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ArticleSeptember 14, 2023

Optimization of a Multiphase Mixed Flow Field in Backfill Slurry Preparation Based on Multiphase Flow Interaction
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Rugao Gao
Rugao Gao
School of Resource & Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
School of Resources and Safety Engineering, Central South University, Changsha 410083, China
Department of Mining and Materials Engineering, McGill University, 3450 Rue University, Montreal, QC H3A 2A7, Canada
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Weijun Wang
Weijun Wang
School of Resource & Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
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Keping Zhou
Keping Zhou
School of Resources and Safety Engineering, Central South University, Changsha 410083, China
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Yanlin Zhao
Yanlin Zhao
School of Resource & Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
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Chun Yang
Chun Yang
School of Resources and Safety Engineering, Central South University, Changsha 410083, China
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Qifan Ren*
Qifan Ren
CERIS, Department of Civil Engineering, Architecture and Georesources, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
*Email: [email protected]
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https://orcid.org/0000-0002-9814-834X

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ACS Omega

Cite this: ACS Omega 2023, 8, 38, 34698–34709

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https://doi.org/10.1021/acsomega.3c03660

Published September 14, 2023

CC-BY-NC-ND 4.0 .

Abstract

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The paper analyzes the dynamic behavior during the preparation of cemented backfill slurry by combining the structural performance analysis of the double-shaft mixer and the Euler multiphase flow field computational fluid dynamics model. Considering the interaction between phases and gas phase disturbances, the transient kinetic parameters and the interaction between gas and liquid phases were introduced. According to the modified lift model, the user-defined function of the net lateral lift coefficient and the turbulence energy equation was adjusted. Taking the parameters of flow field velocity, gas phase mixing, uniformity, and turbulent energy dissipation as the evaluation indexes of the mixing effect, the double-shaft mixer at a rotation velocity of 45 rpm and with a blade installation angle of 25° is the optimal design in this study. Experimental tests were carried out and confirmed that the refined two-fluid model of interphase interaction can provide a basis for the performance evaluation of material mixing equipment.

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Subjects

1. Introduction

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To serve the production and construction of mines, backfill mining plays an increasingly important role. By turning the solid waste materials into high-concentrated paste tailing backfill materials, they can be recycled so as to effectively assist the ground pressure management of mining enterprises. (1−5) The double-shaft mixer is widely applied in mixing tailing backfill slurry and is developing rapidly. At present, in the mining industry, the application of mixing equipment is mostly based on empirical parameter methods, and there are few theoretical studies. In fact, the entire operation of the backfill mining system is overlapped with multiphase flow discipline. As the core process, the slurry mixing process is actually the process of multiphase flow formation and multifield motion. (6−8) Currently, as to the backfill fluid theory, most of the research studies still stay in the ideal fluid stage such as Newton flow and Bingham flow, which are less combined with the essential characteristics of multiphase flow. However, no matter what the purpose is, slurry performance, fluidization characteristics, interphase interaction, and the law of multifield mechanics are all important factors in the research of backfill fluid mechanics, which are directly related to the safety and economic effect of the backfill process and are also the core problems restricting the resource development technology. (9,10) The introduction of a multiphase flow analysis method will constantly advance the discipline and industrial innovation in terms of concept, theory, and method. (11)

As one of the research methods of fluid mechanics, computational fluid dynamics (CFD) takes a computer numerical method as the analysis method and adopts certain computing techniques to seek discrete numerical solutions to various complex problems in fluid mechanics. (12−14) In the 1980s, researchers first applied fluid dynamics to the mixing process in agitated flow fields. In terms of scientific research and industrial applications, as early as the early 20th century, Drew and Lahey had proposed the idea of using a numerical method to solve fluid mechanics problems. (15) In the 1970s, they proceeded from the basic conservation principle and derived the basic equations of two-phase flow through strict mathematical deduction, but they were not widely acknowledged. The general method at the current stage is as follows: (1) Two-fluid model (TFM). In the cases where the two phases are equivalent, the mathematical and physical equations of the single phases are established, taking into account physical factors such as the resistance, relative displacement, momentum, and heat exchange (transfer) between the phases. (2) Homogeneous model. As to the two-phase mixing uniform flow, it can be generalized into a homogeneous (continuous medium) model and a diffusion model and analyzed by the classic hydraulics method. (3) Statistical group model. As for the two-phase flow of particles (bubbles, droplets, and solid particles are collectively referred to as particles), a random analysis is used to establish a statistical group (particle group) model. Regarding the combination of multiphase flow and CFD, the researchers derived the continuity, energy, and motion equations of solid–liquid two-phase flow according to the field view. Dam and Schuck (16) calculated the concentration and velocity distribution of the slurry in the horizontal pipeline via a numerical algorithm. Fang et al. (17) applied the Euler–Lagrange mathematical model to calculate the effect of solid particles on flow velocity and pressure. Kang and Guo (18) summarized the N-S equation of the slurry under laminar flow through numerical calculations and found the law of changes in volume fraction and solid particle settling velocity.

In the stirring equipment, the rotation of the blades generates kinetic energy in the watershed so that the fluid can flow in the stirring watershed, thereby achieving the exchange of substances and energy. This type of calculation mainly involves inviscid flow and viscous flow. (19,20) The former includes low-velocity flow, transonic flow, and supersonic flow, while the latter includes turbulent flow, boundary layer flow, etc. Computational fluid dynamics (CFD) has become an effective tool for learning about complex phenomena in fluidized bed systems. Conventionally, two types of CFD models will be employed, namely, Euler–Euler model and Euler–Lagrange model. (21,22) In the first model, both the fluid and solid are regarded as continuous phases, while in the second model, the fluid is regarded as a continuous phase, the solid is regarded as a discrete one, and the motion of each particle is tracked. The interphase force model plays a key part in multiphase flow simulation. (23) Concerning the drag coefficient, different correlations are provided in the literature, and models like the Syamlal-O’Brien model and the Gidaspow model are frequently applied. McKeen and Pugsley (24) proposed a resistance model, considering the effect of cohesion between particles on particle agglomeration, and researchers also applied it further. In recent years, to study the interaction between phases, researchers often employ new drag coefficient models in consideration of drag and lift forces. (25−28) Momentum transfer and phase to phase interaction of fluid flow are very important because it determines the velocity and pressure distribution in the device, which directly affects the mass and energy transfer process. It can be concluded that the internal structure of the mixing device and the fluid motion mode in the flow field determine the stirring and mixing effect of the multiphase fluid. If the fluid flow contains a multiphase fluid system, then the system analysis needs to consider the law of conservation of mass; if the fluid flow is in a turbulent state, then the system needs to solve the instantaneous control equation of the turbulent flow.

Therefore, to optimize the design of the stirring and mixing equipment, the working mode of the stirring equipment should be taken into consideration to study the flow state and form of the multiphase fluid so as to better solve practical problems. This paper analyzed the structural performance and technical parameters of the double-shaft mixer, studied the production efficiency and conveying performance of the mixing equipment, and revealed the mixing state of materials in the double-shaft mixer. Based on the structural principle of the mixer and the actual production effect, the CFD two-fluid mixing model was established to perform the multiphase flow material mixing transient numerical calculation. The interphase interaction model and the turbulent energy equation were introduced through a refined custom function to complete the flow field analysis and efficiency evaluation of the double-shaft mixer during work of different design parameters. The research results can provide a reliable basis for the optimization of the mixer structure and the study of the characteristics of the material mixing flow field.

2. Materials and Methods

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2.1. Analysis of Structural Performance of the Double-Shaft Mixer

Since the double-shaft mixer is propelled in the form of a screw, the mechanism of conveying capacity can be applied to derive the estimation formula of the mixer. The production capacity formula is as follows: (29)

Q = 60 π \cdot D^{2} \cdot s \cdot n \cdot ρ \cdot φ / 4

(1)

In the formula, Q is the production capacity, t/h; D represents the swivel diameter, m; s refers to the lead, m; n is the rotation velocity of the shaft, rpm; ρ is the density, t/m³; φ is the backfill coefficient, and it is generally set at 0.55.

The material has both axial displacement and circumferential displacement during the mixing process. Its main manifestation is axial displacement, and the trajectory of the circumferential displacement is approximately a spiral. Therefore, the calculation of the axial movement velocity V_k of the material in the mixer needs to consider the spiral coefficient:

η = \frac{1}{1 + \tan α \cdot \tan (α + β)}

(2)

V_{k} = b \cdot \sin α \cdot n \cdot η \cdot η_{1} \cdot z / 60

(3)

In the formula, V_k is the material movement velocity, m/s; b is the average blade width, and b = 0.5 m; α is the blade installation angle, °; β is the friction angle and is set at the value of 30°; n is the rotation velocity of the mixing shaft, rpm; η is the helix coefficient; η₁ is the lateral resistance coefficient; z is the number of blades in one pitch, and z = 4.

The residence time of materials in the mixer can be estimated by the following formula:

t = \frac{L}{V_{k}}

(4)

In the formula, t is the material mixing time, s; L is the center distance between the inlet and outlet of the mixer, m.

2.2. Calculation Equation of the Gas–Liquid Interaction System

Solid–liquid dense-phase flow is widely applied in many industrial processes. Due to the limitations in experimental research of measurement technology and equipment size, accurate numerical simulation of multiphase flow, dense multiphase flow in particular, is of great significance.

2.2.1. Two-Fluid Characteristic Equation

Just like other fluid flow issues, the flow in the mixer must be governed by the law of conservation of mass and momentum. If the fluid flow includes heat exchange, the system must also observe the law of conservation of energy; if the fluid flow involves the mixing or interaction of different components, the system must also observe the law of conservation of component mass; if the fluid flow is in a turbulent state, the system needs to solve the turbulent flow instantaneous control equation. The governing equation is a mathematical description of the many conservation laws followed by the system. The continuity equation is as follows: (26,30)

\frac{\partial}{\partial t} (α_{q} ρ_{q}) + \nabla g (α_{q} ρ_{q} \overset{⇀}{v_{q}}) = 0

(5)

In the equation, ρ_q, α_q, and

\overset{⇀}{v_{q}}

represent the fluid density, volumetric content, and motion velocity vector, respectively. In the multiphase flow system, the gas phase and liquid phase are usually calculated as continuous phases.

2.2.2. Discretization of Transient Dynamic Equations

As for the transient problem, the governing equation is similar to the steady-state problem, and the main concern is the discretization of the transient term. The general governing equation is as follows:

\frac{\partial (ρ ϕ)}{\partial t} + \frac{\partial (ρ u ϕ)}{\partial x} = \frac{\partial}{\partial x} (Γ \frac{\partial ϕ}{\partial x}) + S

(6)

They refer to convection term, diffusion term, and source term, respectively. ϕ is the generalized variable and can be defined as some physical quantity to be solved, such as velocity, temperature, or concentration. Γ is the corresponding diffusion coefficient, and S is the generalized source term.

When dealing with the discretized mixing model, the transient structural dynamic equation can be derived from the principle of minimum potential energy: (31,32)

[M] {\ddot{q}} + [C] {\dot{q}} + [K] {q} = {F^{a}}

(7)

In the equation, [M], [C], and [K] represent the mass, damping, and stiffness matrix of the mixing point, respectively. {q̈}, {q̇}, {q}, and {F^a} refer to the node acceleration, velocity, displacement, and corresponding external force of the finite volume method, respectively.

2.2.3. Interphase Interaction

The state expressed by the Euler multiphase mixing model is that each phase is not constrained by the phase state and can be combined arbitrarily without being affected by the concentration. Furthermore, a series of equations with different phases can be solved simultaneously to meet the needs of actual simulation. In this model, each phase itself also satisfies the volume conservation law of multiphase flow: (33)

V_{q} = \int_{V} α_{q} d V

(8)

∑_q = 1ⁿα_q = 1, V_q is the volume fraction of the q phase. This statistical method will be used in the subsequent calculations.

Figure 1 shows the interaction between the gas and liquid phases. The basic equations of fluid mechanics are closed-formed, (34) while regarding multiphase flow, the interphase interaction equations are used to describe the fluid forces. (35) To date, most studies believe that the drag force plays a significant role in the momentum exchange process between phases, as shown in Figure 1. The relative friction and slip between the two phases can resist the phase dispersed in a opposite direction. Different publications concerning the flow characterization of the interphase state induced by the drag force have confirmed that the drag force can achieve the momentum transfer between the interphase mean flow and turbulent flow, (36) as well as the entrainment transport of the fluid relative to the discrete phase. (37) Therefore, drag force is applied to define different scenarios in simulation of the multiphase mixed flow field.

Figure 1. Schematic diagram of interphase action.

To fully study the velocity gradient in the continuous phase flow field, the multiphase flow model in this research considers the relative motion and action of gas phase and slurry to the full and defines the function of the lift force so as to accurately reproduce the effect of air mixing into the flow field during the mixing process. The operation mechanism of slurry mixing is shown in Figure 2.

Figure 2. Operation mechanism of slurry mixing TFM.

In the study of the lift effect, Tomiyama defined the theoretical lift model in the flow field containing gas and acquired the following formula: (38−40)

F_{T} = F_{L F} + F_{T L} = - (C_{L F} + C_{T L}) ρ_{L} \frac{π d^{3}}{6} (V_{G} - V_{L}) \times rot V_{L} = - C_{T} ρ_{L} \frac{π d^{3}}{6} (V_{G} - V_{L}) \times rot V_{L}

(9)

In the formula, F_T refers to the lift force; F_TL represents the tensile lift force; F_LF refers to the shear lift force, and C_T is the net lateral lift coefficient.

The ratio of buoyancy to surface tension E_0d is expressed as follows:

E_{0 d} = \frac{g (ρ_{L} - ρ_{G}) d_{H}^{2}}{σ}

(10)

In the formula, d_H refers to the size of gas phase and σ is the surface tension.

The net lateral lift coefficient can be expressed as the relationship between the Reynolds number and E_0d; thus, the corresponding range can be defined as follows:

C_{T} = {\begin{matrix} \min [0.228 \tanh (0.121 R e), f (E_{0 d})] for E_{0 d} \leq 4 \\ f (E_{0 d}) for 4 \leq E_{0 d} \leq 10.7 \end{matrix}

(11)

f (E_{0 d}) = 0.00105 E_{0 d}^{3} - 0.0159 E_{0 d}^{2} - 0.0204 E_{0 d} + 0.474

(12)

The lift force is the key force to promote the radial movement of gas, and it is also the difficult point of gas–liquid mixture simulation. User-defined function is adopted to define the relationship between the net lateral lift coefficient and lift model parameters, and the multiphase flow model is modified accordingly. The computational model is shown in Figure 3, and parameters are listed in Table 1.

Figure 3. Distribution and grid division of double-shaft mixing.

Table 1. Computational Model Parameters

parameters	value
tailing slurry density (kg/m³)	1950
cement slurry density (kg/m³)	1842
gas density (kg/m³)	1.225
flow field dimension (m)	2.025 × 0.736 × 1.110
number of blades in a pitch	4
rotation diameter (m)	0.70
initial blade angle (°)	15
filling factor of mixer	0.55
inlet boundary condition type	inlet-velocity
outlet boundary condition type	pressure-outlet
method	SIMPLEC
under-relaxation factors
pressure	0.3
momentum	0.7
volume fraction	0.5

3. Results and Discussion

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3.1. Reliability Analysis of Gas Liquid Interaction Simulation

Figure 4 indicates the velocity distribution of the flow field center at different elevations perpendicular to the y-axis section. It can be concluded that the region where the turbulence occurs most violently is the region where the rotating coordinate system is staggered. The peak value of each curve is staggered, forming the flow field oscillation, which is beneficial to the mixing effect. The maximum velocity is 1.40 m/s, at the elevation of −0.25 m. The peak value of each curve is concentrated in the middle of the mixing tank, so a large range of upward flow will be produced in the vertical direction of the middle of the flow field at the initial stage of mixing, which is consistent with the effect of industrial production. To investigate the influence of different forces on the reliability of the simulation results, three drag models were employed to simulate the gas–liquid flow field under the same gas–liquid boundary conditions.

