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Solids flow mapping in a gas–solid riser: Mean holdup and velocity fields
Powder Technology 163 (2006) 98 – 123 www.elsevier.com/locate/powtec
Solids flow mapping in a gas–solid riser: Mean holdup and velocity fields Satish Bhusarapu 1 , Muthanna H. Al-Dahhan, Milorad P. Duduković ⁎ Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Campus Box 1198, 1 Brookings Drive, Washington University, St. Louis, MO 63130-4899, USA Available online 4 April 2006
Abstract In this study, solids flow dynamics has been investigated in a 6 in. “cold-flow” circulating fluidized bed riser using non-invasive flow techniques. Gamma ray Computed Tomography (CT) has been used to measure the time-averaged cross-sectional solids holdup distribution. The time-averaged mean and fluctuating solids velocity fields have been quantified using the Computer Automated Radioactive Particle Tracking (CARPT) technique. Details of the experimental techniques, protocol of implementation and data analysis are discussed. The experimental studies examine operating conditions in fast fluidization and dilute phase transport regimes. Comparative and symbiotic analyses of the results obtained from CARPT and CT have been used to develop a coherent picture of the solids flow field. In addition, this work also demonstrates the power of CARPT and CT as flow mapping techniques in studying highly turbulent and opaque multiphase systems. © 2006 Elsevier B.V. All rights reserved. Keywords: Riser; Solids; Fluid dynamics; Computed tomography; Radioactive particle tracking
1. Introduction Contacting solid particles with gases is often a necessity in chemical processes, in the pharmaceutical and metallurgical industries, in mineral processing, energy related processes, etc. The Circulating Fluidized Bed (CFB) is one of the widely employed reactors for gas–solid systems because of its efficiency, operational flexibility, and overall profitability [1]. Fluid catalytic cracking (FCC) and circulating fluidized bed combustion (CFBC) are by far the largest technologies that utilize CFBs. Other applications have been investigated, and some have been developed commercially or are under development. Further details and use of CFB technology can be found in Berruti et al. [1] and Grace and Bi [2]. Risers, which are an important part of CFBs, pose a considerable challenge in design and scale-up because it is not yet possible to produce ab initio predictions of their complex fluid dynamics, which impairs reactor modeling. In particular, quantification of solids holdup and velocity field is important. Existing models describing this complex flow often lack ⁎ Corresponding author. E-mail address: [email protected] (M.P. Duduković). 1 Present address: Harper International Corp., West Drullard Ave, Lancaster, NY 14086, United States. 0032-5910/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2006.01.013
relevant experimental data needed for model validation and refinement [3]. Moreover, many of the phenomenological and Computational Fluid Dynamic (CFD) models require empirical inputs, and their quality depends on the availability and accuracy of the measurement techniques and data. Hence, to properly understand and quantify the solids flow inside risers, it is first necessary to map the solids flow field inside a riser. Almost all the experimental techniques used to characterize CFB systems are intrusive (probe techniques), with measured variables having appreciable errors in large scale, high mass flux systems [1,4]. Moreover, CFB systems are opaque due to high solids mass fluxes and holdups, and, hence, one cannot “see” into the risers. Therefore, commonly used, sophisticated and nonintrusive, optical techniques such as Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV) cannot be used for investigation of solids flow and mixing in such opaque systems. At best, these techniques provide some Eulerian measurements, in a very local region of the riser close to the outside wall. The solids flow structure in CFB risers is inherently complex. Risers exhibit axial solids holdup distribution, with a certain degree of densification at the bottom of the column where the solids are introduced from the downcomer. The solids holdup decreases along the riser as the solids are accelerated by the high velocity gas stream [5,6]. Provided the riser is long enough, fully developed flow conditions are reached beyond a certain height,
