Computational Fluid Dynamics Simulations Research Articles

Two-Dimensional Prediction of Transient Cavitating Flow Around Hydrofoils Using a DeepCFD Model

Cavitation is a common phenomenon in naval and ocean engineering, typically occurring in the wakes of high-speed rotating propellers and on the surfaces of fast-moving underwater vehicles. To investigate cavitation phenomena, computational fluid dynamics (CFD) simulations are indispensable. Nevertheless, the inherently complex nature of cavitation, which involves phase transitions, heat transfer, and significant pressure fluctuations, often results in high computational costs for these simulations. To address the computational challenges associated with cavitation simulations, a DeepCFD model, which leverages convolutional neural networks (CNNs), was employed to accurately predict cavitation around hydrofoils. Through specific modifications, the DeepCFD model was trained on 400 hydrofoil configurations, learned from CFD simulations. The numerical methods were validated against a modified NACA66 hydrofoil. It was found that the model could accurately predict cavitation shapes under various flow conditions, although it showed some discrepancies in velocity predictions, especially for detached cavitating flows. The significance of this study lies in its potential to simply predict cavitating flows and expedite marine vehicle design through the application of CNNs in cavitation prediction, offering a novel and impactful approach to computational fluid dynamics in the field.

An Analysis and Comparison of the Hydrodynamic Behavior of Ships Using Mesh-Based and Meshless Computational Fluid Dynamics Simulations

This paper presents a comparison of two turbulence models implemented in two different frameworks (Eulerian and Lagrangian) in order to simulate the motion in calm water of a displacement hull. The hydrodynamic resistance is calculated using two open-source Computational Fluid Dynamics (CFD) software packages: OpenFOAM and DualSPHysics. These two packages are employed with two different numerical treatments to introduce turbulence closure effects. The methodology includes rigorous validation using a Wigley hull with experimental data taken from the literature. Then, the validated frameworks are applied to model a ship hull with a 30 m length overall (LOA), and their results discussed, outlining the advantages and disadvantages of the two turbulence treatments. In conclusion, the resistance calculated with OpenFOAM offers the best compactness of results and a shorter simulation time, whereas DualSPHysics can better capture the free-surface deformations, preserving similar accuracy.

Simulated inter-filament fusion in embedded 3D printing

In embedded 3D printing (EMB3D), a nozzle extrudes continuous filaments inside of a viscoelastic support bath. Compared to other extrusion processes, EMB3D enables softer structures and print paths that conform better to the shape of the part, allowing for complex structures such as tissues and organs. However, strategies for high-quality dimensional accuracy and mechanical properties remain undocumented in EMB3D. This work uses computational fluid dynamics simulations in OpenFOAM to probe the underlying physics behind two processes: deformation of the printed part due to nearby nozzle motion and fusion between neighboring filaments during printing. Through simulations, we disentangle yielding from viscous dissipation, and we isolate interfacial tension effects from rheology effects, which are difficult to separate in experiments. Critically, these simulations find that disturbance and fusion are controlled by the flow of support fluid around the nozzle. To avoid part deformation, the nozzle must remain far from existing parts during non-printing moves, moreso when traveling next to the part than above the part and especially when the interfacial tension between the ink and support is non-zero. Additionally, because support can become trapped between filaments at zero interfacial tension, the spacing between filaments must be tight enough to produce over-printing, or printing too much material for the designed space. In non-Newtonian fluids, spacings for vertical walls must be even tighter than spacings for horizontal planes. At these spacings, printing a new filament sometimes creates and sometimes mitigates shape defects in the old filament. While non-zero ink-support interfacial tensions produce better inter-filament fusion than zero interfacial tension, interfacial tension also produces shape defects. Slicing algorithms that consider these unique EMB3D defects are needed to improve mechanical properties and dimensional accuracy of bioprinted constructs.

Enhanced Hemodynamics of Anisometric TPMS Topology Reduce Blood Clotting in 3D Printed Blood Contactors.

