Flow Behavior Research Articles

Enhancing retention of biological fluid transport of magnetized thermal radiative pseudoplastic nanofluid with double diffusion convection, viscous dissipation and boundary slips

This study investigates how thermal radiation, viscous dissipation, double-diffusive convection, and slip boundaries collectively affect the peristaltic movement of a magneto-pseudoplastic nanofluid within a uniform channel. The inclusion of slip boundary conditions at the channel walls helps to accurately represent the flow behavior of the nanofluid near these boundaries. The magneto-pseudoplastic nanofluid exhibits peculiar rheological features to flow dynamics due to pseudoplastic characteristics of nanoparticles in its composition and exposure to magnetic force. The mathematical formulation of motion equations is done through appropriate technique combining the properties of heat radiation, magnetic flux, double diffusion convection, and rheological features. The equation is further simplified by suitable method. The current study aims to evaluate the peristaltic movement under influence of slip boundaries characteristics, sort of concentration, heat radioactivity, flux properties, and temperature profile. Moreover, it will assess the flow dynamics with ratio of mass and heat exchange under the effect of critical parameters which include Prandtl number, Grashof number, slip limitations, and Hartmann number. So, the research will widen the theoretical underpinning of complex fluid transportation of magneto-pseudoplastic nanofluids under peristaltic flux and explicate the practical outcomes in terms of slip boundary settings in such systems. The results and conclusions are imperative for restructuring and devising biomedicine engineering, microfluidic equipment and gadgets, manufacturing techniques for complex fluid with peristaltic flow under the influence of slip limitations and magnetic force.

Numerical Methods in Modelling of Red Blood Cellflow Behaviour Through a Specific Stacking Pattern

Abstract: The dynamics of red blood cells (RBCs) is one of the major aspects of the cardiovascular system that has been studied intensively in the past few decades. Using computational fluid dynamics, complex nonlinear fluid flows have been modeled. The dynamics of biconcave RBCs are thought to have major influences in cardiovascular diseases and other problems associated with cardiovascular flow behaviour, and the determination of blood rheology and properties. Most reported computational models have been confined to the behaviour of a single RBC in 2-dimensional domains, under physiological flow conditions. This work investigates a particular stacking pattern in analyzing the RBC flow behavior under physiological flow conditions, using the D2Q9 lattice Boltzmann numerical method created using Matlab. Prior to the analysis the Matlab script was benchmarked using the Poiseuille flow and the flow around the cross-section of a cylinder, after which the accuracy of the method used was determined. The benchmarks showed that the lattice Boltzmann code had minimal error. The accuracy was determined using the data obtained from Matlab and a created excel program. It also showed that the lattice Boltzmann method was of the first order, which corresponds with results existing in literatures. The analysis of the stacking pattern showed how RBC flows through the chosen stacking pattern, and the results are shown.

Flow and heat transfer characteristics of low water content jet fuel in U-bend tubes: A numerical study using LES and DPM approaches

This study provides an in-depth analysis of the flow and heat transfer behavior of low-water-content jet fuel (α ≤ 2 %) in U-bend tubes, utilizing Large Eddy Simulations (LES) and Discrete Phase Models (DPM). The research focus on the influence of radii of curvature ratio (r/D), flow rates (Qtp) and α on flow dynamics and heat transfer mechanisms. Flow fields for r/D = 1 and r/D ≥ 2.5, where distinct secondary flow structures, play a critical role in shaping internal flow behavior. These vortices significantly enhance flow mixing and heat transfer, especially on the inner wall, through complex multi-level vortex interactions. The local wall Nusselt number shows a close correlation with vorticity trends, initially increasing and then decreasing, with notable deviations near the inlet and outlet regions. This non-uniform heat transfer is primarily driven by the interaction of secondary flow structures and adverse pressure gradients near the inner wall, while higher Qtp and smaller r/D can improve heat transfer uniformity under certain flow conditions. The presence of droplets increases the total wall Nusselt number by 4 % to 60 % compared to single-phase jet fuel flow, due to two-phase interaction and boundary layer disruption. Finally, the study proposes modified correlations for pressure drop gradients and total wall Nusselt numbers, accounting for effects of r/D and multiphase heat transfer processes. These correlations, validated with RRMSEs of 3.54 % and 6.80 % respectively, provide valuable insights for improving heat transfer efficiency in fuel systems and form a theoretical foundation for real-time monitoring technologies in aircraft fuel lines.

