One-dimensional Description Research Articles

One-dimensional reduction of viscous jets. I. Theory.

We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model whose sections are circular. However, when including the first corrections, we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model since it amounts to selectively discard some corrections. However, in a fast rotating frame, we find that the dominant effects induced by inertial and Coriolis forces should be correctly described by rod models. For completeness, we also recover the constitutive relations for forces and torques in rod models and exhibit a missing term in the lowest order expression of viscous torque. Given that our method is based on tensors, the complexity of all computations has been beaten down by using an appropriate tensor algebra package such as xAct, allowing us to obtain a one-dimensional description of curved viscous jets with all the first order corrections consistently included. Finally, we find a description for straight fibers with elliptic sections as a special case of these results, and recover that ellipticity is dynamically damped by surface tension. An application to toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev. E 97, 043116 (2018)10.1103/PhysRevE.97.043116].

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

Velocity profiles description and shape factors inclusion in a hyperbolic, one-dimensional, transient two-fluid model for stratified and slug flow simulations in pipes

Abstract In a previous work it has been shown that a one-dimensional, hyperbolic, transient five equations two-fluid model is able to numerically describe stratified, wavy, and slug flow in horizontal and near-horizontal pipes. Slug statistical characteristics can be numerically predicted with results in good agreement with experimental data and well-known empirical relations. In this model some approximated and simplified assumptions are adopted to describe shear stresses at wall and at phase interface. In this paper, we focus on the possibility to account for the cross sectional flow by inserting shape factors into the momentum balance equations of the aforementioned model. Velocity profiles are obtained by a pre-integrated model and they are computed at each time step and at each computational cell. Once that the velocity profiles are known, the obtained shape factors are inserted in the numerical resolution. In this way it is possible to recover part of the information lost due to the one-dimensional flow description. Velocity profiles computed in stratified conditions are compared against experimental profiles measured by PIV technique; a method to compute the velocity profile during slug initiation and growth has been developed and the computed velocity distribution in the liquid phase was compared against the one-seventh power law.

Estimation of the radon surface exhalation rate from a wall as related to that from its building material sample

The calculated radon areal exhalation rate from a wall, based on the one-dimensional diffusion description by Fick’s law, is found to be different from that calculated from a building material samp...

Gas Flow and Ion Transfer in Heated ESI Capillary Interfaces.

Transfer capillaries are the preferred means to transport ions, generated by electrospray ionization, from ambient conditions to vacuum. During the transfer of ions through the narrow, long tubes into vacuum, substantial losses are typical. However, recently it was demonstrated that these losses can be avoided altogether. To understand the experimental observation and provide a general model for the ion transport, here, we investigate the ion transport through capillaries by numerical simulation of interacting ions. The simulation encompasses all relevant factors, such as space charge, diffusion, gas flow, and heating. Special attention is paid to the influence of the gas flow on the transmission and especially the change imposed by heating. The gas flow is modeled by a one-dimensional gas dynamics description. A large number of ions are treated as point particles in this gas flow. This allows to investigate the influence of the capillary heating on the gas flow and by this on the ion transport. The results are compared with experimental findings. Graphical Abstract ᅟ.

Relaxation of Rayleigh and Lorentz Gases in Shock Waves

Two-dimensional Fokker–Planck type kinetic equations were derived, and some calculation results are presented to illustrate the principal distinction of the process of translational relaxation in a flow behind the front of a shock wave from the one-dimensional description that is valid for a stationary gas. In contrast to a Lorentz gas (a small admixture of light particles in a thermostat of heavy particles), the process of translational relaxation in a Rayleigh gas (a small admixture of heavy particles in a thermostat of low-weight gas particles) has an obvious two-dimensional character.

ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ТЕПЛОМАССОПЕРЕНОСА В ПАРОГЕНЕРАТОРЕ РЕАКТОРНОЙ УСТАНОВКИ ТИПА БРЕСТ ПРИ ВОЗНИКНОВЕНИИ КРИСТАЛЛИЗАЦИИ СВИНЦОВОГО ТЕПЛОНОСИТЕЛЯ

The method of numerical simulation has been developed describing non-stationary heat and mass transfer and thermal conductivity in a steam generator with liquid metal coolant when there is a crystallization process. The method takes into account the differences of the process depending on the condition of the contact surfaces. On its basis the dynamics of solid phase formation in a lead-coolant of reactor plant BREST type during the accident with the steam generator steam line depressurization has been studied. The calculations are carried out with using of the RASPLAV software complex, which allows modeling the interconnected dynamics of thermal-hydraulic processes in the first and second circuits in terms of the one-dimensional equilibrium approximation. It is shown that at failure of feed water lock-regulatory armature there is a full closure of flow section of the emergency steam generator first circuit by solid phase. Depending on the condition of the protective oxide layer of the heat exchange surface the solidification of lead coolant takes place either on the heat exchanger tubes or in the lower part of the steam generator reservoir. In both cases, there is a threat of cessation of circulation in the emergency loop. A brief description of the mathematical model of the steam generator and the reactor plant circuit as a whole is given. A one-dimensional description of heat and mass transfer is used. A thermodynamic equilibrium of the phases at the boundary of phase transfer is postulated. The test results of the programmed numerical model are given. The calculation of the high pressure pipeline rupture is tested by comparison with the experimental data. The calculation of the solid layer formation dynamics on the surface of heat exchange tubes is tested by comparing the numerical solution with the analytical solution of the Stefan problem. The results of this research can be used for design of reactors with a lead coolant.Keywords: Stefan problem, stop valve, mathematical model, steam generator, reactor plant, lead coolant, surface wettability, mixing feedwater heater, crystallization process, phase transfer.

Three-dimensional, time-dependent modeling of rainfall-induced landslides over a digital landscape: a case study

Physically based approaches for the regional assessment of slope stability using digital elevation model (DEM) topography usually consist of one-dimensional (1D) descriptions and often include more simplifying assumptions than realistic, three-dimensional (3D) analyses. We investigated a new application of the well-known, publicly available software TRIGRS (Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Model) in combination with Scoops3D to analyze 3D slope stability throughout a digital landscape in a time-dependent fashion, typically not implemented in three-dimensional models. TRIGRS simulated the dynamic hydraulic conditions within slopes induced by a rainstorm, and Scoops3D used the resulting pore water pressure for 3D stability assessment. We applied this approach to the July 2011 landslide event at Mount Umyeon, South Korea, and compared the results with the landslide initiation locations reported for this rainfall event. We described soil depth in the study area by three different simple models. Stability maps, obtained by the 1D (TRIGRS only) and 3D (TRIGRS and Scoops3D) time-dependent approaches, were compared with observations to assess the timing and locations of unstable sites via a synthetic index, previously developed specifically for dealing with point landslide locations. We highlight the performance of the 3D approach versus the 1D method represented by TRIGRS alone, as well as the consistency of the time dependence of the results obtained using the combined approach with the observations.

One-dimensional description of driven diffusion in periodic channels.

Diffusion of point-like particles driven by a constant longitudinal force in two-dimensional channels of periodically varying width is studied. The dynamics of such systems can be effectively described by the one-dimensional Smoluchowski(-Fick-Jacobs) equation in the longitudinal coordinate x, extended by a space dependent effective diffusion coefficient D(x). Our paper is focused on calculation of this function for an arbitrary channel shaping function h(x). Unlike the previous algorithms based on scaling of the transverse lengths, the method presented here uses periodicity of the channel. Instead of complicated expansion containing higher order derivatives of h(x), the proposed algorithm results in an integral formula for D(x), enabling us to study the system for wide range of the driving force and various (periodic) shaping functions h(x).

First passage, looping, and direct transition in expanding and narrowing tubes: Effects of the entropy potential.

