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SOLID ENTRAINMENT INTO A HORIZONTAL SUBMERGED JET WITHIN A FLUIDIZED BED

Shashank Natesh (0995005)

1. INTRODUCTION

Modeling of gas-solid flows is very common in industrial processes like fluid coking, oil shale retorting, coal gasification and polymerization. Computational fluid dynamics plays a vital role in analyzing these processes and exploring the influence of various flow and geometric parameters which would lead to an eventual improvement. Fluidized beds employ such kind of flows where the material to be ‘processed’ is impregnated laterally with a gas stream. Lately, industries have been using multiple fluidized beds to improve the plant efficiency. But to avoid long transfer lines (leading to mechanical valve corrosion/plugging, erosion and insulation problems) to shuttle solids from one fluidized bed to the other, they have incorporated a new system called as a compartmentalized fluidized bed. It contains a gas jet which entrains solids from one compartment to other via a draft tube. Since both compartments use different fluidization velocities, the main aim of such a system is to avoid gaseous cross contamination between the beds. Thus, it is necessary to circulate solids in a regulated manner to limit the amount of gas being transported between beds. The most important factors that govern the flow in such a submerged nozzle-draft tube system are jet penetration length and solid-gas mixture entrainment into the incoming jet. Felli [1] and Hulet [2] investigated the entrainment process in submerged jets by experimental work and measured the solid entrainment rates into the jet. A suitable model on the theory of turbulent jets is proposed by Abramovich [3]. Fig. 1 depicts three vital regions of a typical submerged turbulent jet, the potential core region, the transition region and the fully developed region. A pressure difference is created between the high speed jet and the turbulent shear layers at the bed-jet interface. If the bed void fraction and the jet gas flow rate are appropriate, the solid particles would be entrained towards the draft tube and then re-injected to the core of the bed. Idelchek [4] discusses the flow patterns and ways to reduce the resistance to flow at the entrance into conduits. Bohnet & Teifke [5] concluded that apart from the jet momentum and particle properties, the particle’s position within the jet stream determines when it first contacts the jet. After detailed study of [4] and [5], it was clear that altering the design of the region between the jet and draft tube by introducing different solid structures termed as shrouds would increase the entrainment rate of solids into the jet. Hulet et al. [6] performed a numerical investigation explaining the effect of shroud on the solid entrainment of a submerged jet. Numerical work performed by Taghipour et al. [7] and Tyler & Mees [8] were carefully reviewed to understand the hydrodynamics of fluidization and used as a stepping stone for the completion of this project. The former involves the study of bed expansion ratio and pressure drop inside a fluidized bed, while the latter studies flow around a horizontally submerged jet in a fluidized bed. Many drag coefficient correlations have been suggested

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by various scientists but there is still no consensus on which drag model to use for a specific fluidized bed problem.

Fig. 1. A typical submerged turbulent jet (from Hulet et al. [2])

The present manuscript compares the flow fields inside 2D fluidized beds for both configurations, with and without shrouds, and studies how the introduction of two modified drag models influences solid entrainment. The results are then compared to the work of Hulet et al. [6] and half-jet videos for solid and gas flow patterns obtained using a special transparent plate in the wall of the fluidized bed and measured solid and gas entrainment levels inside the bed [9]. The CFD software FLUENT (version 6.3.26) was used for this study. FLUENT models gas-solid two-phase flows in two ways: Eulerian two-fluid approach and Eulerian-Lagrangian approach. The former treats both the gas and solid phase as an immersed continuum. The latter tracks each particle by solving its equation of motion in the Lagrangian frame. The remaining sections describe the geometry, governing equations, modeling and simulation approach using the Eulerian two-fluid model and results of the parametric study. 2. THEORETICAL BACKGROUND 2.1. Governing Equations

2.1.1. Conservation of mass and balance of momentum The continuity equation and the momentum balance equations for phase i are represented by equations (1) and (2) respectively.

(1)

(2)

Zero mass transfer is assumed between the two phases and both phase volume fractions must sum to 1. For the ith phase with shear and bulk viscosities µq and λq, respectively, the Reynolds stress tensor is given by equation (3):

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(3)

For the gas phase, equation (3) becomes:

(4)

where µg,e is the effective turbulent viscosity comprising of both the turbulent and laminar viscosities. Similarly, the Reynolds stress tensor for solids is given below.

(5)

The solids bulk viscosity λs is a measure of resistance of the particle phase to compression and expression forces, obtained using the form:

(6)

The shear viscosity µs includes two parts: one due to translation (µs,kin) and the other due to collision (µs,col)of the particulate phase.

