Numerical and Experimental Investigation of Bubbling GasâSolid

ARTICLE pubs.acs.org/IECR

Numerical and Experimental Investigation of Bubbling GasSolid Fluidized Beds with Dense Immersed Tube Bundles Matthias Schreiber,*,† Teklay W. Asegehegn,† and Hans J. Krautz† †

Chair of Power Plant Technology, Brandenburg University of Technology Cottbus, Walther-Pauer-Strasse 5, 03046 Cottbus, Germany ABSTRACT: Numerical simulations of gassolid bubbling fluidized beds with and without dense immersed horizontal tubes were performed using the Eulerian-Eulerian Two Fluid Model (TFM) and applying the Kinetic Theory of Granular Flow (KTGF). The results were compared with experimental data obtained from a pseudo-2D fluidized bed test rig using a developed digital image analysis technique (DIAT). The influences of dense immersed horizontal tubes on bed properties (bed pressure drop and expansion ratio) and bubble hydrodynamics (bubble size, rise velocity, aspect ratio, and shape factor) were investigated numerically as well as experimentally. In the first part grid sensitivity with different mesh sizes was checked and effects using 2D and 3D domains were examined. Simulations with 3D domains gave better agreement with experimental data but were seen to be computationally expensive. For conducting intensive parametric studies of fluidized bed behavior the use of 2D domains remains indispensable. In the second part it could be shown that dense tube arrangements in the fluidized bed lead to repeated bubble break-up and coalescence in the tube bank region and therefore to fluctuating values of bubble size, rise velocity, aspect ratio, and shape factor. For different superficial velocities similar results were found which shows the high influence of dense immersed tubes on fluidized bed behavior. In addition no significant differences between staggered and in-line tube arrangement were observed. In general the simulations based on the Two Fluid Model showed good agreement with the experimental results.

1. INTRODUCTION Gassolid fluidized beds are widely applied in chemical engineering technology for combustion, drying, granulation, polymerization, and many other processes. They are characterized by intensive solid mixing, high heat transfer, and chemical conversion rates and the capability of continuous operation with wide ranges of solids. In many applications tubes are inserted to enhance the transfer and conversion rates, control the operating temperature, and reduce gulf circulation of solids. However, the lack of comprehensive understanding of the multiphase flow involved in these systems makes their design and scale-up very difficult. Particularly, the bubbling characteristics of fluidized bed systems are very complex, vary with the geometric construction and operating conditions, and influence the performance. The presence of tubes further complicates the fluid dynamics inside the reactors and strongly influence the gas and solid flow pattern through the bed. Understanding these influences on bubble hydrodynamics is the key issue for improving the design and operation of fluidized beds. Sitnai and Whitehead1 reviewed early experimental studies regarding the influence of immersed obstacles on the hydrodynamics of gassolid multiphase systems. They concluded that only little attention was given to the investigation of the influence of immersed tubes on bubbling behavior of fluidized beds. Even afterward only a few experimental investigations were done in this field. This was mainly due to lack of appropriate and reliable experimental procedures to overcome the harsh environment and opaque nature of the systems in order to accurately measure bubble properties of the whole fluidized bed. Almstedt and coworkers (e.g., Olowson,2 Olsson et al.3 and Johansson et al.4) measured bubble pierced length and rise velocity at discrete points using capacitance probe methods. Hull et al.5 were able to r 2011 American Chemical Society

experimentally measure bubble size, rise velocity and volume fraction along the whole bed height applying an imaging technique. In recent years the development of imaging techniques like digital image analysis has successfully improved the analysis of bubble properties (e.g., Shen et al.6 and Busciglio et al.7). In the last two decades, due to rapid growth of computer capacity and development of efficient numerical algorithms and codes, computational fluid dynamics (CFD) has become a powerful tool in determining the macro- and microscopic phenomena of gassolid fluidized beds. Numerical simulations are more flexible and less expensive to perform parametric studies of different bed geometries and operating conditions. Moreover, they can provide extensive data of bed and bubble characteristics for the complete reactor volume. However, these numerical models require intensive validation with experiments before using them for design and scale-up procedures. In general, two different types of models are widely applied today, the Discrete Particle Model (DPM) based on the Eulerian-Lagrangian approach and the Two Fluid Model (TFM) based on the Eulerian-Eulerian approach. The DPM treats the gas phase as continuous, while the solid phase is described as discrete particles, thus the Newton’s equations of motion for each particle are solved taking the total force acting on the particle including particleparticle and particlewall interactions into account. It is a more fundamental approach for fluidized bed applications, but its very high computational effort makes it prohibitive and limited to only a few particles and small beds. Deen et al.8 had reviewed the state of the art of Received: February 8, 2011 Accepted: April 28, 2011 Revised: April 7, 2011 Published: April 28, 2011 7653

dx.doi.org/10.1021/ie2002457 | Ind. Eng. Chem. Res. 2011, 50, 7653–7666

Industrial & Engineering Chemistry Research

ARTICLE

Figure 1. Setup of the pseudo-2D fluidized bed test rig: (a) hydraulic and (b) optical schemes.

the DPM applied to fluidized beds. The TFM, on the other hand, treats both the gas and solid phase as fully interpenetrating continua, thus averaged NavierStokes equations are solved for each phase with appropriate interaction terms between the phases. It requires less computational time and remains the only realistic approach for parametric investigation of fluidized beds of engineering scales (van Wachem et al.,9 van der Hoef et al.10). For the past few years the Two Fluid Model has been utilized intensively for parametric investigations of the macroscopic bed and bubble characteristics. For free bubbling fluidized beds many works can be found in the literature (e.g., van Wachem et al.,9,11 Hulme et al.,12 Patil et al.,13 Taghipour et al.,14 Lindborg et al.15). For fluidized beds with immersed horizontal tubes, however, the number of numerical studies of bubble hydrodynamics is relatively limited. Bouillard et al.16 studied the effect of internals on the porosity distribution using a single rectangular pipe immersed in a two-dimensional fluidized bed. Gamwo et al.17 performed computer simulation using TFM and compared the solid flow pattern of a 3D bed with staggered horizontal tubes based on the contour plots of voidage and solid velocity vectors. Gustavsson and Almstedt18 simulated a 2D bubbling fluidized bed containing two horizontal heat exchanger tubes. They investigated bubble properties at different pressure levels and compared with the experimental data of a 3D bed obtained by Olowson2 using capacitance probe measurements. Das Sharma and Mohan19 used the experimental results of Hull et al.5 to validate their numerical simulation of bubble properties. Yurong et al.20 studied the behavior of particles and bubbles using the TFM and used a body fitted coordinate system in order to match the boundaries of the immersed tubes. Schmidt and Renz21 and Gao et al.22 measured the solid volume fraction distributions around immersed tubes and gas flow behavior near immersed tubes respectively. But their main focuses were on the calculation of the heat transfer coefficients between the emulsion phase and the immersed tubes. Lyczkowski et al.23 used the experimental and numerical setup of Gamwo et al.17 and measured bubble diameter and rise velocity at three probe points.

