Simple Transport Model Research Articles

A reinterpreted discrete fracture model for Darcy–Forchheimer flow in fractured porous media

We propose a novel hybrid-dimensional model for the Darcy–Forchheimer flow in fractured rigid porous media, with a natural applicability to non-conforming meshes. Motivated by the previous work on the reinterpreted discrete fracture model (RDFM) for Darcy flows, we extend its key idea to non-Darcy flows. Coupling the Darcy’s law in the matrix and the Forchheimer’s law in the fractures through the introduction of the Dirac-δ functions to characterize the fractures, we derive a relationship between the total flow velocity in the porous media and the fluid velocity in the fractures. With this relation, it is natural to model the Darcy–Forchheimer flow in the whole computational domain by one equation. The local discontinuous Galerkin (LDG) method is applied for numerical discretization of the steady-state single-phase flow problem and a time-marching method is adopted to find the solution of the resulting nonlinear system. Besides, we construct a direct solver for the nonlinear equation of the fluid velocity in fracture to save computational cost. As an application, we discuss a simple transport model coupled with the flow equation. Several numerical experiments validate the performance of the model with its effectiveness on non-conforming meshes. We observe that the Darcy–Forchheimer model effectively reduce the flow rates and make the predictions more realistic in case of excessive fracture velocities.

Simplified Stability-Based Transition Transport Modeling for Unstructured Computational Fluid Dynamics

Inspired by the model framework, a new -based model was developed and implemented into an unstructured Reynolds-averaged Navier–Stokes (RANS) code. The new model applies a modified version of the -transport equation of the model. This new implementation applies an alternative local formulation for the pressure-gradient parameter that allows the local assessment of the transition criterion within the boundary layer and, thereby, simplifies the model and increases the accuracy of the transition onset location. The resulting prediction approach is robust, user-friendly, and suitable for unstructured RANS solvers with high parallelization. To attain a wide application range of the prediction method, while keeping the simplicity of the approach, a physical path-independent transition criterion was adopted, which was calibrated based on linear stability theory results. The approach was successfully validated against experimental data for various relevant test cases. In addition, results were also compared with results obtained with the model and, for some cases, with the method, which showed a strong similarity in the predictions of the method and the new model.

Toward a multivariate formulation of the parametric Kalman filter assimilation: application to a simplified chemical transport model

Abstract. This contribution explores a new approach to forecasting multivariate covariances for atmospheric chemistry through the use of the parametric Kalman filter (PKF). In the PKF formalism, the error covariance matrix is modellized by a covariance model relying on parameters, for which the dynamics are then computed. The PKF has been previously formulated in univariate cases, and a multivariate extension for chemical transport models is explored here. This contribution focuses on the situation where the uncertainty is due to the chemistry but not due to the uncertainty of the weather. To do so, a simplified two-species chemical transport model over a 1D domain is introduced, based on the non-linear Lotka–Volterra equations, which allows us to propose a multivariate pseudo covariance model. Then, the multivariate PKF dynamics are formulated and their results are compared with a large ensemble Kalman filter (EnKF) in several numerical experiments. In these experiments, the PKF accurately reproduces the EnKF. Eventually, the PKF is formulated for a more complex chemical model composed of six chemical species (generic reaction set). Again, the PKF succeeds at reproducing the multivariate covariances diagnosed on the large ensemble.

On the Mechanisms Generating the Nearshore Bars on a Sandy Coastal Slope

The study is aimed at investigation of the problem in what conditions the morphodynamic self-organizational mechanism controlling the growth of small perturbations arisen on bed could be responsible for the nearshore bars development. A simplified sediment transport model is used in which the sediment discharge is turned out directly proportional to the local bed slope. This model allows reducing the problem to an analytical solving of the diffusion equation which gives the base to predict the evolution of perturbation arisen on bed. The conclusion is argued that the favorable preconditions for the nearshore bar formation can exist in the case of onshore sediment transport associated with the dominating contribution of wave asymmetry in transport process. However under conditions of steep stormy waves the undertow is developed providing offshore sediment flux from the beach. In this case, the breaker bar is formed by two mechanisms–self-organization and convergence of opposite sediment fluxes. The results obtained are in agreement with available data and also assist to explain some properties of multiple-bar systems found out from observations.

