Full Two-dimensional Model Research Articles

Dual-switching behavior of nonlocal interfaces

Nonlinear interfaces separating two diffusive Kerr-type media exhibit dual switching between total internal reflection and transmission. This property is found within a weakly nonlocal regime when both a nonparaxial treatment of the problem and a full two-dimensional model for carrier diffusion are assumed. The theoretical model is shown to predict an effective cubic-quintic nonlinearity with competing terms that produces such property. The validity of the analysis is contrasted with a full set of numerical simulations.

Verified reduction of dimensionality for an all-vanadium redox flow battery model

The computational cost for all-vanadium redox flow batteries (VRFB) models that seek to capture the transport phenomena usually increases with the number of spatial dimensions considered. In this context, we carry out scale analysis to derive a reduced zero-dimensional model. Two nondimensional numbers and their limits to support the model reduction are identified. We verify the reduced model by comparing its charge–discharge curve predictions with that of a full two-dimensional model. The proposed analysis leading to reduction in dimensionality is generic and can be employed for other types of redox flow batteries.

Evaluation of Simulation Models of Lateral Spread Sites Treated with Prefabricated Vertical Drains

AbstractFinite-element analyses are performed of centrifuge tests consisting of untreated and drain-treated lateral spread sites, with the goal of evaluating the ability of numerical simulations to predict the response of sites improved with prefabricated vertical drains. Finite-element models of varying complexity are analyzed: a two-dimensional model of the full centrifuge test, a three-dimensional unit cell model around a single drain, and a two-dimensional unit cell model. All the finite-element models predict pore pressures consistent with the centrifuge tests. The deformation responses of the finite-element models show that unit cell analyses produce significantly larger deformations than those observed in the centrifuge. This result is caused by the fact that the centrifuge test geometry is not well represented by the infinite slope condition assumed in a unit cell. The full two-dimensional model predicts deformations that are more consistent with those of the centrifuge because it can capture the ...

Coupling of full two-dimensional and depth-averaged models for granular flows

We develop a full two-dimensional Coulomb-viscoplastic model and apply it for inclined channel flows of granular materials from initiation to deposition. The presented model includes the basic features and observed phenomena in dense granular flows like the exhibition of a yield strength and a non-zero slip velocity. A pressure-dependent yield strength is proposed to account for the frictional nature of granular materials. The yield strength can be related to the internal friction angle of the material and plays an important role, e.g., in deposition processes. The interaction of the flow with the solid boundary is modelled by a pressure and rate-dependent Coulomb-viscoplastic sliding law. We develop an innovative multiscale strategy to couple the full two-dimensional, non-depth-averaged model (N-DAM) with a one-dimensional, depth-averaged model (DAM). With the coupled model the computational complexity reduces dramatically by using DAM in regions with smooth changes of flow variables. In regions where depth-averaging becomes inaccurate, like in the initiation and deposition regions and particularly, when the flow hits an obstacle or a defence structure, N-DAM must be used, because in these regions the momentum transfer must be considered in all directions. The performance of the coupling is very high: The numerical results obtained by the coupled model deviate only slightly from the ones generated with the full two-dimensional model. This shows that the coupled model, which retains all the basic physics of the flow, is an attractive alternative to an expensive, full two-dimensional model.

Two-Dimensional Effects in Laser Ablation of Carbon

This article studies the importance of two-dimensional effects in laser ablation of carbon. It describes the process by using the kinetic theory model of laser ablation based on the moment solution of the Boltzmann equation for arbitrary strong evaporation, and compares the predictions of the full two-dimensional model and of the two other models that use quasi-one-dimensional approximation in the solid or in the gas. All models estimate the total ablated mass reasonably well. However, comparison of their predictions shows that, surprisingly, two-dimensional effects are more important for the heat transfer in the solid than for the gas dynamics.

Full Two-Dimensional Model for Rolling Resistance. II: Viscoelastic Cylinders on Rigid Ground

Following the previous paper, “Full two-dimensional model for rolling resistance: Hard cylinder on viscoelastic foundation of finite thickness,” addressing modeling of rigid cylinder rolling against viscoelastic foundation of finite thickness, this paper focuses on the development of a rigorous full two-dimensional semianalytical model for viscoelastic rollers with layered structure rolling against a rigid ground. In this model, the polar coordinate system is used, the solution is expanded into a set of Fourier series corresponding to the angular coordinate, the frequency domain master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special condensed structure model based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. Examples are given to show the model capabilities to efficiently handle rolling resistance and contact stresses, and capture major characteristics of standing-wave phenomenon, such as sharp rise of rolling resistance, emergence of standing waves and material dynamic softening as the rolling speed approaches a critical value. The methodology may be of interest to industrial roller designers.

Full Two-Dimensional Model for Rolling Resistance: Hard Cylinder on Viscoelastic Foundation of Finite Thickness

A new full two-dimensional semianalytical method is developed to rigorously and efficiently solve the problem of a rigid cylinder rolling with any given constant speed over a viscoelastic foundation of finite thickness. In this new method, the solution is expanded into a set of Fourier series, the master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special boundary element based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. A verification example is given to validate the methodology. Several numerical examples are given to study the influences of various factors on rolling resistance. The method as well as the conclusions drawn from the examples may be of interest to roller and belt-conveyor designers. This approach can be easily generalized to solve the general rolling contact problems of two viscoelastic bodies.

Heterogeneous/homogeneous reactions and transport coupling for catalytic combustion systems: a review of model alternatives

In applying catalysis to real combustor applications the modeling of transport and chemistry interactions can be key to understanding combustion characteristics. For example the effect of boundary-layer flow and heterogeneous /homogeneous chemistry can determine product selectivity for catalytically promoted oxidation of chlorinated hydrocarbons. In this paper we discuss parameter regions where different flow models including lumped-parameter-transport laminar boundary-layer and full twodimensional models can be used for obtaining design insights. The degree of detail required in the gas phase chemistry models and surface chemistry models depends both on the system and the properties to be predicted. Definition of different regimes of operation and limits of applicability for parameric scaling relationships are key to the design of catalytic combustors for incineration or power generation. In addition, a theoretically-based rational strategy for applying catalytic boundary conditions in turbulent flow models would provide a valuable design tool. Examples of alternative modeling strategies are given below along with possible applications for the design of practical catalytic combustion systems.