Flows In Complex Geometries Research Articles

Analysis of droplet behavior and breakup mechanisms on wet solid surfaces

The behavior and dynamics of droplet spreading are pivotal phenomena that exert a profound influence on numerous scientific disciplines, technological advancements, and natural processes. This study was conducted with the aim to investigate factors influencing the shape and geometry of a liquid droplet on a solid surface using the lattice Boltzmann method (LBM). LBM as a mesoscale numerical fluid simulation has gained increasing popularity among the most favorable numerical methods for simulating multi-phase/multi-component fluid flow in complex geometries. Accordingly, parameters dependency, surface tension, two-phase diagram, and wettability were evaluated in the LBM, and stable and calibrated forms were used for the droplet simulations. Also, an equation was obtained to determine the contact angle in the LBM system with a determination coefficient of 0.988. Then, droplet behavior was examined for its dependency on wettability, interfacial tension, and line tension. The results showed droplets breakup in a certain interfacial tension at high adhesive force. These breakups were due to the force balance in the triple line. They were not monotonic and first decreased and then increased the volume of the droplets.

Wall-less Flow Phantoms with 3D printed Soluble Filament for Ultrasonic Experiments

Abstract Tissue-mimicking materials (TMMs) typically used for ultrasound phantoms include gelatin, agarose and polyvinyl alcohol (PVA). These materials have shown sufficient similarity in ultrasound parameters compared to human tissue. Despite their extensive use for years to generate ultrasound phantoms, no simple and easily reproducible way to generate complex, wall-less ultrasound flow phantoms has been introduced. Commercially available ultrasound flow phantoms are limited to simple flow geometries that do not reflect the complex blood flow in humans. Flow phantoms with complex geometries presented in scientific publications either have walls between TMMs and the flow channel, are limited to one material, or are complicated to produce. In this contribution, we present a method using 3D printing and soluble filament that allows for the reliable and consistent production of complex flow geometries with the typical materials used for ultrasound phantoms and without any walls.

DEM-LBM coupling for partially saturated granular assemblies

In this paper, we propose a phase-field-based Lattice Boltzmann Method (LBM) model coupled with the Discrete Element Method (DEM) for simulating unsaturated granular media over a large range of degrees of saturation. The formation of capillary bridges between grains is computed via an LBM scheme that solves Navier–Stokes and Allen–Cahn equations for multi-phase flow in complex geometries. As for the motions of the grains, these are computed within DEM where the contact behavior between spherical particles is based on a simple elastic–plastic contact law. Using an efficient DEM-LBM coupling framework, capillarity effects are explored at the pore scale with the collapse of a sandcastle as a classic illustration. This is done by considering an assembly of several thousands of spherical particles connected by capillary bridges for different degrees of saturation. It is shown that the mean capillary stress increases with the degree of saturation up to a certain threshold beyond which capillary stress drops until complete saturation. In addition, the Soil Water Characteristic Curve is qualitatively recovered and compared to a theoretical model. As such, the proposed DEM-LBM coupling scheme becomes a viable numerical tool that can explicitly model and explore pore-scale phenomena in unsaturated soils.

Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems

In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it possible to robustly address multi-objective and multiscale problems. BPINNs are a popular framework for data assimilation, combining the constraints of Uncertainty Quantification (UQ) and Partial Differential Equation (PDE). The relative weights of the BPINN target distribution terms are directly related to the inherent uncertainty in the respective learning tasks. Yet, they are usually manually set a-priori, that can lead to pathological behavior, stability concerns, and to conflicts between tasks which are obstacles that have deterred the use of BPINNs for inverse problems with multiscale dynamics.The present weighting strategy automatically tunes the weights by considering the multitask nature of target posterior distribution. We show that this remedies the failure modes of BPINNs and provides efficient exploration of the optimal Pareto front. This leads to better convergence and stability of BPINN training while reducing sampling bias. The determined weights moreover carry information about task uncertainties, reflecting noise levels in the data and adequacy of the PDE model.We demonstrate this in numerical experiments in Sobolev training, and compare them to analytically ε-optimal baseline, and in a multiscale Lotka-Volterra inverse problem. We eventually apply this framework to an inpainting task and an inverse problem, involving latent field recovery for incompressible flow in complex geometries.