(7)

(8)

If the solid volume fraction is less than the maximum packing limit (compressible regime), the solids pressure is calculated according to equation (9) and included in the granular momentum equation as the gradient of pressure.

(9)

where ess is the coefficient of restitution of the particle-particle collisions, g0,ss is the radial distribution function, and Θs is the granular temperature. According to the kinetic theory of granular flow, the granular temperature is proportional to the kinetic energy of the moving particle. The expression for g0,ss used in the study is;

(10)

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And, the granular temperature is defined using a partial differential equation in the equation (11), given by Ding and Gidaspow.

(11)

2.1.2. Interphase exchange coefficients Drag force on the gas by the particle phase is one of the dominant forces in a fluidized bed. It can be generally represented as in equation (12).

(12)

The correlation is dependent on the solid volume fraction and slip Reynolds number.

(13)

where τs is the particle relaxation time and f is defined according to a specific drag model. Two drag models are used for the closure expression: the Syamlal & O’Brien drag model based on the terminal velocity of the fluidized beds and the Gidaspow model which is a combination of Wen & Yu model and Ergun equation. The modified equations of both these models, listed in Table 1 are incorporated into FLUENT via user defined functions.

1. Syamlal & O’Brien drag model

The coefficients A and B are given by the following equations.

Referring to the work in [6], the modified values of A and B were 1.03 and 1.095 respectively.

2. Gidaspow drag model If αg > 0.8, the gas-solid interchange coefficient takes the form:

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When αg ≤ 0.8,

Table 1 Gas-Solid Interphase Drag Model Equations

3. MODELING 3.1. Computational Domain and Operational Parameters One of the major assumptions of this study is that it is two-dimensional. The computational domain contains only a portion of the compartmentalized fluidized bed including the nozzle (jet), draft tube, partition wall and front and rear walls.

Fig. 2. Schematic of experimental fluidized bed (left) and the computational domain section (right) (from Hulet et al. [6]).

To emulate the numerical setup of Cui et al. [10] and reduce the size of the computational domain, only a segment of the nozzle was considered and the boundary face on the left was considered to be a wall. Fig. 2 shows the computational domain, which is a vertical slice of the grid used in [6], since it is a 2D investigation. The length L* (x-axis) and the height H* (y-axis) of the domain are 0.1143 m and 0.1016 m respectively. Table 2 summarizes the important geometric and operational parameters used in the study. Primarily, four cases

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were studied by incorporating two drag models for both the shrouded and non-shrouded configuration (for a fixed distance l). It also shows the geometric parameters for the shroud, selected corresponding to the numerical results [6] which demonstrated the most significant increase in the solid entrainment rate (Fs).

Variable Value Description

L* 0.1143 m Length of one fluidized bed (x-axis) H* 0.1016 m Height of the computational domain (y-axis) l 0.038 m Distance between the jet tip and the draft tube inlet D 0.025 m Diameter of the draft tube d 0.0045 m Diameter of the nozzle/jet L 0.051 m Length of the adjoining draft tube Fg 0.00075 kg/sec Gas flow rate from the nozzle Ds 0.044 m Shroud Diameter

Ls 0.019 m Shroud Depth (50% shrouded)

Table 2 Geometric and Operational Parameters used in the CFD runs

The solid particles used in the simulation were Geldart-B particles with a mean diameter of 135 µm (assuming monotonic size distribution). The particle and air densities were assumed to be constant at 1400 and 1.225 kg/m3. 3.2. Mesh Fig. 3 shows the computational grids constructed and meshed in GAMBIT. A structured Quad-type mesh was generated and then adapted in FLUENT further to run grid and time independency tests.

Fig. 3. Uniform mesh generated for a shrouded configuration in GAMBIT and exported via FLUENT.

The basic coarse grid size was taken as 0.00225 m. In total, two grids were built, for a shrouded and a non-shrouded configuration. 3.3. Boundary and Initial conditions The boundary conditions for both gas and solid phase are given in Table 3. The pressure outlet condition on the draft tube exit is set using a user-defined function (UDF), a profile

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mimicking the pressure distribution in the experimental fluidized bed. Similarly the top pressure inlet condition is set to a value of static pressure for a bed of height 1.27 m. Zero penetration and zero solid-accumulation at the walls is assumed for the left, partition and nozzle walls. Remaining settings were left at their default values as given by FLUENT. Turbulent intensity and length scales were selected as given in [6], according to the size of the each boundary face. For the bed, the length scale was chosen to be 0.07 times the hydraulic diameter (DH) which is given by equation (14):

(14)

