Critical heat flux is a major thermal limit in water-cooled nuclear reactors because heat-transfer deterioration can produce a rapid rise in fuel-cladding temperature and potentially damage the cladding. Under non-uniform axial heating, the local margin is not determined solely by pressure, mass flux, geometry, or equilibrium quality. It also depends on where heat has been deposited earlier along the channel, which alters the evolving two-phase flow and thermodynamic state. Engineering methods commonly begin with a critical heat-flux value for equivalent uniform heating and then apply a correction representing the axial power history. The study keeps that structure, using a frozen neural network trained on a large uniform-heating database as the baseline and training a compact transformer only to estimate the additional non-uniform-heating correction.

The experimental basis was a benchmark-ready database derived from non-uniform critical-heat-flux measurements compiled in a Korea Atomic Energy Research Institute report. Its 888 experiments were divided among inlet-peaked, middle-peaked, outlet-peaked, and spike-like axial power profiles. Before modeling, the researchers excluded 39 cases with two-phase inlet conditions because the frozen uniform-heating backbone produced unreliable predictions for them. They also excluded 123 cases that required the backbone to extrapolate beyond its diameter, mass-flux, or equilibrium-quality ranges. The resulting 726 experiments were randomly divided at the experiment level into training, validation, and test sets at 70%, 15%, and 15%. These exclusions define the model’s applicability domain and are not intrinsic limitations of the transformer architecture. A separate leave-one-profile-family-out evaluation tested what happened when an entire heating-profile family was withheld from training and validation.

For each axial location, the transformer received the normalized axial position, local equilibrium quality, and normalized axial heat-flux shape as a sequence token. Average heat flux and mass flux were also included, while mass flux was treated as a global operating-condition variable because it was conserved along the steady, constant-area test channels. The model used one encoder layer, a 32-dimensional embedding, two attention heads, a 64-unit feed-forward layer, GELU activation, and 0.10 dropout. No index-based positional encoding was added because physical axial position was already represented explicitly. A causal attention mask prevented downstream locations from influencing the correction at an upstream location, allowing the correction to depend on the current and accessible upstream history without using information from the future. After attention, a two-layer feed-forward head predicted an unconstrained value that was mapped to a positive correction factor through a bounded exponential transformation.

Training targeted the experiment-level minimum departure from nucleate boiling ratio, the minimum local thermal margin that determines the limiting critical-heat-flux condition. The objective penalized squared deviation of that minimum from a value of one while regularizing corrections away from unity along the sequence. This differs from pointwise training on the local critical heat flux, because the experimental data provide an experiment-level critical condition rather than separate local targets at every axial position. The researchers stated that alternative objectives, including logarithmic percentage-error losses, were not evaluated. Predicted correction factors ranged from 0.354 to 2.948 across all locations in the primary test set and from 0.814 to 2.493 at the transformer-selected limiting locations, so the numerical bounds were not approached closely. The authors also emphasized that the broad bounds were safeguards against extreme training values, not mechanistic limits on physical critical heat flux.

On the primary random split, the frozen uniform-heating neural network without any non-uniform correction substantially overpredicted the limiting critical heat flux. Its prediction-to-measurement mean was 1.247, its standard deviation was 0.388, and its mean absolute percentage error was 0.313. Applying the classical correction reduced the standard deviation to 0.143 and the mean absolute percentage error to 0.122. The Tong F-factor correction also improved on the uncorrected neural network but was less accurate on this test set, with a standard deviation of 0.246 and mean absolute percentage error of 0.178. Look-up-table predictions had still greater scatter, although they were evaluated on 108 of the 109 test cases because one middle-peaked case selected a limiting location outside the usable quality range. On the common 108-case subset, the transformer retained lower standard deviation and error than the classical correction, so the conclusion did not depend on the excluded look-up-table case. Paired bootstrap comparisons using 200,000 experiment-level resamples produced 95% confidence intervals below zero for differences in error and scatter, although no multiple-comparison adjustment was applied.

Results differed by axial profile. The transformer had lower scatter and mean absolute percentage error for the inlet-peaked and middle-peaked cases, which made up most of the test set. For 15 outlet-peaked cases, its standard deviation was close to that of the classical correction, while its error and mean were slightly better. Only one spike-like case appeared in the primary test set, so its result could not support a profile-level conclusion. The leave-one-family-out analysis revealed the model’s most important limitation. It retained lower scatter and error when the middle-peaked family was hidden, but performed worse than the classical correction when either the inlet-peaked or outlet-peaked family was held out. For the unseen inlet-peaked family, transformer scatter and mean absolute percentage error were 0.332 and 0.349, versus 0.235 and 0.200 for the classical correction. The corresponding held-out outlet-peaked values were 0.250 and 0.224 for the transformer and 0.182 and 0.152 for the baseline. Generalization to an entirely unseen profile family was therefore uneven.