Toward the use of LES for industrial complex geometries. Part I: automatic mesh definition

With the constant increase of computational power for the past years, Computational Fluid Dynamics (CFD) has become an essential part of the design in complex industrial processes. In this context, among the scale resolving numerical methods, Large-Eddy Simulation (LES) has become a valuable tool for the simulation of complex unsteady flows. To generalise the industrial use of LES, two main limitations are identified. First, the generation of a proper mesh can be a difficult task, which often relies on user-experience. Secondly, the ‘time-to-solution’ associated with the LES approach can be prohibitive in an industrial context. In this work, these two challenges are addressed in two parts. In this Part I, an automatic procedure for mesh definition is proposed, whereas the Part II is devoted to numerical technique to reduce the LES ‘time-to-solution’. The main goal of these works is then to develop an accurate LES strategy at an optimised computational cost. Concerning the mesh definition, because LES is based on separation between resolved and modelled subgrid-scales, the quality of the computed solution is then directly linked to the quality of the mesh. However, the definition of an adequate mesh is still an issue when LES is used to predict the flow in an industrial complex geometry without a priori knowledge of the flow dynamics. This first part presents a user-independent approach for both the generation of an initial mesh and the convergence of the mesh in the LES framework. An automatic mesh convergence strategy is proposed to ensure LES accuracy. This strategy is built to guarantee a mesh-independent mean field kinetic energy budget. The mean field kinetic energy is indeed expected to be mesh independent since only turbulent scales should be unresolved in LES. The approach is validated on canonical cases, a turbulent round jet and a turbulent pipe flow. Finally, the PRECCINSTA swirl burner is considered as a representative case of complex geometry. First, an algorithm for the generation of an unstructured mesh from a STL file is proposed to generate a coarse initial mesh, before applying the mesh convergence procedure. The overall strategy including automatic first mesh generation and its automatic adaptation paves the way to use LES approach as a decision support tool for various applications, provided that the ‘time-to-solution’ is compatible with the applications constraint. A second paper, referred as Part II, is devoted to the reduction of this time.

A phenomenological model for plasma-assisted combustion with NRP discharges in methane-air mixtures: PACMIND

The recent advances in plasma-assisted combustion must now be strengthened through high-fidelity numerical simulations. However, detailed plasma-combustion coupled simulations in complex geometry and turbulent flow involving hundreds of discharges are still unaffordable due to prohibitive computational costs. In this work, a Plasma-Assisted Combustion phenoMenological modelIng for Non-equilibrium Discharges (PACMIND) is proposed. The model aims to avoid computing in detail the plasma phase and consists of incorporating the leading order plasma effects on the reactive compressible Navier–Stokes equations. It consists of two ultra-fast effects with radical productions and gas heating, as well as a slower gas heating due to vibrational energy relaxation. Based on detailed kinetic simulations, the model has been applied to air and methane-air mixtures and contains respectively 5 species, 3 reactions and 12 species, 7 reactions. The model has been validated against experiments in air and detailed plasma-assisted combustion ignition simulations in methane-air at various equivalence ratios and reduced electric fields. Significant improvements regarding ignition delay times have been observed by comparison with an existing model. In addition, the model accounts for NOx production by plasma discharge and covers the full range of conditions encountered in a premixed flame. Hence, it opens the way to the simulation of realistic 3D turbulent configurations with minimal over-costs.

A Highly Scalable Direction-Splitting Solver on Regular Cartesian Grid to Compute Flows in Complex Geometries Described by STL Files

We implement the Direction-Splitting solver originally proposed by Keating and Minev in 2013 and allow complex geometries to be described by a triangulation defined in STL files. We develop an algorithm that computes intersections and distances between the regular Cartesian grid and the surface triangulation using a ray-tracing method. We thoroughly validate the implementation on assorted flow configurations. Finally, we illustrate the scalability of our implementation on a test case of a steady flow through 144,327 spherical obstacles randomly distributed in a tri-periodic box at Re=19.2. The grid comprises 6.8 billion cells and the computation runs on 6800 cores of a supercomputer in less than 48 h.

