The study, published in Frontiers in Water by researchers at the University of Technology-Iraq and Al-Mustansiriyah University in Baghdad, tackles a familiar bottleneck in early-stage engineering. Computational Fluid Dynamics, the workhorse simulation tool for studying how fluids move through hardware, delivers rich detail but demands considerable setup time, meshing effort, and computational cost, especially when dozens of geometries and operating conditions must be compared. Physical experiments are even slower. The research team, led by Luttfi A. Al-Haddad, therefore turned to Extreme Gradient Boosting, or XGBoost, an ensemble machine learning algorithm that combines many weak decision-tree learners sequentially to capture non-linear relationships while regularization keeps overfitting under control. Before settling on XGBoost, the authors compared it against alternative models and found it delivered the best overall prediction accuracy, error reduction, and classification stability for their dataset.

What makes the new framework distinctive is its data foundation. Rather than training purely on simulations, the model was built from a combined experimental and CFD-supported dataset drawn from published measurements of 3D-printed water-flow distributors. The experimental portion came from water-flow tests of three distributor families: rectangular manifold-type distributors and conical distributors, the latter both with and without an internal obstacle, each manufactured at heights of 13, 26, and 52 millimeters and tested across flow rates from 100 to 400 milliliters per minute. The simulation portion added Volume of Fluid (VOF) and single-phase flow results for selected conical configurations. Five input variables—distributor family, height, flow rate, data source, and simulation method—fed the model, while the prediction target was the non-uniformity flow coefficient, Φ, a percentage that quantifies just how far the flow sharing deviates from perfect uniformity.

The experimental baseline itself tells a striking geometric story. The worst performer, a shallow rectangular distributor labeled RD13, produced a maldistribution coefficient of 34.22 percent at the lowest flow rate of 100 milliliters per minute—meaning flow sharing was wildly uneven—before improving to 2.04 percent at 400 milliliters per minute. The taller RD52 began at 13.96 percent and also improved with flow rate. The conical geometries behaved far better: the CDO26 distributor with an internal obstacle varied only between 0.94 and 2.13 percent across all tested flow rates, while the smooth CD13 cone stayed between 0.63 and 2.30 percent. Averaged over all conditions, the best distributors, including CDO13, CDO52, and CD26, achieved average non-uniformity coefficients below one percent, whereas RD13 averaged a troubling 8.236 percent with a large standard deviation of 5.636. The lesson is clear: tapered, conical flow paths share water far more stably than rectangular manifolds, particularly at low flow rates where inertial forces are weak.

The CFD comparison added an important layer of nuance. Simulations using the Volume of Fluid approach captured the strong low-flow maldistribution of the tallest conical configuration, CDO52, much better than single-phase modeling, which produced smoother and generally lower predictions of Φ. For CDO52, the average experimental coefficient was 1.98 percent and the VOF average was a close 1.92 percent, while single-phase flow predicted only 0.73 percent. The authors attribute discrepancies between measurement and simulation to real-world effects that experiments capture but models idealize: 3D-printing tolerances, surface roughness, flow disturbances, and measurement variability on one side, and model assumptions, boundary conditions, and numerical formulation on the other. Rather than treating those differences as a problem, the team deliberately trained the AI on both data sources so the model would learn the realistic range of possible flow behavior instead of a single idealized version of it.

The machine learning architecture pairs regression with classification in a two-stage decision framework. The regression model predicts Φ as a continuous output, expressed as the sum of contributions from fifty regression trees, each with a maximum depth of two and a conservative learning rate of 0.05, alongside L1 and L2 regularization to suppress overfitting on the limited 90-sample dataset. A separate multiclass XGBoost classifier, using the multi:softprob objective, then assigns each design to one of four pragmatic severity categories defined by the authors: Low for Φ at or below 1 percent, Moderate between 1 and 5 percent, High between 5 and 10 percent, and Severe above 10 percent. These thresholds were introduced as engineering classification boundaries for comparative evaluation rather than adopted from any international standard, but they convert an abstract coefficient into an immediately actionable design verdict.

The performance numbers are impressive for such a compact dataset. Across the full combined dataset, the regression model achieved a coefficient of determination of 0.962, meaning it explained over 96 percent of the variance in maldistribution, with a mean absolute error of 0.126, a root mean square error of 0.161, a mean absolute percentage error of 4.87 percent, and a coefficient of variation of the RMSE of 6.12 percent. The best configuration-level performance came from the smooth CD26 cone, with an R² of 0.970 and MAE of 0.087, while the erratic RD13 rectangle proved hardest to fit, with an MAE of 0.185. Notably, the conical distributors yielded lower prediction errors across the board, consistent with their more stable flow behavior. The classifier matched this success, achieving 92.22 percent accuracy, 92.90 percent precision, 92.22 percent recall, and an F1-score of 92.36 percent.

