The use of implicit flux limiting schemes in the simulation of the drying process: A new maximum flow sensor applied to phase mobilities

In this work, a previously proposed two-dimensional wood drying computational model is modified so that an analysis of the use of flux limiters for reducing numerical dispersion in the drying kinetics can be undertaken. In particular, a new sensor based on the ratio of phase fluxes is used to flux limit the liquid and gas phase mobility tensors. An extremely important physical phenomenon that arises during high temperature drying, and one that is exacerbated by the use of the flux limiter, relates to the medium becoming fully saturated. To overcome the numerical convergence problems associated with this phenomenon, the concept of a fixed compressible phase is introduced within the model and the averaged air density is used as one of the primary solution variables. A comparison of the simulation results for high temperature drying will be presented for three different case studies. In case one, a completely isotropic sample is considered while in case two, a slight anisotropy (1:2) is introduced for the modelling of a radial–transverse wood cross-section. In case three, for a wood sample modelled in the radial–longitudinal cross-section, a strongly anisotropic medium (1:1000) is analysed. It is found in all cases that when the new sensor is used during flux limiting, superior results to upstream weighting are obtained. In fact, it is possible with this method to attain the accuracy offered by upstream weighting on a much finer mesh at a considerable reduction of at least a factor of 5 in the overall computation time.     

Modeling and parameter identification of a maltodextrin DE 12 drying process in a convection oven

The drying kinetics of maltodextrin DE 12 in a convection oven are modeled using Fick's second law of diffusion and following the William, Landel and Ferry (WLF) equation for the moisture and temperature dependence of the effective diffusivity. An experimental design with a temperature range from 70°C to 140°C and sample amount varying from 4 to 12 ml is used. The resulting diffusion equation describing the dynamics of moisture content is highly nonlinear and possesses Dirichlet and Neumann boundary conditions. Ordinary differential equations are added to take the time-dependent variation of temperature into account. The method of lines is applied to discretize the partial differential equation w.r.t. the space variable leading to a highly stiff and numerically unstable system of ordinary differential equations. The data fitting problem is formulated to estimate some unknown model parameters simultaneously for 18 data sets under consideration.     

Water uptake and mechanical characteristics of wood fiber-polypropylene composites

The influence of mixing process (in a two-roll mill, high-speed mixer, or twin-screw extruder) on the strength properties of polypropylene/wood fiber composites was studied. The best results were obtained for composites compounded in a twin-screw extruder. The water uptake and the influence of moisture on the flexural strength (σ_fl) and modulus (E_fl) were studied by immersion of the composites in water at 20, 50, and 90°C. Most strongly the moisture affected the value of E_fl, but the degree of water uptake and the change in σ_fl and E_fl also depended on temperature and the presence of a modificator—maleated polypropylene (MAH). MAH improved the strength properties of the composites both in dry and wet states and also decreased the extent of water uptake and swelling in cyclic (soaking/drying) tests. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 101–114, January–February, 2006.     

The thermistor: A problem in heat and current flow

The thermistor is an electrical device that can be used as a current surge protector. The basis of its operation is the temperature-dependent electrical conductivity that drops by 4 to 5 orders of magnitude over a temperature range of 100–200°C. In the present work the coupled heat and electrical current problems are examined with the conductivity modeled by a step function. A numerical scheme is suggested for the nonlinear coupled problem. Convergence of this scheme for some boundary conditions is demonstrated and some numerical results are given.     

Evaluation of thermal comfort conditions in a classroom equipped with radiant cooling systems and subjected to uniform convective environment