A generalized bodyforce scheme for lattice Boltzmann simulations of incompressible flow in complex geometries

We present a general procedure for reducing compressibility effects in pressure driven lattice Boltzmann simulations involving complex geometries. We do this by introducing a preconditioning step for the flow system in order to reduce these often undesirable effects, rather than directly modifying the flow algorithm itself. The method consists of determining the geometry dependent contribution to a pressure field induced by a given set of pressure boundary conditions. We show that this may be done through solving a set of Laplace's equations that do not need re-evaluation during flow simulations. This preconditioning method is not limited to stationary flows but is directly applicable to time-varying flows, without any recalculation of the preconditioning step. In this paper, we apply the procedure to the lattice Boltzmann algorithm, but it may be utilized in any flow simulation algorithm based on artificial compressibility methods. The method is demonstrated in both stationary and non-stationary flow situations. This includes examples from flow in porous media and hemodynamics. All the presented examples are compared to conventional methods for implementing pressure driven flow in lattice Boltzmann. In all the examples, it is shown that the proposed method considerably reduces the undesirable features exhibited by the conventional methods.

Reynolds scaling analysis of the Landau–de Gennes equations for nematic liquid crystals

Using the Reynolds scaling analysis, we simplify the Landau-de Gennes (LdG) equations for the flow of liquid crystals (LCs) in thin gaps. Then, both the simplified LdG equations and the full LdG equations are applied to a Couette geometry and a slider bearing geometry for the evaluation and verification of the simplified LdG equations by comparing results. The use of the simplified LdG equations results in a large decrease in wall time, which has the potential to significantly reduce the computational resources needed for simulating LC flows in complex geometries.

A Diffuse-Domain Phase-Field Lattice Boltzmann Method for Two-Phase Flows in Complex Geometries

This study constructs a new diffuse-domain (DD) lattice Boltzmann (LB) method for two-phase flows in complex geometries. We first coupled the DD method with the consistent and conservative phase-field (CCPF) method which can be described by the DD-CC Navier–Stokes–Cahn–Hilliard (NSCH) equations with the consistency of reduction, the consistency of mass and momentum transport, and the consistency of mass conservation. Then we conducted a matched asymptotic analysis and found that the DD-CCNSCH equations would converge to the CCNSCH equations as the thickness of the DD interface approaches to zero. Since the boundary conditions imposed on the complex geometries are incorporated into the DD-CCNSCH equations as the source terms, the system can be implemented more readily in a large and regular domain, and there is no need to treat the complex boundary conditions specially. We further developed a DD-CCPFLB method, and through the Chapman–Enskog analysis, the DD-CCPFLB method can correctly recover the DD-CCNSCH equations for two-phase flows in complex geometries. To quantitatively validate the DD-CCPFLB method, three benchmark problems are considered, and the numerical results are in agreement with those obtained through directly solving the CCNSCH equations combined with the original boundary conditions, the analytical solution, or the reported data. Finally, the present method is used to study the problems of two-phase flows in complex geometries, including the droplet dynamics in the Y-shaped channel and a droplet passing through cylindrical obstacles. The effects of the wettability and viscosity ratio are mainly investigated, and it is found that these two factors have significant impacts on the droplet dynamics.

Numerical analysis of heat and mass transfer through beds of spherical and non-spherical elements

Many issues related to mass and heat transfer through beds of granular materials are still not fully understood. In this work, non-isothermal turbulent flow is analysed within granular layers of spherical and non-spherical elements. We apply a volume penalization (VP) approach formulated in the framework of an immersed boundary technique (IB) on Cartesian computational meshes. It allows modelling flows around solid objects with almost arbitrarily complex shapes and in any form of contact. The validation of the solution accuracy is performed against ANSYS Fluent simulations using body-fitted meshes and experimental literature data. It shows the capability of the IB-VP approach for the simulations of flows in complex geometries. The main research focuses on the comparison of the influence of various types of particles and their temperature on vorticity, turbulence level and pressure drop inside and behind the granular bed. In particular, we analyse how the shape of the solid particles affects the efficiency of heat transfer in different flow conditions. The obtained results reveal the occurrence of very complex flow structures (recirculation and stagnation regions) inside beds. Comparison of results also point out preferred configurations of the beds.