Many of the mentioned studies were limited to beds with single or few immersed tubes. Moreover, their validations are mainly qualitative comparison such as voidage distribution and solid circulation near the tube surface in an attempt to investigate the heat transfer coefficient or erosion characteristics of the tubes. In this study detailed comparison and validation of the TFM with experimental results were performed for fluidized beds with dense immersed tubes. The bubbling characteristics of the beds were thoroughly analyzed and validated as well as compared to beds without tubes.

2. EXPERIMENTAL SETUP 2.1. Fluidized Bed Test Rig. The experiments were performed on a pseudo-2D fluidized bed test rig; its schematic diagram is shown in Figure 1. The bed has a height of 1200 mm, a width of 320 mm, and a thickness of 20 mm. At the bottom a windbox with an integrated porous plate distributor equalizes the gas flow and generates a sufficiently high pressure drop. To reduce electrostatic effects in the bed and therefore avoid inaccurate results the fluidizing air was humidified via a spray nozzle. The relative humidity was kept between 50 and 70%, which is within the suggested range of Park et al.24 The front and back plates are transparent to be able to use optical measurement techniques. Plastic tubes made of polyoxymethylene were attached to the back plate of the bed in order to simulate an immersed tube bank. Several staggered and in-line tube arrangements with different vertical and horizontal pitches are available and can be easily changed. To measure the pressure drop across the distributor and the bed height five differential pressure and one gauge pressure measurements were installed, see Figure 1(a). These data and the measured volume flow rate, temperature, and relative humidity of the fluidizing air were recorded and then analyzed. In Figure 2 the dimensions of the investigated fluidized beds with no tube, staggered, and in-line tube arrangement are shown. For the tube cases the vertical and horizontal pitch to tube 7654

dx.doi.org/10.1021/ie2002457 |Ind. Eng. Chem. Res. 2011, 50, 7653–7666


ARTICLE

Figure 2. Dimensions of the no tube (NT), staggered (S6), and in-line (I6) fluidized bed.

diameter ratios are equal to 2. They are based on dense immersed tube banks applied for pressurized steam drying of lignite in a bubbling fluidized bed dryer as described by Hoehne et al.25 As granular material spherical glass beads with a density of 2500 kg/m3 were used. The beads were sieved to get a narrow quasi-monodisperse size range from 300 to 400 μm with a mean diameter of 350 μm. 2.2. Digital Image Analysis Technique. In order to measure bed properties and bubble hydrodynamics from experiment and simulation an automatic digital image analysis technique (DIAT) was developed. This nonintrusive method of measurement allows to simultaneously observe the whole bed at once without interfering with the complex multiphase flow. An in-house software tool was programmed using Matlab/Simulink together with the Image Processing Toolbox for analyzing properties such as bed expansion, bubble size, bubble shape, and bubble rise velocity for experimental as well as numerical data sets automatically. Here, only a compact description of the developed DIAT will follow. For more detailed explanations see Asegehegn et al.26 The analysis is performed in five steps: 1) Image Acquisition During the experiments images of the whole fluidized bed were captured to allow a complete bed analysis of the bubbling fluidization dynamics. The flow structure of the bubbles was made visible using three cool white high intensity LED flood lights to uniformly illuminate the bed from the back, see also Figure 1(b). The rising bubbles transmit the light and therefore appear as white areas, while the emulsion phase is indicated by black areas. To eliminate any interference by external light the experimental room was completely darkened. A commercial digital camcorder was placed in front of the bed and captured images of the bubble movement with a resolution of 1280 720 pixels at a frame rate of 50 Hz. For each measurement images were recorded for 5 min. This was found to be sufficient for the statistical analysis of the bubble properties. In order to analyze the results of the simulations contour plots of the solid volume fraction with the same frequency

of 50 frames per second were generated. The bubbles were delineated using a certain threshold value. Hulme et al.12 compared different values and showed that a value of 0.2 for solid volume fraction gave best agreement with experimental results. Asegehegn et al.27 confirmed this finding. 2) Image Preparation and Conversion At first the images of the experimental and the numerical output are cropped to exclude all the unnecessary surrounding area including the walls of the fluidized bed. Next, to discriminate the bubbles from the rest of the bed, the actual RGB images from the camcorder are converted to grayscale then to binary images, see also Figure 3. For the simulation images this step can be skipped as the discriminated bubbles can be generated from the CFD code directly. Identifying the proper threshold value for delineating the bubbles is done by analyzing the grayscale histogram of the pixel intensity. The minimum between the two peaks, black as the emulsion phase and white as bubbles, describes the boundary and gives the discriminating threshold value. 3) Bubble Property Calculation Once the bubble is delineated and identified its projected area AB, horizontal and vertical coordinates of its center of gravity (centroid), and horizontal and vertical extremes are determined. Then the bubble properties aspect ratio, shape factor, diameter, and rise velocity as well as its location are calculated using eqs 1 to 5, respectively. The bubble dimensions are given in Figure 4. The bubble aspect ratio AR and shape factor SF are defined as dy dx

ð1Þ

πdB PB

ð2Þ

AR ¼

SF ¼ 7655



ARTICLE

Figure 3. Bubble delineation: original RGB image (left), gray scale image (center), and binary image (right).

where dy and dx are the vertical and horizontal extremes of the bubble, and PB is its perimeter. The equivalent bubble diameter dB is calculated from the projected area AB rffiffiffiffiffiffiffiffi 4AB ð3Þ dB ¼ π To measure the bubble properties with bed height, the whole bed was divided into sections of 0.01 m height from 0.05 to 0.50 m above the distributor. Thus, the bed height was divided into 45 equal sections, each including the full bed width. The bubble properties aspect ratio, shape factor, and diameter are then assigned to one of the sections depending on the location of the vertical coordinate of the centroid. The rise velocity is calculated from the difference in the vertical centroid movement between consecutive time frames uB ¼

yg ðt þ ΔtÞ yg ðtÞ Δt

Figure 4. Bubble dimensions.

