Publications of PN 1

Abstract

Water ingestion in gas turbines is used in industrial applications to improve the thermal efficiency by cooling the air before and throughout compression. However, this also leads to interactions between the liquid droplets and the compressor parts, which cause a faster degradation of the structure. The current work addresses the numerical investigation of the atomization process at the trailing edge of a compressor blade as there have only been experimental investigations in literature considering the ambient conditions in a gas turbine compressor. Direct numerical simulations (DNS) are carried out using the multiphase flow solver Free Surface 3D (FS3D). Therefore, a numerical setup has been developed to model the trailing edge as a thin plate corresponding to experiments performed at ITLR 22. Four different cases have been performed to take the experimentally observed atomization processes into account. Additionally, the dependence of the simulation results on the grid resolution and with it the limits to reproduce the experimental findings has been investigated in a grid study. The results show that the developed numerical setup works well and the different atomization processes are reproduced qualitatively, with best results for very high grid resolutions.

Abstract

Turbulent inflow methods offer new possibilities for an efficient simulation by reducing the computational domain to the interesting parts. Typical examples are turbulent flow over cavities, around obstacles or in the context of zonal large eddy simulations. Within this work, we present the current state of two turbulent inflow methods implemented in our high order discontinuous Galerkin code FLEXI with special focus laid on HPC applications. We present the recycling-rescaling anisotropic linear forcing (RRALF), a combination of a modified recycling-rescaling approach and an anisotropic linear forcing, and a synthetic eddy method (SEM). For both methods, the simulation of a turbulent boundary layer along a flat plate is used as validation case. For the RRALF method, a zonal large eddy simulation of the rear part of a tripped subsonic turbulent boundary layer over a flat plate is presented. The SEM is validated in the case of a supersonic turbulent boundary layer using data from literature at the inflow. In the course of the cluster upgrade to the HPE Apollo system at HLRS, our framework was examined for performance on the new hardware architecture. Optimizations and adaptations were carried out, for which we will present current performance data.

Abstract

Liquids with a non-Newtonian rheological behavior are frequently encountered in engineering applications, where multiple phases can be involved. A rather scarcely investigated non-Newtonian behavior is thixotropy, in which the fluid’s viscosity depends on the shear rate as well as on the deformation history. In this study, a fundamental case of an oscillating droplet consisting of an ideal thixotropic fluid is numerically investigated with the in-house multiphase flow solver Free Surface 3D. The ideal thixotropic behavior is modeled by an additional kinetic equation which involves a structural breakdown and recovery term. The influence of both terms on the evolution of the spatially averaged structural parameter λ is studied. The numerical results show that λ oscillates around a steady-state value, which is reached quicker for faster recovery of the structure. The occurring maxima of λ are shifted in relation to the oscillation modes. This effect is more pronounced for a lower breakdown strength and for a slower recovery rate.

Abstract

We study single-phase flow in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. We derive a new mixed-dimensional model, where fractures are represented by $(n-1)$-dimensional interfaces between $n$-dimensional subdomains for $n2$. In particular, we suggest a generalization of the model in~22 by accounting for asymmetric fractures with spatially varying aperture. Thus, the new model is particularly convenient for the description of surface roughness or for modeling curvilinear or winding fractures. The wellposedness of the new model is proven under appropriate conditions. Further, we formulate a discontinuous Galerkin discretization of the new model and validate the model by performing two- and three-dimensional numerical experiments.

Abstract

Phosphate is vital for plant and algae growth, yield, and survival, but in most environments, it is poorly available. To cope with phosphate starvation, photosynthetic organisms used their phospholipids as a phosphate reserve. In microalgae, betaine lipids replace phospholipids whereas, in higher plants, betaine lipid synthesis is lost, driving plants to other strategies. The aim of this work was to evaluate to what extent betaine lipids and PC lipids share physicochemical properties and could thus substitute each other. Using neutron diffraction and molecular dynamics simulations of two synthetic lipids, dipalmitoylphosphatidylcholine (DPPC) and dipalmitoyl-diacylglyceryl-N,N,N-trimethylhomoserine (DP-DGTS), we show that DP-DGTS bilayers are thicker, more rigid, and mutually more repulsive than DPPC bilayers. The different properties and hydration response of PC and DGTS provide an explanation for the diversity of betaine lipids observed in marine organisms and for their disappearance in seed plants.Competing Interest StatementThe authors have declared no competing interest.

Abstract

Standard kernel methods for machine learning usually struggle when dealing with large datasets. We review a recently introduced Structured Deep Kernel Network (SDKN) approach that is capable of dealing with high-dimensional and huge datasets - and enjoys typical standard machine learning approximation properties.

Abstract

The condition for the formation of droplet groups in liquid sprays is poorly understood. This study looks at a simplified model system consisting of two iso-propanol droplets of equal diameter, Dd0, in tandem, separated initially by a center-to-center distance, a20, and moving in the direction of gravity with an initial velocity, Vd0\>Vt, where Vt is the terminal velocity of an isolated droplet from Stokes flow analysis. A theoretical analysis based on Stokes flow around this double-droplet system is presented, including an inertial correction factor in terms of drag coefficient to account for large Reynolds numbers (&\#8811;1). From this analysis, it is observed that the drag force experienced by the leading droplet is higher than that experienced by the trailing droplet. The temporal evolutions of the velocity, Vd(t), of the droplets, as well as their separation distance, a2(t), are presented, and the time to at which the droplets come in contact with each other and their approach velocity at this time, \ΔVd0, are calculated. The effects of the droplet diameter, Dd0, the initial droplet velocity, Vd0, and the initial separation, a20 on to and \ΔVd0 are reported. The agreement between the theoretical predictions and experimental data in the literature is good.

Abstract

Models for the co-transport of two different colloids commonly assume a one-way coupling. This is because often a large colloid and small colloid are involved. Therefore, they assume that the spread of smaller colloid is affected by the transport of larger colloids, but not the other way around. However, a number of studies have shown that this assumption is not valid, even for large and small colloids. Therefore, in this study, a two-way coupled model is developed to simulate the co-transport of two different colloids in porous media and their effect on each other. We have considered the interactions of the two colloids with the grain surface, kinetics of heteroaggregation (of the two colloids), and heteroaggregate deposition onto the grain surface. We assumed a first-order kinetic model to represent heteroaggregate formation and its deposition on the grain surface. The model is evaluated by fitting the experimental data reported in four different papers from the literature on the co-transport of clay colloids and viruses, bacteria and graphene oxide nanoparticles, and clay colloids and graphene oxide nanoparticles. The model performance is compared with the commonly-used one-way coupled model. The two-way coupled model is found to satisfactorily simulate most of the experimental conditions reported in the above papers, except for the co-transport of montmorillonite–adenovirus, and Staphylococcus aureus- graphene oxide nanoparticles.

