2421 generated the lowest reported lift forces, 4,290.9 and 5,290.7 newtons, respectively, and also had the lowest drag values, 130 and 153.5 newtons. Their L/D ratios reached 33.01 and 34.47, but neither matched NACA 2412.

The pressure results also emphasized that absolute static pressure alone cannot explain the aerodynamic ranking. NACA 2408 and 2415 recorded the highest reported static pressures, 103,034 and 103,035 pascals, while NACA 2418 and 2421 recorded 101,242 and 101,178 pascals. NACA 2412 occupied an intermediate position at 102,553 pascals while achieving the highest lift and L/D. The investigators’ streamline analysis described faster flow over the upper surface and comparatively higher pressure below the airfoil, producing a pressure differential associated with lift. The relatively smooth streamlines and limited wake disturbance were interpreted as evidence of stable flow development at the selected zero-degree condition, although the study did not test a broad range of angles of attack or stall conditions.

To add experimental evidence, the researchers fabricated a geometrically similar 1:20-scale NACA 2412 model using high-resolution three-dimensional printing. The model, with a measured mass of 0.026 kilograms, was tested in a low-speed, low-turbulence subsonic wind tunnel with a 250-by-250-millimetre test section and an operating range of 2 to 40 metres per second. The experimental calculations used a reference area of 0.0907 square metres, while pressure points on the upper and lower surfaces were used to examine static-pressure distribution. The printed model preserved the selected airfoil’s camber, leading-edge radius and thickness distribution, allowing physical testing without the material cost and fabrication difficulty of a full-scale wing section.

The wind-tunnel model measured a lift force of 20.6 newtons, drag of 0.5828 newtons, static pressure of 101,432 pascals and an L/D ratio of 35.34. For a like-for-like numerical comparison, the team also ran a CFD case using the 1:20 geometry and the experimental flow conditions. That scaled simulation predicted 21.43 newtons of lift, 0.5920 newtons of drag, 101,513 pascals of static pressure and an L/D ratio of 36.20. The reported differences between scaled CFD and experiment were 3.87 percent for lift, 1.55 percent for drag, 0.08 percent for static pressure and 2.36 percent for L/D.

Those close numerical-experimental differences support the reported aerodynamic behaviour of NACA 2412, but they must be interpreted within an important limitation. Scaling the chord by 1:20 preserved geometric similarity, not dynamic similarity, and the model therefore operated at a substantially lower Reynolds number than the 100-millimetre CFD configuration. The physical measurements consequently provide complementary evidence rather than a strict Reynolds-number-matched validation. The researchers noted that small discrepancies could also arise from manufacturing tolerances, measurement uncertainty, flow non-uniformity, support interference and differences between numerical assumptions and practical tunnel conditions. The comparison was also limited to one selected profile, one zero-degree simulation condition, steady incompressible flow and five related airfoils.

Within that scope, the study identifies NACA 2412 as the most aerodynamically efficient of the five profiles in the common CFD comparison. Its leading result reflects a combination of high reported lift and comparatively low drag, not a universal advantage for every operating condition. The authors say further work should examine a wider range of Reynolds numbers and angles of attack, compressibility and advanced turbulence models such as SST k–ω, RSM, LES and DES. They also identify transient calculations, three-dimensional wing geometries, aeroelastic effects, fluid–structure interaction, optimisation, machine learning and multi-objective design as avenues for work that would better represent practical aircraft. The present results therefore offer a controlled baseline for preliminary airfoil selection, not a final determination of performance across real flight envelopes.

Subject of Research: Comparative low-speed aerodynamic performance of five NACA 24-series airfoils using CFD and wind-tunnel testing.

Article Title: Comparative aerodynamic analysis of NACA 24-series airfoils at low Reynolds number using computational fluid dynamics and wind-tunnel experiments

Article References: Sadaq, S. I., Kumar, P., Agarwal, A., Wa Kalenga, M. K., Yelamasetti, B., Saniya, S., & Singh, V. D. (2026). Comparative aerodynamic analysis of NACA 24-series airfoils at low Reynolds number using computational fluid dynamics and wind-tunnel experiments. Frontiers in Mechanical Engineering, 12, Article 1987465. https://doi.org/10.3389/fmech.2026.1987465

Image Credits: AI Generated

DOI: 10.3389/fmech.2026.1987465

Keywords: aerodynamics, NACA 2412, NACA airfoils, computational fluid dynamics, wind-tunnel testing, low Reynolds number, lift-to-drag ratio, airfoil efficiency, unmanned aerial vehicles, Comparative, aerodynamic, analysis

It also released the most energy per meter of enclosure depth and achieved the highest cyclic thermal efficiency among the simulated layouts, showing that the most effective design depends on balancing fin conduction, retained storage material and liquid circulation rather than simply adding more fin surface. The research used an enthalpy–porosity computational fluid dynamics model to represent the melting and solidification of Lauric acid. The PCM was treated as an incompressible, Newtonian, laminar medium, with buoyancy incorporated through the Boussinesq approximation.

Its phase-change interval extended from a solidus temperature of 316.65 K to a liquidus temperature of 321.35 K. Melting was considered complete when the domain-averaged liquid fraction exceeded 0.99, while solidification was considered complete when the average solid fraction exceeded 0.99. Carman–Kozeny momentum sinks damped flow in mushy and solid cells, while conjugate conduction was solved through the aluminum fins.

The cavity began fully solid at 298.15 K. During charging, the right vertical wall was maintained at 343.15 K while the left, upper and lower boundaries were insulated. Discharging began from the terminal charging field, or a nearly fully melted state, and the same active wall was reset to 298.15 K, below the Lauric-acid freezing interval.

The other boundaries remained insulated in both stages. Because the model was two-dimensional, energy and power were reported per meter of enclosure depth; end effects and depthwise circulation were not resolved. Four nested configurations were compared.

Case 01 was the finless baseline. Case 02 contained one L-shaped fin with a 132 mm vertical leg, a 52 mm horizontal leg and a thickness of 1.2 mm. Case 03 used two L-shaped fins, with leg dimensions of 132 by 52 mm and 88 by 40 mm; both were 0.6 mm thick.

