Slurry Flow Modelling by CFD.pdf

Available on line at Association of the Chemical Engineers AChE www.ache.org.rs/CICEQ Chemical Industry & Chemical Engineering Quarterly 16 (4) 295−308 (2010)

SANDIP KUMAR LAHIRI K.C. GHANTA Department Of Chemical Engineering, Nit, Durgapur, West Bengal, India SCIENTIFIC PAPER UDC 66:532.4 DOI 10.2298/CICEQ091030034L

CI&CEQ

SLURRY FLOW MODELLING BY CFD An attempt has been made in the present study to develop a generalized slurry flow model using CFD and utilize the model to predict concentration profile. The purpose of the CFD model is to gain better insight into the solid liquid slurry flow in pipelines. Initially a three-dimensional model problem was developed to understand the influence of the particle drag coefficient on the solid concentration profile. The preliminary simulations highlighted the need for correct modelling of the inter phase drag force. The various drag correlations available in the literature were incorporated into a two-fluid model (Euler-Euler) along with the standard k-ε turbulence model with mixture properties to simulate the turbulent solid-liquid flow in a pipeline. The computational model was mapped on to a commercial CFD solver FLUENT6.2 (of Fluent Inc., USA). To push the envelope of applicability of the simulation, recent data from Kaushal (2005) (with solid concentration up to 50%) was selected to validate the three dimensional simulations. The experimental data consisted of water-glass bead slurry at 125 and 440-micron particle with different flow velocity (from 1 to 5 m/s) and overall concentration up to 10 to 50% by volume. The predicted pressure drop and concentration profile were validated by experimental data and showed excellent agreement. Interesting findings came out from the parametric study of velocity and concentration profiles. The computational model and results discussed in this work would be useful for extending the applications of CFD models for simulating large slurry pipelines. Key words: CFD; slurry flow; drag coefficient; concentration profile; velocity profile.

Particle transport through pipes is an important operation in many industries including food, pharmaceutical, chemical, oil, mining, construction and power generation industries. In many of these applications the carrier fluid may be highly viscous and may have a Newtonian or non-Newtonian rheology and flow is usually turbulent. It has been a serious concern of researchers around the world to develop accurate models for pressure drop and concentration distribution in slurry pipelines over the years. The need and benefits of accurately predicting velocity profiles, concentration profiles and pressure drop of slurry pipelines during the design phase is enormous as it gives better selection of slurry pumps, optimization of power consumption and thereby helps maximize the economic benefit. Concentration distribution may be used to determine the parameters of direct importance (mixture and solid flow rates) and Correspondening author: S.K. Lahiri, Department Of Chemical Engineering, Nit, Durgapur, West Bengal, India. E-mail: [email protected] Paper received: 29 November, 2009 Paper revised: 20 April, 2010 Paper accepted: 22 June, 2010

secondary effects such as wall abrasion and particle degradation. The recent works of Kaushal and Tomita [1] and Kumar et al. [2-4] are worth mentioning in the field of concentration distribution in slurry pipelines. Despite significant research efforts, prediction of solid concentration profile in slurry pipelines is still an open problem for design engineers. Design of slurry pipelines relies on empirical correlations obtained from experimental data. These correlations are prone to great uncertainty as one departs from the limited database that supports them. Moreover, for higher values of solid concentration, very little experimental data on local solid concentration is available because of the difficulties in the measurement techniques. Considering this, it would be most useful to develop computational models, which will allow a priori estimation of the solid concentration profile over the pipe cross section. In spite of the inadequate fundamental knowledge required for the formulation and modelling of multiphase turbulent flows, the need to predict slurry behaviour handled in various industries has motivated work, aiming at obtaining approximate solutions. Ef-