Artificial organs, such as extracorporeal membrane oxygenators, dialyzers, and hemoadsorber cartridges, face persistent challenges related to the flow distribution within the cartridge. This uneven flow distribution leads to clot formation and inefficient mass transfer over the device's functional surface. In this work, a comprehensive methodology is presented for precisely integrating triply periodic minimal surfaces (TPMS) into module housings and question whether the internal surface topology determining the flow distribution affects blood coagulation. Three module types are compared with different internal topologies: tubular, isometric, and anisometric TPMS. First, this study includes a computational fluid dynamics (CFD) simulation of the internal hemodynamics, validated through experimental residence time distributions (RTD). Blood tests using human whole blood and subsequent visualization of blood clots by computed tomography, allow the quantification of structure-induced blood clotting. The results indicate that TPMS topologies, particularly anisometric ones, serve as effective flow distributors and significantly reduce and delay blood clotting compared to conventional tubular geometries. For these novel TPMS modules, the inner surfaces can be activated chemically or functionalized to function as a selective adsorption site or biocatalytic surface or made of a permeable material to facilitate masstransfer.

Investigation of Erosion and Deposition Due to Flows with Particles.

In this work, we employed experimental technique to study the issue of particle erosion and deposition in multiphase flows involving both particles of micro/meso- and nanoscale (sand particles and iron oxide particles). Especially, liquids with immersed nanoparticles gained a lot of interest in the recent years due to their enhanced thermal properties. At the same time, this type of fluids is still not widely used in practical and engineering applications, and one of the reasons is a risk of leading to erosion and deposition on, for instance, pipe walls. In our experiments, an aluminum plate was subjected to a flow with particles by immersing it in a beaker with a rotating fluid for 530 h. After this, the plate was investigated using scanning electron microscopy (SEM) and atomic force microscopy (AFM), followed by energy dispersive X-ray (EDX) analysis. According to our observations, the erosion was mainly caused by the largest particles (sand particles), while the nanoparticles did not lead to clear erosion but resulted in significant deposition due to strong adhesion, as well as corrosion, resulting in aluminum oxide formation. This issue was also confirmed through theoretical analysis by comparing the momentum response time and the characteristic time of the flow, as well as computational fluid dynamics (CFD) simulations.

Optimizing vortex-induced vibration suppression in π-shaped girders using wind tunnel testing and CFD analysis

This investigation meticulously explores the vortex-induced vibration (VIV) characteristics in Π-shaped girders within long-span cable-stayed bridges, presenting novel VIV mitigation techniques. Employing detailed wind tunnel evaluations of a 1:50 scale model alongside computational fluid dynamics (CFD) analyses to model the two-dimensional flow around the girder, this study reveals the formation and shedding of vortices behind the railings and main steel girder, which significantly contribute to VIV in such structures. The introduction of horizontal splitter plates, one m in width, in conjunction with two-m-wide V-shaped guide vanes, was found to substantially reduce the VIV amplitude of the Π-shaped girder, minimizing vortex generation on the deck’s sides and dramatically reducing the maximum vertical VIV amplitude from 208.75 mm to only 5.56 mm. CFD simulations confirm the effectiveness of these measures in suppressing Karman vortex street formation, thereby significantly improving downstream airflow characteristics. These findings offer pivotal insights for the advancement of bridge design and the proactive management of VIV, showcasing the potential of integrated aerodynamic modifications to enhance structural resilience and performance.

Assessing the Effect of Uneven Inlet Velocity on the 24 ft Diameter MinwaterCSP Fan Using a Unique Pressure Sensing System

An industrial-grade pressure sensing system was designed for installation on the surface of the 24 ft (7.315 m) diameter M-fan that is installed on the MinwaterCSP test facility. The facility has significant cross draft effects due to the proximity of a canal that runs underneath the centre of the facility. This canal causes disturbance of the inlet air flow distribution. Due to the constant rapid change in air velocity and direction with blade rotation, the pressure on the blade fluctuates. The velocity distribution was measured experimentally using the installed anemometers. The uneven inlet velocity distribution led to fluctuations in blade surface pressures, which were measured using the uniquely designed pressure sensing system. The measured results were compared to the results of a Computational Fluid Dynamics (CFD) model of the MinwaterCSP test facility. The CFD simulations consisted of two parts. Firstly a 3-dimensional representation of the facility, which was used to get the velocity distribution data and secondly a 2-dimensional airfoil simulation which was used to obtain the surface pressure distribution on the blade surface. The 3-dimensional CFD model made use of an actuator disk model to represent the effect of the fan. The experimental results showed a higher velocity and relative surface pressure distribution at locations correlating to the location of the canal. The simulation was able to replicate these distribution fluctuations. The results of the experimentally measured fan blade surface pressure at the fan suction side correlated within 9% to those of the simulation results.

