Project Review

Optimization of Design of a Compact Cell Settler

Report submitted on April 25, 2016

Under Guidance of Prof. Pushpavanam

Submitted by:

Rohit Singh

5th Year Dual Degree Student

Chemical Engineering

In this report we describe the work carried out in the period from August 2015 to March 2016. The work has been carried out in a systematic manner to help logically analyze the results. First we discuss the sedimentation in a batch vessel which is vertical and then is inclined. Then we extend this to a continuous system. The analysis is done using Fluent as the platform for all simulations.

INTRODUCTION

Suspension mammalian cell culture processes for the production of biologic therapeutics (antibodies) are operated in a variety of modes such as: batch, fed-batch, chemostat, and perfusion.In perfusion culture, a continuous supply of fresh media is fed into the bioreactor while growth-inhibitory by-products are constantly removed. The advantages of perfusion cell culture, in particular, include high volumetric productivities via higher cell densities than the other modes and better cell physiology control. Perfusion is also advantageous when product stability is a concern as the product can be harvested continuously as opposed to waiting for the duration of a batch or fed-batch process.

Hybridoma is a hybrid cell used as the basis for the production of antibodies in large amounts for diagnostic or therapeutic use. Early studies in batch hybridoma culturing showed that monoclonal antibody production is proportional to the number of viable cells in the culture [1,2] .Nonviable or dead cells do not lose significant amounts of antibody and, consequently, contribute negligibly to the productivity of a culture [3]. Thus, high productivity of monoclonal antibody in suspension culture can be attained not by maximal cell growth rate but by maintaining high viable cell concentrations.The accumulation of nonviable cells and the removal of viable cells along with nonviable cells limit the culture productivity. Limitations in culture productivity may be overcome by continuously removing only nonviable cells from the reactor while selectively retaining all viable cells in the reactor, provided that a method may be developed for accomplishing a selective separation of these subpopulations.

Cell retention devices are employed in perfusion processes to separate the cells from the product-containing supernatant (harvest) and to ideally retain the viable, product-producing cells in the bioreactor. Such cell-separating devices include centrifuges, hollow-fiber filters, hydrocyclones, gravity settlers, spin filters and ultrasonic separators.High viable cell concentrations in suspension bioreactors are currently achieved

by using various cell retention or recycle devices. Filter devices can be detrimental to long-term culture productivity because the cells are subjected to excessive shear forces, resulting in higher cell death rates. Inclined plate settlers have various advantages over traditional settling devices. It can be operated continuously unlike the batch sedimentation devices. Inclined settlers generally do not contain any internal moving parts and accomplish the separation by utilizing the force of gravity within an environment of minimal shear stress.

It is expected that the desired selective cell separation may be accomplished by exploiting the different sedimentation velocities of viable and nonviable cells by using inclined sedimentation. Larger cells are removed from suspension by settling onto the upward-facing surfaces of the settler, where they form thin sediment layers that slide down to be collected at the bottom of the vessel.

Batt et al [6] performed experiments and concluded that at high dilution rates ,over 95% of the viable cells could be partitioned to the bottom of the settler while over 50 % of the nonviable cells are removed through the top of the settler. This successful separation is due to the significantly larger size of the viable cells than the nonviable ones.

THE BOYCOTT EFFECT & INCLINED PLATE SETTLERS

The benefit of inclined sedimentation is that cells need to settle only a distance on the order of the narrow spacing between the inclined walls of the settler in order to be removed from suspension, rather than a distance on the order of the settler height as in vertical sedimentation. In order to explain the Boycott effect, Ponder (1925) and Nakamura and Kuroda (1937) independently proposed an analytical model to predict the sedimentation rate for a monodisperse suspension in a parallel-plate container. This model is called the ‘‘PNK theory.’’[4-5]

According to the PNK theory, the settling rate is

dhdt = -Vo(1 + hbsinA )

A is the angle of inclination and Vo is the suspension interface velocity in a vertical container of the same dimensions. It is clear that the settling rate is enhanced by a factor (h/b) sin A. That is, the settling rate will be improved for a larger ratio of the suspension length to the width, b, or by a larger inclination angle. Kinosita (1949) experimentally observed convection currents in an inclined tube, which generated a strong vortex. He found that some particles trapped in the vortex move up to 100 times faster than those sedimentation particles. Hill et al. (1977) proposed a continuum model, and he was followed by Acrivos and Herbolzheimer (1979), Borhan and Acrivos (1988), and Kapoor and Acrivos (1995). In these studies, Acrivos and his coworkers paid attention to the modeling of the sediment layer on the upward-facing surface and the way it drains towards the bottom of the container. Their results agree better with the experimental data than the PNK theory does.