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forts are still on to develop more reasonable correlation based models for the prediction of concentration profile in pipes and in this direction, the work of Roco and Shook [5,6], Gillies et al. [7,8], Mukhtar [9] and Kaushal et al. [10] is worth mentioning. Most of the equations available in the literature for predicting vertical solids concentration profiles in slurry pipeline are empirical in nature and have been developed based on limited data for materials having equi-sized or narrow size-range particles with very low concentrations. Most of the earlier studies on slurry pipeline systems are based on moderate volumetric concentrations of solids (say up to 20%). Much larger concentrations now coming into common use show more complicated behaviour. Also in any practical situation, the solids are coarser in size with broad particle grading being transported at large flow velocities. An attempt has been made in the present study to develop a generalized slurry flow model using CFD and utilize the model to predict the concentration profile. A comprehensive computational fluid dynamics (CFD) model was developed in the present study to gain insight into the solid-liquid slurry flow in pipelines. In recent years, CFD becomes a powerful tool being used in areas like fluid flow, heat/mass transfer, chemical reactions and related phenomena by solving mathematical equations that govern these processes using a numerical algorithm on a computer. A brief review of recent literature shows little progress in simulating flow in slurry pipelines using CFD. For solid–liquid multiphase flows, the complexity of modelling increases considerably and this remains an area for further research and development. Due to the inherent complexity of multiphase flows, from a physical as well as a numerical point of view, “general” applicable CFD codes are non-existent. The reasons for the lack of fundamental knowledge on multiphase flows are three-fold: 1) Multiphase flow is a very complex physical phenomenon where many flow types can occur (solid– –liquid, gas–solid, gas–liquid, liquid–liquid, etc.) and within each flow type several possible flow regimes can exist (e.g. in slurry flow four regimes exist, namely homogeneous flow, heterogeneous flow, flow with moving bed and saltation). 2) The complex physical laws and mathematical treatment of phenomena occurring in the presence of the two phases (interface dynamics, coalescence, break-up, drag, solid–liquid interaction,...) are still largely underdeveloped. For example, to date there is still no agreement on the governing equations. In addition, proposed constitutive models are empirical but

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often lack experimental validation for the conditions they are applied under. 3) The numerics for solving the governing equations and closure laws of multiphase flows are extremely complex. Very often multiphase flows show inherent oscillatory behaviour, requiring costly transient solution algorithms. Almost all CFD codes apply extensions of single-phase solving procedures, leading to diffusive or unstable solutions, and require very short time-steps. In spite of the major difficulties mentioned above, attempts have been made to simulate solid-liquid flow in pipelines. A small number of studies is focused on predicting the solid concentration distribution in the experimental slurry pipelines. Although some degree of success is reported, a number of limitations are apparent. Considering the limitations in the published studies, the present work has been undertaken to systematically develop a CFD based model to predict the solid concentration profile in slurry pipeline. The aim is to explore the capability of CFD to model such complex flow. In this work, a solid suspension in a fully developed pipe flow was simulated. The two-fluid model based on the Eulerian-Eulerian approach along with a standard k-ε turbulence model with mixture properties was used. The computational model developed in this work was used to simulate solid-liquid flow in the experimental setup used by Kaushal et al. [11]. The model predictions were evaluated by comparing predictions with the experimental data. BACKGROUND WORKS CFD studies on solid-liquid slurry flow in pipelines have not been widely performed as observed from the literature and majority of the documented data focuses on empirical correlations of concentration profile of water-based slurries of fine particles. There is, therefore, a clear need for experimental data and CFD models to describe the flow of large particles in Newtonian fluids as they are relevant to a number of industrial applications such as the conveying of particulate food mixtures, gravel, and coal lumps. The use of CFD, however, has been hampered by lack of understanding of the complex solid–liquid flows and that result has only been addressed in a handful of studies [12-21]. Detailed measurements of the flow field and pressure drop in these systems are scarce. Some limited studies experimented with magnetic resonance imaging [22] and ultrasound Doppler velocimetry


