Computational Fluid Dynamics Simulations Research Articles

POD and mesh-adaptivity based reduce order model: Application to solve PDEs and inviscid flows

Time efficiency is a critical concern in Computational Fluid Dynamics (CFD) simulations of industrial applications. Despite the extensive research to improve the underlying numerical schemes to reduce the processing time, many CFD applications still need to improve on this issue. Reduced-Order Models (ROM) appeared as a promising alternative for significantly enhancing cost-effectiveness. The dimension of the initial problem is reduced significantly while keeping an acceptable level of accuracy. Proper Orthogonal Decomposition (POD), a data analysis technique, is widely used to construct a ROM to solve Euler and Navier-Stokes equations in CFD. Many aspects, however, need to be improved. In this paper, first, a general upper-bound error formula is derived, and second, a mesh-adaptivity based algorithm for snapshot locations in parameter space is provided (a sensitive step for POD-based ROM) in the context of Partial Differential Equations (PDE). The method’s efficiency is demonstrated through numerical tests by comparison to exact solutions and numerical results of a finite volume scheme on inviscid flow over a NACA0012.

Numerical simulation of cavitation flow around a wing with new tubercles design

The study investigates the benefits of adding non-uniform leading-edge tubercles to hydrofoils, drawing inspiration from the complex shaping of humpback whale flippers. The focus is on managing cavitation, a phenomenon that can affect hydrofoil performance. While previous research has mainly looked at uniform sinusoidal tubercles and their positive impact on flow dynamics and cavitation control, this study introduces a new perspective by examining the effects of non-uniform tubercles on hydrofoil performance. Advanced computational fluid dynamics (CFD) simulations using ANSYS Fluent 2024 were used to assess how these non-uniform tubercles affect the lift, drag, and cavitation characteristics of the NACA 634-021 hydrofoil. The simulations incorporated the Schnerr-Sauer cavitation model and the SST k-ω turbulence model to accurately capture the flow dynamics. The results show that non-uniform tubercles improve cavitation control by disrupting the flow in a way that delays the onset and reduces the severity of cavitation. The modified hydrofoils (non-uniform tubercles) display improved hydrodynamic performance compared to baseline designs, with significant reductions in drag and increased lift at higher angles of attack. This study provides valuable insights into the potential of mimicking natural designs to enhance flow stability and address cavitation issues, offering a significant contribution to advanced hydrofoil design in scenarios where controlling cavitation is essential. The broader implications of this research underscore the potential of mimicking natural designs to transform hydrofoil engineering and enhance flow stability in various applications.

CFD Modeling of HBI/scrap Melting in Industrial EAF and the Impact of Charge Layering on Melting Performance.

The melting of scrap and hot briquetted iron (HBI) in an AC electric arc furnace (EAF) is simulated by an advanced 3D computational fluid dynamics (CFD) model that captures the arc heating, the scrap/HBI melting process, and the solid collapse mechanisms. The CFD model is used to simulate a scenario where charge layering and EAF power profiles are provided by a real EAF operation. CFD simulation of the EAF operation shows proper prediction of the charge melting when compared with standard industry practice. Namely, the CFD model predicts a 32.5%/67.5% ratio of solid/liquid steel at the beginning of refining, which approaches the 30%/70% ratio used in standard practice. Based on this prediction, the melting rate in the CFD results differs by 8.3% from actual EAF operation. The impact of charge layering on melting is also investigated. CFD results show that distributing charge material into a greater number of layers in the first bucket (10 layers as compared to 4) enhances the melting rate by 12%. However, including dense material at the bottom of the furnace deteriorates melting performance, reducing the impact of the number of layers of the charge. The CFD platform can be used to optimize the use of HBI/scrap in real EAF operations and to determine best recipe practices.