Input ablations showed that the transformer relied on more than a single thermal variable. Removing global mass flux increased prediction scatter from 0.115 to 0.150, indicating that channel-level mass flux supplies important scaling information. Removing the normalized heat-flux profile raised scatter to 0.144, making the model comparable to the classical correction in that measure. Removing equilibrium-quality history produced the largest mean absolute percentage error among the ablations, 0.115, and shifted the prediction-to-measurement mean below unity. The complete model therefore provided the best balance of scatter, bias, and absolute error in the reported test set. The model also transferred between axial resolutions without retraining: a model trained at 200 locations was evaluated at 40, 100, 200, and 400 locations, and its prediction-to-measurement standard deviation remained between 0.114 and 0.115. The study did not investigate alternative global-conditioning strategies, and the results did not establish that the particular conditioning strategy used was optimal.

Robustness testing also exposed variation associated with model initialization. Across four training seeds, the transformer produced a lower mean absolute percentage error than the classical correction in every run. It reduced prediction scatter in three runs, but one seed yielded a standard deviation of 0.164, above the classical correction’s 0.143, although that seed still had a lower mean absolute percentage error of 0.115. The researchers said that engineering use would require further characterization or mitigation of this stochastic variability. Ensembling was suggested as a possible strategy but was not tested. Attention diagnostics at selected limiting locations showed that the model generally distributed attention over multiple accessible upstream positions rather than depending on one point. Weighting changed with the power-profile shape, including concentrations nearer earlier high-power regions for some profiles and closer to the downstream high-power region in an outlet-peaked case. These visualizations were treated as qualitative representations of learned information flow, not direct proof of physical causality or a complete account of any prediction.

Overall, the study shows that a small causal transformer can learn useful sequence-dependent corrections for critical heat flux under non-uniform axial heating while preserving a familiar engineering formulation. Its strongest reported advantage was narrower prediction error on the primary benchmark, with additional support from ablations, resolution-transfer tests, seed checks, and paired bootstrap analysis. Its weaknesses were equally concrete: the non-uniform database was small and imbalanced, unseen profile families produced inconsistent results, and the baseline was specific to one frozen uniform-heating neural network. The study did not compare alternative baseline predictors or establish an improved allowable design margin, because the statistical treatment of prediction errors and other uncertainties needed for such a limit was not developed. The authors characterized the result as a data-driven correction-factor model rather than a mechanistic model of critical heat flux.

Subject of Research: Machine-learning correction of critical heat-flux predictions under non-uniform axial reactor heating

Article Title: A transformer-based correction factor for critical heat flux prediction under non-uniform axial heating

Article References: Bourisaw, R., & Iskhakov, A. S. (2026). A transformer-based correction factor for critical heat flux prediction under non-uniform axial heating. Frontiers in Mechanical Engineering, 12, Article 1980739. https://doi.org/10.3389/fmech.2026.1980739

Image Credits: AI Generated

DOI: 10.3389/fmech.2026.1980739

Keywords: critical heat flux, non-uniform axial heating, causal transformer, neural networks, nuclear reactors, two-phase flow, minimum DNBR, model robustness, correction factor, transformer-based, correction, factor

The researchers investigated two types of parts with different wall-thickness distributions. They developed a three-dimensional, two-phase flow model that coupled the Navier–Stokes equations with the level set equation. The model used a collocated-grid finite-volume discretization, with the SIMPLE algorithm handling pressure–velocity coupling.

According to the published abstract, the model accurately predicted the evolution of the melt front in complex cavities and captured race-tracking and air entrapment during filling. The results also indicate that wall-thickness distribution is an important factor in both effects, with the response of trapped-air area differing by cavity geometry: the increase associated with a decreasing thin-to-thick ratio was reported for circular cavities.

This is a study of polymer filling processes based on numerical simulation combined with experimental observations, rather than a clinical or biological investigation. The reported evidence concerns two part geometries and focuses specifically on the influence of the thin-to-thick wall-thickness ratio. Because only the abstract and article summary were available for this report, details of the experimental protocol, quantitative uncertainty, validation measurements, and the range of geometries and ratios examined cannot be assessed. The source also identifies the publication as an early-access version of accepted peer-reviewed research that may undergo further editing.