Case 04 added a third, smaller pair of legs measuring 44 by 28 mm and reduced each fin’s thickness to 0.3 mm. This stepwise adjustment was intended to keep the PCM volume nearly similar among the finned cases, making it possible to compare fin geometry and conductive cross-section without treating a large change in material volume as the sole cause of performance. A single fin already produced a substantial change in the modeled thermal response.

Charging fell to 39.42 minutes, about 79.5% below the baseline, while discharging fell to 1,330.7 minutes, approximately 17.2% below the finless result. The two-fin configuration performed better across the complete cycle. Its charging time was another 8% shorter than that of the one-fin design, and its 1,223.3-minute discharging time was the lowest of the four cases.

It stored 1.8765 MJ per meter and released 1.7887 MJ per meter, corresponding to a cyclic thermal efficiency of 0.9532. Its average charging and discharging powers were also highest, at 862.78 and 24.37 W per meter, respectively. The three-fin configuration remained better than the finless baseline but did not surpass the two-fin design.

Its charging and discharging times were 115.75 and 1,347.7 minutes, and its cyclic efficiency was 0.9502. The simulations suggest that reducing each fin to 0.3 mm weakened its conductive cross-section even as additional surfaces were introduced. The extra solid boundaries could also restrict circulation in liquid regions.

In this model, therefore, adding more fin elements did not necessarily improve full-cycle performance once conduction, PCM volume and fluid movement were considered together. Transient fields illustrate two distinct roles for the fins. During charging, aluminum legs divided the original wall-driven melting front into several fronts and carried heat into areas that would otherwise remain conduction limited.

After local melting began, buoyancy-driven circulation around the legs redistributed heat through the liquid PCM. During discharge, the fins continued to shorten conduction paths and extract heat toward the cold wall, but their benefit was smaller. As solidification progressed, the growing solid layer suppressed natural convection and increased the resistance between the remaining liquid and the active wall.

Later-stage solidification was therefore more strongly conduction controlled than early-stage melting. Time histories supported this distinction. The finless cavity melted gradually as the front advanced from the hot wall, whereas the finned cases activated PCM around the fin network much earlier.

Wall heat-transfer rates peaked initially and then declined during both stages. During charging, the decline reflected a diminishing temperature difference as the adjacent PCM warmed; during discharge, it reflected increasing thermal resistance from the growing solid layer. Maximum fluid velocity increased after a liquid region formed during melting, but declined as the liquid volume contracted during solidification, indicating that natural convection made a larger contribution to charging than to the later discharge period.

Sensitivity calculations for the three-fin case showed that hot-wall temperature was the dominant influence on charging time. Raising it from 333.15 to 348.15 K reduced the modeled melting time from 51.40 to 18.50 minutes by strengthening both early conduction and later buoyancy-assisted transport. Cold-wall temperature had the strongest effect on discharge: increasing it from 293.15 to 308.15 K increased solidification time from 935.83 to 1,962.17 minutes.

Under the warmer discharge condition, recovered energy declined from 1,845.85 to 1,658.43 kJ per meter and cyclic efficiency fell from 0.9807 to 0.8811. Increasing the assumed latent heat from 170,000 to 200,000 J per kilogram raised stored energy from 1,748.76 to 1,984.15 kJ per meter and released energy from 1,650.34 to 1,887.29 kJ per meter, but lengthened both phase-change stages because more energy had to be absorbed and removed. The researchers then fitted quadratic response-surface models relating fin number and thickness to charging time, discharging time, stored energy and cyclic efficiency.

A central composite design supplied the modeling data, and a weighted Derringer–Suich desirability function combined the four objectives. The models for discharging time and cyclic efficiency showed strong agreement, with R² values of 0.9937 and 0.9995 and predictive Q² values of 0.9016 and 0.9930. The charging-time and stored-energy models also had R² values of 0.9182 and 0.9295, but each had a negative predictive Q², indicating weaker leave-one-out prediction.

Consequently, the continuous desirability maximum could not be presented as a statistically validated optimum. An apparent high-desirability region near three fins and a thickness of approximately 0.73 mm, with a composite value of about 0.895, was therefore treated only as a candidate for confirmation rather than the final design. Numerical checks supported the finest tested grid and two-second time step for comparative calculations, but they did not establish experimental accuracy.

Grids of 31 by 71, 45 by 105 and 61 by 141 control volumes produced charging completion times between 22.20 and 25.27 minutes for the representative three-fin case. The variation was not strictly monotonic, which the authors linked to changes in the alignment of the moving phase-change band and fin edges with grid faces. Time-step tests from one to four seconds produced values identical at the displayed precision, although rounding could conceal smaller transient differences.

Within the study’s stated limits, the direct comparison identifies two moderately thick L-shaped fins as the strongest full-cycle design among the cases actually simulated, not as a universal optimum for every enclosure. The model omitted radiation, fin–wall contact resistance, three-dimensional effects and experimentally measured property uncertainty, and its four prescribed layouts did not cover all possible fin topologies. Establishing a dependable continuous optimum would require a larger space-filling set of CFD cases, non-quadratic surrogate models, repeated cross-validation, confirmation simulations and three-dimensional experimental validation.

The central engineering result is nevertheless clear within the tested system: one fin provides a major charging benefit, while two preserve a more favorable balance of conduction, storage capacity and liquid-phase transport than three very thin fins.