Numerical Study on the Operational Ventilation Patterns of Alternative Jet Fans in Curved Tunnels

In tunnel operation ventilation systems, the arrangement of jet fans plays a decisive role in ensuring ventilation efficiency. Curved tunnels, due to their unique radius of curvature, exhibit significant differences in fan installation parameters and jet flow field distribution compared to traditional straight-line tunnels. In order to investigate the distinct characteristics, this research utilized computational fluid dynamics (CFD) simulation methods to analyze the ventilation performance of both an innovative, adjustable jet fan system and conventional jet fans within the context of curved tunnel configurations. The findings reveal that by adjusting the horizontal deflection angle of the novel jet fan, the flow field distribution can be effectively optimized, and the jet effect can be enhanced, thereby improving ventilation efficiency. Compared to traditional jet fans, the novel fan demonstrates a significantly greater capability in flow field optimization, especially when its horizontal deflection angle is adjusted, showing a trend where the jet effect initially increases and then decreases, with the longitudinal impact range being adjustable within a range of 5 m to 25 m.

An actuator-disk model augmentation for low-pressure axial fan simulation

Abstract Actuator-disk rotor models are important simulation tools for cost-effective industrial axial fan system analysis. Actuator-disk fan model performance, however, is constrained by the conventional use of 2D airfoil coefficient input data which limits the accuracy of the models to a narrow operating range free from significant secondary radial blade flow effects. Radial blade flow is characteristic of off-design fan operation which is often unavoidable within typical industrial fan system environments, so the enhancement of actuator-disk model performance for these conditions is desired. This paper accordingly presents a new means of robustly determining actuator-disk model coefficient inputs that are suitable for a wide range of fan operating conditions. The proposed Augmented Actuator-disk Method (AADM) capitalizes on new insights on the unique aerodynamic behavior of low-pressure axial fan rotors. The performance of the AADM is evaluated for two different industrial cooling fans and is shown to outperform existing actuator-disk coefficient formulations through computational fluid dynamics (CFD) simulations. The AADM is shown to better predict key fan performance metrics, spanwise blade force distributions, and to produce flow fields that are more physically representative (an important feature for industrial heat exchanger studies where the AADM is anticipated to be commonly applied). The AADM has been developed to be easily adopted in generic industrial fan analyses and is expected to serve as a valuable springboard for future actuator-disk fan model developments.

Simulation analysis and experimental research on static performance of water-hydraulic pressure difference control valve

Many hydraulic tools, like hydraulic cylinders and hydraulic artificial muscle joints are operated by adjusting pressure differences between different zones. Typically, the method employed to change the pressure difference is establishing hydraulic bridges and adjusting liquid resistance. While effective, this method's drawback is complex structures. To address this issue, a water-hydraulic pressure difference control valve, integrating two hydraulic bridges, was designed. The static performances including the output pressure difference, the flow rate and the force acting on the valve core were analyzed using AMESim and computational fluid dynamics simulations. Based on the simulation results, a prototype of voice coil motor direct drive pressure difference control valve was manufactured and the corresponding experiments were carried out. The computational fluid dynamics simulation results show that the internal leakage and the through-flow capacity difference between throttling grooves affect the flow field characteristics of the valve. When the pump pressure is 3 MPa and the valve opening is at the middle position, the internal leakage increases the flow rate from 2.25 L/min to 2.38 L/min, and the through-flow capacity difference reduces the control port pressure from the theoretical analysis of 1.5 MPa–1.41 MPa. Furthermore, combined with the analysis of the external liquid resistance, the AMESim model of the pressure difference control valve is modified. When the pump pressure is 3 MPa, the pressure difference and flow rate average deviations between the modified AMESim model and the experiment are 0.021 MPa and 0.048 L/min. Finally, a rotational angle experiment for a water hydraulic artificial muscle joints showed satisfactory control effects, suggesting the valve's application in controlling hydraulic tools and actuators.

