生物多孔介质热风干燥数学模型及数值模拟

为了研究生物多孔介质在热风干燥过程中的热质传递机理以及其内部应力应变分布规律,根据生物多孔介质中温度、水分及应力之间复杂的耦合关系,基于菲克扩散定律、傅立叶导热定律和热弹性力学理论,建立了对流干燥条件下,含湿多孔介质内部传热传质过程热-湿-力双向耦合的数学模型。采用有限差分法编制相应的计算程序,对其进行数值计算,数值结果与马铃薯和胡萝卜对流干燥试验结果之间的相对误差均小于5%;进一步分析了干燥特性曲线,以及温度、干基含水率和应力应变的时空分布;最后分析了风温、风速等干燥条件以及多孔介质厚度对干燥过程的影响,结果表明:在一定试验条件下,风温越高,风速越大,切片厚度越薄,干燥时间越短。研究为改善生物多孔介质热质传递现象物理机理的理解提供参考。

Mathematical model and numerical simulation of biological porous medium during hot air drying

Abstract: Drying is a very important unit operation in many industries such as food, pharmaceuticals, chemicals and ceramics. In most cases, wet materials are dried by forced convection using a hot air flow. Heat and mass transfer processes during drying have been studied by both experimental and numerical simulation methods. For the purpose of studying the mechanism of heat and mass transfer and stress-strain distribution during the hot air drying of biological porous medium, 2-way coupled thermo-hydro-mechanical mathematical model has been developed to simulate the hot air convective drying process of biological porous media on basis of Fickian diffusion theory, Fourier's law of heat conduction and thermoelasticity mechanics. The following assumptions were made in order to find a solution to the hot air drying model: the biological porous medium is homogeneous and isotropic; the deformation during drying is elastic. The transient model, composed of a system of partial differential equations, was solved by finite difference methods. The computational procedure was programmed using C language. Some physical and mechanical properties of carrot changing with dry basis moisture content and temperature were considered. The numerical results were compared with available experimental data obtained during the drying of potatoes and carrots. The relative errors between numerical results and experimental data were both less than 5%, which shows the numerical results obtained using the mathematical model were in good agreement with the experimental data. Numerical simulations of the drying curve variations and the spatio-temporal distributions of moisture, temperature and drying stresses and strains of carrot were also evaluated. The temperature and moisture content show a gradient inside carrot slice during drying. As the drying process proceeded, the temperature inside the carrot slice initially increased to reach the wet bulb temperature of the environment and eventually leveled off. The dry basis moisture content inside the carrot slice decreased, with the fastest decrease at the heat and mass transfer interface, eventually reaching the equilibrium moisture content of the potato and leveling off. Both the moisture content gradient and the temperature gradient decreased gradually in the thickness direction. The normal stress was negative in all parts of the carrot slice, and the larger the closer to the evaporation interface. The shear stress was positive in all parts of the carrot slice, and the maximum shear stress occurred in the middle of the carrot slice. As in the case of the normal stress, the values of the normal strain are negative. The change trend of normal strain with time is consistent with that of moisture content. These results indicate that the observed physical deformations are caused by the dehydration of carrot slice during drying. The influence of drying conditions, such as air temperature, air velocity and the thickness of porous media on drying process was analyzed. Analysis showed that under certain drying conditions, the higher air temperature, the greater air velocity and the thinner slice thickness, the shorter drying time. This work should help in developing an understanding of the relationship between mass and heat transfer, shrinkage, stress, strains and physical degradation.