**2. Design and formulation of mixing tank problems**

#### **2.1. Design parameters and process optimization**

In fluid engineering problems, research has shown that it is possible to optimize all influencing process parameters in an evolutionary manner right from the conceptual design to the final performance testing phase. This will entail the integration of the fluid flow investigation with the process reactor conceptual design and system optimization [1]. Nowadays, this multistage process design and optimization work flow shown in **Figure 1** can be fully automated through the use of computational platform. In formulating and developing a numerical solution strategy to a particular physical problem involving fluid-particle interactions, a sound theoretical

**Figure 1.** Reactor design and process optimization parameters in mixing tank applications.

understanding and analysis of the problem is often required. This will assist in the selection of appropriate experimental data collection methods and mathematical models that sufficiently encapsulate the physics of the problem. A number of numerical approaches and solution strategies discussed in the subsequent sections have been developed for a multitude of fluid flow scenarios. Therefore, it is important to evaluate each circumstance individually and form an opinion regarding which model would provide the best fit for a particular fluid engineering problem. It has been suggested that the robustness of any mathematical model is a function of the numerical code being used and the flow scenario being modeled [7].

#### **2.2. Fluid dynamics and governing equations**

**Figure 1.** Reactor design and process optimization parameters in mixing tank applications.

industrial scale. Regardless of the focus of these studies, it is quite apparent that valuable information can be obtained from the basic study of fluid flow dynamics in process units especially

A quick survey of the studies in this field shows that many innovative process reactors have been successfully tested on different scales for a wide variety of technical applications ranging from fine particle separation and water purification to cell culture preparation [1–6]. Experimental data, which are collected in these studies for numerical validation purposes, are often used to characterize the hydrodynamic behaviour as well as to quantify the fluid parameters of interest such as the flow velocity profile, vorticity, turbulent kinetic energy and its rate of dissipation, turbulent intensity, and so on. While there is a large body of scientific literature focusing on the hydrodynamics and physicochemical processes in stirred tank reactors, the aim of the present communication is to briefly summarize developments in this field especially in the application of the knowledge of the fluid dynamics to fluid-particle reactor

In fluid engineering problems, research has shown that it is possible to optimize all influencing process parameters in an evolutionary manner right from the conceptual design to the final performance testing phase. This will entail the integration of the fluid flow investigation with the process reactor conceptual design and system optimization [1]. Nowadays, this multistage process design and optimization work flow shown in **Figure 1** can be fully automated through the use of computational platform. In formulating and developing a numerical solution strategy to a particular physical problem involving fluid-particle interactions, a sound theoretical

from design and optimization perspective.

58 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

design, development and optimization.

**2.1. Design parameters and process optimization**

**2. Design and formulation of mixing tank problems**

The interactions of different phases in fluid flow occur on different scales of the fluid motion as depicted in **Figure 2**. Fluid dynamics is primarily focused on the macroscopic phenomena of the fluid flow in which the fluid is treated as a continuum. For instance, a fluid element is composed of many molecules, and the fluid dynamics represent the behaviour of the numerous molecules within the system. This concept with certain assumptions forms the basis of the derivation of fluid conservation equations of mass and momentum also known as the Navier-Stokes equation using a fluid control volume [8, 9]. The general form of the governing equations of mass and momentum conservation in any fluid flow system can be written as follows (Eqs. (1) and (2)):

$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{\mathbf{v}}) = \mathbf{S}\_m \tag{1}$$

$$\frac{\partial}{\partial t}(\rho \vec{\mathbf{v}}) + \nabla \cdot (\rho \vec{\mathbf{v}} \vec{\mathbf{v}}) = -\nabla \mathbf{p} + \nabla \cdot (\overline{\nabla}) + \rho \vec{\mathbf{g}} + \vec{\mathbf{F}} \tag{2}$$

**Figure 2.** Multiscale modeling approach to fluid-particle interactions (reproduced from [14] with permissions © 2017 Springer).

