Numerical analysis of dilute gas-solid flows in a horizontal pipe and a 90° bend coupled with a newly developed drag model

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Abstract

The influence of particle concentration on the drag force of a particle deserves attention when using the Lagrangian Particle Tracking methods for the prediction of industrial type gas-solid flows. The Lagrangian approach is best suited to applications where the solids volume fraction is low, and the effect of particle concentration can be ignored. In the present work, a 3D time dependent numerical analysis is performed to study the effect of Lagrangian model improvements to replicate experimental studies of straight horizontal pipe flow and flow through a 90° horizontal-to-vertical bend. The present predictions are compared with published experimental data of Tsuji and Morikawa (1982), and Yilmaz (1997). Special attention is paid to influence of particle mass-flow rates and conveying velocity on the particle motion within the system. This study used a CFX-4 package, where the ability to modify the code was necessary to include particle model improvements. These improvements included implementing a newly drag force model developed as a part of this research work. Particle-wall collision and particle-particle collision models developed by Sommerfeld (1992), and Sommerfeld (2001) are also implemented in the CFD model. The standard k–ε dispersed turbulence model was utilized as the predictions for the gas phase only gave similar predicted axial velocity compared to the more computationally demanding Reynolds stress model. The results showed that the inclusion of the various improvements lead to reasonable predicted particle velocities in both the upper and lower regions of the straight horizontal pipe which denote the dilute and dense regions respectively. It was also found that the inclusion of the rough-wall particle wall collision model decreases the axial particle velocity in the lower region where the bulk of the particle wall collisions occur. While the inclusion of the particle collision models tends to disperse the particles away from the lower region resulting in a less dense lower section and a distinctly more homogenous particle distribution compared with the standard model predictions. Further, the increase in particle concentration leads to a reduction in axial velocity due to a loss of momentum through particle-wall and particle-particle collisions. Finally, the improved CFD model best predicted both the reduction and increase in the particle velocities in the different regions.

Introduction

gas-solid flows through horizontal pipes are of considerable importance in many technical and industrial processes to efficiently transport solid particles with different sizes and densities (Senapati and Dash, 2019; Yan et al., 2019). The application includes, but not limited to pneumatic conveying, fluidized beds, vertical risers, classifiers, cyclones, and flow mixing devices (Chinenye-Kanu et al., 2019; Liu et al., 2017). Pneumatic conveying is widely used in industry for numerous physical and chemical applications such as cement industries, food processing, and transporting coals in power stations. The major advantages of using pneumatic conveying compared with other conventional methods are environmentally friendly, inherent safety, and less maintenance and low operating costs (Ariyaratne et al., 2018). Therefore, the pneumatic conveying of solids particles has received considerable attention and become the focus of many researchers (Hu et al., 2017; Zhou et al., 2016). However, one of the greatest challenges facing designers and researchers in this field is that making any small change in the design of the piping system or the type of the transported solid particles significantly affects the performance of these systems (Kumar Senapati and Kumar Dash, 2019). On the other hand, the phenomena that govern the flow of solids particles within the pipe networks for pneumatic conveying are complicated since particles will not only interact with the gas phase but also will collide with other particles and the wall of pipes.

For many years the experimental approaches usually were utilized to investigate the motion of particle streams of gas–solid flows (Levy and Mason, 1998; Quek et al., 2005; Tsuji and Morikawa, 2006). Lee and Durst (1982) measured the mean of velocities of both the single sized particle phase and that of the conveying gas phase in an upward vertical pipe flow. The results showed that as the particle sizing increased the relative velocity between particle and gas also increased. Rautiainen et al. (1999) experimentally considered the influence of solids mass loading and superficial gas velocity on the slip velocity between 64 μm particles and gas. The findings show that the slip velocity increased as the mass loading increased, and the superficial gas velocity decreased. Tsuji and Morikawa (1982) experimentally studied the behavior of two-phase flow in a horizontal pipe. The findings of their study showed that at higher particle concentrations, the distributions took a more asymmetrical profile. This was more pronounced at the lower air velocity. Laı́n et al. (2002) considered the flow of particulate matter in a small hydraulic diameter channel. For the case of 100 μm particles, where the data was presented for different mass loadings, it was clear to see that an increase of mass loading resulted in a direct reduction of particle velocity towards the center of the pipe. Kussin and Sommerfeld (2002) further to the work of (Laı́n et al., 2002) looked at the effect of channel wall material and specifically the wall roughness and the behavior of the particle motion. The results showed that the introduction of a rougher wall material, considerably reduced the axial velocity profiles due mainly to the momentum transfer from the axial to the transverse direction. Due to experimental findings that the particle velocity is highly influenced by such factors as mass-loading, particle size and conveying air velocity and wall roughness characteristics to name a few, the number of numerical studies to increase prediction accuracy over the past thirty years is great (Lu et al., 2017; Luo et al., 2019; Varaksin, 2019). This had led to several proposed numerical models to better capture the trends seen in experimental works on horizontal two-phase pipe/channel flow.