Table 1 Sources of experimental data for solids velocity in gas–solid risers Reference
Measurement technique
Invasive techniques Bader et al. [7] Pitot tube Fiedler et al. [33] Harris et al. [68] Hartge et al. [69]
CCD based spatial filter Pitot tube/isokinetic probe Optical fiber probe
Herbert et al. [70] Optical fiber probe Optical fiber probe Optical fiber probe Optical fiber probe/ dynamic pressure Extraction probe
Miller and Gidaspow [30] Parssinen and Zhu Optical fiber probe [73] Wang et al. [74] Particle dynamic anlyser (phase/Doppler) Zhou et al. [75] Optical fiber probe
Non-invasive techniques Cody et al. [76] Acoustic shot noise (ASN) excitation Donsi and Osseo Laser Doppler [77] anemometer Godfroy et al. [11] Radioactive particle tracking Li and Tomita Photographic imaging [78] technique
Solids material/ diameter
30.5 × 12.2, abrupt exit 40 × 15.6, abrupt 14 × 5.1, abrupt exit
FCC, 76μm Sand, 120μm FCC, 60μm
40 × 8.4, abrupt exit
FCC, CFBC ash; 85, 120μm 41 × 8.5, abrupt exit FCC, glass beads; 42–300μm 5 × 2.79, smooth exit FCC, 60μm 5 × 2.79, smooth exit FCC, 60μm 7.5 × 10, – FCC, 54μm 7.5 × 6.58, smooth FCC, 75μm exit 7.6 × 10, smooth exit FCC, 67μm 22.2 × 22.2 × 300 Sand, 530μm cm3, elbow exit 14.6 × 14.6 × 914cm3, Sand, 213μm abrupt exit
Operating conditions
Measurement region
Measured solids velocity
Comments
3.7; 98
H = 4, 9.1 m
4–6; 28 2.6, 3; 26–52
H = 1.7, 10.7m H = 4.4m
Mean radial profile of axial velocity Particle velocity distribution Mean radial profile of ax. vel
Core-annulus flow structure with parabolic profile Two phase flow Wavy annular structure
3.8–5.4; 27–70
H = 0.9–4.7 m
Two phase flow
≤13; ≤250
H = 4, 4.2 m
1.17, 1.29; 11.7, 11.25 H = 0.36, 1.06, 1.63m 1.29; 10.7 H = 0.36. 1.06, 1.63 2.5; 62 H = 6.5m
Mean radial profile of axial velocity Mean radial profile of axial velocity Mean radial profile of ax. vel Mean radial profile (clusters) Instantaneous and mean radial
Core-annulus with the influence of particle diameter Annular flow with clusters Cluster velocity profiles Radial profiles
2.61–3.84; 12–32.8
H = 1.86–5.52m
Mean radial profile
Core-annulus flow structure
5.5, 8, 10; 100, 300, 400, 550 5.85; 25.4
H = 1.53–9.42m
S-shaped, linear, parabolic in 4 longitudinal sections Core-annulus flow structure
5.5, 7; 20, 40
H = 5.13, 6.2, 8.98m
Mean radial and averaged axial profiles 3 components of particle velocities, TKE Vertical and lateral profiles of particle vel.
H = 5–40 ft. (from feed Average axial velocities, RMS Granular temperature variation with Ug injection) acceleration (at the wall) H = 270cm
Mean radial profiles
H = 4–5m (above distributor) 20 cm regions at 0.7, 5.7, 11.7 m from feed
3-D Eulerian and Lagrangian Clusters with core-annulus, dispersion velocity field (of a large particle) coefficients variation Mean radial profile Uniform profiles (swirling and axial)
0.1 × 0.1 m2 at 3.5m from the distributor 0.1 × 0.1 × 0.1 m3
Downward velocity of particle swarms near the wall 3-D Eulerian and Lagrangian velocity field
Three flow forms — dilute, dense and swarm were found near the riser wall Presence of small vortex in both the beds
H = 4–6m 2.5 × 10− 4 mm3 volume at H = 1.5–6.2m H = 6, 14 m
Mean radial profile Radial mean and RMS fluctuating profiles Mean radial profile, PDD curves of particle velocity
Radial profile obeys 1/7 power law Core-annulus with radial profiles as parabolic and Boltzman function Dispersed particle and cluster two phase flow
Gs Ug (m s− 1) (kg m− 2 s− 1)
61–274 × –
FCC, 60μm
4 × 10 × 460 cm3, smooth exit 8.2 × 7, elbow exit
Glass, 94μm
Q = 233–1333kg s− 1 Gs = 152– 1247kg m− 2 s− 1 10–25; 50–350
Sand, 150μm
4; 23–75
Polyethylene, 3.2 mm, 946kg m− 3 Alumina, 75μm
9–25; O (0.01)
8 × 12, elbow exit
Rhodes et al. [79] High speed video camera 30.5 × 6.6
3–5; 2–80 Ug = 0.972 m s− 1 Q = 0.121kg s− 1
Wang et al. [80] Wei et al. [81]
Positron Emission 10 × 10 × 10cm3 Glass, 700μm Particle Tracking (PEPT) (interconnected fluidized beds) LDV 14 × 10.4, abrupt exit FCC, 36μm LDV 18.6 × 8, abrupt exit FCC, 54μm
Zhang et al. [82]
LDV
2.7–3.7; 29.7–44
Stellema [10]
41.8 × 18, abrupt
FCC, 77μm
3.49–4.78; 2.6–78.3 2.3–6.2; 18–200
H = 1.19–2.24m
Core-annulus flow structure
Turbulent profile with no downflow