Figure 1: Schematic of inclined plate cell settler

b: plate spacing;

n: number of plates;

w: plate width;

l: plate length;

Θ: settler angle

A kinematic theory for inclined sedimentation was developed more than a half-century ago. This theory states that the volumetric production rate of clarified fluid from an inclined channel due to particle sedimentation is equal to the vertical settling velocity of the particles multiplied by the horizontal projected area of the channel surface available for sedimentation [4-5].

S(u)= uw (Lsin Θ + b cos Θ) (1)

Where S(u) is the volumetric rate of production of fluid clarified of particles with settling velocity u ,w is the width of the settler, L is the length of the settler, b is the spacing.

The scale-up of an inclined sedimentation device can be accomplished by either increasing the dimensions of a single plate, which can result in long cell residence times and cumbersome physical sizes, or by utilizing multiple plates.

These multiple plate designs, however, share two common problems. First, a single pump removes the overflow for many plates, causing inevitable flow distribution problems. For example, it is impossible to maintain identical flow rates up each of the channels. The second, more serious problem is that cells which have settled and are sliding off the top channels will be re-entrained in the up flow through lower channels. In this manner, viable cells will not be swiftly returned to the bioreactor upon settling, and the residence time of cells of the settler can be increased dramatically.Selective removal of nonviable cells can be achieved by adjusting the settler overflow rate so that the residence time of the suspension in the settler is in between the settling times of two subpopulations of different sizes.For a given cell culture growing at a particular rate, the degree of cell separation was found to depend on the overflow rate through the settler, which determines the residence time of suspended cells in the sedimentation channel.An efficient settler will rapidly return all cells to the bioreactor, so that they can continue to produce product uninhibited by the low settler temperatures and uncontrolled nutrient conditions. The length of time that cells spend in the settler is therefore critical to considerations of settler dynamics.

Conical Spiral Settler device

This is a proprietary patent-pending design (shown in Figures 2 and 3) of Compact cell settler developed by Sudhin Biopharma Co. It exploits the centrifugal forces on cells (in the cell culture medium from the bioreactor) entering tangentially near the top of cylindrical portion of the cyclone assembly. Cells pushed against the spiral cylindrical walls settle down vertically to reach the conical bottom of the cyclone housing and its internal inclined surfaces, which enhances the cell settling as discovered by Boycott (1920) with blood cells and confirmed by Batt et al., (1990) for hybridoma cells and Searles et al., (1994) for CHO cells.

1. Cylindrical portion of cyclone holding vessel;

2. Conical bottom section of cyclone vessel;

3. Top headplate sealed with o-rings on cylcone;

4. Central top outlet port welded into headplate;

5. Screws attaching the lid to the cyclone

6. Tangential port near the top for inlet of cell culture medium from bioreactor;

7. Vertical spiral plate with constant spacing between successive rings;

8. Conical spiral surface (a single continuous surface or several angled plates) welded to the vertical spiral plate; and,

9. Bottom outlet port for returning settled cells back to the bioreactor.*

This prototype was constructed and housed inside a cyclone of 12 inches outer diameter and 12 inches total height as shown in Figure 2. It is a vertical spiral plate turning 5 full circles, with several angled plates welded at the bottom. In the initial experiments with this device at a perfusion rate of 5 liters/day harvested from yeast Pichia cells growing in 5-liter bioreactor contained only 5 – 10 % of the cell concentration in the bioreactor sample.

Under the microscope and with a Coulter counter, the yeast cells exiting in the harvest were significantly smaller than those in the bioreactor.

Figure 2. Sectional view of a Conical Spiral Settler device

Figure 3. Top view of a Conical Spiral Settler device

PROBLEM STATEMENT

To find the optimal parameters and design specifications for the above described cell settler.For the design optimization, some of the suggestions given to us were to change the height of cylindrical portion keeping the volume constant and seeing its effect.Simulating the above problem and geometry was a challenging task. For simulating the above geometry, we first needed to understand the dynamics of the system. After understanding the system and developing an appropriate model for a simpler system, we can extrapolate it to the much complex system.