Numerical and Design Study of Beehive in Building for Thermal Storage During Hours of Absence of Solar Radiation

This study investigates the numerical and design performance of Phase Change Materials (PCMs) embedded in a beehive structure within building envelopes for thermal energy storage during periods without solar radiation. Using Computational Fluid Dynamics (CFD) simulations in ANSYS Fluent, the study examines how the PCM system stabilizes indoor temperatures and improves energy efficiency. The research focuses on three months: January, November, and December, in Baghdad, Iraq, where diurnal solar radiation variations and temperature patterns are prevalent. Results reveal that the PCM-enhanced structure effectively absorbs heat during peak solar radiation hours, with solar radiation peaking at 574 W/m² in January, 596 W/m² in November, and 557 W/m² in December. The heat storage and release ability of the PCM keep up the interior temperature at its maximum of 309.96K and 310.04 K in Jan and Nov and 309.23 K in Dec with slightly less drop in the evening. The heat transfer coefficient was maximum in November 11.37 W/m²·K, while the PCM mass fractions showed significant phase change and the maximum value 0.425 in November. The thermal efficiency of the system was highest in November at 68.23% and also fluctuates slightly in the other remaining months. This study suggests that PCM systems, especially with the beehive structure, additionally improve isothermal stability and energy densities of the buildings in the changing climate, which is cost-effective and a more environmentally friendly strategy for regulating heating and cooling requirements.

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.

Heat recovery from hot water drainage: CFD simulation, energy efficiency and exergoeconomic analysis of concentric tube heat exchangers

This study investigates the performance and economic viability of a heat recovery concentric tube heat exchanger (HR-CTHE) integrated with water heating systems using either electricity or natural gas. The system recovers heat from hot water drainage to preheat cold water, thereby enhancing energy efficiency. Computational Fluid Dynamics (CFD) simulations are conducted, examining cold and hot water drain Reynolds numbers ranging from 1,000 to 20,000, hot water drain inlet temperatures from 303 K to 333 K, diameter ratios from 1.25 to 3, and inner diameters from 0.01 m to 0.05 m. Results indicate that at an inlet temperature of 333 K and a hot water Reynolds number of 20,000, the heat recovery rate reaches approximately 20,000 W, and the preheated cold water temperature can achieve 316 K. Exergetic efficiency is highest at 0.4392 for a diameter ratio of 1.25 and an inner diameter of 0.01 m. Economic evaluations using Net Present Value (NPV) and discounted payback period indicate that coupling HR-CTHE with electric heaters is more attractive, providing higher savings and quicker returns on investment compared to natural gas heaters. For instance, integrating HR-CTHE with electric water heaters yields a discounted payback period as short as 0.2 years. In contrast, for natural gas heaters, the payback period is around 2.2 years under similar conditions. The exergoeconomic analysis further demonstrates that natural gas heaters achieve cost-effectiveness only under high hot water Reynolds numbers and inlet temperatures, while electric heaters show significant benefits at moderate to high Reh. The study concludes with recommendations for optimizing HR-CTHE performance and cost-effectiveness, emphasizing higher hot water inlet temperatures, lower diameter ratios, and appropriate Reynolds numbers for both fluids.

A preoperative planning procedure of septal myectomy for hypertrophic obstructive cardiomyopathy using image-based computational fluid dynamics simulations and shape optimization.

Although septal myectomy is the preferred treatment for medication-refractory hypertrophic obstructive cardiomyopathy (HOCM), the procedure remains subjective. A preoperative planning procedure is proposed using computational fluid dynamics simulations and shape optimization to assist in the objective assessment of the adequacy of the resection. 3 patients with HOCM were chosen for the application of the proposed procedure. The geometries of the preoperative left ventricular outflow tract (LVOT) of patients in the systolic phase were reconstructed from medical images. Computaional fluid dynamics (CFD) simulations were performed to assess hemodynamics within LVOT. Sensitivity analysis was performed to determine the resection extent on the septal wall, and the depth of the resection was optimized to relieve LVOT obstruction while minimizing damage to the septum. The optimized resection was then transferred from systole to diastole to provide surgeons with instructive guidance for septal myectomy. Comparison between preoperative and postoperative hemodynamics showed an evident improvement with respect to the pressure gradient throughout the LVOT. The resected myocardium in the diastolic phase is more extended and thinner than its state in the systolic phase. The proposed preoperative planning procedure may be a viable addition to the current preoperative assessment of patients with HOCM.