Figure 4. Distribution and grid division of double-shaft mixing.

To investigate the influence of different forces on the reliability of the simulation results, three drag models were employed to simulate the gas–liquid flow field under the same gas–liquid boundary conditions.

3.1.1. Standard S-N Model

This model is a classic model established by Schiller and Naumann and is also the default option in the calculation of gas–liquid problems on the Fluent platform. (41) It is generally applicable and can predict the movement of the gas phase in the liquid phase, but it fails to fully consider the movement of the gas in the turbulent flow.

3.1.2. Modified S-N Model

In light of the effect of liquid phase turbulence on the drag coefficient and the size change during gas movement, the effect of liquid phase turbulent flow on reducing the slip velocity is introduced. This model is based on the classic Schiller and Naumann model with the effect on the turbulence added. The equation is as follows: (42)

f = \frac{C_{D} R e}{24}

(13)

In the equation, C_D refers to the drag coefficient and can be calculated by the following equation:

(14)

R e = \frac{ρ_{g} d_{g} | \overset{⇀}{v_{g}} - \overset{⇀}{v_{l}} |}{μ^{*}}

(15)

Among them, μ* is the modified viscosity of the liquid phase, mainly including the vortex viscosity μ_t and the bulk viscosity μ_l:

μ^{*} = μ_{l} + C^{*} μ_{t}

(16)

C* is introduced into the equation to characterize the inhibition of liquid turbulent flow on the slip velocity between phases, the value of which is usually set as 0.3.

3.1.3. Tsuchiya Model

On the basis of previous experimental verification, the effects of turbulent flow and stagnation flow are taken into consideration in this study. Therefore, the Tsuchiya et al. (43) drag correlation coefficient model is introduced to consider the influence of turbulence on the drag coefficient by using the size of discrete phase and turbulence length:

\frac{C_{D} - {C_{D}}_{0}}{{C_{D}}_{0}} = K {(\frac{d_{g}}{λ})}^{3}

(17)

This model can predict the motion of the gas phase in the liquid phase, and the influence of turbulence flow is also considered. The values of K are set at 8.67 × 10^–4. d_g and λ are the gas phase size and Kolmogorov length size, which are used to describe the minimum turbulence scale. The following function is defined by the hydrodynamic viscosity and the average turbulent flow energy dissipation rate progression:

λ = {(\frac{ν^{3}}{ε})}^{0.25}

(18)

In the model, the drag coefficients in turbulent fluids and viscous fluids are denoted by C_D and C_D0, respectively, to describe the drag effect of gas in viscous flow:

{C_{D}}_{0} = \max {(\frac{2.667 E_{0}}{E_{0} + 4}), \frac{24}{{R e}_{g}} (1 + 0.15 {R e}_{g}^{0.687})}

(19)

E_{0} = \frac{(ρ_{l} - ρ_{g}) g d_{g}^{2}}{σ}

(20)

Among them, E₀ represents the ratio of buoyancy to surface tension.

Based on the simulation scheme, the state of the mixer running for 10 s was selected for analysis. At this moment, the slurry has not yet entered the mixing tank, and the gas–liquid junction state is also very obvious. Figure5 is a description of the transient simulation total pressure distribution and gas phase volume fraction.

Figure 5. Gas–liquid interaction simulation results of different drag models.

The total pressure distribution in the flow field indicates that the overall pressure distribution gradually increases from the top of the stirring tank. As the slurry is injected, the original air in the empty tank will be progressively discharged, resulting in the change of total internal pressure. At the moment of running for 10 s, the S-N model still maintains a relatively uniform pressure distribution, and no obvious turbulent flow occurs, which is considerably different from the actual situation. The modified S-N drag model ameliorates the distribution in the flow field. With the rotation of the stirring blades, pressure changes appear in the upper part of the flow field, but this model is not accurate enough to predict the changes in dynamic pressure. In contrast, dynamic pressure changes of the operating conditions of the Tsuchiya model have taken place near the rotation domain, which is more in line with the trend of turbulent changes in the flow field.

The movement characteristics of gas–liquid two-phase flow are the key to the model calculation. In general, the predicted gas phase distribution by the S-N drag model is far from the actual situation in the three drag models, while the Tsuchiya drag model offers more reliable results in line with the actual gas distribution. This is because the gas–liquid two-phase flow is in a strong turbulence state in the simulation system, but the influence of liquid turbulence on the drag coefficient is not considered in the S-N drag model. The ratio of turbulence length scale is used to correlate the influence of turbulent motion on the drag coefficient in the Tsuchiya drag model, which improves the ability to predict the flow field characteristics in the gas–liquid interaction simulation of double-shaft mixing. Naturally, the Tsuchiya drag model is the best option for this study.

3.2. Case Analysis on Performance Optimization of the Double-Shaft Mixer

In the process of stirring and mixing, the core part of the whole mixer is the mixing blade. The mixer blade transfers the mechanical energy generated by its rotation to the surrounding fluid while working, causing the nearby fluid to rotate and produce turbulence in the flow field. In the operation of materials in the stirring tank, to achieve a variety of mixing purposes is usually a plus. The appropriate fluid movement state will be selected to make the most of its mixing effect. This paper is aimed to realize the best mixing effect.

3.2.1. Influence of Different Blade Installation Angles on the Flow Field

Four blade agitators with four different installation angles (15, 20, 25, and 30°) were used to simulate the transient state of double-shaft stirring at a rotation velocity of 40 rpm. The geometric model and physical model of the stirring tank were consistent with the previous model. According to eqs 3 and 4, with the increase in blade angle, the residence time of materials in the mixer gradoublely becomes shorter, but when it increases to a certain angle, the time becomes longer. This is due to the fact that the material particles do not move directly along the axis but motion complexly along the direction of approximately vertical blade surface in the curve. The longest stay time is 102.2 s under 15° blade angle, and the other three are 87.6, 82.3, and 83.6 s, respectively. In the transient simulation environment, the final moment of each blade installation angle scheme is calibrated in turn, and the calculation results are extracted for analysis, as shown in Figure 6. The flow velocity in the double-shaft blade stirring tank in Figure 6 suggests that the velocity distribution in the flow field is relatively uniform, implying that the influence of double-shaft blades on the flow field is relatively smooth. The flow velocity in the blade and nearby area is relatively large, with a maximum of 1.40 m/s. The velocity in the bottom center of the tank, the middle part of the upper layer of the flow field, and the lower part of the blade is lower, which is not conducive to mixing. From the velocity vector diagram of the stirring tank, it can be seen that a vortex is formed at the top and bottom of the impeller, while a small amount of an inverted cone-shaped induction area is formed in the local part of the double-shaft stirring tank, and the velocity under the blade is relatively low. The influence of air phase is considered in the distribution of mortar volume fraction. Although the volume fraction of mortar in most areas is relatively average, there is still an area with a volume fraction of 1, which shows an obvious mortar agglomeration phenomenon. That is, the scheme of blade angle of 15° still fails to achieve the ideal mixing effect in a long mixing time.

Figure 6. Flow field characteristics of different blade angles.

From the comparison of the volume fraction distribution nephogram of the tail mortar, it can be concluded that the radial flow caused by the rotation region of the blade increases obviously due to the increase in the blade installation angle, especially in the blade part. This also results in the obvious change of flow pattern and phase distribution. Different from the scheme with a blade angle of 15°, due to the appearance of a push-down flow pattern, there is no more area with a volume fraction of 1 in other schemes, and the distribution of tailing slurry is more and more uniform. However, there are still some discrete phase concentration at the bottom of the mixing tank. These areas are the low-velocity areas in the velocity vector. With the increase in blade angle, the concentration degree decreases. Comparing the various schemes, it can be concluded that with the continuous increase in blade angle, the influence of radial flow is intensified, but the influence of axial flow is reduced, which directly affects the uniformity and transportation velocity of slurry. Although the mixing time is longer, the scheme with 30° blade angle is higher than that with 25° blade angle, which is not conducive to uniform mixing. Therefore, increasing the blade installation angle is conducive to the mixing effect to some extent, but it is not the greater the angle, the better.

When Kolmogoroff was studying the theory of local isotropy, he pointed out that the energy added in the form of stirring would form large-scale vortices in the system, and these large vortices would transfer part of their energy to medium-sized vortices and then transfer part of it to small eddies. In the process of energy transmission, as the energy is consumed, the number of micro vortices increases, and the energy consumption also increases. The turbulent energy dissipation rate is an important characterization of energy efficiency. (44,45) The variation law of the turbulent energy dissipation rate in the stirring tank in Figure 7 indicates that compared with the turbulent kinetic energy, the fluctuation of the dissipation rate becomes slower. Only the peak value of the turbulent kinetic energy increases obviously in each scheme, and the rest of the areas are relatively gentle. The maxima in each scheme are 2.08 × 10^–3, 2.28 × 10^–3, 3.51 × 10^–3, and 3.95 × 10^–3 m²/s³, respectively, and the maximum turbulent energy dissipation rate appears in the middle of the flow field. Even though the flow velocity in some areas is relatively large, it only acts in the plane and lacks the influence of axial flow, so there is no obvious change in size and direction, and the utilization rate of effective energy consumption cannot be improved substantially. Compared with other schemes, the scheme with a blade angle of 25° has the most obvious effect on the turbulent kinetic energy at the bottom of the tank, and its turbulent energy dissipation rate is also the highest, which can significantly promote the reduction of the vortex dead zone at the bottom of the trough.

Figure 7. Variation of the turbulent energy dissipation rate of the vertical axis in different angle schemes.

To accurately analyze the mixing effect of different schemes, the volume fraction of slurry in the lower part of the mixing tank is extracted for comparison, which is to effectively control the interference of the air phase. Moreover, it can be seen from the results of the simulation cloud picture above that due to the influence of the flow rate, it is more difficult for the lower part of the mixing tank to achieve a uniform effect. The volume fraction ratio of cement slurry and tailing slurry at different height baseline positions is plotted to obtain the slurry mixing ratio in the mixing tank at the final moment in different blade installation angle schemes, as shown in Figure 7. Considering the density of slurry and the cemented-tailing ratio of 1:4, 0.2647:1 is set as the reference line of mixing uniformity.

Figure 8 shows that with the progress of mixing, the slurry mixing ratio approaches the preset cemented-tailing ratio. From the curve characteristics of each scheme, it can be concluded that with the decrease in height, the mixing ratio also goes down due to the fact that the density of tailing slurry is larger than that of cement slurry, and the deposition at the bottom of the mixing tank is more obvious. This result is consistent with the actual situation. The curve suggests that the maximum mixing ratio is 0.477:1, while the minimum is 0.155:1, both of which appear in the scheme with a blade angle of 15°, indicating that it is the one with the worst uniformity.

Figure 8. Distribution of the slurry mixing curve with different blade angles.

As the blade angle expands, the mixing ratio curve gradually approaches the baseline. Among them, the scheme with blade angle of 25° is the closest to the ideal value whose mixing effect is the best. However, as the angle keeps on being enlarged, although the velocities of both the inner diameter and tangential flow rise, the velocity of the axial flow begins to decrease, which is the reason why the mixing time is longer when the blade angle is 30°. According to the analysis results of volume fraction data and cloud chart, the scheme of blade angle 30° fails to form a better uniformity effect. Therefore, it is insufficient to only rely on increasing the blade installation angle to improve the mixing effect. Taking all the factors into consideration, the mixing effect and conveying time in the scheme with the blade angle of 25° are the most desirable, which is the optimal scheme. In this simulation, the preset cemented-tailing ratio of different slurries makes the results more intuitive and effective.

3.2.2. Influence of Different Rotation Velocity on the Flow Field

In the mixing process, the rotation velocity of the mixing blade is the biggest factor affecting the whole mixing system. The higher the stirring velocity, the greater the turbulence degree of the fluid, which fully promotes the mixing of different slurry particles from the microperspective; the longer the feeding time, the easier the tailing slurry to be mixed with the cement slurry in the mixing tank. For further quantitative analysis, the angle of 25° standard four blade stirring shaft obtained from the previous optimization was selected, and four rotation velocities (40, 45, 50, and 55 rpm) were adopted to simulate the transient state of double-shaft stirring at the standard height. The geometric model and physical model of the stirring tank were consistent with the previous model.

The mixing blade of the double-shaft mixer forms a spiral surface when it rotates, which produces strong mixing force, intensifies the radial movement and axial propulsion of the material, and results in a violent boiling state of the material. With the change in the blade direction in the flow field, the material is able to obtain additional axial material flow, radial material flow, and shear material flow so that the mixing and conveying can be realized in a short time, and the mixing efficiency is improved. According to eqs 8 and 9, as the mixing velocity accelerates, the residence time of materials in the mixer gradoublely becomes shorter. The residence times of slurry in the stirring tank are 82.3, 73.2, 65.8, and 59.9 s, respectively, at different rotation velocities.

In the transient simulation environment, the final time of the mixing velocity in each scheme is calibrated in turn, and the calculation results are extracted and analyzed, as shown in Figure 8. The flow velocity in the stirring tank with double-shaft blades implies that except for some high-velocity areas, the direction of the velocity vector in the flow field changes obviously, forming a large number of vortices with different scales, but the velocity distribution is relatively uniform, and the flow velocity in the rotating area of the blade and the nearby area is relatively large. The low velocity region still appears in the bottom center of the trough, the middle part of the upper layer of the flow field, and the lower part of the blade. Due to the fixed blade installation angle, the vector distribution and flow pattern of each scheme are relatively close, and the high-velocity zone is concentrated at the intersection of the two axis rotation domains.

Figure 9 shows the cloud chart of mortar volume fraction distribution at the final moment. Considering the influence of air phase, it can be seen that due to the inconsistency of mixing velocity, the time of material entering and leaving the flow field changes. The mortar distribution behavior and volume integral value of each scheme are different. Although the slurry volume fraction in most areas of some schemes is relatively average, there are still some large volume fraction areas.

Figure 9. Flow field characteristics at different rotation velocities.

Comparing the different rotation velocity schemes, it can be concluded that in the condition where the shape of the blade is fixed, the radial velocity near the rotating zone of the flow field increases obviously with the lift of the rotation velocity. From the cross section, the effect of the blade on the flow field in the stirring tank is more significant. The maximum velocities in the four schemes are 1.57, 1.79, 1.95, and 2.15 m/s, respectively. The faster the rotation velocity, the more obvious the acceleration effect. The increase in velocity has a great impact on eliminating the deposition area in the flow field. According to the distribution characteristics of the velocity vector, the velocity vector diagram and flow pattern in the other schemes are basically consistent with the scheme in which the rotation velocity is 40 rpm. It mainly increases the velocity under the blade to intensify the mixing effect.

When the rotation velocity of the stirring shaft is slow, the turbulent kinetic energy in the stirring tank is small. As shown in Figure 10, with the increase in double-shaft stirring velocity, the velocity in the flow field changes obviously, and the distribution of turbulent kinetic energy fluctuates continuously, which is conducive to the formation of mixing vortex. As the flow velocity goes up, the maximum value and influence range of turbulent kinetic energy progressively increase, and the maximum turbulent kinetic energy values of each scheme reach 5.45 × 10^–3, 6.23 × 10^–3, 6.99 × 10^–3, and 7.61 × 10^–3 m²/s², respectively. It implies that the increase in the blade rotation velocity raises the radial and tangential velocity, which is beneficial to the growth of kinetic energy. In the case where the stirring time is satisfied, the faster the rotation velocity, the stronger the effect of stirring flow field, thus conducive to uniform mixing.

Figure 10. Variation of turbulent kinetic energy along the vertical axis in different rotation velocity schemes.

To accurately analyze the mixing effect in different schemes, the volume fraction of slurry in the lower part of the mixing tank is extracted for comparison, which is to effectively control the interference of air phase. Moreover, it can be seen from the results of the simulation cloud picture above that due to the influence of the flow rate, it is more difficult for the lower part of the mixing tank to achieve a uniform effect. The volume fraction ratio of cement slurry and tailing slurry at different height baselines is plotted to obtain the slurry mixing ratio in the mixing tank at the final time in different stirring shaft velocity schemes, as presented in Figure 10. In consideration of the density of slurry and the cemented-tailing ratio of 1:4, 0.2647:1 is set as the reference line of mixing uniformity.

