Coupled fields in a deformable unsaturated medium

This paper considers several problems involving coupled heat–moisture–air flow indeformable unsaturated media. A set of coupled non-linear governing equations expressed in terms of displacements, capillary pressure, air pressure and temperature are used in the analysis. The mathematical model accounts for fully coupled heat and moisture flow, volume strain effects on water-air-heat flow, stress and temperature dependence of the water retention curve, heat sink due to thermal expansion, phase change between liquid water and vapour water, and compressibility of liquid water. Numerical solutions are obtained by using the finite element method. Comparisons with existing analytical and experimental results for problems involving infiltration, drying–rewetting (hysteresis effects) and heating confirm the general validity of the present mathematical model. Coupled fields in a confined clay cylinder are also examined. It is found that consideration of absorbed liquid flow due to thermal gradients (thermo-osmosis effect) results in increased drying and shrinkage near the heated boundary. The case of a confined clay cylinder under combined heating and infiltration is also studied. Important features of coupled fields are discussed.     

A Water Retention Curve Model for the Simulation of Coupled Thermo-Hydro-Mechanical Processes in Geological Porous Media

This paper presents a new water retention curve (WRC) model for the simulation of coupled thermo-hydro-mechanical processes in geological porous media. The model simultaneously considers the impact of porosity and temperature on suction, for both wetting processes and drying processes. The model is based on an idealization of porous geological media as having an isotropic and homogeneous microscopic pore structure. Suction is expressed as a function of degree of saturation, porosity, surface tension of the water–air interface, and the length of air bubble perimeter of the pores per unit area on a random 2D cross-section of the medium. The tension of water–air interface is written as a function of temperature, and the length of perimeter of the water–air interface of the pores becomes a function of porosity and degree of saturation. The final equation of the new WRC is a function of suction, effective degree of saturation, temperature, porosity, pore-gas pressure, and the rate of degree of saturation change with time for both wetting and drying processes. The model was used to fit experimental data of the FEBEX bentonite, with good agreements between measured and calculated results.     

Multiphase transfer model for intermittent microwave-convective drying of food: Considering shrinkage and pore evolution

Intermittent microwave convective (IMCD) drying is an advanced drying technology that improves both energy efficiency and food quality during drying. Although many experimental studies on IMCD have been conducted, there is no complete multiphase porous media model describing the physics of the process available in the literature. A multiphase porous media model considering liquid water, gases and the solid matrix of food during drying can provide in-depth understanding of IMCD process. Currently there is no IMCD model that have taken shrinkage and pore evolution during drying into consideration. In this study, first a multiphase porous media model with shrinkage (IMCD2) has been developed for IMCD. Then the model has been compared with IMCD model without shrinkage (IMCD1). Simulated temperature, moisture content, density, porosity from IMCD2 are then validated against experimental data. The profile of vapour pressures and evaporation during IMCD are also presented and discussed.     

Drop trajectory predictions and their importance in the design of spray dryers

A knowledge of the trajectories of atomized droplets in both the nozzle zone (where the droplets are rapidly decelerating from their initial high velocity) and in the free-entrainment zone (where the droplets are conveyed by the drying gas) is required for the design of spray dryers, since it governs the evaporative capacity and thermal efficiency of the chamber, while affecting the moisture content and general quality of the product through the control of the drying time.

The trajectories of droplets in three-dimensional motion were determined theoretically in both zones. In the case of two-fluid pneumatic atomizers, the characteristics of the jet of atomizing fluid were found to be important in both the zones.

Predictions of droplet trajectories were tested in an experimental circular cocurrent spray-drying chamber with a conical bottom, in which the drying air was introduced tangentially near the top. Water was used as the feed material. A study was made of the effects of liquid feed rate and temperature, drying air flowrate and temperature, and of nozzle position on the thermal efficiency and evaporative capacity of the chamber. The results were interpreted in the light of the droplet trajectories predicted.     

A diffusion based model for intermittent drying of rough rice

In this study, intermittent drying behavior of single layer rough rice with a moisture content of between 22 and 24% on the dry basis was simulated by means of a liquid diffusion model based on a prolate spheroid geometry. For this purpose, solution of the liquid diffusion equation was fitted to the experimental data for the drying air temperature 40°C, drying velocity 1.5 ms⁻¹ and tempering periods ranging from 0 to 1 h. In order to make a comparison, solution of the liquid diffusion equation for a finite cylindrical geometry was also fitted to the experimental data. The results show that the liquid diffusion model based on a prolate spheroid geometry explains the drying behavior of rough rice more accurately. The results also show that greater variations occur in diffusion coefficient with increasing tempering time for prolate spheroid geometry which is more realistic geometry for a rough rice grain.

