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## Über dieses Buch

This book presents a new computational methodology called Computational Mass Transfer (CMT). It offers an approach to rigorously simulating the mass, heat and momentum transfer under turbulent flow conditions with the help of two newly published models, namely the C’2—εC’ model and the Reynolds mass flux model, especially with regard to predictions of concentration, temperature and velocity distributions in chemical and related processes. The book will also allow readers to understand the interfacial phenomena accompanying the mass transfer process and methods for modeling the interfacial effect, such as the influences of Marangoni convection and Rayleigh convection. The CMT methodology is demonstrated by means of its applications to typical separation and chemical reaction processes and equipment, including distillation, absorption, adsorption and chemical reactors.

Professor Kuo-Tsong Yu is a Member of the Chinese Academy of Sciences. Dr. Xigang Yuan is a Professor at the School of Chemical Engineering and Technology, Tianjin University, China.

## Inhaltsverzeichnis

### Chapter 1. Related Field (I): Fundamentals of Computational Fluid Dynamics

Abstract
Computational fluid dynamics (CFD) is the basic methodology used extensively in engineering works and also accompanied with the computational mass transfer (CMT) method as presented in this book. In this chapter, the Reynolds averaging method in CFD for turbulent flow is summarized as a preparatory material on computational methodology in this book. Emphasis is made on developing approaches to the closure of the time-averaged Navier–Stokes equations by modeling the second-order covariant term in the equations. Two modeling methods are described in detail: the k-ε method, which is a widely adopted two-equation model for engineering applications, and the Reynolds stress modeling method, in which the covariant term is modeled and computed directly. The k-ε method is easy to apply but its weakness is that an isotropic eddy viscosity must be adopted and may result in discrepancy when applying to the case of anisotropic flow. The Reynolds stress method needs more computational work, but it is anisotropic and rigorous. For reducing the computing load, an Algebraic Reynolds stress model is also introduced.
Kuo-Tsong Yu, Xigang Yuan

### Chapter 2. Related Field (II): Fundamentals of Computational Heat Transfer

Abstract
Computational heat transfer (CHT) should be included in the computational mass transfer (CMT) model system if thermal effect is involved in the simulated process. In this chapter, as a preparatory material parallel to Chap.​ 1, the CHT method for turbulent flow is summarized. This chapter focuses on the closure of the time-averaged energy equation. The unknown term to be solved is the covariant composed of the velocity and temperature fluctuations. Two modeling methods for this term are introduced, namely: the two-equation $$\overline{{T^{\prime 2} }} - \varepsilon_{{{\text{T}^{\prime}}}}$$ method and the Reynolds heat flux method. The former is easy to apply but must introduce the isotropic eddy heat diffusivity; and thus, it is not suitable for the case of anisotropic flow. The Reynolds heat flux method needs more computational work, but it is anisotropic and rigorous.
Kuo-Tsong Yu, Xigang Yuan

### Chapter 3. Basic Models of Computational Mass Transfer

Abstract
The computational mass transfer (CMT) aims to find the concentration profile in process equipment, which is the most important basis for evaluating the process efficiency as well as the effectiveness of an existing mass transfer equipment. This chapter is dedicated to the description of the fundamentals and the recently published models of CMT for obtaining simultaneously the concentration, velocity and temperature distributions. The challenge is the closure of the differential species conservation equation for the mass transfer in a turbulent flow. Two models are presented. The first is a two-equation model termed as $$\overline{{c^{{{\prime }2}} }} - \varepsilon_{{{\text{c}}^{{\prime }} }}$$ model, which is based on the Boussinesq postulate by introducing an isotropic turbulent mass transfer diffusivity. The other is the Reynolds mass flux model, in which the variable covariant term in the equation is modeled and computed directly, and so it is anisotropic and rigorous. Both methods are validated by comparing with experimental data.
Kuo-Tsong Yu, Xigang Yuan

### Chapter 4. Application of Computational Mass Transfer (I): Distillation Process

Abstract
In this chapter, the application of computational mass transfer (CMT) method in the forms of two-equation model and Rayleigh mass flux model as developed in previous chapters to the simulation of distillation process is described for tray column and packed column. The simulation of tray column includes the individual tray efficiency and the outlet composition of each tray of an industrial-scale column. Methods for estimating various source terms in the model equations are presented and discussed for the implementation of the CMT method. The simulated results are presented and compared with published experimental data. The superiority of using standard Reynolds mass flux model is shown in the detailed prediction of circulating flow contours in the segmental area of the tray. In addition, the capability of using CMT method to predict the tray efficiency with different tray structures for assessment is illustrated. The prediction of tray efficiency for multicomponent system and the bizarre phenomena is also described. For the packed column, both CMT models are used for the simulation of an industrial-scale column with success in predicting the axial concentrations and HETP. The influence of fluctuating mass flux is discussed.
Kuo-Tsong Yu, Xigang Yuan