Use of intrinsic hysteresis for the active control of internal transport barriers in magnetically confined fusion plasmas

In magnetically confined fusion devices, control of internal transport barriers (ITBs) is important both to enhance and suppress the turbulent transport to improve confinement control. Barrier control should allow for the improvement of confinement to aid in achieving the needed fusion criteria while also permitting the degradation of confinement to control profiles and clean the device by moving out the impurities accumulated near the core. In this work, we present a novel control scenario that takes advantage of the hysteresis intrinsic to transport barriers to easily cycle through enhanced and degraded confinement regimes. The control scenario is illustrated using a five-field simplified transport model for an ITB using typical parameters of a neutral beam injection-heated DIII-D tokamak discharge. Pellets and ion cyclotron resonance frequency power are used as control knobs for this active control scenario. These knobs adequately modify at will the local gradients and, therefore, the growth rates and shearing rates, allowing for easy and efficient control of the barrier by taking advantage of the barrier hysteresis. The result is a control cycle that could be operated with a relatively small amount of power in high performance regimes which, nowadays, typically require large power to control. It may also have advantages to avoid, or at least ameliorate, the appearance of magnetohydrodynamic instabilities in the barrier region.

Oceanic bottom mixed layer in the Clarion-Clipperton Zone: potential influence on deep-seabed mining plume dispersal

The oceanic bottom mixed layer (BML) is a well mixed, weakly stratified, turbulent boundary layer. Adjacent to the seabed, the BML is of intrinsic importance for studying ocean mixing, energy dissipation, particle cycling and sediment-water interactions. While deep-seabed mining of polymetallic nodules is anticipated to commence in the Clarion-Clipperton Zone (CCZ) of the northeastern tropical Pacific Ocean, knowledge gaps regarding the form of the BML and its potentially key influence on the dispersal of sediment plumes generated by deep-seabed mining activities are yet to be addressed. Here, we report recent field observations from the German mining licence area in the CCZ that characterise the structure and variability of the BML locally. Quasi-uniform profiles of potential temperature extending from the seafloor reveal the presence of a spatially and temporally variable BML with an average local thickness of approximately 250 m. Deep horizontal currents in the region have a mean speed of 3.5 cm s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} and a maximum speed of 12 cm s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} at 18.63 ms above bottom over an 11 month record. The near-bottom currents initially have a net southeastward flow, followed by westward and southward flows with the development of complex, anticyclonic flow patterns. Theoretical predictions and historical data show broad consistency with mean BML thickness but cannot explain the observed heterogeneity of local BML thickness. We postulate that deep pressure anomalies induced by passing surface mesoscale eddies and abyssal thermal fronts could affect BML thickness, in addition to local topographic effects. A simplified transport model is then used to study the influence of the BML on the interplay between turbulent diffusion and sediment settling in the transport of deep-seabed mining induced sediment plumes. Over a range of realistic parameter values, the effects of BML on plume evolution can vary significantly, highlighting that resolving the BML will be a crucial step for accurate numerical modelling of plume dispersal.