Viscoelastic behavior of dilute polyelectrolyte solutions in complex geometries

In this work, we develop a theoretical model describing the viscoelastic behavior of dilute polyelectrolyte (PE) solutions using Onsager’s variational principle, with the effect of the polyelectrolyte charge and solvent salinity accounted for. The PE molecules are described as finitely extensible charged dumbbells suspended in a solvent containing ionic species which screen the charged sites on the macromolecules. The performance of the model was examined and compared against experimental data in simple flows, accounting for the magnitude of charge on the PE molecules and counterion screening effects. Numerical simulations of the flow past a single cylinder and an idealized porous medium with multiple cylinders were carried out and compared to flow of uncharged polymers in the same geometries to explore the effect of intramolecular electrostatic repulsion on the flow behavior. The extra rigidity offered by the repulsion between the charged monomeric units of the PE, and screening of these charged sites by the ionic species in the solvent led to significantly different behavior in complex flows when compared to that of uncharged polymers. The normal stresses generated in a complex flow show an increase with the polyelectrolyte molecule charge density, whereas enhanced screening of the charged sites by counterions suppresses this effect, showing behavior closer to that of uncharged polymers. Drag on a cylinder placed in the flow and pressure drop across the porous geometry increased with charge density of the molecules, exhibiting rheological behavior in complex geometries not shown by their uncharged counterparts. The results show the effects of the degree of hydrolysis and solvent salinity on the flow behavior of dilute PE solutions in complex geometries and has implications for biological systems in which PE species are commonly encountered, as well as operation of industrial processes such as enhanced oil recovery, which frequently involve the flow of dilute polyelectrolyte solutions in porous media. • Macroscopic flow behavior of dilute polyelectrolyte solutions is investigated. • Onsager’s Variational Principle used for developing model from first principles. • Reformulation of charged dumbbell model for simulating flows in complex geometries. • Polyelectrolyte charge density and solvent salinity influence flow behavior. • Drag coefficients and normal stresses increase with charged nature of molecules.

A semi-implicit meshless method for incompressible flows in complex geometries

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions (RBF) as interpolants. Higher-order polynomials are appended to the polyharmonic splines (PHS-RBF) and a collocation method is used to derive the interpolation coefficients. The interpolating kernels are then differentiated and the partial-differential equations are satisfied by collocation at the scattered points. The PHS-RBF interpolation is shown to be exponentially convergent with discretization errors decreasing as a high power of a representative distance between points. We present here a semi-implicit algorithm for time-dependent and steady state fluid flows in complex domains. At each time step, several iterations are performed to converge the momentum and continuity equations. A Poisson equation for pressure corrections is formulated by imposing divergence free condition on the iterated velocity field. At each time step, the momentum and pressure correction equations are repeatedly solved until the velocities and pressure converge to a pre-specified tolerance. We have demonstrated the convergence and discretization accuracy of the algorithm for two model problems and simulated four other complex problems. In all cases, the algorithm is stable for Courant numbers in excess of ten. The algorithm has the potential to accurately and efficiently solve many fluid flow and heat transfer problems in complex domains. An open source code Meshless Multi-Physics Software (MeMPhyS) [1] is available for interested users of the algorithm.

Low Mach number lattice Boltzmann model for turbulent combustion: Flow in confined geometries

A hybrid lattice Boltzmann/finite-difference solver for low Mach thermo-compressible flows developed in earlier works is extended to more realistic and challenging configurations involving turbulence and complex geometries in the present article. The major novelty here as compared to previous contributions is the application of a more robust collision operator, considerably extending the stability of the original single relaxation time model and facilitating larger Reynolds number flow simulations. Additionally, a subgrid model and the thickened flame approach have also been added allowing for efficient large eddy simulations of turbulent reactive flows in complex geometries. This robust solver, in combination with appropriate treatment of boundary conditions, is used to simulate combustion in two configurations: flame front propagation in a 2-D combustion chamber with several obstacles, and the 3-D PRECCINSTA swirl burner. Time evolution of the flame surface in the 2-D configuration shows very good agreement compared to direct numerical and large eddy simulation results available in the literature. The simulation of the PRECCINSTA burner is first performed in the case of cold flow using two different grid resolutions. Comparisons with experimental data reveal very good agreement even at lower resolution. The model is then used, with a 2-step chemistry and multi-component transport/thermodynamics, to simulate the combustor at operating conditions similar to previously reported experimental/numerical studies for ϕ=0.83. Results are again in very good agreement compared with available large eddy simulation results as well as experimental data, demonstrating the excellent performance of the hybrid solver.