Boundary Face Gas Solids

Nozzle Inlet & Grid inlet Type Velocity Inlet Direction Specification x-axis & y-axis Value (m/sec) 162 & 0.11 Turbulent Intensity 5% Length Scale 0.0045 m & 0.07DH Granular Temperature (m2/sec2) n/a 0.0001 Volume Fraction 1 0 Draft Tube Outlet & Top Free Surface Type Pressure Outlet & Pressure Inlet Value (Pa) gαs (ρs-ρg) (Hbed – y) & 8978 Turbulent Intensity 5% Length Scale 0.05D & 0.07DH Backflow Granular Temperature (m2/sec2) n/a 0.0001 Backflow Volume Fraction 0.44 0.56

Table 3 Boundary Conditions for both solid and gas phase

The solution was initialized by averaging boundary conditions from all the zones. The nozzle inlet velocity was calculated on the basis of air mass flow rate of 0.00075 kg/sec. A fluidization velocity of 0.11 m/sec was imparted from the grid inlet zone. The backflow volume fraction at the pressure inlet and outlet faces was considered on the basis of assumptions made in [6]. 3.4. Simulation Settings All runs are conducted using a double precision pressure-based segregated solver and an Eulerian two fluid description of both phases. All the flow, volume fraction and turbulence equations were solved using a Phase Coupled SIMPLE approach. The FLUENT user manual recommended using a first order method for discretization of the flow variables and a standard k-ε model for the first few hundred time steps in order to maintain numerical stability. Then, the RNG k-ε model and QUICK discretization scheme was employed. This optimal approach was taken on the basis of comparison between the numerically diffusive first order scheme and the more accurate second order QUICK scheme. The rate of change of variable was controlled by the under-relaxation factors. They were chosen to undergo proper discretization of the flow variables and attain quicker convergence. The value of C1-

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ε was changed to 1.56 as suggested by Hulet et al. [6]. The operating pressure was set to 101,325 Pa and gravitational effects were included. Both the Syamlal and Gidaspow drag force models were modified by means of a UDF. The residuals were set to 5e-05 for all variables except continuity which was set at 1e-05. 3.5. Solution Settings Grid size and time step independency tests were conducted on the non-shrouded grid to ensure that the solid entrainment rates were not dependent on one particular chosen time step/grid size. The coarse grid was imported into FLUENT and the region between the jet and draft tube was refined twice. The relative change in the elements inside the grid is shown in Table 5.

Non-Shrouded Case Grid Size (mm) Number of cells Time Step Size (sec)

Basic Grid 2.25 2444 1e-04 After 1st Adaption 1.125 3884 5e-05 After 2nd Adaption 0.5625 9776 2e-05

Table 5 Parameters for grid-size and time step size independency tests

Fig. 5 depicts the solid entrainment rates at different grid sizes for the non-shrouded configuration and the Gidaspow drag model. The average solid entrainment rates after 0.3 sec of computational time are 0.0893 kg/sec and 0.0905 kg/sec for time steps 5e-05 sec and 1e-04 sec respectively. Thus a time step of 1e-04 sec was used for all computational runs. 4. RESULTS AND DISCUSSION 4.1. Time Dependent Variation of Fs The graph below shows the variation of the solid entrainment rate exiting out of the draft tube with respect to time.

Fig. 4. Non-shrouded case: Variation of solid entrainment rate with respect to time

The spike with maximum value of Fs is seen very early in the flow and during its development. It is clearly evident from Fig. 4 that the solid entrainment rate does not

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fluctuate over lesser values after about 0.7 seconds. Authors in [6] also show a similar graph where after 0.8 seconds of computational time, the solution reaches a quasi-steady state. Since the simulations for all four cases are performed for a 1 sec time period, the values of solid entrainment rates listed in Table 6 are averaged over that time. Along with the current numerical results, the CFD simulation and experimental results from [6] are also listed for direct comparison.

Simulation Case Drag model l (m) Solid Entrainment Rate (kg/sec)

