INTEGRAL EQUATION APPEOACH FOZ SIHULATION-OF - HEAT AND MASS TRANSFER PROCESSES

An integral equation approach was recommended for modelling and simulation of heat and mass transfer processes. It was shown that several mixing models that have been dealt with up to now dlfferently, can be unified in a single integral equation. An effective numerical method was developed for the solution of non-linear integral equation. A construction method for the source and kernel functions were lntroduced in connection with the simulation and control of heat treatlng processes taking place in tunnel kiln and heat and mass transfer processes in tunnel dryer.

We have concluded that our method is advantageous If the slmulated process 1s slgnlficantly affected by the degree of mixing and/or the kernel function can be determined by direct measurement of the streaming phases including feedback, recirculation etc.     

EXPERIMENTAL INVESTIGATION OF FLOW PATTERN IN A SPRAY DRYER

1nvest.igation of flow pattern in a cocurrent disk spray dryer by means of measurement, of the kernel function is described. The obtained measurement results not only inform on the air flow type but ran be directly applied as input in the integral equation based simulation of heat and mass transfer.     

EXPERIMENTAL INVESTIGATION OF FLOW PATTERN IN A SPRAY DRYER

1nvest.igation of flow pattern in a cocurrent disk spray dryer by means of measurement, of the kernel function is described. The obtained measurement results not only inform on the air flow type but ran be directly applied as input in the integral equation based simulation of heat and mass transfer.     

A DISTRIBUTED PARAMETER APPROACH TO THE DYNAMICS OF ROTARY DRYING PROCESSES

A nonequilibrium distributed parameter model for rotary drying and cooling processes described by a set of partial differitial equations with nonlinear algebraic constraints is developed in this work. These equations arise from the multi-phase heat and mass balances on a typical rotary dryer. A computational algorithm is devekped by employing a polynonial approximation ( orthogonal collocation) with a glotal splinc technique leading to a differential-algebraic equation ( DAE) system. The numerical solution is carried out by using a standard DAE solver.

The two- phase-flow heat transfer coelficient is computed by introducing a correction factor to the commonly accepted correlations. Since interaction between the falling particles are considered in the correction factor,the results are more reliable than those computed by assuming that heat transfer between a single falling particle and the drying air is unaffected by other particles. The heat transfer computations can be further justified via a study on the analogies between heat and mass transfer.

The general model devloped in this work is mathematically more ritorous yet more flexible that the lumped parameter models established by one of the authors (Douglas et al., (1993)). The three major assumptions of an equilibrium operation, perfect mixing and constant drying raic, are removed in the distributed parameter model.

The simulation results are compared with the operational data from an industrial sugar dryer and predictions from earlier models. The model and algorithm successfully predict the steady state behaviour of rotary dryers and collers. The generalized model can be applied to fertilizer drying processes in which the assumption of constant drying rate is no longer valid and the existing dynamic models are not applicable.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

Nonlinear coupled heat and mass exchange in a cross-flow regenerator

Simultaneous heat and mass exchange in a cross-flow regenerator has been formulated using Schumann's model. A generalized equilibrium relationship at the gas—solid interface led to a non-linear coupling between the heat and mass transfer processes. The Green's matrix, obtained for the problem of heat transfer alone, has been used to set up integral equations to represent this problem of nonlinear coupled heat and mass exchange. A numerical scheme has been developed for solving the resulting system of multidimensional, nonlinear, Volterra-type integral equations using a modified block-by-block method.It is shown that cross-cooled dehumidifiers can be both smaller and require less power than corresponding adiabatic exchangers.     

Flow phenomena and local heat and mass transfer in corrugated passages

Flow phenomena, local heat and mass transfer and pressure drop of corrugated passages in process equipment are examined. Based on a method for measuring local heat and mass transfer, developed in previous investigations, a procedure has been formulated for the determination of local heat and mass transfer in corrugated passages. Using the analogy between heat and mass transfer, this technique allows the determination of heat transfer distributions in any structures with high local resolution. The corresponding pressure drop is presented together with the local and integral heat and mass transfer of different structures. It is shown that differences in heat and mass transfer as well as in pressure drop are due to different flow phenomena which also characterize mixing behaviour.     