Model reduction of coagulation cascade based on genetic algorithm.

Fibrin is an important product of the coagulation cascade, and plays an eminent role in platelet stabilization. Since coagulation cascade models typically involve the reaction kinetics of dozens of proteins, which will incur burdensome computational costs when coupled to blood flow in complex geometries, researchers often ignore this process when constructing thrombosis models. However, previous studies have shown that fundamental aspects of coagulation can be reproduced with simpler models, which motivated us to obtain a reduced-order model of fibrin generation through a systematic approach. Therefore, we introduced a semi-automatic framework to perform model-reduction of cascade reactions in this study, which consisted of two processes. Specifically, the retained protein species and cascade reactions were determined based on published studies and simulation results from the full cascade model, while the optimal reaction rates for the new cascade network were determined using a genetic algorithm. The framework has been applied to a 19-species coagulation model that triggers fibrin generation in internal fields via reactive boundaries, and a 10-species reduced-order model was obtained to reproduce the kinetics of fibrinogenesis in the full cascade model at different boundary tissue factor concentrations. This reduced-order model of fibrinogenesis would be valuable for thrombosis modeling that considers both the coagulation cascade and platelet activity. Furthermore, the framework proposed herein can also be applied to the reductions of other cascade reaction models.

A new dual matrix burner for one-dimensional investigation of aerosol flames

In spray-flame synthesis of nanoparticles, a precise understanding of the reaction processes is necessary to find optimal process parameters for the formation of the desired products. Coupling the chemistries of flame, solvent, and gas-phase species initially formed from the particle precursor in combination with the complex flow geometry of the spray flame means a special challenge for the modeling of the reaction processes. A new burner has been developed that is capable to observe the reaction of precursor solutions frequently used in spray-flame synthesis. The burner provides an almost flat, laminar, and steady flame with homogeneous addition of a fine aerosol and thus enables detailed investigation and modeling of the coupled reactions independent of spray formation and turbulent mixing. With its two separate supply channel matrices, the burner also enables the use of reactants that would otherwise react with each other already before reaching the flame. These features enable the investigation of a wide range of flame-based synthesis methods for nanoparticles and, due to the flat-flame geometry, kinetics models for these processes can be developed and validated. This work describes the matrix burner development and its gas flow optimization by simulation. Droplet-size distributions generated by ultrasonic nebulization and their interaction with the burner structure are investigated by phase-Doppler anemometry. As an example for nanoparticle-forming flames from solutions, iron-oxide nanoparticle-generating flames using iron(III) nitrate nonahydrate dissolved in 1-butanol were investigated. This effort includes measurements of two-dimensional maps of the flame temperature by a thermocouple and height-dependent concentration profiles of the main species by time-of-flight mass spectrometry. Experimental data are compared with 1D simulations using a reduced reaction mechanism. The results show that the new burner is well suited for the development of reaction models for precursors supplied in the liquid phase usually applied in spray-flame synthesis configurations.

Constrained least-squares based adaptive-order finite-volume WENO scheme for the simulation of viscous compressible flows on unstructured grids