Retinal and cerebral hemodynamics redistribute to favor thermoregulation in response to passive environmental heating and heated exercise in humans

ABSTRACT Core temperature (TC) changes, alongside exercise, affect hemodynamic responses across different conduit and microvascular beds. This study investigated impacts of ecologically valid environmental heat and exercise exposures on cerebral, skin and retinal vascular responses by combining physiological assessments alongside computational fluid dynamics (CFD) modeling. Young, healthy participants (n = 12) were exposed to environmental passive heating (PH), and heated exercise (HE) (ergometer cycling), in climate-controlled conditions (50 mins, 40°C, 50% relative humidity) while maintaining upright posture. Blood flow responses in the common carotid (CCA), internal carotid (ICA) and central retinal (CRA) arteries were assessed using Duplex ultrasound, while forearm skin microvascular blood flow responses were measured using optical coherence tomography angiography. Three-dimensional retinal hemodynamics (flow and pressure) were calculated via CFD simulation, enabling assessment of wall shear stress (WSS). TC rose following PH (+0.2°C, p = 0.004) and HE (+1.4°C, p < 0.001). PH increased skin microvascular blood flow (p < 0.001), whereas microvascular CRA flow decreased (p = 0.038), despite unchanged ICA flow. HE exacerbated these differences, with increased CCA flow (p = 0.007), unchanging ICA flow and decreased CRA flow (p < 0.001), and interactions between vascular (CCA vs. ICA p = 0.018; CCA vs. CRA p = 0.004) and microvascular (skin vs. retinal arteriolar p < 0.001) territories. Simulations revealed patterns of WSS and lumen pressure that uniformly decreased following HE. Under ecologically valid thermal challenge, different responses occur in distinct conduit and microvascular territories, with blood flow distribution favoring systemic thermoregulation, while flow may redistribute within the brain.

Comparative analysis of inlet and outlet cavity designs on the thermal-hydraulic performance of compact heat exchangers for combustion engine exhaust heat recovery

ABSTRACT Improving the Internal Combustion Engines (ICEs) overall thermal efficiency is crucial to reduce fuel consumption and emissions. To achieve this goal, waste heat recovery from exhaust gases remains the most promising strategy, which involves the utilization of compact heat exchangers. This study evaluates the performance of novel Monolithic Integrated Thermal Exchange Matrixes (MITEMs) designs for recovering exhaust heat from a 70 hp diesel engine, focusing on the impact of inlet/outlet cavities. Computational Fluid Dynamics simulations were employed to analyze the heat transfer rate, pressure drop, and overall thermal-hydraulic performance of different MITEM designs. The Rectangular Channels with Large Cavities (RCLC) design exhibited superior performance, enhancing the heat transfer rate by 14.7% compared to the baseline design while limiting pressure drop increase to 9.2%. The RCLC design increased local Nusselt numbers and heat transfer coefficients by up to 60%, achieving peak velocities of 98 m/s within cross-sectional planes. These findings provide valuable insights for optimizing exhaust heat recovery systems in diesel engines.

CFD Simulation of Dynamic Temperature Variations Induced by Tunnel Ventilation in a Broiler House.