Simulation of Batch sedimentation flows in vertical and inclined channels

1. Vertical bimodal sedimentation

The geometry considered for the study was a vertical cuboidal sedimentation column, 100 cm tall and has a square cross-section with 5 cm side. Two types of particles were considered for the simulations. Group 1: 137 microns, initial volume fraction 0.01, density=2440 kg/m3 and Group 2: 198 microns, initial volume fraction 0.04, density = 2990 kg/m3 .Both types of particles were studied individually.

The suspending medium (fluid) consisted of a mixture of Union Carbide UCON oils and Monsanto HB40 hydrogenated terphenyl oil which had a Newtonian fluid with density = 992 kg/m3 and viscosity = 0.0677 kg / m-s. This viscosity is sixty seven times higher than that of water. The maximum particle volume fraction (packing fraction) is 0.53 [3] This choice of parameters is based on the experimental study in the literature and is used to validate the numerical code developed.

The geometry being simulated is shown in Fig.4. All the simulations are performed in 2-D as we can find a plane of symmetry (XY plane). The number of cells in the x and y directions are 16 and 160 respectively.

Geometry Meshed Geometry

Figure 4 : Geometry and meshing of the vertical sedimentation column

Model and Solver Specifications

Euler –Euler Granular Model is used for carrying out the simulations. The key features of the model are now described.

To take into account the sliding of particles on the inclined surface, a slip boundary condition is used for particle-wall interaction. No slip condition is used for fluid-wall interaction.

The coefficient of restitution between particle-particle is set as 1 (collisions are elastic) since there exists a thin liquid film covering the particle surface.

The coefficient of restitution between particle-wall is set as 0 (inelastic collision). This implies that the particles are assumed to be deposited when they come in contact with the wall.

The drag model used is the classical Schiller Naumann model. The particle viscosity and particle collision stress is modeled by the kinetic theory of granular flows. Solids phase properties become functions of the solids phase volume fraction and the granular temperature which accounts for velocity fluctuations owing to particle-to-particle collisions. [9,15]

A second order upwind scheme is used to solve the momentum equations for the convective terms.

Number of x cells =16

Number of y cells = 160

A transient coupled solver was used to solve the momentum, continuity, granular temperature and energy equations. Time step size for the simulation was determined on a case-by-case basis and was chosen to be as large as possible such that the solution converged. The time step size used varies from 5x10-3 s to 2x10-2 s for most simulations.

For convergence of the solution, the residuals were monitored .The criterion used for convergence was residuals had to reach 10-3 at every time step. The time step was chosen such that for each time step the numerical scheme converges in 5-10 iterations.

Results

The experimental data was obtained from Davis R.H et al (1982) ‘The sedimentation of polydispere suspensions in vessels having inclined wall’. Simulation of sedimentation in a vertical column was done in Fluent 14.1.

Fig.5 shows the comparison between experimental data and simulated data for the two particles. It can be seen that the simulation is able to predict the experimental behavior for both types of particles.

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Figure 5 : Comparision of experimental data with simulated results

2. Simulation of vertical and inclined unimodal sedimentation

For these simulations the vertical height was kept constant at 40 cm and the cross-section of the geometry was a square with side 5 cm. The particles were assumed to be monodisperse with a size of 137 microns and density of 2420 kg/m3. Initial volume fraction of particles was taken as 0.1 .The maximum particle volume fraction (packing fraction) = 0.53

The fluid properties considered chosen were density = 992 kg/m3 and viscosity = 0.0677 kg / m-s. This channel was analyzed for three different inclinations; 350, 200

and 00.

Meshing

The solution obtained depends on the grid size chosen. The final solution which has numerically converged should be independent of the grid. The solution changed initially when we went from coarse mesh to fine mesh. But after a critical mesh size, the solution becomes independent of the grid size.

The final mesh size used has a maximum face size of 1 mm. This gave a total of 19138 elements and 18590 nodes.

Another mesh of Maximum face size 1.5mm having 8292 elements and 7948 nodes was also used. No significant difference (less than 5%) was observed in the results obtained by these two meshes. Hence all simulations were carried out with the finer mesh.