We develop a novel constrained least-squares technique for fourth-order weighted essentially non-oscillatory (WENO) polynomial reconstruction on general unstructured grids composed of curved-edged quadrilateral elements. Our technique relies on a segregation of the conditions that match the spatial averages of the candidate WENO polynomial and the reconstructed state variable over stencil-forming cells into two sets. The first set consists of exactly enforced linearly independent constraints that are applied only over the central cell and its edge-sharing neighbors. The second set consists of the remaining conditions and are enforced only approximately in a least-squares sense. We develop a specialized technique that reduces the computational burden associated with the numerical solution of the constrained least-squares system for the WENO interpolation coefficients. For a comparable computational expense, our constrained reconstruction approach yields pointwise estimates that are consistently more accurate than the conventional least-squares based estimates over a wide spectrum of spatial wavenumbers. This enhanced spectral resolution yields a significant, over two-fold increase in the accuracy with which unsteady smooth flow features, such as an advecting isentropic vortex, are captured over highly distorted curvilinear unstructured grids. Our constraint based reconstruction framework is generic, facilitates implementation of high-order boundary closures, and is amenable to large scale parallelization over several thousand CPU cores. Numerical tests over a range of inviscid and viscous flow configurations are presented to demonstrate the accuracy and robustness of our technique. Our constrained least-squares based adaptive WENO discretization faithfully captures intricate features that arise in strongly shocked, and highly unsteady and separated complex geometry flows. Our results suggest exact preservation of the match between the cell averages of the interpolant and the reconstructed state variable over the nearest neighbors to be quite an effective strategy that dramatically enhances the accuracy and spectral resolution of the high-order finite-volume reconstruction operation.

Granular packing in complex flow geometries

We examine the packing fraction and stress ratio in different granular flow geometries. In isochoric systems, we find that the packing fraction response versus inertial number is qualitatively similar to the more well established stress ratio response. As a result, the packing fraction is well-characterized as a local function of stress across a range of geometries and flow conditions. In a non-isochoric system, specifically a hopper, we find the response is more complex. By examining the flow onset in shear cell and chute systems, we attribute the different response in the hopper to the differing time scales for the development of stress versus packing in dense, low shear flow regions.

Smoothed boundary method for simulating incompressible flow in complex geometries

Simulating flow through porous media with explicit considerations of complex microstructures is very challenging using conventional sharp-interface methods because of the difficulties in generating meshes conformal to complex geometries. In this work, a diffuse interface embedded boundary method known as the Smoothed Boundary Method (SBM) is utilized to facilitate simulations of fluid dynamics involving complex geometries. In diffuse-interface methods, the geometry is described by a domain parameter. The SBM allows the straightforward reformulation of the time-dependent Navier–Stokes equations in terms of this domain parameter, using only differentiation identities. Thus, enforcing the appropriate boundary conditions at the irregular embedded boundary is greatly simplified. Adaptive mesh refinement is used to increase the accuracy of the diffuse interface method by allowing a thinner interfacial thickness to be used in the domain parameter. The SBM-formulated Navier–Stokes equations are solved with the Finite Difference Method on refined mesh systems. Sharp-interface Finite Element Method simulations using the commercial software COMSOL on body-conforming meshes are also provided for comparison. Favorable agreement between the two methods is observed. Since it is no longer necessary for the mesh to conform to the complex geometry, the grid system for the SBM simulations can be generated rapidly and without additional manual interventions, making the entire simulation process more expedient.

Numerical Investigations of Liquid Film Offtake by Transverse Gas Flow in a Downcomer Annulus Geometry

Advances in computational power have enabled the application of computational fluid dynamics (CFD) to nuclear reactor safety analyses, which require accurate predictability for two-phase flow in complex geometries. This study is aimed at validating CFD simulation of liquid film off-take in a 1/10-scale downcomer of a reactor pressure vessel under emergency core coolant (ECC) bypass conditions. Even though different flow regimes can exist simultaneously in real flow, the traditional two-phase flow models used in CFD have a disadvantage with respect to regime dependency. In this study, VOF–slip, which is a hybrid model that combines volume-of-fluid (VOF) and mixture models and is offered in STAR-CCM+ 15.04, was used to simulate the film off-take phenomenon. The key parameters in the simulation were found to be the droplet diameter and interface turbulence damping coefficient. A parametric study was performed to determine the value of the parameters that yield a reasonable liquid film thickness and ECC bypass fraction which were measured at the Seoul National University (SNU) experiment facility. For the conditions of the SNU experiment, the droplet diameter was found to be 150 μm, and the interface turbulence damping coefficient was found to be in the range of 0–30. The validation results confirmed that the VOF–slip model can describe the behavior of the liquid film and the unresolved droplet appropriately. This resulted in an improvement in predicting the ECC bypass fraction in comparison to the results using the conventional VOF model.