The aim of this work is to evaluate numerically the human thermal response that 24 students and 1 teacher feel in a classroom equipped with radiant cooling systems and subjected to uniform convective environments, in lightly warm conditions. The evolution of thermal comfort conditions, using the PMV index, is made by the multi-nodal human thermal comfort model.In this numerical model, that works in transient or steady-state conditions and simulates simultaneously a group of persons, the three-dimensional body is divided in 24 cylindrical and 1 spherical elements. Each element is divided in four parts (core, muscle, fat and skin), sub-divided in several layers, and protected by several clothing layers. This numerical model is divided in six parts: human body thermal system, clothing thermal system, integral equations resolution system, thermoregulatory system, heat exchange between the body and the environment and thermal comfort evaluation.Seven different radiant systems are combined to three convective environments. In the radiant systems (1) no radiant system without warmed curtain, (2) no radiant system with warmed curtain, (3) radiant floors cooling system with warmed curtain, (4) radiant panels cooling system with warmed curtain, (5) radiant ceiling cooling system with warmed curtain, (6) radiant floor and panels cooling system with warmed curtain and (7) radiant ceiling and panels cooling system with warmed curtain are analysed, while in the convective environments (1) without air velocity field and with uniform air velocity field of (2) 0.2 m/s and (3) 0.6 m/s are also analysed. The internal air temperature and internal surfaces temperature are 28 °C, the radiant cooling surfaces temperature are 19 °C and the warmed internal curtains surfaces temperatures, subjected to direct solar radiation, are 40 °C.The numerical model calculates the Mean Radiant Temperature field, the human bodies’ temperatures field and the thermal comfort level, for the 25 occupants, for the 21 analysed situations.Without uniform air velocity field, when only one individual radiant cooling system is used, the Predicted Percentage of Dissatisfied people is lowest when the radiant floor cooling system is applied and is highest when the radiant panel cooling system is applied. When are combined the radiant ceiling or the floor cooling systems with the radiant panel cooling system the Predicted Percentage of Dissatisfied people decreases.When the uniform air velocity increases the thermal comfort level, that the occupants are subjected, increases. When the radiant floor cooling system or the combination of radiant floor and panel cooling systems without uniform air velocity field is applied, the Category C is verified for some occupants. However, with a convective uniform air velocity field of 0.2 m/s the Category B is verified and with a convective uniform air velocity field of 0.6 m/s the Category A is verify for some occupants. In the last situation the Category C is verified, in general, for all occupants.     

Comparison between experimental data and theoretical calculations of free convection in water near its density maximum

Experimental data on free convection of water in the region of maximum density are interpreted by a theoretical model. The agreement between our theory and experimental data is excellent.Typical arrests in the temperature versus time curves and loops in warming-cooling cycles indicate large effects on convection generated by small changes in the space-time density profiles. These observations are fully explained by an extended theoretical approach which takes into account complex phenomena occurring in the boundary layer region. The comparison between theory and experiments indicates how the convective motion propagates from the boundary layer to the internal region of the fluid (central nucleus). Thanks to the extreme sensitivity of the temperature behaviour to relatively small density variations, a complete information about density profile around 4°C can be obtained by a quite simple experimental apparatus. Experimental data at temperature ranges between 0°C and 8°C can “feel” the asymmetry in the density curve around 4°C which is of about 8 parts per million. Our results can bring some light on the experiments performed by Azouni about the water hysteresis loop around 4°C.     

Simulation of microstructural damage evolution during very high cycle fatigue (VHCF) using the boundary element method

A simulation model for damage evolution in slip bands under VHCF condition is presented. By use of a numerical method it is applied to a real simulated microstructure of AISI304. It considers orientations of slip systems as well as individual anisotropic elastic properties in each grain. The numerical method is the two-dimensional boundary element method which is based on two integral equations and implies fundamental solutions for anisotropic elastic solids. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

非匹配网格上Stokes-Darcy 问题非协调元离散的两水平和多水平方法

本文讨论了非匹配网格上Stokes-Darcy 问题的两种低阶非协调元方法, 给出了误差估计, 对耦合的非协调元离散问题, 通过粗网格求得的界面条件, 我们提出了一个解耦的两水平算法. 并且我们将两水平方法推广到多水平情形, 其只需在一个很粗的网格上解一耦合问题, 然后在逐步加细的网格上求解解耦的问题, 理论分析和数值试验都说明方法的高效性.     

Numerical simulation of immersion quenching process of an engine cylinder head

In this article, we present the numerical simulations of a real cylinder head quench cooling process employing a newly developed boiling phase change model using the commercial CFD code AVL-FIRE v8.5. Separate computational domains constructed for the solid and liquid regions are numerically coupled at the interface of the solid–liquid boundaries using the AVL-Code-Coupling-Interface (ACCI) feature. The boiling phase change process triggered by the dipping hot metal and the ensuing two-phase flow is handled using an Eulerian two-fluid method. Multitude of flow features such as vapor pocket generation, bubble clustering and their disposition, are captured very effectively during the computation, in addition to the variation of the temperature pattern within the solid region. A comparison of the registered temperature readings at different monitoring locations with the numerical results generates an overall very good agreement and indicates the presence of intense non-uniformity in the temperature distribution within the solid. Overall, the predictive capability of the new boiling model is well demonstrated for real-time quenching applications.     

