Stress Generated During Drying of Saturated Porous Media

The article is a contribution for the modelling of heat and mass transfers coupled to strain–stress equations during drying of deformable two-phase media. Both unidirectional and bidirectional configurations are examined. In order to compare the results, one assumes the material of a convectively dried clay slab in two configurations. Numerical calculations of the temperature, drying curves variations and the spatio-temporal distributions of moisture, temperature and drying induced stresses are evaluated. A significant difference was observed between the results obtained for both configurations particularly in intensity of the shear stress that caused cracking.     

2-D hydro-viscoelastic model for convective drying of deformable and unsaturated porous material

The aim of this work was to simulate in two dimensions the spatio-temporal evolution of the moisture content, the temperature, the solid (dry matter) concentration, the dry product total porosity, the gas porosity, and the mechanical stress within a deformable and unsaturated product during convective drying. The material under study was an elongated cellulose–clay composite sample with a square section placed in hot air flow. Currently, this innovative composite is used in the processing of boxes devoted to the preservation of heritage and precious objects against fire damage and other degradation (moisture, insects, etc.). A comprehensive and rigorous hydrothermal model had been merged with a dynamic linear viscoelasticity model based on Bishop's effective stress theory, assuming that the stress tensor is the sum of solid, liquid, and gas stresses. The material viscoelastic properties were measured by means of stress relaxation tests for different water contents. The viscoelastic behaviour was described by a generalized Maxwell model whose parameters were correlated to the water content. The equations of our model were solved by means of the ‘COMSOL Multiphysics’ software. The hydrothermal part of the model was validated by comparison with experimental drying curves obtained in a laboratory hot-air dryer. The simulations of the spatio-temporal distributions of mechanical stress were performed and interpreted in terms of material potential damage. The sample shape was also predicted all over the drying process.     

Stresses in dried wood. Modelling and experimental identification

The paper presents a simple mathematical model of drying that permits evaluation of moisture content distribution in dried wood during the constant and falling drying rate periods and, in particular, estimation of stresses generated from the moment when the moisture content at the body surface reaches the fibre saturation point (FSP). The acoustic emission method (AE) is used for monitoring the state of stress in dried wood. The numerically evaluated drying induced stresses are compared with the number of acoustic signals and their energy monitored on line during drying tests. It can be stated that the enhanced emission of acoustic signals occurs at those moments when the drying induced stresses approach their maximum. Both the numerical calculus and the experimental tests were conducted on a pine-wood sample in the form of a disk.     

Drying Induced Stresses in a Swelling Porous Wall

The present paper is concerned with the stresses generated in a capillary-porous wall saturated from the bottom and dried naturally on its side planes. The upper cross-section of the wall is totally isolated and no heat and moisture transfer occurs through it, while the bottom one has an a priori determined temperature and moisture content. The vertical planes of the wall are surrounded by air having different temperatures and moisture contents on the left and the right sides. The problem is solved numerically based on a mechanistic model of drying earlier developed by the authors. The distributions of temperature, moisture content, and the drying induced stresses are determined. The variation of temperature on the wall left and right surfaces is analysed dependent on the surroundings temperature. The influence of boundary conditions on the stress distribution in the wall is discussed.     

An anisotropic fibre-network model for mechano-sorptive creep in paper

In this paper a simplified network model for mechano-sorptive creep is presented, which is a further development of an earlier paper [Strömbro, J., Gudmundson, P., 2008. Mechano-sorptive creep under compressive loading – a micromechanical model. International Journal of Solids and Structures 45 (9), 2420–2450.]. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive effects in compression than in tension. Moisture dependent material parameters and anisotropy in the fibre distribution have been introduced. Theoretical predictions based on the model are compared to experimental results for an anisotropic paper both under tensile and compressive loading at varying moisture content and it is found that the important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined.     