A Comprehensive Methodology for Investigating Cocurrent Spontaneous Imbibition in Coal.

Visualizing and quantifying fluid distribution during spontaneous imbibition at the nanomicro scale is vital for understanding microfluid flow and dynamic wettability in coalbed methane (CBM) reservoirs, which could serve as a fundamental basis for optimizing the parameters of the hydraulic fracturing process. In this study, fluid distribution and flow behavior can be acquired by combining nuclear magnetic resonance (NMR) and in situ X-ray microcomputed tomography (μ-CT) technologies. Meanwhile, spontaneous imbibition stages were studied to analyze gas-water exchange efficiency. Additionally, dynamic wettability of gas-water was calculated during the process of spontaneous imbibition based on NMR. The results show that imbibition characteristics can be divided into three categories based on NMR. In type I, changes in imbibition fluid within nanopores are not obvious, while significant changes occur in micro pore-fractures, especially during the early stage of imbibition (0-2 h) for type I, which is almost the opposite of type II. Coal samples of type III exhibit low porosity and permeability, making it difficult for water to flow through the pores in coal due to capillary forces. The dynamic process of spontaneous imbibition can be divided into four stages using μ-CT equipment, with the third stage displaying the highest imbibition efficiency. This stage is characterized by frequent imbibition fluid exchange among various-scale fractures, which is related to the wettability and pore-fracture of the coal sample. A negative correlation between contact angle and T 2g was observed, where hydrophobic samples corresponded to a smaller geometric average of T 2g in the sample. In addition, the wettability of coal samples changed dynamically during the process of imbibition, with the contact angle gradually decreasing as imbibition time increased, which may be related to the formation of water film and hydration reactions.

Leak-Rate Through Carbon Brush Seals: Experimental Tests Versus Predictions From a Porous Medium Approach

Abstract This study presents a detailed comparative analysis between experimental leakage flow rates and numerical predictions for carbon brush seals with long bristles, utilizing a porous medium model approach. A series of tests were carried out on a static rig (without rotor rotation). The experimental setup allows tests under various interference conditions, revealing significant insights into the flow behavior through the brush seal. A numerical model based on the Darcy-Forchheimer equation is developed to interpret the complex flow dynamics within the brush seal, accounting for viscous, compressible and inertial effects. The study evaluates the impact of brush deformation and porosity on flow resistance, leveraging experimental data to refine the numerical model parameters. This investigation not only deepens the understanding of brush seal flow physics but also improves the predictive accuracy of the numerical model in simulating operational conditions.

Numerical and experimental investigation on mixed convection heat transfer inside cavity heated from below with reciprocating moving upper surface

This investigation involves a numerical and experimental work on mixed convective heat transfer inside cavity heated from below and reciprocating moving upper surface. For the experimental work, the smoke method is used for the air flow visualization. The experiments include the measurements of air temperature inside the cavity and upper and lower surfaces of duct. For the numerical work, the velocity boundary condition of the upper surface is defined asu=umaxsinωt with low constant temperature (Tc), whereas the lower surface of duct is kept at constant wall temperature (Th) and the vertical walls are well insulted. The mathematical model adopted in the calculations are solved by building an own code using finite difference method in MATLAB software The influences of Richardson number (Ri), Aspect Ratio (AR) and dimensionless period (dp) on the flow behavior and average Nusselt number (Nu) are investigated. The experimental and numerical outcomes are compared under identical conditions, where the comparison gives a good matching between them. The numerical outcomes demonstrated that the rising in AR with constant Ri leads to increase the Nu values. For AR=1 and Ri=0.01, the average Nu increases with dp. The experimental results show that the Nu value increases to 3.2 with increasing AR to 2 under constant Ri=10. The dp decreases to 33 s when AR is increased under constant Ri value. The data indicated that Nu rises with reducing in Ri for all AR values. The value of Nu depends on dp, AR and Ri. The multi-cells flow is observed when Ri is raised under constant AR value. The maximum Nu value is obtained for low values of AR and Ri. The profiles of Nu reveal that AR, Ri and dp have considerable influences on the heat transfer.

