Finite-element Flow Model Research Articles

Impact of Hydrogen Voiding in Chip-to-Chip Electroless All-Copper Interconnections.

Three-dimensional (3D) integration has become a leading approach in chip packaging. The interconnection density and reliability of micro-bumps in chip stacking are often threatened by high bonding temperatures. The method of building chip-to-chip interconnections by electroless deposition of metal has its distinct merit, while the interfacial defect issue, especially that related to voiding during the merging of opposite sides, remains largely unsolved. In this study, to trace the influencing factors in the voiding, the growth characteristics of the electroless all-copper interconnections were examined by carrying out deposition experiments in a microfluidic channel device. The results show that when the gap between the opposite copper bumps to be electrolessly merged is as low as 10 μm, significant voids appear at the inflow side and the top of the copper bumps because the hydrogen cannot be expelled in time. A finite-element flow model of the plating solution between the chips was established, which showed that the flow rate of the plating solution around the copper bumps was much higher than in the merging gap, causing an uneven supply of reactants. Based on these findings, we proposed two potential solutions, one is to improve the flow mode of the plating solution, and the other is to add the reaction inhibitor, 2,2'-bipyridine. Finally, the combination of these two approaches successfully achieved an improved merging quality of the copper joints.

Flow Mechanisms and Lubrication Performance of Water-Lubricated Thrust Bearings with Herringbone Grooves

Due to their excellent stability and zero leakage capability, thrust bearings with herringbone spiral grooves are frequently used in transmission mechanisms. However, the lubrication mechanism of thrust bearings has not been clearly understood and explained, preventing the optimization of the bearing performance. Thus, this paper is devoted to solving this problem by building a three-dimensional finite element flow model. In this model, the change in viscosity temperature is considered using Roelands equation, and the turbulence and cavitation are taken into consideration. Using the established model, the influence of parameters such as spiral angle, groove width ratio, and rotational speed on the cavitation area of the thrust bearing are analyzed. The pressure contour and speed distribution are obtained inside the clearance, as well as the volume fraction of the gas phase at the end face. Finally, according to the analysis results, the optimum structural parameter for the herringbone spiral groove structure is proposed, which enables higher bearing stability and provides a reference for engineering practice.

A robust fully mixed finite element model for flow and transport in unsaturated fractured porous media

A fully mixed finite element (MFE) model is developed for nonlinear flow and transport in unsaturated fractured porous media with matrix-fracture and fracture-fracture fluid and mass exchanges. The model is based on the discrete fracture matrix (DFM) approach and assumes cross-flow equilibrium in the fractures. The MFE method is employed for the spatial discretization of both flow and transport on the 2D-matrix elements as well as on the 1D-fracture elements. An upwind scheme is employed to avoid unphysical oscillations in the case of advection dominant transport. The temporal discretization is performed using high-order time integration methods and efficient automatic time-stepping schemes via the MOL.Two test problems dealing with flow and mass transport in saturated and unsaturated fractured porous media are simulated to show the validity of the new model by comparison against (i) a 1D-2D Comsol finite element model and (ii) a 2D-2D Discontinuous Galerkin (DG) model where both fractures and matrix continua are discretized with small 2D mesh elements. The robustness and efficiency of the developed 1D-2D MFE model are then investigated for a challenging problem dealing with infiltration of contaminated water into an initially dry soil involving a fracture network.The new model yields stable results for advection-dominated and advection-dispersion transport configurations. Further, the results of the 1D-2D MFE model are in very good agreement with those of the 2D-2D DG model for both configurations. The simulation of infiltration of contaminated water into a dry fractured soil shows that the 1D-2D MFE model is within 15 times more efficient than the 2D-2D DG model, which confirms the high benefit of using robust and efficient DFM models for the simulation of flow and transport in fractured porous media.