[23]. Barigou et al. used positron emission particle tracking (PEPT) to study the flow of coarse (d = 5 or 10 mm) nearly neutrally-buoyant alginate particles in shear-thinning carboxymethyl cellulose (CMC) fluids and reported information on flow regimes, solid phase velocity profiles, and particle passage time distributions [21]. Computational modelling in this specific area has been even more limited. In a rare attempt, Krampa-Morlu et al. used CFD to study the flow features of coarse aqueous solid–liquid slurries in turbulent upward flow including velocity profiles [24]. The model, implemented using the commercial CFD software CFX4.4 (Ansys Inc.), was tested using experimental data from Sumner et al. [25]. The particles had a density of 2650 kg/m3 and a diameter of 0.47 or 1.7 mm and were simulated at concentrations up to 30% by volume. The authors concluded that, using the default settings, the code failed to accurately predict important features of the flow. Recently, Eesa and Barigou investigated the capabilities of CFD to model the flow of coarse nearly-neutral buoyant particles in shear-thinning CMC fluids in a horizontal pipe for a limited number of flow cases [21]. CFD results of particle velocity profiles were validated with experimental data obtained by PEPT, while pressure drop predictions were compared with a number of selected correlations from the literature. In a recent paper [26], a CFD model based on the commercial code ANSYS CFX 10.0, is used to conduct a detailed parametric study of the transport of nearly neutral-buoyant coarse particles in laminar non Newtonian both horizontal and vertical flow. FORMULATION OF MULTIPHASE CFD MODEL The Eulerian–Eulerian two-fluid model was adopted here, whereby both the liquid and solid phases are considered as continua. Treating the solid phase as an Eulerian phase is possible provided that the inter-phase interactions are adequately modelled. In fact, the Eulerian approach has been reported to be efficient for simulating multiphase flows once the interaction terms are included [27]. The Eulerian–Lagrangian model, however, which simulates the solid phase as a discrete phase and thus allows particle tracking, is in principle more realistic. However, after evaluating the relevant literature as well as conducting a number of simulation trials, it was concluded that the number of dispersed particles that can be tracked within all the different commercial CFD software available is currently very limited, thus restricting the applicability of the Eulerian–Lagrangian model to only dilute mixtures well below 5% by volume [28].

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Eulerian Model In the Eulerian-Eulerian approach, two phases are considered to be interpenetrating continua. For the present CFD simulations, the Eulerian-Eulerian multiphase model implemented in the commercial code Fluent 6.2 was used. With this approach, the continuity and the momentum equations are solved for each phase and therefore, the determination of separate flow field solutions is allowed. The Eulerian model is the most complex and computationally intensive among the multiphase models. It solves a set of “n” momentum and continuity equations for each phase. Coupling is achieved through the pressure and interphase exchange coefficients. For granular flows, the properties are obtained from application of kinetic theory.

Continuity Equation The continuity equation for a generic phase q is given by:

∂ (α qρ q) + ∇(α qρ qν q) = 0 ∂t

(1)

The solution of this equation for each secondary phase, along with the condition that the volume fractions sum to one, allows for the calculation of the primary-phase volume fraction.

Momentum Equations Fluid-fluid momentum equations. The conservation of momentum for a fluid phase q is:     ∂ (αq ρq ν q ) + ∇(αq ρq ν q ν q ) = −αq∇p + ∇ τ q + αq ρq g + ∂t    + αq ρq (F q + F lift,q + F vm,q ) +    n +  K pq (υp − υq ) + m pq υpq

(2)

p =1





Fq is an external body force, F lift,q is a lift force, F vm,q is a virtual mass force, Kpq is an interaction force between phases, and p is the pressure shared by all phases.

Fluid-solid momentum equations FLUENT uses a multi-fluid granular model to describe the flow behavior of a fluid-solid mixture. The solid-phase stresses are derived by making an analogy between the random particle motion arising from particle-particle collisions and the thermal motion of molecules in a gas, taking into account the inelasticity of the granular phase. As the case for a gas, the intensity of the particle velocity fluctuations determines the stresses, viscosity, and pressure of the solid phase. The kinetic energy associated with the particle velocity fluctuations is represented by a

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“pseudo-thermal” or granular temperature which is proportional to the mean square of the random motion of particles. The conservation of momentum for the 8th solid phase is:

    ∂ (αs ρs ν s ) + ∇(αs ρs ν s ν s ) = −αs∇p + ∇ τ s + αs ρs g + ∂t    + αs ρs (F s + F lift,s + F vm,s ) +    n +  K ls (υl − υs ) + m ls υls

(3)

p =1

where ps is the sth solid’s pressure, Kls = Ksl is the momentum exchange coefficient between fluid phase l and solid phase  s, n is the total number of phases.  The lift force F lift,s and the virtual mass force F vm,s have been neglected in the calculations, because they give a minor contribution to the solution with respect to the other terms.