Current study Numerical value Experimental value

Non-shrouded Syamlal O’Brien 0.038 0.087 0.091 0.103

Shrouded (50%) Syamlal O’Brien 0.038 0.0714 0.069 0.066

Non-shrouded Gidaspow 0.038 0.089 0.0934 0.103

Shrouded (50%) Gidaspow 0.038 0.073 0.0682 0.066

Table 6 Time averaged solid entrainment rate at the exit of draft tube

It can be observed form the above table that the simulated values in this study are not very far off the referred numerical value owing to the facts that: (1) two-dimensional study is conducted and (2) the drag models over-predict the flow inside the bed. But one would think that including a shroud type configuration would increase the solid entrainment rate at the exit of the draft tube, contrary to what the table suggests. Although the flow rate of solids decrease after the shroud is kept in place but the results show a decrease in the gas flow rate as well. This means that when the less amount of gas is required to entrain more or less the same amount of solids from one bed to the other than when the shroud was not present. 4.2. Solids Holdup Fig. 5 shows the contour plots of solids volume fraction at five equal spaced times in one approximate period. In all these figures, gravity points downwards. A periodic process of entrainment of solids can be observed for a total period of 1 sec. At t = 0.1 s, a dense cloud of solid particles is observed near the shear layer of the jet around the draft tube. With increasing time, this cloud is drawn into the region between the jet and the draft tube and dragged near the exit. But in the penultimate contour, the dense cloud begins to re-form as the flow field approaches the start of the next entrainment cycle. The flow is not symmetric is nature because of the influence of gravity on the flow in the vicinity of the jet.

a) t = 0.1 sec b) t = 0.3 sec

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c) t = 0.5 sec d) t = 0.7 sec

e) t = 0.9 sec

Fig. 5. Contours of solid volume fraction at five equally spaced times

The entrainment process basically transforms all the kinetic energy of the jet into some kind of work to accelerate the solid-gas mixture. And since there is no pressure recovery for the jet because of the same static pressure profile of the draft tube and fluidized bed, the two main driving forces in the solid entrainment are the pressure-ratio at the jet exit region and the drag force at the edge of the jet. The former attracts the solid particles into a region of vacuum pressure created by the expanding jet and then these particles are pushed towards the draft tube. Higher the velocity of the jet, higher would be the pressure ratio and entrainment rate at the exit would be enhanced. While the latter results from the stress created by the difference between the velocities of gas and solids (slip velocity). The slip velocity term is included in the drag model equations and it can be seen that higher the velocity of the gas, more would be drag force on the solid and hence increased entrainment. 4.3. Air flow field: With & without shroud The flow patterns of gas (air) phase are illustrated for an l distance of 0.038 m for both shrouded and non-shrouded cases. The gravity again points downward for all these vector-plots. Fig. 6 shows a vector-plot of the air flow field at t=0.9 sec seen in both shrouded and non-shrouded configurations for the Syamlal drag model case. After a closer look at the velocity vector plots of the gas phase, we can observe strong recirculation zones at the tip of the jet when the shroud is in place. These recirculation zones have two major advantages with respect to the entrainment of solids into the region between jet and draft tube: (1) Due to enhanced vortices at the tip of the nozzle, low pressure is created in that zone and as

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described earlier, they tend to suck more gas-solid mixture through the turbulent shear layer of the jet; (2) Even though more gas-solid mixture is entrained, less gas is used to shuttle solids towards the draft tube exit because the recirculation zones would keep on recycling the same gas around the nozzle tip before getting pushed away to the shroud inlet.

a) Without shroud b) With shroud

Fig. 6. Gas velocity vectors showing the effect of shroud on solid entrainment

The observation above is also supported by results of the experimental CO2 tracer study, which measured a 50% decrease in the gas flow rate when the shroud was in place. The shroud also influences the flow of gas as it moves counter-current to the jet. 4.3. Solids flow field: With & without shroud The experiments conducted in [9] showed that the solids were observed to move in intermittent waves and a very unstable behavior was depicted in the absence of the shroud. The jet is also seen to diverge as the solids react with the cross flow of fluidization from the grid-inlet, creating rising bubbles. But when the shroud is present, the solids move in the opposite direction to the jet and particles above the jet moved faster than below it. Such flow patterns in solids are also observed in the current simulated cases and are explained using Fig. 7. The shrouded jet is narrower and more stable due to improved interaction between the jet and the gas-solid mixture. Even though the shrouded jet is stable, the fluidization velocity tends to divert and solid particles get partially de-fluidized once entering the shroud cavity. This would certainly decrease the void fraction of the bed thereby decreasing the spacing between the solid particles. Now this would correspond to increase in the gas velocity as the high velocity jet would find more space to travel within the interstices. Drag force exerted on the particle is thus enhanced and thereby the solid entrainment. There is one more striking difference between the gas and solid vector plots. The recirculation zones in the solid vectors are very weak and are only seen near the inside wall of the shroud cavity. There are several reasons behind this physical observation: (1) The density of solids is nearly 1000 times that of air.