Subject of Research: CFD optimization of L-shaped fins for full-cycle Lauric-acid phase-change thermal energy storage

Article Title: Multi-objective optimization of Lauric-acid PCM storage in a rectangular enclosure using L-shaped longitudinal fins: Mathematical modeling, design, and simulation

Article References: Rasool, G. (2026). Multi-objective optimization of Lauric-acid PCM storage in a rectangular enclosure using L-shaped longitudinal fins: Mathematical modeling, design, and simulation. Results in Engineering, 32, Article 113558. https://doi.org/10.1016/j.rineng.2026.113558

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113558

Keywords: Lauric acid, phase-change material, thermal energy storage, L-shaped fins, computational fluid dynamics, enthalpy–porosity method, multi-objective optimization, response surface methodology, natural convection, solidification, thermal conductivity, Multi-objective

The computer-based lab is integrated into the 'Process Heat Transfer' module offered to undergraduate and postgraduate chemical engineering students. Over three-hour sessions, students build a digital model of a double pipe heat exchanger in COMSOL Multiphysics, defining the geometry, applying boundary conditions for velocity, pressure, and temperature, and then solving the coupled mass and heat transport equations. Once the model is built, students generate color-coded maps of the velocity, temperature, and pressure fields within both the inner tube and the surrounding annulus.

These visualizations reveal characteristic features of turbulent pipe flow, including a flat velocity profile across most of the pipe cross-section with steep gradients near the wall due to the no-slip condition. The pressure field shows that the annulus side experiences higher pressure drops than the inner tube, prompting class discussions about which fluid should be routed through which passage to minimize pumping costs. The temperature field demonstrates how the two streams exchange heat along the length of the exchanger.

Students observe that the stream with the lower heat capacity rate undergoes a larger temperature change, and that the temperature difference between the hot and cold fluids decreases with distance in a parallel-flow arrangement but is sustained along the entire length in counter-flow operation. This visual evidence helps explain why counter-flow heat exchangers achieve higher thermal effectiveness than parallel-flow designs. To validate the simulation results, students compare the computed heat transfer effectiveness against the analytical effectiveness-NTU relationship.

The agreement between the COMSOL simulations and theory is excellent, with relative deviations of less than 1.5 percent across all tested conditions. The exercise also introduces students to practical design trade-offs: while increasing the heat exchanger length raises effectiveness, the gains diminish beyond a certain point, and longer exchangers incur higher pressure drops and operating costs. The researchers evaluated the pedagogical impact using anonymous pre- and post-tests consisting of nine true/false questions targeting common misconceptions about heat exchanger operation.

The average number of correct answers increased from 7.35 to 8.12 out of nine, a statistically significant improvement confirmed by Welch's two-sample t-test (p = 0.030) with a moderate-to-large effect size (Hedges' g = 0.77). The largest gains appeared in questions related to counter-flow configuration, which was the primary exercise students completed during the session. Student feedback collected through an anonymous survey was overwhelmingly positive.

All respondents appreciated the opportunity to receive training on a computational software package, and 92 percent acknowledged that the laboratory helped them better understand heat exchanger operation. Approximately 73 percent expressed interest in applying the software to future projects, including final-year design projects and master's research. Students particularly valued the ability to visualize phenomena discussed in lectures and to interact with an industry-relevant tool.

The authors acknowledge several practical considerations for institutions wishing to adopt a similar approach. Because students typically have no prior experience with COMSOL Multiphysics, detailed installation guides, step-by-step video tutorials, and progressively released solution files are essential. In-class support from lecturers and teaching assistants is crucial during the early stages of model construction, particularly when students define geometries and boundary conditions.

Once a working model is established, students become more independent and focus on interpreting results and exploring alternative operating scenarios. The study's findings support the broader integration of simulation-based learning environments into engineering curricula. By developing a digital model that serves as a cognitive tool, the exercise encourages students to undertake parametric studies and explore more advanced problems, reinforcing theoretical concepts while building computational competencies increasingly demanded in modern engineering practice.

The module has since expanded to include plate-fin and shell-and-tube heat exchanger sessions, extending the same modeling workflow to more complex industrial geometries.

Subject of Research: A computer-based CFD laboratory using COMSOL Multiphysics for teaching heat exchanger design to chemical engineering students

Article Title: Teaching heat exchanger design using COMSOL Multiphysics in a computer-based lab

Article References: Pini, R., Büchner, D., Millan-Agorio, M., Eckel, A.-M., Hejazi, S. A. H., Zavate, A.-G., & Zhang, Y. (2026). Teaching heat exchanger design using COMSOL Multiphysics in a computer-based lab. Discover Education, 5(1), Article 911. https://doi.org/10.1007/s44217-026-02039-y

Image Credits: AI Generated

DOI: 10.1007/s44217-026-02039-y

Keywords: heat exchanger, COMSOL Multiphysics, computational fluid dynamics, chemical engineering education, process heat transfer, double pipe heat exchanger, active learning, simulation-based learning, counter-flow, effectiveness-NTU, student misconceptions, Imperial College London

The work targets a computationally demanding part of cerebrovascular analysis. Patient-specific computational fluid dynamics can estimate three-dimensional velocity, pressure and wall-shear-stress fields from medical images, but each analysis requires segmentation, geometry repair, mesh generation and an iterative numerical solution. Repeating that process across many aneurysm shapes or inlet-flow conditions can become prohibitively expensive. A reusable surrogate could accelerate parametric studies and potentially provide rapid hemodynamic estimates during vascular interventions, although the study did not test clinical use or robot navigation. Its results concern steady, incompressible Newtonian flow in idealized vessel models derived from a computational dataset.

PIReN represents a flow field as the sum of a learnable baseline and a residual correction. Its inputs are a point’s three-dimensional coordinates, the local equivalent vessel diameter and the inlet mass flow rate; its outputs are three velocity components and pressure. A compact baseline branch with two fully connected hidden layers supplies the overall flow pattern. A dual-branch decoder then adds localized corrections. One branch processes the baseline together with the input variables, while a second, “prior-aware” branch extracts flow-conditioning features independently of the baseline. Both use residual multilayer perceptron blocks with 128 features in the default configuration, and a channel-wise gate adaptively combines their outputs.

Training combined a supervised mean-squared-error loss with dimensionless residuals from mass continuity and the steady Navier–Stokes momentum equation. The continuity term penalizes violations of incompressibility, while the momentum term measures the consistency of velocity gradients and pressure gradients with fluid motion. Automatic differentiation calculated the required spatial derivatives in physical units, and characteristic scales estimated from the training subset made the two residual terms numerically comparable. Their weights rose gradually: continuity was inactive for the first 15 epochs and reached its final value after epoch 40, while momentum began at epoch 40 and reached its final value after epoch 90. This staged activation was intended to prevent the physics terms from overwhelming data fitting early in optimization.