Interphase exchange coefficient It can be seen in Eqs. (2) and (3) that momentum exchange between the phases is based on the value of the fluid-fluid exchange coefficient Kpq and, for granular flows, the fluid-solid and solid-solid exchange coefficients Kls. Fluid-solid exchange coefficient. The fluid-solid exchange coefficient Kls is in the following general form:

K ls =

αs ρsf τs

(4)

ρsd s2 18 μl

(5)

where d s is the diameter of particles of phase s. All definitions of f include a drag function (CD) that is based on the relative Reynolds number (Res). It is the drag function that differs among the exchange coefficient models. The following three models were found in the literature which are promising and widely used for calculating solid liquid interaction in slurry flow. Syamlal-O’Brien model [29]: For this model, f is defined as:

C Re α f = D s2 l 24 μvl r,s

(6)

where the drag function has a form derived by Dalla Valle [30]:

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CD = (0.63 +

4.8

Re s v r,s

)2

(7)

This model is based on measurements of the terminal velocities of particles in fluidized or settling beds, with correlations which are functions of the volume fraction and the relative Reynolds number:   ρld s v s −v l Re s = (8) μl where the subscript l is for the lth fluid phase, s is for the sth solid phase, and ds is the diameter of the sth solid phase particles.

The fluid-solid exchange coefficient has the form: K ls =

  3αs αl ρl Re s C D v s −v l 2 4v r,sd s μl v r,s

(9)

where vr,s is the terminal velocity correlation for the solid phase: v r,s = 0.5( A − 0.06Re s + + (0.06Re s )2 + 0.12Re s (2B − A ) + A 2 )

(10)

with

A = αl4.14

(11)

and

B = 0.8αl1.28 for αl ≤ 0.85

where f is defined differently for the different exchange coefficient models (as described below), and τs, the “particulate relaxation time”, is defined as: τs =

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(12)

or

B = 0.8αl2.65 for αl > 0.85

(13)

This model is appropriate when the solids shear stresses are defined according to Syamlal et al. [31]. Wen and Yu model [32]: For the model of Wen and Yu, the fluid-solid exchange coefficient is of the following form:

3 4

K ls = CD

αs αl ρl 

ds



v s −v l αl-2.65

(14)

where:

CD =

24 (1 + 0.15(αlRe s )0.687 ) αlRe s

(15)

This model is appropriate for dilute systems. Gidaspow model [33]: The Gidaspow model is a combination of the Wen and Yu model and the Ergun equation [34]. The fluid-solid exchange coefficient, Kls, is of the form given by Eq. (14). When αl ≤ 0.8:


K ls = 150

αs (1 − αl ) μl α ρ   + 1.75CD s l v s −v l 2 ds αld s

(16)

This model is recommended for dense fluidized beds.

Solid-solid exchange coefficient. The solid-solid exchange coefficient, Kss, has the following form (Syamlal [35]): K ss =

π π2 3(1 + e ls )( + C fr,ls )αs ρsαl ρl (d l + d s )2 g 0,ls   (17) 2 8 = v l −v s 2π( ρld l3 + ρsd s3 )

where: els - coefficient of restitution, Cfr,ls - coefficient of friction between the lth and sth solid-phase particles (Cfr,ls = 0), dl - the diameter of the particles of solid and g0,ls - the radial distribution coefficient. Implementation of CFD model The geometry used consisted of a pipe of diameter D = 105 mm. The pipe length, L, was much greater than the maximum entrance length, Le, required for fully developed flow. In single-phase Newtonian laminar flow, Le can be estimated from [36]:

Le = 0.062Re t D where

Re t =

ρfu mD μf

is the tube Reynolds number and um is the mean flow velocity. There is no correlation available for estimating Le in two-phase solid–liquid flow. However, for almost all the particles used here, the above equation should give a reasonable estimate of Le. Whilst such estimates were used as a guide, a series of numerical trials were conducted using different pipe lengths. For all of the cases simulated here, a pipe length of 3 m was sufficient to give a fully developed solid–liquid flow through most of the pipe length whilst keeping computational cost low. Using a longer pipe did not affect the results. The geometry was meshed in to approximately 1.8×105 tetrahedral cells. For Eulerian multiphase calculations, we used the Phase Coupled SIMPLE (PC-SIMPLE) algorithm [37] for the pressure-velocity coupling. PC-SIMPLE is an extension of the SIMPLE algorithm to multiphase flows. The velocities are solved coupled by phases, but in a segregated fashion. The geometry was meshed into approximately 50000 quadrilateral cells in GAMBIT 2.2 pre-processor. A dense computational grid was used because of the pilot-scale pipe dimen-