Therefore, compared to researchers who applied DIAT for fluidized beds without immersed tubes (e.g., Busciglio et al.7 and Utikar and Ranade28), the tracking algorithm and criteria need to be modified and enhanced in order to provide realistic results for the tube bank region where very high bubble splitting and coalescence and rapid change of bubble shapes occur. The most distinguished difference of the presented DIAT is to include negative rise velocities. It was observed that at the bottom of the immersed tubes bubbles can grow without moving upward which results in a lower centroid than in the previous time frame. This gives a negative or zero rise velocity, which has to be taken in account. This effect was explained by Asegehegn and Krautz.29 5) Property Averaging Once the instantaneous bubble properties at each bed section are calculated, a number averaging was used to calculate the time-averaged bubble properties with bed height

ð4Þ

Here yg is the vertical component of the bubble centroid, and Δt is the time delay between consecutive frames. The bubble rise velocity is attributed to its mean vertical height according to h¼

yg ðt þ ΔtÞ þ yg ðtÞ 2

ð5Þ

4) Bubble Tracking The calculation of the rise velocity requires correct matches between the bubbles in consecutive time frames. Tracking bubbles from frame to frame is the most difficult task of the digital image analysis technique as they can coalesce, break-up, or even disappear during the interval. The presence of immersed tubes further complicates the bubbles dynamics which worsen the scenario.

n

δ¼ 7656

∑ δi

i¼1

n

ð6Þ



ARTICLE

Here δ represents any of the bubble properties such as diameter, rise velocity, shape factor, and aspect ratio, whereas n is the total number of bubble properties measurements recorded during the total averaging time considered in a section.

3. NUMERICAL MODELING 3.1. Governing Equations. The simulations were performed using the Two Fluid Model (TFM) implemented in the commercial CFD software package Fluent 12.1.30 The model equations and parameters used in this study are discussed in detail below. The conservation of mass for both the gas (g) and the solid (s) phase can be described as

Dðεg Fg Þ Dt

þ r 3 ðεg Fg ug Þ ¼ 0

Dðεs Fs Þ þ r 3 ðεs Fs us Þ ¼ 0 Dt The volume fractions are related as εs þ εg ¼ 1

to describe the rheology of the particles, i.e. the solid pressure Ps and the solid phase shear stress τs. These are derived from the Kinetic Theory of Granular Flow (KTGF), which is an extension of the Kinetic Theory of Gases for granular materials considering nonideal particleparticle collisions. As a result of shearing of the solid phase the particle collisions result in a random granular motion. These fluctuations generate an effective pressure and an effective viscosity in the particulate phase, that resist shearing of the particle assembly. To describe the particle fluctuations the so-called granular temperature was introduced, which varies with time and position in the fluidized bed and strongly influences the solid phase rheology. A detailed and comprehensive description of the KTGF was given by Gidaspow.32 The granular temperature Θ is defined based on the solid fluctuating velocity us0 as

ð7Þ

1 Θ ¼ u0s2 3

ð8Þ

The conservation of the fluctuating granular energy is written as

ð9Þ

3 Dðεs Fs ΘÞ þ r 3 ðεs Fs us ΘÞ ¼ ðPs I þ τs Þ : rus r 3 q γ J 2 Dt

ð16Þ

The conservation of momentum for both phases is given by Dðεg Fg ug Þ Dt

þ r 3 ðεg Fg ug ug Þ ¼ r 3 ðτg Þ εg rP βðug us Þ þ εg Fg g

ð10Þ

Dðεs Fs us Þ þ r 3 ðεs Fs us us Þ ¼ r 3 ðτs Þ εs rP Dt rPs þ βðug us Þ þ εs Fs g

ð11Þ

The interphase momentum transfer coefficient β represents the gassolid drag and strongly couples the two phases. There are several empirical correlations available in the literature. For an overview see e.g. Vejahati et al.31 In this study the widely applied drag model of Gidaspow32 was used, which combines the equation given by Ergun33 and the correlation of Wen and Yu34

8 2 > μg Fg 1 εg > > > 150 < 2 þ 1:75ð1 εg Þ jug us j εg dp ðdp Þ β¼ > ε ð1 ε Þ 3 > g g > Cd > Fg jug us jε2:65 :4 g dp

, ∈g < 0:8 , ∈g g 0:8

ð12Þ 35

The drag coefficient Cd was described by Rowe 8 > < 24 ½1 þ 0:15ðRep Þ0:687 , Rep < 1000 Cd ¼ Rep > : 0:44 , Rep g 1000

Rep ¼

εg Fg jug us jdp μg

The left-hand side of eq 16 represents the net change of fluctuating energy. The first term on the right-hand side is the generation of fluctuating energy due to local acceleration of the particles, which includes the solid pressure and shear stress tensor. The second term gives the diffusion, while the third term represents the dissipation of fluctuating energy due to inelastic particleparticle collisions. The last term on the right-hand side is the exchange of fluctuating granular energy, which accounts for the energy loss due to friction between the gas and the solid phase. Instead of solving the complete granular energy conservation Syamlal et al.36 proposed an algebraic form of the equation. They assumed a local equilibrium between generation and dissipation of the granular energy as these terms are the most dominant terms in dense regions. Thus, the other terms can be neglected and eq 16 reduces to 0 ¼ ðPs I þ τs Þ : rus γ

ð14Þ

ð17Þ

Van Wachem et al.9 and Boemer et al.37 showed that using this equation hardly affects the simulation results, while significant computational time can be saved. In this work the algebraic form was used. The expression which describes the dissipation of fluctuating energy is given by Lun et al.38

ð13Þ

The particle Reynolds number Rep is given by

ð15Þ

γ¼

12ð1 e2 Þgo 2 pffiffiffi εs Fs Θ3=2 dp π

ð18Þ

The solid pressure represents the normal forces of the solid phase due to particleparticle interactions and prevents it from reaching unrealistic high solid volume fractions. It can be written as the sum of a kinetic and a collisional term as given by Lun et al.38