Ductile failure prediction during the flow forming process

Flow forming is an incremental metal-forming technique used for manufacturing thin-walled seamless tubes where a hollow metal material flows axially along the mandrel by a rotating mandrel and multiple cylinders. Flow formed materials are frequently used in the aviation and defence industry and it is crucial to examine the influence of the process on the material in terms of ductile fracture. However, the process requires in-depth failure analysis considering different process parameters and materials. The current study is concerned with investigating the ductile fracture behavior during flow forming process which includes complex stress states in terms of stress triaxiality and Lode parameter. Ductile fracture is simulated through the modified Mohr-Coulomb model. A user material subroutine (VUMAT) has been developed to implement the plasticity behavior and the damage accumulation rule. The model is validated through finite element (FE) simulations performed in Abaqus/Explicit and using the experimental data in Granum et al. (2021). The validated framework is applied to a finite element model of flow forming process with single and three rollers. The incremental forming with three rollers significantly reduces the damage accumulation. The initial results show a highly damaged region outer and inner surfaces of the workpiece after 40% thickness reduction ratio, and the forming limit is predicted as about 40-45%. The modeling framework is planned to be applied using various process parameter for different materials.

Optimized Pumping Strategy for Reducing the Spatial Extent of Saltwater Intrusion along the Coast of Wadi Ham, UAE

Many coastal aquifers are facing severe anthropogenic impacts such as urbanization, industrialization and agricultural activities are resulting in a saltwater intrusion. This establishes the need for a sustainable groundwater management strategy aimed to overcome the situation. Pumping of brackish/saline water to mitigate saltwater intrusion is a major potential approach to effectively control saltwater intrusion. However, this method has many challenges including selection of appropriate discharge rates under an optimum number of pumping wells and at specified wells distance from the shoreline. Hence, this study developed a Finite Element Flow and solute transport model (FEFLOW) to simulate three scenarios to assess the most appropriate pumping rates, number of wells and optimum well locations from the shoreline. These parameters were assessed and evaluated with respect to the change in groundwater saline concentration at different distance from the coastline. The 15,000 mg L−1 isosalinity contour line was used as a linear threshold to assess the progression of saltwater intrusion along three major locations in the aquifer. Scenario One was simulated with a constant number of wells and rate of pumping. Shifting of pumping wells to several distances from the shoreline was conducted. Scenario Two assessed the most appropriate number of pumping wells under constant pumping rates and distances from the shoreline and in scenario 3, the optimum pumping rates under a constant number of wells and distance from the shoreline were simulated. The results showed that the pumping of brackish/saline water from a distance of 1500 m from the shoreline using 16 pumping wells at a total pumping rate of 8000 m3 d−1 is the most effective solution in contrasting the saltwater intrusion in the Wadi Ham coastal aquifer.

Three-dimensional flow model development for thermal mixing and stratification modeling in reactor system transients analyses

Mixing, thermal-stratification, and mass transport phenomena in large pools or enclosures play major roles for the safety of reactor systems. Depending on the fidelity requirement and computational resources, various modeling methods, from the 0-D perfect mixing model to 3-D Computational Fluid Dynamics (CFD) models, are available. Each is associated with its own advantages and shortcomings. It is very desirable to develop an advanced and efficient thermal mixing and stratification modeling capability embedded in a modern system analysis code to improve the accuracy of reactor safety analyses and to reduce modeling uncertainties.An advanced system analysis tool, SAM, is being developed at Argonne National Laboratory for advanced non-LWR reactor safety analysis. While SAM is being developed as a system-level modeling and simulation tool, a reduced-order three-dimensional module is under development to model the multi-dimensional flow and thermal mixing and stratification in large enclosures of reactor systems. This paper provides an overview of the three-dimensional finite element flow model in SAM, including the governing equations, stabilization scheme, and solution methods. Additionally, several verification and validation tests are presented, including lid-driven cavity flow, natural convection inside a cavity, laminar flow in a channel of parallel plates. Based on the comparisons with the analytical solutions and experimental results, it is demonstrated that the developed 3-D fluid model can perform very well for a wide range of flow problems.