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sions. The initial conditions were: a) uniform fully developed velocity profile at pipe inlet and b) the solid particles uniformly distributed at pipe inlet. The first-order upwind discretization scheme was used for the volume fraction, momentum equations, turbulence kinetic energy (k), and turbulence dissipation rate (ε). All the simulations were performed in double precision. Simulations of the carrier fluid flowing alone were performed first to serve both as an initial validation of the code and the numerical grid, and to reveal the effects of solid particles on the liquid velocity (by deselecting the volume fraction equations). Once the initial solution for the primary phase was obtained, the volume fraction equations were turned back on and the calculation continued with all phases. An inlet flow rate boundary condition was used at the pipe inlet, while static pressure was specified at the outlet. The homogeneous volumetric fraction of each phase was specified at the inlet. Using flow rate as a boundary condition is the common way of formulating pipe flow problems, i.e. one designs a system to deliver a given flow rate. It is noted however that using a pressurespecified inlet boundary condition is a stricter way of testing the CFD code as a flow rate boundary condition may be perceived as a way of helping to steer the simulation towards the right solution. This pressure option was tested but it did not affect the results of the CFD computations. The usual no-slip boundary condition was adopted at the pipe wall. Simulation was steady state. The concentration distribution was uniform in z direction. The solution was assumed to have converged when the mass and momentum residuals reached 10–4 for all of the equations solved. Also the slopes of residuals approach to zero. This typically required 150 iterations. Due to the complexity of the solid–liquid flows considered here, the simulations initially required a great deal of experimentation and optimization. Of primary importance was the appropriate modelling of forces and interactions between the two phases. The drag force was modelled using the Syamlal-O’Brien model (1993), Wen and Yu (1966) model and Gidaspow model (1992). RESULTS AND DISCUSSION OF 3D SIMULATION Concentration profile Figures 1–4 show the experimental and CFD predicted vertical concentration profile of slurry of 125 and 440 μm glass beads in 54.9 mm diameter pipe at different efflux concentrations and flow velocity. The

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Figure 1. Comparison of experimental and calculated vertical concentration profile for flow of 125 μm glass beads in 54.9 mm diameter pipe at different efflux concentration and flow velocity.

Figure 2. Comparison of experimental and calculated vertical concentration profile for flow of 125 μm glass beads in 54.9 mm diameter pipe at different efflux concentration and flow velocity

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Figure 3. Experimental and calculated vertical concentration profile for flow of 440 μm glass beads in 54.9 mm diameter pipe.

Figure 4. Experimental and calculated vertical concentration profile for flow of 440 μm glass beads in 54.9 mm diameter pipe.

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agreement between calculated and experimental concentration profiles is quite good as evident from these curves. However the discrepancy found between the experimental results and the calculated results in case of low solid concentration and low velocity (Cvf = = 9.4% vm = 1 m/s) indicate that the developed CFD model is not fully capable to capture the phenomena at very low velocity where the gradient of solid profile is more in vertical plane. Figures 5 and 6 show concentration profiles in the vertical plane for slurry of 125 and 440 μm, respectively, by Cv/Cvf vs. y/D, where Cv is the volumetric concentration at y = y/D, y being distance from the pipe bottom and D the pipe diameter. It is observed that the particles are asymmetrically distributed in the vertical plane with the degree of asymmetry increasing with increase in particle size because of the gravitational effect. It is also observed that the degree of asymmetry for the same overall concentration of slurry increases with decreasing flow velocity. This is expected because with decrease in flow velocity there will be a decrease in turbulent energy, which is responsible for keeping the solids in suspension. From

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these figures, it is also observed that for a given velocity, increasing concentration reduces the asymmetry because of enhanced interference effect between solid particles. The effect of this interference is so strong that the asymmetry even at lower velocities is very much reduced at higher concentrations. Therefore it can be concluded that the degree of asymmetry in the concentration profiles in the vertical plane depends upon particle size, flow velocity and overall concentration of slurry. Measured concentration profiles show a distinct change in the shape for slurries of coarser particle size (i.e., 440 µm) with higher concentrations at lower velocities (Figures 3 and 4). It is observed that the maximum concentration at the bottom does not change and extends up to centre of the pipeline, thus making a sudden drop in the concentration in the upper half of the pipeline. The reason for such a distinct change in shape of concentration profiles may be attributed to the sliding bed regime for coarser particles at lower velocities and higher concentrations.

Figure 5. Concentration profiles in the vertical plane for slurry of 125 μm particle size. a) Case-a: Feed conc. = 10%; b) case-b: Feed conc. = 30%; c) case-c: Feed conc. = 50%.

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Figure 6. Concentration profiles in the vertical plane for slurry of 440 μm particle size. a) Case-a: Feed conc. = 10%; b) case-b: Feed conc. = 30%; c) case-c: Feed conc. = 40%.