The dataset was assembled from the open Aneumo intracranial-aneurysm computational fluid dynamics collection. Seven deformable models derived from one patient anatomy formed geometry set A, while 16 models from a second anatomy formed set B. Each model was evaluated at five inlet mass flow rates from 0.0025 to 0.0040 kilograms per second, corresponding to Reynolds numbers of approximately 250 to 720. Points where all velocity components vanished were removed as no-slip wall locations, and 20,000 interior points were sampled from each file. The researchers used a blood density of 1,060 kilograms per cubic meter and dynamic viscosity of 3.45 × 10−3 pascal-seconds, matching the original simulations.

The main in-domain experiment was an optimistic interpolation test rather than a test of extrapolation. Geometry set A was divided into training, validation and test subsets at an 8:1:1 ratio, allowing a held-out point to have nearby training neighbors. Under that protocol, PIReN used 186,472 trainable parameters, compared with 199,940 for the standard physics-informed network and 173,956 for the supervised model. Its mean normalized absolute error was 1.11%, versus 1.61% for the standard network and 1.84% for the supervised model. Its continuity residual, DIV, was 0.0113, compared with 0.0858 and 4.7996, respectively, while its momentum residual, MOM, was also lower. On representative sections, 72.1% of PIReN test points met the predefined continuity criterion |DIV| < 0.01, against 28.3% for the standard network and 4.8% for the supervised model.

Ablation experiments separated the effects of architecture from those of the physics losses. Removing the residual decoder was the most damaging architectural change: aggregate relative error rose from 11.34% to 30.89%, and DIV increased to 1.2314. Removing the baseline field produced a smaller accuracy penalty, with error reaching 12.16%, but DIV rose to 0.0442. Replacing channel-wise gating with simple concatenation and linear projection yielded 12.69% error and a DIV of 0.0514. The physics constraints produced a different trade-off. Removing both governing-equation losses actually lowered in-domain pointwise error to 9.64%, but DIV surged to 3.0351, about 269 times the full model’s value, and MOM increased to 26.4607. Their principal role was therefore to suppress physically inconsistent solutions rather than minimize interpolation error in this setup.

In a zero-shot test, a model trained only on geometry set A was evaluated without adaptation on all 16 models in set B. PIReN’s aggregate error increased from 11.34% on set A to 42.71% on set B, whereas the standard physics-informed network rose from 16.57% to 121.92%. On the unseen geometry, PIReN reduced error by 65.0% relative to the standard network; it also produced 82.1% lower mean normalized absolute error, 93.1% lower DIV and 82.2% lower MOM. This was nevertheless a compound distribution shift: the two sets came from different anatomies, had different morphologies and occupied nonoverlapping coordinate frames about 29.7 millimeters apart. Their characteristic physical diameters differed by only 1.2%, so the result cannot isolate generalization to morphology alone.

Five-fold leave-one-flow-rate-out testing produced a similar pattern. In each fold, one of the five flow rates was entirely withheld while the model was trained on the other four. Across the folds, PIReN’s average aggregate error on the held-out conditions was 36.83%, compared with 106.11% for the standard physics-informed network, a 65.3% relative reduction. PIReN also had lower mean normalized absolute error, DIV and MOM in all five held-out conditions. A stricter spatial-block test then removed neighboring-point leakage by holding out one of five contiguous regions along the vessel axis. Averaged over the five flow conditions, PIReN achieved an aggregate relative L2 error of 0.3035 ± 0.0255 under this protocol, versus 0.3927 ± 0.0285 for the standard network. PIReN performed better in all 40 combinations of four metrics, two partition schemes and five flow configurations, and its absolute error margin widened when the test became spatially stricter.

Several limitations define what the experiments do—and do not—establish. The models assumed steady flow, rigid walls, incompressible Newtonian fluid and no explicit boundary penalties; physics losses were evaluated only at sampled interior points. The continuity formulation also omitted an additional geometric contribution where local diameter changes rapidly, particularly near bifurcations and aneurysm necks, so reported DIV values may underestimate local mass-conservation errors there. The study used synthetic CFD reference data, rigid-wall models and two related anatomy groups rather than independent patient cohorts. It did not evaluate pulsatile flow, compliant vessels, fluid–structure interaction or clinical decision-making. The researchers also note that simply enlarging either model did not guarantee better performance: both architectures worsened at their largest tested sizes, underscoring that the favorable result came from a specific combination of architecture, data protocol and physics-based regularization rather than from raw model capacity alone.

Subject of Research: Physics-informed neural-network reconstruction of cerebrovascular flow fields in intracranial aneurysm models

Article Title: Cerebrovascular flow field reconstruction method based on residual network of physical information

Article References: Teng, Z., Hou, Y., Liu, J., & Wang, Q. (2026). Cerebrovascular flow field reconstruction method based on residual network of physical information. Frontiers in Bioengineering and Biotechnology, 14, Article 1970931. https://doi.org/10.3389/fbioe.2026.1970931

Image Credits: AI Generated

DOI: 10.3389/fbioe.2026.1970931

Keywords: physics-informed neural networks, intracranial aneurysms, cerebrovascular flow, surrogate modeling, Navier–Stokes equations, computational fluid dynamics, out-of-distribution generalization, hemodynamics, Cerebrovascular, flow, field, reconstruction

The work is a computational demonstration based on simulation data, not a field trial, and the preprint is currently under review in Wind Energy Science. The reference simulations used in the study covered terrain domains as large as 3 by 3 kilometres at 30-metre resolution and represented the flow around solar installations and wind turbines at 0.5-metre resolution. Obtaining these fields with a conventional computational fluid dynamics calculation is expensive, particularly when many candidate configurations must be considered.

The proposed surrogate is intended to address that computational cost by producing full fields rapidly after it has been trained against OpenFOAM results. The first architecture tested was a point-wise hybrid model combining a coordinate multilayer perceptron with two-dimensional convolutional terrain encoders. The second was a three-dimensional grid-based U-Net.