3.2. Solid Stress Modeling. As the result of volumeaveraging, the Two Fluid Model requires closure equations

Ps, KTGF ¼ εs Fs Θ þ 2go ε2s Fs Θð1 þ eÞ 7657

ð19Þ



ARTICLE

To describe the solid shear stress usually the Newtonian stressstrain relation is assumed for the solid phase 2 T τs ¼ εs ξs μs ðr 3 us ÞI þ μs ððrus Þ þ ðrus Þ Þ 3

Table 1. Physical Properties and Simulation Parameters parameter

ð20Þ The solid bulk viscosity ξs describes the resistance of the solid phase against compression and expansion. In this work the expression of Lun et al.38 was applied rffiffiffiffi 4 Θ ð21Þ ξs ¼ εs Fs dp go ð1 þ eÞ 3 π The solid shear viscosity μs represents the tangential forces due to translational and collisional interaction of particles. In general, it is written as the sum of a collisional and a kinetic part μs, KTGF ¼ μs, col þ μs, kin

ð22Þ

value

gas density, kg/m3

1.2

gas viscosity, Pa 3 s

1.79 105

particle density, kg/m3

2500

particle diameter, μm

350

minimum fluidization velocity, m/s

0.13

minimum fluidization void fraction

0.4

bed height at minimum fluidization, m

0.5

restitution coefficient superficial velocity, m/s

0.9 0.260.52

maximum particle packing limit

0.63

specularity coefficient

0.25

angle of internal friction, °

28.5

time step size, s

5 105

residual criterion

103

32

Here, the expressions given by Gidaspow were used rffiffiffiffi 4 Θ μs, col ¼ εs Fs dp go ð1 þ eÞ 5 π μs, kin ¼

2 10pffiffiffiffiffiffiffi Fs ds 4 Θπ 1 þ go εs ð1 þ eÞ 96 5 ð1 þ eÞεs go

ð23Þ ð24Þ

The radial distribution function go appearing in eqs 18, 19, 21, 23, and 24 can be interpreted as a coefficient considering the dense effect when the particle collision probabilities are calculated. It increases with increasing solid volume fraction and therefore ensures that the maximum packing limit εs,max will not be exceeded and more accurate flow characteristics can be achieved. In this work the expression proposed by Savage39 was applied 2 !1=3 31 ε s 5 ð25Þ go ¼ 41 εs, max In regions with high solid volume fractions the collisions between particles are no longer binary and quasi-instantaneous as assumed in the KTGF. Here multiparticle contacts dominate the stress generation. These frictional stresses need to be included in the model. Usually they are simply added to the solid stresses when the solid volume fraction exceeds a certain value εs,min, which is usually set to 0.5, see e.g. van Wachem et al.9 Ps ¼ Ps, KTGF þ Ps, f

ð26Þ

μs ¼ μs, KTGF þ μs, f

ð27Þ

the frictional shear To describe the frictional pressure Ps,f and 40 viscosity μs,f the models of Johnson et al. and Schaeffer41 were applied respectively Ps, f ¼ Fr

ðεs εs, min Þn ðεs, max εs Þp

ð28Þ

The constants are Fr = 0.05 N/m2, n = 2, p = 5, εs,min = 0.5, and εs,max = 0.63. μs, f ¼

Ps sin φ pffiffiffiffiffiffi 2 I2D

I2D

ð29Þ

" Duy, s Duz, s 2 1 Dux, s Duy, s 2 ¼ þ 6 Dx Dy Dy Dz " Duz, s Dux, s 2 1 Dux, s Duy, s 2 þ þ þ 4 Dz Dx Dy Dx 2 2 Duy, s Duz, s Duz, s Dux, s þ þ þ þ Dz Dy Dx Dz

ð30Þ

3.3. Simulation Setup. For spatial discretization of the continuity and momentum equations the QUICK and second order upwind scheme were employed respectively, while time was discretized using first order implicit scheme. The pressurevelocity coupling was realized applying the Phase-Coupled SIMPLE algorithm of Vasquez and Ivanov.42 At the inlet a Dirichlet boundary condition with uniform superficial velocity of the gas phase was set. Assuming a fully developed flow at the outlet because of the long freeboard, a zero gradient Neumann boundary condition for the mixture pressure was applied. At the walls and tubes no slip conditions were chosen for the gas phase, while partial slip was assumed for the solid phase. Therefore the equation of Johnson and Jackson43 was applied pffiffiffiffi usl φ0 πFs εs go Θ ðτs Þ 3 n þ pffiffiffi usl þ ðn 3 τs; f 3 nÞtan φ ¼ 0 ð31Þ jusl j 3 2 3εs, max

The simulation was initialized with the minimum fluidization conditions. Additional physical properties and numerical parameters used are given in Table 1. Each simulation ran for 20 s of real flow time. To avoid the influence of the start-up effect, time-averaging of the result values was started after the first 5 s. Asegehegn et al.27 showed that the resulting averaging period of 15 s is sufficient to obtain accurate mean values for this kind of bed scale.

4. RESULTS AND DISCUSSION 4.1. Grid Sensitivity and 2D-3D Comparison. In order to obtain an optimum between computational effort and accuracy a study with grids of different sizes and dimensions was performed. 7658



ARTICLE

Figure 5. Mean bubble diameter for different mesh sizes: (a) no tube and (b) staggered arrangement (u = 3 Umf).