Over the years, many researchers have investigated the CFD modelling of fluid flows and the degree of accuracy has greatly improved with advances in turbulence modelling and computing power (Banakermani et al., 2018; Jones and Launder, 1972; Tu and Fletcher, 1995). Although the particle modelling has also been extensively researched, the degrees of accuracy for the particulate phase are yet to rival those of the fluid phase. Tsuji et al. (1985) used numerical simulation to predict the flow of two-phase flow in horizontal pipes. The simulations included the drag force; lift force due to rotation (Magnus effect) and a modified particle-wall collision model. The authors concluded that particle trajectories and pressure drop in the pipe were successfully captured, but a lack of velocity comparison fails to show how quantitatively the simulations reproduce the experiment findings in terms of axial flow. Tsuji et al. (1991) further continued their emphasis on numerical modelling of horizontal pipe flow to develop and improve the Lagrangian models to produce greater accuracy predictions. Similar trends were noticed for the simulation results concerning the particle diameter whereby as the particle diameter increased the normalized particle velocity decreased which has discussed previously in the experimental findings. Sommerfeld (2001) considered the effect of inter-particle collisions of the behavior of particle in horizontal flow configuration. The main findings of the paper showed how even at mass loadings well below unity, the inter-particle collision model enhanced the accuracy of the predicted results.

The major effect pipe bends have on flows especially those conveying denser particulate matter is the time taken for the particles to respond to the sudden change in flow direction leading to, in most cases, inertia forces of the particle dictating the behavior of the particle motion (Banakermani et al., 2018; El-Behery et al., 2009; Tu and Fletcher, 1995). The configurations for 90° bend models vary from horizontal-to-horizontal, horizontal-to-vertical or vice versa, square or circular cross section duct, bend radius and up flow/ down flow just to name a few. On top of these flow characteristics such as particle size, density and mass loading as well as conveying air velocity make for numerous different and generally independent factors making the knowledge of pipe bend characterization still in its infancy (Hu et al., 2017). Kliafas and Holt (1987) were amongst the first to investigate two phase particle flow through a 90° bend. The configuration considered was a square sectioned vertical-to-horizontal bend. The major findings of the work showed that the particle trajectories, particularly those of the larger particle size (100 μm) tended to be more straight due to gravity and inertia than curved to follow the gas flow. Iacovides et al. (1987) numerically simulated single-phase gas flow based on the experimental data and using a standard k-ε model for the bulk of the flow found predicted results agreed surprisingly well. Although the axial profiles seemed to match quite well, the degree of secondary motioned published would suggest that the secondary flow patterns showed some discrepancy from reported experiment material.

Although the simulation of pipe gas flow is relatively simple in nature and quite well predicted by common CFD, the introduction of particles, particularly those with a higher density ratio, causes problems for CFD. Being a gas driven particle flow, the bulk velocity and the particle density ratio play major roles in the continuous flow of the particle. Due to gravity, heavier particles migrate downwards and form densely concentrated regions towards the bottom of the pipe. Increasing the driving gas velocity can minimize this effect but the particles themselves also play a pivotal role in resuspending themselves along the pipe by what can only be explained by particle-particle collisions and particle-wall collisions whereby the inherent roughness of the surface randomly disperses the particle throughout the pipe. This work presents a CFD investigation into gas driven gas-particle flows through a straight horizontal pipe and through a 90° horizontal-to-vertical bend. This CFD work will be compared to experimental work available in the literature and will validate the new drag model and an existing collision model, which was implemented into CFX4-4, under gas driven flow conditions.

Section snippets

Mathematical models

This section covers the numerical methods used to solve the motion of both the continuous fluid and the dispersed particle motion. The continuous fluid phase is calculated by solving the governing equations. The dispersed phase is solved in the Lagrangian framework using Newton’s law to describe individual representative particle motion. In present work, Computational Fluid Dynamics (CFD) technique is used as a tool to develop a new particle drag force equation to better simulate the flow of

Description of the simulated cases

The pipes utilized for investigating the gas-particle flow through a horizontal straight pipe and through a 90° horizontal-to-vertical bend are introduced and described in this section. The work of Tsuji and Morikawa (1982), and Yilmaz (1997) were used to validate the predicted results of the present model. The predicted results of the CFD models was compared first with the available experimental results. Then the CFD models were utilized to examine the proposed drag model and an existing

Horizontal straight pipe

To check the validity of the chosen turbulence model, a comparison of the standard simple k - epsilon turbulence model is compared to the more computationally expensive Reynolds Stress turbulence model as shown in Fig. 1. Both of these results are plotted against the experimental results of Tsuji et al. (1982)’s unladen gas phase. The predicted results for both turbulence models compare quite well to those of the experimental work. There is a little discrepancy toward the pipe walls where the

Summary and conclusions

In this work, available experimental data for horizontal straight pipe particle flow and 90° horizontal-to-vertical pipe flow were simulated using the improved CFD model coupled with a new drag force model. This study utilized the k-ε turbulence model, as the predictions for the gas phase only gave similar predicted axial velocity compared to the more computationally demanding Reynolds stress model.

The horizontal pipe flow of Tsuji and Morikawa (1982) considered mono-sized particle at various

Declaration of interest statement

There is no Conflict of Interest.

Declaration of Competing Interest

The authors report no declarations of interest.

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