A DISTRIBUTED PARAMETER APPROACH TO THE DYNAMICS OF ROTARY DRYING PROCESSES

ABSTRACT

A nonequilibrium distributed parameter model for rotary drying and cooling processes described by a set of partial differitial equations with nonlinear algebraic constraints is developed in this work. These equations arise from the multi–phase heat and mass balances on a typical rotary dryer. A computational algorithm is devekped by employing a polynonial approximation ( orthogonal collocation) with a glotal splinc technique leading to a differential–algebraic equation ( DAE) system. The numerical solution is carried out by using a standard DAE solver.

The two– phase–flow heat transfer coelficient is computed by introducing a correction factor to the commonly accepted correlations. Since interaction between the falling particles are considered in the correction factor,the results are more reliable than those computed by assuming that heat transfer between a single falling particle and the drying air is unaffected by other particles. The heat transfer computations can be further justified via a study on the analogies between heat and mass transfer.

The general model devloped in this work is mathematically more ritorous yet more flexible that the lumped parameter models established by one of the authors (Douglas et al., (1993)). The three major assumptions of an equilibrium operation, perfect mixing and constant drying raic, are removed in the distributed parameter model.

The simulation results are compared with the operational data from an industrial sugar dryer and predictions from earlier models. The model and algorithm successfully predict the steady state behaviour of rotary dryers and collers. The generalized model can be applied to fertilizer drying processes in which the assumption of constant drying rate is no longer valid and the existing dynamic models are not applicable.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

ABSTRACT

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

Analysis of the integro-differential equation of constant-rate particle transfer

Some conclusions from the integro-differential equation of constant-rate particle transfer were considered. In a sense, this equation is a microscopic kinetic equation for the phenomenological macroscopic equations of heat transfer, diffusion, and other transfer processes. It was shown that, in the limiting case, the above integro-differential equation can be reduced to these macroscopic equations. Formulas were derived for calculating the thermal conductivity and the diffusion coefficient as tensor quantities. With the use of the concepts of Galerkin’s method, the hyperbolic differential equations of heat and mass transfer were obtained.     

风洞真空排气系统直接接触传热过程

某风洞真空排气系统在运行过程中,会产生大量含水蒸气的混合气体。为了提高排气效率降低能耗,本文引入冷凝塔工艺,采用直接接触换热冷凝方式使来流含水蒸气的混合气体降温冷凝。基于微元塔高传质模型,对进入冷凝塔的热流气体与冷却水直接接触换热过程分析,推导出传质系数数学方程表达式。结合实验数据考察了进气压力与冷凝降温排出气体中水蒸气含量的影响,并拟合得到一定温度下进气压力与该气体水蒸气含量的数学表达式;也考察了冷却水质量通量和气液比变化对传质系数、体积传热系数、出气温度的影响,在此基础上拟合得到针对风洞气流直接接触换热气液比与体积传热系数数学关系式,并计算出最优气液比。实验得出的规律对风洞气流的直接接触换热优化设计和应用起到了指导作用。     

变系数各向异性热传导问题边界元解法

提出了一种用边界元法求解一般变系数各向异性热传导问题时建立基本解的方法,并导出了求解一般二维和三维各向异性稳态热传导问题的纯边界积分方程。所建立的基本解考虑了热导率是空间坐标的函数,因此所导出的积分方程可用于求解非均质材料传热问题。由热源项引起的域积分,运用径向积分法将其转换成边界积分,形成不需要内部点的纯边界元算法。给出了二维和三维问题3个分析算例,并通过将边界元法结果与有限元法结果进行对比,证明了方法的正确性和有效性。     

A numerical method for simulation of heat and mass transfer processes

The transport equation of heat and mass transfer processes are given in integral equation form. To solve this Hammerstein type integral equation system a new, numerically stable algorithm has been elaborated. We discuss the structure of this algorithm and compare it to other numerical methods. The application is illustrated on an example of adiabatic adsorption.     