---

Relative permeability relations: A key factor for a drying model

In the modelling of heat, mass and momentum transfer phenomena which occur in a capillary porous medium during drying, the liquid and gas flows are usually described by the generalised Darcy laws. Nevertheless, the question of how to determine experimentally the relative permeability relations remains unanswered for most materials that consist of water and humid air, and as a result, arbitrary functions are used in the drying codes. In this paper, the emphasis is on deducing from both numerical and experimental studies a method for estimating pertinent relations for these key parameters. In the first part, the sensitivity of liquid velocity and, consequently, of drying kinetics in the variation of the relative permeabilities is investigated numerically by testing various forms. It is concluded that in order to predict a realistic liquid velocity behaviour, relative permeabilities can be linked to a measurable quantity: the capillary pressure. An estimation technique, based on simulations coupled with experimental measurements of capillary pressure, together with moisture content kinetics obtained for low or middle temperature convective drying, is deduced. In the second part, the proposed methodology is applied to pine wood. It is shown that the obtained relations provide closer representation of physical reality than those commonly used.     

Effects of Anisotropy and Drying Air Parameters on Drying of Deformable Porous Media Hydro-Dynamically and Thermally Anisotropic

The purpose of this work was to investigate numerically the drying of saturated deformable porous media. The considered sample is a rectangular porous plate which assumed to be both hydro-dynamically and thermally anisotropic, while the mechanical behavior of the sample is supposed to be isotropic. All walls of the plate are subjected to a convective heat flux. Moreover, the top and bottom walls are allowed the mass transfer. The Darcy–Brinkman extended model was used as the momentum balance equation for the liquid and solid phases. The energy balance equation is based on the local thermodynamic equilibrium assumption between the both phases. The lattice Boltzmann method is used to solve the governing differential equation system. A comprehensive analysis of the effect of anisotropy and the drying air parameters on macroscopic fields is investigated throughout this work.     

Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Desorption isotherms and mathematical modeling of thin layer drying kinetics of tomato

In recent years, there is an increased demand on the international market of dried fruits and vegetables with significant added value. Due to its important production, consumption and nutrient intake, drying of tomato has become a subject of extended and varied research works. The present work is focused on the drying behavior of thin-layer tomato and its mathematical modeling in order to optimize the drying processes. The moisture desorption isotherms of raw tomato were determined at four temperature levels namely 45, 50, 60 and 65 °C using the static gravimetric method. The experimental data obtained were modeled by five equations and the (GAB) model was found to be the best-describing these isotherms. The drying kinetics were experimentally investigated at 45, 55 and 65 °C and performed at air velocities of 0.5 and 2 m/s. In order to investigate the effect of the exchange surface on drying time, samples were dried into two different shapes: tomato halves and tomato quarters. The impact of various drying parameters was also studied (temperature, air velocity and air humidity). The drying curves showed only the preheating period and the falling drying rate period. In this study, attention was paid to the modeling of experimental thin-layer drying kinetics. The experimental results were fitted with four different models.     

Non-linear Heat and Mass Transfer During Convective Drying of Kaolin Cylinder Under Non-steady Conditions

The self-consistent model of heat and mass transfer during convective drying of capillary porous media describing both the first and the second periods of drying is presented in Musielak (Wydawnictwo Politechniki Poznańskiej, seria Rozprawy, nr 386 (2004a); Chem. Process Eng. 25, 393–409 (2004b)). The results of simulations of processes in steady conditions are shown (Musielak Wydawnictwo Politechniki Poznańskiej, seria Rozprawy, nr 386 (2004a); Chem. Process Eng. 25, 393–409 (2004b)). The main aim of the present work is to compare experimental results with those from numerical simulations. Three convective drying processes have been performed experimentally. The first and the second periods of drying are considered, during which the humidity of air in the dryer changes due to evaporation. The first process is used to establish drying parameters, whereafter the two remaining processes are simulated. Good agreement between experimental and simulation results is found, both qualitative and quantitative.     

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.     

高气液比垂直管流连续携液实验

在可视化管流实验架上, 采用压缩空气和雾化液体作为实验介质, 模拟连续携液过程并测试 实验参数; 采用高速摄像仪捕捉到气流中液滴实际形状------椭球体. 实验发现: 圆球体模型、 椭球体模型计算结果与实验值分别偏差10{\%}, 58.3{\%}. 分析椭球体受力状态并结合实验数据导出了新的椭球体数学模型, 按照新模型计算的结 果与7口产水气井生产情况一致.     