Electrochemically assisted transport of chlorinated hydrocarbons from aged to clean silt

In this work, the electrokinetic transport of pollutants from polluted to clean soil at two different temperatures is evaluated and validated with a simple phenomenological transport model. For this purpose, real samples highly contaminated with residues from the industrial production of lindane are used. The results show that the dragging of aged pollutant is almost nil (below 0.1% of the initial content), regardless of the experimental conditions tested. During the treatment, the resulting intensity decreases due to ion depletion in the silt. Electro-osmotic fluxes are quite low (0.7 cm d−1) and do not depend importantly on temperature. As well, the amounts of pollutants collected in electrolyte wells are negligible. However, there is an important volatilization (from 9 to 12% depending on operation temperature) of the chlorinated organic compounds (COCs) (mainly of lowly chlorinated organics and the gamma and delta isomers of hexachlorocyclohexane) but they are not recovered in the granular activated carbon adsorption but accumulated in the walls and pipes of the mockups. These results are confirmed by volatilization tests in closed bottles dragging the pollutants with an air flow. Additionally, the results accurately fit to a 1-D non-reactive model previously proposed to evaluate the transport of COCs from polluted to clean soil. Effective diffusion coefficients of COCs do not depend on the number of chlorine substitutions.

A simplified model to estimate nonlinear turbulent transport by linear dynamics in plasma turbulence

A simplified model to estimate nonlinear turbulent transport only by linear calculations is proposed, where the turbulent heat diffusivity in tokamak ion temperature gradient(ITG) driven turbulence is reproduced for a wide parameter range including near- and far-marginal ITG stability. The optimal nonlinear functional relation(NFR) between the turbulent diffusivity, the turbulence intensity mathcal{T}, and the zonal-flow intensity mathcal{Z} is determined by means of mathematical optimization methods. Then, an extended modeling for mathcal{T} and mathcal{Z} to incorporate the turbulence suppression effects and the temperature gradient dependence is carried out. The simplified transport model is expressed as a modified nonlinear function composed of the linear growth rate and the linear zonal-flow decay time. Good accuracy and wide applicability of the model are demonstrated, where the regression error of sigma _{textrm{model}} = 0.157 indicates improvement by a factor of about 1/4 in comparison to that in the previous works.

Interpreting Concentrations Sampled in Long-Screened Wells with Borehole Flow: An Inverse Modeling Approach.

New approaches are needed to assess contaminant mass based on samples from long-screened wells and open boreholes (LSW&OB). The interpretation of concentration samples collected in LSW&OB is complicated in the presence of vertical flow within the well. In the absence of pumping (i.e., ambient conditions), the well provides a conduit for flow to occur between aquifer layers or fractures as a result of head differences. Under pumping conditions, vertical borehole flow may vary with depth depending on far-field heads and hydraulic conductivity; furthermore, if pumping fails to overcome ambient gradients, outflow from the well to the aquifer may occur. Concentration samples thus represent flow-weighted averages of formation concentrations, but the averaging process is commonly unknown or difficult to identify. Recognition of the importance of borehole flow has motivated the use of multi-level wells, packers, and well liners; however, LSW&OB remain common for numerous reasons, including cost, multi-purpose design requirements (e.g., pump-and-treat, water supply), logging, and installation of instrumentation. Here, we present a simple analytical model for flow and transport within a well and interaction with the surrounding aquifer. We formulate an inverse problem to estimate formation concentration based on sampled concentrations and data from flowmeter logs. The approach is demonstrated using synthetic examples. Our results (1) underscore the importance of interpreting sampled concentrations within the context of hydraulic conditions and aquifer/well exchange; (2) demonstrate the value of flowmeter measurements for this purpose; and (3) point to the potential of the new inverse approach to better interpret results from samples collected in LSW&OB.

A simple calculation model for transport of visitors on a closed circuit

It is examined a very simple, geometrically closed configuration concerning transport systems. The problem analyzed is a multi-objective optimization problem, in which an ever increasing set of visitors is urged to visit and move from a given set of sites on a closed path. An essentially kinematic approach is developed and the performance evaluation is obtained by means of a combinations of variables. It is also examined a particular realization in which one makes use of C_0-functions instead of discrete variables, in the spirit of classical mathematical physics. Some features of the model show relevant differences with others concerned with traffic and transport problems, for the presence of Diophantine integral evolution equations in place of statistical and/or numerical complex evaluation methods. This work is the first part of a more thorough discussion on dynamical equations in transport systems, including simulations and optimization schemes.