A Numerical Approach for Non-Linear Moisture Flow in Porous Materials with Account to Sorption Hysteresis

A numerical approach for moisture transport in porous materials like concrete is presented. The model considers mass balance equations for the vapour phase and the water phase in the material together with constitutive equations for the mass flows and for the exchange of mass between the two phases. History-dependent sorption behaviour is introduced by considering scanning curves between the bounding desorption and absorption curves. The method, therefore, makes it possible to calculate equilibrium water contents for arbitrary relative humidity variations at every material point considered. The scanning curves for different wetting and drying conditions are constructed by using third degree polynomial expressions. The three coefficients describing the scanning curves is determined for each wetting and drying case by assuming a relation between the slope of boundary sorption curve and the scanning curve at the point where the moisture response enters the scanning domain. Furthermore, assuming that the slope of the scanning curve is the same as the boundary curve at the junction point, that is, at the point where the scanning curve hits the boundary curve once leaving the scanning domain, a complete cyclic behaviour can be considered. A finite element approach is described, which is capable of solving the non-linear coupled equation system. The numerical calculation is based on a Taylor expansion of the residual of the stated problem together with the establishment of a Newton–Raphson equilibrium iteration scheme within the time steps. Examples are presented illustrating the performance and potential of the model. Two different types of measurements on moisture content profiles in concrete are used to verify the relevance of the novel proposed model for moisture transport and sorption. It is shown that a good match between experimental results and model predictions can be obtained by fitting the included material constants and parameters.     

The vapour–liquid interface and stresses in dried bodies

The paper presents a contribution to modelling the problem of vapour–liquid interface receding into dried body and stresses induced by drying of capillary-porous bodies. A complex algorithm comprising the specific mechanisms of drying in the first and second periods of drying is constructed. It enables calculation and drawing of the body temperature and drying curves for the whole drying process and identification of the vapour–liquid interface receding into the body. The drying induced stresses caused by the receding vapour–liquid interface and the non-uniform distribution of moisture content and/or temperature are analyzed. Numerical calculations of the temperature and drying curves and the drying induced stresses are carried out for the example of a finite dimensional kaolin cylinder dried convectively.     

Combined resistance bubbling bed model for drying of solids in fluidized beds

Fluidized bed drying kinetics of highly porous material which offers free flow of moisture to surface of the material is modeled utilizing the simplified bubbling bed model. The simplification step utilizes estimation of the overall transfer resistance, by summing all the resistances from the bubble phase to the emulsion phase. The model predictions are compared with the published experimental data covering the operating variables such as the inlet air temperature, the air flow rate, material characteristics and are found to match satisfactorily. The model highlights the importance of bubble size estimation, as it largely dictates the drying kinetics.     

Microwave drying of various shape particles suspended in an air stream

Fluidization is an efficient way to dry granular materials. Incorporating microwave heating into the fluidization makes the overall drying process shorter, and the quality of the final products can be improved. However, in order to understand the mechanisms of water removal, an exact knowledge of changes inside the dried material is necessary. The temperature and moisture distribution pattern within the heated material should be identified and analyzed. Unfortunately, the microwave environment makes the measurements very difficult. This paper gives new information on the temperature distribution inside small particles of various shapes dried with microwaves. The tests were carried out in a laboratory-scale, fluid-bed dryer equipped with a microwave source. Five different shapes were examined: sphere, cylinder, half-cylinder, rectangular prism, and prism with triangle base. All particles tested were suspended in an air stream and heated with microwaves. The internal temperature distribution has been analyzed in each case. The rate of drying is also presented and discussed for every case tested.     

Moisture transfer analysis during drying of slab woods

This article presents an analytical technique for determining the moisture diffusivities and moisture transfer coefficients for slab shaped woods subjects to drying process. The analysis of transient moisture diffusion is carried out on the basis of two important practical criteria: 0.1<Bi<100 and Bi>100. The drying coefficients and lag factors are defined for wood-drying applications and incorporated into the models. In order to verify the present models, the model results are compared with experimental measurements taken from the literature and good agreement was found. Results show that the technique presented here is capable of determining the moisture diffusivities and moisture transfer coefficients for slab woods in a simple and accurate manner for practical applications and will be beneficial to the relevant wood␣drying industries. This approach can be extended to␣different wood products of regular and irregular shapes. Received on 23 January 1998     

Amorphous particle deposition and product quality under different conditions in a spray dryer

Deposition of amorphous particles, as a prevalent problem particularly in the spray drying of fruit and vegetable juices, is due to low-molecular weight sugars and is strongly dependent on the condition of the particles upon collision with the dryer wall. This paper investigates the condition of the amorphous particles impacting the wall at different drying conditions with the aim of elucidating the deposition mechanism and physical phenomena in the drying chamber. A model sucrose-maltodextrin solution was used to represent the low-molecular-weight sugar. Particle deposits were collected on sampling plates placed inside the dryer for analyses of moisture content, particle rigidity (using SEM) and size distribution. Moisture content was adopted as a general indicator of stickiness. Product particles collected at the bottom of the experimental dryer were found to have higher moisture than particle deposits on samplers inside the dryer. Moisture content profile in the dryer shows that apart from the atomizer region, where particles are relatively wet, particle deposits at other regions exhibit similar lower moisture content. At the highest temperature adopted in the experiments, particles became rubbery suggesting liquid-bridge formation as the dominant deposition mechanism. Further analysis on particles size distribution reveals a particle segregation mechanism whereby smaller particles follow preferentially to the central air stream while larger particles tend to re-circulate in the chamber, as predicted in past CFD simulation. The findings from this work will form the basis and provide validating data for further modeling of wall deposition of amorphous particles in spray drying using CFD.     