Numerical and experimental investigation of convective drying in unsaturated porous media with bound water

The heat and mass transfer in an unsaturated wet cylindrical porous bed packed with quartz particles was investigated theoretically for relatively low convective drying rates. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous media using the energy and mass conservation equations to describe the heat and mass transfer during the drying. The drying model included convection and capillary transport of the free water, diffusion of bound water, and convection and diffusion of the gas. The numerical results indicated that the drying process could be divided into three periods, the temperature rise period, the constant drying rate period and the decreasing drying rate period. The numerical results agreed well with the experimental data verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. The effects of drying conditions such as the ambient temperature, the relative humidity, and the velocity of the drying air, on the drying process were evaluated by numerical solution.     

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.     

Investigation on the generation process of impact-driven high-speed liquid jets using a CFD technique

High-speed liquid jets have been applied to many fields of engineering, science and medicine. It is therefore of benefit to all these areas to investigate their characteristics by modern and inexpensive methods using a computational fluid dynamics (CFD) technique. Previously, high-speed liquid jets have been studied experimentally using a momentum exchange method, called the “impact driven method (IDM)”, by which the impact of a high-velocity projectile on the liquid package contained in the nozzle cavity produced the jet. The shock pulse reflections in the cavity caused by the impact then drove a multiple pulsed jet from the nozzle exit. In this study, a two-fluid simulation consisting of liquid and air can be successfully calculated by using a two-phase flow mixture model and a moving mesh for the projectile motion. The CFD results show good agreement to the results of previous experimental studies, both quantitatively and qualitatively. For the first time, the wave propagation within the liquid in the nozzle has been captured and analyzed, thereby demonstrating the dynamic characteristics of multiple pulsed high-speed liquid jets initiated by the IDM. This provides a breakthrough in the simulation of the supersonic injection of a liquid into air by using a well-known and user-friendly CFD software. It is useful fundamental knowledge for future studies of high-speed injection with applications in all its related fields.     

Diffusion properties of aqueous slurries in evaporative spray drying of copper (II) chloride dihydrate

This study examines the evaporative heat transfer and diffusive mass transfer of a droplet of CuCl₂ solution. The validation of a new predictive model involves comparisons with experimental data from previous studies of different fluids based on non-dimensional analysis. The study provides new insight about the effects of different concentrations of water on the CuCl₂ slurry drying at low to moderate air temperatures. Predictive correlations of heat and mass transfer are developed for the aqueous solution, subject to various drying conditions. The analysis is performed for moist air in contact with a sprayed aqueous solution of copper (II) chloride dihydrate [CuCl₂·(2H₂O)]. Results are presented and discussed for the drying processes.     

Experimental study of convective heat transfer under arrays of impinging air jets from slots and circular holes

 Impinging air jets are widely used in industry, for heating, cooling, drying, etc, because of the high heat transfer rates which is developed in the impingement region. To provide data for designers of industrial equipment, a large multi-nozzle rig was used to measure average heat transfer coefficients under arrays of both slot nozzles and circular holes. The aim of the present paper is to develop the relationship between heat transfer coefficient, air mass flow and fan power which is required for the optimum design of nozzle systems. The optimum free area was obtained directly from experimental results. The theory of optimum free area was analysed and good agreement was found between theoretical and experimental results. It was also possible to optimise the variables, to achieve minimum capital and running costs. Received on 21 November 2000 / Published online: 29 November 2001     

A rigorous analysis of simultaneous heat and mass transfer in the pasta drying process

This study presents a two dimensional analysis of coupled heat and mass transfer during the process of pasta drying. Velocity and temperature distributions of air flowing around the pasta are predicted in steady state condition. Using these profiles and the similarity between heat and mass boundary layers, local convective heat and mass transfer coefficients were determined on different points of pasta surface. By employing these values, the solution of coupled heat and mass transfer equations within the pasta object in unsteady state condition was obtained. Furthermore the effects of operating conditions such as velocity, temperature and relative humidity of air flow on drying rate of pasta were studied. Sensitivity analysis results show that the effects of air temperature and relative humidity on the rate of drying are more important than the effect of air velocity. Finally, the results obtained from this analysis were compared with the experimental data reported in the literatures and a good agreement was observed while, no adjustable parameter is used in the presented model.     

Convective and radiant drying of a polymer aqueous solution

The aim of this work is to minimize the drying time of a polymer aqueous solution placed into a Petri dish while respecting strict constraints. Several experiments performed in a laboratory setup have shown the interest of a drying combining convective and infrared radiation as long as irradiation is correctly controlled. In this way, a one dimensional liquid diffusion model taking into account the product shrinkage was developed. Model predictions are in good adequacy to mass and temperature experimental data.