### Chapter 5. Application of Computational Mass Transfer (II): Chemical Absorption Process

Abstract
In this chapter, the two CMT models, i.e., $$\overline{{c^{{{\prime }2}} }} - \varepsilon_{{c^{\prime } }}$$ model and Reynolds mass flux model (in standard, hybrid, and algebraic forms) are used for simulating the chemical absorption of CO2 in packed column by using MEA, AMP, and NaOH separately and their simulated results are closely checked with the experimental data. It is noted that the radial distribution of D t is similar to α t but quite different from μ t. It means that the conventional assumption on the analogy between the momentum transfer and the mass transfer in turbulent fluids is unjustified, and thus, the use of CMT method for simulation is necessary. In the analysis of the simulation results, some transport phenomena are interpreted in terms of the co-action or counteraction of the turbulent mass flux diffusion.
Kuo-Tsong Yu, Xigang Yuan

### Chapter 6. Application of Computational Mass Transfer (III): Adsorption Process

Abstract
In this chapter, adsorption process is simulated by using computational mass transfer (CMT) models as presented in Chap.​ 3. As the adsorption process is unsteady and accompanied with heat effect, the time parameter and the energy equation as presented in Chap.​ 2 are involved in the model equations. The simulated concentration profile of the column at different times enables to show the progress of adsorption along the column as an indication of the process dynamics. The simulated breakthrough curve and regeneration curve for adsorption and desorption by the two CMT models, i.e., the $$\overline{{c^{{{\prime}2}}}} - \varepsilon_{{{\text{c}}^{{\prime}} }}$$ model and the Reynolds mass flux model, are well checked with the experimental data. Some issues that may cause discrepancies are discussed.
Kuo-Tsong Yu, Xigang Yuan

### Chapter 7. Application of Computational Mass Transfer (IV): Fixed-Bed Catalytic Reaction

Abstract
In this chapter, an exothermic catalytic reaction process is simulated by using computational mass transfer (CMT) models as presented in Chap.​ 3. The difference between the simulation in this chapter from those in Chaps.​ 4, 5, and 6 is that chemical reaction is involved. The source term S n in the species conservation equation represents not only the mass transferred from one phase to the other, but also the mass created or depleted by a chemical reaction. Thus, the application of the CMT model is extended to simulating the chemical reactor. The simulation is carried out on a wall-cooled catalytic reactor for the synthesis of vinyl acetate from acetic acid and acetylene by using both $$\overline{{c^{\prime 2} }} - \varepsilon_{{{\text{c}}^{\prime } }}$$ model and Reynolds mass flux model. The simulated axial concentration and temperature distributions are in agreement with the experimental measurement. As the distribution of $$\mu_{\text{t}}$$ shows dissimilarity with D t and $$\alpha_{\text{t}}$$, the Sc t or Pr t are thus varying throughout the reactor. The anisotropic axial and radial turbulent mass transfer diffusivities are predicted where the wavy shape of axial diffusivity D t,x along the radial direction indicates the important influence of catalysis porosity distribution on the performance of a reactor.
Kuo-Tsong Yu, Xigang Yuan

### Chapter 8. Simulation of Interfacial Effect on Mass Transfer

Abstract
The mass transferred from one phase to the adjacent phase must diffuse through the interface and subsequently may produce interfacial effect. In this chapter, two kinds of important interfacial effects are discussed: Marangoni effect and Rayleigh effect. The theoretical background and method of computation are described including origin of interfacial convection, mathematical expression, observation, theoretical analysis (interface instability, on-set condition), experimental and theoretical study on enhancement factor of mass transfer. The details of interfacial effects are simulated by using CMT differential equations.
Kuo-Tsong Yu, Xigang Yuan

### Chapter 9. Simulation of Interfacial Behaviors by Lattice Boltzmann Method

Abstract
In this chapter, the mesoscale computational methodology, Lattice Boltzmann Method (LBM), is introduced for the simulation of the interfacial Marangoni and Rayleigh effects as described and discussed in Chap.​ 8. The fundamentals of LBM are briefly introduced and discussed. By the simulation using the LBM, some mechanisms and phenomena of the interfacial effect are studied, including the patterns of the interfacial disturbance for inducing the interfacial convections, conditions of initiating interfacial instability and interfacial convection as well as the effect on interfacial mass transfer.
Kuo-Tsong Yu, Xigang Yuan
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