Maintaining the optimal microclimate in broiler houses is crucial for bird productivity, yet enabling efficient temperature control remains a significant challenge. This study developed and validated a computational fluid dynamics (CFD) model to predict temporal changes in indoor air temperature in response to variable ventilation operations in a commercial broiler house. The model accurately simulated air velocity and airflow distribution for different numbers of tunnel fans in operation, with air-velocity errors ranging from -0.22 to 0.32 m s-1. The predicted airflow rates through inlets and cooling pads showed good agreement with measured values with an accuracy of up to 108.1%. Additionally, the CFD model effectively predicted temperature dynamics, accounting for chicken heat production and ventilation effect. The model successfully predicted the longitudinal temperature gradients and their variations during ventilation cycles, validating its reliability through comparison with experimental data. This study also explored different variable inlet configurations to mitigate the temperature gradient. The variable inlet adjustment showed the potential to relieve the high temperatures but may reduce overall ventilation efficiency or intensify temperature gradients, which confirms the importance of optimising ventilation strategies. This CFD model provides a valuable tool for evaluating and improving ventilation systems and contributes to enhanced indoor microclimates and productivity in poultry houses.

Computational Fluid Dynamics Modelling of Hydrogen Production via Water Splitting in Oxygen Membrane Reactors.

The utilization of oxygen transport membranes enables the production of high-purity hydrogen by the thermal decomposition of water below 1000 °C. This process is based on a chemical potential gradient across the membrane, which is usually achieved by introducing a reducing gas. Computational fluid dynamics (CFD) can be used to model reactors based on this concept. In this study, a modelling approach for water splitting is presented in which oxygen transport through the membrane acts as the rate-determining process for the overall reaction. This transport step is implemented in the CFD simulation. Both gas compartments are modelled in the simulations. Hydrogen and methane are used as reducing gases. The model is validated using experimental data from the literature and compared with a simplified perfect mixing modelling approach. Although the main focus of this work is to propose an approach to implement the water splitting in CFD simulations, a simulation study was conducted to exemplify how CFD modelling can be utilized in design optimization. Simplified 2-dimensional and rotational symmetric reactor geometries were compared. This study shows that a parallel overflow of the membrane in an elongated reactor is advantageous, as this reduces the back diffusion of the reaction products, which increases the mean driving force for oxygen transport through the membrane.

Numerical Modelling Of A Primary Heat Exchanger in sCO2 Power Cycles for Thermal Energy Storage Systems

Abstract Renewable energy sources are the key for long-term decarbonization of energy. However, the intermittent nature of renewables does not always meet the energy demand in the electrical grid. Thus, electrical heated Thermal Energy Storage systems (TES) coupled with sCO2 power cycles are investigated at Helmholtz-Zentrum Dresden-Rossendorf as a possible solution to balance this mismatch. In this study, a Printed Circuit Heat Exchanger (PCHE) is considered as candidate for the 1 MW primary heat exchanger, given the mechanical challenge induced by drastic pressure difference between the hot fluid of the TES and the cold fluid of the power cycle. The present work consists of two parts, one elaborates a 1D model in order to optimize the PCHE regarding the pump power required to compensate the pressure loss. It was found that the hot fluid coming from the TES accounts for 80 % of the total pump power after optimization because of its low density and its high mass flow rate. Furthermore, 3D simulations by Computational Fluid Dynamics (CFD) were done and compared to the results from the 1D model to ensure its validity. It was observed that the results from the 1D model and the CFD simulations are consistent, with a slight potential deviation in the calculation of the pressure profile.

Experimental and numerical study of characteristic parameters of Taylor bubble in vertical pipe under short-time gas injection