Experimental observation of the role of countercations in modulating the electrical conductance of Preyssler-type polyoxometalate nanodevices.

Polyoxometalates are nanoscale molecular oxides with promising properties that are currently explored for molecule-based memory devices. In this work, we synthesize a series of Preyssler polyoxometalates (POMs), [Na⊂P5W30O110]14-, stabilized with four different counterions, H+, K+, NH4+, and tetrabutylammonium (TBA+). We study the electron transport properties at the nanoscale (conductive atomic force microscopy, C-AFM) of molecular junctions formed by self-assembled monolayers (SAMs) of POMs electrostatically deposited on the ultraflat gold surface prefunctionalized with a positively charged SAM of amine-terminated alkylthiol chains. We report that the electron transport properties of P5W30-based molecular junctions depend on the nature of the counterions; the low-bias current (in the voltage range [-0.6 V; 0.6 V]) gradually increases by a factor of ∼100 by changing the counterion in the order: K+, NH4+, H+ and TBA+. From a statistical study (hundreds of current-voltage traces) using a simple analytical model for charge transport in nanoscale devices, we show that the energy position of the lowest unoccupied molecular orbital (LUMO) of P5W30 with respect to the Fermi energy of the electrodes increases from ∼0.4 eV to ∼0.7 eV and that the electrode coupling energy also increases from ∼0.05 to 1 meV in the same order from K+, NH4+, H+ to TBA+. We discuss several hypotheses on the possible origin of these features, such as a counterion-dependent dipole at the POM/electrode interface and counterion-modulated molecule/electrode hybridization, with, in both cases, the largest effect in the case of TBA+ counterions.

Comparison of a hybrid model and experimental measurements for a dielectric-coated coaxial ECR thruster

Electrostatic probe and thrust balance measurements of a coaxial electron-cyclotron-resonance plasma thruster with magnetic nozzle are compared against numerical simulations of the device that solve self-consistently the plasma transport problem with a hybrid particle-in-cell/fluid approach and the microwave electromagnetic fields using mixed finite elements. A simple phenomenological anomalous transport model similar to those used in Hall thruster modeling is applied. Reasonable average relative errors are reported on the ion current density (8.7%) and plasma density (12.8%) profiles along the plume. Good agreement is found in terms of relative errors on thruster performance parameters as the 90%-current divergence angle (0%–3%), utilization efficiency (3%–10%), peak ion energy (9%–15%), and energy efficiency (2%–17%). The comparison suggests that enhanced cross-field diffusion is present in the plasma. Differences in the experimental and numerical behavior of electron temperature point to the areas of the model that could be improved. These include the electron heat flux closure relation, which must correctly account for the axial electron cooling observed.

A three-dimensional coupled thermo-hydro model for geothermal development in discrete fracture networks of hot dry rock reservoirs

Three-dimensional (3D) fluid flow and thermal transport modeling in discrete fracture networks (DFNs) is critical for geothermal energy recovery from enhanced geothermal systems (EGSs). Considering nonlinear fluid flow models, a 3D coupled thermo-hydro (T-H) model based on the Galerkin finite element method was developed for DFNs. Forchheimer flow was considered in this fluid flow model, and a simplified thermal transport model was adopted based on the local thermal non-equilibrium theory. Finite element spatial discretization of fluid flow and thermal transport models in DFNs was formulated. A simple upwind scheme was adopted as the numerical strategy of the thermal transport model, avoiding its solution oscillation. In addition, the proposed numerical method for the fluid flow and thermal transport was verified by comparing the model results with experimental, analytical, and numerical solutions. This approach was further applied to the modeling of heat extraction in a Habanero EGS reservoir for a period of 40 years under different injection pressures. The results demonstrated that the proposed approach was effective for simulating coupled T-H processes in 3D DFNs. With increasing the injection pressure, the power generation of reservoir increased, but its life span decreased. Injection temperature had positive effect on life span for power generation.