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Horio et al. [71] Ishii et al. [16] Qian and Li [72]
Riser geometry (Dia × height, cm × m)
99
100
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corresponding to a solids holdup which is approximately invariant with height. Some of the early studies provided some experimental evidence that the riser flow structure consists of two characteristic regions: a dilute gas–solid suspension preferentially traveling upward in the center (core) and a dense phase of particle clusters, or strands, moving downward along the wall (annulus) (e.g. [7–9]). Such an annulus-core structure is usually assumed by those that model the riser reactor. Thus it is important to quantify solids distribution, velocity and mixing in the riser. Table 1 lists the sources of experimental data on solids velocity in gas–solid risers. The experimental techniques employed are invasive and non-invasive. Invasive methods are optical fiber probes, extraction probes, pitot tubes, isokinetic probes, and spatial filter processes. The advantages of using such probes are the ease of use at industrially relevant high flux conditions. However, the disadvantages, apart from intrusiveness, are: a) complicated calibration procedure, b) need for manual probe positioning and, c) fouling effects due to the ports on the walls. Moreover, only point measurements are obtained, and thus only the mean radial profile of axial velocity can be derived. The non-invasive methods are either based on optical techniques such as PIV, LDV, and high-speed cameras, on electrical and magnetic field measurements and on the use of radioisotopes, such as the Positron Emission Particle Tracking (PEPT) employed by Stellema [10], and the gamma emitting Radioactive Particle Tracking (RPT) used by Godfroy et al. [11]. The RPT technique developed by Larachi et al. [12] and applied by Godfroy et al. [11] in a CFB riser is similar to that of previous researchers [13–15] who used the RPT technique in fluidized beds. In the open literature, the study of Godfroy et al. [11] is the only work that presents the particle trajectories in a CFB riser in a full 3-D field and gives particle velocities. They indicated that the solids velocity and solids dispersion coefficient in the longitudinal direction decrease with increasing solids circulation rates due to a decrease in the turbulent axial velocities. Annulus diameter increases with increasing solids circulation rate. However, there are a few shortcomings of their study: a) The radioactive tracer used is approximately 27 times larger in volume (dp = 500 μm) than the solids used, which had mean particle size of dp = 150μm. Due to higher inertia of the tracer particle, the results represent the motion of a large particle among the smaller solids; this large particle has smaller fluctuating velocity components; b) The data acquisition frequency used by Godfroy et al. [11] was 100 Hz, which might not provide a good temporal resolution; c) It is difficult to validate a CFD or mechanistic model for the velocity profiles using the results of Godfroy et al. [11] because there is no reliable model to predict the behavior of a large tracer particle surrounded by smaller particles. Table 1 reveals that no experimental study provides all the information on solids velocity field that one requires for CFD model validation. Most of the studies either provide only the time-averaged velocity profiles at few axial locations, or at best provide 2-D velocity components in 3-D columns. None of the experimental studies report turbulence stresses, turbulent kinetic energy (granular temperature), diffusivity (axial, radial), return length distributions, circulation time distributions. All these flow and mixing parameters are required to understand the mecha-