Both predict the local wind velocity and kinematic pressure rather than a single summary value for a site. The two families were designed as two-stage cascades: an initial model estimates the broad terrain-scale background, and a second stage refines the prediction around the structures. Both cascades were trained as physics-regularised surrogates, meaning that their losses combined disagreement with the CFD reference data with penalties for departures from specified physical and numerical conditions.

Those penalties covered mass conservation, momentum conservation, the prescribed inflow profile, outlet pressure, and impermeable lateral and top boundaries. This training arrangement links the learned predictions to the governing conservation requirements and boundary conditions represented in the reference setup. It does not mean that the networks solve the full CFD equations from first principles; the study evaluates them as learned surrogates trained from simulations, with additional penalties for violations of selected constraints.

With the full training budget of 292 domains, the final models produced normalised wind-speed root mean square errors of approximately 0.16 over the global background domain and 0.17 within regions of interest. The two architectures reached comparable aggregate values. Pressure was more difficult over the full domain, where the normalised root mean square error was about 0.24, while the corresponding regional value was around 0.12.

The authors also address a definitional ambiguity in kinematic pressure, which is physically determined only up to a constant. Removing the arbitrary offset for each case with a gauge correction lowered the global pressure error to roughly 0.18–0.20 and the regional error to about 0.09. Matched comparisons between physics-regularised and data-only models indicated that the clearest contribution of the additional penalties was consistency with mass and momentum conservation rather than a decisive improvement in supervised accuracy.

Differences in wind-speed error were within the spread between random training seeds, so the study did not establish a distinct accuracy advantage on that measure. The physical residuals showed more direct effects: continuity and momentum residuals were approximately halved in regions containing structures and were reduced by 15% to 65% at terrain scale when physics penalties were included. In other words, the regularised models better respected the conservation behaviour encoded in the training setup while retaining broadly similar agreement with the CFD data.

The researchers also used active learning to expand the simulation dataset. Beginning with 120 domains, they added simulations according to a score-based selection procedure until the training set contained 292 domains. This expansion reduced terrain-scale test error by about 30%, with the normalised wind-speed root mean square error decreasing from 0.26 to 0.18.

At a matched training budget, the score-based selection strategy outperformed random selection. The reported result supports targeted acquisition of additional simulations within this particular setup, but the training process still depends on the availability of CFD outputs and does not demonstrate that new simulations will no longer be necessary. Although their aggregate error levels were similar, the two architectures showed a practical trade-off.

The point-wise hybrid model attained the best aggregate errors and could evaluate flexible point locations, allowing selected outputs to be obtained without requiring only a complete grid prediction. The three-dimensional U-Net better resolved channelling jets between closely spaced structures. Such narrow flow features were scarcely registered by volume-averaged metrics, which could therefore make the models appear more alike than their spatial outputs actually were.

The comparison does not establish one architecture as universally superior: the hybrid performed better in aggregate error, while the U-Net captured specific fine-scale structures more effectively. The main practical attraction is the time required to obtain a prediction. Once trained, the surrogate returns complete wind and pressure fields in seconds, making rapid micro-siting comparisons, alternative layout evaluation and preliminary loading studies feasible without launching a new high-resolution CFD calculation for every iteration.

The results do not show that the system can replace OpenFOAM for every application. The study is limited to steady-state RANS reference simulations over complex Swiss terrain and the specific solar and wind-energy structures represented in the dataset, and its performance was assessed against those simulations rather than an equivalent body of field measurements. The preprint remains open for discussion and has not yet completed journal peer review.

Within those limits, the study presents a practical division of labour between high-cost simulation and rapid inference. OpenFOAM simulations provide the reference data from which the surrogates learn, while score-based selection identifies cases for further acquisition. After that development stage, the trained networks can explore many fine-scale scenarios in seconds.

The central measured finding is not that physics penalties made the surrogate uniformly more accurate, but that they improved conservation consistency with little clear change in wind-speed accuracy, while active learning improved terrain-scale test performance and two complementary architectures exposed different spatial strengths. Together, these results suggest that physics-aware neural surrogates could accelerate renewable-energy layout exploration while preserving the detailed three-dimensional fields needed for engineering evaluation.

Subject of Research: Neural-network surrogates for wind and pressure fields over complex terrain and renewable-energy structures

Article Title: Physics-regularised neural network surrogates for fine-scale wind and pressure fields over complex terrain and structures

Article References: Gasser, J., Frischholz, Y., & Lehning, M. (2026). Physics-regularised neural network surrogates for fine-scale wind and pressure fields over complex terrain and structures. https://doi.org/10.5194/wes-2026-179

Image Credits: AI Generated

DOI: 10.5194/wes-2026-179

Keywords: neural-network surrogates, computational fluid dynamics, wind flow, pressure fields, complex terrain, renewable-energy siting, wind turbines, photovoltaic structures, physics-informed learning, active learning, Physics-regularised, neural

The study was published in the Annals of Biomedical Engineering and analyzed MRI data from 218 people, from whom 240 stenosed and 106 non-stenosed carotid bifurcations were reconstructed. Some participants contributed both sides: among the 128 people with two bifurcations, 47 had different disease status on the left and right. The stenosed group had a mean area-based narrowing of 34.74% with a standard deviation of 16.98 percentage points. Because several patients contributed more than one artery, the researchers also used subject-clustered analyses and cross-validation in which both sides from a person remained in the same data fold. These safeguards did not materially change the main results.

MRI was performed on a 3-tesla clinical scanner using an electrocardiographically triggered, time-resolved three-dimensional phase-contrast sequence. An automated neural-network segmentation system isolated the vessels, achieving a median Dice similarity coefficient of 0.88 on its test set. The processed velocity fields were then used to define inlet and outlet boundary conditions for computational fluid dynamics simulations. These simulations were conducted as quasi-direct numerical simulations with a maximum cell size of 0.07 millimeters, locally refined around stenoses and the carotid bulb, and five near-wall cell layers. Each case covered three cardiac cycles, with the first two discarded so that the reported averages were not dominated by the initial condition. A typical simulation required about 21 hours on 256 processor cores.