where ρ is the density, p is the static pressure, v <sup>→</sup> is the velocity component, Sm is the source term that represent the mass added to the continuous phase from the disperse phase or any user define source, τ̿ represents the stress tensor due to viscous stress, ρg <sup>→</sup> is the gravitational force and F → represent the exerted body forces [10–13].

have been developed for resolving turbulence parameters in steady-state Reynolds Averaged Navier-Stokes (RANS) equations. The two equation eddy viscosity models such as k-ε and k-ω have been found to perform reasonably well in the modeling of rotating flows in process reactors with the only drawback being the assumption of local isotropic turbulence. The underlying theoretical assumptions underpinning the use of these models can be found in the following reference texts [12, 13]. Since the reactors encountered in most of the practical physicochemical processes contain moving or rotating parts, it is therefore necessary to take this into consideration in the preparation of the computational grid. The most common strategy for steady-state calculations include the single reference frame (SRF), multiple reference frame (MRF) or frozen rotor approach, mixing plane model (MPM) and snapshot approach, while the sliding or dynamic mesh is frequently used in transient calculations of fluid flow. For detailed information on the practical applications of the above-mentioned methods, readers

Hydrodynamic Characterization of Physicochemical Process in Stirred Tanks and Agglomeration Reactors

http://dx.doi.org/ 10.5772/intechopen.77014

61

Modeling complex physicochemical processes involving fluid flow sometimes necessitates the integration of the existing mathematical models in order to appropriately describe the physics of the problem. This can be achieved through the use of specially developed or customized in-house numerical codes or a modification of the existing ones with several software package vendors offering a platform for software improvement through the use of Application Programming Interface API or Application Customization Toolkit ACT. Such flexibility allows engineers and researchers to extend the capability and versatility of the existing numerical codes. Many software vendors go a step further in this respect by actively encouraging the development of scalable apps that extend the capability of their core software; an excellent example is the mixing tank template released by ANSYS Inc. for the automation of mixing tank simulation process. However, there exist several other flexible options for numerical code development using the open source platform, and the readers are advised

Several analytical and instrumental techniques have been developed for the study of complex hydrodynamic-mediated processes found in particle-laden flow—flocculation, wet agglomeration, sedimentation, floatation, fluidization and crystallization that often occur in a wide range of process conditions. These techniques shown in **Figure 4** are used either in the quantification of the hydrodynamics of the carrier and dispersed phase, or in the determination of the spatial and temporal evolution of the discrete phase properties such as the change in the particle size and distribution. In the case of the hydrodynamic interactions of the carrier and dispersed phase, a number of laser-based fluid flow techniques such as particle image velocimetry (PIV), particle tracking velocimetry (PTV), laser Doppler anaemometry (LDA), laser Doppler velocimetry (LDV), and more recently, radioactive tracking techniques such as positron emission particle tracking (PEPT) and computer-aided radioactive particle tracking (CARPT) have gained wider acceptance in the scientific community and in industry due to

are referred to the following reference texts [20, 21].

to consider available options for their specific problem.

**3. Experimental analysis of physicochemical processes**

*2.3.2. Model coupling for multiphase flow problems*

#### **2.3. Modeling approach and solution strategies**

In modeling complex single and multiphase flows in mixing tanks and process reactors, there exist two common numerical solution strategies, namely Eulerian-Eulerian and Eulerian-Lagrangian modeling approach, depending on the scale of the fluid flow as shown schematically in **Figure 3**. In the former, the fluid domain is treated as an interpenetrating continuum, while in the latter, the discrete or distinct particles of the dispersed phase are tracked in the Lagrangian reference frame. In addition to the flow field, information on the particle population such as the mean size, mass or volume fraction, and number density can be obtained using either of the two approaches [10]. Several variants of these two classes exist such as the Eulerian granular model based on the kinetic theory of granular flow (KTGF), disperse phase model (DPM), discrete element model (DEM) and the macroscopic particle model (MPM). In the case of Eulerian-Eulerian approach, the species distribution of the discrete phase may be accounted for using the population balance model (PBM), while the Eulerian-Lagrangian models can directly compute the particle size distribution while taking into account different collision and interaction mechanisms using DEM [15–18].