Perhaps most encouraging is how the model failed. In the confusion matrix, it correctly classified 38 Low, 36 Moderate, 6 High, and 3 Severe samples, and every error landed in an adjacent severity class—never did a Low design get labeled Severe or vice versa. The predicted class distribution deviated from the actual distribution by only a sample or two in each category. To test generalizability beyond the fitting stage, the team evaluated a 50-sample holdout subset restricted to the Moderate class, chosen deliberately because it sits between the Low and High decision boundaries and therefore poses a sensitive discrimination test. The trained classifier correctly identified 47 of the 50 unseen samples as Moderate, an external accuracy of 94 percent, with the three errors again confined to neighboring classes and no sample mistaken for Severe.

The practical payoff is speed. Instead of running repeated CFD simulations or printing and testing distributor after distributor, engineers can use the trained model as a rapid screening layer that estimates both the magnitude and the severity of maldistribution for candidate geometries, then reserve detailed CFD and physical testing for the most critical or borderline cases. Detailed simulation remains essential for resolving pressure contours, secondary-flow structures, and velocity profiles that a tree-based surrogate cannot see, but the AI layer trims the brute-force search dramatically. The authors frame the work as a decision-support tool that maintains attention to pressure balance, flow uniformity, and stable convective heat transfer while accelerating preliminary thermal-fluid assessment.

The study also candidly acknowledges its limits. The dataset is small, built from published secondary measurements rather than newly generated laboratory data, and covers a restricted set of geometries, flow rates, and CFD cases; simulation values were available for only selected configurations, limiting the model’s generality across wider hydraulic conditions. Future work, the authors suggest, should expand the dataset with additional 3D-printed designs, broader flow-rate ranges, direct CFD outputs, pressure-drop data, temperature-field measurements, and heat-transfer indicators such as the Nusselt number, potentially incorporating physics-informed learning, uncertainty quantification, and digital-twin implementations. Even so, the message resonates well beyond water distributors: with the right combined experimental and simulation data, machine learning can compress weeks of simulation-and-prototype iteration into seconds of inference, offering engineers a fast, physics-aware first look at whether their design will share its flow evenly—or send one channel starving while another drowns.

Subject of Research: AI-based prediction of flow maldistribution in 3D-printed water-flow distributors using combined experimental and CFD data

Article Title: Prediction of flow maldistribution in 3D-printed water-flow distributors for thermal-fluid system design

Article References: Prediction of flow maldistribution in 3D-printed water-flow distributors for thermal-fluid system design. (n.d.). https://doi.org/10.3389/frwa.2026.1921076

Image Credits: AI Generated

DOI: 10.3389/frwa.2026.1921076

Keywords: flow maldistribution, 3D printing, water-flow distributors, XGBoost, machine learning, computational fluid dynamics, thermal-fluid systems, heat transfer, non-uniformity coefficient, Volume of Fluid, design screening, hydraulic engineering

A new computational study by Nahid Mirizadeh and Mohammad Manafpour, published in Results in Engineering, offers the most systematic answer yet. Using high-resolution computational fluid dynamics simulations in the open-source OpenFOAM platform, the researchers modeled a classical hydraulic jump at an upstream Froude number of 7.5, a regime typical of high-velocity spillway flows, while systematically varying the inflow air concentration from zero to fifty percent. Crucially, unlike most previous investigations, which examined only a handful of aeration levels, the study anchored every aerated scenario against a rigorously validated non-aerated baseline, allowing the progressive influence of air to be isolated and quantified for the first time across the full practical spectrum.

The numerical framework itself represents a careful exercise in verification. The team solved the unsteady Reynolds-averaged Navier-Stokes equations for a two-phase air-water mixture, tracking the free surface with the Volume of Fluid method, in which a scalar indicator function defines the fractional volume of water in each computational cell. Three turbulence closures were tested against laboratory measurements from the University of Queensland, where a horizontal rectangular flume 3.2 meters long, half a meter wide, and 0.41 meters high produced a well-defined jump with a Reynolds number near 140,000. The standard k-epsilon model emerged as the clear winner, predicting the roller length with only a 3.7 percent deviation from experiment, while the SST k-omega and Realizable k-epsilon models erred by 20 and 30 percent respectively.

Validation extended well beyond a single metric. The simulated free-surface profile matched laboratory data with a coefficient of determination of 0.99 and a Kling-Gupta Efficiency of 0.94, a score classified as excellent. The predicted secondary flow depth agreed with the theoretical Bélanger equation to within two percent, and velocity fields reproduced the characteristic structure of the jump: a high-velocity jet hugging the bed, a recirculating roller of reverse flow above it, and a shear layer between the two where turbulence is generated most intensely. A grid convergence analysis using the Grid Convergence Index confirmed that results were mesh-independent, with roller length varying by less than 2.5 percent between medium and fine grids.