Subject of Research: Numerical modeling of race-tracking and air entrapment during polymer filling

Article Title: 3D numerical study of race-tracking and air entrapment phenomena in polymer filling process

Article References: Liu, Y., Liu, Q., & Jiang, C. (2026). 3D numerical study of race-tracking and air entrapment phenomena in polymer filling process. Scientific Reports. https://doi.org/10.1038/s41598-026-74878-6

Image Credits: AI Generated

DOI: 10.1038/s41598-026-74878-6

Keywords: polymer filling, injection molding, race-tracking, air entrapment, two-phase flow, numerical simulation, melt-front evolution, wall-thickness ratio, circular cavities, numerical, entrapment, phenomena

The challenge the researchers set out to solve is rooted in physics. Inside a heat pump, the refrigerant constantly shifts between liquid, two-phase mixture, and vapor, and the boundaries between those regions slide back and forth during every startup, shutdown, and capacity change. Detailed computational fluid dynamics can track these phenomena with high fidelity, but a single operating condition can demand hours or even days of computation, making CFD useless for real-time applications. At the other extreme, simple lumped-parameter models run quickly but assume uniform temperatures and pressures within each control volume, which badly distorts their predictions precisely where it matters most: during phase change.

Between those poles sit two established families of low-order models. Moving-boundary formulations divide the exchanger into subcooled, two-phase, and superheated zones and track the interfaces between them, offering a reasonable compromise, but their structure is rigidly tied to predefined flow regimes and they approximate wall temperatures too coarsely. That shortcoming becomes critical in winter, when accurate local surface temperatures are essential for predicting frost formation on the coil. Segment-by-segment, or finite-volume, models reconstruct the refrigerant state along the entire flow path and capture local heat transfer coefficients and pressure drops with precision, but they typically need many control volumes, and the best-known implementations, such as NIST’s EVAP-COND and CoilDesigner, are built for steady-state design rather than transient simulation, are closed-source, and are too slow for control integration.

The new model threads this needle by discretizing the refrigerant side into a chain of finite control volumes along the flow direction, each governed by one-dimensional mass, momentum, and energy balances. Crucially, the formulation explicitly accounts for the dynamic compressibility of the refrigerant, its thermal inertia, and the thermal inertia of the exchanger wall, so transient mass accumulation and shifting phase boundaries are captured rather than averaged away. The framework was written natively in the Simscape language within the Simulink environment, giving it a white-box architecture in which every governing equation and empirical correlation is transparent and directly coupled to control algorithms without cumbersome co-simulation interfaces.

One of the model’s most elegant tricks concerns the mathematical discontinuities that plague phase-change simulation. Heat transfer correlations for single-phase flow, such as the Gnielinski correlation for turbulent liquid or vapor, differ sharply from two-phase correlations like Cavallini-Zecchin for condensation and Shah for evaporation. Switching abruptly between them produces jumps in the heat transfer coefficient that can destabilize a solver. Instead of tracking flow regimes with expensive algorithms, the team applies a cubic Hermite spline over narrow vapor-quality intervals near zero and one, smoothly blending the correlations and eliminating artificial discontinuities. The same blending strategy is applied to pressure-drop modeling, where the Lockhart-Martinelli separated-flow correlation is merged with a simpler homogeneous-flow model at the vapor-quality extremes, where the well-mixed assumption actually becomes more valid.

On the air side, the model handles the moist-air physics that dominates real heat pump operation. When the wall surface temperature falls below the dew point, water vapor condenses on the coil, releasing latent heat; the model switches automatically between dry and wet heat transfer using the saturation humidity ratio at the wall. Bulk-flow condensation, which prevents the simulated air from exceeding 100 percent relative humidity, is governed by a condensation time constant, and a sensitivity analysis showed that values of 10 milliseconds or larger introduce errors of up to 103 watts in total heat flow and more than 12 percentage points in outlet relative humidity during rapid transients. The team settled on 0.1 milliseconds, which restores thermodynamic equilibrium almost instantly without numerical stiffness. Air-side friction and heat transfer are computed with established correlations from Wang and colleagues for plain and louvered fins, evaluated segment by segment so that multidimensional flow effects are folded into the one-dimensional framework.

Validation proceeded on two fronts. First, the team compared steady-state predictions against EVAP-COND 5.0, the industry-standard tool from NIST, for a three-row, fifteen-tube-per-row exchanger with two parallel refrigerant circuits running R32. Under condenser conditions, the converged model deviated from the reference by only about 2.7 percent, or 85 watts. Under evaporator conditions, the total capacity error shrank to just 0.36 percent, a mere 9 watts, because a 2.4 percent underprediction of sensible heat was nearly cancelled by a 6.8 percent overprediction of latent heat. A sensitivity analysis traced that latent discrepancy to the different empirical correlations used for refrigerant-side heat transfer: simply raising the coefficient by 20 percent cut the latent error from 6.8 percent to 1.1 percent.

Perhaps the most practically valuable insight emerged from a grid convergence study. The transition from two-phase flow to superheated vapor occurred within the second tube row of the evaporator, creating a steep wall-temperature gradient that made latent heat transfer acutely sensitive to spatial resolution there, while the first and third rows barely mattered. By refining only the rows with sharp thermodynamic gradients, the researchers achieved convergence with nine segments instead of the fourteen required by uniform discretization, cutting computational cost by roughly 36 percent. The strategy is generalizable: selectively refining only where phase transitions occur offers a systematic route to efficiency across different operating scenarios.