Sedimentation rate was found to increase as we used a finer mesh. This also gave a realistic solution (closer to experimental results) while using a very fine mesh. In particular it was necessary for the meshing near the boundary (walls) to be very fine (1 mm) as sedimentation is a boundary phenomenon.

Models and solvers used here are same as that used for the vertical bimodal sedimentation case. Meshing is different for the inclined channels to take into account the formation of sediment layer and its sliding on the boundary.

Geometry

Case 1: Inclination 350 Case 2: Inclination 200 Case 3: Inclination 00

Figure 6 : Geometry of the inclined and vertical column

Fig.6 represents the three cases being modeled. The angle of inclination is measured from the vertical.

Results

The experimental data for the inclined channels were obtained from [9]. Simulations of inclined columns were done in Fluent 14.1. Fig.7 shows the comparison between experimental data and simulation predictions for the case of the vertical channel and two different inclinations of 20 and 35 degrees. A good agreement between the experimental and simulated data is observed. This validates the model.

The location where the concentration was 50% of the initial concentration was taken to be the interface height (i.e., cell fraction =0.05).

It must be emphasized that while the experiments were carried out by using polydisperse particles around a mean diameter, the simulations are based on a monodisperse suspension being used.

For the broad size distribution, the concentration just above the top of suspension is zero, whereas, for the narrower distributions, it is not. The effect of the polydispersity is to spread out the particles in the upper portion of the settling vessel. [11-12]

In sedimentation experiments for monodisperse particles, Laux H. et al (1997) encountered a comparatively sharp interface below which the particle volume fraction equals its initial value and above which it is virtually zero. In the computed solution, however, numerical diffusion tends to smear the interface such that it does not appear sharp any longer [14]. It seemed natural to define the interface position by the contour line for half of the initial particle volume fraction [15].

The height settled in 600 seconds is 7.3 cm for the vertical geometry as compared to 21.5 cm for 350 inclined geometry. The 350 inclined settler gave a much higher settling as compared to the vertical channel. This shows that the CFD model used with the different assumptions is able to capture the Boycott Effect and can be applied to a continuous system.

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Figure 7 : Comparision of experimental data with simulated result

The velocity field in settling

The settling of the particles induces a velocity field in the liquid phase. This is readily predicted by the CFD simulations. The velocity flow field thus determined helps us in understanding the cause behind increased settling in inclined channels. Kohara et al. [10] previously used a fluid mechanical model to develop a better understanding of the enhanced settling of mammalian cells within open-ended inclined spaces. They found that the convective flow within the plates was 20 times the Stokes’ velocity of the cells.Figure 8 (a) depicts the velocity contours and 8 (b) the velocity vectors in a channel inclined at 35 degrees to the vertical. Figure 9 is a zoomed version of the channel which shows the recirculation at the top and bottom. This clearly confirms the circulation pattern in the inclined channel.

Inclination of 350 (case 1 from Section 2)

Figure 8 (a) Velocity contour (b) Velocity vectors (zoomed in)

Figure 9 : Velocity vectors (zoomed in) reveal a circulating pattern

For the particle size chosen (137 µm), the Stokes settling velocity of particle is = 0.0215 cm/s and is obtained from

vs=g (ρp−ρf )D

2

18 μ

For hindered settling, this reduces by a factor of (1-volume frac)4.6 This comes by following Richardson & Zaki’s method where Vhindered

= Vterminal (1- volume fraction)n , n=4.6 in this case .This corresponds to the domain where particle Reynolds number Rep is less than 0.2 . Using this, the hindered Settling velocity of particles is obtained as 0.013 cm/s

We now discuss the y velocity component in the system which determines the settling velocity. This is depicted in Figures 10 and 11 for a vertical and inclined channel respectively.

It can be seen that for the vertical system the y-velocity of the particles are comparable to the hindered sttling velocity predicted by Richardson and Zaki correlation. However for an inclined channel, the y-velocity of particles trapped in the vortex ranges from -0.24 to -1.73 cm/s (at time = 100 s). This settling velocity is 20-150 times that calculated by Richardson & Zaki’s method see Fig.11.

For 350 inclined system,

Figure 10 (a) : Y-velocity profile at time = 100 s

Figure 10 (b) : Y-velocity profile at time = 300 s (Double arrow indicates the height at which velocity profile is calculated)

The vortex comes down and becomes smaller when the particles settle. Also, their respective velocities decrease with time. Comparing the Y-velocity at 100 s and 300 s, we can see that the maximum Y-velocity decreased from 1.6 cm/s to 1.2 cm/s. This was expected as rate of sedimentation decreases with time.