We study transitions of diffusing particles between the left and right ends of expanding and narrowing conical tubes. In an expanding tube, such transitions occur faster than in the narrowing tube of the same length and radius variation rate. This happens because the entropy potential pushes the particle towards the wide tube end, thus accelerating the transitions in the expanding tube and slowing them down in the narrowing tube. To gain deeper insight into how the transitions occur, we divide each trajectory into the direct-transit and looping segments. The former is the final part of the trajectory, where the particle starting from the left tube end goes to the right end without returning to the left one. The rest of the trajectory is the looping segment, where the particle, starting from the left tube end, returns to this end again and again until the direct transition happens. Our focus is on the durations of the two segments and their sum, which is the duration of the particle first passage between the left and right ends of the tube. We approach the problem using the one-dimensional description of the particle diffusion along the tube axis in terms of the modified Fick-Jacobs equation. This allows us to derive analytical expressions for the Laplace transforms of the probability densities of the first-passage, direct-transit, and looping times, which we use to find the mean values of these random variables. Our results show that the direct transits are independent of the entropy potential and occur as in free diffusion. However, this "free diffusion" occurs with the effective diffusivity entering the modified Fick-Jacobs equation, which is smaller than the particle diffusivity in a cylindrical tube. This is the only way how the varying tube geometry manifests itself in the direct transits. Since direct-transit times are direction-independent, the difference in the first-passage times in the tubes of the two types is due to the difference in the durations of the looping segments in the expanding and narrowing tubes. Obtained analytical results are supported by three-dimensional Brownian dynamics simulations.

A computationally efficient pseudo-3D model for the numerical analysis of borehole heat exchangers

Ground-Source Heat Pump (GSHP) systems represent one of the most efficient renewable energy technologies. Their efficiency is highly influenced by the thermal properties of the ground, which are often measured in-situ using the Thermal Response Tests (TRTs). While three-dimensional mechanistic models offer significant advantages over analytical solutions for the numerical interpretation of TRTs, their computational cost represents a limiting factor. Moreover, most of the existing models do not include a comprehensive description of hydrological processes, which have proven to strongly influence the behavior of GSHP. Thus, in this study, we propose a computationally efficient pseudo-3D model for the numerical analysis and interpretation of TRTs. The numerical approach combines a one-dimensional description of the heat transport in the buried tubes of the exchanger with a two-dimensional description of the heat transfer and water flow in the surrounding subsurface soil, thus reducing the dimensionality of the problem and the computational cost. The modeling framework includes the widely used hydrological model, HYDRUS, which can simulate the movement of water, heat, and multiple solutes in variably-saturated porous media. First, the proposed model is validated against experimental data collected at two different experimental sites in Japan, with satisfactory results. Then, it is combined with the Morris method to carry out a sensitivity analysis of thermal properties. Finally, the model is exploited to investigate the influence of groundwater and lithologic heterogeneities on the thermal behavior of the GSHP.

A 1D+1D Model of Direct Ethanol Fuel Cells Based on an Optimized Kinetic Mechanism for Ethanol Electro-Oxidation Involving Free and Adsorbed Intermediate Species

A 1D+1D model for liquid-feed direct ethanol fuel cells with detailed ethanol electro-oxidation kinetics is presented. One-dimensional convective transport along the flow channels is coupled to a one-dimensional description for species transport across the MEA accounting for the effect of the electrochemical reactions and the mixed potential due to ethanol and acetaldehyde crossover. The model, validated against previous experimental data, provides the variation of the concentrations of the free species and the output and parasitic current densities along the flow channels. The downstream evolution of ethanol and acetaldehyde affects the anode reaction rates and the ethanol and acetaldehyde crossover fluxes, which in turn impacts on the cathode reaction rates. Polarization curves obtained at different positions along the flow channels show the effect of ethanol consumption and acetaldehyde upstream production and downstream consumption. Power density, parasitic current, fuel utilization and product selectivity curves are presented and discussed for different ethanol feed concentrations and flow rates.