Table 2. Comparison of Simulation Time domain

geometry

mesh size

number of cells

time ratio

2D

NT

2 mm 4 mm

96000 24000

15.2 3.9

5 mm

15300

2.6

10 mm

3840

1.0

2 mm

101838

16.3

4 mm

27694

5.8

5 mm

18469

4.5

10 mm

5190

2.4

NT

4 mm 5 mm

120000 61440

34.5 16.7

S6

4 mm

145705

47.6

5 mm

72924

22.8

S6

3D

First, the sensitivity of the investigated bed properties and bubble characteristics on rectangular 2D grids with different mesh sizes was investigated. Therefore the different bed geometries were meshed using a uniform mesh size of 2, 4, 5, and 10 mm. In the tube cases refinements near the tubes down to half of the regular cell size were applied to capture the high gradients there. The superficial velocity was twice the minimum fluidization velocity. The different grids showed no influence on the bed properties: The mean bed pressure drop was 7040 Pa with a maximum deviation of (25 Pa for all geometries. Also the mean bed expansion ratio, defined as the ratio of the mean actual bed height and the bed height at minimum fluidization conditions, was basically independent of the grid size. In the no tube case the ratio was 1.243 ( 0.009, whereas in the tube cases 1.261 ( 0.003 was determined. In the case of the bubble characteristics the differences were recognizable. In Figure 5 the mean bubble diameter with bed height is shown for the no tube (NT) and staggered (S6) geometry for different grid sizes. There are no significant differences of the mean bubble diameters for the 2, 4, and 5 mm grids. For the 10 mm grid however larger deviations can be noticed. This behavior was qualitatively also seen for the other bubble properties (rise velocity, aspect ratio, and shape factor) as well as the other geometries. To

Figure 6. Mesh detail in the tube bank region.

avoid redundancy the corresponding plots are not shown here. The results indicated that a mesh size of 5 mm is sufficient to capture the bed properties and bubble characteristics with acceptable computational time. This slightly exceeded the suggestion to use a mesh size of 10 times the particle diameter to get grid-independent results, as suggested by e.g. Guenther and Syamlal44 and Syamlal and O’Brien,45 but seems to be sufficient for the given cases. Both results were in very good agreement with the findings of Vejahati et al.31 and Xie et al.,46 who investigated the grid sensitivity based on mean bed voidage for a comparable particle size and fluidized beds without immersed tubes. Therefore, taking into account the computational time needed (as shown in Table 2), a mesh size of 5 mm was chosen for the numerical simulations reported in this work. A detail of this mesh in shown in Figure 6. Second, the influence of 2D and 3D simulations was studied. Peirano et al.47 observed significant differences of the flow behavior in these two domains. In Figure 7 the simulated bubble size and rise velocity with bed height of both 2D and 3D grid were compared for the no tube bed. The results of the 3D simulation 7659



ARTICLE

Figure 7. (a) Mean bubble diameter and (b) rise velocity for the no tube (NT) bed in the 2D and 3D domains (u = 3 Umf).

Table 3. Time-Averaged Bed Pressure Drop ΔP in Pa experiment

Table 4. Time-Averaged Bed Expansion Ratio H/Hmf

simulation

experiment

NT

S6

I6

NT

S6

I6

simulation

NT

S6

I6

NT

S6

I6

2 Umf

6857

6764

6703

7024

7037

7004

2 Umf

1.14

1.10

1.11

1.23

1.26

1.27

3 Umf

6997

6774

6835

6951

7030

6998

3 Umf

1.23

1.17

1.20

1.37

1.42

1.42

4 Umf

7005

6780

6843

6923

7020

6962

4 Umf

1.40

1.26

1.28

1.49

1.56

1.56

were extracted using contour plots of the plain in the middle of the bed. With increasing bed height the difference in bubble size between both domains slightly increases with the bigger size appearing in 3D simulation. This corresponds to the results of Cammarata et al.48 The reason will be the presence of walls in the third dimension, which compressed the bubbles and lead to bigger projected bubbles. For the bubble rise velocity significantly lower values in the 3D case can be noticed especially in the upper part of the bed. It is also caused by the wall influence which introduces an additional drag on the bubble and strongly reduces the rise velocity, see Krishna et al.49 This general behavior was also found for the staggered and in-line bed geometry outside the tube bank region. Due to the strong influence of the dense immersed tubes the 2D-3D-differences were suppressed in the tube region (see also section 4.3). Simulations in 3D, although physically more appropriate and realistic than 2D simulations, led to very high computational effort. In Table 2 the different computational times needed normalized by the simulation time of the smallest case are compared for the different domains, geometries, and mesh sizes. The 3D simulations of the investigated fluidized beds are 5 to 9 times more expensive than their 2D equivalents. Just in order to simulate 20 s of flow time in the 2D grid with a mesh size of 5 mm using the no tube geometry 57 h of simulation time were necessary on a double Quad-Core Intel Xeon processor (3 GHz each) workstation. Therefore, as also deduced by Xie et al.46 and Cammarata et al.,48 especially for conducting extensive parametric studies, 2D simulations of fluidized beds remain indispensable. 4.2. Bed Properties. In Tables 3 and 4 the experimental and numerical results of the mean bed pressure drop and bed

expansion ratio for different superficial velocities and bed geometries are given. In general the different pressure drops extracted from the simulations are in good agreement with the experiments. With a deviation of less than 2.5% from the mean value, the bed pressure drops are basically independent of the superficial velocity and the bed geometry; only the experimental tube cases show a slightly lower drop than the no tube ones. In case of the bed expansion ratio both experiment and simulation show the well-known increase with increasing superficial velocity. The simulations are able to reproduce this behavior qualitatively but show a relatively large overprediction for all geometries and velocities. This indicates the necessity to apply adjusted drag laws as the standard Gidaspow model fails to predict the correct drag force, see Vejahati et al.31 4.3. Bubble Characteristics. 4.3.1. Bubble Diameter. The influence of bed geometries on the bubble diameter in both experiment and simulation is shown in Figure 8 for a superficial velocity of three times the minimum fluidization velocity. In the free bubbling bed without any obstacles the bubble size increases with increasing bed height due to bubble coalescence. Qualitatively both the numerical and experimental results showed a similar trend of bubble growth for both bed without and with immersed tubes. In quantitative manners, however, relatively large differences occur, which can be explained by the simulated 2D domain (see also section 4.1). The behavior was different in the case of dense immersed tubes. When reaching the first row of tubes the bubbles were forced to split and decrease their size. After passing the tubes the bubbles coalesced again increasing their size. This was repeated for every present row and led to a characteristic zigzag pattern. Due to the dense tube bundle bubble growth and shrinkage were limited in the bank 7660



ARTICLE

Figure 8. Mean bubble diameter for different bed geometries: (a) experiment and (b) simulation (u = 3 Umf).