The flow field in the particle-containing region was considerably more complex and several interesting phenomena were observed. At the start of the experiment, a rapid circulating motion developed throughout most of the suspension. The observed circulation was due to continuity which requires that there be no net flow across a plane of constant x; hence the upward flow of the suspension caused by the motion of the clear-fluid layer must be accompanied by a corresponding downward flow elsewhere in the suspension.

The particles close to the clear-fluid interface were observed to rise rapidly, come to an abrupt stop at the top of the suspension, and then descend rapidly in a thin layer immediately adjacent to that where the particles were rising. This can be inferred from Figure 9.

For vertical system,

Figure 11 : Y-velocity profile at height = 25 cm at time = 100 s and 300 s (Double arrow indicates the height at which velocity profile is calculated)

Y-velocity ranges from -0.03 to -0.005 cm/s. Hindered Settling velocity of particles as calculated by Richardson & Zaki’s method is 0.013 cm/s. The Hindered settling velocity of particles as calculated by Richardson & Zaki’s method and the settling velocities of particles obtained from simulations are in agreement.

Time = 100 s

Time = 300 s

Studying the impact of inclined surface on settling

To study the effect of impact of inclined surface on settling we study three different geometries each have a different ratio of the vertical and inclined portions. These are depicted in Fig.9 .The three cases are such that

Case 1: More straight (30 cm), less inclined (15 cm)

Case 2: Equal straight, Equal inclined

Case 3: Less straight (8.5 cm), more inclined (42 cm)

Angle of inclination is 450

Case 1 Case 2 Case 3

Figure 12 : Geometry of the three cases

All the three geometries have a constant volume and vertical height of 40 cm.

At time = 600 s, Interface heights obtained by the simulations were:

Case 1: 29.0 cmCase 2: 25.4 cm

Case 3: 19.2 cmThe clear interface is marked at the position where the particle volume fraction reduces to half of the initial concentration. The interface heights are measured from the bottom.

Comparing above results with the ones stated earlier, Fig. 10 contains the simulation predictions of the interface height versus time for the different geometries.

Figure 13 : Comparision of settling rate from the simulated results

It is clear from the above graph that the larger the fraction of the inclined surface, the more is the settling. This was expected as there is more area available for the particles to settle and slide.

Continuous Flow System

As the batch system simulation predictions were in line with the experimental data, it is fair to assume that the models and the way the simulation is set up are accurate. We now discuss the behavior of the continuous flow sedimentation system.

For the validation of model for the continuous system, The experimental data was obtained from Batt BC, Davis RH, Kompala DS. Inclined sedimentation for selective retention of viable hybridomas in a continuous suspension bioreactor. Biotechnol Prog. 1990;6:458–464.

The continuous separation of nonviable hybridoma cells (8 Microns) from viable hybridoma cells (13 Microns) by using a narrow rectangular channel that is inclined from the vertical was investigated experimentally. It was found that at high dilution rates through the chemostat, over 95% of the viable cells could be partitioned to the bottom of the settler while over 50% of the nonviable cells are removed through the top of the settler. This successful separation is due to the significantly larger size of the viable hybridomas than the nonviable ones.

The effectiveness of the settler in selectively retaining viable hybridomas in the bioreactor while permitting the removal of nonviable hybridomas was shown to depend on the flow rate through the settler.

The cell density was not determined exactly, but a crude neutral buoyancy measurement indicated that it is approximately 1.06 g/cm3.

Two inclined sedimentation channels were used in this study. Each was made of glass and had the same rectangular dimensions of 5 cm in width and a 0.5 cm separation between the two inclined surfaces. One sedimentation channel had a length of 37 cm, while the other was 23 cm long.

Particles considered for the simulation are nonviable hybridoma cells (8 Microns) and viable hybridoma cells (13 Microns) . The fluid properties considered were density = 998 kg/m3 and viscosity = 0.001 kg / m-s. The maximum particle volume fraction (packing fraction) = 0.53

The external inclined sedimentation channel was kept at a constant angle of 30° from the vertical, in order to provide sufficient area for sedimentation while allowing the sediment to easily slide down the inclined wall. Flow through the inclined settler was generated by a peristaltic pump at the settler outlet. Cells that settle completely from suspension are returned to the bioreactor by gravity flow of the sediment layer. Smaller cells that do not have sufficient time to be removed from suspension are washed out in the settler overflow stream.