Increased radiation due to non-coronal effects on DIII-D and MAST-U with varying input power

Through SOLPS-ITER simulations of DIII-D and MAST-U, an X-divertor (XD) on DIII-D and a super X-divertor (SXD) on MAST-U were shown to have increased carbon emissivity (P Rad/n e n I) over corresponding standard divertors (SD) at similar degrees of partial detachment. The reasons behind the increased emissivity in the DIII-D XD and SXD are analyzed using a simple 0D transport model. From the transport model, it is seen that a major cause of the increased emissivity in the XD and SXD over the SDs is a shorter impurity confinement time. An additional cause (for the SXD) is an increase in the ratio of neutral hydrogen to electron density. The input power (P in) was varied and the XD had a higher emissivity at the higher P in, unlike the SDs which had the emissivity decrease with increasing P in. A basic geometrical reason is given to explain both the benefits of the XD over the SD as well as the increase in the XD’s emissivity with P in.

A novel concept for estimating the contaminant mass discharge of chlorinated ethenes emanating from clay till sites

Interest in using contaminant mass discharge (CMD) for risk assessment of contaminated sites has increased over the years, as it accounts for the contaminant mass that is moving and posing a risk to water resources and receptors. The most common investigation of CMD involves a transect of multilevel wells; however, this is an expensive undertaking, and it is difficult to place it in the right position in a plume. Additionally, infrastructure at the site needs to be considered. To derive an initial CMD estimate at a contaminated site and to allow for the prioritization of further investigations and remedial actions, the ProfileFlux method has been developed. It is targeted at former industrial sites with a source zone in a low conductivity layer with primarily vertical flow overlying an aquifer with primarily horizontal groundwater flow. The ProfileFlux method was developed for mature chlorinated solvent plumes, typically originating from more than 30 to 50-year-old spills, as the usage of chlorinated solvents is mainly historical. Thus, it is assumed that the contaminant had time to distribute in the low conductivity layer by mainly diffusive processes. Today the contamination is continuously released to the underlying aquifer, where advection and dispersive (other than diffusive) processes are of higher importance. The approach combines high-resolution, depth-discrete vertical concentration profiles and a simple 2D flow and transport model to estimate CMD by comparing measured and simulated concentration profiles in the aquifer. The study presented herein includes a global sensitivity analysis, in order to identify crucial field parameters, and of particular importance in this regard are source length, groundwater flux and infiltration. The ProfileFlux method was tested at a well-examined industrial site primarily contaminated with trichloroethylene, thereby allowing a comparison between CMD from the ProfileFlux method and the traditional transect method. CMD was estimated at 117–170 g/year, when using the ProfileFlux method, against 143 g/year with the transect method, thus validating ProfileFlux method's ability to estimate CMD. In addition, applying the method identified weak points in the conceptual site model. The method will be incorporated into a user-friendly online tool directed at environmental consultants and decision-makers working on the risk assessment and prioritization of contaminated sites with the specific hydrogeological conditions of an aquifer with an overlying low permeability layer.

Review of magnetic islands from the divertor perspective and a simplified heat transport model for the island divertor

Magnetic islands in toroidal confinement devices are reviewed from the viewpoint of their divertor potential. Divertor-relevant geometric parameters are derived analytically, and the relationships among them are revealed. We explain how the island geometry limits the target length and demonstrate the importance of an appropriate numerical tool to minimize the risk of thermal overload of plasma-facing components in the divertor design. The currently available three-dimensional (3D) models are briefly discussed, and their strengths and weaknesses are evaluated. The highlight will be the introduction of a new energy transport model recently developed within the framework of the EMC3 code (Feng et al 2004 Contrib. Plasma Phys. 44 57)—the so-called EMC3-Lite version—primarily for the design and optimization of 3D divertors involving thermal overload concerns. While still undergoing experimental validation with the current graphite divertor of W7-X, it is already being used to develop a subsequent tungsten divertor for W7-X.