Abstract

In this work, we present a novel hybrid Discontinuous Galerkin scheme with hp-adaptivity capabilities for the compressible Euler equations. In smooth regions, an efficient and accurate discretization is achieved via local p-adaptation. At strong discontinuities and shocks, a finite volume scheme on an h-refined element-local subgrid gives robustness. Thus, we obtain a hp-adaptive scheme that exploits both the high convergence rate and efficiency of a p-adaptive high order scheme as well as the stable and accurate shock capturing abilities of a low order finite volume scheme, but avoids the inherent resolution loss through h-refinement. A single a priori indicator, based on the modal decay of the local polynomial solution representation, is used to distinguish between discontinuous and smooth regions and control the p-refinement. Our method is implemented as an extension to the open source software FLEXI. Hence, the efficient implementation of the method for high performance computers was an important criterion during the development. The efficiency of our adaptive scheme is demonstrated for a variety of test cases, where results are compared against non adaptive simulations. Our findings suggest that the proposed adaptive method produces comparable or even better results with significantly less computational costs.

Abstract

The exact knowledge of droplet clustering or grouping is important in many technical applications , such as fuel injection, ink-jet printing or in medical nebulizers. Despite their relevance, the fundamentals of grouping processes are yet to be fully understood. Recent studies comprise the experimental and numerical investigation of single monodisperse streams in well-defined droplet arrangements. Moving towards more complex configurations, such as multiple streams in close proximity, is a challenging task experimentally. This study aims at bridging this gap numerically with the aid of the in-house multiphase code Free Surface 3D to assess the effect of multiple droplet streams on grouping behavior. Three streams of droplets in a coplanar arrangement are simulated for which the center stream is compared to a single reference stream without the influence of neighboring droplets. To determine the impact of the outer streams on the center stream regarding grouping time, relative droplet velocity, drag forces as well as pressure and shear stress distribution, the following input parameters are changed systematically: the initial lateral distance to the center stream and the initial Reynolds number. Results show that the presence of neighboring streams with a lateral distance of less than 5 droplet diameters has a significant influence on the grouping behavior of the central stream. The process can be divided into a first part (I) where the outer streams confine the interaction with the surroundings, slowing down grouping tendencies and reducing drag forces in the middle stream; and a second part (II) where the coalescence of the outer streams imposes a substantial disturbance on the middle stream leading to an abrupt increase in the forces acting upon the droplets. Additionally, the lateral drift of the outside streams is compared qualitatively to literature studies and shows good agreement. For lateral distances of more than 10 droplet diameters, the interaction of the streams is negligible and the behavior of a single, isolated stream is retained.

Abstract

Droplet grouping is important in technical applications and in nature where more than one droplet is seen. Despite its relevance for such problems, the fundamentals of the grouping processes are not yet fully understood. Initial conditions that expedite or impede the formation of droplet groups have been studied, but a thorough investigation of the temporal and spatial evolution of the forces at play has not been conducted. In this work, the grouping process in monodisperse droplet streams is examined in detail by direct numerical simulation (DNS), for the first time, using the multiphase code Free Surface 3D. The code framework is based on the volume-of-fluid method and uses the piecewise linear interface calculation method to reconstruct the interface. A method is established to quantify the development and evolving differences of pressure and shear drag forces on each droplet in the stream using the available DNS data. The results show a linear increase in the difference between the forces, where the drag force on the leading droplet is always larger than that on the trailing droplet. A comprehensive parametric study reveals that, on the one hand, large initial inter-droplet separation and small group distances increase grouping time due to reduced difference in the drag coefficients. On the other hand, higher initial Reynolds numbers and larger irregularities in the geometrical arrangement promote droplet grouping. The flow field shows stable wake structures at initial Reynolds numbers of 300 and the onset of vortex shedding at Reynolds numbers of 500, affecting the next pair of droplets, even for larger separation distances.

Abstract

Under ambient atmospheric conditions, a thin film of water wets many solid surfaces, including insulators, ice, and salt. The film thickness as well as its transport behavior sensitively depend on the surrounding humidity. Understanding this intricate interplay is of highest relevance for water transport through porous media, particularly in the context of soil salinization induced by evaporation. Here, we use molecular simulations to evaluate the transport properties of thin water films on prototypical salt and soil interfaces, namely NaCl and silica solid surfaces. Our results showtwo distinct regimes for water transport: at low water coverage, the film permeance scales linearly with the adsorbed amount, in agreement with the activated random walk model.For thicker water films, the permeance scales as the adsorbed amount to the power of 3, in line with the Stokes equation. By comparing results obtained for silica and NaCl surfaces, we find that, at low water coverage, water permeance at the silica surface is considerably lower than at the NaCl surface, which we attribute to difference in hydrogen bonding. We also investigate the effect of atomic surface defects on the transport properties. Finally, in the context of water transport through porous material, we determine the humidity-dependent crossover between a vapor dominated and a thin film dominated transport regimes depending on the pore size.

Abstract

Several environmental phenomena require monitoring time-dependent densities in porous media, e.g., clogging of river sediments, mineral dissolution/precipitation, or variably-saturated multiphase flow. Gamma-ray attenuation (GRA) can monitor time-dependent densities without being destructive or invasive under laboratory conditions. GRA sends gamma rays through a material, where they are attenuated by photoelectric absorption and then recorded by a photon detector. The attenuated intensity of the emerging beam relates to the density of the traversed material via Beer--Lambert's law. An important parameter for designing time-variable GRA is the exposure time, the time the detector takes to gather and count photons before converting the recorded intensity to a density. Large exposure times capture the time evolution poorly (temporal raster error, inaccurate temporal discretization), while small exposure times yield imprecise intensity values (noise-related error, i.e. small signal-to-noise ratio). Together, these two make up the total error of observing time-dependent densities by GRA. Our goal is to provide an optimization framework for time-dependent GRA experiments with respect to exposure time and other key parameters, thus facilitating neater experimental data for improved process understanding. Experimentalists set, or iterate over, several experimental input parameters (e.g., Beer--Lambert parameters) and expectations on the yet unknown dynamics (e.g., mean and amplitude of density and characteristic time of density changes). We model the yet unknown dynamics as a random Gaussian Process to derive expressions for expected errors prior to the experiment as a function of key experimental parameters. Based on this, we provide an optimization framework that allows finding the optimal (minimal-total-error) setup and demonstrate its application on synthetic experiments.