The speed figures are where the work becomes genuinely striking. EVAP-COND 5.0 needed 5.8 seconds to reach a steady-state solution, and even its coarsest setting saved only 0.2 seconds. The new dynamic model, by contrast, simulated 2000 seconds of transient operation in about 1.20 seconds for the condenser and 1.77 seconds for the evaporator on an Intel Core Ultra 7-265K processor, corresponding to run-to-simulation time ratios below one millisecond per simulated second. A dynamic model, which must solve time-dependent balances at every step, outpacing a dedicated steady-state design tool underscores just how far the numerical optimization has gone, and confirms suitability for hardware-in-the-loop testing and system-level digital twins.

Experimental validation completed the picture. Drawing on a prior system-level study of an exhaust air heat pump, the team imposed the exact measured air-side and refrigerant-side boundary conditions from 21 steady-state summer test cases onto standalone component models. Predictions for both evaporator and condenser fell largely within a plus-or-minus 10 percent error band, with mean absolute percentage errors of 6 percent for the evaporator and 5 percent for the condenser, and root-mean-square percentage errors of 7 and 6 percent respectively. Those figures are comparable to published validation results for EVAP-COND itself, which showed deviations of roughly 7 to 8 percent, and better than the EVSIM software, whose errors reached 12 percent. With the code openly available and future work targeting transient experimental validation and a frost-formation module for winter operation, the model positions itself as a building block for the next generation of intelligent, self-optimizing heat pump systems.

Subject of Research: Dynamic low-order modeling of fin-and-tube heat exchangers for real-time heat pump simulation

Article Title: An accurate low-order model of a fin-and-tube heat exchanger for the dynamic simulation of heat pumps

Article References: Sedoni, R., Santangelo, P. E., & Angeli, D. (2026). An accurate low-order model of a fin-and-tube heat exchanger for the dynamic simulation of heat pumps. Results in Engineering, 32, Article 113465. https://doi.org/10.1016/j.rineng.2026.113465

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113465

Keywords: heat pumps, heat exchangers, fin-and-tube, digital twins, model predictive control, two-phase flow, finite volume model, condensation, evaporation, HVAC, Simscape, real-time simulation

The new work, published in Frontiers in Thermal Engineering, builds on the level set method, one of the most popular interface-capturing techniques in computational fluid dynamics. In a level set formulation, the interface is not drawn explicitly; instead, it hides inside a smooth function as the set of points where that function equals zero. Typically this function is a signed distance function, meaning its value tells you how far you are from the interface and on which side. Moving the interface is then simply a matter of transporting this function along with the flow. The elegance of the approach explains its enduring popularity, but it comes with a well-known Achilles heel: mass loss.

The trouble arises because the interface must periodically be re-regularized. As the flow deforms the distance function, its defining property—that its gradient has unit magnitude everywhere—degrades, so a reinitialization equation must be solved to restore it. Every round of reinitialization nudges the zero contour slightly, and those tiny nudges accumulate. Over long simulations, droplets can shrink and bubbles can evaporate numerically, not because of any physics but because of the bookkeeping itself. Previous fixes have ranged from coupling level sets with volume-of-fluid methods to seeding the interface with Lagrangian particles, or from adding source terms to solving extra correction equations. Each works to some degree, but all add computational steps, implementation complexity, or both.

The NTNU-led team took a different route, borrowing an idea from a parallel line of research on phase field methods. Recent formulations—the conservative phase field (CPF) method of Chiu and Lin, refined by Jain, and the conservative diffuse interface (CDI) method proposed by Mirjalili and colleagues—advect a hyperbolic tangent profile across the interface instead of a signed distance function. This profile is carried by a compressive-diffusive equation with a regularization term that keeps the interface sharp, and crucially, it can preserve the interface function within strict bounds between zero and one using nothing more exotic than central-difference discretization. No separate reinitialization equation is needed at all.

The researchers realized this conservative advection machinery could be grafted onto their existing sharp interface level set solver designed for co-located grids, a solver they call SI-LSMcol. The result is the new sharp interface conservative level set method on a co-located grid, or SI-CLSMcol. Where the old method solved a pseudo-time reinitialization equation after every advection step, the new method advects the bounded hyperbolic tangent profile in a single step and then recovers the signed distance function through a simple algebraic relation. That substitution removes the most expensive and mass-eroding step in the pipeline while leaving everything else—momentum solving, pressure projection, jump conditions at the interface—untouched.