It can be seen from Figure 11 that with the progress of mixing, the slurry mixing ratio gradually approaches the preset cemented-tailing ratio. According to the results of the curve, the maximum mixing ratio is 0.561:1, and the minimum one is 0.113:1, both of which appear in the scheme where the stirring velocity is 55 rpm, reflecting that it is the scheme with the worst uniformity. As the stirring velocity increases, the mixing ratio curve gradually approaches the reference line. The axial flow of the flow field also accelerates due to the increase in the flow velocity, which makes the residence time of slurry in the stirring tank shorter. Among them, the scheme with the stirring velocity of 45 rpm is the closest to the ideal value whose stirring effect is the optimum. In view of the analysis results of volume fraction data and cloud chart, the uniformity effect is not preferable only by increasing the velocity of mixing shaft. Therefore, apart from the mixing efficiency, the actual uniformity effect must also be taken into consideration. To sum up, the mixing effect, conveying time, and slurry uniformity in the scheme with the stirring velocity of 45 rpm are the most desirable among all the schemes.

Figure 11. Distribution of slurry mixing curve in different stirring velocity schemes.

4. Experimental Validation

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A semi-industrial experiment was carried out to validate the simulation result, as illustrated in Figure 12. The slump is used to evaluate the fluidity, cohesion, and water retention of the filling slurry. These properties are indirectly related to the mixing process: under an optimal mixing condition, two phases can be homogeneously mixed to reach the satisfactory properties (as well as slump) and vice versa. Therefore, the mixture at the bottom of the mixer should be consolidated while the top is diluted slurry. Meanwhile, the slurry mixing ratio illustrated in Figure 11 can also be used to evaluate the mixing outcome. Accordingly, the idea is to determine the slump of filling slurry at different stirring velocities and depths to compare the simulation results of slurry mixing ratio. It is noteworthy that the trend variation and the optimal stirring velocity should be compared regarding the mixing ratio (from simulation) and slump (from experiment). The blade installation angle in the mining is fixed of 25°. Figure 12 shows the slump testing results of 45 and 50 rpm.

Figure 12. Experimental process on the workability of filling slurry.

Figure 13 shows the measurement results on slump of mixture at different stirring velocities and depths. The depth is the distance from the sampling location to the surface of the double-shaft mixer. One can observe that the slump has a decreasing trend with the depth increase, which is due to the solid settling at the bottom. The decreasing trend is more relevant to the 55 rpm, indicating that the materials are not well mixed. The slump also has a considerable decrease around 1 mm regarding 40 and 50 rpm. The slump of 45 rpm has a limited variation (from 27.7 to 27.3 mm), indicating the hardly no segregation occurring and homogeneous mixture. The observation demonstrates that the mixer at a stirring velocity of 45 rpm can reach a satisfactory mixture, which agrees with the analysis based on simulation.

Figure 13. Slump of mixture at different stirring velocities and depths.

5. Conclusions

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Based on the finite volume discretization, phase to phase traction effect, and related theories, the production efficiency and conveying performance of the mixing equipment were studied by analyzing the structural performance and technical parameters of the double-shaft mixer. According to the structural principle of the mixer and the actual production effect, a CFD two-fluid mixing model was established for transient numerical calculation of multiphase flow material mixing. By introducing the interphase drag force, lift model, and turbulent energy equation, the flow field analysis and efficiency evaluation of the double-shaft mixer under different design parameters were completed. The main conclusions of the research are as follows:

(1)	The working principle and structural parameters of the double-shaft mixer were analyzed, and the relevant production and conveying capacity calculation equations were introduced, which provides the basis for determining the calculation time of the model. The residence time of materials in the double-shaft mixer is mainly determined by the angle of the mixing blade and the axis and the rotation velocity of the shaft. The optimal mixing time of materials is supposed to be determined according to the uniformity of materials and process balance after mixing, which has also been verified in the numerical simulation;
(2)	Regarding the flow rate analysis, phase distribution, turbulent kinetic energy effect, and mixing ratio were employed as the evaluation indexes to analyze and compare the schemes with different blade installation angles and rotation velocity. The results show that as the blade angle expands, the velocity and turbulent kinetic energy also increase, while the velocity of axial flow decreases, bringing about the decrease in conveying capacity and stirring effect; as the mixing velocity elevates, the mixing effect will be strengthened. However, due to the increase in flow rate, the velocity of axial flow also accelerates, and the residence time of slurry in the stirring tank is shortened. Ultimately, it is proved that the most ideal scheme is the one with the blade installation angle of 25° and the stirring shaft velocity of 45 rpm, which has the best mixing uniformity effect, preferable conveying velocity, and desirable production capacity. The experimental observation validates the simulation results and demonstrates that the stirring shaft velocity of 45 rpm can reach the optimal slump and the most homogeneous mixture;
(3)	The influence of air on multiphase flow field is considered in the calculation. The transient dynamic parameters and the lift effect between gas and liquid are introduced to modify the multiphase flow model. The net lateral lift coefficient and Reynolds number calculation are adjusted according to the Tomiyama lift model. By analyzing the mixing flow pattern of the two-fluid model at different times, it is found that the area with the most severe turbulence is the staggered one of the rotating coordinate systems. The fluid forms two large slewing flows near the rotating coordinate system in the horizontal direction and generates a large circulating flow in the vertical direction, which improves the stirring efficiency and conforms to the actual working conditions, indicating that the two-fluid model can provide an effective basis for industrial parameter optimization.

Author Information

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Corresponding Author
- Qifan Ren - CERIS, Department of Civil Engineering, Architecture and Georesources, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal; https://orcid.org/0000-0002-9814-834X; Email: [email protected]
Authors
- Rugao Gao - School of Resource & Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China; School of Resources and Safety Engineering, Central South University, Changsha 410083, China; Department of Mining and Materials Engineering, McGill University, 3450 Rue University, Montreal, QC H3A 2A7, Canada
- Weijun Wang - School of Resource & Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
- Keping Zhou - School of Resources and Safety Engineering, Central South University, Changsha 410083, China
- Yanlin Zhao - School of Resource & Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
- Chun Yang - School of Resources and Safety Engineering, Central South University, Changsha 410083, China
Notes
The authors declare no competing financial interest.

Acknowledgments

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The authors greatly acknowledge the National Natural Science Foundation of China [grant number: 52274118 and 52274080] and project supported by the Natural Science Foundation of Hunan Province, China [grant number 2023JJ40283].