Effect of settler overflow rate on the concentrations of viable and nonviable cells in the overflow stream relative to those in the reactor. An inclined settler 37 cm in length at an angle of inclination 300 was used in the study

Instead of recycling the settler overflow stream, the overflow stream became the reactor effluent. The feed rate was adjusted to exceed the overflow rate slightly, with the effluent tube employed in chemostat operation used as a level control to maintain constant culture volume.

The final mesh size used has a Maximum face size of 0.5 mm. Further, inflation boundary layer meshing is used wherever required (Case 3 and 4).

Figure 14 : Continuous Inclined cell settler Setup

Figure 15 : Geometry and meshing (zoomed in) of the inclined sedimentation channel

Figure 16 : Geometry and meshing (zoomed in) of the inclined (with plates) sedimentation channel

Case 1 Case 2 Case 3 Case 4

Vertical Inclined Inclined (4 Plates) Inclined (7 Plates)

Figure 17 : Geometry of the four cases which are being simulated

A line probe ( a yellow line) is inserted from the inlet to the outlet. As it is a 2-dimensional simulation, the probe lies in the plane of the inclined settler. Volume fraction of particles is plotted at this line for different cases.

Inlet

Recirculation

Outlet

Grid independence Study

A grid independence study was conducted to ensure that the final solution was independent of the mesh size. The final converged solution of Case 4 (inclined settler with 7 plates) is used for the same.

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Grid independence StudyVolume fraction vs Length

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Figure 18 : Grid independence study

There is no significant difference (< 5% error) between the steady state results obtained by using 0.5 mm and 0.4 mm mesh.

Solution Method

Pseudo transient approach is used to find a steady state solution for continuous systems. Pseudo time step size used is 2 seconds. For convergence of the solution, the residuals were monitored. All scaled residuals were less than 10-4 for the converged steady state solution. Alternatively, when the solution stops changing with time and scaled residuals are below 10-3, the solution obtained is a steady state solution.

Results

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Figure 19 : Comparision of simulated results under varying conditions.

The difference in curvature [between inclined(no plates) and 4-7 plates] can be attributed to the fact that it is easier to drain fluid out as compared to the particles.This is because of the lower drag offered to fluid as compared to particles. Particles are heavier so they are subjected to a larger force in vertical direction. When the particles are completely settled ( as in case of 4-7 plates), this behaviour is not visible. But in the vertical case and the inclined case, there is still a large proportion of particles near the outlet. So, more fluid is being drained out of the system as compared to the particles.

As the number of plates increases, settling increases as the particles have a lot more area to settle. Also, the particles have to travel a smaller vertical distance till it reaches a wall as compared to the case without plates. So, we expect settling to increase as more and more plates are introduced to the settler.

Case 1 (Vertical) Case 2 (Inclined)

Case 3 (4 plates) Case 4 (7 plates) Figure 20: Particle Volume fraction contours at steady state under varying --conditions

As can be seen from the contours in Fig 20, inclining the vertical system gave a higher settling. Dark blue colored contour represents the clear fluid. Comparing the contours for Cases 2, 3 and 4 suggests that increasing the number of inclined plate

results in increased settling of particles. Introducing plates in the inclined system further enhanced the settling by decreasing the distance particle has to settle before it could roll down the inclined plate and reach the underflow (recirculation outlet).

The above inference is clearly visible from the volume fraction v/s length plots as depicted in Fig. 19.

EFFECT OF MESH SIZE ON SEDIMENTATION CFD ANALYSIS

When dealing with micron size particles, mesh sizing becomes an important factor. As the particles are very small (micron size) , the meshes near the boundary should also be fine enough to capture the particle wall interaction.

Without the use of inflation meshing, we would have to mesh the whole geometry with elements of sizes comparable to that of the sediment. The use of inflation layer boundary mesh significantly reduces the number of elements in the mesh as we selectively mesh the region where the settling is predominant ,i.e., near the wall boundary.

In particle solutions, the grid cell size should be large enough to contain a number of particle parcels. The grid must also be fine enough to resolve the physics of the problem. A check is made to evaluate the infuence of the grid on the sedimentation calculations.