The co-located grid part of the story matters just as much. Many production codes store velocity and pressure at the same grid points rather than on staggered meshes, which is memory-friendly and simpler to parallelize, but it introduces a risk of pressure–interfacial force imbalance: when surface tension is not discretized in perfect balance with the pressure gradient, unphysical spurious currents ripple through the flow. The team’s approach sidesteps this by treating surface tension not as a volumetric source term but as a jump condition—an interfacial boundary condition—imposed directly at the interface. The new study extends this jump-condition framework, previously demonstrated only in two dimensions, to full three-dimensional Cartesian simulations with high density ratios, showing it remains robust under those demanding conditions.

Validation proceeded through a gauntlet of canonical benchmarks. First came the Young–Laplace law: a static droplet suspended in equilibrium, where the pressure jump across the curved interface must exactly match the surface tension times curvature. Across density ratios of 1, 10, and 100, the new method matched the old one’s accuracy almost exactly, with comparable magnitudes of spurious currents—confirming that swapping the advection equation did not disturb the delicate pressure–surface tension balance. A grid refinement study then revealed the headline result: the conservative method achieved two to three orders of magnitude less mass loss than its predecessor, while converging at a rate between first and second order as the mesh was refined.

The dynamic test cases told a consistent story. For a buoyancy-driven bubble rising in three dimensions, the simulated rise velocities agreed with previously published benchmark results, and the new method cut computational time by a factor of about two while improving mass conservation by a factor of roughly 45. For a falling droplet, validation against level set and coupled level set–volume of fluid results showed excellent agreement in the droplet’s trajectory, with improvements of about 3.25 times in speed and a several-fold gain in mass conservation. The droplet coalescence case—a droplet merging into a quiescent liquid pool, a surface-tension-dominated problem with severe interface deformation—matched experimental data within a few percent, with a 1.66-fold speedup and a 4.28-fold reduction in mass loss.

What makes the advance practical rather than merely academic is its plug-and-play character. Because the jump-condition source terms and the overall solution algorithm remain unchanged, the conservative advection equation can be dropped into an existing sharp interface solver with minimal re-engineering. The authors recommend choosing the regularization parameters so the interface function stays strictly bounded between zero and one, keeping the transition layer as thin as stability allows—a choice that sharpens the estimates of interface normals and curvature on which the whole sharp interface framework depends. The interface advection itself is discretized with a fifth-order WENO scheme in space and a third-order Runge–Kutta scheme in time, while the flow equations use a semi-explicit pressure-projection algorithm with a third-order TVD scheme for momentum advection.

For engineers simulating boiling, atomization, droplet dynamics, or any application where two immiscible fluids interact over long times, the implications are straightforward: simulations that keep their mass, run faster, and behave identically to trusted methods when checked against known physics. The work was supported by the Research Council of Norway and computed on the IDUN cluster at NTNU. As multiphase flow simulation pushes into ever more complex regimes—phase change, turbulent sprays, dense suspensions—methods that quietly eliminate accumulated numerical error while saving computation are exactly the kind of unglamorous but essential progress on which the field depends. This one, its authors show, can be adopted almost as easily as it was conceived.

Subject of Research: A mass-conservative sharp interface level set method for two-phase flow simulation on co-located grids

Article Title: A fast and improved mass-conservative approach for a sharp interface-level set method on co-located grid

Article References: Chirammel, S. S., Mukherjee, A., Brandt, L., & Solsvik, J. (2026). A fast and improved mass-conservative approach for a sharp interface-level set method on co-located grid. Frontiers in Thermal Engineering, 6, Article 1916556. https://doi.org/10.3389/fther.2026.1916556

Image Credits: AI Generated

DOI: 10.3389/fther.2026.1916556

Keywords: level set method, multiphase flow, mass conservation, co-located grid, sharp interface, computational fluid dynamics, surface tension, phase field method, two-phase flow, numerical simulation, jump conditions, reinitialization

The research team, led by Jinrong Cao of the Geological Carbon Dioxide Storage Technology Research Association and the Research Institute of Innovative Technology for the Earth in Japan, combined three observational streams in a single experiment: distributed fiber-optic strain sensing, time-lapse X-ray computed tomography, and coupled numerical modeling of two-phase flow and poroelastic deformation. Their specimen was a cylindrical tuffaceous sandstone core, 34.83 millimeters in diameter and 179.50 millimeters long, drilled from the Sarukawa oil field in Oga, Akita Prefecture, an area selected for a Japanese advanced carbon storage program targeted to begin operations by 2030. The rock had a porosity of 25.06 percent and an intrinsic permeability of 5.41 millidarcys, with a mineral framework dominated by the zeolite clinoptilolite at roughly 63 percent, alongside quartz, albite, anorthite, and heulandite.