Velocity profile

Pressure drop

Figures 7–9 show the corresponding vertical velocity profile across the pipe cross section at pipe outlet. Due to the unavailability of experimental data, the agreement between experimental and predicted velocity profile could not be judged. However, the velocity profile patterns in those figures match the theoretical understanding. Therefore, it may be concluded indirectly that the CFD model is capable of validating the velocity profile for slurry flow. The solid phase velocity profile is generally asymmetrical about the central axis at low velocity (say 1 m/s). The asymmetry in the solid phase velocity profile is a result of particle settling due to the density difference between the two phases. The asymmetrical nature of velocity profile is reduced at higher velocity range (say 3-5 m/s) and velocity profile becomes symmetrical. Figure 10 shows the comparison of velocity profile at different efflux concentration for different flow velocity for 125 μm particles. From this figure, it can be concluded that the velocity profile does not change much due to increase in concentration from 10 to 50%.

The parity plot of predicted and experimental pressure drop is shown in Figure 11. From this figure, it is evident that the agreement between the calculated and experimental pressure drop is quite good. The calculated pressure drops for slurry of 125 μm particles are presented in Figure 12 at overall area-average concentrations around 10, 20, 30, 40 and 50%. It is observed that the pressure drop at any given flow velocity increases with increase in concentration. This trend is seen for all concentrations at all velocities. The rate of increase in pressure with concentration is small at low velocities but it increases rapidly at higher velocities. The pressure drops for slurry of 440 μm particles are presented in Figure 13 at overall area-average concentrations around 10, 20, 30 and 40%. From this figure, it is observed that the pressure drop at any given flow velocity increases with increase in concentration, but the rate of increase is comparatively smaller at higher flow velocities. Furthermore, at lower velocities, the pressure drop remains constant at lower concentrations and decreases with flow velo-

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Figure 7. CFD predicted solid phase vertical velocity profile for flow of 125 μm glass beads in 54.9 mm diameter pipe at different efflux concentration and flow velocity.

Figure 8. CFD predicted solid phase vertical velocity profile for flow of 440 μm glass beads in 54.9 mm diameter pipe

city at higher concentrations. From Figures 12 and 13, it is observed that finer-sized particles have less pressure drop at lower flow velocities and more pressure drop at higher flow velocities than coarser particles. Such an increase in pressure drop for coarser particles at lower velocity is due to the increased amount of particles moving in the bed due to the gravitational effect, while, in the case of finer particle size at higher velocities, the pressure drop is more due to greater surface area causing more frictional losses in suspension.

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Contours of solid concentration and velocity Figures 13 to 43 (Supplementary material) show contours of volume fraction of solid and contours of solid velocity at the pipe outlet at different flow velocities and efflux concentration. These pictures help visualize the solids distribution across the pipe cross section. One of the biggest advantages of CFD is the ability to generate such types of concentration and velocity contours. Figure 14 shows how solid settled at the bottom of the pipe (indicated by red colour at the bottom). Solid concentration at the top of the pipe


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Figure 9. Comparison of vertical velocity profile at a) 1, b) 3 and c) 5 m/s for different efflux concentration.

Figure 10. Parity plot of predicted vs. experimental pressure drop for slurry flow at different overall area-average concentrations and flow velocities.

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Figure 11. Pressure drop for slurry of 125 µm particle size at different overall area-average concentrations and flow velocities.

Figure 12. Pressure drop for slurry of 440 µm particle size at different overall area-average concentrations and flow velocities.

is very low and at the top most points are virtually absent (indicated by the blue colour at the top of the pipe). In the large area at the centre portion of the pipe, the solid concentration remains uniform (indicated by green colour). Figure 15 shows the velocity contours across the pipe cross section at the outlet of the pipe. From this picture it is clear that maximum velocity is not at the centre of the pipe but slightly lower than the pipe axis. This is due to solids tending to settle at the bottom of the pipe due to low velocity (1 m/s) of slurry which makes the velocity profile asymmetrical. A comparison of velocity profiles in Figures 15 and 19 reveals the fact that at a higher velocity (5 m/s), the velocity profile becomes symmetrical and maximum velocity occurs at the pipe axis. This may be due to the flat concentration profile for higher turbulence at higher velocity. Another marked difference of velocity profiles in Figures 15 and 26 shows that with the increase of solid concentration (from 9.4 to 30.3%) at same slurry velocity (1 m/s), the asym-