Explosion risks: Variety of deflagration-to-detonation transition scenarios in smooth tubes

In the framework of comprehensive assessment of explosion risks on board of spacecrafts and on the facilities of launch places, the paper is focused on the detailed analysis of particular scenarios of deflagration-to-detonation transition taking place in smooth tubes filled with acetylene-oxygen mixtures of different compositions. By means of precise numerical simulation it is demonstrated that various scenarios of detonation onset can take place depending on the mixture composition and its initial thermodynamic state. It is demonstrated that independent on the particular scenario always the basic mechanism of detonation onset via the formation of strong enough shock wave takes place. In more reactive mixtures the strong shock originates from the self-sustained process of joint pressure build up and reaction intensification exactly at the flame front. In less reactive mixtures the transient flow behavior leads to the shock waves generation and interaction. As a result, a brand new reaction kernel could arise in the area of shock waves interaction. In number of cases, that leads to the coupling between the shock wave and the newborn reaction front and results in the strong shock formation and further detonation onset.

Hemodynamic characteristics of pulsatile blood flow through bifurcated stenosed carotid artery

PurposeCarotid artery is often associated with plaque deposition because of its shape and associated flow features. The shape of stenosed bifurcation is characterised by bifurcation angle (ß), planarity angle (α) and severity of stenosis (b). In the present work, three-dimensional numerical computations have been performed to analyse the effect of these geometrical parameters of carotid bifurcation on the characteristics of flow.Design/methodology/approachGoverning equations of this study were solved using ANSYS Fluent 20.1 and the blood flow was considered as laminar, pulsatile and non-Newtonian. Instantaneous flow behaviour has been illustrated using vorticity, velocity and helicity contours, whereas the time-averaged wall shear stress (τw¯) and oscillatory shear index (OSI) quantify the time-averaged behaviour.FindingsThe recirculation zone and secondary flow are ascertained to be stronger for higher bifurcation angle as compared to the lower bifurcation angle. Strength of the secondary flow is found to reduce with increase in α from 0° to 10°, whereas it grows as α varies from 10° to 20°. For higher bifurcation angles, τw¯ is lower than 2 Pa and OSI is greater than 0.2 on the outer walls. Similar observations were made for τw¯ and OSI distribution on bottom wall in non-planar cases, which predicted atherogenic locations.Originality/valueThe values for ß were taken as 30°, 45°, 60° and 75°, whereas for α, range of 0°–20° was chosen. The stenosis was considered on the outer wall of internal carotid artery and its severity was considered within the range of 0%–60%.

Machine Learning-Based Predictions of Flow and Heat Transfer Characteristics in a Lid-Driven Cavity with a Rotating Cylinder

Machine learning-based predictions of heat transfer characteristics in lid-driven cavities are transforming the field of computational fluid dynamics (CFD). Lid-driven cavities are a fundamental problem in fluid mechanics, characterized by the motion of a fluid inside a square cavity driven by the motion of one of its walls. The goal of this study was to develop multiple machine-learning regression models and highlight the discrepancies between the predicted and actual average Nusselt numbers. Additionally, the study utilized physics-informed neural networks (PINNs) to model the flow and thermal behavior at both low and high Reynolds numbers. The results were compared among actual data from computational fluid dynamics (CFD) simulations, PINN models trained with CFD data, and purely PINN models created without any prior data input. The findings of this study showed that the random forest model exhibited an exceptional stability in its predictions, consistently maintaining low errors even as the Reynolds number increased compared with other machine-learning regression models. Further, the results of this study in terms of flow and thermal behavior within the cavity were found to depend significantly on the PINN method. The data-driven PINN exhibited a much lower mean average errors at both Reynolds numbers, while the physics-based PINN showed lower physics loss.

Couette flow of micropolar fluid in a channel filled with anisotropic porous medium

This paper presents a mathematical model for the flow of micropolar fluid in a horizontal channel filled with an anisotropic porous medium, bounded by two parallel plates—where the upper plate is stationary, and the lower plate moves at a constant velocity. The flow, driven by both a constant pressure gradient and the movement of the lower plate, is governed by the Darcy-Brinkman equation. Using no-slip and no-spin boundary conditions, we analytically derive expressions for the velocity, microrotational velocity, and stress distributions. The study provides a graphical analysis of the flow behavior influenced by key parameters such as the Darcy number, porous medium anisotropy, anisotropy angle, and the micropolar fluid’s material parameters. Furthermore, the effects of the material parameters and Darcy number on shear stress and couple stress are thoroughly investigated. The findings have applications in modeling fluid flow in striated or fractured rock formations.