The sensing element was a single-mode silica fiber bonded to the core surface with epoxy at an optimized wrap angle of 80 degrees relative to the core axis. This helical geometry converts one continuous fiber into a dense array of quasi-independent strain sensors, resolving circumferential, or hoop, strain at one-centimeter spatial resolution along the full specimen length. The interrogator, a Neubrex 7020 unit, works by measuring Rayleigh frequency shifts in backscattered laser light using a tunable wavelength coherent optical time-domain reflectometer. Because strain and temperature both shift the Rayleigh spectrum, the team held the experiment at a stable 40 degrees Celsius and applied a calibrated strain coefficient of minus 0.153 gigahertz per microstrain, yielding a strain resolution of about half a microstrain for comparable measurements, far finer than the tens to roughly one hundred microstrains observed during injection.

Before introducing carbon dioxide, the researchers ran a single-phase water flow test to pin down permeability and validate their poroelastic model. When upstream pressure reached 10.5 megapascals, circumferential strain near the inlet jumped to approximately 75 microstrains within a single sampling interval of 36 seconds or less, while the downstream end of the core registered only a few microstrains. Numerical simulations showed that the sub-second initial response could not be resolved experimentally, but by roughly half a second to one second the simulated strain gradient matched the first measured profile, and a steady inlet-to-outlet strain gradient established itself within about one second. This close agreement between measurement and model confirmed that, in fully water-saturated rock, deformation is governed by pore water pressure gradients acting through Biot-style poroelastic coupling.

The main event was the supercritical carbon dioxide flood. Time-lapse CT scans, taken at 60 seconds per volume using an iodide-rich contrast solution to sharpen fluid-rock contrast, tracked the drainage process in detail. During the first 1.6 minutes, corresponding to 0.036 injected pore volumes, carbon dioxide accumulated mainly near the inlet. By 2.67 minutes the saturation field had become spatially nonuniform, reflecting variability in pore accessibility and capillary entry conditions across the zeolite-rich framework. At 4.27 minutes the front reached the specimen midpoint, and breakthrough occurred at 8.0 minutes, when average carbon dioxide saturation hit 19.4 percent. Differential pressure during drainage held steady between 0.45 and 0.48 megapascals at a flow rate near one milliliter per minute.

The striking result was how differently the strain field evolved from the saturation field. At the onset of injection, a pronounced strain gradient appeared immediately: strain near the inlet climbed to roughly 80 microstrains, while even the outlet showed a small but detectable response. The strain front was far more spatially diffuse than the comparatively sharp saturation front imaged by CT. By breakthrough, strain had reached about 100 microstrains near the inlet and 20 microstrains near the outlet. Most tellingly, at a position 0.09 meters from the inlet, a distinct strain increase appeared near the very start of injection, while local carbon dioxide saturation remained at zero for the first four minutes. The delay between strain onset and saturation onset grew with distance from the inlet, exactly the pattern expected if pressure disturbances propagate through the connected aqueous phase faster than the capillary-controlled gas front advances.

The coupled numerical model, a two-dimensional axisymmetric finite-element representation of the full specimen, provided the physics-based bridge between the observable strain and the unmeasured internal pressure. The team calibrated two-phase flow parameters exclusively against the CT-derived saturation profiles, then compared the predicted strain against the fiber measurements as an independent test. Simulated pore gas and pore water pressures evolved concurrently but with different spatial patterns, related through capillary pressure, and the modeled strain reproduced both the magnitude and the timing of the measured response. Because the sandstone’s apparent drained bulk modulus of roughly one to two gigapascals makes it relatively compliant, a given pressure perturbation produces a large, measurable strain. The authors are careful to stress that the fiber does not measure pressure directly; the strain signal is a model-constrained poroelastic proxy for the evolving pressure footprint, not a standalone pressure gauge.

The engineering implications reach well beyond the laboratory. Operational surveillance of storage sites typically relies on wellhead and bottomhole pressure, flow rates, sparse downhole gauges, and episodic plume imaging, none of which uniquely constrains the internal pressure field. Distributed strain sensing adds a spatially continuous constraint that can be folded into coupled flow and geomechanical models, helping to characterize uncertain formation properties and to evaluate deformation relevant to reservoir, caprock, and wellbore integrity. Field deployments already hint at feasibility: distributed fiber sensing has been demonstrated under field-scale injection conditions at the CO2CRC Otway site in Australia, a pumping test at Mobara in Japan captured pressure-related reservoir deformation, and behind-casing water-injection measurements show that injection-induced strain is detectable through a casing-cement-formation system.