Purpose This study aims to investigate the formation and characteristics of Taylor bubbles resulting from short-time gas injection in liquid-conveying pipelines. Understanding these characteristics is crucial for optimizing pipeline efficiency and enhancing production safety. Design/methodology/approach The authors conducted short-time gas injection experiments in a vertical rectangular pipe, focusing on Taylor bubble formation time and stable length. Computational fluid dynamics simulations using large eddy simulation and volume of fluid models were used to complement the experiments. Findings Results reveal that the stable length of Taylor bubbles is significantly influenced by gas injection velocity and duration. Specifically, high injection velocity and duration lead to increased bubble aggregation and recirculation region capture, extending the stable length. Additionally, a higher injection velocity accelerates reaching the critical local gas volume fraction, thereby reducing formation time. The developed fitting formulas for stable length and formation time show good agreement with experimental data, with average errors of 6.5% and 7.39%, respectively. The predicted values of the formulas in glycerol-water and ethanol solutions are also in good agreement with the simulation results. Originality/value This research provides new insights into Taylor bubble dynamics under short-time gas injection, offering predictive formulas for bubble formation time and stable length. These findings are valuable for optimizing industrial pipeline designs and mitigating potential safety issues.

Computational Fluid Dynamics (CFD) in Arteriovenous (AV) Graft Implantation Through End-to-Side Anastomosis with Varying Tube Diameters Across Different Vascular Access Locations for Dialysis Treatment.

Background/Objectives: Arteriovenous (AV) graft is a procedure for hemodialysis performed in the arm. Optimizing AV graft design is vital to enhance haemodialytic efficiency in patients with kidney disease. Despite being a standard procedure, making it work optimally is still difficult due to various graft diameters and anastomosis configurations, which have limited studies. This research aims to find the ideal AV graft tube diameter on blood flow and pressure gradients and the ideal body site for AV graft implantation and to study their angles for dialysate flow. Methods: Nine models were designed in Autodesk Fusion 360 with 40°, 50°, and 60° angles each having 2 mm, 5.1 mm, and 14.5 mm diameters, all following specific equations on continuity, momentum (Navier-Stokes Equation)), and the Reynolds Stress Model (RSM). The CFD simulation of these models was performed in ANSYS Fluent with an established parameter of 0.3 m/s inlet velocity and stiff/no-slip graft and artery wall boundary condition. Results: As a result, the design with a diameter of 14.5 mm and a 40° angle was overall the most ideal in terms of minimal wall shear stress and turbulence. Conclusions: Thus the brachiocephalic area or the forearm is calculated to be the most optimal implantation site. Additionally, varying angles do affect dialysate flow, as smaller values cause less stress.

Convection flow of NE-phase change material-water mixture in evacuated tube solar collector manifold: Numerical analysis of MHD double-diffusive convection and exothermic reaction

This study investigates the convection flow of nano-encapsulated phase change material (NEPCM)-water mixture in an evacuated tube solar collector manifold, focusing on the effects of magnetohydrodynamic (MHD) double-diffusive convection and exothermic reaction. Computational fluid dynamics simulations using the Galerkin finite element method were employed to analyze temperature and concentration distributions, fluid flow, melting zone of PCM nanocapsules, Nusselt number, Sherwood number, entropy generation, and thermal performance. The numerical analysis considers a range of dimensionless parameters, including Rayleigh number (Ra=103−105), Lewis number (Le=0.1−10), buoyancy ratio (Nz=1−5), nanoparticle concentration (ϕ=0.01−0.035), fusion temperature (ϴf=0.1−0.9), Stefan number (Ste=0.1−0.9), Hartmann number (Ha=0−50), magnetic field inclination angle (γ=0°−90°), and Frank-Kamenetskii number (FK=0−2.5). Results show that increasing Ra enhances the average Nusselt number (Nuav) by up to 156.1 % and the average Sherwood number (Shav) by up to 104.5 %, while increasing the total entropy generation by up to 13,155 %. Increasing FK reduces Nuav by up to 42.2 % but increases Shav by up to 13.1 %. The Lewis number and buoyancy ratio significantly influence the hydrothermal performance, with Nuav exhibiting non-monotonic behavior and Shav increasing by up to 240.9 % as Le increases. The nanoparticle concentration enhances Nuav by up to 49.7 %. Interestingly, the magnetic field effects are less pronounced than in previous studies, with Ha having a minor impact on Nuav and Shav. These findings have significant implications for the design and optimization of evacuated tube solar collectors and other thermal energy storage systems, potentially leading to improved efficiency and performance in real-world applications.