Figure 9. Series of solid volume fraction contour plots for S6 geometry with Δt = 0.02 s.

region and remained in a constant value range. It can be noticed that no major differences between staggered and in-line arrangement occurred. The model is able to adequately predict these characteristics. In Figure 9 a series of solid volume fraction contour plots for the staggered arrangement is shown. Furthermore, the influence of superficial velocity was investigated. For the no tube bed the bubble size as expected increased with increasing superficial velocity. Figure 10 shows the mean bubble diameter for different superficial velocities for the S6 geometry. The plots show similar values of bubble sizes inside the tube bank for different superficial velocities. Here, for the investigated ranges the bubble sizes seem to be mainly characterized by the spacing between the tubes rather than the superficial velocity of the fluidization. The same results were seen for the I6 geometry. Besides a slight overestimation in the region near the distributor the experimental values could be successfully reproduced by the performed numerical simulations. 4.3.2. Bubble Rise Velocity. In Figure 11 the time-averaged bubble rise velocities for experiment and simulation are shown

for different bed geometries and a superficial velocity of three times the minimum fluidization velocity. In the no tube bed continuously increasing bubble rise velocities were measured, while in the tube cases the plots showed a zigzag pattern in the tube bank region. Due to the forced splitting and the additional friction acting on the bubbles their rise velocities reduced when reaching a row of tubes. After passing it, similar to the effects observed for the bubble size, the coalescence of bubbles led to increasing rise velocities until the next row is reached. The simulations showed a relatively high overprediction of the velocities for the no tube case and in tube free regions of the beds with internals. As discussed in section 4.1 this is caused by the missing wall effects in the 2D simulation. Inside the tube bank region the simulation showed good agreement with the experimental results. Again, no significant difference between staggered and in-line tube arrangement can be noticed. As seen in Figure 12 the variation of the superficial gas velocity showed no influence on the bubble rise velocity for the S6 7661



ARTICLE

Figure 10. Mean bubble diameter for S6 geometry and different superficial velocities: (a) experiment and (b) simulation.

Figure 11. Mean bubble rise velocity for different bed geometries: (a) experiment and (b) simulation (u = 3 Umf).

Figure 12. Mean bubble rise velocity for S6 geometry and different superficial velocities: (a) experiment and (b) simulation. 7662



ARTICLE

Figure 13. Mean bubble aspect ratio for different bed geometries: (a) experiment and (b) simulation (u = 3 Umf).

Figure 14. Mean bubble shape factor for different bed geometries: (a) experiment and (b) simulation (u = 3 Umf).

geometry. This is consistent with the results of the bubble size in section 4.3.1 as size and rise velocity are coupled in fluidized beds. The simulation results are in good agreement with the experiment. Larger discrepancies were again mainly seen outside the tube bank region due to the 2D simulation. 4.3.3. Bubble Aspect Ratio and Shape Factor. Figure 13 shows the time-averaged bubble aspect ratio for different bed geometries and a superficial velocity of three times the minimum fluidization velocity. With increasing bed height bubbles in the no tube bed elongate vertically due to increasing rise velocities. The simulation gives slightly higher aspect ratios than the experiment because of higher simulated rise velocities. When dense tube banks are immersed in the bed, bubbles are forced to squeeze between the tubes, thus the aspect ratio has to rise until the row is passed. In the simulation no differences between staggered and in-line arrangement were seen, whereas the experimental data of the in-line case showed higher aspect ratios in the upper part of the tube bank region. Besides this, the simulation gave good agreement with experiment. In Figure 14 the time-averaged bubble shape factor is plotted for different bed geometries and a superficial velocity of three

times the minimum fluidization velocity. Both the experiment and simulation showed a relatively constant shape factor with bed height for the no tube bed and were in good agreement. In the tube cases the bubbles were more deforming their shape in the bank region. This zigzag pattern is predicted at lower values in the 2D simulation. Further investigations showed that using a 3D computational domain for the tube cases gave more realistic values of the bubble shape.

5. CONCLUSIONS The influence of dense immersed horizontal tubes on bed properties and bubble hydrodynamics of gassolid fluidized beds was investigated. Numerical simulations using the EulerianEulerian Two Fluid Model were compared with experimental data obtained from a pseudo-2D fluidized bed test rig using an digital image analysis technique. In the first part of the study the grid sensitivity of the investigated parameters was checked. Furthermore, simulations using 2D and 3D domains were compared. The latter gave better results but were computationally too expensive. For performing 7663


Industrial & Engineering Chemistry Research extensive parametric studies of fluidized beds 2D simulations remain indispensable. While the determined bed pressure drops of experiment and simulation showed good agreement for all geometries, the bed expansion ratios were overpredicted by the simulation using the common Gidaspow drag law. The dense immersed tubes highly influenced the bubble hydrodynamics (size, rise velocity, and shape). When reaching the first row of tubes the bubbles were forced to split, decreased their size and rise velocity as well as elongated in the vertical direction, and became more non spherical. After passing the tubes the bubbles coalesced again increasing their size and rise velocity and became more spherical. This was repeated for every present row and led to a characteristic zigzag pattern in the respective plots. Due to the high influence of the dense tube arrangements the bubble size and rise velocity in the tube bank region became almost independent of the superficial velocity. The simulations were able to adequately predict the bubble hydrodynamics for the different geometries and superficial velocities. The biggest deviations occurred outside the tube bank region and in the no tube bed due to the neglected front and back plate in the 2D simulations. For all investigated parameters and for both experiment and simulation no significant difference between staggered and in-line tube arrangement could be noticed. In general, the Two Fluid Model is capable of predicting the main characteristics of bubble behavior inside gassolid fluidized beds with dense immersed tubes and therefore a promising tool for parametric investigation of fluidized bed reactors. However, further intensive investigations and experimental validations with more tube arrangements are required for a better understanding of the influence of immersed tubes on fluidized bed properties before using numerical simulations as a commanding method for the design and scale-up of these processes.