References

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Huang, Y.; Zhuang, Y.; Wan, D. C. Hydrodynamic Study and Performance Analysis of the OC4-DeepCWind Platform by CFD Method. Int. J. Comput. Methods. 2021, 18, 2050020, DOI: 10.1142/S0219876220500206
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Liu, C. L.; Zheng, Q.; Wang, Q.; Lin, A. Q.; Jiang, Y. T.; Luo, M. C. Sensitivity Analysis of Multistage Compressor Characteristics Under the Spray Atomization Effect Using a CFD Model. Energies 2019, 12, 301, DOI: 10.3390/en12020301
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Drew, D. A.; Lahey, R. T., Jr. Application of general constitutive principles to the derivation of multidimensional two-phase flow equations. Int. J. Multiph. Flow. 1979, 5, 243– 264, DOI: 10.1016/0301-9322(79)90024-7
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Dam, J.; Schuck, P. Calculating Sedimentation Coefficient Distributions by Direct Modeling of Sedimentation Velocity Concentration Profiles. Methods Enzymol. 2004, 384, 185– 212, DOI: 10.1016/S0076-6879(04)84012-6
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Calculating sedimentation coefficient distributions by direct modeling of sedimentation velocity concentration profiles
Dam, Julie; Schuck, Peter
Methods in Enzymology (2004), 384 (Numerical Computer Methods, Part E), 185-212CODEN: MENZAU; ISSN:0076-6879. (Elsevier)
A review describes computational approaches for calcg. sedimentation coeff. distributions (c(s)), together with a discussion of exptl. requirements and examples for the application to mixts. of non-interacting and interacting proteins. The development of fast finite element methods for solving the Lamm equation in combination with algebraic techniques for the detection and elimination of systematic noise in sedimentation velocity expts. enabled high-resoln., diffusion deconvoluted c(s). They are solns. of Fredholm integral equations of the first kind, calcd. with max. entropy or Tikhonov-Phillips regularization, and based on approxns. of the relationship between the diffusion and sedimentation coeff. D(s) derived from hydrodynamic considerations. The use of numerical solns. of the Lamm equation in c(s) permits a more flexible and general approach, analogous to continuous parameter distributions well-known in other biophys. techniques, such as dynamic light scattering, fluorescence anisotropy, and optical affinity biosensing.
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Fang, L. P.; Liu, R.; Li, J.; Xu, C. H.; Huang, L. Z.; Wang, D. S. Magnetite/Lanthanum hydroxide for phosphate sequestration and recovery from lake and the attenuation effects of sediment particles. Water Res. 2018, 130, 243– 254, DOI: 10.1016/j.watres.2017.12.008
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Magnetite/Lanthanum hydroxide for phosphate sequestration and recovery from lake and the attenuation effects of sediment particles
Fang, Liping; Liu, Ru; Li, Ji; Xu, Cuihong; Huang, Li-Zhi; Wang, Dongsheng
Water Research (2018), 130 (), 243-254CODEN: WATRAG; ISSN:0043-1354. (Elsevier Ltd.)
An effective approach for eutrophication control and phosphate recovery remains a longstanding challenge. Herein, we present a new technique for phosphate sequestration in lake and phosphate recovery using novel magnetically recoverable magnetite/lanthanum hydroxide [M-La(OH)3] hybrids that can be prepd. using a simple one-pot synthesis method. Batch studies show that M-La(OH)3 exhibits a strong sorption towards phosphate with sorption capacities of up to 52.7 mg-P/g at pH 7.0 in water. A simple model indicates that the efficiency of M-La(OH)3 for phosphate sequestration in lake is significantly attenuated by 34-45% compared to that in water, due to interference from sediment particles. However, our results demonstrate that sediments suspensions mixed with a M-La(OH)3 content of 1-3% exhibit a capability of up to 1.2 mg-P/g for sequestering external phosphate compared with that of 0.2 mg-P/g for pristine sediment at pH 7.3. M-La(OH)3-mixed sediment suspensions appear to effectively sequester phosphate over an environmentally relevant pH range from 4 to 8.5. Phosphorus (P) fractionation expts. indicate that the enhanced phosphate sorption by M-La(OH)3-mixed sediment suspensions is mainly due to the increased fractions of NaOH-P and inorg. P. This work indicates that the M-La(OH)3 has the potential for phosphate sequestration and recovery from lake.
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Kang, L.; Guo, L. Eulerian–Lagrangian simulation of aeolian sand transport. Powder Technol. 2006, 162, 111– 120, DOI: 10.1016/j.powtec.2005.12.002
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Eulerian-Lagrangian simulation of aeolian sand transport
Kang, Liqiang; Guo, Liejin
Powder Technology (2006), 162 (2), 111-120CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
A numerical investigation of eolian sand transport is performed with an Eulerian-Lagrangian model. In this model, the gas phase is described by the vol.-averaged Navier-Stokes equations of two-phase flow. The particle motion is obtained by solving Newton's second law of motion taking into account the interparticle collisions, where a soft sphere model is used to describe interparticle collisions. The dynamic process of eolian sand transport is simulated. The simulation results show that the variation of mean horizontal velocity of the particles with height can be expressed by a logarithmic function or a power function at h > 0.02 m, and the power function can be described below 0.02 m. The sand mass flux decreases exponentially with height for h > 0.02 m, but there is a deviation from the exponential decay due to the creep grains in the near-bed region. It is also shown that the inter-particle collisions play an important role in sand saltation. Therefore the present numerical model is capable of being applied to the study of windblown sand movement.
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Zheng, J. X.; Li, Y. K.; Wan, Z. Q.; Hong, W. P.; Wang, L. Modification of the agglomeration kernel and simulation of the flow pattern in acoustic field with fine particles. Powder Technol. 2019, 356, 930– 940, DOI: 10.1016/j.powtec.2019.09.022
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Modification of the agglomeration kernel and simulation of the flow pattern in acoustic field with fine particles
Zheng, Jianxiang; Li, Yukai; Wan, Zongqun; Hong, Wenpeng; Wang, Long
Powder Technology (2019), 356 (), 930-940CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
This paper studies the acoustic agglomeration of fine particles of the coal fly ash in the acoustic field agglomeration device, based on the coupling population balance model (PBM) for acoustic agglomeration of fine particles and the modified kinetic theory of the fine particle flow. The new root mean square of the agglomeration kernel function operates according to the acoustic agglomeration mechanism. We present the theor. investigation of the problem and then compare it with exptl. results. The results show that the agglomeration process of particles in different size ranges is dominated by different agglomeration mechanisms. Moreover, we show the numerical simulation of the acoustic agglomeration process of the particles using the new agglomeration kernel function, which is consistent with the exptl. results. In addn., the particle flow in the acoustic field agglomeration device presents a typical turbulent structure, and a large particle agglomeration occurs near the wall and outlet.
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Li, L.; Qi, H.; Yin, Z. C.; Li, D. F.; Zhu, Z. L.; Tangwarodomnukun, V.; Tan, D. P. Investigation on the multiphase sink vortex Ekman pumping effects by CFD-DEM coupling method. Powder Technol. 2020, 360, 462– 480, DOI: 10.1016/j.powtec.2019.06.036
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Investigation on the multiphase sink vortex Ekman pumping effects by CFD-DEM coupling method
Li, Lin; Qi, Huan; Yin, Zichao; Li, Daifeng; Zhu, Zhiliang; Tangwarodomnukun, Viboon; Tan, Dapeng
Powder Technology (2020), 360 (), 462-480CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
The gas-liq.-solid multiphase sink vortex is a complex turbulent mech. phenomenon, in which the pumping effects of Ekman boundary layer involved in the above process has the important scientific value and engineering significance. To address the matter, a coupled Computational Fluid Dynamic and Discrete Element Method (CFD-DEM) method for the simulation of the multiphase sink vortex is proposed based on the realizable k-ε turbulent model and the soft sphere model. The suction and extn. regularities of gas-liq. coupling process are analyzed to reveal the matter transfer mechanism of Ekman boundary layer. Then, the phenomenon for the particle sucked by sink vortex is investigated to obtain the Ekman pumping effects. Finally, the influences of Ekman pumping effects on particles with respect to different densities are studied to verify the validity and reliability of the proposed method. Numerical results demonstrate that the suction and extn. intensities constitute a data set that is dependent on the initial disturbance components; there is an apparent upwelling phenomenon in the liq. boundary layer, which is caused by the spiral coupling structure of Ekman boundary layer. The Ekman pumping process for particles has three typical stage: Ekman suction-extn. state, Ekman horizontal pumping state, and Ekman upwelling state, wherein the flow patterns are dominated by the initial disturbance and appear a complex nonlinear turbulence features; with the particle d. increasing, the effects of Ekman suction-extn. state and horizontal pumping state are enhanced, but the Ekman upwelling effect for particle has apparent decreased.
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Kasbaoui, M. H.; Koch, D. L.; Desjardins, O. Clustering in Euler–Euler and Euler–Lagrange simulations of unbounded homogeneous particle-laden shear. J. Fluid Mech. 2019, 859, 174– 203, DOI: 10.1017/jfm.2018.796
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Clustering in Euler-Euler and Euler-Lagrange simulations of unbounded homogeneous particle-laden shear
Kasbaoui, M. Houssem; Koch, Donald L.; Desjardins, Olivier
Journal of Fluid Mechanics (2019), 859 (), 174-203CODEN: JFLSA7; ISSN:0022-1120. (Cambridge University Press)
Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle vol. fractions, the two-way coupling can be significant due to the large particle to gas d. ratio. In this semi-dil. regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The anal. of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concn. of inertial particles in the stretching regions of the flow leads to the formation of highly concd. particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh-Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler-Lagrange formalism are compared to Euler-Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.
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Liu, Y.; Ersson, M.; Liu, H.; Jönsson, P.; Gan, Y. Comparison of Euler-Euler Approach and Euler–Lagrange Approach to Model Gas Injection in a Ladle. Steel Res. Int. 2019, 90, 1800494, DOI: 10.1002/srin.201800494
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Li, P.; Lan, X. Y.; Xu, C. M.; Wang, G.; Lu, C. X.; Gao, J. S. Drag models for simulating gas–solid flow in the turbulent fluidization of FCC particles. Particuology. 2009, 7, 269– 277, DOI: 10.1016/j.partic.2009.03.010
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McKeen, T.; Pugsley, T. Simulation and experimental validation of a freely bubbling bed of FCC catalyst. Powder Technol. 2003, 129, 139– 152, DOI: 10.1016/S0032-5910(02)00294-2
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Simulation and experimental validation of a freely bubbling bed of FCC catalyst
McKeen, Tim; Pugsley, Todd
Powder Technology (2003), 129 (1-3), 139-152CODEN: POTEBX; ISSN:0032-5910. (Elsevier Science B.V.)
A validation and mesh refinement study was performed for the simulation of a freely bubbling bed of fluid catalytic cracking (FCC) catalyst operating at superficial gas velocities in the range of 0.05 to 0.20 m/s, using the two-fluid computational fluid dynamics (CFD) code Multiphase Flow with Interphase eXchanges (MFIX). The simulation results were compared to exptl. data collected using an elec. capacitance tomog. (ECT) imaging system as well as data from the literature. A comparison was made based on the bed expansion, and bubble diams. and rise velocities. A novel method was used to ext. bubble properties from ECT data and simulation results. A modified gas-solids drag law, corresponding to an effective particle agglomerate diam. in the range of 135 to 170 μm for FCC particles of actual 75 μm mean diam., was required to adequately predict the fluidization behavior obsd. exptl. These findings support the argument that cohesive interparticle forces lead to agglomeration of FCC catalyst powder and significantly affect the fluidization quality. The model is the first presented in the open literature to successfully apply CFD to obtain realistic predictions of FCC bubbling bed behavior.
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Yang, N.; Wang, W.; Ge, W.; Li, J. H. CFD simulation of concurrent-up gas–solid flow in circulating fluidized beds with structure-dependent drag coefficient. Chem. Eng. J. 2003, 96, 71– 80, DOI: 10.1016/j.cej.2003.08.006
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CFD simulation of concurrent-up gas-solid flow in circulating fluidized beds with structure-dependent drag coefficient
Yang, Ning; Wang, Wei; Ge, Wei; Li, Jinghai
Chemical Engineering Journal (Amsterdam, Netherlands) (2003), 96 (1-3), 71-80CODEN: CMEJAJ; ISSN:1385-8947. (Elsevier Science B.V.)
Meso-scale structure existing in the form of particle clusters or strands in concurrent-up gas-solid two-phase flow has been extensively corroborated in exptl. research. However, its significant effects on interfacial drag coeff. are seldom taken into account in current computational fluid dynamic (CFD) simulations by using the two-fluid models. The energy-minimization multi-scale (EMMS) approach, in which the heterogeneous structure is described by the so-called multi-scale resoln. and energy-minimization method, is adapted for investigating the dependence of drag coeff. on structure parameters. The structure-dependent drag coeffs. calcd. from the EMMS approach are then incorporated into the two-fluid model to simulate the behavior of the concurrent-up gas-solid flow in a riser. Simulation results indicate that the simulated solid concn. with the Wen and Yu/Ergun drag correlations is rather dil., leading to a more homogeneous structure; while the dynamic formation and dissoln. of clusters can be captured with the drag correlations derived from the EMMS approach, and the simulated outlet solid flux and voidage profile in both radial and axial directions are in reasonable agreement with exptl. results, suggesting the feasibility for the EMMS approach to be used as a sub-grid closure law for drag coeff.
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Zhou, K. P.; Gao, R. G.; Gao, F. Particle Flow Characteristics and Transportation Optimization of Superfine Unclassified Backfilling. Minerals. 2017, 7, 6, DOI: 10.3390/min7010006
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Particle flow characteristics and transportation optimization of superfine unclassified backfilling
Zhou, Ke-ping; Gao, Rugao; Gao, Feng
Minerals (Basel, Switzerland) (2017), 7 (1), 6/1-6/21CODEN: MBSIBI; ISSN:2075-163X. (MDPI AG)
In order to investigate the high vol. fraction problem of the solid phase in superfine unclassified backfilling pipeline transportation, characteristic parameters were obtained by fitting to test data with an R-R particle size distribution function; then, a Euler dense-phase DPM (Discrete phase model) model was established by applying solid-liq. two-phase flow theory and the kinetic theory of granular flow (KTGF). The collision and friction of particles were imported by the UDF (User-define function) function, and the pipeline fluidization system, dominated by interphase drag forces, was analyzed. The best concn. and flow rate were finally obtained by comparing the results of the stress conditions, flow field characteristics, and the discrete phase distributions. It is revealed that reducing the concn. and flow rate could control pressure loss and pipe damage to a certain degree, while lower parameters show neg. effects on the transportation integrity and backfilling strength. Indoor tests and field industrial tests verify the reliability of the results of the numerical simulations. Research shows that the model optimization method is versatile and practical for other, similar, complex flow field working conditions.
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Whittaker, P.; Wilson, C.; Aberle, J.; Rauch, H. P.; Xavier, P. A drag force model to incorporate the reconfiguration of full-scale riparian trees under hydrodynamic loading. J. Hydraul. Res. 2013, 51, 569– 580, DOI: 10.1080/00221686.2013.822936
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Ren, W. C.; Wang, S. H.; Gao, R. G.; Qiao, D. P. Operational process simulation and optimization of a continuous-discharge system in a backfilling system. Mater. Tehnol. 2019, 53, 101, DOI: 10.17222/mit.2018.181
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Zhu, K., Xu, L.. 2016. Handbook of Building Material Machinery Industry, Wuhan University of Technology Press, Wuhan.
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Nguyen, V.-D.; Heo, W.-H.; Kubuya, R.; Lee, C.-W. Pressurization Ventilation Technique for Controlling Gas Leakage and Dispersion at Backfilled Working Faces in Large-Opening Underground Mines: CFD Analysis and Experimental Tests. Sustainability. 2019, 11, 3313, DOI: 10.3390/su11123313
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Tyson, W. C.; Roy, C. J. A higher-order error estimation framework for finite-volume CFD. J. Comput. Phys. 2019, 394, 632– 657, DOI: 10.1016/j.jcp.2019.06.017
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There is no corresponding record for this reference.
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Mohammed, H. A.; Fathinia, F.; Vuthaluru, H. B.; Liu, S. CFD based investigations on the effects of blockage shapes on transient mixed convective nanofluid flow over a backward facing step. Powder Technol. 2019, 346, 441– 451, DOI: 10.1016/j.powtec.2019.02.002
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CFD based investigations on the effects of blockage shapes on transient mixed convective nanofluid flow over a backward facing step
Mohammed, Hussein A.; Fathinia, F.; Vuthaluru, Hari B.; Liu, Shaomin
Powder Technology (2019), 346 (), 441-451CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
The sepn. and reattachment flow occurs in a backward-facing step (BFS) is available in various industrial applications such as gas turbine engines, combustors, aircraft, buildings and many other devices of heat transfer. It represents the pillar key of detg. the flow structure and significantly affecting the heat transfer mechanism. This work studies numerically the effects of four various types of blockage shapes on transient laminar mixed convective nanofluid flow over a horizontal BFS placed in a duct. Nanoparticles of SiO2 with ethylene glycol as a base fluid at 2% of vol. fraction and 20 nm of nanoparticle diam. are considered to examine the effect of different blockage shape on the thermal and flow fields at different time scales. The downstream of the step is kept at a const. heat flux of 500 W/m2, while other walls and sides of the duct are considered thermally insulated. The Reynolds no. used in this study is in the range of 50-200. The relevant governing equations (continuity, momentum and energy) along with the boundary conditions are solved with the aid of finite vol. method (FVM). The results reveal that after dimensionless time of τ = 5 the trend of nanofluid flow and recirculation area near the step and behind the blockage shape does not change significantly and this time is selected as a quasi-steady state time and the point of comparison. The velocity distributions for front facing triangular blockage decreased and this blockage shape has the highest value of skin friction coeff. beyond Re = 150. The results indicate that the front facing triangular blockage has the highest value of av. Nusselt no. and performance evaluation index while the trapezoidal blockage has the lowest value.