Measurement of shock roughness due to phase plate speckle imprinting relevant for x-ray diffraction experiments on 3rd and 4th generation light sources

Laser-shock compression experiments at 3rd and 4th generation light sources generally employ phase plates, which are inserted into the beamline to achieve a repeatable intensity distribution at the focal plane. Here, the laser intensity profile is characterized by a high-contrast, high-frequency laser speckle. Without sufficient smoothing, these laser non-uniformities can translate to a significant pressure distribution within the sample layer and can affect data interpretation in x-ray diffraction experiments. Here, we use a combination of one- and two-dimensional velocity interferometry to directly measure the extent to which spatial frequencies within the laser focal spot intensity pattern are smoothed out during propagation within the laser plasma and a polyimide ablator. We find that the use of thicker polyimide layers results in spatially smoother shock fronts, with the greatest degree of smoothing associated with the highest spatial frequencies. Focal spots with the smallest initial speckle separation produce the most rapid smoothing. Laser systems that employ smoothing by spectral dispersion techniques to rapidly modulate the focal plane intensity distribution are shown to be the most effective ones in producing a spatially smooth shock front. We show that a simple transport model combined with the known polyimide Hugoniot adequately describes the extent of shock smoothness as a function of polyimide thickness. Our results provide a description of spatial structure smoothing across a shock front, which can be used to design targets on x-ray free electron laser facilities.

Boğaziçi Geçişleri için Optimal Geçiş Ücreti Tasarımı Üzerine

For many years, two toll bridges served commuter demand to cross the strait called Bosporus in Istanbul, Turkey. An underground connection called the Eurasian tunnel had been recently launched to relieve the strait's traffic. We study a simple transportation model that incorporates the forces that have come into play after the opening of the Eurasian tunnel. We find that for welfare maximisation, the premium paid for using the tunnel should be fixed in the two directions and not excessive. The current toll regime violates these features, and we recommend its amendment in light of our findings.

Modeling of a retarding potential analyzer and comparison with Express-A in-flight measurements

In-flight data from the retarding potential analyzers (RPAs) on the Russian geostationary telecommunication satellite Express-A #3 are used to validate electric thruster plume simulations. The RPAs placed on the solar array have made it possible to measure ion properties, current densities, and ion energy distribution functions (IEDFs) at different distances and field-of-view configurations with regard to the thrusters. The present work shows that the conventional probe theory used to interpret measurements is only valid if the probe is oriented toward the thruster. In most Express-A #3 measurements, this is not the case, and it leads to incorrect interpretations. In this study, a new RPA probe model is presented. It enables the physics of a tilted probe to be described more accurately, taking into account the view angle between the RPA entrance surface normal relative to the incoming flux direction, the flux direction nonaligned with the collection surface normal, the internal RPA electric fields, and masking effects due to RPA walls. This probe model is coupled with a simple model for ion transport from an electric thruster source to the probe to allow a comparison with in-flight data. The comparison between Express-A #3 RPA collected currents and calculations from the new model discriminates true ion energy shift from probe misorientation effects. It also shows that highly tilted RPA measurements that were previously never interpreted can be understood and analyzed.

Towards explanation of ‘broad’ and ‘narrow’ ECRH regimes observed in the GDT experiment

In the experiments with combined ECRH and NBI plasma heating started at the GDT facility (Budker Institute) in 2014, two quite different scenarios of plasma discharges were realized. The first one was characterized by a broad radial distribution of the absorbed ECRH power and a stable plasma with improved energy confinement of fast ions, while in the other the electron temperature profile was highly peaked with local values of T e > 500 eV, but plasma was susceptible to low-frequency instabilities that had a net negative effect on confinement. We discuss the first theoretical explanation of these phenomena. Essentially different temperature profiles are considered as a result of self-consistent evolution in time after the ECRH is switched on. To explore this concept, we combine an advanced quasi-optical model for the calculation of microwave power absorption with a simple transport model describing electron energy balance in a gas-dynamic trap.