nism of mixing (e.g. lateral segregation) and its variation with the operating parameters. Several experimental methods of characterizing the solids concentration distribution in a cross-section of the riser are listed in Table 2. The key observations regarding the experimental results of each researcher are also presented in Table 2. Strong radial suspension density gradients have been experimentally found and reported, with a maximum at the wall and a minimum at the center, which agree well with the core-annulus approximate description of the solids flow field. A critical examination of the experimental results for radial solids concentration distribution suggests that neither the core-annular theory [9] nor the clustering approach [16] alone can fully describe the riser dynamics. For example, instantaneous data indicate intermittent passage of solids clusters, while time-averaged data, obtained at several radial locations, suggest core-annulus flow structure. It is evident that both phenomena coexist and that a rigorous interpretation should take into consideration both clusters and core-annulus flow. Tomography proved to be a valuable tool for determining the solids concentration distribution non-invasively and was used by several researchers, as indicated in Table 2. In contrast to electrical capacitance tomography (ECT) and X-ray tomography, γ-ray tomography, with proper source shielding, can be used in dense flows, but the weight of the experimental setup reduces the attainable temporal resolution and restricts its applicability to selected positions along the riser length. Martin et al. [17] and Azzi et al. [18] are the only studies that presented 2-D concentration maps using γ-ray tomography in CFB risers. However, both studies used relatively few projections (27 and 21 projections, respectively), which result in a coarse reconstruction. The main improvement in this work is the use of a large number of projections, which improves the spatial resolution. The motivation for this study was provided by the availability of specialized gamma ray based techniques in our Chemical Reaction Engineering Laboratory (CREL) and the need of the community for improved and more detailed data base for solids flow in risers. We utilized the Computer Automated Radioactive Particle Tracking (CARPT) technique [19,20] to obtain the complete Lagrangian description of solids flow in the riser including ensemble average and statistical properties of the flows. Gamma ray computed tomography (CT) [21,22] is used to obtain the solids holdup distribution in cross-section of the riser. The objective was to generate the data base for an improved phenomenological model of the riser to be coupled with the appropriate kinetic studies and to provide data for CFB models of the riser that include novel turbulence closures. Our effort was part of the work conducted by the Multiphase Fluid Dynamics Research Consortium (MFDRC) funded by the Department of Energy (DOE), Office of Industrial Technology (OIT). 2. Experimental setup The gas–solid CFB shown in Fig. 1a was used. The total height of the glass riser is 26ft. (7.9 m) and the internal diameter is 6in. (15.2 cm). The solids are soft, approximately spherical, glass beads with a mean diameter (dp) of 150 μm and particle
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Table 2 Sources of experimental data for solids concentration in gas–solid risers Reference
Measurement technique
Riser Solids geometrya material/ (Dia × height, diameter cm × m) 14 × 5.1, abrupt exit 40 × 8.4, abrupt exit
Herbert et al. [70]
Pitot tube/ isokinetic probe Capacitance probes/optic fiber probe Optical fiber probe
41 × 8.5, abrupt exit
Horio et al. [71] Issangya et al. [83,65]
Optical fiber probe Optical fiber probe
5 × 2.79, smooth exit 7.6 × 6.1, smooth exit
Kato et al. Optical [84] fiber probe Parssinen and Zhu Optical [85] fiber probe Schlichthaerle and Optical probe, Werther [61] γ-ray densitometry Schuurmans [86] γ-ray absorption Tanner et al. [87] Optical fiber probe Wang et al. [80] Optical density sensor Wei et al. [81] Optical fiber probe Xu et al. [63] Optical probe
Invasive techniques Harris et al. [68] Hartge et al. [69]
Operating conditions Gs Ug (m s− 1) (kg m− 2 s− 1)
Measurement regionb
Measured parameters
Comments
Mean radial profile Mean radial and axial profiles
Wavy annular structure
Core-annulus with the influence of particle diameter Annular flow with clusters
FCC, 60μm
2.6, 3; 26–52
H = 4.4m
Sand, FCC, CFBC ash; 56, 85, 120 FCC, glass beads; 42–300μm FCC, 60μm
3.8–5.4; 27–100
H = 0.6–4.7m
≤13; ≤250
H = 4, 4.2m
Mean radial and axial profile
FCC, 70μm
1.17, 1.29; 11.7, 11.25 4–8; 14–425
H = 0.36, 1.06, 1.63m H = 0.97– 5.23m
15 × 3, abrupt exit 7.6 × 10, smooth exit
FCC, 74μm
2.4–4; 9–53
H = 70–230cm
FCC, 67μm
5.5, 8, 10; 100, 300, 400, 550
H = 1.53– 9.42m
40 × 15.6, abrupt exit