The authors are equally candid about the limitations that separate their benchtop result from routine field practice. The adhesive layer bonding the fiber to the core was not independently calibrated, so perfect strain transfer was assumed. Field fibers are usually installed axially behind casing, where recorded amplitude depends on cable orientation, completion design, cement properties, gauge length, and strain-transfer efficiency, and axial strain is not generally equivalent to the hoop strain measured here. Stiffer formations or rocks with a lower Biot-Willis coefficient would produce smaller strains that may fall below detection thresholds, meaning an absent strain signal cannot be read as absent pressure communication. The homogeneous axisymmetric model also cannot capture localized effects of bedding, fractures, or anisotropic permeability, and longer-term chemical interactions between carbon dioxide, brine, and reactive minerals may gradually alter rock stiffness and fracture behavior.

Even with those caveats, the study delivers a compelling proof of concept: the mechanical consequences of injection arrive before the plume does, and a helically wound strand of glass can watch them happen. Future priorities include experiments on rocks with contrasting stiffness and capillary behavior, direct internal pressure measurements, three-dimensional models that explicitly represent the helical fiber geometry, and field studies that integrate distributed strain with pressure gauges, time-lapse geophysics, distributed acoustic and temperature sensing, and surface deformation observations. As global net-zero pathways call for roughly ten gigatons of carbon dioxide storage per year by 2050, tools that convert invisible pressure transients into measurable, interpretable strain signals could become an essential part of the monitoring toolkit, giving operators and regulators earlier and more defensible warnings about where the subsurface is being mechanically stressed.

Subject of Research: Distributed fiber-optic sensing of poroelastic strain precursors during supercritical CO2 core flooding in sandstone

Article Title: Poroelastic strain precursors during laboratory carbon dioxide core flooding revealed by helically bonded fiber sensing

Article References: Cao, J., Park, H., Xue, Z., Nakajima, T., Amer, R., & Ouchi, W. (2026). Poroelastic strain precursors during laboratory carbon dioxide core flooding revealed by helically bonded fiber sensing. Communications Engineering, 5(1), Article 164. https://doi.org/10.1038/s44172-026-00783-5

Image Credits: AI Generated

DOI: 10.1038/s44172-026-00783-5

Keywords: carbon capture and storage, distributed fiber-optic sensing, poroelasticity, CO2 core flooding, X-ray computed tomography, pore pressure, geomechanics, sandstone, capillary pressure, geological storage, strain sensing, two-phase flow

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

The two-fluid four-equation model is a compact mathematical description of two-phase flow in which each phase, for example liquid and gas, obeys its own conservation equations for mass and momentum, but both phases share a single pressure field. This shared-pressure assumption makes the model relatively easy to implement and computationally affordable, which is why variants of it appear in reactor safety codes such as RELAP, TRAC, and CATHARE, and in pipeline simulators used across the oil industry. However, the formulation carries a well-known mathematical weakness: when two fluids flow together under a common pressure with different velocities, the system of equations can lose a property called hyperbolicity. This loss is tied to the physical Kelvin-Helmholtz instability and renders the underlying problem ill-posed, producing violent non-physical oscillations that can destroy a simulation.

To tame this instability, the researchers incorporated an artificial interfacial pressure-difference term based on the CATHARE model, a formulation originally developed for nuclear thermal-hydraulics. This term introduces a controlled amount of numerical diffusion that keeps the equations well-behaved without requiring manual tuning of an adjustable shape parameter, an advantage over the alternative Toumi model. The team also combined the high-order spatial method with a staggered-grid arrangement, in which scalar quantities such as pressure and density are stored at cell centers while velocities live on cell faces. This classic layout prevents a troublesome pressure-velocity decoupling phenomenon, and the authors coupled it with the semi-implicit SIMPLE algorithm, a robust pressure-correction procedure widely used in practical flow solvers.

The Flux Reconstruction method itself is an elegant framework developed by H.T. Huynh in 2007. Within each control volume, the solution is represented by a polynomial of chosen degree, and the fluxes are reconstructed as continuous functions across the domain by applying correction functions at element interfaces, informed by an approximate Riemann solver. A remarkable feature of FR is its unifying character: by swapping correction functions, it can recover simplified versions of the Nodal Discontinuous Galerkin, Spectral Volume, and Spectral Difference methods, and even generate new schemes. Compared with the popular Discontinuous Galerkin approach, FR requires fewer volumetric integration operations, making it computationally lighter, and its minimal inter-element connectivity favors parallel scalability on modern hardware.

In the new implementation, the researchers evaluated polynomial degrees from P1 to P3, corresponding to formal accuracy from second to fourth order for smooth solutions, with P2 and P3 classified as very high order. Two correction functions were tested, one yielding an FR-NDG variant and the other an FR-SD variant. A key technical innovation lies in how the staggered grids communicate: instead of the low-order interpolations that conventional finite-volume schemes require, variables are transferred between the primal and dual grids directly through the FR polynomial reconstructions, preserving the high-order spatial representation throughout the calculation. Non-physical oscillations near steep fronts are controlled by the hierarchical Multidimensional Limiting Process, or hMLP limiter, and time integration uses a third-order Total Variation Diminishing Runge-Kutta scheme with a dynamically adjusted time step.