Abstract

The motion of two dissimilar spherical non-evaporating liquid droplets moving vertically along their line of centers is analysed mathematically. The stimulus for the study is evidence from the literature that, under appropriate operating conditions, droplet grouping can occur. Carefully controlled experiments, aimed at providing a paradigm for understanding this phenomenon, considered the configuration of the current work. The governing non-linear ordinary differential equation describing the behaviour of the distance between the droplets is solved analytically for the first time, using the homotopy analysis method. In order to successfully implement the latter, the fact that the two consecutive droplets considered are mildly different in size was exploited. This enabled a considerable reduction of the complicated expressions for the drag forces acting on the two droplets. Whilst retaining generality, further simplification was achieved using curve fitting for some of the key expressions appearing in the reduced form of the drag forces. The resulting nonlinear equation was then tractable for straightforward application of the homotopy analysis method. For almost identical droplets, validation of the solution is afforded by experimental data from the literature. Comparison between the predictions of the new analytical solution and a numerical solution of the relevant ODE yielded excellent agreement thereby ratifying the proposed combined approach. The results indicate that the larger droplet of the pair approaches the leading droplet more slowly than if the two droplets are equal in size.

Abstract

The present study proposes a methodology for predicting the vertical light nonaqueous-phase liquids (LNAPLs) distribution within an aquifer by considering the influence of water table fluctuations. The LNAPL distribution is predicted by combining (1) information on air/LNAPL and LNAPL/water interface elevations with (2) the initial elevation of the water table without LNAPL effect. Data used in the present study were collected during groundwater monitoring undertaken over a period of 4 months at a LNAPL-impacted observation well. In this study, the water table fluctuations raised the free LNAPL in the subsurface to an elevation of 206.63 m, while the lowest elevation was 205.70 m, forming a thickness of 0.93 m of LNAPL-impacted soil. Results show that the apparent LNAPL thickness in the observation well is found to be three times greater than the actual free LNAPL thickness in soil; a finding that agrees with previous studies reporting that apparent LNAPL thickness in observation wells typically exceeds the free LNAPL thickness within soil by a factor estimated to range between 2 and 10. The present study provides insights concerning the transient variation of LNAPL distribution within the subsurface and highlights the capability of the proposed methodology to mathematically predict the actual LNAPL thickness in the subsurface, without the need to conduct laborious field tests. Practitioners can use the proposed methodology to determine by how much the water table should be lowered, through pumping, to isolate the LNAPL-impacted soil within the unsaturated zone, which can then be subjected to in situ vadose zone remedial treatment.

Abstract

In a previous study, acoustic waves were shown to have the potential to induce grouping of particles in exhaust systems 1. In the present study, three-dimensional CFD simulations of single isopropanol droplet streams moving in air subjected to an acoustic field were performed with ANSYS Fluent. The Eulerian-Lagrangian approach was utilized based on the classical work of Gor’kov 2, 3 with the generalization of Settnes and Bruus 4. The simulations reveal a grouping dynamics behavior of the droplets in acoustic standing waves (ASWs). The distances between the droplets in the stream are mainly affected by the droplet residence time which is the time a droplet spends in the ASW. The grouping dynamics also depend on the number of pressure nodes in the field.

Abstract

The typical characteristic of a thin porous layer is that its thickness is much smaller than its in-plane dimensions. This often leads to physical behaviors that are different from three-dimensional porous media. The classical Richards equation is insufficient to simulate many flow conditions in thin porous media. Here, we have provided an alternative approach by accounting for the dynamic capillarity effect. In this study, we have presented a set of one-dimensional in-plane imbibition and subsequent drainage experiments in a thin fibrous layer. The X-ray transmission method was used to measure saturation distributions along the fibrous sample. We simulated the experimental results using Richards equation either with classical capillary equation or with a so-called dynamic capillarity term. We have found that the standard Richards equation was not able to simulate the experimental results, and the dynamic capillarity effect should be taken into account in order to model the spontaneous imbibition. The experimental data presented here may also be used by other researchers to validate their models.

Abstract

In this work, we present a novel higher-order smooth artificial viscosity method for the discontinuous Galerkin spectral element method and related high order methods. A neural network is used to detect the need for stabilization. Inspired by techniques from image edge detection, the neural network locates discontinuities inside mesh elements on a sub-cell level. Once the sub-cell positions of the shock fronts have been identified, the use of radial basis functions enables the construction of a high order smooth artificial viscosity field on quadrilateral meshes. We show the superiority of using higher order smooth artificial viscosity over piecewise linear approaches in particular on coarse meshes. The capabilities of the novel method are illustrated with typical applications.

Abstract

We perform a numerical and experimental study of immiscible two-phase flows within predominantly 2D transparent PDMS microfluidic domains with disordered pillar-like obstacles, that effectively serve as artificial porous structures. Using a high sensitivity pressure sensor at the flow inlet, we capture experimentally the pressure dynamics under fixed flow rate conditions as the fluid–fluid interface advances within the porous domain, while also monitoring the corresponding phase distribution patterns using optical microscopy. Our experimental study covers 4 orders of magnitude with respect to the injection flow rate and highlights the characteristics of immiscible displacement processes during the transition from the capillarity-controlled interface displacement regime at lower flow rates, where the pores are invaded sequentially in the form of Haines jumps, to the viscosity-dominated regime, where multiple pores are invaded simultaneously. In the capillary regime, we recover a clear correlation between the recorded inlet pressure and the pore-throat diameter invaded by the interface that follows the Young–Laplace equation, while during the transition to the viscous regime such a correlation is no longer evident due to multiple pore-throats being invaded simultaneously (but also due to significant viscous pressure drop along the inlet and outlet channels, that effectively mask capillary effects). The performed experimental study serves for the validation of a robust Level-Set model capable of explicitly tracking interfacial dynamics at sub-pore scale resolutions under identical flow conditions. The numerical model is validated against both well-established theoretical flow models, that account for the effects of viscous and capillary forces on interfacial dynamics, and the experimental results obtained using the developed microfluidic setup over a wide range of capillary numbers. Our results show that the proposed numerical model recovers very well the experimentally observed flow dynamics in terms of phase distribution patterns and inlet pressures, but also the effects of viscous flow on the apparent (i.e. dynamic) contact angles in the vicinity of the pore walls. For the first time in the literature, this work clearly shows that the proposed numerical approach has an undoubtable strong potential to simulate multiphase flow in porous domains over a wide range of Capillary numbers.