Sand, 200μm 3–5; 5–50
H = 0.29–1m
Mean radial profile Mean and standard deviation profile Mean radial profiles Mean radial and averaged axial profiles Mean radial and averaged axial
Cracking unit 41.1 × 8.5, smooth exit 14 × 10.4, abrupt exit 18.6 × 8, abrupt exit 9 × 11, elbow exit
–
–
–
Glass beads, 110μm FCC, 36μm
2.5, 4.5, 6.5; 30, 79, 107 2.6, 3; 26–52
–
FCC, 54μm
3.8–5.4; 27–100
FCC, 54μm
0.11–3.15; 0–65
2.5 × 10− 4 H = 1.5–6.2m H = 3m
H = 4–6m
Zhang et al. [82]
Optical density probe
41.8 × 18, abrupt exit
FCC, 77μm
2.7–3.7; 29.7–44
H = 6, 14m
Zhang et al. [62]
Optical probe
FCC, HGB, ALO
1–4; 5–300
H = 1.27, 4.27, 3.77m
Zhu et al. [88]
Optical probe
3.2, 9, 30 × 2.8, 10, 12, abrupt exit 7.6 × 3, –
Non-invasive techniques Azzi et al. [18] γ-ray densitometry Berker and Tulig γ-ray camera [89] Du and Fan [90], ECT Du et al. [91] Grassler and X-ray tomography Wirth [67] Jaworski and ECT Dyakowski [92] Li and Tomita [78] Photographic imaging technique Malcus et al. [55]
ECT
Two phase flow
Core-annulus structure in ‘dense suspension’ and FF regimes Core-annulus in turbulent and FF Constant in the center and decreasing near the wall with height Presence of local acceleration effects
Mean radial profile Mean radial and averaged axial Mean radial profiles Radial mean profiles Radial profiles of mean and fluctuations Mean radial profile, PDD curves of conc. Mean radial profiles and wave forms in 3 regimes
Near parabolic profile
Radial profile independent of Ug, Gs, if CS averaged voidage is constant Ring internals result in uniform profiles
Gas and slip velocity profiles estimated Three kinds of profiles: dense, ring and aggregative Similar profile given Boltzman function Two distinctive regions of lateral profiles Dispersed particle and cluster two phase flow
Sand, 169μm 6, 8; 71, 214
H = 1.61–2m
Mean radial and axial profiles
19 × 11.7; 70 × – 17.8 × –
FCC, 75μm
6.1, 21; 150, 1080
H = 3.1–4.8m
Mean radial profile 2-D concentration map
FCC, –
9.4, 15.3; 122, 310
H = 5.34m
Mean radial profile k–ε turbulence model
10 × 6.3, abrupt exit 19 × 15
Glass; FCC 0.97–3.4; 1.32–35.7 240; 60μm Glass, 60μm 2.7, 5.6; 195, 415
Instantaneous 3D profiles 2-D holdup maps
3m vertical channel 8 × 12, elbow exit
Polyamide, 1–5; Q ≤ 900kg s− 1 3 3 × 3 × 1mm Polyethylene, 9–25; O (0.01) 3.2mm, 946kg m− 3 FCC, 89μm 3.7–4.7; 148–302
H = 0.4–0.6m 4.4–6.3m H = 4.4, 6.8, 11.6m –
14 × 7, smooth exit
Choking flow structures Core-annulus structure
Instantaneous Train of plugs with 2D profiles downflow at the wall Mean radial profile Symmetric profiles (swirling and axial)
20 cm regions at 0.7, 5.7, 11.7m from feed H = 1.55, 2.1 m Radial, PDD, standard deviation profiles
Core-annulus structure
(continued on next page)
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Table 2 (continued) Reference
Solids Riser material/ geometrya (Dia × height, diameter cm × m)
Measurement technique
Non-invasive techniques Martin et al. [17] γ-ray tomography 19 × 11.7 Miller and Gidaspow [30] Rhodes et al. [64]
X-ray densitometry ECT
Saxton and Worley [93] Weinstein et al. [94]
γ-ray absorption X-ray absorption
7.5 × 6.58, smooth exit 9 × 7.2, smooth exit – 15.2 × 8.5, abrupt exit
62 μm, 1560kg m− 3 FCC, 75μm
Operating conditions Gs Ug (m s− 1) (kg m− 2 s− 1)
4.2, 6.3; 114, 308, 202 2.61–3.84; 12–32.8
Measurement regionb
Measured parameters
H = 4m
Mean radial 2-D concentration maps, and axial profiles core-annulus flow Mean radial profile Core-annulus flow structure
H = 1.86–5.52m
Sand, 100μm 4; 150
H = 2.8–4.3 m
–
–
–
HFZ-33, 59 um
1.1–5; 12–154
H = 1.64m
Contours of constant conc. Mean radial profiles Mean radial profiles
Comments
Core-annulus, annulus width decreases height Dense wall, dilute core 3rd order polynomial radial profile
Ug — gas superficial velocity (m s− 1). Gs — overall solids mass flux (kg m− 2 s− 1). Q — overall solids flow rate (kg s− 1). ‘–’ indicates data not reported. a Risers with circular cross-section are defined by diameter × height, while the ones with rectangular are defined by length × width × height; 90° exits are termed as elbow exits, risers with increased diameter at the exit (disengagement section) are termed as smooth exits and others are termed as abrupt exits. No attempt is made to quantify the smoothness of the riser exit. b H — height from the distributor, where measurements are reported.