Hydrodynamic analysis of core annular flow with a viscoplastic lubricant

Core annular flow (CAF) with viscoplastic lubrication (VPL) is an attractive proposition for pipeline transportation of high viscous oil, slurries and suspensions. Past studies have performed stability analysis to show that the unyielded zone at the liquid-liquid interface stabilizes CAF by suppressing interfacial instabilities. However, an in-depth investigation of the flow hydrodynamics and the conditions which reduce the pumping power within stable CAF range using VPL has not been reported till date. Moreover, most of the studies have considered a Bingham Plastic liquid in the annulus. Only a single study (Usha & Sahu, 2019) is reported with Herschel-Bulkley (HB) liquid in the annulus that considers the entire annulus to be in the shear zone. Another experimental study (Huen et al., 2007) has demonstrated stable core annular flow with a shear thinning core and a HB annulus. In the present work, we analyze viscoplastically lubricated CAF for a Newtonian core where the yield stress annular liquid is described by the generalized HB model. The simplified analysis can predict CAF stability and is further explored to (i) assess the efficacy of VPL for stable energy-efficient oil transportation, and (ii) enhanced throughput without clogging during suspension transportation. The analysis, validated against data from literature, unravels the influence of rheological properties on flow hydrodynamics. We note that an annular liquid with low flow behavior index, n and yield stress, τy lowers pumping power, but the yield stress should be sufficient to form a plug zone at the interface for suppressing instabilities and stabilizing CAF. For viscous oil, a phase diagram in dimensionless coordinates (Reynolds number of the oil core and Herschel-Bulkley number of the annular liquid, both expressed at the inlet conditions) suggests the range of operation where an available HB liquid can serve as an effective annular lubricant for energy-efficient transportation.

A peridynamics approach modeling gas flow in porous media with damaged regions

The study of gas flow within porous media, particularly those characterized by complex pore-fracture networks, is critical for applications in fields such as shale gas engineering, gas extraction, and hydrogeology. This paper proposes a convenient and novel peridynamics approach to describe gas flow behavior in fracture regions and transition regions between fractured and intact regions in porous media, where the bonds naturally describe the interactions between material points in damaged areas. For implementation, we interpolate the permeability of the bonds in the transition region by using local damage values, and adopt a meshfree discretization approach that does not require additional mesh refinement for damaged or fractured regions. Numerical examples are provided and compared with the traditional finite element method to verify the accuracy and effectiveness of the proposed method.

Simulating conjugate heat and mass transfer by the advanced perforated wall model for effusion cooling

Full-scale Computational Fluid Dynamics (CFD) numerical simulations can accurately predict the heat flux and metal wall temperature of gas turbine combustor liners, but they require considerable computational resources. In present work, an Advanced Perforated Wall model (A-PWM) has been developed to resolve the flow and heat transfer behaviors in this confined region. The geometric structure of the effusion cooling perforated plate is simplified, while the fluid-solid coupling heat transfer processes are still fully considered in details. The three-dimensional Reynolds Average Navier–Stokes simulations have been carried out for both a single-hole cooling plate and a multi-hole perforated cooling plate by using A-PWM. For simulations of the single-hole cooling plate, the cooling effectiveness in the downstream of the jet flow with the x/D ranging from 2 to 8 predicted by A-PWM shows good agreement with conjugate heat transfer model and experimental results. For multi-hole perforated cooling plate, the differences of cooling effectiveness between the prediction results by A-PWM and experimental results are just within 5%, confirming the developed model’s accuracy in predicting the effusion cooling. In addition, the A-PWM can also be employed to analyze the temperature distribution inside the solid zone. In simulations of both the single-hole cooling plate and the multi-hole perforated cooling plate, the use of the A-PWM model can lead to a reduction of over 35% in grid count compared to the conjugate heat transfer model, significantly reducing the computational time.