Abstract

Many engineering technologies such as electronic cooling and thermal desalination exemplify the enhancement of evaporation and boiling heat transfer by surface modification. Nevertheless, the core parameters of heat transfer such as critical heat flux and heat transfer coefficient are associated with surface wettability and morphology. Herein, for the first time, a metal–organic framework (MOF) film, viz. HKUST-1, was integrated into a metallic woven mesh (macroporous support) for enhancing liquid rewetting and capillary-driven evaporation and boiling heat transfer. Compared to bare copper mesh, this architecture was found to significantly increase the critical heat flux by 205% and the heat transfer coefficient by 90%. The complex coupled two-phase (liquid and gas) transport process involving capillary wicking, evaporation, adsorption and desorption were critically examined by analysing the dynamics of multiple interfaces during horizontal wicking. Relying upon visible colorimetric changes, HKUST-1 sustained on the copper woven mesh could expedite quantitative analysis of the coupled capillary evaporation process. In principle, this is primed to offer fundamental insights into the mechanisms of transport phenomena. Introduction of such previously unreported hierarchical porous structures could also potentially advance the state-of-the-art of passive thermal management technologies. In essence, a new route to elicit superhydrophilic surfaces emerges, paving new ways for understanding the intrinsic mechanisms of phase-change heat transfer.

Abstract

Enzymatically induced calcite precipitation (EICP) in porous media can be used as an engineering option to achieve precipitation in the pore space, for example, aiming at a targeted sealing of existing flow paths. This is accomplished through a porosity and consequent permeability alteration. A major source of uncertainty in modeling EICP is in the quantitative description of permeability alteration due to precipitation. This report presents methods for investigating experimentally the time-resolved effects of growing precipitates on porosity and permeability on the pore scale, in a poly-di-methyl-siloxane microfluidic flow cell. These methods include the design and production of the microfluidic cells, the preparation and usage of the chemical solutions, the injection strategy, and the monitoring of pressure drops for given fluxes for the determination of permeability. EICP imaging methods are explained, including optical microscopy and X-ray microcomputed tomography (XRCT), and the corresponding image processing and analysis. We present and discuss a new experimental procedure using a microfluidic cell, as well as the general perspectives for further experimental and numerical simulation studies on induced calcite precipitation. The results of this study show the enormous benefits and insights achieved by combining both light microscopy and XRCT with hydraulic measurements in microfluidic chips. This allows for a quantitative analysis of the evolution of precipitates with respect to their size and shape, while monitoring their influence on permeability. We consider this to be an improvement of the existing methods in the literature regarding the interpretation of recorded data (pressure, flux, and visualization) during pore morphology alteration.

Abstract

Turbulent channel flow with a porous wall is investigated using direct numerical simulation, where the porous media domain consists of regular or random circular cylinder arrays. We compare the statistics and structure of the mean flow and turbulence in the channel flow with a bulk Reynolds number of 2500 and two porosities (u ¼ 0:6 and 0.8) for the porous media. It is shown that the random interface significantly affects the dynamics of turbulence and the time-averaged flow. More intense mixing is observed near the random interface due to augmented form-induced shear stresses. Due to the strong dependence of induced flow direction on the interface geometry, we segmented the flow field into two types of areas based on the slope angle formed by the top-layer cylinders: the windward area and leeward area. The conditional average of turbulence kinematic energy budget over each type of area reveals their respective role in turbulence transportation more explicitly. In addition, we use finite-time Lyapunov exponents to inspect the Lagrangian coherent structures in the flow fields, which reveal the preferential fluid trajectories in the random porous medium geometry.

Abstract

The interaction between the flow above and below a permeable wall is a central topic in the study of porous media. While previous investigations have provided compelling evidence of the strong coupling between the two regions, few studies have quantitatively measured the directionality, i.e. cause-and-effect relations, of this interaction. To shed light on the problem, interface-resolved direct numerical simulations of channel flow over a cylinder array for porosity $=0.4$–$0.9$ are performed, and the friction Reynolds number of the top smooth wall is controlled to be $Re_180$. We use transfer entropy as a marker to evaluate the causal interaction between the free turbulent flow and the porous medium. Correlation analysis and linear coherence spectra are also leveraged to complete the study. Our results show that the permeability of the porous medium has a profound impact on the intensity, time scale and spatial extent of surface–subsurface interactions. The interaction of the free flow and porous medium is further decomposed into two coupling directions, namely, top-down and bottom-up. For low-porosity cases, top-down and bottom-up interactions are strongly asymmetric, the former being mostly influenced by small near-wall eddies, and the latter reflecting the onset of Kelvin–Helmholtz type instabilities due to the perturbation from the porous medium. As the porosity increases, both top-down and bottom-up interactions are dominated by shear-flow instabilities.

Abstract

The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny–Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.

Abstract

The scenario of an impacting drop onto a film is highly relevant in many natural and technical systems. A fundamental and often required parameter of these interactions is the so called splashing threshold above which secondary droplets are generated. For interactions with differing liquid properties for the film and the impacting drop a general splashing threshold is, however, still unknown because an experimental determination is difficult to achieve. For this reason, we investigate the suitability of a numerical determination of this threshold by means of direct numerical simulation using the multiphase flow solver Free Surface 3D (FS3D). Simulations across an already existing splashing threshold are performed stemming from an empirical correlation. In order to determine the necessary grid resolution for accurately reproducing the corresponding impact regime, all interactions are simulated for several grids. A detailed grid study shows that only by using very high grid resolutions the threshold can be reproduced with a sufficient accuracy, whereas the use of coarser resolutions leads to a significant underestimation of the threshold. Additionally, simulations of highly resolved impact phenomena on thin films depend heavily on the efficient solution of the problem with most of the computational costs affiliated to solving the Pressure Poisson Equation within the FS3D framework. Therefore, the implemented multigrid solver was optimized employing advanced tree structured communication during coarsening and refinement on the levels during the solution cycle. A performance analysis of FS3D using the original and the improved multigrid solver shows that the implemented tree structured communication leads to a remarkable speed-up.