To model blood, the investigators used a Newtonian fluid with a viscosity of 0.004 pascal-seconds and a density of 1,060 kilograms per cubic metre. The vessel walls were assumed to be rigid, and the external carotid outlet used a zero-normal-gradient condition, meaning that no specific pressure level or flow rate was imposed there. The internal carotid outlet flow was adjusted to conserve mass while retaining the MRI-derived division of flow between the internal and external carotid arteries. These assumptions are standard simplifications, but they mean that the absolute simulated shear measurements are model-dependent. The authors cited prior estimates indicating that geometric uncertainty can affect carotid wall-shear calculations substantially more than rheology, although rigid and compliant walls can still produce marked differences in peak systolic wall stress.

Among 240 stenosed and 106 non-stenosed bifurcations, several geometric differences were clear. Stenosed arteries had significantly larger bifurcation angles, internal carotid angles, tortuosity and offset flow divider, with adjusted analyses preserving these associations at a p-value below 0.001. The offset flow divider was a new automated descriptor designed to quantify lateral displacement of the actual flow divider from the projected centerline, providing information about apex asymmetry that conventional angles do not directly capture. A four-feature model using bifurcation angle, internal carotid angle, offset flow divider and internal carotid planarity achieved a cross-validated area under the receiver operating characteristic curve, or AUROC, of 0.767, with a 95% confidence interval of 0.716 to 0.818. Its recall was 0.90 for stenosed cases but only 0.39 for non-stenosed cases, confirming that the model is not a ready-made diagnostic test.

The stenosis label itself was assigned from morphometric criteria applied to the same segmented three-dimensional surfaces used for the geometric measurements. One mechanism identified reduced cross-sectional roundness, with a threshold of 0.95, while another detected a relative change of at least 3% per millimetre along a branch. This shared imaging foundation creates an important limitation: the classification and anatomical features are not fully independent, and the study demonstrates association with prevalent stenosis rather than the ability to forecast future narrowing. The modest discrimination also reflects an imbalance in the cohort, since 69.4% of the bifurcations were stenosed. In a balanced version of the model, sensitivity was 0.76 and specificity 0.67, with no improvement in overall discrimination.

Patient-specific simulations in 101 stenosed and 75 non-stenosed bifurcations revealed a more detailed relationship between anatomy and flow. The degree of narrowing itself correlated only weakly with the post-stenotic hemodynamic indices: the correlations were 0.09 for time-averaged wall shear stress, 0.28 for the oscillatory shear index and -0.13 for relative residence time. By contrast, the ratio describing expansion immediately beyond the stenosis was associated with stronger disturbance. In moderate stenoses, expansion correlated with the oscillatory shear index at r = 0.80 and with the backflow index at r = 0.77. The association weakened among severe cases, although the researchers did not formally test whether correlations differed between severity groups and noted that estimates in the smallest subgroup were sensitive to one influential case and to acquisition differences.

The clearest result emerged in the 75 non-stenosed bifurcations. After the measured outcomes were normalized by each participant’s mean common carotid flow rate, models based on seven geometric features explained 57.5% of the variation in minimum time-averaged wall shear stress, 60.3% in maximum relative residence time and 49.0% in maximum oscillatory shear. Bulb area was the largest independent correlate of low wall shear and long residence, uniquely accounting for 22.6% and 21.2% of their variance, respectively. Area ratio was the strongest independent correlate of oscillatory shear, with a unique contribution of 18.2%. A composite ranking of internal carotid angle, bulb area and area ratio correlated with the combined low-shear, high-oscillation and long-residence profile at Spearman rho = 0.750, although this was an exploratory within-sample result rather than independent validation.

Representative cases illustrated the contrast: four non-stenosed bifurcations with large bulbs had relative residence times of roughly 7 to 17, compared with about 0.7 to 1.1 in four cases with small bulbs. Their wall maps showed the largest low-shear and high-oscillation regions along the outer wall of the internal carotid artery, a location commonly associated with plaque initiation. The findings are not evidence that a particular individual will develop plaque, nor do they establish that the measured flow patterns cause atherosclerosis. The cross-sectional design cannot determine whether abnormal geometry created the flow disturbance, plaque remodeling produced both altered angles and stenosis, or both processes contributed. The cohort was older, lacked external validation, did not model plaque composition, and drew from two MRI acquisition protocols with different velocity-encoding settings. Despite these constraints, the analysis identifies measurable anatomical variables for longitudinal testing: the structure of the carotid bulb may reveal a disturbed-flow environment even before narrowing becomes apparent, while post-stenotic expansion may describe the local flow burden more fully than narrowing percentage alone.

Subject of Research: Associations between carotid bifurcation geometry, stenosis, and simulated local hemodynamics

Article Title: Hemodynamic and Geometrical Parameters Associated with Carotid Artery Stenosis: A Cross-Sectional Study Using 4D Flow MRI and CFD

Article References: Mokhtari, A., Bergmann, A., Strecker, C., Andrae, J., Harloff, A., & Obrist, D. (2026). Hemodynamic and Geometrical Parameters Associated with Carotid Artery Stenosis: A Cross-Sectional Study Using 4D Flow MRI and CFD. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04417-x

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04417-x

Keywords: carotid stenosis, 4D flow MRI, computational fluid dynamics, arterial geometry, wall shear stress, atherosclerosis, blood flow, carotid bifurcation, medical imaging, Hemodynamic, Geometrical, Parameters

The problem, according to Hamza Latif Mehr, Imran Akhtar, and Haris Moazam Sheikh, is decades of inherited intuition. Drag-based Savonius rotors and lift-based Darrieus turbines were shaped by engineering judgment built on horizontal-axis research, but vertical-axis turbines live in a fundamentally different aerodynamic world. Their blades sweep through the wind, stall, and recover in a continuously rotating flow, so the shapes that work best do not necessarily resemble anything a designer would sketch by hand. The team’s answer was to remove human intuition from the loop almost entirely, letting an algorithm morph blade shapes into configurations no conventional parameterization would ever produce.