Dot-array porous medium model for windscreen and its simulation accuracy analysis

Porous medium models have long been prevalent numerical computation tools. Although they exhibit swift computational speed, their accuracy in simulating windscreen perforation structures is challenged. This paper introduces the innovative dot-array porous medium (DAPM) model, which accurately portrays the perforation structure and material characteristics of a windscreen by establishing virtual holes on the porous medium. Not only does it simplify modeling by eliminating complex perforation processes, but it also adeptly simulates the flow behavior of the windscreen. The comprehensive comparison between the DAPM model and the physical mesh model, traditional porous medium model, as well as wind tunnel test results, demonstrates that the DAPM model not only possesses rapid computational speed but also delivers outstanding precision in results. In terms of velocity distribution, vortex distribution, and flow intensity in the flow field, the model indicates a high level of accuracy, clearly exceeding that of the porous medium model. Moreover, the DAPM model showcases high versatility and adjustability in practical applications. By adjusting dimension parameters, it demonstrates the capability to precisely simulate any windscreen with holes arranged in a matrix pattern. This research provides an efficient and reliable tool for the numerical simulation of windscreens, with broad application prospects.

Deformation behavior of Gd alloyed CoCrFeNi high entropy alloy at high temperature under the influence of local nano-ordered structure and misorientation

The thermomechanical processing (TMP), which is an industrial process that includes deformation and heat treatment, represents a novel approach to enhancing the mechanical properties of metallic materials. However, it requires extensive research on the high-temperature deformation behavior of alloys during its application process. The present study conducts hot compression tests at 700 °C and 800 °C, as well as detailed microstructural characterization of the deformed material after hot deformation, to comprehensively discuss the mechanical properties and deformation behavior at high temperature of the (CoCrFeNi)100-xGdx (x = 0, 0.5, 1, 2, 3 at.%) HEAs. The (CoCrFeNi)100-xGdx HEAs exhibit an excellent combination of strength and plasticity in high temperature. The original dendritic microstructure in the (CoCrFeNi)100-xGdx HEAs was completely fractured and transformed into a mass of deformed structures during thermal deformation. The mechanical properties at high temperature of the alloy system originate from the misorientation in the microstructure. Dislocation slip is the main deformation mechanism of the alloy system at high temperature. The coordinated deformation of the soft orientation for FCC phase and the hard orientation for HS phase affects the dislocation morphology in the microstructure. Dynamic recovery (DRV) plays a dominant role in the flow behavior of the alloy at high temperature, and work hardening is the main strengthening mechanism during plastic deformation. The correlation between microstructure evolution and mechanical properties of Gd alloyed CoCrFeNi HEAs during hot deformation has been established through comprehensive studies on deformation behavior.

The pinning characteristics of droplets and the self-repair mechanism of lubricating film on nanoporous surface: A molecular dynamics perspective

The nanoscale pore gives rich dynamic information to the flow behavior of the droplets exuded on the SLIPS (Smooth Liquid-Infused Porous Surface). The key to realizing fast self-healing of lubricating film is to understand the dynamic law of droplets at nano-orifice. In this paper, a dynamics model of the exudation and spreading behavior is established by the non-equilibrium molecular dynamics simulation. The characteristics and the mechanism of pinning and spreading of nano-droplets were studied. We found that adjusting the wettability and pore diameter can change the liquid exudation and the pinning time of droplets at the orifice. The weaker wettability and larger pore diameter both can increase the exudation velocity and reduce the pinning time of the droplets, which then improves the spreading of exuded droplets and the self-repairing efficiency of the damaged liquid film. As the pore diameter increases, the spreading area of the droplets on the surface of the pore increases. The increase in the wettability also facilitates the spreading behavior, but the outflow rate of the liquid from the pore decreases. Under the combined effect of the two factors, the spreading area of droplets first increases and then decreases with the wettability increases. The results provide potential insights into the spreading mechanism of nanodroplets on porous surfaces.

Effect of solids concentration and operational variables on the performance of a geometrically optimized concentrator hydrocyclone employing a pseudoplastic fluid

The employment of hydrocyclones in thickening operations is an attractive option when compared to centrifuges and filters due to their low operating, maintenance, and acquisition costs. However, the performance of hydrocyclone separation is impaired as the concentration of solids and the viscosity of the suspension increases. Using geometric optimization techniques, the Federal University of Uberlândia developed one concentrator hydrocyclone named HC. When working with diluted and Newtonian slurries, the HC could generate a stream 45 times more concentrated than the one fed into it. In this study, the HC performance was evaluated when operating pseudoplastic fluids containing up to 10% solids by volume. The combination of the underflow diameter and vortex finder length with an adequate supply of pressure energy maintained the thickening potential of the HC even when the rheology of the fluid was changed. For different working suspensions, the HC hydrocyclone achieved a minimum water split to underflow of 5%, a maximum concentration ratio of 7.0, and a maximum efficiency of 49%. The encouraging results obtained by the HC validated the benefits of the geometric optimization, as they point to a significant advance in the thickening operation of non–Newtonian sludges with a flow behavior index greater than 0.5.