Abstract

Of relevance to energy storage, electrochemistry and catalysis, ionic and dipolar liquids display unexpected behaviours---especially in confinement. Beyond adsorption, over-screening and crowding effects, experiments have highlighted novel phenomena, such as unconventional screening and the impact of the electronic nature---metallic versus insulating---of the confining surface. Such behaviours, which challenge existing frameworks, highlight the need for tools to fully embrace the properties of confined liquids. Here we introduce a novel approach that involves electronic screening while capturing molecular aspects of interfacial fluids. Although available strategies consider perfect metal or insulator surfaces, we build on the Thomas--Fermi formalism to develop an effective approach that deals with any imperfect metal between these asymptotes. Our approach describes electrostatic interactions within the metal through a `virtual' Thomas--Fermi fluid of charged particles, whose Debye length sets the screening length $łambda$. We show that this method captures the electrostatic interaction decay and electrochemical behaviour on varying $łambda$. By applying this strategy to an ionic liquid, we unveil a wetting transition on switching from insulating to metallic conditions.

Abstract

We consider a class of stochastic evolution equations that include in particular the stochastic Camassa–Holm equation. For the initial value problem on a torus, we first establish the local existence and uniqueness of pathwise solutions in the Sobolev spaces Hs with s>3/2. Then we show that strong enough nonlinear noise can prevent blow-up almost surely. To analyze the effects of weaker noise, we consider a linearly multiplicative noise with non-autonomous pre-factor. Then, we formulate precise conditions on the initial data that lead to global existence of strong solutions or to blow-up. The blow-up occurs as wave breaking. For blow-up with positive probability, we derive lower bounds for these probabilities. Finally, the blow-up rate of these solutions is precisely analyzed.

Abstract

Medical inhalers have been used for the treatment of a wide range of respiratory diseases including COVID-19. In this study, we investigate the annular liquid jet breakup with a coaxial supersonic gas jet using large eddy simulations. This contributes to a further understanding and improvement of medical inhaler designs. The liquid is sucked in by the low pressure as a result of the high velocity gas jet and breaks up due to the interaction with the gas jet. This type of spray nozzle configuration is commonly used in medical inhalers. Two different gas nozzle diameters are studied. The simulated liquid structure is compared with preliminary, qualitative experimental results. The gas jet pressure and radial velocity of the liquid are found to be coupled and the interaction between them plays an important role in formation of the liquid structure. The effect of gas nozzle diameter on flow rate, mean radius of the liquid, and mean radial velocity, as well as its oscillation behavior has been investigated. The power development of dominate frequencies of averaged radial liquid velocity along the flow direction is shown. The growth of the instabilities can be observed from these results.

Abstract

Conventional macroscale two-phase flow equations for porous media (such as Darcy's law and Richards Equation) require a constitutive relation for capillary pressure (Pc). The capillary pressure relation significantly impacts the behavior and prediction of fluid flow in porous media, and needs to accurately characterize the capillary forces. In a typical laboratory experiment, a functional macroscopic capillary pressure-saturation (Pc-Sw) relationship is measured as the difference between the pressures of the non-wetting-phase reservoir at the inlet (Pnw) and wetting-phase reservoir at the outlet (Pw) of a porous medium. It is well-known that this traditional macroscopic capillary pressure definition is valid only at equilibrium conditions and if the phases are connected. Under non-equilibrium (dynamic) conditions, when the fluids are moving, the macroscopic capillary pressure measured in experiments implicitly includes the pressure head caused by viscous effects. The goal of the present effort is to understand how well the traditional macroscopic capillary pressure definition represents the pore-scale capillary forces under different flow conditions. Using direct numerical simulations (DNS) of two-phase flow in a porous medium, we evaluate the capillary pressure at the pore-scale, and compare it to the macroscopic capillary pressure, Pc(Sw), that is typically measured in experiments using pressure transducers. The pore-scale capillary pressure is the pressure difference across the interface between two fluids as the fluids move through a porous medium; the interface pressure differences at fluid-fluid invasion front are averaged across all the pores of the porous medium to yield a representative pore-scale capillary pressure curve, referred to as the interface capillary pressure. The pore-scale interface capillary pressure represents the “true” capillary forces in the system, since depends only on the pore morphology (shape) and interfacial energy of the two fluids, and does not account for the viscous dissipation. In experiments it is difficult to measure the interface capillary pressure jump without accounting for the viscous pressure head, which is at least an order of magnitude larger. Upscaling the pore-scale capillary pressure is an essential step for complete characterization of capillary-dominant two-phase flow in a porous medium at the laboratory scale. Drainage is simulated under equilibrium (quasi-static) and non-equilibrium (dynamic) conditions for various capillary numbers. The Navier–Stokes (NS) equations are solved in the pore space using the open-source finite-volume computational fluid dynamics (CFD) code, OpenFOAM. The Volume-of-Fluid (VOF) method is employed to track the evolution of the fluid–fluid interfaces, and a contact angle is used to account for the effect of wall adhesion. The simulations are first validated with published experimental data for dynamic and quasi-static drainage in a micromodel. From the microscale simulations, the interface capillary pressure is determined, and compared to the macroscopic capillary pressure under equilibrium and non-equilibrium conditions. Our results show the traditionally-measured macroscopic capillary pressure curves exhibit a strong dependence on the capillary number under dynamic flow conditions. In contrast, the interface capillary pressure-saturation relation, which relies on pore-scale pressure differences at the invasion front, is almost invariant of flow conditions (dynamic and quasi-static).

Abstract

We present version 3 of the open-source simulator for flow and transport processes in porous media DuMux. DuMux is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMux, version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.

Abstract

The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modeling for situations with complex thermodynamic behavior. In this series, we compare numerical solutions of the macroscopic flow equations with molecular dynamics simulation data. To enable molecular dynamics for sufficiently large scales in time and space, we selected the truncated and shifted Lennard-Jones potential, for which also highly accurate equations of state are available. A comparison of a two-phase Riemann problem is shown, which involves a liquid and a vapor phase, with an undergoing phase transition. The loss of hyperbolicity allows for the occurrence of anomalous wave structures. We successfully compare the molecular dynamics data with two macroscopic numerical solutions obtained by either assuming local phase equilibrium or by imposing a kinetic relation and allowing for metastable states.