The centerpiece of the framework is a technique called Design-by-Morphing, or DbM. Instead of manipulating control points on a blade surface the way traditional shape parameterization methods do, DbM treats entire geometries as points in a continuous space. Any two shapes bounded by a single continuous surface are topologically compatible, meaning they can be mapped onto one another through a set of collocation points. New blades are then generated by morphing among a set of baseline shapes with smooth weight factors, allowing both interpolation between existing designs and, crucially, extrapolation beyond them through negative weights that produce geometries unlike any of the originals.

For this study, the researchers chose three conventional vertical-axis turbine profiles as their morphing baselines: the lift-based Darrieus NACA 0021 airfoil, a hybrid cusped Gottingen 395 profile, and the drag-based Savonius bucket shape. By varying two spherical weight factors across a discretized range, the framework generated 169 distinct blade morphologies, many of them hybrids that combine drag and lift characteristics in proportions no human designer would have proposed. When blade tilt, inter-blade spacing, vertical placement, tip-speed ratio, and rotation direction were added, the complete design space swelled to roughly 5.8 million unique configurations.

Extrapolation comes with a catch. Negative morphing weights occasionally produce self-intersecting blade profiles or blades that overlap one another in physically impossible ways. Rather than discarding these candidates and shrinking the design space, the team built automated geometric correction algorithms that detect intersections, reorder coordinate points, and smooth sharp curvature until a valid continuous contour emerges. The corrections proved remarkably gentle: among the corrected geometries that produced positive power, the enclosed area changed by less than one percent on average, and none of the three highest-performing designs required any correction at all.

Evaluating each candidate required an unsteady computational fluid dynamics simulation, which is expensive enough that brute-force search across millions of designs would be hopeless. The optimizer therefore needed to be stingy with its simulations, and the researchers turned to Bayesian optimization through a framework called MixMOBO. The algorithm builds a Gaussian-process surrogate model of the design space, balancing exploration of uncertain regions against exploitation of promising ones, and adaptively selects from a portfolio of acquisition strategies including Expected Improvement, Probability of Improvement, GP Upper Confidence Bound, and Thompson Sampling. Before unleashing it on the turbines, the team validated MixMOBO on five standard benchmark functions, confirming it reliably approached the global optimum within the allotted budget.

The optimization campaign began with 50 randomly sampled designs evaluated by CFD, followed by 180 sequentially proposed candidates, for a total of 230 simulations. The best configuration emerged remarkably early, after just 13 optimizer-guided evaluations, landing at the 63rd simulation of the entire campaign. Its blade geometry, defined by morphing angles of 120 and 179 degrees with zero horizontal offset and full vertical placement, reached a power coefficient of 0.3285 at a tip-speed ratio of 1.17. That represents a 21.26 percent improvement over the maximum power coefficient of the reconstructed Savonius benchmark and a 77.8 percent improvement over the Darrieus benchmark, within the same two-dimensional numerical framework.

The winning design is a strange creature: an extrapolated DbM geometry that resembles a high-solidity drag-based shape with contours borrowed from lift-based profiles. Its azimuthal torque rises smoothly from a minimum near the start of rotation to a sharp peak of 10.01 at about 115 degrees of azimuth before declining with stall, and the curve mirrors itself across the second half of the revolution. Fast Fourier analysis of the torque signal revealed a dominant spectral peak at 4.44 hertz, almost exactly matching the expected two-blade passing frequency of 4.46 hertz, indicating that the principal torque fluctuation comes from clean, periodic blade loading rather than chaotic aerodynamic instability. Vorticity contours showed a coherent vortex forming along the blade, detaching, and convecting downstream in a stable periodic street.

Sensitivity analyses added further texture to the result. Conventional wisdom suggests that introducing an overlap gap between Savonius buckets can improve efficiency by directing flow through the inter-bucket passage, but the optimizer’s best geometry performed best with zero spacing, achieving 29.4 percent higher maximum power than a spacing ratio of 0.09 and 38.8 percent higher than 0.18. Pressure contours revealed why: the gap creates a localized pressure depression that equalizes the pressure difference across the torque-producing blade surfaces, bleeding away useful aerodynamic torque. A Reynolds number sweep showed the design is tuned for moderate Reynolds numbers around 4 times 10 to the fifth, performing 15.83 percent better there than at 1.3 times 10 to the sixth, where lift-based designs generally dominate.

The authors are careful about what the numbers mean. Because the entire campaign ran in two-dimensional unsteady Reynolds-averaged Navier-Stokes simulations, the reported 21.26 percent gain is a relative prediction within that common numerical framework, not an experimentally demonstrated performance improvement. Three-dimensional effects such as tip losses and spanwise flow remain uncaptured, and the best-found geometry has not yet been validated experimentally or in 3D CFD. The optimization also targeted a single objective, cycle-averaged power coefficient, leaving starting torque, structural loads, and noise for future multi-objective work. Still, the framework itself is the real prize: a scalable, sample-efficient pipeline that couples morphing-based geometry generation with Bayesian optimization, ready to be pointed at any expensive aerodynamic design problem where human intuition has run out of ideas.

Subject of Research: A data-driven framework combining Design-by-Morphing and Bayesian optimization to discover high-performance vertical-axis wind turbine blade shapes beyond conventional designs.

Article Title: A data-driven design framework for wind turbines via Design-by-Morphing and Bayesian optimization

Article References: Mehr, H. L., Akhtar, I., & Sheikh, H. M. (2026). A data-driven design framework for wind turbines via Design-by-Morphing and Bayesian optimization. Results in Engineering, 32, Article 113463. https://doi.org/10.1016/j.rineng.2026.113463

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113463

Keywords: vertical-axis wind turbines, Design-by-Morphing, Bayesian optimization, computational fluid dynamics, blade shape optimization, Savonius turbine, Darrieus turbine, power coefficient, aerodynamic design, renewable energy, data-driven, design

The research team, led by Soo Hyun Ryu, Young Jin Kim, and colleagues at Yonsei University in South Korea, confronted a limitation that has shaped bioprocess engineering for decades. The conventional scale-up parameter for stirred-tank reactors, power input per unit volume (P/V), depends on impeller characteristics such as rotational frequency, impeller diameter, and power number. Those impeller-based calculations simply do not exist for rocking systems, which have no impeller at all. When engineers try to transfer a process from a stirred tank to a rocking bioreactor, they lack a common currency for comparing how much energy each system dissipates into the culture. The result is a costly cycle of trial-and-error experiments every time a process crosses platform boundaries.