Competition for light and water in a coupled soil-plant system

It is generally accepted that resource availability shapes the structure and function of many ecosystems. Within the soil-plant-atmosphere (SPA) system, resource availability fluctuates in space and time whereas access to resources by individuals is further impacted by plant-to-plant competition. Likewise, transport and transformation of resources within an individual plant is governed by numerous interacting biotic and abiotic processes. The work here explores the co-limitations on water losses and carbon uptake within the SPA arising from fluctuating resource availability and competition. In particular, the goal is to unfold the interplay between plant access and competition for water and light, as well as the impact of transport/redistribution processes on leaf-level carbon assimilation and water fluxes within forest stands. A framework is proposed that couples a three-dimensional representation of soil-root exchanges with a one-dimensional description of stem water flow and storage, canopy photosynthesis, and transpiration. The model links soil moisture redistribution, root water uptake, xylem water flow and storage, leaf potential and stomatal conductance as driven by supply and demand for water and carbon. The model is then used to investigate plant drought resilience of overstory-understory trees simultaneously competing for water and light. Simulation results reveal that understory-overstory interactions increase ecosystem resilience to drought (i.e. stand-level carbon assimilation rates and water fluxes can be sustained at lower root-zone soil water potentials). This resilience enhancement originates from reduced transpiration (due to shading) and hydraulic redistribution in soil supporting photosynthesis over prolonged periods of drought. In particular, the presence of different rooting systems generates localized hydraulic redistribution fluxes that sustain understory transpiration through overstory-understory interactions. Such complex SPA dynamics cannot be properly summarized by equivalent ecosystem-scale Resistor-Capacitor (RC) representation. However our results show that, with proper averaging across water flow paths, RC models can provide reasonable estimates of stand-level water and carbon fluxes during inter-storm periods.

A one-dimensional model of flow in a junction of thin channels, including arterial trees

We study a Stokes flow in a junction of thin channels (of diameter ) for fixed flows of the fluid at the inlet cross-sections and fixed peripheral pressure at the outlet cross-sections. On the basis of the idea of the pressure drop matrix, apart from Neumann conditions (fixed flow) and Dirichlet conditions (fixed pressure) at the outer vertices, the ordinary one-dimensional Reynolds equations on the edges of the graph are equipped with transmission conditions containing a small parameter at the inner vertices, which are transformed into the classical Kirchhoff conditions as . We establish that the pre-limit transmission conditions ensure an exponentially small error , , in the calculation of the three-dimensional solution, but the Kirchhoff conditions only give polynomially small error. For the arterial tree, under the assumption that the walls of the blood vessels are rigid, for every bifurcation node a ()-pressure drop matrix appears, and its influence on the transmission conditions is taken into account by means of small variations of the lengths of the graph and by introducing effective lengths of the one-dimensional description of blood vessels whilst keeping the Kirchhoff conditions and exponentially small approximation errors. We discuss concrete forms of arterial bifurcation and available generalizations of the results, in particular, the Navier-Stokes system of equations. Bibliography: 59 titles.

Distributed-Charge Transfer Model Analysis of SDC-based IT-SOFCs for the Electrochemical Oxidation of Syngas and Biogas

Aim of this work is the development of a distributed charge-transfer numeric model for intermediate temperature solid oxide fuel cells (IT-SOFCs) with composite electrodes. The model describes the leakage current inside a mixed ionic electronic conducting (MIEC) electrolyte. The reaction interface is extended along the whole length of the electrodes and a one-dimensional description of charge transfer phenomena is entailed. The profiles of the ionic and the electronic current density, as well as the profiles of the ionic and the electronic potentials are described along the whole length of the cell. The model is applied to analyze the experimental results of IT-SOFCs based on Samarium doped Ceria (SDC) electrolytes, Cu-Pd-CZ80 anodes and LSCF cathodes. Hydrogen electro-oxidation experiments are examined first, then the analysis is extended to the simulation of OCV data collected when feeding biogas mixtures to the anode

Temporal model for quasi-phase matching in high-order harmonic generation.