Numerical Investigation and Validation of Noise Sources of a Distributed Propulsion System

This study delves into the exploration of a distributed propulsion system consisting of three co-rotating propellers in front of a high-lift wing system, with a primary focus on understanding its acoustic characteristics. Employing high-fidelity computational fluid dynamics simulations, the flow field is simulated in climb condition. Subsequently, acoustic transport to far-field observers is conducted using the Ffowcs–Williams and Hawkings equation. Because the noise mechanisms of such a configuration are not fully understood yet, several permeable and impermeable surfaces as input for the acoustic simulation are used, aiming to separate the various noise source contributions. Results reveal that in addition to the rotor-alone noise from the propellers, noise arising from propeller–wing interaction emerges as dominant, emitting mostly at the blade passing frequency. Moreover, a boundary element method tool is applied to observe the scattering effect of propeller-generated noise by the wing. Furthermore, this study incorporates consideration of structural components in close proximity to the model, thereby achieving a more realistic acoustic field. With this knowledge, the simulation is validated with experimental data from an open wind tunnel test campaign. An overall good agreement is observed between the simulated and experimental results, substantiating the reliability of both aerodynamic and acoustic predictions.

Abstract 4117345: Predicting Downstream Aneurysmal Degeneration Following Type A Dissection Repair With Computational Fluid Dynamics

Introduction: Acute type A aortic dissection (ATAAD) is typically treated by replacement of the ascending aorta (+/- root) and proximal arch. However, 70-85% of patients have residual distal dissection post-repair, and 20-40% require late reoperation for aneurysmal degeneration of the distal aorta (ADDA). Since an individual patient’s risk of ADDA cannot be accurately predicted, current guidelines recommend lifelong aortic surveillance imaging for all patients. Hypothesis: Computational fluid dynamics (CFD) simulations of aortic hemodynamics post-repair can accurately identify patients at late risk of ADDA. Methods: We performed CFD simulations of 50 patients following hemi-arch replacement for ATAAD. Patient-specific 3D models were generated from the aortic root to iliac bifurcation (including arch branches) from postoperative 0.6mm contrast-enhanced CT angiograms taken <1 year after index repair (Figure). Exclusion criteria were known heritable thoracic aortic disease and absence of residual dissection. The primary outcome was ADDA, defined as late growth of the distal arch/descending thoracic aorta (DTA) to a diameter ≥5.5cm. Hemodynamic simulations were run for 6 cardiac cycles on a high-performance computing cluster using HARVEY, a CFD solver implementing the lattice Boltzmann method. The primary hemodynamic metric was time-averaged wall shear stress (TAWSS) ratio between the false and true lumens. Results: ADDA developed in 22 patients (44%) at a mean of 3.2 years postoperatively. There were no significant clinical differences between those with and without ADDA (Table). The development of late aneurysm growth was significantly associated with a higher TAWSS ratio in the proximal DTA ( p <0.05, Figure). Conclusion: ADDA following hemi-arch repair for ATAAD is associated with significantly higher false lumen TAWSS as early as the first surveillance scan. CFD simulations may help clinicians risk-stratify patients years before they meet reoperation criteria.

Reduction of Submicron-Sized Aerosols by Aerodynamically Assisted Electrical Attraction with Micron-Sized Aerosols

A vortex generator was installed inside an electric agglomeration device to apply aerodynamic agglomeration in the same space as electric agglomeration. Computational fluid dynamics simulation was utilized to assess the combined effects of electric and aerodynamic agglomeration, and this was subsequently validated through experiments. The discrete phase model was used to track particle trajectories. The results showed that both the aerodynamic agglomeration through the vortex generator and the electric agglomeration through the electric field were effective. When these two agglomerations existed individually in series, the total removal efficiency for submicron particles was 32.5%. However, when they coexisted in the same space, the efficiency increased to 50%. This increase is attributed to the increase in residence time when the vortex generator was added to a space with an electric field. This led to particles being exposed to the electric field for a longer duration, thus generating a synergistic effect.