Abstract

Previous laboratory experiments with the kinetic interface sensitive (KIS) tracers have shown promising results with respect to the quantification of the fluid-fluid interfacial area (IFA) under dynamic, two-phase flow conditions. However, pore-scale effects relevant to two-phase flow (e.g., the formation of hydrodynamically stagnant/immobile zones) are not yet fully understood, and quantitative information about how far these effects influence the transport of the tracer reaction products is not yet available. Therefore, a pore-scale numerical model that includes two-phase, reactive flow, and transport of the KIS tracer at the fluid-fluid interface is developed. We propose a new method to quantitatively analyze how the mass of the KIS-tracer reaction product in the flowing water is affected by the presence of the immobile zones. The model employs the phase field method (PFM) and a new continuous mass transfer formulation, consistent with the PFM. We verify the model with the analytical solutions of transport involving advection, reaction and diffusion processes. The model is tested for two-phase flow conditions in a conceptual 2D slit. The applicability of the model is demonstrated in NAPL/water drainage scenarios in a conceptual porous domain, comparing the results in terms of the spatial distribution of the phases and solute concentration. Furthermore, we distinguish the mobile and immobile zones based on the local Péclet number, and the corresponding IFA, and solute mass in these two zones is quantified. Finally, we show that the solute mass in flowing water can be employed to selectively determine the mobile part of the IFA.

Abstract

Porous media surface roughness strongly influences the transport of solutes during drainage due to the formation of thick water films (capillary condensation) on the surface of the porous medium. For interfacially-reacted, water-based solutes, these water films increase both the solute production at the fluid-fluid interface, due to the increased number of fluid-fluid interfaces, and the loss of the solute due to retention in the water films. This study applied a pore-scale, direct numerical simulation with the phase-field method-based continuous solute transport model to simulate the reactive transport of the kinetic interfacial sensitive tracer. The study is implemented during primary drainage in a 2D slit with rough solid walls, where the fractal geometries of the solid surfaces were generated numerically. The moving interfacial area is found to be changing non-monotonically with the root mean square of surface roughness. With increasing root mean square roughness, the average film thickness increases linearly, whereas the film-associated interfacial area per smooth surface area converges to a value slightly larger than one. The retention of the solute mass produced by the moving meniscus in the water film is observed, and this is described by a film-associated mobile mass retention term. An implicit relation between the mobile interfacial area and the solute mass in flowing zones is found. Finally, it is found that the film-associated mobile mass retention term is linearly related to the root mean square roughness.

Abstract

Abstract Accurately predicting bare-soil evaporation requires the proper characterization of the near-surface atmospheric conditions. These conditions, dependent on factors such as surface microtopography and wind velocity, vary greatly and therefore require high-resolution datasets to be fully incorporated into evaporation models. These factors are oftentimes parameterized in models through the aerodynamic resistance (ra), in which the vapor roughness length (z0v) and the momentum roughness length (z0m) are two crucial parameters that describe the transport near the soil-atmosphere interface. Typically, when evaluating bare-soil evaporation, these two characteristic lengths are assumed equal, although differences are likely to occur especially in turbulent flows over undulating surfaces. Thus, this study aims to investigate the relationship between z0v and z0m above undulating surfaces to ultimately improve accuracy in estimating evaporation rate. To achieve this goal, four uniquely designed wind tunnel—soil tank experiments were conducted considering different wind speeds and undulation spacings. Particle image velocimetry (PIV) was used to measure the velocity field above the undulating surface in high resolution. Using the high-fidelity data set, the logarithmic ratio of z0v to z0m is determined and used to estimate ra. Results confirm that these lengths differ significantly, with the logarithmic ratio roughly ranging from −15 to −5 under the conditions tested. PIV-measured results demonstrate this ratio is closely tied to the mass and momentum transport behaviors influenced by surface undulations. Using the data-integrated formulation of ra, predictions of evaporation rate were prepared for both the laboratory and lysimeter experiments, demonstrating the efficacy of the proposed approach in this study.

Abstract

In article number 2007982, Holger Steeb, Sabine Ludwigs, and co-workers present humidity-triggered bending actuators based on simple polymer bilayers and their in-depth mechanical characterization. A loop consisting of the mechanical characterization and a simple analytical model allows the prediction of deformations of in principle any complex geometry and material combination, for example, for moving parts and curvatures in soft robotics.

Abstract

In this study, the complexity of a steady-state flow through porous media is revealed using confocal laser scanning microscopy (CLSM). Micro-particle image velocimetry (micro-PIV) is applied to construct movies of colloidal particles. The calculated velocity vector fields from images are further utilized to obtain laminar flow streamlines. Fluid flow through a single straight channel is used to confirm that quantitative CLSM measurements can be conducted. Next, the coupling between the flow in a channel and the movement within an intersecting dead-end region is studied. Quantitative CLSM measurements confirm the numerically determined coupling parameter from earlier work of the authors. The fluid flow complexity is demonstrated using a porous medium consisting of a regular grid of pores in contact with a flowing fluid channel. The porous media structure was further used as the simulation domain for numerical modeling. Both the simulation, based on solving Stokes equations, and the experimental data show presence of non-trivial streamline trajectories across the pore structures. In view of the results, we argue that the hydrodynamic mixing is a combination of non-trivial streamline routing and Brownian motion by pore-scale diffusion. The results provide insight into challenges in upscaling hydrodynamic dispersion from pore scale to representative elementary volume (REV) scale. Furthermore, the successful quantitative validation of CLSM-based data from a microfluidic model fed by an electrical syringe pump provided a valuable benchmark for qualitative validation of computer simulation results.

Abstract

Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers (Re≈3000,6000) and two porosities (φ=0.5,0.8). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Kármán constant of the mean velocity profile.