建筑外表面对流传质系数的测量方法

建筑外表面对流传质系数是围护结构热湿耦合计算和建筑能耗模拟中的重要参数。为直接准确得到该参数,提出了建筑物壁面对流传质系数的测量方法,该方法通过测量萘试件的质量通量和表面温度,即可计算得到壁面传质系数。为验证该方法的准确性及可靠性,在风洞内设置6组不同风速工况,分别采用了萘升华法与传统热平衡法进行对比。结果表明：随风速的增加,萘试件表面温度随之降低,而对流传质系数逐渐增加。两种方法测试结果接近,二者所得对流传质系数相差在10%以内,不同风速条件下平均偏差小于5%,认为该测量方法可行。该研究可为室外真实条件下建筑外表面对流传质系数提供测试方法指导,对热湿耦合计算和墙体蒸发换热的研究也具有重要意义。     

Thermal Blending Time Associated With a Charge of Hot Particles Added to a Fluidized Bed of Uniform Temperature

The process of heat transfer between particles in a fluidized bed is important for many industrial fluidized bed processes. The problem associated with studying this phenomenon is the confounding effect of particle mixing on heat transfer. The work described here was undertaken to describe the process in which heat is added to a fluid bed process by adding a hot charge of particles to a colder fluidized bed. The rate of heat transfer in this instance can have a significant impact on performance of the fluid bed process, depending upon its application. Both the method of analysis and the results of the work are applicable to other fluidized bed processes, particularly those associated with the thermal upgrading of heavy oil. The method of data analysis, based on binomial statistics, allowed useful data to be extracted from a complex system without the need for a large number of experiments. The analysis also allowed for some assessment of the relative importance of mixing and heat transfer, which has not been possible with other approaches. The results of the experiments were further explored using a bubbling bed model that incorporated both heat transfer and solids mixing. This allowed for the formation of a conceptual model, validated by the experimentation, that explains the relative functions of the two transfer processes in the dispersion of heat from a hot charge of particles to the bulk of a fluidized bed.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

Application of mathematical modelling in a two-component layer crystallisation process

An algorithm for the computation of design variables in layer crystallisation processes is presented, based on an algebraic solution of the moving boundary equation for heat transfer, as well as on an expression for the concentration profile. The algorithm was applied to the discontinuous crystallisation of a NaCl-H₂O solution around the wall of an internally cooled cylindrical tube. Good agreement between simulation results and laboratory experiments was observed. After input of experimentally measurable values of the distribution coefficient, the algorithm enables the prediction of the following process variables along the crystallisation time: layer thickness, temperature, and composition profiles across the layer, as well as the end-values of solid and liquid mass and concentrations. Multistage processes can be studied by the series association of crystallisation cycles, enabling the determination of the optimal number of stages that meets a specific design criterion.     

HEAT EFFECTS FOR PHYSICAL AND CHEMICAL ABSORPTION IN TURBULENT LIQUID FILMS

An eddy diffusivity model was used to describe simultaneous heat and mass transfer for chemical absorption in turbulent liquid films. For absorption accompanied by a first-order reaction an approximate expression for the mass transfer coefficient is derived and shown to be in excellent agreement with exact numerical calculations. An equation is developed for the temperature rise at the free surface due to both the heat of reaction and the heat of solution. Relationships are also developed for the concentration of the liquid phase product at the free surface and the depletion of the liquid phase reactant at the free surface.

The temperature rise at the free surface for gas absorption accompanied by an instantaneous reaction due to both the heat of solution and the heat of reaction was determined. An equation is also derived for the concentration of liquid phase product at the free surface for the case of an instantaneous reaction.