Twisted-tape inserts of rectangular and triangular sections in turbulent flow of CMC/CuO non-Newtonian nanofluid into an oval tube

Purpose This paper aims to study numerically the non-Newtonian solution of carboxymethyl cellulose in water along with copper oxide nanoparticles, which flow turbulently through twisted smooth and finned tubes. Design/methodology/approach The twisted-tape inserts of rectangular and triangular sections are investigated under constant wall heat flux and the nanoparticle concentration varies between 0% and 1.5%. Computational fluid dynamics simulation is first validated by experimental information from two test cases, showing that the numerical results are in good agreement with previous studies. Here, the impact of nanoparticle concentration, tube twist and fins shape on the heat transfer and pressure loss of the system is measured. It is accomplished using longitudinal rectangular and triangular fins in a wide range of prominent parameters. Findings The results show that first, both the Nusselt number and friction factor increase with the rise in the concentration of nanoparticles and twist of the tube. Second, the trend is repeated by adding fins, but it is more intense in the triangular cases. The tube twist increases the Nusselt number up to 9%, 20% and 46% corresponding to smooth tube, rectangular and triangular fins, respectively. The most twisted tube with triangular fins and the highest value of concentration acquires the largest performance evaluation criterion at 1.3, 30% more efficient than the plain tube with 0% nanoparticle concentration. Originality/value This study explores an innovative approach to enhancing heat transfer in a non-Newtonian nanofluid flowing through an oval tube. The use of twisted-tape inserts with rectangular and triangular sections in this specific configuration represents a novel method to improve fluid flow characteristics and heat transfer efficiency. This study stands out for its originality in combining non-Newtonian fluid dynamics, nanofluid properties and geometric considerations to optimize heat transfer performance. The results of this work can be dramatically considered in advanced heat exchange applications.

Aeroelastic analysis of non-conventional and slender suspension bridges

The aim of this study was to investigate the dynamic effects of wind actions on bridge cross sections, with a goal to propose design charts for non-conventional and slender bridge decks. An eigenvalue analysis was conducted first and the results were validated experimentally. Subsequently, aeroelastic analysis of the bridge deck section was performed. This analysis encompassed the analytical method adhering to the Eurocode and computational fluid dynamics simulations. Both methodologies indicated that the bridge was susceptible to vortex-induced vibrations. To mitigate these vibrations, wind noses provide better stability than the currently used guide vanes. The effect of changing deck width was also studied. Wider and more streamlined sections displayed better aeroelastic performance. The study also revealed that the Eurocode overestimates the derivatives of aerodynamic moment coefficient by 53% to 93%. Consequently, optimized charts are proposed to enhance the accuracy of torsional divergence and flutter speed calculations, facilitating the safe and efficient design of such bridges.

Influence of Urban Morphologies on the Effective Mean Age of Air at Pedestrian Level and Mass Transport Within Urban Canopy Layer

This study adapted the mean age of air, a time scale widely utilized in evaluating indoor ventilation, to assess the impact of building layouts on urban ventilation capacity. To distinguish it from its applications in enclosed indoor environments, the adapted index was termed the effective mean age of air (τ¯E). Based on an experimentally validated method, computational fluid dynamic (CFD) simulations were performed for parametric studies on four generic parameters that describe urban morphologies, including building height, building density, and variations in the heights or frontal areas of adjacent buildings. At the breathing level (z = 1.7 m), the results indicated three distinct distribution patterns of insufficiently ventilated areas: within recirculation zones behind buildings, in the downstream sections of the main road, or within recirculation zones near lateral facades. The spatial heterogeneity of ventilation capacity was emphasized through the statistical distributions of τ¯E. In most cases, convective transport dominates the purging process for the whole canopy zone, while turbulent transport prevails for the pedestrian zone. Additionally, comparisons with a reference case simulating an open area highlighted the dual effects of buildings on urban ventilation, notably through the enhanced dilution promoted by the helical flows between buildings. This study also serves as a preliminary CFD practice utilizing τ¯E with the homogenous emission method, and demonstrates its capability for assessing urban ventilation potential in urban planning.

CFD Analysis of UV-C Intensity Radiation Distribution and Inactivation of Foodborne Pathogens on Whole and Minimally Processed Mango

Ultraviolet shortwave (UV-C) is a technology for postharvest fruit disinfection. This study aimed to use computational fluid dynamics (CFD) based on the discrete ordinate (DO) radiation model to analyze the distribution of UV-C intensity on whole and minimally processed mangoes within a disinfection chamber and to predict treatments against foodborne pathogens. The mango spears were oriented both parallel and perpendicular to the lamp and positioned at varying distances from the radiation source (50, 75, and 100 mm for spears and 100 mm for whole fruit). CFD simulations integrated with in vitro kinetic parameters enabled predictions of the time and doses needed to inactivate one to three logarithmic units of pathogens on the fruit surface. The highest average radiation intensity values were recorded for the whole mango oriented parallel to the lamp at 100 mm and the spears oriented normally to the lamp at 50 mm. The estimated times to achieve inactivation of one to three logarithmic units of microorganisms ranged from approximately 15 to 6540 s, while the doses necessary for this inactivation were, on average, 1.854, 5.291, and 10.656 kJ/m2, respectively. CFD simulations are valuable for optimizing UV-C treatments in large-scale designing from both microbicide and sustainable perspectives.