Abstract

The microscopic structure of porous walls modulates the turbulent flow above. The standard approach, the volume-averaged modelling of the porous wall, does not resolve the pore structure. To systematically link geometric characteristics with flow properites, direct numerical simulations are conducted which are fully-resolving the microscopic structure. A high-order spectral/hp element solver is adopted to solve the incompressible Navier-Stokes equations. Resolving the full energy-spectra relies on a zonal polynomial refinement based on a conforming mesh. A low and a high porosity case with in-line arrays of cylinders are analysed for two Reynolds numbers. The peak in the streamwise energy spectra is shifted towards the pore unit length for both cases. Proper Orthogonal Decomposition (POD) shows that the fluctuations in the porous wall are linked to the structures above. Q2 structures are linked with blowing events and Q4 structures with suction events in the first pore row. The numerical solver Nektar exhibits an excellent scalability up to 96k cores on “Hazel Hen” where a slightly improved performance is observed on the brand new HPE “Hawk” system. Strong scaling tests indicate an efficiency of 70% with around 5, 000 mesh-nodes per core, which indicates a high potential for an adequate use of a HPC platform to investigate turbulent flows above porous walls while resolving the pore structure.

Abstract

Experimental and field studies reported a significant discrepancy between the cleanup and contamination time scales, while its cause is not yet addressed. Using high-resolution fast synchrotron x-ray computed tomography, we characterized the solute transport in a fully saturated sand packing for both contamination and cleanup processes at similar hydrodynamic conditions. The discrepancy in the time scales has been demonstrated by the nonuniqueness of hydrodynamic dispersion coefficient versus injection rate (Péclet number). Observations show that in the mixed advection-diffusion regime, the hydrodynamic dispersion coefficient of cleanup is significantly larger than that of the contamination process. This nonuniqueness has been attributed to the concentration-dependent diffusion coefficient during the cocurrent and countercurrent advection and diffusion, present in contamination and cleanup processes. The new findings enhance our fundamental understanding of transport processes and improve our capability to estimate the transport time scales of chemicals or pollution in geological and engineering systems.

Abstract

In order to control ink droplet movement into the printing-paper layer, a set of pore-scale two-phase flow simulations were performed. The high-resolution three-dimensional pore space of the paper was obtained using focused ion beam scanning electron microscopy (FIB-SEM). Solving Navier-Stokes equations yielded details about dynamic movement of a droplet into the layer. To evaluate simulation results, for the first time, confocal laser microscopy imaging technique was integrated into a FIB-SEM chamber. Doing so, high resolution imaging of the droplet penetration inside paper was conducted and computed volume of penetrated ink at final stage was compared to the imaged volume. The ink penetration and spreading extent showed a good agreement with simulation results. Therefore, the developed simulation case was further investigated to study impact of liquid contact angle, real ink properties, and droplet arrival velocity on paper surface on final print quality. A faster penetration into the paper coating was observed for smaller equilibrium contact angles; meanwhile, more radial wicking was observed. In case of velocity of impact, higher velocity caused creation of irregular shapes of the ink footprint on paper surface. In addition to that, higher velocity caused ink splash which consequently created satellite droplets and lowered the print quality. Comparing ink-like liquid (representing real ink liquid properties) with water, water moves faster than ink-like liquid into the paper. This is mainly due to the higher viscosity and lower surface tension of the ink-like liquid.

Abstract

We establish a local theory, i.e., existence, uniqueness and blow-up criterion, for a general family of singular SDEs in Hilbert spaces. The key requirement relies on an approximation property that allows us to embed the singular drift and diffusion mappings into a hierarchy of regular mappings that are invariant with respect to the Hilbert space and enjoy a cancellation property. Various nonlinear models in fluid dynamics with transport noise belong to this type of singular SDEs. By establishing a cancellation estimate for certain differential operators of order one with suitable coefficients, we give the detailed constructions of such regular approximations for certain examples. In particular, we show novel local-in-time results for the stochastic two-component Camassa–Holm system and for the stochastic Córdoba–Córdoba–Fontelos model.

Abstract

The mechanism of dynamic wetting and the fluid dynamics during the onset of droplet mobilization driven by a microchannel flow are not clearly understood. In this work, we use microparticle tracking velocimetry to visualize the velocity distribution inside the droplet both prior to and during mobilization. Time-averaged and instantaneous velocity vectors are determined using fluorescent microscopy for various capillary numbers. A circulating flow exists inside the droplet at a subcritical capillary number, in which case the droplet is pinned to the channel walls. When the capillary number exceeds a critical value, droplet mobilization occurs, and this process can be divided into two stages. In the first stage, the location of the internal circulation vortex center moves to the rear of the droplet and the droplet deforms, but the contact lines at the top walls remain fixed. In the second stage, the droplet rolls along the solid wall, with fixed contact angles keeping the vortex center in the rear part of the droplet. The critical capillary number for the droplet mobilization is larger for the droplet fluid with a larger viscosity. A force-balance model of the droplet, considering the effect of fluid properties, is formulated to explain the experimental trends of advancing and receding contact angles with the capillary number. Numerical simulations on internal circulations for the pinned droplet indicate that the reversed flow rate, when normalized by the inlet flow rate and the kinematic viscosity ratio of the wetting and nonwetting phases, is independent of the capillary number and the droplet composition.

Abstract

A discretization is proposed for models coupling free flow with anisotropic porous-medium flow. Our approach employs a staggered-grid finite volume method for the Navier-Stokes equations in the free-flow subdomain and a MPFA finite volume method to solve Darcy flow in the porous medium. After appropriate spatial refinement in the free-flow domain, the degrees of freedom are conveniently located to allow for a natural coupling of the two discretization schemes. In turn, we automatically obtain a more accurate description of the flow field surrounding the porous medium. Numerical experiments highlight the stability and applicability of the scheme in the presence of anisotropy and second-order grid convergence was found in both domains, verifying our approach.

Abstract

The subject of this paper is a generalized Camassa–Holm equation under random perturbation. We first establish local existence and uniqueness results as well as blow-up criteria for pathwise solutions in the Sobolev spaces Hs with s>3/2. Then we analyze how noise affects the dependence of solutions on initial data. Even though the noise has some already known regularization effects, much less is known concerning the dependence on initial data. As a new concept we introduce the notion of stability of exiting times and construct an example showing that multiplicative noise (in Itô sense) cannot improve the stability of the exiting time, and simultaneously improve the continuity of the dependence on initial data. Finally, we obtain global existence theorems and estimate associated probabilities.