Mechano-sorptive creep under compressive loading – A micromechanical model

The creep of paper is accelerated by moisture cycling, an effect known as mechano-sorptive creep. It has also been observed that the mechano-sorptive effects are larger in compression than in tension. In this paper a simplified network model for mechano-sorptive creep is presented. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre–fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys constitutive laws that are non-linear in stress. Geometrical fibre effects are included in the model in order to capture experimental observations of the differences between paper loaded in tension and compression. Theoretical predictions based on the developed model are compared to experimental results for paper both under tensile and compressive loading at varying moisture content. The important features in the experiments are captured by the model, i.e. the creep is accelerated by the moisture cycling and the mechano-sorptive effects are larger in compression than in tension.     

Drying stress formation by inhomogeneous moisture and temperature distribution

The field of moisture concentration and the field of temperature are the two factors that induce stresses in dried materials. The main aim of this paper is to estimate the influence of these two factors on the formation of drying-induced stresses. The considerations are based on the model elaborated by the authors and the analysis of the drying-induced stresses is carried out on a convectively dried prismatic bar.     

Linear constitutive model for mechano-sorptive creep in paper

The creep of paper is accelerated by moisture cycling. This effect is known as mechano-sorptive creep. It is assumed that this is an effect of transient stresses produced during moisture content changes in combination with non-linear creep behaviour of the fibres. The stresses produced by the moisture content changes are often much larger than the applied mechanical loads. If this is the case, the mechanical loads are only a perturbation to the internal stress state, and it will appear as if the mechano-sorptive creep is linear in stress. It is possible to take advantage of this feature. In the present report the pure moisture problem is first solved. The mechanical load is then treated as a perturbation of the solution to the moisture problem. Using this strategy, it is possible to linearize a non-linear network model for mechano-sorptive creep and to formulate a continuum model. As a result, the number of variables in the model is reduced. This is a significant improvement as it will be possible to use the linearized model to describe the material in a finite element program and solve problems with complicated geometries.     

混凝土核安全壳干缩应力的计算

提出内约束干缩应力和外约束干缩应力的概念,利用混凝土的蠕变理论,建立了考虑施工过程的有限元计算模型,编制了电算程序,计算了秦山核安全壳在施工过程中的干缩应力。     

Modeling of vacuum desorption of multicomponent moisture in freeze drying

A mathematical model of multicomponent vacuum desorption, which occurs in the vacuum freeze drying process has been developed. Drying with conductive heating and constant contact surface temperature was considered. Pressure drop in the layer of the material to be dried was taken into account in the model formulation and process simulation. Equilibrium moisture content for pure water, toluene, and m-xylene and their two- and three-component mixtures on zeolite DAY 20F were described by means of the multitemperature extended Langmuir isotherm equation. Model equations were solved by the numerical method of lines. Moisture content and temperature distributions within the drying material were predicted from the model as a function of drying time.     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

Analysis of the Mechanism of Counter-current Spray Drying

Results of experimental investigations of the effect of drying and atomization parameters on counter-current spray drying are discussed. Based on 96 experimental tests, the local and global distributions of velocity, temperature, drying air humidity and moisture content of material dried in the drying tower were determined. Analysis of the results showed that the process of agglomeration during counter-current spray drying depended mainly on air temperature in the atomization zone.     

Thermal stress investigation in unidirectional composites under the hyperbolic energy model

The hyperbolic energy model is applied in this paper for determining transient temperature variation across a unidirectional composite plate subjected to different temperature changes at the boundaries. Thermal stresses developed are then analyzed for different material properties. Governing equations are solved numerically using implicit methods. The results are presented over a wide range of variables commonly found in most composite materials. The transient thermal stresses generated inside the plate were found to fluctuate between compressive and tensile quantities, a result that was not predicted using the classical heat model. Consequently, this will lead to an earlier crack initiation and failure of the material.