Evaluation of reduced-order models for the rapid aerodynamic analysis of supersonic and hypersonic bodies

Abstract This paper presents a comprehensive evaluation of reduced-order models (ROMs) for the determination of pressure coefficient distributions on supersonic and hypersonic bodies. The study investigates the limitations, aerodynamic precision and computational performance associated with various methodologies, ranging from simplistic Newtonian theory-based approaches to more advanced first and second-order shock-expansion theories. Validation is performed by comparing computed results with experimental and computational data for pressure distributions, drag and lift coefficients and centres of pressure for fundamental geometries and authentic vehicle design over a wide range of freestream conditions. The study also includes a comprehensive computational complexity analysis, demonstrating the superiority of finite-element ROM approaches over traditional finite-volume computational fluid dynamics (CFD) simulations. The primary objective of this paper is to scrutinise the extension of these methodological classes to the low supersonic regime. Hence, thermo-chemical reactions within the flow are disregarded, and the ideal gas law is adopted. A value of $\gamma = 1.4$ is chosen for consistency and comparability across the analyses. The proposed ROMs show remarkable potential for reducing high-speed simulation execution times by four orders of magnitude, maintaining accuracy within 20 per cent and as low as 1 per cent. The study unveils three key findings: first, the accuracy degradation of Newtonian-based theories for inclined elements, particularly around 45 degrees, and their reduced dependency on Mach number at large inclination. Secondly, the study presents novel insights into the impact of shock-wave-Mach-wave interactions on pressure distribution calculations, emphasising the Mach number as a crucial metric governing recompression effects. Lastly, the study demonstrates the exceptional accuracy of DeJarnette’s method, providing ${C_P}$ results within 2 per cent for a wide range of conditions, offering an attractive alternative to the Taylor-Maccoll equation.

Deep learning based hybrid POD-LSTM framework for laminar natural convection flow in a rectangular enclosure

Abstract Laminar natural convection in side-heated enclosures is characterized by transient phenomena of the working fluid till it reaches steady state. The side heating can done in several ways the most common way being heating one end at constant temperature and cooling the other end. One of the other ways is heating both sides of the enclosure at a constant heat flux. Mathematical modeling of such problems using Computational Fluid Dynamics (CFD) essentially involves considerable amount of computational time and power to predict the flow phenomena observed in actual experimentation. In the last few years, data driven model frameworks have proven to be anefficient way in saving both time and computational cost in several applications. In the present study, a data driven model framework using a combination of unsupervised machine learning (using Proper Orthogonal Decomposition [POD]) and supervised deep learning models (using Long Short Term Memory [LSTM]) has been developed and referred to as POD-LSTM framework. The selection of a few dominant spatial bases and accompanying temporal modes provides us with a reduced order model of the system. The flow is then reconstructed and compared with results of CFD simulations. The Rayleigh number (Ra) chosen for the study is 3.27 × 1010. The estimated time to reach stedy state for this Ra number is 15,000 s. The POD-LSTM framework is trained using data obtained from a validated CFD model for the first 1,000 s. The trained model was then tested to predict temporal dynamics for the entire 15,000 s. The predictions provided by POD-LSTM framework were found upto 98 % accurate compared to the ones predicted by CFD. The computational time and power was however an order of magnitude lower for the POD-LSTM framework than that required for the CFD model.

Perforated plate ventilation system and dynamics of infectious respiratory particle transmission