With the model proven trustworthy, the researchers turned to the central question, and the answer they found is strikingly nonlinear. For aeration levels up to thirty percent, the free-surface profile of the jump barely budges, with normalized water depths changing by less than 1.5 percent. But at forty and fifty percent air concentration, the surface elevation at the beginning of the transition zone rises by roughly six to nine percent compared with the non-aerated case. The mechanism is physical rather than mysterious: the entrained air increases the volume of the air-water mixture and locally reduces its bulk density, forcing the flow to occupy a greater depth. For dam designers, this means that heavily aerated spillways may demand deeper tailwater to keep the jump anchored in its stilling basin.

The roller, the churning recirculation zone that gives the hydraulic jump its characteristic white-water appearance, responds even more dramatically. Low to moderate aeration of up to twenty percent lengthened the roller by 11.6 percent, but at forty and fifty percent aeration the roller stretched by 26.9 and 34.9 percent respectively. The authors attribute this elongation to two-phase flow mechanisms that slow the decay of turbulence: compressible air bubbles temporarily store turbulent energy and release it gradually, while buoyancy-driven secondary currents disrupt the main vortical structures. Because the mean streamwise velocity remains largely unchanged, the turbulence simply lingers longer, and the roller must extend downstream to complete the dissipation of kinetic energy. Since roller length often dictates the required basin length and the placement of baffle blocks, this finding carries direct consequences for structural design.

The most reassuring result concerns cavitation protection, the original motivation for pre-aeration in the first place. In the non-aerated simulation, the void fraction near the channel bed within the jump body remains essentially zero, leaving the boundary vulnerable to cavitation erosion. At forty and fifty percent inflow aeration, however, near-bed air concentrations reach approximately seven and twelve percent, with the higher value comfortably exceeding the eight percent threshold long associated with cavitation mitigation in the classic experimental literature. The study also confirms that peak air entrainment occurs in the initial portion of the shear layer, where the violent vortices at the jump toe drag air bubbles downward and transport them along the high-shear interface, in agreement with decades of experimental observation.

The velocity and turbulence fields reveal further subtleties. High aeration levels increased near-bed streamwise velocity by three to six percent, apparently because bubble penetration and slip effects reduce effective friction at the wall. While moderate, this change implies altered shear stresses that could shift scour patterns within and downstream of the stilling basin. Turbulent kinetic energy, meanwhile, peaked at the jump toe and concentrated in the shear layer, climbing by 18.3 percent at fifty percent aeration to reach approximately 2.76 square meters per second squared. Intriguingly, the normalized turbulence intensity first held steady, then rose sharply at thirty to forty percent aeration, and finally dropped at fifty percent, because the increase in maximum velocity outpaced the growth in turbulent fluctuations. The authors caution that RANS closures may underrepresent large-scale rotational eddies in highly aerated regions, suggesting that large-eddy simulation will be needed to fully resolve these structures.

Perhaps the most counterintuitive finding is what did not change: overall energy dissipation. Across the entire range of inflow air concentrations from zero to fifty percent, computed energy losses varied only between 63 and 64 percent, compared with 64.8 percent for the laboratory reference case. Because most of the entrained air is released downstream of the jump, the tailwater depth and velocity remain nearly identical to the non-aerated case, and the small residual differences stem mainly from variations in initial flow depth. This echoes earlier experimental work reporting less than two percent variation in dissipation between moderate aeration levels, and it means that pre-aeration delivers cavitation protection without sacrificing the jump’s core job of destroying excess kinetic energy.

Taken together, the results sketch a threshold-type picture of aerated hydraulic jumps that engineers can act on directly. Aeration up to twenty percent produces only minor hydraulic modifications, making it a low-cost, low-risk option. At forty percent and above, the benefits of robust cavitation protection arrive alongside measurable costs: deeper flow, rollers up to a third longer, higher near-bed velocities, and elevated turbulence that could increase dynamic loads on basin linings. The authors argue that these trade-offs should be explicitly built into tailwater calculations, basin dimensioning, and scour assessments for chute spillways and stilling basins operating at high Froude numbers. They also acknowledge the study’s limitations, including its reliance on RANS turbulence modeling, a two-dimensional idealization, and a single Froude number, and they call for future work spanning wider flow regimes, prototype-scale field validation, and design aids that translate these quantitative trends into practical engineering guidelines. For the dams that hold back the world’s rivers, even a few well-placed bubbles may prove to be the difference between a structure that endures and one that slowly crumbles.

Subject of Research: Effects of upstream flow aeration on two-phase hydraulic jump dynamics in rectangular channels using CFD simulation

Article Title: Progressive effects of upstream flow aeration on two-phase hydraulic jump dynamics in rectangular channels: a CFD investigation

Article References: Mirizadeh, N., & Manafpour, M. (2026). Progressive effects of upstream flow aeration on two-phase hydraulic jump dynamics in rectangular channels: a CFD investigation. Results in Engineering, 32, Article 113234. https://doi.org/10.1016/j.rineng.2026.113234

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113234

Keywords: hydraulic jump, CFD, OpenFOAM, pre-aeration, cavitation, stilling basin, spillway, two-phase flow, Volume of Fluid, turbulence, roller length, energy dissipation