We present a model for quasi-phase matching (QPM) in high-order harmonic generation (HHG). Using a one-dimensional description, we analyze the time-dependent, ultrafast wave-vector balance to calculate the on-axis harmonic output versus time, from which we obtain the output pulse energy. Considering, as an example, periodically patterned argon gas, as may be provided with a grid in a cluster jet, we calculate the harmonic output during different time intervals within the drive laser pulse duration. We find that identifying a suitable single spatial period is not straightforward due to the complex and ultrafast plasma dynamics that underlies HHG at increased intensities. The maximum on-axis harmonic pulse energy is obtained when choosing the QPM period to phase match HHG at the leading edge of the drive laser pulse.

Engineering bright matter-wave solitons of dipolar condensates

We present a comprehensive analysis of the form and interaction of dipolar bright solitons across the full parameter space afforded by dipolar Bose–Einstein condensates, revealing the rich behavior introduced by the non-local nonlinearity. Working within an effective one-dimensional description, we map out the existence of the soliton solutions and show three collisional regimes: free collisions, bound state formation and soliton fusion. Finally, we examine the solitons in their full three-dimensional form through a variational approach; along with regimes of instability to collapse and runaway expansion, we identify regimes of stability which are accessible to current experiments.

A global mathematical model for the simulation of stenoses and bypass placement in the human arterial system

This paper is concerned with a global mathematical model for the human circulation; we describe its construction, its validation and its application to study the haemodynamical effect of stenoses and bypass placement in the arterial system. A geometric multiscale approach is adopted combining one-dimensional (1D) descriptions to represent 55 major arteries and zero-dimensional (0D) compartmental descriptions for the heart, lungs, the venous system and the microcirculation. Modern non-linear numerical methods are implemented for solving the 1D systems of hyperbolic partial differential equations and high-order Runge–Kutta methods are used to solve the systems of Ordinary Differential Equations resulting from the compartmental models. The complete global mathematical model is then validated for healthy and stenotic cases comparing numerical predictions from the model against in-vivo measurements. Results show overall satisfactory agreement. In addition, a sensitivity analysis is conducted in order to assess the influence of the most important parameters on some haemodynamical quantities of interest. We then apply the model to simulate the haemodynamics for healthy controls and subjects with arterial stenosis. We study the haemodynamical effect of bypass placement, considering different locations in the arterial system, different degrees of severity, for both single and multiple arterial stenoses. Haemodynamical quantities of interest in the study are local pressure and flow rate. We observe that large stenotic plaques near the heart cause abnormally strong pressure waves in the circulatory system and two adjacent occlusions worsen the phenomenon. We find that the mathematical model is capable of predicting the most convenient bypass location and graft dimensions, consistent with normal haemodynamics.

On the description of Brownian particles in confinement on a non-Cartesian coordinates basis.

We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.

On Parameterization of the Global Electric Circuit Generators

We consider the problem of generator parameterization in the global electric circuit (GEC) models. The relationship between the charge density and external current density distributions inside a thundercloud is studied using a one-dimensional description and a three-dimensional GEC model. It is shown that drastic conductivity variations in the vicinity of the cloud boundaries have a significant impact on the structure of the charge distribution inside the cloud. Certain restrictions on the charge density distribution in a realistic thunderstorm are found. The possibility to allow for conductivity inhomogeneities in the thunderstorm regions by introducing an effective external current density is demonstrated. Replacement of realistic thunderstorms with equivalent current dipoles in the GEC models is substantiated, an equation for the equivalent current is obtained, and the applicability range of this equation is analyzed. Relationships between the main GEC characteristics under variable parameterization of GEC generators are discussed.