AbstractWith the removal of indoor pollutants and the assurance of air quality emerging as critical research topics, the optimization of the internal environment in offices, where people stay for extended periods, is essential for controlling the spread of infectious respiratory particles. Frequent movements of personnel and the operation of doors and windows within offices significantly impact the mechanisms of droplet transmission, warranting further investigation. This study employs computational fluid dynamics simulations to explore the droplet dispersion characteristics and pollutant removal efficiency of the simplified model of perforated plate ventilation system (PPVS) (the diameter of the air supply openings has been reasonably simplified and uniformly set to 0.02 m) in office settings, as well as the impact of dynamic door operation scenarios on droplet spread and concentrations in breathing zones. To optimize the ventilation system's pollutant removal efficiency, airflow velocities (2.86, 3.18, and 5.00 m/s) are varied, with simulations conducted at the optimal velocity of 3.18 m/s. The effects of continuous door operations, door‐opening directions (towards the office and towards the isolation room), and opening speeds (π/4, π/6, π/8, and π/10 rad/s) are also examined, revealing significant impacts on droplet spread. Results indicate that PPVS effectively reduces indoor pollutant concentrations at all tested airflow velocities, with the optimal speed identified as 3.18 m/s. Additionally, door‐opening direction and speed can significantly influence droplet spread. Opening doors towards isolation rooms at smaller angles (less than 30°) effectively reduces droplet concentrations in personnel breathing zones, thereby mitigating the risk of droplet transmission. Faster door‐opening speeds also contribute to lower droplet concentrations in these zones. This innovative study explores the impacts of PPVS and dynamic door operation dynamics on droplet transmission during respiratory disease outbreaks, providing valuable theoretical insights and technical support for disease prevention and indoor air quality improvement.

Study on cavitation erosion mechanism of UHMWPE and PTFE

Polymer materials possess low density, high strength, corrosion resistance, and excellent cavitation erosion resistance. As a result, they are widely used in marine, water conservancy, and other engineering equipment as replacements for metal materials. However, polymer friction pairs working in a water environment for an extended period are easily damaged by cavitation erosion. In this work, the cavitation behavior of polytetrafluoroethylene (PTFE) and ultra-high molecular weight polyethylene (UHMWPE) in deionized water and seawater is investigated through experiments and computational fluid dynamics (CFD) simulations. The results indicate that the cavitation erosion resistance of UHMWPE is significantly better than that of PTFE, and the UHMWPE has four cavitation process stages, while the PTFE has only three cavitation stages. 316L counterparts in the seawater corrosion and cavitation coupling effect of a large number of metal particles off and wash polymer material surface, so that the cavitation erosion of PTFE and UHMWPE is more serious in seawater environment. CFD simulation demonstrates that the cavitation erosion zone under the radiator shows a semicircular distribution. Meanwhile, the formation of ring-shaped cavitation pit is related to the distribution of bubbles on the surface of the radiator. The cavitation rate of PTFE and UHMWPE is slowed down by the “water cushion effect”.

Combing mobile electrical capacitance tomography with Fourier neural operator for 3D fluidized beds measurement

AbstractDespite the practical importance, 3D measurements of gas–solid distribution in fluidized beds calls for further breakthroughs. Here an approach combing a recently developed mobile electrical capacitance tomography (ECT) sensor with Fourier Neural Operator (FNO) is developed, in which the fluidized bed is divided into a series of cross‐sectional slices along axial direction. At any given instant, the gas–solid distribution in one slice is measured by mobile ECT and the others, meantime, are predicted by FNO pre‐trained using experimental data. We verified this approach via computational fluid dynamics (CFD) simulations and experimental measurement of static object (i.e., cone, cylinder, and sphere) in fluidized bed. Following we applied this approach to direct measure 3D gas–solid distribution in a bubbling fluidized bed, and found that satisfactory image correlation coefficients and solid concentration average absolute deviation could be obtained, which indicates the proposed approach is promising for 3D fluidized bed measurements.

Mathematical Approach for Directly Solving Air–Water Interfaces in Water Emptying Processes

Emptying processes are operations frequently required in hydraulic installations by water utilities. These processes can result in drops to sub-atmospheric pressure pulses, which may lead to pipeline collapse depending on soil characteristics and the stiffness of a pipe class. One-dimensional mathematical models and 3D computational fluid dynamics (CFD) simulations have been employed to analyse the behaviour of the air–water interface during these events. The numerical resolution of these models is challenging, as 1D models necessitate solving a system of algebraic differential equations. At the same time, 3D CFD simulations can take months to complete depending on the characteristics of the pipeline. This presents a mathematical approach for directly solving air–water interactions in emptying processes involving entrapped air, providing a predictive tool for water utilities. The proposed mathematical approach enables water utilities to predict emptying operations in water pipelines without needing 2D/3D CFD simulations or the resolution of a differential algebraic equations system (1D model). A practical application is demonstrated in a case study of a 350 m long pipe with an internal diameter of 350 mm, investigating the influence of air pocket size, friction factor, polytropic coefficient, pipe diameter, resistance coefficient, and pipe slope. The mathematical approach is validated using an experimental facility that is 7.36 m long, comparing it with 1D mathematical models and 3D CFD simulations. The results confirm that the derived mathematical expression effectively predicts emptying operations in single water installations.