Development of a groundwater/surface finite-element flow model: application to the Barcés watershed

A finite-element model has been developed in MATLAB to solve the groundwater flow in natural watersheds. The present model incorporates some efficient tools that evaluate the natural conditions of the water catchments including an evaluation of the free water flow based on the continuity of mass. The resulting model does not include the verification of the continuity of momentum nor a turbulence model, but still provides a proper overall assessment of the flow in the watershed, that can be refined with a further turbulent assessment of the free surface flow. The model has been verified through its comparison with some benchmark problems showing to be both accurate and numerically efficient. Finally, it has been used in the resolution of some practical cases that show its capabilities with a special focus on the Barces river watershed, intensely monitored by this research group in the last decades.

Flow forming process of thin-walled tubular parts with cross inner ribs

In order to manufacture high-performance thin-walled tubular parts with cross inner ribs (longitudinal and transverse inner ribs), a finite element model of flow forming process has been built and the corresponding spinning mandrel with a good stripping ability was designed to study the forming process of thin-walled tubular parts with cross inner ribs both in simulation and experiments. The typical deformation characteristics and forming defects in the flow forming process have been studied.

Parameterization of Battery Electrothermal Models Coupled With Finite Element Flow Models for Cooling

Developing and parameterizing models that accurately predict the battery voltage and temperature in a vehicle battery pack are challenging due to the complex geometries of the airflow that influence the convective heat transfer. This paper addresses the difficulty in parameterizing low-order models which rely on coupling with finite element simulations. First, we propose a methodology to couple the parameterization of an equivalent circuit model (ECM) for both the electrical and thermal battery behavior with a finite element model (FEM) for the parameterization of the convective cooling of the airflow. In air-cooled battery packs with complex geometries and cooling channels, an FEM can provide the physics basis for the parameterization of the ECM that might have different convective coefficients between the cells depending on the airflow patterns. The second major contribution of this work includes validation of the ECM against the data collected from a three-cell fixture that emulates a segment of the pack with relevant cooling conditions for a hybrid vehicle. The validation is performed using an array of thin film temperature sensors covering the surface of the cell. Experiments with pulsing currents and drive cycles are used for validation over a wide range of operating conditions (ambient temperature, state of charge, current amplitude, and pulse width).

On the possible contribution of clayey inter-layers to delayed land subsidence above producing aquifers

Abstract. In recent years, measurements of land subsidence above pumped aquifers by permanent GPS and InSAR have exhibited some delay relative to drawdown ranging from months to years. The current modeling approaches accounting for water fluid dynamics and porous medium geomechanics may fail to predict such a delay and may underestimate the land settlement after the well shutdown. In the present communication, an investigation is made on the residual compaction of the intervening clayey formations as a possible contribution to retarded land subsidence. The pore pressure variation within the aquifer and its propagation in the clay are simulated by a finite element flow model, with the resulting pore pressure decline used as input data in a hypo-plastic geomechanical model. A proper sensitivity analysis on (i) aquifer depth, (ii) ratio between the sandy and the clayey layers thickness and hydraulic conductivity, (iii) oedometric compressibility in first and second loading cycles, is performed for a typical geology of a Quaternary sedimentary basin. The results show that a certain fraction, up to 20 % of the overall land subsidence, can take place after the shutdown of the producing wells depending on actual basin, litho-stratigraphy and parameter values.

An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

This paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heat transfer in a heat exchanger.

A reduced-order model for porous flow through thin, structured materials

Darcy’s equations are frequently used as a coarse-grained numerical expedient for modeling multiphase flow through complex porous materials. In some applications, the porous material may be quite thin, allowing the possibility of further simplification of the equations. In this paper we derive a reduced-order shell finite-element model for flow through thin porous materials using an approach similar to that taken to derive the Reynolds’ lubrication equation. We advance first a formulation that addresses generalized unstructured porous materials and then specialize the equations for certain structured cases. We also extend the model to account for multiphase, confined lubrication flow in an adjoining layer and gas transport within the pores. We apply the model to several problems of topical interest in micro- and nano-manufacturing processes.