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metrical nature of velocity profile increases and the maximum velocity location moves more towards the bottom of the pipe. Comparison of concentration profile contour in figures 18, 23, 29 and 33 reveals that at a fixed flow velocity (say 5 m/s), when solid concentration increases from 10 to 50%, the asymmetry nature of concentration profile reduces because of enhanced interference effect between solid particles. The measured concentration profiles show a distinct change in the shape for slurries of coarser particle size (i.e., 440 µm) at lower velocities (Figures 42–44). It was observed that most of the solid settled down at the bottom of the pipe for coarser particle resulting in steep concentration gradient. CONCLUSION In this study, the capability of CFD was explored to model complex solid liquid slurry flow in pipeline. It was found that the commercial CFD software (FLUENT)


is capable to successfully model the solid–liquid interactions in slurry flow and the predicted concentration profiles results show reasonably good agreement with the experimental data. The following conclusions have been drawn on the basis of present study: 1. The particle concentration profile was modelled for high concentration slurry transport where the maximum overall area-average concentration is 50% by volume employing coarse particles and higher flow velocities up to 5 m/s. 2. It was observed that the particles were asymmetrically distributed in the vertical plane with the degree of asymmetry increasing with increase in particle size because of the gravitational effect. It was also observed that the degree of asymmetry for the same overall concentration of slurry increased with decreasing flow velocity. 3. For a given velocity, increasing concentration reduced the asymmetry because of enhanced interference effect between the solid particles. The effect of this interference was so strong that the asymmetry even at lower velocities is very much reduced at higher concentrations. 4. A distinct change in the shape of concentration profiles was observed indicating the sliding bed regime for coarser particles at lower flow velocities. 5. The solid phase velocity profile is generally asymmetrical about the central axis at low velocity (say 1 m/s). The asymmetry in the solid phase velocity profile is a result of particle settling due to the density difference between the two phases. The asymmetrical nature of velocity profile is reduced at higher velocity range (say 3-5 m/s) and velocity profile becomes symmetrical. 6. Pressure drop at any given flow velocity increases with increase in concentration. This trend is seen for all concentrations at all velocities. The rate of increase in pressure with concentration is small at low velocities but it increases rapidly at higher velocities. The computational model and results discussed in this work would be useful for extending the applications of CFD models for simulating large slurry pipelines.

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SANDIP KUMAR LAHIRI K.C. GHANTA Department Of Chemical Engineering, Nit, Durgapur, West Bengal, India NAUČNI RAD

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MODELOVANJE STRUJANJA SUSPENZIJE POMOĆU RAČUNARSKE TEHNIKE SIMULACIJE STRUJANJA FLUIDA (CFD) U ovoj studiji je razvijen opšti model toka suspenzije pomoću računarske tehnike simulacija strujanja fluida (CFD) u cilju predviđanja profila koncentracije. Primenom CFD modela se stiče bolji uvid u fenomene vezane za proticanje suspenzije kroz cevi. Razvijen je trodimenzioni model radi ispitivanja uticaja koeficijenta trenja na profil koncentracije. Preliminarna simulacija ukazuje na potrebu proširenja modela za opisivanje međufazne sile trenja. Različite korelacije za određivanje koeficijenta trenja, koje su dostupne u literaturi, su uključene u dvofazni model (Euler-Euler). Ovaj model je prikazan pored standardnog k-ε modela koji opisuje turbulentni tok smeše kroz cev. Za izračunavanja primenom modela korišćen je komercijalni CFD program Fluent 6.2 (Fluent Inc., USA). Radi ilustracije primenljivosti trodimenzione simulacije korišćeni su podaci Kaushal-a (2005) (za koncentraciju čvrste faze 50 %). Model je primenjen na suspenziju čestica stakla dimenzija 125 i 440 μm u vodi pri različitim protocima (od 1-5 m/s) i ukupnu koncentraciju čvrste faze od 10 do 50 vol.%. Izračunate vrednosti pada pritiska i koncentracioni profili dobijeni primenom modela i eksperimentalni podaci pokazali su odlično slaganje. Interesantni fenomeni su primećeni pri korelisanju brzine i profila koncentracije čvrste faze. Primena modela može biti korisna pri simulaciji toka u velikim protočnim sistemima. Ključne reči: CFD; tok suspenzije; koeficijent trenja; profil koncentracije; profil brzine.

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