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Li, P.; Zhang, X. H.; Lu, X. B. Three-dimensional Eulerian modeling of gas–liquid–solid flow with gas hydrate dissociation in a vertical pipe. Chem. Eng. Sci. 2019, 196, 145– 165, DOI: 10.1016/j.ces.2018.10.053
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Three-dimensional Eulerian modeling of gas-liquid-solid flow with gas hydrate dissociation in a vertical pipe
Li, Peng; Zhang, Xuhui; Lu, Xiaobing
Chemical Engineering Science (2019), 196 (), 145-165CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
The pipe transportation of gas hydrate-bearing sediments (GHBS) GHBS-gas hydrate-bearing sediments is one of the key problems in mech.-thermal exploitation of gas hydrate (GH) GH-gas hydrate in marine stratum. It is a gas-liq.-solid (methane gas-seawater-GHBS particles) three-phase flow, accompanied by GH dissocn. In this study, a three-dimensional Eulerian model combined with the kinetic theory of granular flow (KTGF) was adopted to simulate the gas-liq.-solid flow with GH dissocn. The com. CFD software FLUENT 16.2 was employed, considering the hydrodynamics, heat and mass transfer, and GH dissocn. simultaneously. A kinetic model for GH dissocn. in the GHBS particles is presented, considering the effect of multiphase flow on dissocn. rate. The model can capture the transition from the initial liq.-solid two-phase flow to gas-liq.-solid three-phase flow, describing the distribution of the phase vol. fraction, velocity, temp., and dissocn. rate. The interaction between GH dissocn. and multiphase flow is discussed. The simulation results indicate that the continuous prodn. of gas bubbles by GH dissocn. leads to more violent fluctuations in the pressure gradient and a more marked elevation of the solid particles compared with the liq.-solid two-phase flow without GH dissocn. In addn., the effect of GH dissocn. on the multiphase flow under different hydrate saturations was analyzed.
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Chamani, H.; Matsuura, T.; Rana, D.; Lan, C. Q. Examination of the bubble gas transport method to estimate the membrane pore size distribution. Desalination 2022, 531, 115714 DOI: 10.1016/j.desal.2022.115714
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Examination of the bubble gas transport method to estimate the membrane pore size distribution
Chamani, Hooman; Matsuura, Takeshi; Rana, Dipak; Lan, Christopher Q.
Desalination (2022), 531 (), 115714CODEN: DSLNAH; ISSN:0011-9164. (Elsevier B.V.)
The pore size distribution (PSD) of the membrane is often measured by the bubble gas transport method. However, the method is not free from some concerns over its accuracy. In the present work, two questions are raised; (1) the validity of the computational procedure commonly used to calc. PSD (2) the validity of the assumption that all pores are open to gas transport in the linear part of the flow rate vs. pressure curve. To answer these questions, the flow rate vs. pressure lines were generated rigorously based on a given PSD by the model that we have recently developed, and using the lines so produced, the PSD was back-calcd. It was found that the agreement of original PSD and the back-calcd. PSD is reasonable when the PSD is narrow, but when the PSD is broad, the back-calcd. PSD shifts toward the larger pore sizes. It was also found that the calcd. PSD is slightly affected when some small pores are not included in the linear part of flow rate vs. pressure wet-line.
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Chamani, H.; Matsuura, T.; Rana, D.; Lan, C. Q. Transport characteristics of liquid-gas interface in a capillary membrane pore. J. Memb. Sci. 2020, 611, 118387, DOI: 10.1016/j.memsci.2020.118387
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Transport characteristics of liquid-gas interface in a capillary membrane pore
Chamani, Hooman; Matsuura, Takeshi; Rana, Dipak; Lan, Christopher Q.
Journal of Membrane Science (2020), 611 (), 118387CODEN: JMESDO; ISSN:0376-7388. (Elsevier B.V.)
Interface displacement of two phases mainly caused by replacement of one fluid with another one can occur inside the membrane pore during membrane prepn. and characterization. This phenomenon is exemplified by measurement of liq. entry pressure (LEP) in membrane distn., measurement of pore size and pore size distribution by the bubble point method, measurement of pore size and pore size distribution by porometry, wetting of dry membrane and also drying of wet membrane. In most of the theor. studies, focus was on the transmembrane pressure required for one phase to enter into the membrane pores filled with another phase and little attention was paid to the movement of interface in the capillary. This paper attempts to discuss quant. the movement of interface, water/air interface in particular. Therefore, movement of interface was tracked using a well-founded model and consequently the pressure and velocity at the interface and the required time for replacement were studied. In addn., the influence of different parameters including pore radius, contact angle, and membrane thickness was assessed. It was found that the low resistance for the air flow, assumed in Washburn's equation, can be justified as an approxn. Moreover, the model proposed in this work can predict that the pressure at the water/air interface (when air replaces liq. water) may become significantly lower than the atm. pressure at the pore exit, causing pore shrinkage. As well, the pressure at the air/water interface (when liq. water replaces air) may become significantly higher than the feed pressure applied at the pore entrance, causing pore expansion.
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Rana, D.; Matsuura, T.; Lan, C. Q. Work needed to force the water-air interface down in the re-entrant structured capillary pore. Desalination 2022, 541, 116058 DOI: 10.1016/j.desal.2022.116058
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Work needed to force the water-air interface down in the re-entrant structured capillary pore
Rana, Dipak; Matsuura, Takeshi; Lan, Christopher Q.
Desalination (2022), 541 (), 116058CODEN: DSLNAH; ISSN:0011-9164. (Elsevier B.V.)
The re-entrant structure of the membrane surface has attracted researchers' attention recently, due to its ability to make the membrane surface more wetting resistant-either in water or in liqs. of low surface tension. The underlying principle of this approach is that an energy barrier has to be overcome when the transition occurs from the Cassie Baxter state to the Wenzel state of the rough membrane surface, which prevents the passage of liq. through the membrane pore. In this work, the energy barrier was evaluated for the cone-shaped pore based on Young's theory of the capillary force. It was found that the energy barrier is enhanced by increasing the angle of the apex of the cone, the pore length, and the contact angle. The effects of the first two geometrical factors, the angle of apex of cone and pore length, are much stronger than the effect of the contact angle. It is believed that this work will offer a guideline for the rational membrane design to reduce, and even prevent, the pore wetting of membranes, particularly for oil/water sepn. and membrane distn.
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Qtaishat, M. R.; Chamani, H.; Matsuura, T.; Rana, D.; Lan, C. Q. Modeling of the movement of two immiscible liquids in membrane pores. Int. J. Multiph. Flow. 2022, 157, 104282 DOI: 10.1016/j.ijmultiphaseflow.2022.104282
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Tomiyama, A.; Tamai, H.; Zun, I.; Hosokawa, S. Transverse migration of single bubbles in simple shear flows. Chem. Eng. Sci. 2002, 57, 1849– 1858, DOI: 10.1016/S0009-2509(02)00085-4
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Transverse migration of single bubbles in simple shear flows
Tomiyama, Akio; Tamai, Hidesada; Zun, Iztok; Hosokawa, Shigeo
Chemical Engineering Science (2002), 57 (11), 1849-1858CODEN: CESCAC; ISSN:0009-2509. (Elsevier Science Ltd.)
Trajectories of single air bubbles in simple shear flows of glycerol-water soln. were measured to evaluate transverse lift force acting on single bubbles. Expts. were conducted under the conditions of -5.5 ≤ log10 M ≤ -2.8, 1.39 ≤ Eo ≤ 5.74 and 0 ≤ |dVL/dy| ≤ 8.3 s-1, where M is the Morton no., Eo the Eotvos no., and dVL/dy the velocity gradient of the shear flow. A net transverse lift coeff., CT, was evaluated by making use of all the measured trajectories and an equation of bubble motion. It was confirmed that CT for small bubbles is a function of the bubble Reynolds no. Re, whereas CT for larger bubbles is well correlated with a modified Eotvos no. Eod which employs the max. horizontal dimension of a deformed bubble as a characteristic length. An empirical correlation of CT was therefore summarized as a function of Re and Eod. The crit. bubble diam. causing the radial void profile transition from wall peaking to core peaking in an air-water bubbly flow evaluated by the proposed CT correlation coincided with available exptl. data.
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Hosokawa, S.; Tomiyama, A. Multi-fluid simulation of turbulent bubbly pipe flows. Chem. Eng. Sci. 2009, 64, 5308– 5318, DOI: 10.1016/j.ces.2009.09.017
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Hosokawa, Shigeo; Tomiyama, Akio
Chemical Engineering Science (2009), 64 (24), 5308-5318CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
Radial distributions of void fraction, bubble aspect ratio, phasic velocities, and turbulent kinetic energy in bubbly pipe flows are measured using an image processing method and a laser Doppler velocimetry. Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows. The exptl. results indicate that aspect ratio of bubbles in the near wall region takes a higher value than that of free rising bubbles due to the presence of wall, and that the change in the aspect ratio induces decrease in relative velocity between bubbles and liq. in the near wall region. Drag coeff., CD, of a bubble in a bubbly pipe flow tends to increase with magnitude of shear flow, and the effect of shear flow on CD is estd. by the correlation proposed by D. Legendre and J. Magnaudet (1998). Comparison between the simulated and the measured results indicate that the effects of bubble shape and shear flow on drag force acting on bubbles should be taken into account for accurate predictions of bubbly pipe flows. The turbulence models proposed by M. Lopez de Bertodano et al.(1994) and by S. Hosokawa and A. Tomiyama (2004) give good predictions for turbulence modification caused by bubbles.
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Tomiyama, A.; Celata, G. P.; Hosokawa, S.; Yoshida, S. Terminal velocity of single bubbles in surface tension force dominant regime. Int. J. Multiph. Flow. 2002, 28, 1497– 1519, DOI: 10.1016/S0301-9322(02)00032-0
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Simulation and experimental investigation of power consumption, gas dispersion and mass transfer coefficient in a multi-phase stirred bioreactor
Chen, Yuanfeng
Brazilian Journal of Chemical Engineering (2019), 36 (4), 1439-1451CODEN: BJCEFZ; ISSN:1678-4383. (Brazilian Society of Chemical Engineering)
Bio-oxidn. leaching of refractory gold conc. was carried out in a typical gas-liq.-solid three-phase stirred bioreactor. The bacteria, which adhered to solid particle surfaces and spread over the liq. phase, require sufficient oxygen and nutrient of carbon and nitrogen, and then the mass transfer rate should be considered. However, the mass transfer coeff., which could be used to evaluate the mass transfer rate, was detd. by gas holdup, bubble diam. and power consumption. Therefore, a three-phase Eulerian equation with k-e turbulence model and addnl. models of two bubble diam., a torque and a mass transfer coeff. were applied in the simulation. The simulation results were validated with exptl. data and used to analyze the spatial distribution of the mass transfer coeff. The results demonstrated that the simulation and exptl. data of Sauter mean bubble diam. and power no. were in good agreement and the simulation results of the mass transfer coeff. were agree with the values calcd. by an empirical correlation. The Davoody model can be strongly recommended for further simulation of the bubble diam., and the gas holdup and mass transfer coeff. were very unevenly distributed in the lower zone. Hence, the lower impeller clearance should be considered.
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Tsuchiya, K.; Furumoto, A.; Fan, L.-S.; Zhang, J. P. Suspension viscosity and bubble rise velocity in liquid-solid fluidized beds. Chem. Eng. Sci. 1997, 52, 3053– 3066, DOI: 10.1016/S0009-2509(97)00127-9
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Chemical Engineering Science (1997), 52 (18), 3053-3066CODEN: CESCAC; ISSN:0009-2509. (Elsevier)
The effective viscosity which characterizes the pseudo-homogeneous property of the liq.-solid suspension in gas-liq.-solid fluidization is examd. in light of the velocity of single bubbles rising through the suspension. Expts. conducted in this study cover a wide range of bubble diams. (2-23 mm) under high solids holdup (0.48-0.57) conditions. The study reveals that the liq.-solid medium exhibits a homogeneous, Newtonian property at any given solids holdup when the bubble diams. are greater than 12-17 mm. The effective viscosities obtained in this study based on equivalency of the single bubble rise velocity in Newtonian media as well as those reported in the literature are found to follow the Mooney-type relation for solids holdup dependence. The two parameters underlying this relation can be correlated as a function of the particle terminal velocity, particle shape and packed solids holdup. When the bubble diams. are smaller than 12-17 mm, the effective viscosity of the liq.-solid medium deviates from the viscosity of the corresponding Newtonian liq. The deviation which marks the redn. in the bubble rise velocity reflects a significant close-range interaction between particles. In this bubble size range, the liq.-solid medium exhibits a non-Newtonian property characterized by shear-thinning behavior with flow index ≈ 1/2.
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Booth, C. P.; Leggoe, J. W.; Aman, Z. M. The use of computational fluid dynamics to predict the turbulent dissipation rate and droplet size in a stirred autoclave. Chem. Eng. Sci. 2019, 196, 433– 443, DOI: 10.1016/j.ces.2018.11.017
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The use of computational fluid dynamics to predict the turbulent dissipation rate and droplet size in a stirred autoclave
Booth, Craig P.; Leggoe, Jeremy W.; Aman, Zachary M.
Chemical Engineering Science (2019), 196 (), 433-443CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
The prediction of droplet sizes in emulsions is important for fields ranging from the chem. process industry to emergency planning in the event of an underwater oil release. Typically scale models have needed to be built and the results scaled up, but as computational resources have grown and turbulence models have matured it has become possible to use computational fluid dynamics (CFD) to simulate the behavior of the fluid/s. While direct simulation of multiphase breakup at high Reynolds no. is currently computationally impractical, this paper looks into the use of CFD along with a correlation function based on max. turbulent kinetic energy dissipation rate to predict the Sauter mean diam. of drops in a 1 in. baffle-and-vane type autoclave. The results show that using a RNG-kε turbulence model with a simplified 2D geometry gave drop sizes within 26.2 μm of the Sauter mean diam. obsd. in expts. with no addnl. tuning of parameters. Correlating pipe and autoclave flows through the Reynolds no. and the turbulent kinetic energy dissipation rate was also investigated. Using the traditional definitions of the Reynolds nos. the correlation is poor, the coeff. of detn. of the linear fit to the log-log data is 0.64. The first modification replaced the diam. of the blade as characteristic length with the tip swept circumference which increased the coeff. of detn. to 0.960. A further modification using data obtained from the turbulent fields of the simulation showed a significant improvement with the coeff. of detn. increasing to 0.988.
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45
Feng, Q.; Ge, R.; Sun, Y. Q.; Fang, F.; Luo, J. Y.; Xue, Z. X.; Cao, J. S.; Li, M. Revealing hydrodynamic effects on flocculation performance and surface properties of sludge by comparing aeration and stirring systems via computational fluid dynamics aided calculation. Water Res. 2020, 172, 115500 DOI: 10.1016/j.watres.2020.115500
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45
Revealing hydrodynamic effects on flocculation performance and surface properties of sludge by comparing aeration and stirring systems via computational fluid dynamics aided calculation
Feng, Qian; Ge, Ran; Sun, Yaqing; Fang, Fang; Luo, Jingyang; Xue, Zhaoxia; Cao, Jiashun; Li, Ming
Water Research (2020), 172 (), 115500CODEN: WATRAG; ISSN:0043-1354. (Elsevier Ltd.)
The effects of aeration and stirring systems on the phys. properties of sludge were analyzed using a computational fluid dynamics (CFD) model. The aims of this study were to (1) compare the effects of aeration and stirring on sludge properties using the same turbulent mixing intensity, and (2) to reveal the relationship between sludge properties and hydrodynamic indicators to det. how hydrodynamic conditions influence sludge flocculation. Mixing expts. with stirring and aeration were carried out in 2-L beakers with the av. velocity gradient (G) set to 90, 190, or 280 s-1. The sludge flocculation performance, zeta potential, and Gibbs free energy (ΔG) were analyzed and the flow velocity, turbulence energy, turbulence dissipation rate, and Kolmogorov microscale were calcd. as hydrodynamic parameters. The av. flow velocity and the turbulence dissipation rate were obviously higher in the stirring system than in the aeration system at the same G. However, the turbulence energy and Kolmogorov microscale in the aeration system were much higher than those in the stirring system. Both the zeta potential and ΔG were lower in the aeration system than the stirring system. The zeta potential and ΔG results for the two systems suggest that aeration is more beneficial for sludge flocculation than stirring even though the sludge flocculation performance F/F0 in the stirring and aeration systems showed no obvious differences. Significant relationships between hydrodynamic parameters calcd. based on the CFD model and av. values of sludge properties in the stable phase showed that the Kolmogorov microscale, av. flow velocity, and turbulence energy were appropriate hydrodynamic parameters for evaluating the flocculation performance F/F0, zeta potential, and ΔG, resp.
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Published September 14, 2023