#### *2.3.1. Treatment of flow domain and turbulent flow conditions*

Turbulence modeling forms an integral part of the numerical analysis of complex fluid flows since most engineering fluid flows entail certain form of instability. Several closure models

**Figure 3.** Parametric relationships between different modeling strategies (reproduced from [19] with permissions © 2015 Annual Reviews).

have been developed for resolving turbulence parameters in steady-state Reynolds Averaged Navier-Stokes (RANS) equations. The two equation eddy viscosity models such as k-ε and k-ω have been found to perform reasonably well in the modeling of rotating flows in process reactors with the only drawback being the assumption of local isotropic turbulence. The underlying theoretical assumptions underpinning the use of these models can be found in the following reference texts [12, 13]. Since the reactors encountered in most of the practical physicochemical processes contain moving or rotating parts, it is therefore necessary to take this into consideration in the preparation of the computational grid. The most common strategy for steady-state calculations include the single reference frame (SRF), multiple reference frame (MRF) or frozen rotor approach, mixing plane model (MPM) and snapshot approach, while the sliding or dynamic mesh is frequently used in transient calculations of fluid flow. For detailed information on the practical applications of the above-mentioned methods, readers are referred to the following reference texts [20, 21].

#### *2.3.2. Model coupling for multiphase flow problems*

where ρ is the density, p is the static pressure, v

60 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

**2.3. Modeling approach and solution strategies**

collision and interaction mechanisms using DEM [15–18].

*2.3.1. Treatment of flow domain and turbulent flow conditions*

represent the exerted body forces [10–13].

user define source, τ̿

→

force and F

Annual Reviews).

term that represent the mass added to the continuous phase from the disperse phase or any

represents the stress tensor due to viscous stress, ρg

In modeling complex single and multiphase flows in mixing tanks and process reactors, there exist two common numerical solution strategies, namely Eulerian-Eulerian and Eulerian-Lagrangian modeling approach, depending on the scale of the fluid flow as shown schematically in **Figure 3**. In the former, the fluid domain is treated as an interpenetrating continuum, while in the latter, the discrete or distinct particles of the dispersed phase are tracked in the Lagrangian reference frame. In addition to the flow field, information on the particle population such as the mean size, mass or volume fraction, and number density can be obtained using either of the two approaches [10]. Several variants of these two classes exist such as the Eulerian granular model based on the kinetic theory of granular flow (KTGF), disperse phase model (DPM), discrete element model (DEM) and the macroscopic particle model (MPM). In the case of Eulerian-Eulerian approach, the species distribution of the discrete phase may be accounted for using the population balance model (PBM), while the Eulerian-Lagrangian models can directly compute the particle size distribution while taking into account different

Turbulence modeling forms an integral part of the numerical analysis of complex fluid flows since most engineering fluid flows entail certain form of instability. Several closure models

**Figure 3.** Parametric relationships between different modeling strategies (reproduced from [19] with permissions © 2015

<sup>→</sup> is the velocity component, Sm is the source

<sup>→</sup> is the gravitational

Modeling complex physicochemical processes involving fluid flow sometimes necessitates the integration of the existing mathematical models in order to appropriately describe the physics of the problem. This can be achieved through the use of specially developed or customized in-house numerical codes or a modification of the existing ones with several software package vendors offering a platform for software improvement through the use of Application Programming Interface API or Application Customization Toolkit ACT. Such flexibility allows engineers and researchers to extend the capability and versatility of the existing numerical codes. Many software vendors go a step further in this respect by actively encouraging the development of scalable apps that extend the capability of their core software; an excellent example is the mixing tank template released by ANSYS Inc. for the automation of mixing tank simulation process. However, there exist several other flexible options for numerical code development using the open source platform, and the readers are advised to consider available options for their specific problem.