’ AUTHOR INFORMATION Corresponding Author

*Phone: þ49-355-69-4006. Fax: þ49-355-69-4011. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors gratefully acknowledge the funding of this research project by the “Entrepreneurial Regions”-Initiative and the COORETEC-Initiative established by the German Federal Ministries of Education & Research and Economics & Technology, respectively. ’ NOMENCLATURE Abbreviations

AR = aspect ratio CFD = Computational Fluid Dynamics DIAT = Digital Image Analysis Technique DPM = Discrete Particle Model I6 = in-line tube arrangement with 6 rows KTGF = Kinetic Theory of Granular Flow NT = no tube arrangement RGB = Red Green Blue S6 = staggered tube arrangement with 6 rows SF = shape factor TFM = Two Fluid Model

ARTICLE

Symbols

A = area, m2 Cd = drag coefficient d = diameter, m e = coefficient of restitution Fr = constant in Johnson et al.40 friction model, N/m2 g = gravitational acceleration, m/s2 go = radial distribution function h = height, m I = unit tensor I2D = second invariant of the deviatoric stress tensor J = granular energy transfer, kg/m/s3 n = constant in Johnson et al.40 friction model p = constant in Johnson et al.40 friction model p = perimeter, m P = pressure, Pa q = diffusion of fluctuating energy, kg/s3 Re = Reynolds number t = time, s u = velocity, m/s u0 = fluctuating velocity, m/s y = vertical component of bubble centroid, m Greek Letters

β = interphase drag coefficient, kg/m3/s γ = dissipation of fluctuating energy, kg/m/s3 δ = bubble property ε = volume fraction Θ = granular temperature, m2/s2 μ = shear viscosity, Pa 3 s ξ = bulk viscosity, Pa 3 s F = density, kg/m3 τ = shear stress tensor, N/m2 φ = angle of internal friction, ° φ0 = specularity coefficient Subscripts

B = bubble col = collisional f = frictional g = gas phase kin = kinetic KTGF = Kinetic Theory of Granular Flow max = maximum mf = minimum fluidization min = minimum p = particle s = solid phase sl = slip x = Cartesian coordinate y = Cartesian coordinate z = Cartesian coordinate

’ REFERENCES (1) Sitnai, O.; Whitehead, A. B. Immersed Tubes and Other Internals. In Fluidization - 2nd ed.; Davidson, J. F., Clift, R., Harrison, D., Eds.; Academic Press: London, 1985; Chapter 14, p 473. (2) Olowson, P. A. Influence of pressure and fluidization velocity on the hydrodynamics of a fluidized bed containing horizontal tubes. Chem. Eng. Sci. 1994, 49, 2437. (3) Olsson, S. E.; Wiman, J.; Almstedt, A. E. Hydrodynamics of a Pressurized Fluidized Bed with Horizontal Tubes: Influence of Pressure, 7664


Industrial & Engineering Chemistry Research Fluidization Velocity and Tube-Bank Geometry. Chem. Eng. Sci. 1995, 50, 581. (4) Johansson, K.; Norling, R.; Hj€ornhede, A.; Almstedt, A. E.; Johnsson, F.; Nylund, A. Hydrodynamics and steel tube wastage in a fluidized bed at elevated temperature. Chem. Eng. Sci. 2004, 59, 31. (5) Hull, A. S.; Chen, Z.; Fritz, J. W.; Agarwal, P. K. Influence of Horizontal Tube Banks on the Behavior of Bubbling Fluidized Beds: 1. Bubble Hydrodynamics. Powder Technol. 1999, 103, 230. (6) Shen, L.; Johnsson, F.; Leckner, B. Digital Image Analysis of Hydrodynamics Two-Dimensional Bubbling Fluidized Beds. Chem. Eng. Sci. 2004, 59, 2607. (7) Busciglio, A.; Vella, G.; Micale, G.; Rizzuti, L. Analysis of the Bubbling Behaviour of 2D Gas Solid Fluidized Beds Part I. Digital Image Analysis Technique. Chem. Eng. J. 2008, 140, 398. (8) Deen, N. G.; van Sint Annaland, M.; van der Hoef, M. A.; Kuipers, J. A. M. Review of Discrete Particle Modeling of Fluidized Beds. Chem. Eng. Sci. 2007, 62, 28. (9) van Wachem, B. G. M.; Schouten, J. C.; van den Bleek, C. M.; Krishna, R.; Sinclair, J. L. Comparative Analysis of CFD Models of Dense Gas-Solid Systems. AIChE J. 2001, 47, 1035. (10) van der Hoef, M. A.; van Sint Annaland, M.; Deen, N. G.; Kuipers, J. A. M. Numerical Simulation of Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy. Annu. Rev. Fluid Mech. 2008, 40, 47. (11) van Wachem, B. G. M.; Schouten, J. C.; Krishna, R.; van den Bleek, C. M. Validation of the Eulerian Simulated Dynamic Behaviour of Gas-Solid Fluidized Beds. Chem. Eng. Sci. 1999, 54, 2141. (12) Hulme, I.; Clavelle, E.; van der Lee, L.; Kantzas, A. CFD Modeling and Validation of Bubble Properties for a Bubbling Fluidized Bed. Ind. Eng. Chem. Res. 2005, 44, 4254. (13) Patil, D. J.; van Sint Annaland, M.; Kuipers, J. A. M. Critical Comparison of Hydrodynamic Models for Gas-Solid Fluidized Beds Part II: freely bubbling gas-solid fluidized beds. Chem. Eng. Sci. 2005, 60, 73. (14) Taghipour, F.; Ellis, N.; Wong, C. Experimental and Computational Study of Gas-Solid Fluidized Bed hydrodynamics. Chem. Eng. Sci. 2005, 60, 6857. (15) Lindborg, H.; Lysberg, M.; Jakobsen, H. A. Practical Validation of the Two-Fluid Model Applied to Dense Gas-Solid Flows in Fluidized Beds. Chem. Eng. Sci. 2007, 62, 5854. (16) Bouillard, J. X.; Lyczkowski, R. W.; Gidaspow, D. Porosity Distributions in a Fluidized Bed with an Immersed Obstacle. AIChE J. 1989, 35, 908. (17) Gamwo, I. K.; Soong, Y.; Lyczkowski, R. W. Numerical Simulation and Experimental Validation of Solids Flows in a Bubbling Fluidized Bed. Powder Technol. 1999, 103, 117. (18) Gustavsson, M.; Almstedt, A. E. Numerical Simulation of Fluid Dynamics in Fluidized Beds with Horizontal Heat Exchanger Tubes. Chem. Eng. Sci. 2000, 55, 857. (19) Das Sharma, S. K.; Mohan, R. Numerical study of the influence of horizontal tube banks on the hydrodynamics of a dense gas-solid bubbling fluidized bed. Int. J. Chem. React. Eng. 2003, 1, A26. (20) Yurong, H.; Huilin, L.; Qiaoqun, S.; Lidan, Y.; Yunhua, Z.; Gidaspow, D.; Bouillard, J. Hydrodynamics of Gas-Solid Flow Around Immersed Tubes in Bubbling Fluidized Beds. Powder Technol. 2004, 145, 88. (21) Schmidt, A.; Renz, U. Numerical prediction of heat transfer between a bubbling fluidized bed and an immersed tube bundle. Heat Mass Transfer 2005, 41, 257. (22) Gao, W. M.; Kong, L. X.; Hodgson, P. D. Computational simulation of gas flow and heat transfer near an immersed object in fluidized beds. Adv. Eng. Software 2007, 38, 826. (23) Lyczkowski, R. W.; Bouillard, J. X.; Gamwo, I. K.; Torpey, M. R.; Montrone, E. D. Experimental and CFD analyses of bubble parameters in a variable-thickness fluidized bed. Ind. Eng. Chem. Res. 2010, 49, 5166. (24) Park, A.-H.; Bi, H.; Grace, J. R. Reduction of electrostatic charges in gas-solid fluidized beds. Chem. Eng. Sci. 2002, 57, 153.