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Abstract
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Figure 1
Figure 1. Schematic diagram of interphase action.
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Figure 2
Figure 2. Operation mechanism of slurry mixing TFM.
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Figure 3
Figure 3. Distribution and grid division of double-shaft mixing.
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Figure 4
Figure 4. Distribution and grid division of double-shaft mixing.
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Figure 5
Figure 5. Gas–liquid interaction simulation results of different drag models.
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Figure 6
Figure 6. Flow field characteristics of different blade angles.
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Figure 7
Figure 7. Variation of the turbulent energy dissipation rate of the vertical axis in different angle schemes.
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Figure 8
Figure 8. Distribution of the slurry mixing curve with different blade angles.
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Figure 9
Figure 9. Flow field characteristics at different rotation velocities.
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Figure 10
Figure 10. Variation of turbulent kinetic energy along the vertical axis in different rotation velocity schemes.
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Figure 11
Figure 11. Distribution of slurry mixing curve in different stirring velocity schemes.
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Figure 12
Figure 12. Experimental process on the workability of filling slurry.
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Figure 13
Figure 13. Slump of mixture at different stirring velocities and depths.
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References
This article references 45 other publications.
1. 1
  Qi, C. C.; Chen, Q. S.; Fourie, A.; Zhao, J. W.; Zhang, Q. L. Pressure drop in pipe flow of cemented paste backfill: Experimental and modeling study. Powder Technol. 2018, 333, 9– 18, DOI: 10.1016/j.powtec.2018.03.070
  1
  Pressure drop in pipe flow of cemented paste backfill: Experimental and modeling study
  Qi, Chongchong; Chen, Qiusong; Fourie, Andy; Zhao, Jianwen; Zhang, Qinli
  Powder Technology (2018), 333 (), 9-18CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
  Advances in pipe transportation have contributed significantly to the application of cemented paste backfill (CPB). However, the pressure drop during pipe transportation with complex circuit shapes has not been fully investigated. Currently, research in the field is largely expt.-centered, where extensive test loop expts. need to be performed for a specific CPB material. By comparison, computational modeling of the pressure drop during pipe transportation through complex circuits is still in its infancy and is hindered by the challenges of technique availability and data scarcity. In this article, we present a framework for investigating and modeling the pressure drop of CPB during pipe transportation with complex circuit shapes. A test loop system was used to investigate the pressure drop of CPB under different influencing variables. Based on the exptl. data, gradient boosting regression tree (GBRT) was utilized to develop a prediction model for the CPB pressure drop in the pipe loop. We first discussed the effect of solids content, cement-tailings ratio, inlet pressure, and circuit shape on the CPB pressure drop. The feasibility of GBRT modeling was demonstrated by comparing the predicted pressure drop with the exptl. result on both the training and testing sets. We also investigated the relative importance of influencing variables on the pressure drop of CPB. Harnessing such a modeling approach extends recent efforts to det. the pressure drop during CPB pipe transportation and can significantly accelerate the application of CPB in the future.
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2. 2
  Feng, Y.; Kero, J.; Yang, Q. . X.; Chen, Q. S.; Engström, F.; Samuelsson, C.; Qi, C. C. Mechanical Activation of Granulated Copper Slag and Its Influence on Hydration Heat and Compressive Strength of Blended Cement. Materials. 2019, 12, 772, DOI: 10.3390/ma12050772
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  Mechanical activation of granulated copper slag and its influence on hydration heat and compressive strength of blended cement
  Feng, Yan; Kero, Jakob; Yang, Qixing; Chen, Qiusong; Engstrom, Fredrik; Samuelsson, Caisa; Qi, Chongchong
  Materials (2019), 12 (5), 772CODEN: MATEG9; ISSN:1996-1944. (MDPI AG)
  Mech. activation of granulated copper slag (GCS) is carried out in the present study for the purposes of enhancing pozzolanic activity for the GCS. A vibration mill mills the GCS for 1, 2, and 3 h to produce samples with sp. surface area of 0.67, 1.03 and 1.37 m2/g, resp. The samples are used to replace 30% cement (PC) to get 3 PC-GCS binders. The hydration heat and compressive strength are measured for the binders and deriv. thermogravimetric /thermogravimetric anal. (DTG/TGA), Fourier transform IR spectroscopy (FTIR), and SEM (SEM) are used to characterize the paste samples. It is shown that cumulative heat and compressive strength at different ages of hydration and curing, resp., are higher for the binders blending the GCS milled for a longer time. The compressive strength after 90 d of curing for the binder with the longest milling time reaches 35.7 MPa, which is higher than the strength of other binders and close to the strength value of 39.3 MPa obtained by the PC pastes. The percentage of fixed lime by the binder pastes at 28 days is correlated with the degree of pozzolanic reaction and strength development. The percentage is higher for the binder blending the GCS with longer milling time and higher sp. surface area. The pastes with binders blending the GCS of sp. surface area of 0.67 and 1.37 m2/g fix lime of 15.20 and 21.15%, resp. These results together with results from X-ray diffraction (XRD), FTIR, and SEM investigations demonstrate that the mech. activation via vibratory milling is an effective method to enhance the pozzolanic activity and the extent for cement substitution by the GCS as a suitable supplementary cementitious material (SCM).
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3. 3
  Hu, J. H.; Ren, Q. F.; Ding, X. T.; Jiang, Q. Trans-scale relationship analysis between the pore structure and macro parameters of backfill and slurry. R. Soc. Open Sci. 2019, 6, 190389 DOI: 10.1098/rsos.190389
  3
  Trans-scale relationship analysis between the pore structure and macro parameters of backfill and slurry
  Hu, Jianhua; Ren, Qifan; Ding, Xiaotian; Jiang, Quan
  Royal Society Open Science (2019), 6 (6), 190389CODEN: RSOSAV; ISSN:2054-5703. (Royal Society)
  The characteristics of the porous structure of backfill are directly related to the macro parameters of the flowability of the filling slurry and the mech. features of the backfill, which are fundamental to the study of multiscale mechanics of backfill. Based on the geometry and fractal theory, SEM images of backfill were analyzed by image anal. methods such as OTSU and box counting. The fractal dimension of the pore structure was calcd. By quant. characterizing the pore structure, the trans-scale relationships between the fractal dimension of the pore structure and the macro parameters of the filling slurry were established in terms of equil. shear stress (ESS) and equil. apparent viscosity (EAV). In addn., the correlations between the fractal dimension and macro parameters of backfill were obtained in terms of uniaxial compressive strength (UCS), water content (WC) and porosity. The influence of the microstructure on the macro parameters was discussed. The results show the following: (i) the fractal dimension of the backfill pore structure can characterize the complexity of the structure; (ii) the fractal dimension of the pore structure is neg. correlated with the ESS and EAV of the filling slurry. The UCS of the backfill is pos. correlated with the flowability parameter; (iii) the fractal dimension of the pore structure has a certain correlation with some macro parameters of the backfill, i.e. the fractal dimension is neg. correlated with the UCS and pos. correlated with the WC and (iv) the linear correlations between the pore fractal dimension and UCS and WC are established. The correlation coeff. between the fractal dimension and UCS has an R2 value of 20.638, while the corresponding value of the fractal dimension and WC is 0.604. UCS and WC can be predicted by the fractal dimension of pores.
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4. 4
  Li, S.; Wang, X. . M. Fly-ash-based magnetic coagulant for rapid sedimentation of electronegative slimes and ultrafine tailings. Powder Technol. 2016, 303, 20– 26, DOI: 10.1016/j.powtec.2016.09.016
  4
  Fly-ash-based magnetic coagulant for rapid sedimentation of electronegative slimes and ultrafine tailings
  Li, Shuai; Wang, Xin-min
  Powder Technology (2016), 303 (), 20-26CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
  To accelerate the flocculation and sedimentation of the electroneg. slimes and ultrafine tailings in Sijiaying, a fly-ash-based magnetic coagulant (FMC) was prepd. by leaching fly ash in acid mine drainage. Univariate expts., Plackett-Burman design, steepest-ascent method, and Box-Behnken design were employed to obtain the optimum levels of the factors for the max. settled height (SH). In addn., the action mechanism of FMC was analyzed and the application effects in Sijiaying were evaluated. The results show that the neutralization and magnetic sepn. are the main action mechanism of FMC. Significant economic and environmental benefits will be brought by FMC through reducing the flocculant costs greatly, recycling the overflow water for beneficiation directly, and reusing the fly ash and acid mine drainage environmentally.
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5. 5
  Gao, R. G.; Zhou, K. P.; Zhou, Y. L.; Yang, C. Research on the fluid characteristics of cemented backfill pipeline transportation of mineral processing tailings. Alex. Eng. J. 2020, 59, 4409– 4426, DOI: 10.1016/j.aej.2020.07.047
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6. 6
  Chen, Q. S.; Zhang, Q. L.; Fourie, A.; Xin, C. Utilization of phosphogypsum and phosphate tailings for cemented paste backfill. J. Environ. Manage. 2017, 201, 19– 27, DOI: 10.1016/j.jenvman.2017.06.027
  6
  Utilization of phosphogypsum and phosphate tailings for cemented paste backfill
  Chen, Qiusong; Zhang, Qinli; Fourie, Andy; Xin, Chen
  Journal of Environmental Management (2017), 201 (), 19-27CODEN: JEVMAW; ISSN:0301-4797. (Elsevier Ltd.)
  A review. This research is an investigation of the feasibility of utilizing phosphogypsum (PG) and phosphate tailings (PTS) for cemented paste backfill. Some expts. were conducted with various combinations of PTS and PG as aggregates, along with slags and/or Portland cement as binders and CaO as an additive. The influence of the PG's ageing time on the consolidation of backfill was also explored. The unconfined compressive strength (UCS), the generated gases and the scanning electron microscope (SEM) were all tested and used in the anal. of backfill characteristics. The results show that (i) the highest UCS of backfill prepd. by PG and PTS after curing for either 7 days or 28 days is still less than 1.0 MPa, with a large amt. of CO2 and SO2 generated; (ii) the slags can improve the UCS by a factor of three, but not without a vast generation of CO2, SO2, and H2S. However, the gases were not produced when CaO was added, but the UCS decreases suddenly to 0.2 or 0.4 MPa after curing for 7 days or 28 days, resp.; (iii) the UCS of backfill increases linearly with increasing cement content. When the CaO was added at 2%, the UCS reached 3.36 MPa after curing for 7 days and 4.44 MPa after curing for 28 days, and no gases were generated; (iv) the influence of the PG's ageing time on the UCS is negligible after 4 days of aging. Based on these results, it was concluded that PG and PTS can be utilized as backfill materials when Portland cement is used as a binder and CaO is used as an additive.
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7. 7
  Chen, X.; Shi, X. Z.; Zhou, J.; Chen, Q. S.; Yang, C. Feasibility of Recycling Ultrafine Leaching Residue by Backfill: Experimental and CFD Approaches. Minerals. 2017, 7, 54, DOI: 10.3390/min7040054
  7
  Feasibility of recycling ultrafine leaching residue by backfill: experimental and CFD approaches
  Chen, Xin; Shi, Xiuzhi; Zhou, Jian; Chen, Qiusong; Yang, Chao
  Minerals (Basel, Switzerland) (2017), 7 (4), 54/1-54/13CODEN: MBSIBI; ISSN:2075-163X. (MDPI AG)
  Large amts. of leaching residue are released into tailings dams from mines, and their acid content can cause environmental pollution. The aim of this study was to research the feasibility and value of a leaching residue backfill recycling method. The combination of property detection, lab. tests (the neutralization method, strength test and diffusivity test) and numerical simulation methods (3D computational fluid dynamics (CFD) simulations of pipeline transportation properties) were used to assess the performance of the leaching residue backfill. The results show that backfill body with the cement:sand mass ratio of 1:3, the leaching residue:classified tailings ratio of 1:6, and slurry mass concn. of 71 wt % can meet the strength and pipeline self-flowing transportation requirements of mine backfill. The leaching residue is a good backfill aggregate, and its recovery ratio can reach 19.5 wt %. In addn., the recycling of leaching residue effectively alleviates the problem of mine waste emissions and protects the ecol. environment surrounding the mining area. This study serves as a guide for the recycling of fine tailings and the environmental governance of the mining area.
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8. 8
  Chen, Q. S.; Zhang, Q. L.; Qi, C. C.; Fourie, A.; Xiao, C. C. Recycling phosphogypsum and construction demolition waste for cemented paste backfill and its environmental impact. J. Cleaner Prod. 2018, 186, 418– 429, DOI: 10.1016/j.jclepro.2018.03.131
  8
  Recycling phosphogypsum and construction demolition waste for cemented paste backfill and its environmental impact
  Chen, Qiusong; Zhang, Qinli; Qi, Chongchong; Fourie, Andy; Xiao, Chongchun
  Journal of Cleaner Production (2018), 186 (), 418-429CODEN: JCROE8; ISSN:0959-6526. (Elsevier Ltd.)
  A review. Solid waste management has become an important global issue, and the collection, recycling, and disposal of solid waste have great environmental impacts. This study investigates the feasibility of recycling two different solid wastes, phosphogypsum (PG) and construction demolition waste (CDW), as cemented paste backfill (CPB). The properties of the CPB were first demonstrated through a slump test, setting time detection and unconfined compressive strength (UCS) tests, and microstructural anal. The environmental impact of the PG and CDW-based CPB was investigated through a static leaching expt., a rotary acid leaching procedure, and index detection. A novel backfill system and process was also developed for engineering applications. The results show that (1) the solid concn. of CPB increased from 60 wt% to 70 wt% and the initial/final setting time decreased to 20-30% with the addn. of CDW (from 0 wt% to 40 wt%); (2) the UCS of the CPB samples after 28 days of curing reached 1.74 MPa at 40 wt% CDW proportion, a cement/sand ratio of 1:6, and 70 wt% solid concn.; (3) the CPB samples had a high residual strength (80% of the UCS), indicating d and CDW-based CPB can support an underground stope after failure; and (4) the environmental indexes for the bleed water and leachates of CPB satisfied the category III requirements of China's environmental std. (DZ/T 0290-2015). The results suggest that the proposed technol. is a reliable and environmentally friendly alternative for recycling PG and CDW while simultaneously supporting safe mining.
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9. 9
  Lim, S.-Y.; Chang, H.-J. Development of a high performance static air mixer with a short mixing distance. J. Cleaner Prod. 2019, 224, 686– 696, DOI: 10.1016/j.jclepro.2019.03.245
  There is no corresponding record for this reference.
10. 10
  Gu, Y. Q.; Liu, N. J.; Mou, J.; Zhou, P.; Qian, H.; Dai, D. Study on solid–liquid two-phase flow characteristics of centrifugal pump impeller with non-smooth surface. Adv. Mech. Eng. 2019, 11, 1687814019848269, DOI: 10.1177/1687814019848269
  There is no corresponding record for this reference.
11. 11
  Helmig, R.. Multiphase flow and transport processes in the subsurface: a contribution to the modeling of hydrosystems. Springer-Verlag, 1997.
  There is no corresponding record for this reference.
12. 12
  Liu, H.; Geng, C.; Yang, Z.; Cui, Y.; Yao, M. Effect of Wall Temperature on Acetylene Diffusion Flame–Wall Interaction Based on Optical Diagnostics and CFD Simulation. Energies. 2018, 11, 1264, DOI: 10.3390/en11051264
  12
  Effect of wall temperature on acetylene diffusion flame-wall interaction based on optical diagnostics and CFD Simulation
  Liu, Haifeng; Geng, Chao; Yang, Zhi; Cui, Yanqing; Yao, Mingfa
  Energies (Basel, Switzerland) (2018), 11 (5), 1264/1-1264/15CODEN: ENERGA; ISSN:1996-1073. (MDPI AG)
  In order to elucidate the effect of wall temp. on a diffusion flame-wall interaction, an acetylene diffusion flame in a head-on quenching type was investigated. Direct photog., two-color thermometry, soot-LII (laser-induced incandescence), OH-LIF (laser-induced fluorescence) and numerical simulation with detailed reaction mechanisms were employed to find out the influence mechanism of wall temp. on near-wall combustion performance and emission characteristics. It is clearly shown through optical diagnostics and computation fluid dynamics (CFD) simulation that, compared with cold wall, the high temp. zone for hot wall becomes wider, and the smaller quenching layer is formed due to the higher wall heat flux. High-concn. soot emission is formed primarily near the outer flame far from the wall. CH2O, CO and HC emissions are decreased as wall temp. rises, while the formation of soot and A4 is increased. A diffusion flame-wall interaction structure is proposed to reveal the influence mechanism of wall temp.
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13. 13
  Huang, Y.; Zhuang, Y.; Wan, D. C. Hydrodynamic Study and Performance Analysis of the OC4-DeepCWind Platform by CFD Method. Int. J. Comput. Methods. 2021, 18, 2050020, DOI: 10.1142/S0219876220500206
  There is no corresponding record for this reference.
14. 14
  Liu, C. L.; Zheng, Q.; Wang, Q.; Lin, A. Q.; Jiang, Y. T.; Luo, M. C. Sensitivity Analysis of Multistage Compressor Characteristics Under the Spray Atomization Effect Using a CFD Model. Energies 2019, 12, 301, DOI: 10.3390/en12020301
  There is no corresponding record for this reference.
15. 15
  Drew, D. A.; Lahey, R. T., Jr. Application of general constitutive principles to the derivation of multidimensional two-phase flow equations. Int. J. Multiph. Flow. 1979, 5, 243– 264, DOI: 10.1016/0301-9322(79)90024-7
  There is no corresponding record for this reference.
16. 16
  Dam, J.; Schuck, P. Calculating Sedimentation Coefficient Distributions by Direct Modeling of Sedimentation Velocity Concentration Profiles. Methods Enzymol. 2004, 384, 185– 212, DOI: 10.1016/S0076-6879(04)84012-6
  16
  Calculating sedimentation coefficient distributions by direct modeling of sedimentation velocity concentration profiles
  Dam, Julie; Schuck, Peter
  Methods in Enzymology (2004), 384 (Numerical Computer Methods, Part E), 185-212CODEN: MENZAU; ISSN:0076-6879. (Elsevier)