Modelling of airflow through a stack in a timber-drying kiln

A two-dimensional pore-scale model is used to predict air flow through a wood drying stack for which both the interstitial and the average flow can be considered as two-dimensional.     

Two-dimensional heat and mass transfer during drying of deformable media

Drying is an essential step in many production and treatment processes. The control of the dry product quality is more and more required in order to ensure effective use or handling of the material. The aim of this study is to develop a two-dimensional drying model which takes into account heat and mass transfer and the accompanying deformation of the dried material. The model tries to be relatively simple but sufficiently complete in order to predict and analyze the spatio-temporal distribution of the temperature, the moisture and the solid displacement during the process. The product was considered as a two-phases, homogeneous, hygroscopic, isotropic and highly shrinkable medium. The model was solved numerically by a finite difference method. The simulation allowed the obtention of the time and space evolutions of several parameters such as product temperature, moisture content and solid displacement.     

A convection model for fire spread simulation

We present a convection model which can be coupled with fire propagation models in order to take into account the wind and the slope which are two of the most relevant factors affecting surface fire spread. An asymptotic analysis gives a three-dimensional convective model governed by a two-dimensional equation.     

Numerical Solution of the Kiessl Model

The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE's. Some existence and regularity results for these problems are proved and an efficient numerical approach based on a certain special linearization scheme and the Petrov-Galerkin method is suggested.     

Numerical analysis of a strongly coupled system of two singularly perturbed convection–diffusion problems

A system of two coupled singularly perturbed convection–diffusion ordinary differential equations is examined. The diffusion term in each equation is multiplied by a small parameter, and the equations are coupled through their convective terms. The problem does not satisfy a conventional maximum principle. Its solution is decomposed into regular and layer components. Bounds on the derivatives of these components are established that show explicitly their dependence on the small parameter. A numerical method consisting of simple upwinding and an appropriate piecewise-uniform Shishkin mesh is shown to generate numerical approximations that are essentially first order convergent, uniformly in the small parameter, to the true solution in the discrete maximum norm.      

Coupled heat and moisture transport in paper with application to a warm print surface

In this work we present a mathematical model describing the coupled heat and moisture transport in paper. The model is solved numerically and the numerical solution is used to study the interdependency of the moisture and temperature distribution in paper. The results show that variation with temperature of the saturated water vapor concentration and the sorption isotherm parameters are both important for inducing moisture desorption. It is also found that for steep relative humidity ramps moisture sorption generates temperature increments that slow down the sorption process itself. The model is also used to study the moisture gradients in a paper sheet inside a printer from Océ Technologies, which contains a warm print surface. The results predict changes in moisture content of only 0.2%, which suggests that no deformations are induced on the printed sheet.     

A two-dimensional time-dependent model for surface shear and buoyancy-driven flows in domains with large aspect ratio

A two-dimensional numerical model has been developed for studying flows in enclosures having a large length-to-depth ratio. The model solves the two-dimensional Navier-Stokes and energy equations subject to hydrostatic, Boussinesq, and rigid-lid assumptions. Turbulent momentum and heat diffusion are incorporated using variable eddy coefficients. The flow is driven by surface wind shear and heat transfer. Two cases were run for a rectangular domain, subject to a suddenly imposed surface shear stress while the surface and bottom were maintained at two different but constant temperatures. The difference between the cases was the formulation used for predicting the eddy viscosities and diffusivities. The variations of velocities and temperatures with time were studied. Both velocities and temperatures were found to undergo a sudden rapid change, after an initial period of slow change, before attaining steady stage. This has been explained in light of the differences in the convective and diffusive time scales and the nature of coupling between the governing equations.     

Boundary element method based algorithm for simulation of fluid flow in 3D

A boundary element method based numerical scheme that solves the velocity-vorticity formulation of Navier-Stokes equation is presented. The developed method is validated and used to simulate laminar viscous flow coupled with heat transfer in 3D. Benchmark test cases were use to determine the validity of the method. Flow around a hotstrip is presented as a test case. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)