The team validated the framework on five benchmark problems of escalating difficulty. The first, a smooth non-linear transport problem derived from the inviscid Burgers equation, isolated the spatial discretization from the complexities of two-fluid physics. The results confirmed that the FR schemes achieved convergence rates close to their theoretical asymptotic orders, with the P3 variants approaching fourth-order accuracy, while the First-Order Upwind method, the workhorse of commercial one-dimensional pipeline simulators, lagged far behind. In cost-benefit terms, the FR-NDG-P3 scheme delivered the best accuracy per unit of CPU time, and the FR-NDG variant consistently edged out its FR-SD counterpart on this particular problem.

The second and third benchmarks introduced genuine two-phase discontinuities. In the moving-discontinuity case, a sharp front in the gas volume fraction is advected through a horizontal pipe, and in the classical water faucet problem, water accelerates downward under gravity through air in a vertical duct, creating a shock-like front. On both tests, all FR variants outperformed MUSCL, a standard second-order scheme, with the FR-NDG-P1 results already more accurate. A pointwise error analysis for the water faucet problem at a fixed location showed the First-Order Upwind scheme erring by 13.30 percent, MUSCL by 6.41 percent, and the FR formulations by roughly 5 to 6 percent, using only 64 control volumes. Notably, those FR errors were comparable to or better than values previously reported in the literature on a mesh ten times finer.

Perhaps the most intriguing finding came from a hyperbolicity analysis of the water faucet case. By computing the eigenvalues of the governing system along the pipe, the researchers identified regions where the eigenvalues turn complex, signaling local loss of hyperbolicity. They found that the high-order FR reconstruction detects the onset of these non-hyperbolic conditions earlier and over a wider region than the lower-order MUSCL scheme, because the polynomial reconstruction is more sensitive to incipient gradients. Rather than being a defect, the authors argue this makes the FR framework useful as a diagnostic tool for locating the ill-posed regions inherent to the single-pressure two-fluid model, while the stabilization mechanisms keep the solution stable and physically consistent even where complex eigenvalues appear.

The final two cases pushed the method toward industrial reality. In a downward vertical annular flow of oil and water with wall and interfacial friction, the in-house solver reproduced pressure, water velocity, and oil volume fraction profiles from the commercial simulator ALFAsim with maximum relative errors of just 1.55, 0.2, and 0.7 percent respectively, differences the authors attribute mainly to differing empirical friction closures rather than the numerics. The closing feasibility study simulated a kilometer-long vertical well in which a sudden increase in water cut propagates upward, a scenario of direct relevance to petroleum production. Using only 128 control volumes, the FR solutions tracked the front predicted by a refined ALFAsim run with 7,500 control volumes, with L1 errors between 0.138 and 0.170 percent, whereas ALFAsim on the same coarse mesh deviated by about 2.35 percent, and front positions agreed within roughly 1.5 to 3.4 meters versus 5.5 meters for the coarse commercial run.

The study’s authors caution that comparisons with ALFAsim must be interpreted carefully, since the two simulators rely on different physical and closure models, but the overall message is clear: very high-order Flux Reconstruction can dramatically reduce numerical diffusion and mesh requirements in two-phase pipeline simulation. For an industry where flow assurance failures, from hydrate plugs to slug transients, translate into enormous financial and environmental costs, a method that resolves sharp fronts on coarse grids is more than an academic curiosity. The team now plans to extend the framework to thermal effects, flow-pattern prediction, and automatic h-p adaptation, steps that could eventually bring this class of high-fidelity simulation into routine engineering practice.

Subject of Research: Very high-order Flux Reconstruction numerical simulation of one-dimensional two-fluid four-equation two-phase flow in pipelines

Article Title: Numerical simulation of the 1-D two-fluid four-equation model in pipelines using the very high order flux reconstruction (FR) method

Article References: Nascimento, A. V. D., Silva, C. E., Silva, G. M. D., Freitas, T. C., Fontes, R. A., Silva, M. T. D., Silva, J. D. M., Lyra, P. R., Antunes, A. R., & Carvalho, D. K. D. (2026). Numerical simulation of the 1-D two-fluid four-equation model in pipelines using the very high order flux reconstruction (FR) method. Results in Engineering, 32, Article 113206. https://doi.org/10.1016/j.rineng.2026.113206

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113206

Keywords: flux reconstruction, two-fluid model, two-phase flow, pipelines, computational fluid dynamics, hyperbolicity, SIMPLE algorithm, staggered grid, hMLP limiter, oil industry, flow assurance, numerical simulation