4 different types of meshes were used in this analysis. The whole idea behind this was to get a converged solution with least number of nodes (for reducing the computational time).

Some terminologies used in Inflation meshing are defined below:

The growth rate (g) determines the relative thickness of the adjacent inflation layer. As we move away from the face to which the inflation control is applied, each successive layer is approximately one growth rate thicker than the previous one. For e.g., a growth rate of 1.2 implies that the successive layer will be 1.2 times or 20% thicker than the previous one.

The number of layers (n) control determines the actual number of inflation boundary layers in the mesh.

First layer height (h1) determines the height of the first inflation layer.

S. No.

Mesh size

No. of elements

No. of nodes Boundary layer inflation

No. of Boundary layer (n)

Growth rate (g)

First layer height (h1)

1 1 mm 13380 26050 Yes 4 1.2 0.01 mm

2 1 mm 12672 24304 Yes 4 1.2 0.1 mm

3 0.7 mm 25769 51950 Yes 6 1.2 0.02 mm

4 1.5 mm 9484 18339 Yes 5 1.2 0.015 mm

Figure 21: (a) Mesh 1 ,Mesh size =1mm, n =4 , g =1.2 , h1 =0.01 mm (b) Zoomed in inflation boundary layer meshing

Figure 22: Mesh 2 Mesh size = 1 mm, n =4, g = 1.2 , h1 =0.1 mm

Figure 23 (a) : Mesh 3 , Mesh size = 0.7 mm, n =6 , g =1.2 , h1 =0.02 mm

Figure 23 (b) : Zoomed in inflation boundary layer meshing

Figure 24 (a): Mesh 4 Mesh size =1.5 mm , n =5 , g = 1.2 , h1 =0.015 mm

Figure 24 (b): Zoomed in inflation boundary layer meshing

RESULTS

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Figure 25 : Comparision of simulated results under varying meshes.

Comparing Mesh 2 with the other three meshes, we can clearly see the impact that boundary layer meshing has on settling behaviour.

The first layer height of Mesh 2 is 5-10 times that of the other meshes. As settling is a boundary (wall) layer phenomena, the first layer height has a very significant impact on the sedimentation of particles.

Number of elements in Mesh 2 (12672) is more than that in Mesh 4 (9484). Inspite of that , Mesh 2 underestimates the sedimentation of particles . This is because of the larger first layer height is Mesh 2 (0.1 mm) as compared to Mesh 2 (0.015 mm). As the particles are very small, the meshes near the boundary should also be fine enough to capture the particle wall interaction.

The mesh size in regions apart from the boundary has a minimal impact on the settling rate.This can be seen by comparing the particle volume fraction profiles obtained from Meshes 1,3 and 4. These three meshes differ significantly in the mesh size and consequently the number of elements. The first layer thickness of Mesh 1,3 and 4 are 0.01, 0.02 and 0.015 respectively. Inspite of different mesh sizes, all the three meshes gave nearly the same solution. This suggests that the mesh sizing does not have a significant impact in regions apart from the boundary.

Particle deposition assumption can also be used to reduce the computational time. According to this assumption, the particles are supposed to be deposited as soon as they reach the wall. The particles leave the system when they come in contact with the wall.

The problem with the above assumption is that it is only valid at small concentrations. As long as the deposited sediment does not influence the fluid above it, this assumption holds true. But at higher concentrations (say 30% v/v ), this assumption may not hold true.

Experiment Studies and their CFD SimulationsExperiments were conducted in cylindrical test tubes of diameter 4.5 cm. The fluid medium is water having density of 998 kg/m3 and viscosity of 0.001 kg / m-s. Calcium carbonate was used in this sedimentation analysis. Mean diameter of calcium carbonate is 18 microns. Density of Calcium carbonate is 2800 kg/m3.

Angle of inclination is 150. Concentration of calcium carbonate is 5% w/w. This is equal to 1.8% v/v.

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50

60

70

80

Conc. = 5%

Inclinedl Settling - 15*Vertica SettlingSimulated inclinedSimulated vertical

Time (sec)

Heig

ht(c

m)

Figure 26 : Comparision of experimental data with simulated results

Even though the particles used are not monodisperse and standardized , CFD simulations are still in line with the expermental data.