Groundwater flow and its effect on salt dissolution in Gypsum Canyon watershed, Paradox Basin, southeast Utah, USA

Groundwater flow is an important control on subsurface evaporite (salt) dissolution. Salt dissolution can drive faulting and associated subsidence on the land surface and increase salinity in groundwater. This study aims to understand the groundwater flow system of Gypsum Canyon watershed in the Paradox Basin, Utah, USA, and whether or not groundwater-driven dissolution affects surface deformation. The work characterizes the groundwater flow and solute transport systems of the watershed using a three-dimensional (3D) finite element flow and transport model, SUTRA. Spring samples were analyzed for stable isotopes of water and total dissolved solids. Spring water and hydraulic conductivity data provide constraints for model parameters. Model results indicate that regional groundwater flow is to the northwest towards the Colorado River, and shallow flow systems are influenced by topography. The low permeability obtained from laboratory tests is inconsistent with field observed discharges, supporting the notion that fracture permeability plays a significant role in controlling groundwater flow. Model output implies that groundwater-driven dissolution is small on average, and cannot account for volume changes in the evaporite deposits that could cause surface deformation, but it is speculated that dissolution may be highly localized and/or weaken evaporite deposits, and could lead to surface deformation over time.

Olive-oil mill wastewater transport under unsaturated and saturated laboratory conditions using the geoelectrical resistivity tomography method and the FEFLOW model

An integrated approach for monitoring the vertical transport of a solute into the subsurface by using a geophysical method and a simulation model is proposed and evaluated. A medium-scale (1 m3) laboratory tank experiment was constructed to represent a real subsurface system, where an olive-oil mill wastewater (OOMW) spill might occur. High-resolution cross-hole electrical resistivity tomography (ERT) was performed to monitor the OOMW transport. Time-lapse ERT images defined the spatial geometry of the interface between the contaminated and uncontaminated soil into the unsaturated and saturated zones. Knowing the subsurface characteristics, the finite element flow and transport model FEFLOW was used for simulating the contaminant movement, utilizing the ERT results as a surrogate for concentration measurements for the calibration process. A statistical analysis of the ERT measurements and the corresponding transport model results for various time steps showed a good agreement between them. In addition, a sensitivity analysis of the most important parameters of the simulation model (unsaturated flow, saturated flow and transport) was performed. This laboratory-scale study emphasizes that the combined use of geophysical and transport-modeling approaches can be useful for small-scale field applications where contaminant concentration measurements are scarce, provided that its transferability from laboratory to field conditions is investigated thoroughly.

Contaminant intrusion in water distribution systems: An ingress model

In a water distribution system, low or negative pressure may occur under normal operation of the system and may lead to contaminant intrusion. To assess the risk associated with contaminant intrusion, exposure assessment is required. To have more accurate intrusion exposure assessment, the effects of the surrounding soil on the intrusion rate must be considered. This research proposes a model to create a more realistic estimation of intrusion rate. A two‐level factorial design was used to screen the effect of pipe internal pressure, soil porosity, average diameter of soil particles, size of the leak point, and pipe burial depth. The Buckingham p theorem was applied to group the influential factors into a set of dimensionless p parameters. The relationship among the p parameters was obtained by using the numerical data generated by a two‐dimensional finite element model for flow in a saturated zone surrounding a pipe. A regression analysis was then applied to find the best fit for the data.

A novel meshing and finite element flow model for porous media

This work presents a new fully-unstructured meshing scheme for generating simulation meshes, coupled with a novel simulation method for fluid flow models in porous media. We use unstructured tetrahedral meshing algorithms to generate meshes that rigorously adhere to structural and depositional heterogeneity in geological reservoir models at multiple scales. Geological heterogeneity is represented using numerous surfaces, in contrast with traditional pixel- or grid-based methods. This approach allows the generation of meshes which capture heterogeneity more efficiently and accurately than structured or partially-structured grids. The flow simulations are performed using a new hybrid discontinuous Galerkin/control volume based method which combines continuous pressure and discontinuous velocities. Our approach rigorously enforces material balance equations while ensuring crucial scalar fields such as pressure and saturation remain positive and bounded. This research has direct application to aquifer flow systems. We report the results of single-phase flow simulations on unstructured meshes for complex geological systems. These simulations accurately model the spread of groundwater contaminants such as methyl tertiary butyl ether (MTBE) ormetals such as arsenic that behave as tracers in aquifers. Initially, simulations are run on simple anisotropic geological systems for two-dimensional flow to benchmark against analytical solutions and validate the accuracy of the simulator for simple flow problems. Next, simulations for tracer flow are performed on 3D channelized and fractured reservoir systems to demonstrate the robustness and accuracy of the new grids and simulator in complex reservoir geology. We present numerical simulations of single-phase flow for a variety of geological systems of increasing complexity, culminating in systems which would be impossible to mesh and solve with structured meshes. This is also a first step towards a more complex multi-phase and multi-component implementation of the novel methods for flow through porous media.