The influencing factors and mechanisms of granular flow dynamics

This study proposes an approach that combines experimental and numerical simulations to comprehensively elucidate the factors influencing the physical behaviour of granular flows. The rotating drum experiments are used to investigate the behaviour of mono-sized and poly-sized particle systems under increasing rotational speed of the drum. The experimental data is then integrated with GPU-based DEM simulations. This allows for the inverse calibration of key parameters like dynamic friction and damping ratios. These calibrated parameters are subsequently utilized throughout the study to explore the influence of various factors on granular flow dynamics. The increase in RPM leads to a rise in particle dispersion due to the interplay between centrifugal forces and particle collisions. The higher dynamic friction angles result in a steeper angle of repose and consequently shorter and longer runout distances for both mono-sized and poly-sized particles respectively. Conversely, increasing damping ratios lead to a decrease in the angle of repose and promote a well-organised flow patterns with increased frictional resistance, suggesting a significant impact on overall flow dynamics. The study paves the way for new insights into the behaviour of complex particulate systems, potentially benefiting various fields concerned with granular flow phenomena.

Numerical simulations on non-reactive multiphase flow during the transition from vent activation to venting with vent cap fragments in 18650 lithium-ion batteries

Mandatory safety devices, prevalent in lithium-ion batteries (LIBs), enable current interrupt device (CID)-and vent-activated power-off protection by sensing the electrochemical gas production boost triggered by thermal runaway (TR). For an in-depth understanding of the early warning of safety devices, the thermodynamic and multiphase flow behaviour of gases-vent particles interaction under the non-combustion venting phase is numerically investigated. From the gas phase simulation results, the flow field structure of the counter-rotating vortex pairs (CVPs) bounded by vent cap fragments enhances the heat transfer between ambient air and the venting gas, and the local venting gas temperature can reach a drop of >100 K. The transient three-dimensional spatial evolution characteristics of vent particles interacting with vent cap fragments at the early stage of the venting process after 18650 thermal runaway-induced vent-activation is originally demonstrated, including gas temperature and velocity as well as particle size and temperature. The spatial distributions of polydisperse particle size and temperature under the process of non-combustion venting are used to characterize the ejected particles' behaviour, which reveals the particle trajectories in particle-laden streams and their heat-transfer characteristics. The results show that ejected particles with relatively high temperatures and large sizes are mainly clustered within the cell diameters, and possible thermal runaway propagation inside the module can be triggered by the smaller-size particles of higher temperature sprayed in the periphery when the blocking effect of the vent cap fragment is weakened.

Computationally cost-efficient analysis of the flow behavior of twin-fluid atomizers using computational fluid dynamics

In industrial-scale operations, wet electrostatic precipitators (WESPs) are used to minimize particulate matter, employing atomizers such as single-fluid and twin-fluid atomizers (TFAs). While TFAs provide several benefits over single-fluid atomizers, quantifying their spray characteristics is more complex, necessitating comprehensive case studies to design the internal structure of the spray and achieve desired properties. This study employed computational fluid dynamics (CFD) to simulate the internal and external flow phenomena of TFAs in industrial-scale WESPs, aiming to facilitate various parametric studies by reducing the high computational costs associated with analyzing high-speed internal flows and particle dynamics within the spray system. To decrease computational costs, the simulation was divided into two parts using stepwise segregated scenarios: Part I focused on the high-cost internal flow analysis, examining the spatiotemporal evolution of internal flow until it is fully developed, followed by droplet size distribution estimation at the nozzle. Part II computed the external flow of the spray, assessed potential cost reductions by examining the interactions between dispersed droplets, and validated the spray angle, penetration, and coverage against experimental data. The segregated strategy employed mapping techniques to integrate the two parts seamlessly. The simulation results closely matched the experimental benchmarks for spray angle, penetration, and coverage within a minimal error margin (< 5 %), demonstrating the model’s accuracy in capturing actual spray phenomena in TFAs. This approach significantly reduced the computational cost by more than twentyfold compared to conventional one-step solvers, offering a viable method for conducting various case studies in spray CFD simulations.