Advancing packaging technology: computational fluid dynamics modeling for capillary underfill encapsulant in multi-chip heterogenous packages

Purpose The purpose of this study is to investigate the dynamics of capillary underfill flow (CUF) in flip-chip packaging, particularly in a multi-chip configuration. The study aims to understand how various parameters, such as chip-to-chip spacing (S12), chip thickness (tc) and others, affect the underfill flow process. By using computational fluid dynamics (CFD) simulations and experimental studies, the goal is to provide insights into understanding the dynamics of CUF in heterogeneous electronic packaging. Design/methodology/approach The paper introduces a CFD analysis and experimental study on CUF in a multi-chip configuration, aiming to understand underfill flow dynamics. A 3D geometry models of multi-chip arrangement are created using computer-aided design (CAD) software. After that, the CAD models are meshed and simulated in Ansys Fluent using incompressible and non-Newtonian fluid properties. The study maintains S12 of 2.86 and tc of 22.29 between experimental and simulation data for results validation. Next, a various of S12 values (1.14, 2.86, 5.71, 8.57, 14.29 and 20) which focus on tc of 22.29 have been investigated. Further studies have been conduct using S12 of 5.71 and tc of 8.00, 14.29 and 22.29. Findings Results show a strong correlation between simulation and experiment which validate the correctness and robustness of simulation. Further parameter’s studies using simulation for various of S12 indicated that higher S12 values lead to faster flow. This effect is due to large underfill weight from reservoir able to flow into S12 region which contributed to higher mass momentum movement. Furthermore, the effect of various of tc shows that the thicker the chip the faster the underfill to flow in S12 region. Research limitations/implications The intentional exclusion of solder bump pattern arrangements from the experiment and simulation may limit the study's ability to fully understand the impact of solder bump patterns on underfill flow. Therefore, more parameters can be investigated such as solder bump pattern, underfill weight and dispense pattern in the future using CFD. Practical implications The manuscript provides a comprehensive examination of the contributions of CFD to the advancement of knowledge regarding CUF phenomena in heterogeneous electronic packaging assemblies. Moreover, it delineates the utilization of CFD methodologies to assess the influence of chip-to-chip spacing (S12) and the thickness of the chip (tc) on the underfill flow characteristics. Originality/value This paper fulfills an identified need of computational fluid dynamics method to study capillary underfill flow dynamics in heterogenous electronic packaging.

On the design and fabrication of nanoliter-volume hanging drop networks

Hanging drop cultures provide a favorable environment for the gentle, gel-free formation of highly uniform three-dimensional cell cultures often used in drug screening applications. Initial cell numbers can be limited, as with primary cells provided by minimally invasive biopsies. Therefore, it can be beneficial to divide cells into miniaturized arrays of hanging drops to supply a larger number of samples. Here, we present a framework for the miniaturization of hanging drop networks to nanoliter volumes. The principles of a single hanging drop are described and used to construct the fundamental equations for a microfluidic system composed of multiple connected drops. Constitutive equations for the hanging drop as a nonlinear capacitive element are derived for application in the electronic-hydraulic analogy, forming the basis for more complex, time-dependent numerical modeling of hanging drop networks. This is supplemented by traditional computational fluid dynamics simulation to provide further information about flow conditions within the wells. A fabrication protocol is presented and demonstrated for creating transparent, microscale arrays of pinned hanging drops. A custom interface, pressure-based fluidic system, and environmental chamber have been developed to support the device. Finally, fluid flow on the chip is demonstrated to align with expected behavior based on the principles derived for hanging drop networks. Challenges with the system and potential areas for improvement are discussed. This paper expands on the limited body of hanging drop network literature and provides a framework for designing, fabricating, and operating these systems at the microscale.