ARTICLE

(25) Hoehne, O.; Lechner, S.; Schreiber, M.; Krautz, H. J. Drying of Lignite in a Pressurized Steam Fluidized Bed - Theory and Experiments. Drying Technol. 2010, 28, 5. (26) Asegehegn, T. W.; Schreiber, M.; Krautz, H. J. Investigation of bubbling behavior of fluidized beds with and without immersed horizontal tubes using digital image analysis technique. Powder Technol. 2011, 210, 248. (27) Asegehegn, T. W.; Schreiber, M.; Krautz, H. J. Numerical Study of Bubbling Gas-Solid Fluidized Beds Hydrodynamics: Influence of Immersed Horizontal Tubes and Data Analysis. Int. J. Chem. React. Eng. 2011, 9, A16. (28) Utikar, R. P.; Ranade, V. V. Single jet fluidized bed: Experiments and CFD simulations with glass and polypropylene particles. Chem. Eng. Sci. 2007, 62, 167. (29) Asegehegn, T. W.; Krautz, H. J. Hydrodynamic Simulation of Gas-Solid Bubbling Fluidized Bed Containing Horizontal Tubes. In Proceedings of the 20th International Conference on Fluidized Bed Combustion, China, 2009; Vol. II, p 864. (30) Ansys Inc. FLUENT 12.0 Theory Guide, 2009; Chapter 16.5, pp 16-41. (31) Vejahati, F.; Mahinpey, N.; Ellis, N.; Nikoo, M. B. CFD Simulation of Gas-Solid Bubbling Fluidized Bed: A New Method for Adjusting Drag Law. Can. J. Chem. Eng. 2009, 87, 19. (32) Gidaspow, D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions; Academic Press: Boston, 1994. (33) Ergun, S. Fluid Flow through Packed Columns. Chem. Eng. Prog. 1952, 48, 89. (34) Wen, C. Y.; Yu, Y. H. Mechanics of fluidization. Chem. Eng. Prog., Symp. Ser 1966, 62, 100. (35) Rowe, P. N. Drag Forces in a Hydraulic Model of a Fluidized Bed: Part II. Trans. Inst. Chem. Eng. 1961, 39, 175. (36) Syamlal, M.; Rogers, W.; O’Brien, T. J. MFIX Documentation: Theory Guide; National Technical Information Service, DOE/METC94/1004, 1993. (37) Boemer, A.; Qi, H.; Renz, U. Eulerian Simulation of Bubble Formation at a Jet in a Two-Dimensional Fluidized Bed. Int. J. Multiphase Flow 1997, 23, 927. (38) Lun, C. K. K.; Savage, S. B.; Jeffrey, D. J.; Chepurniy, N. Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field. J. Fluid Mech. 1984, 140, 223. (39) Savage, S. B. Streaming Motions in a Bed of Vibrationally Fluidized Dry Granular Materials. J. Fluid Mech. 1988, 194, 457. (40) Johnson, P. C.; Nott, P.; Jackson, R. Frictional-Collisional Equations of Motion for Particulate Flows and Their Application to Chutes. J. Fluid Mech. 1990, 210, 501. (41) Schaeffer, D. G. Instability in the Evolution Equations Describing Incompressible Granular Flow. J. Differential Equations 1987, 66, 19. (42) Vasquez, S. A.; Ivanov, V. A. A Phase Coupled Method for Solving Multiphase Problems on Unstructured Meshes. In Proceedings of ASME FEDSM’00: ASME 2000 Fluids Engineering Division Summer Meeting, Boston, 2000. (43) Johnson, P. C.; Jackson, R. Frictional-Collisional Constitutive Relations for Granular Materials, with Application to Plane Shearing. J. Fluid Mech. 1987, 176, 67. (44) Guenther, C.; Syamlal, M. The effect of numerical diffusion on simulation of isolated bubbles in a gas-solid fluidized bed. Powder Technol. 2001, 116, 142. (45) Syamlal, M.; O’Brien, T. J. Fluid dynamic simulation of O3 decomposition in bubbling fluidized bed. AIChE J. 2003, 49, 2793. (46) Xie, N.; Battaglia, F.; Pannala, S. Effects of using Two- versus Three-Dimensional Computational Modeling of Fluidized Beds: Part 1, Hydrodynamics. Powder Technol. 2008, 182, 1. (47) Peirano, E.; Delloume, V.; Leckner, B. Two- or three-dimensional simulations of turbulent gas-solid flows applied to fluidization. Chem. Eng. Sci. 2001, 56, 4787. 7665



ARTICLE

(48) Cammarata, L.; Lettieri, P.; Micale, G. D. M.; Colman, D. 2D and 3D CFD simulations of bubbling fluidized beds using eulerianeulerian models. Int. J. Chem. React. Eng. 2003, 1, A48. (49) Krishna, R.; van Baten, J. M.; Urseanu, M. I.; Ellenberger, J. Rise velocity of single circular-cap bubbles in two-dimensional beds of powders and liquids. Chem. Eng. Process. 2000, 39, 433.

7666


Numerical and Experimental Investigation of Bubbling GasâSolid

Recommend Documents

Numerical and Experimental Investigation of Bubbling GasâSolid