  A review describes computational approaches for calcg. sedimentation coeff. distributions (c(s)), together with a discussion of exptl. requirements and examples for the application to mixts. of non-interacting and interacting proteins. The development of fast finite element methods for solving the Lamm equation in combination with algebraic techniques for the detection and elimination of systematic noise in sedimentation velocity expts. enabled high-resoln., diffusion deconvoluted c(s). They are solns. of Fredholm integral equations of the first kind, calcd. with max. entropy or Tikhonov-Phillips regularization, and based on approxns. of the relationship between the diffusion and sedimentation coeff. D(s) derived from hydrodynamic considerations. The use of numerical solns. of the Lamm equation in c(s) permits a more flexible and general approach, analogous to continuous parameter distributions well-known in other biophys. techniques, such as dynamic light scattering, fluorescence anisotropy, and optical affinity biosensing.
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17. 17
  Fang, L. P.; Liu, R.; Li, J.; Xu, C. H.; Huang, L. Z.; Wang, D. S. Magnetite/Lanthanum hydroxide for phosphate sequestration and recovery from lake and the attenuation effects of sediment particles. Water Res. 2018, 130, 243– 254, DOI: 10.1016/j.watres.2017.12.008
  17
  Magnetite/Lanthanum hydroxide for phosphate sequestration and recovery from lake and the attenuation effects of sediment particles
  Fang, Liping; Liu, Ru; Li, Ji; Xu, Cuihong; Huang, Li-Zhi; Wang, Dongsheng
  Water Research (2018), 130 (), 243-254CODEN: WATRAG; ISSN:0043-1354. (Elsevier Ltd.)
  An effective approach for eutrophication control and phosphate recovery remains a longstanding challenge. Herein, we present a new technique for phosphate sequestration in lake and phosphate recovery using novel magnetically recoverable magnetite/lanthanum hydroxide [M-La(OH)3] hybrids that can be prepd. using a simple one-pot synthesis method. Batch studies show that M-La(OH)3 exhibits a strong sorption towards phosphate with sorption capacities of up to 52.7 mg-P/g at pH 7.0 in water. A simple model indicates that the efficiency of M-La(OH)3 for phosphate sequestration in lake is significantly attenuated by 34-45% compared to that in water, due to interference from sediment particles. However, our results demonstrate that sediments suspensions mixed with a M-La(OH)3 content of 1-3% exhibit a capability of up to 1.2 mg-P/g for sequestering external phosphate compared with that of 0.2 mg-P/g for pristine sediment at pH 7.3. M-La(OH)3-mixed sediment suspensions appear to effectively sequester phosphate over an environmentally relevant pH range from 4 to 8.5. Phosphorus (P) fractionation expts. indicate that the enhanced phosphate sorption by M-La(OH)3-mixed sediment suspensions is mainly due to the increased fractions of NaOH-P and inorg. P. This work indicates that the M-La(OH)3 has the potential for phosphate sequestration and recovery from lake.
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18. 18
  Kang, L.; Guo, L. Eulerian–Lagrangian simulation of aeolian sand transport. Powder Technol. 2006, 162, 111– 120, DOI: 10.1016/j.powtec.2005.12.002
  18
  Eulerian-Lagrangian simulation of aeolian sand transport
  Kang, Liqiang; Guo, Liejin
  Powder Technology (2006), 162 (2), 111-120CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
  A numerical investigation of eolian sand transport is performed with an Eulerian-Lagrangian model. In this model, the gas phase is described by the vol.-averaged Navier-Stokes equations of two-phase flow. The particle motion is obtained by solving Newton's second law of motion taking into account the interparticle collisions, where a soft sphere model is used to describe interparticle collisions. The dynamic process of eolian sand transport is simulated. The simulation results show that the variation of mean horizontal velocity of the particles with height can be expressed by a logarithmic function or a power function at h > 0.02 m, and the power function can be described below 0.02 m. The sand mass flux decreases exponentially with height for h > 0.02 m, but there is a deviation from the exponential decay due to the creep grains in the near-bed region. It is also shown that the inter-particle collisions play an important role in sand saltation. Therefore the present numerical model is capable of being applied to the study of windblown sand movement.
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19. 19
  Zheng, J. X.; Li, Y. K.; Wan, Z. Q.; Hong, W. P.; Wang, L. Modification of the agglomeration kernel and simulation of the flow pattern in acoustic field with fine particles. Powder Technol. 2019, 356, 930– 940, DOI: 10.1016/j.powtec.2019.09.022
  19
  Modification of the agglomeration kernel and simulation of the flow pattern in acoustic field with fine particles
  Zheng, Jianxiang; Li, Yukai; Wan, Zongqun; Hong, Wenpeng; Wang, Long
  Powder Technology (2019), 356 (), 930-940CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
  This paper studies the acoustic agglomeration of fine particles of the coal fly ash in the acoustic field agglomeration device, based on the coupling population balance model (PBM) for acoustic agglomeration of fine particles and the modified kinetic theory of the fine particle flow. The new root mean square of the agglomeration kernel function operates according to the acoustic agglomeration mechanism. We present the theor. investigation of the problem and then compare it with exptl. results. The results show that the agglomeration process of particles in different size ranges is dominated by different agglomeration mechanisms. Moreover, we show the numerical simulation of the acoustic agglomeration process of the particles using the new agglomeration kernel function, which is consistent with the exptl. results. In addn., the particle flow in the acoustic field agglomeration device presents a typical turbulent structure, and a large particle agglomeration occurs near the wall and outlet.
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20. 20
  Li, L.; Qi, H.; Yin, Z. C.; Li, D. F.; Zhu, Z. L.; Tangwarodomnukun, V.; Tan, D. P. Investigation on the multiphase sink vortex Ekman pumping effects by CFD-DEM coupling method. Powder Technol. 2020, 360, 462– 480, DOI: 10.1016/j.powtec.2019.06.036
  20
  Investigation on the multiphase sink vortex Ekman pumping effects by CFD-DEM coupling method
  Li, Lin; Qi, Huan; Yin, Zichao; Li, Daifeng; Zhu, Zhiliang; Tangwarodomnukun, Viboon; Tan, Dapeng
  Powder Technology (2020), 360 (), 462-480CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
  The gas-liq.-solid multiphase sink vortex is a complex turbulent mech. phenomenon, in which the pumping effects of Ekman boundary layer involved in the above process has the important scientific value and engineering significance. To address the matter, a coupled Computational Fluid Dynamic and Discrete Element Method (CFD-DEM) method for the simulation of the multiphase sink vortex is proposed based on the realizable k-ε turbulent model and the soft sphere model. The suction and extn. regularities of gas-liq. coupling process are analyzed to reveal the matter transfer mechanism of Ekman boundary layer. Then, the phenomenon for the particle sucked by sink vortex is investigated to obtain the Ekman pumping effects. Finally, the influences of Ekman pumping effects on particles with respect to different densities are studied to verify the validity and reliability of the proposed method. Numerical results demonstrate that the suction and extn. intensities constitute a data set that is dependent on the initial disturbance components; there is an apparent upwelling phenomenon in the liq. boundary layer, which is caused by the spiral coupling structure of Ekman boundary layer. The Ekman pumping process for particles has three typical stage: Ekman suction-extn. state, Ekman horizontal pumping state, and Ekman upwelling state, wherein the flow patterns are dominated by the initial disturbance and appear a complex nonlinear turbulence features; with the particle d. increasing, the effects of Ekman suction-extn. state and horizontal pumping state are enhanced, but the Ekman upwelling effect for particle has apparent decreased.
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21. 21
  Kasbaoui, M. H.; Koch, D. L.; Desjardins, O. Clustering in Euler–Euler and Euler–Lagrange simulations of unbounded homogeneous particle-laden shear. J. Fluid Mech. 2019, 859, 174– 203, DOI: 10.1017/jfm.2018.796
  21
  Clustering in Euler-Euler and Euler-Lagrange simulations of unbounded homogeneous particle-laden shear
  Kasbaoui, M. Houssem; Koch, Donald L.; Desjardins, Olivier
  Journal of Fluid Mechanics (2019), 859 (), 174-203CODEN: JFLSA7; ISSN:0022-1120. (Cambridge University Press)
  Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle vol. fractions, the two-way coupling can be significant due to the large particle to gas d. ratio. In this semi-dil. regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The anal. of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concn. of inertial particles in the stretching regions of the flow leads to the formation of highly concd. particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh-Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler-Lagrange formalism are compared to Euler-Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.
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22. 22
  Liu, Y.; Ersson, M.; Liu, H.; Jönsson, P.; Gan, Y. Comparison of Euler-Euler Approach and Euler–Lagrange Approach to Model Gas Injection in a Ladle. Steel Res. Int. 2019, 90, 1800494, DOI: 10.1002/srin.201800494
  There is no corresponding record for this reference.
23. 23
  Li, P.; Lan, X. Y.; Xu, C. M.; Wang, G.; Lu, C. X.; Gao, J. S. Drag models for simulating gas–solid flow in the turbulent fluidization of FCC particles. Particuology. 2009, 7, 269– 277, DOI: 10.1016/j.partic.2009.03.010
  There is no corresponding record for this reference.
24. 24
  McKeen, T.; Pugsley, T. Simulation and experimental validation of a freely bubbling bed of FCC catalyst. Powder Technol. 2003, 129, 139– 152, DOI: 10.1016/S0032-5910(02)00294-2
  24
  Simulation and experimental validation of a freely bubbling bed of FCC catalyst
  McKeen, Tim; Pugsley, Todd
  Powder Technology (2003), 129 (1-3), 139-152CODEN: POTEBX; ISSN:0032-5910. (Elsevier Science B.V.)
  A validation and mesh refinement study was performed for the simulation of a freely bubbling bed of fluid catalytic cracking (FCC) catalyst operating at superficial gas velocities in the range of 0.05 to 0.20 m/s, using the two-fluid computational fluid dynamics (CFD) code Multiphase Flow with Interphase eXchanges (MFIX). The simulation results were compared to exptl. data collected using an elec. capacitance tomog. (ECT) imaging system as well as data from the literature. A comparison was made based on the bed expansion, and bubble diams. and rise velocities. A novel method was used to ext. bubble properties from ECT data and simulation results. A modified gas-solids drag law, corresponding to an effective particle agglomerate diam. in the range of 135 to 170 μm for FCC particles of actual 75 μm mean diam., was required to adequately predict the fluidization behavior obsd. exptl. These findings support the argument that cohesive interparticle forces lead to agglomeration of FCC catalyst powder and significantly affect the fluidization quality. The model is the first presented in the open literature to successfully apply CFD to obtain realistic predictions of FCC bubbling bed behavior.
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25. 25
  Yang, N.; Wang, W.; Ge, W.; Li, J. H. CFD simulation of concurrent-up gas–solid flow in circulating fluidized beds with structure-dependent drag coefficient. Chem. Eng. J. 2003, 96, 71– 80, DOI: 10.1016/j.cej.2003.08.006
  25
  CFD simulation of concurrent-up gas-solid flow in circulating fluidized beds with structure-dependent drag coefficient
  Yang, Ning; Wang, Wei; Ge, Wei; Li, Jinghai
  Chemical Engineering Journal (Amsterdam, Netherlands) (2003), 96 (1-3), 71-80CODEN: CMEJAJ; ISSN:1385-8947. (Elsevier Science B.V.)
  Meso-scale structure existing in the form of particle clusters or strands in concurrent-up gas-solid two-phase flow has been extensively corroborated in exptl. research. However, its significant effects on interfacial drag coeff. are seldom taken into account in current computational fluid dynamic (CFD) simulations by using the two-fluid models. The energy-minimization multi-scale (EMMS) approach, in which the heterogeneous structure is described by the so-called multi-scale resoln. and energy-minimization method, is adapted for investigating the dependence of drag coeff. on structure parameters. The structure-dependent drag coeffs. calcd. from the EMMS approach are then incorporated into the two-fluid model to simulate the behavior of the concurrent-up gas-solid flow in a riser. Simulation results indicate that the simulated solid concn. with the Wen and Yu/Ergun drag correlations is rather dil., leading to a more homogeneous structure; while the dynamic formation and dissoln. of clusters can be captured with the drag correlations derived from the EMMS approach, and the simulated outlet solid flux and voidage profile in both radial and axial directions are in reasonable agreement with exptl. results, suggesting the feasibility for the EMMS approach to be used as a sub-grid closure law for drag coeff.
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26. 26
  Zhou, K. P.; Gao, R. G.; Gao, F. Particle Flow Characteristics and Transportation Optimization of Superfine Unclassified Backfilling. Minerals. 2017, 7, 6, DOI: 10.3390/min7010006
  26
  Particle flow characteristics and transportation optimization of superfine unclassified backfilling
  Zhou, Ke-ping; Gao, Rugao; Gao, Feng
  Minerals (Basel, Switzerland) (2017), 7 (1), 6/1-6/21CODEN: MBSIBI; ISSN:2075-163X. (MDPI AG)
  In order to investigate the high vol. fraction problem of the solid phase in superfine unclassified backfilling pipeline transportation, characteristic parameters were obtained by fitting to test data with an R-R particle size distribution function; then, a Euler dense-phase DPM (Discrete phase model) model was established by applying solid-liq. two-phase flow theory and the kinetic theory of granular flow (KTGF). The collision and friction of particles were imported by the UDF (User-define function) function, and the pipeline fluidization system, dominated by interphase drag forces, was analyzed. The best concn. and flow rate were finally obtained by comparing the results of the stress conditions, flow field characteristics, and the discrete phase distributions. It is revealed that reducing the concn. and flow rate could control pressure loss and pipe damage to a certain degree, while lower parameters show neg. effects on the transportation integrity and backfilling strength. Indoor tests and field industrial tests verify the reliability of the results of the numerical simulations. Research shows that the model optimization method is versatile and practical for other, similar, complex flow field working conditions.
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27. 27
  Whittaker, P.; Wilson, C.; Aberle, J.; Rauch, H. P.; Xavier, P. A drag force model to incorporate the reconfiguration of full-scale riparian trees under hydrodynamic loading. J. Hydraul. Res. 2013, 51, 569– 580, DOI: 10.1080/00221686.2013.822936
  There is no corresponding record for this reference.
28. 28
  Ren, W. C.; Wang, S. H.; Gao, R. G.; Qiao, D. P. Operational process simulation and optimization of a continuous-discharge system in a backfilling system. Mater. Tehnol. 2019, 53, 101, DOI: 10.17222/mit.2018.181
  There is no corresponding record for this reference.
29. 29
  Zhu, K., Xu, L.. 2016. Handbook of Building Material Machinery Industry, Wuhan University of Technology Press, Wuhan.
  There is no corresponding record for this reference.
30. 30
  Nguyen, V.-D.; Heo, W.-H.; Kubuya, R.; Lee, C.-W. Pressurization Ventilation Technique for Controlling Gas Leakage and Dispersion at Backfilled Working Faces in Large-Opening Underground Mines: CFD Analysis and Experimental Tests. Sustainability. 2019, 11, 3313, DOI: 10.3390/su11123313
  There is no corresponding record for this reference.
31. 31
  Tyson, W. C.; Roy, C. J. A higher-order error estimation framework for finite-volume CFD. J. Comput. Phys. 2019, 394, 632– 657, DOI: 10.1016/j.jcp.2019.06.017
  There is no corresponding record for this reference.
32. 32
  Mohammed, H. A.; Fathinia, F.; Vuthaluru, H. B.; Liu, S. CFD based investigations on the effects of blockage shapes on transient mixed convective nanofluid flow over a backward facing step. Powder Technol. 2019, 346, 441– 451, DOI: 10.1016/j.powtec.2019.02.002
  32
  CFD based investigations on the effects of blockage shapes on transient mixed convective nanofluid flow over a backward facing step
  Mohammed, Hussein A.; Fathinia, F.; Vuthaluru, Hari B.; Liu, Shaomin
  Powder Technology (2019), 346 (), 441-451CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
  The sepn. and reattachment flow occurs in a backward-facing step (BFS) is available in various industrial applications such as gas turbine engines, combustors, aircraft, buildings and many other devices of heat transfer. It represents the pillar key of detg. the flow structure and significantly affecting the heat transfer mechanism. This work studies numerically the effects of four various types of blockage shapes on transient laminar mixed convective nanofluid flow over a horizontal BFS placed in a duct. Nanoparticles of SiO2 with ethylene glycol as a base fluid at 2% of vol. fraction and 20 nm of nanoparticle diam. are considered to examine the effect of different blockage shape on the thermal and flow fields at different time scales. The downstream of the step is kept at a const. heat flux of 500 W/m2, while other walls and sides of the duct are considered thermally insulated. The Reynolds no. used in this study is in the range of 50-200. The relevant governing equations (continuity, momentum and energy) along with the boundary conditions are solved with the aid of finite vol. method (FVM). The results reveal that after dimensionless time of τ = 5 the trend of nanofluid flow and recirculation area near the step and behind the blockage shape does not change significantly and this time is selected as a quasi-steady state time and the point of comparison. The velocity distributions for front facing triangular blockage decreased and this blockage shape has the highest value of skin friction coeff. beyond Re = 150. The results indicate that the front facing triangular blockage has the highest value of av. Nusselt no. and performance evaluation index while the trapezoidal blockage has the lowest value.
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33. 33
  Li, P.; Zhang, X. H.; Lu, X. B. Three-dimensional Eulerian modeling of gas–liquid–solid flow with gas hydrate dissociation in a vertical pipe. Chem. Eng. Sci. 2019, 196, 145– 165, DOI: 10.1016/j.ces.2018.10.053
  33
  Three-dimensional Eulerian modeling of gas-liquid-solid flow with gas hydrate dissociation in a vertical pipe
  Li, Peng; Zhang, Xuhui; Lu, Xiaobing
  Chemical Engineering Science (2019), 196 (), 145-165CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