Stochastic finite element modelling of water flow in variably saturated heterogeneous soils

AbstractWater flow is greatly influenced by the characteristics of the domain through which the process occurs. It is generally accepted that earth materials have extreme variations from point to point in space. Consequently, this heterogeneity results in high variation in hydraulic properties of soil. In order to develop an accurate predictive model for transport processes in soil, the effects of this variability should be considered. In this study a two‐dimensional stochastic finite element flow model was developed for simulation of water flow through unsaturated soils. In this model, the stochastic partial differential governing equation of water flow, obtained from implementation of the perturbation‐spectral stochastic method on classical Richard's equation, was solved using a finite element method in the space domain and a finite difference scheme in the time domain. The effective hydrological parameters embedded in the mathematical model depend on time derivatives of capillary tension head; this makes possible to consider the hysteresis due to large‐scale variability of soil hydrological properties. The model is also capable of simulating infiltration and evaporation events and rapid change in the land surface boundary condition from one type event to another, based on a scheme used in the model for implementation of land surface boundary condition. The model was validated with the data obtained from a layered lysimeter test. The model was also used to simulate water flow under a long irrigation furrow. The results obtained with this model show better agreement with experimental measurements in comparison with a deterministic model. The possible reason for this agreement is that in the developed model, the influence of the variability of the properties of soil and effects of parameter hysteresis on water flow and water content redistribution are considered. Copyright © 2010 John Wiley & Sons, Ltd.

DDA in fluid-structure problems for the study of gravity dam failure

In this paper, we present a 2D coupled fluid-structure interaction procedure to assess the stability of a cracked gravity dam against increasing water level. In this procedure the structure is assumed to be a discontinuous deformable solid containing pre-existing cracks. Thus, the Discontinuous Deformation Analysis DDA method is used to study the solid discontinuous medium, and the continuum finite element flow model to calculate the hydrostatic forces corresponding to the water level. The contact constraints between discrete blocks are imposed through an implicit augmented Lagrangian format. Numerical results show the potential of the proposed coupled model to quantify the direct influence of the nature and location of the internal cracks on the overall stability of common gravity dams.

DDA in fluid-structure problems for the study of gravity dam failure

In this paper, we present a 2D coupled fluid-structure interaction procedure to assess the stability of a cracked gravity dam against increasing water level. In this procedure the structure is assumed to be a discontinuous deformable solid containing pre-existing cracks. Thus, the Discontinuous Deformation Analysis DDA method is used to study the solid discontinuous medium, and the continuum finite element flow model to calculate the hydrostatic forces corresponding to the water level. The contact constraints between discrete blocks are imposed through an implicit augmented Lagrangian format. Numerical results show the potential of the proposed coupled model to quantify the direct influence of the nature and location of the internal cracks on the overall stability of common gravity dams.

Numerical modeling of environmental flows using DAM: Some preliminary results

Development of closures and parameterizations for subgrid scale effects is a significant and longstanding problem in the numerical simulation of environmental flows. The model described herein uses a rigorous approach for developing double-averaged governing equations — first a traditional Reynolds averaging to derive the Reynolds averaged Navier-Stokes equation (RANS), then a volume average to derive a set of double-averaged equations (DANS). An existing finite element flow model is then modified to accommodate these equations. This process gives rise to several new terms that require closures, as well as a new equation for free surface elevation. This paper is directed toward model development and uses several existing closure schemes as test cases.