Comparision of Different Settler Designs for Settling Efficiency

Description of the multiphase system :

For these simulations, the volume was kept constant at 1 cm3. Also, the flow rate was kept constant for system equivalence. The particles were assumed to be monodisperse with a size of 8 microns and density of 1060 kg/m3. Initial volume fraction of particles was taken as 0.1 .The maximum particle volume fraction (packing fraction) = 0.53

The fluid properties considered chosen were density = 1000 kg/m3 and viscosity = 0.001 kg / m-s. These constant volume settlers are then analyzed for their sedimentation efficiency.

For efficiency of a settler , we define E (Sedimentation Efficiency) as the percentage of particles retained in the settler.

E=[ concentration of particles∈the feed−outletconcentration of particles∈the feed ]×100

Meshing

The solution obtained depends on the grid size chosen. The final solution which has numerically converged should be independent of the grid. The solution changed initially when we went from coarse mesh to fine mesh. But after a critical mesh size, the solution becomes independent of the grid size.

The final mesh size used has a maximum face size of 0.5 mm.

Sedimentation rate was found to increase as we used a finer mesh. This also gave a realistic solution (closer to experimental results) while using a very fine mesh. In particular it was necessary for the meshing near the boundary (walls) to be very fine (0.01 mm) as sedimentation is a boundary phenomenon.

Models and solvers used here are same as that used for the vertical bimodal sedimentation case.

The final mesh used for computational fluid dynamics study for different geometries are summarized below:

S. No. Mesh size No. of elements

No. of nodes

Boundary layer inflation

No. of Boundary layer (n)

Growth rate (g)

First layer height (h1)

Design 1 0.5 mm 89127 28749 Yes 5 1.2 0.01 mm

Design 2 0.5 mm Yes 5 1.2 0.01 mm

Design 3 0.5 mm Yes 5 1.2 0.01 mm

Design 4 0.5 mm Yes 5 1.2 0.01 mm

Design 5 0.5 mm Yes 5 1.2 0.01 mm

Design 6 0.5 mm Yes 5 1.2 0.01 mm

Design 1 :

Figure 27

Dimensions of the rectangular inclined channel used are 20 cm x 0.5 cm x 0.1 cm .

Length (l) , height (h) and width (w) of the settler are indicated in figure

Distance between the parallel plates is 0.5 cm

Settling Surface Area = 20 x 0.1 = 2 cm2.

Projected Area = 2 sin 30 = 1 cm2

h

l

w

Figure 28

Phase 2 is the particle phase.

E = [1- (4.445/5.3)] x 100

= 16.13 %

Figure 29

DESIGN 2 : Inclined Cylinder

Figure 30

Radius of the cylinder is 0.112 cm. The volume is kept constant at 1 cm3 . Length of the cylinder is 25.3 cm.

Total curved surface area of the cylinder is 17.858 cm2

Only the bottom half of the cylinder effects the settling. So only the horizontal projection of bottom half of the cylinder is considered.

Effective Area available for sedmentation 3.6 cm2

E = [1- (3.556/5.207)] x 100

= 31.5 %

s

DESIGN 3 :

CONE

Volume is 1 cm3 .

Curved Surface Area of the cone is 5.1425 cm2.

Top radius 0.59 cm Bottom Radius 0.05 cm

Height is 2.5 cm

Sin 15 ( 3.14 x 0.59 x 2.5 )

Horizontal projected Surface area is 1.19 cm2

DESIGN 4

Volume is 1 cm3 .

Surface Area is 7.878 cm2.

Top radius 0.405 cm Bottom Radius 0.02 cm

Height is 5.5 cm

Horizontal projected Surface area is 0.5136 cm2

DESIGN 5

Volume is 1 cm3 .

Surface Area is 6.12 cm2.

Top radius 0.73 cm Bottom Radius 0.02 cm

Height is 1.75 cm

Sin 67.3 x 3.14 x 0.72 x 1.75

Horizontal projected Surface area is 1.67 cm2

DESIGN 6

Volume is 1 cm3 .

Surface Area is 7.07 cm2.

Top radius 0.95 cm Bottom Radius 0.02 cm

Height is 1.032 cm

Horizontal projected Surface area is 2.83 cm2

For a given volume V, maximizing the horizontally projected surface area.

V=13π r2h

Curved Surface Area of the cone CSA=π rl

l=√h2+r2

h=3Vπ r2

DESIGN 6:

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