  The pipe transportation of gas hydrate-bearing sediments (GHBS) GHBS-gas hydrate-bearing sediments is one of the key problems in mech.-thermal exploitation of gas hydrate (GH) GH-gas hydrate in marine stratum. It is a gas-liq.-solid (methane gas-seawater-GHBS particles) three-phase flow, accompanied by GH dissocn. In this study, a three-dimensional Eulerian model combined with the kinetic theory of granular flow (KTGF) was adopted to simulate the gas-liq.-solid flow with GH dissocn. The com. CFD software FLUENT 16.2 was employed, considering the hydrodynamics, heat and mass transfer, and GH dissocn. simultaneously. A kinetic model for GH dissocn. in the GHBS particles is presented, considering the effect of multiphase flow on dissocn. rate. The model can capture the transition from the initial liq.-solid two-phase flow to gas-liq.-solid three-phase flow, describing the distribution of the phase vol. fraction, velocity, temp., and dissocn. rate. The interaction between GH dissocn. and multiphase flow is discussed. The simulation results indicate that the continuous prodn. of gas bubbles by GH dissocn. leads to more violent fluctuations in the pressure gradient and a more marked elevation of the solid particles compared with the liq.-solid two-phase flow without GH dissocn. In addn., the effect of GH dissocn. on the multiphase flow under different hydrate saturations was analyzed.
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34. 34
  Chamani, H.; Matsuura, T.; Rana, D.; Lan, C. Q. Examination of the bubble gas transport method to estimate the membrane pore size distribution. Desalination 2022, 531, 115714 DOI: 10.1016/j.desal.2022.115714
  34
  Examination of the bubble gas transport method to estimate the membrane pore size distribution
  Chamani, Hooman; Matsuura, Takeshi; Rana, Dipak; Lan, Christopher Q.
  Desalination (2022), 531 (), 115714CODEN: DSLNAH; ISSN:0011-9164. (Elsevier B.V.)
  The pore size distribution (PSD) of the membrane is often measured by the bubble gas transport method. However, the method is not free from some concerns over its accuracy. In the present work, two questions are raised; (1) the validity of the computational procedure commonly used to calc. PSD (2) the validity of the assumption that all pores are open to gas transport in the linear part of the flow rate vs. pressure curve. To answer these questions, the flow rate vs. pressure lines were generated rigorously based on a given PSD by the model that we have recently developed, and using the lines so produced, the PSD was back-calcd. It was found that the agreement of original PSD and the back-calcd. PSD is reasonable when the PSD is narrow, but when the PSD is broad, the back-calcd. PSD shifts toward the larger pore sizes. It was also found that the calcd. PSD is slightly affected when some small pores are not included in the linear part of flow rate vs. pressure wet-line.
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35. 35
  Chamani, H.; Matsuura, T.; Rana, D.; Lan, C. Q. Transport characteristics of liquid-gas interface in a capillary membrane pore. J. Memb. Sci. 2020, 611, 118387, DOI: 10.1016/j.memsci.2020.118387
  35
  Transport characteristics of liquid-gas interface in a capillary membrane pore
  Chamani, Hooman; Matsuura, Takeshi; Rana, Dipak; Lan, Christopher Q.
  Journal of Membrane Science (2020), 611 (), 118387CODEN: JMESDO; ISSN:0376-7388. (Elsevier B.V.)
  Interface displacement of two phases mainly caused by replacement of one fluid with another one can occur inside the membrane pore during membrane prepn. and characterization. This phenomenon is exemplified by measurement of liq. entry pressure (LEP) in membrane distn., measurement of pore size and pore size distribution by the bubble point method, measurement of pore size and pore size distribution by porometry, wetting of dry membrane and also drying of wet membrane. In most of the theor. studies, focus was on the transmembrane pressure required for one phase to enter into the membrane pores filled with another phase and little attention was paid to the movement of interface in the capillary. This paper attempts to discuss quant. the movement of interface, water/air interface in particular. Therefore, movement of interface was tracked using a well-founded model and consequently the pressure and velocity at the interface and the required time for replacement were studied. In addn., the influence of different parameters including pore radius, contact angle, and membrane thickness was assessed. It was found that the low resistance for the air flow, assumed in Washburn's equation, can be justified as an approxn. Moreover, the model proposed in this work can predict that the pressure at the water/air interface (when air replaces liq. water) may become significantly lower than the atm. pressure at the pore exit, causing pore shrinkage. As well, the pressure at the air/water interface (when liq. water replaces air) may become significantly higher than the feed pressure applied at the pore entrance, causing pore expansion.
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36. 36
  Rana, D.; Matsuura, T.; Lan, C. Q. Work needed to force the water-air interface down in the re-entrant structured capillary pore. Desalination 2022, 541, 116058 DOI: 10.1016/j.desal.2022.116058
  36
  Work needed to force the water-air interface down in the re-entrant structured capillary pore
  Rana, Dipak; Matsuura, Takeshi; Lan, Christopher Q.
  Desalination (2022), 541 (), 116058CODEN: DSLNAH; ISSN:0011-9164. (Elsevier B.V.)
  The re-entrant structure of the membrane surface has attracted researchers' attention recently, due to its ability to make the membrane surface more wetting resistant-either in water or in liqs. of low surface tension. The underlying principle of this approach is that an energy barrier has to be overcome when the transition occurs from the Cassie Baxter state to the Wenzel state of the rough membrane surface, which prevents the passage of liq. through the membrane pore. In this work, the energy barrier was evaluated for the cone-shaped pore based on Young's theory of the capillary force. It was found that the energy barrier is enhanced by increasing the angle of the apex of the cone, the pore length, and the contact angle. The effects of the first two geometrical factors, the angle of apex of cone and pore length, are much stronger than the effect of the contact angle. It is believed that this work will offer a guideline for the rational membrane design to reduce, and even prevent, the pore wetting of membranes, particularly for oil/water sepn. and membrane distn.
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37. 37
  Qtaishat, M. R.; Chamani, H.; Matsuura, T.; Rana, D.; Lan, C. Q. Modeling of the movement of two immiscible liquids in membrane pores. Int. J. Multiph. Flow. 2022, 157, 104282 DOI: 10.1016/j.ijmultiphaseflow.2022.104282
  There is no corresponding record for this reference.
38. 38
  Tomiyama, A.; Tamai, H.; Zun, I.; Hosokawa, S. Transverse migration of single bubbles in simple shear flows. Chem. Eng. Sci. 2002, 57, 1849– 1858, DOI: 10.1016/S0009-2509(02)00085-4
  38
  Transverse migration of single bubbles in simple shear flows
  Tomiyama, Akio; Tamai, Hidesada; Zun, Iztok; Hosokawa, Shigeo
  Chemical Engineering Science (2002), 57 (11), 1849-1858CODEN: CESCAC; ISSN:0009-2509. (Elsevier Science Ltd.)
  Trajectories of single air bubbles in simple shear flows of glycerol-water soln. were measured to evaluate transverse lift force acting on single bubbles. Expts. were conducted under the conditions of -5.5 ≤ log10 M ≤ -2.8, 1.39 ≤ Eo ≤ 5.74 and 0 ≤ |dVL/dy| ≤ 8.3 s-1, where M is the Morton no., Eo the Eotvos no., and dVL/dy the velocity gradient of the shear flow. A net transverse lift coeff., CT, was evaluated by making use of all the measured trajectories and an equation of bubble motion. It was confirmed that CT for small bubbles is a function of the bubble Reynolds no. Re, whereas CT for larger bubbles is well correlated with a modified Eotvos no. Eod which employs the max. horizontal dimension of a deformed bubble as a characteristic length. An empirical correlation of CT was therefore summarized as a function of Re and Eod. The crit. bubble diam. causing the radial void profile transition from wall peaking to core peaking in an air-water bubbly flow evaluated by the proposed CT correlation coincided with available exptl. data.
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39. 39
  Hosokawa, S.; Tomiyama, A. Multi-fluid simulation of turbulent bubbly pipe flows. Chem. Eng. Sci. 2009, 64, 5308– 5318, DOI: 10.1016/j.ces.2009.09.017
  39
  Multi-fluid simulation of turbulent bubbly pipe flows
  Hosokawa, Shigeo; Tomiyama, Akio
  Chemical Engineering Science (2009), 64 (24), 5308-5318CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
  Radial distributions of void fraction, bubble aspect ratio, phasic velocities, and turbulent kinetic energy in bubbly pipe flows are measured using an image processing method and a laser Doppler velocimetry. Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows. The exptl. results indicate that aspect ratio of bubbles in the near wall region takes a higher value than that of free rising bubbles due to the presence of wall, and that the change in the aspect ratio induces decrease in relative velocity between bubbles and liq. in the near wall region. Drag coeff., CD, of a bubble in a bubbly pipe flow tends to increase with magnitude of shear flow, and the effect of shear flow on CD is estd. by the correlation proposed by D. Legendre and J. Magnaudet (1998). Comparison between the simulated and the measured results indicate that the effects of bubble shape and shear flow on drag force acting on bubbles should be taken into account for accurate predictions of bubbly pipe flows. The turbulence models proposed by M. Lopez de Bertodano et al.(1994) and by S. Hosokawa and A. Tomiyama (2004) give good predictions for turbulence modification caused by bubbles.
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40. 40
  Tomiyama, A.; Celata, G. P.; Hosokawa, S.; Yoshida, S. Terminal velocity of single bubbles in surface tension force dominant regime. Int. J. Multiph. Flow. 2002, 28, 1497– 1519, DOI: 10.1016/S0301-9322(02)00032-0
  There is no corresponding record for this reference.
41. 41
  Chen, J.; Hayashi, K.; Hosokawa, S.; Tomiyama, A. Drag correlations of ellipsoidal bubbles in clean and fully contaminated systems. Multiph. Sci. Technol. 2019, 31, 215– 234, DOI: 10.1615/multscientechn.2019031210
  There is no corresponding record for this reference.
42. 42
  Chen, Y. Simulation and experimental investigation of power consumption, gas dispersion and mass transfer coefficient in a multi-phase stirred bioreactor. Braz. J. Chem. Eng. 2019, 36, 1439– 1451, DOI: 10.1590/0104-6632.20190364s20180450
  42
  Simulation and experimental investigation of power consumption, gas dispersion and mass transfer coefficient in a multi-phase stirred bioreactor
  Chen, Yuanfeng
  Brazilian Journal of Chemical Engineering (2019), 36 (4), 1439-1451CODEN: BJCEFZ; ISSN:1678-4383. (Brazilian Society of Chemical Engineering)
  Bio-oxidn. leaching of refractory gold conc. was carried out in a typical gas-liq.-solid three-phase stirred bioreactor. The bacteria, which adhered to solid particle surfaces and spread over the liq. phase, require sufficient oxygen and nutrient of carbon and nitrogen, and then the mass transfer rate should be considered. However, the mass transfer coeff., which could be used to evaluate the mass transfer rate, was detd. by gas holdup, bubble diam. and power consumption. Therefore, a three-phase Eulerian equation with k-e turbulence model and addnl. models of two bubble diam., a torque and a mass transfer coeff. were applied in the simulation. The simulation results were validated with exptl. data and used to analyze the spatial distribution of the mass transfer coeff. The results demonstrated that the simulation and exptl. data of Sauter mean bubble diam. and power no. were in good agreement and the simulation results of the mass transfer coeff. were agree with the values calcd. by an empirical correlation. The Davoody model can be strongly recommended for further simulation of the bubble diam., and the gas holdup and mass transfer coeff. were very unevenly distributed in the lower zone. Hence, the lower impeller clearance should be considered.
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43. 43
  Tsuchiya, K.; Furumoto, A.; Fan, L.-S.; Zhang, J. P. Suspension viscosity and bubble rise velocity in liquid-solid fluidized beds. Chem. Eng. Sci. 1997, 52, 3053– 3066, DOI: 10.1016/S0009-2509(97)00127-9
  43
  Suspension viscosity and bubble rise velocity in liquid-solid fluidized beds
  Tsuchiya, Katsumi; Furumoto, Akihiko; Fan, Liang-Shih; Zhang, Jianping
  Chemical Engineering Science (1997), 52 (18), 3053-3066CODEN: CESCAC; ISSN:0009-2509. (Elsevier)
  The effective viscosity which characterizes the pseudo-homogeneous property of the liq.-solid suspension in gas-liq.-solid fluidization is examd. in light of the velocity of single bubbles rising through the suspension. Expts. conducted in this study cover a wide range of bubble diams. (2-23 mm) under high solids holdup (0.48-0.57) conditions. The study reveals that the liq.-solid medium exhibits a homogeneous, Newtonian property at any given solids holdup when the bubble diams. are greater than 12-17 mm. The effective viscosities obtained in this study based on equivalency of the single bubble rise velocity in Newtonian media as well as those reported in the literature are found to follow the Mooney-type relation for solids holdup dependence. The two parameters underlying this relation can be correlated as a function of the particle terminal velocity, particle shape and packed solids holdup. When the bubble diams. are smaller than 12-17 mm, the effective viscosity of the liq.-solid medium deviates from the viscosity of the corresponding Newtonian liq. The deviation which marks the redn. in the bubble rise velocity reflects a significant close-range interaction between particles. In this bubble size range, the liq.-solid medium exhibits a non-Newtonian property characterized by shear-thinning behavior with flow index ≈ 1/2.
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44. 44
  Booth, C. P.; Leggoe, J. W.; Aman, Z. M. The use of computational fluid dynamics to predict the turbulent dissipation rate and droplet size in a stirred autoclave. Chem. Eng. Sci. 2019, 196, 433– 443, DOI: 10.1016/j.ces.2018.11.017
  44
  The use of computational fluid dynamics to predict the turbulent dissipation rate and droplet size in a stirred autoclave
  Booth, Craig P.; Leggoe, Jeremy W.; Aman, Zachary M.
  Chemical Engineering Science (2019), 196 (), 433-443CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
  The prediction of droplet sizes in emulsions is important for fields ranging from the chem. process industry to emergency planning in the event of an underwater oil release. Typically scale models have needed to be built and the results scaled up, but as computational resources have grown and turbulence models have matured it has become possible to use computational fluid dynamics (CFD) to simulate the behavior of the fluid/s. While direct simulation of multiphase breakup at high Reynolds no. is currently computationally impractical, this paper looks into the use of CFD along with a correlation function based on max. turbulent kinetic energy dissipation rate to predict the Sauter mean diam. of drops in a 1 in. baffle-and-vane type autoclave. The results show that using a RNG-kε turbulence model with a simplified 2D geometry gave drop sizes within 26.2 μm of the Sauter mean diam. obsd. in expts. with no addnl. tuning of parameters. Correlating pipe and autoclave flows through the Reynolds no. and the turbulent kinetic energy dissipation rate was also investigated. Using the traditional definitions of the Reynolds nos. the correlation is poor, the coeff. of detn. of the linear fit to the log-log data is 0.64. The first modification replaced the diam. of the blade as characteristic length with the tip swept circumference which increased the coeff. of detn. to 0.960. A further modification using data obtained from the turbulent fields of the simulation showed a significant improvement with the coeff. of detn. increasing to 0.988.
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45. 45
  Feng, Q.; Ge, R.; Sun, Y. Q.; Fang, F.; Luo, J. Y.; Xue, Z. X.; Cao, J. S.; Li, M. Revealing hydrodynamic effects on flocculation performance and surface properties of sludge by comparing aeration and stirring systems via computational fluid dynamics aided calculation. Water Res. 2020, 172, 115500 DOI: 10.1016/j.watres.2020.115500
  45
  Revealing hydrodynamic effects on flocculation performance and surface properties of sludge by comparing aeration and stirring systems via computational fluid dynamics aided calculation
  Feng, Qian; Ge, Ran; Sun, Yaqing; Fang, Fang; Luo, Jingyang; Xue, Zhaoxia; Cao, Jiashun; Li, Ming
  Water Research (2020), 172 (), 115500CODEN: WATRAG; ISSN:0043-1354. (Elsevier Ltd.)
  The effects of aeration and stirring systems on the phys. properties of sludge were analyzed using a computational fluid dynamics (CFD) model. The aims of this study were to (1) compare the effects of aeration and stirring on sludge properties using the same turbulent mixing intensity, and (2) to reveal the relationship between sludge properties and hydrodynamic indicators to det. how hydrodynamic conditions influence sludge flocculation. Mixing expts. with stirring and aeration were carried out in 2-L beakers with the av. velocity gradient (G) set to 90, 190, or 280 s-1. The sludge flocculation performance, zeta potential, and Gibbs free energy (ΔG) were analyzed and the flow velocity, turbulence energy, turbulence dissipation rate, and Kolmogorov microscale were calcd. as hydrodynamic parameters. The av. flow velocity and the turbulence dissipation rate were obviously higher in the stirring system than in the aeration system at the same G. However, the turbulence energy and Kolmogorov microscale in the aeration system were much higher than those in the stirring system. Both the zeta potential and ΔG were lower in the aeration system than the stirring system. The zeta potential and ΔG results for the two systems suggest that aeration is more beneficial for sludge flocculation than stirring even though the sludge flocculation performance F/F0 in the stirring and aeration systems showed no obvious differences. Significant relationships between hydrodynamic parameters calcd. based on the CFD model and av. values of sludge properties in the stable phase showed that the Kolmogorov microscale, av. flow velocity, and turbulence energy were appropriate hydrodynamic parameters for evaluating the flocculation performance F/F0, zeta potential, and ΔG, resp.
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Optimization of a Multiphase Mixed Flow Field in Backfill Slurry Preparation Based on Multiphase Flow InteractionClick to copy article linkArticle link copied!

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1. Introduction

2. Materials and Methods

2.1. Analysis of Structural Performance of the Double-Shaft Mixer

2.2. Calculation Equation of the Gas–Liquid Interaction System

2.2.1. Two-Fluid Characteristic Equation

2.2.2. Discretization of Transient Dynamic Equations

2.2.3. Interphase Interaction

Figure 1

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3. Results and Discussion

3.1. Reliability Analysis of Gas Liquid Interaction Simulation

Figure 4

3.1.1. Standard S-N Model

3.1.2. Modified S-N Model

3.1.3. Tsuchiya Model

Figure 5

3.2. Case Analysis on Performance Optimization of the Double-Shaft Mixer

3.2.1. Influence of Different Blade Installation Angles on the Flow Field

Figure 6

Figure 7

Figure 8

3.2.2. Influence of Different Rotation Velocity on the Flow Field

Figure 9

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Figure 11

4. Experimental Validation

Figure 12

Figure 13

5. Conclusions

Author Information

Acknowledgments

References

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Abstract

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Optimization of a Multiphase Mixed Flow Field in Backfill Slurry Preparation Based on Multiphase Flow Interaction
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