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(2) The particle relaxation time is very high, which leads us to explain that particle-gas inter-phase correlation is low (from equation 13). (3) Since the fluid velocity at the shroud wall above the jet is zero and maximum at the tip of the jet, there is a very high shear rate in that region of length 20 mm. This rate of shear would increase the drag on the particles. (4) These shear forces would also induce prominent but weak vortices inside the shroud cavity. And these vortices create low pressure regions thereby increasing the solid entrainment.

a) Without shroud b) With shroud

Fig. 7. Solid velocity vector plots depicting the altering flow patterns due to the presence of shrouds

There is a loss in the jet momentum due to the cross flow of fluidization which results in expending more momentum in entraining solids into the jet. Therefore, if the jet geometric and operational parameters are kept the same, a larger drag force is exerted on the particles inside the shroud compared to the case when the shroud is absent. 4.4. Pressure field

Fig. 8. Variation of pressure field along the length of domain: With & without shroud

The pressure variation across the length of the fluidized bed is depicted in the Fig. 8 for both shrouded and non-shrouded configuration. The graph clearly shows that a low pressure region forms due to the recirculation zones inside the shroud cavity for the

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shrouded case. On the other hand, the non-shrouded case marked a region of high pressure in the area between the jet and the draft tube and an operating pressure near the regions where the shroud would have present. For both cases, pressure gradually decreases as fluid moves towards the draft tube. 5. CONCLUSIONS Eulerian two-fluid model is chosen over the discrete phase Lagrangian method to simulate a section of the compartmentalized fluidized bed. Existing inter-phase drag models were modified and with the use of UDF, were compiled into the solution setup. Solution strategies for Eulerian model listed in the FLUENT’s user guide were strictly followed to obtain a solution closely matching with the referred literature. It can be concluded fairly that a structure like a shroud when placed at an optimum distance from the draft tube inlet, can increase the solid entrainment rate into a horizontal submerged turbulent jet. The increase in the entrainment rate is attributed to various reasons but primarily the solids partially de-fluidizing and decreasing the bed void-fraction. Thus, more drag force is exerted on each solid particle inside the jet for the same amount of gas flow rate. With the shroud in place, the jet entrains less gas and more solid. The shrouded jets are narrower and stable avoiding the formation of bubbles due to less interaction with fluidization cross flow. Vector plots and volume fraction contours demonstrate that shrouds strongly perturb the gas and solid flows in the vicinity of the jet. Insight into the gas-solid interaction phenomena through the use of CFD simulations led us to investigate different secondary flows responsible for the augmentation of the solid entrainment rate into the jet. Recirculation zones for both gas and solid phase are seen at the shroud inlet and shroud inside wall respectively. Although a better drag model needs to be incorporated to predict the flow accurately, but the current numerical study helps us to get a good qualitative as well as quantitative agreement with the numerical results and experimental work in the literature. ACKNOWLEDGEMENTS I would like to thank Dr. Metcalfe for his constant support in the term project development. And I would also be grateful to the personnel at the ECC for helping me out with Linux systems and networking issues. REFERENCES

Top References C. Hulet, C. Briens, F. Berruti, E.W. Chan, Effect of a shroud on entrainment into

a submerged jet within a fluidized bed, Chemical Engineering and Processing 47, 1435–1450 (2008). [6]

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C. Hulet, C. Briens, F. Berruti, E.W. Chan, Visualization of the effect of a shroud on entrainment of fluidized solids into a gas jet, Int. J. Chem. Reactor Eng. 5 (2007) S4. [9]

M. Cui, A.G. Straatman, C. Zhang, A computational study of gas-solid flow in an enhanced solid entrainment (ESE) system, Int. J. Chem. Reactor Eng. 3 (2005) A7. [10]

Other References

[1] V. Felli, Solids entrainment from a fluidized bed into a gas–liquid jet: effect of the draft tube, Diss., The University ofWestern Ontario, 2002.

[2] C. Hulet, C. Briens, F. Berruti, E.W. Chan, S. Ariyapadi, Entrainment and stability of a horizontal gas–liquid jet in a fluidized bed, Int. J. Chem. Reactor Eng. 1 (2003) A60.

[3] G.N. Abramovich, The theory of turbulent jets, M.I.T Press, Massachusetts, 1963. [4] I.E. Idelchek, Handbook of Hydraulic Resistance, CRC Press, Boca Raton, 1994. [5] M. Bohnet, J. Teifke, New results on the efficiency transformation in gas–solids

injectors, in: Proceedings—Reliable Flow of Particulate Solids: EFCE Publication Series, 1985, pp. 383–400.

[7] F. Taghipour, N. Ellis, C. Wong, CFD modeling of a two-dimensional fluidized bed reactor, in: Proceedings of the 11th Annual Conference of the CFD Society of Canada, 2003.

[8] J. Tyler, P. Mees, Using CFD to model the interaction of a horizontal feed jet on fluidized bed hydrodynamics, 11-8-2006.