Abstract

In the present work, we explore the capability of artificial neural networks (ANN) to predict the closure terms for large eddy simulations (LES) solely from coarse-scale data. To this end, we derive a consistent framework for LES closure models, with special emphasis laid upon the incorporation of implicit discretization-based filters and numerical approximation errors. We investigate implicit filter types that are inspired by the solution representation of discontinuous Galerkin and finite volume schemes and mimic the behavior of the discretization operator, and a global Fourier cutoff filter as a representative of a typical explicit LES filter. Within the perfect LES framework, we compute the exact closure terms for the different LES filter functions from direct numerical simulation results of decaying homogeneous isotropic turbulence. Multiple ANN with a multilayer perceptron (MLP) or a gated recurrent unit (GRU) architecture are trained to predict the computed closure terms solely from coarse-scale input data. For the given application, the GRU architecture clearly outperforms the MLP networks in terms of accuracy, whilst reaching up to 99.9% correlation between the networks' predictions and the exact closure terms for all considered filter functions. The GRU networks are also shown to generalize well across different LES filters and resolutions. The present study can thus be seen as a starting point for the investigation of data-based modeling approaches for LES, which not only include the physical closure terms, but account for the discretization effects in implicitly filtered LES as well.

Abstract

Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 μm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids’ topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.

Abstract

Exchange processes between a turbulent free flow and a porous media flow are sensitive to the flow dynamics in both flow regimes, as well as to the interface that separates them. Resolving these complex exchange processes across irregular interfaces is key in understanding many natural and engineered systems. With soil–water evaporation as the natural application of interest, the coupled behavior and exchange between flow regimes are investigated numerically, considering a turbulent free flow as well as interfacial forms and obstacles. Interfacial forms and obstacles will alter the flow conditions at the interface, creating flow structures that either enhance or reduce exchange rates based on their velocity conditions and their mixing with the main flow. To evaluate how these interfacial forms change the exchange rates, interfacial conditions are isolated and investigated numerically. First, different flow speeds are compared for a flat surface. Second, a porous obstacle of varied height is introduced at the interface, and the effects the flow structures that develop have on the interface are analyzed. The flow parameters of this obstacle are then varied and the interfacial exchange rates investigated. Next, to evaluate the interaction of flow structures between obstacles, a second obstacle is introduced, separated by a varied distance. Finally, the shape of these obstacles is modified to create different wave forms. Each of these interfacial forms and obstacles is shown to create different flow structures adjacent to the surface which alter the mass, momentum, and energy conditions at the interface. These changes will enhance the exchange rate in locations where higher velocity gradients and more mixing with the main flow develop, but will reduce the exchange rate in locations where low velocity gradients and limited mixing with the main flow occur.

Abstract

Bubbly turbulent flow in a channel is investigated using interface-resolved direct numerical simulation. An efficient coupled level-set volume-of-fluid solver based on a fast Fourier transform algorithm is implemented to enable a high resolution and fast computation at the same time. Up to 384 bubbles are seeded in the turbulent channel flow corresponding to 5.4\% gas volume fraction. Bubbles are clustered in the channel center due to the downward flow direction. The bubbles induce additional pseudo-turbulence in the channel center and are also able to attenuate the energy in the boundary layer by reducing the shear production. Turbulent kinetic energy budget indicates a significant buoyancy production in the channel center. A local equilibrium between buoyancy production and dissipation is observed here besides the shear production peak in the boundary layer. Comparing the local production and dissipation indicates a coexistence of boundary layer turbulence near the wall and bubble-induced pseudo-turbulence in the channel center. The liquid phase and gas phase are coupled through the complex liquid–gas interface. Local flow topology analysis is depicted in the liquid phase around the bubbles as well as in the gas phase. The flow topology of the liquid phase and the gas phase differs from each other significantly. Local dissipation is more dominant in the liquid phase near the bubble interface, whereas local enstrophy is preferred in the gas phase. In the liquid phase, a high dissipation event is preferred close to the interface, whereas a high enstrophy event is dominant away from the interface.

Abstract

The stable and accurate approximation of discontinuities such as shocks on a finite computational mesh is a challenging task. Detection of shocks or strong discontinuities in the flow solution is typically achieved through a priori troubled cell indicators, which guide the subsequent action of an appropriate shock capturing mechanism. Arriving at a stable and accurate solution often requires empirically based parameter tuning and adjustments of the indicator settings to the discretization and solution at hand. In this work, we propose to separate the task of shock detection and shock capturing more strongly and aim to develop a shock indicator that is robust, accurate, requires minimal user input and is suitable for high order element-based methods like discontinuous Galerkin and flux reconstruction methods. The novel indicator is learned from analytical data through a supervised learning strategy; its input is given by the high order solution field, its output is an element-local map of the shock position. We use state of the art methods from edge detection in image analysis based on deep convolutional multiscale networks and deep supervision to train the indicators. The resulting networks are then used as black box indicators, showing their robustness and accuracy on well established canonical testcases. All simulations are run ab initio using the developed indicators, showing that they provide also stability during the strongly transient phases. In particular for high order schemes with large cells and considerable inner-cell resolution capabilities, we demonstrate how the additional accurate prediction of the position of the shock front can be exploited to guide inner-element shock capturing strategies.

Abstract

Abstract We investigate the influence of near-surface wind conditions on subsurface gas transport and on soil-atmosphere gas exchange for gases of different density. Results of a sand tank experiment are supported by a numerical investigation with a fully coupled porous medium-free flow model, which accounts for wind turbulence. The experiment consists of a two-dimensional bench-scale soil tank containing homogeneous sand and an overlying wind tunnel. A point source was installed at the bottom of the tank. Gas concentrations were measured at multiple horizontal and vertical locations. Tested conditions include four wind velocities (0.2/1.0/2.0/2.7 m/s), three different gases (helium: light, nitrogen: neutral, and carbon dioxide: heavy), and two transport cases (1: steady-state gas supply from the point source; 2: transport under decreasing concentration gradient, subsequent to termination of gas supply). The model was used to assess flow patterns and gas fluxes across the soil surface. Results demonstrate that flow and transport in the vicinity of the surface are strongly coupled to the overlying wind field. An increase in wind velocity accelerates soil-atmosphere gas exchange. This is due to the effect of the wind profile on soil surface concentrations and due to wind-induced advection, which causes subsurface horizontal transport. The presence of gases with pronounced density difference to air adds additional complexity to the transport through the wind-affected soil layers. Wind impact differs between tested gases. Observed transport is multidimensional and shows that heavy as well as light gases cannot be treated as inert tracers, which applies to many gases in environmental studies.