To break that cycle, the team proposed power dissipation per unit volume (Pd/V) as a platform-independent measure of energy input. Unlike impeller-based P/V, Pd/V can be computed directly from the fluid flow field itself, regardless of how the mixing is generated. The researchers built a computational fluid dynamics (CFD) framework using the lattice Boltzmann method (LBM), a numerical technique that solves the Boltzmann equation on a discrete lattice rather than the traditional Navier-Stokes equations on a mesh. This approach, combined with large eddy simulation (LES) for turbulence modeling, allowed the team to resolve the turbulent flow structures inside each bioreactor with high fidelity while running efficiently on graphics processing units.

The CFD simulations covered three distinct platforms: a 2-liter stirred-tank reactor (STR), a 1-D rocking bioreactor (RM20), and an orbital-rocking system (CELBIC50). Each was simulated under diverse operating conditions, spanning different agitation rates, rocking angles, and filling volumes. The simulations revealed that the three platforms produce strikingly different flow patterns even when their overall energy inputs appear similar. Stirred tanks generate localized high-energy zones around the impeller blades, while rocking systems distribute energy more uniformly through the bulk liquid through periodic sloshing and wave motion. These differences matter because cells respond not just to average conditions but to the full spectrum of shear stresses and energy dissipation rates they experience over time.

From the resolved flow fields, the team extracted three key hydrodynamic parameters: power dissipation per unit volume, shear stress, and mixing time. Shear stress, the tangential force per unit area that the fluid exerts on itself, is a critical concern for mammalian cells, which lack the protective cell wall of bacteria and yeast. Mixing time, the time required to achieve homogeneity after a perturbation, determines how quickly nutrients, oxygen, and pH control agents distribute through the vessel. By combining these three parameters into a multi-constraint design space, the researchers created a quantitative map of feasible operating regions for each platform, allowing engineers to identify conditions that satisfy all constraints simultaneously across different reactor types.

The hydrodynamic analysis revealed meaningful differences among the platforms. Under the selected operating conditions, the orbital-rocking CELBIC50 exhibited a lower mean shear stress of 0.012 Pa compared with 0.019 Pa in the 1-D rocking RM20, and it achieved a shorter mixing time of 80.9 seconds versus 146.6 seconds. In other words, the orbital system was both gentler on the fluid and faster at homogenizing it, a combination that would be difficult to predict without the CFD framework. The Kolmogorov length scale, the smallest turbulent eddy size in the flow, provided an additional lens for comparing energy dissipation patterns across platforms, connecting the microscopic structure of turbulence to the macroscopic performance of the bioreactor.

The critical question, of course, was whether these hydrodynamic differences actually affect cell culture performance. To find out, the team ran fed-batch CHO cell cultures producing a monoclonal antibody under the selected conditions in all three platforms. The results were remarkably consistent: viable cell density, productivity, metabolite profiles, and product quality attributes remained comparable across the STR, RM20, and CELBIC50, with most performance variables falling within a common ±2 standard deviation range. Product quality was assessed using capillary electrophoresis–sodium dodecyl sulfate (CE-SDS) and capillary zone electrophoresis (CZE), confirming that the antibody molecules themselves were structurally equivalent regardless of which bioreactor produced them.

This finding carries significant implications for the biopharmaceutical industry. Process transfer between platforms currently demands extensive empirical experimentation, consuming time, materials, and labor that could otherwise support development of new therapies. A validated CFD-based design space changes that equation by allowing engineers to predict, before running a single experiment, which operating conditions in a new platform will reproduce the hydrodynamic environment of the original. The framework supports what the field calls model-informed process development, an approach aligned with modern regulatory expectations for quality by design (QbD), where processes are understood and controlled through systematic, science-based reasoning rather than accumulated trial and error.

The study also fits into a broader movement toward digital twins in biomanufacturing. The research was funded in part by a Korean government program to develop a digital twin system for high-yield fed-batch culture of antibody therapeutics based on AI-QbD technology. Digital twins, virtual replicas of physical processes that update in real time with sensor data, depend on exactly the kind of validated hydrodynamic models this study provides. As single-use bioreactors continue to expand across the industry, the ability to map processes between platforms computationally will become increasingly central to flexible, efficient production of biologics.

For the field of bioprocess engineering, the message is clear: the hydrodynamic design space defined by Pd/V, shear stress, and mixing time offers a common language for describing bioreactor performance across platforms that mix liquid in entirely different ways. Rather than treating each bioreactor type as an isolated system with its own empirical rules, engineers can now use a unified, physics-based framework to identify transferable operating conditions. The study demonstrates that cells grown under hydrodynamically matched conditions perform equivalently, regardless of the mixing mechanism, providing a quantitative foundation for the next generation of biopharmaceutical process development.

Subject of Research: Bioprocess engineering and computational fluid dynamics for bioreactor process transfer

Article Title: Hydrodynamic design space for process transfer across different bioreactor platforms

Article References: Ryu, S. H., Kim, Y. J., Kang, D. E., Kim, M. H., Kim, T.-J., & Hong, J. K. (2026). Hydrodynamic design space for process transfer across different bioreactor platforms. Applied Microbiology and Biotechnology. https://doi.org/10.1007/s00253-026-14067-7

Image Credits: AI Generated

DOI: 10.1007/s00253-026-14067-7

Keywords: computational fluid dynamics, bioreactor hydrodynamics, process transfer, hydrodynamic design space, power dissipation per unit volume, CHO cell culture, biopharmaceutical manufacturing, single-use bioreactors, lattice Boltzmann method, quality by design, Hydrodynamic, design