density (ρs) of 2550 kg m− 3, which fall into Group B of Geldart's classification. The secondary fluid (air) enters the system at the base of the riser, and flow is regulated by a standard air flow meter. The two phase gas–solid suspension in the riser exits into an axi-symmetric disengagement section. Air exits from the disengagement section to a cyclone, connected to the hopper at its bottom. Air from the top of the cyclone exits into a dust collector. The hopper is connected by a flexible pipe to the return leg (downcomer), and the solids return to the base of the riser
through the downcomer. The glass downcomer is 18ft. tall with a 2in. (5.1 cm) internal diameter. The base of the downcomer is connected to the base of the riser with a 45° angled standpipe of 2in. (5.1 cm) diameter, made of glass. To regulate the flow of solids into the riser, a mechanical ball valve was placed between the base of the downcomer and the 45° standpipe. The experimental conditions included three different superficial gas velocities varying from 3.2 to 4.5 m s− 1 and two different solids loading of 140 and 190lbs at ambient
Fig. 1. a) Schematic of CFB setup; b) Photograph of the zone of investigation for CARPT.
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pressure and temperature. This spans from fast fluidization (FF) to dilute phase transport (DPT) operating regimes. The regimes of operation were obtained from the flow regime maps of Bi and Grace [23]. To determine the regime, one needs along with the superficial gas velocity in the riser, which is directly measured, the value of the overall solids mass flux. Our earlier published work [24] reports the method and the data obtained for the overall solids mass flux at each gas velocity. 2.1. Computer Automated Radioactive Particle Tracking (CARPT) Computer Automated Radioactive Particle Tracking (CARPT) is an advanced non-invasive technique for measuring solids (in gas–solid, liquid–solid and gas–solid–liquid systems) or liquid (in gas–liquid systems) flow field and turbulent parameters (e.g. [12,14,19,20,25]). In CARPT we track the motion of a single particle as a marker of the solids phase, if the flow field of solids needs to be measured (e.g. gas–solid riser), or of a neutrally buoyant particle, if the flow field of the liquid phase needs to be measured (e.g. bubble column). Further details regarding the CARPT technique and its ability to provide time-averaged velocities (3-D solids flow field) and turbulence parameters (kinetic energy, shear stress, turbulent eddy diffusivities) can be found elsewhere [12,15,19,25]. For the gas–solid riser study, the challenge is to implement CARPT on a pilot-plant scale, which has never been accomplished before. The scale of the system and the continuous nature of the solids flow, with high velocities and heavy attrition, gave rise to many implementation issues. These include: a) selecting the radioactive particle, b) devising a method for the detector calibration, c) selecting data sampling frequency, d) best positioning of the detectors, e) selecting a safe procedure for introduction and recovery of radioactive tracer, f) post-processing method for the data. A single radioactive particle (46Sc) was used as a tracer. It was tailored by coating a layer of polymer (Parylene N) on the Scandium particle to achieve the same density as the solids used (glass beads) and the same diameter (150 μm) as the mean particle size of glass beads. By tracking this single radioactive tracer at a data acquisition frequency of 200Hz, instantaneous solids velocity field in a developed flow section was measured. A total of 20NaI(Tl) scintillation detectors were positioned around the column and Fig. 1b shows the photograph of such configuration. 18 detectors were positioned close to the column wall (yet far enough to ensure that the detectors do not get saturated) with 3 detectors at each level to determine the position of the tracer particle. This was shown by Roy et al. [26] to lead to good sensitivity and resolution. The zone of interrogation of the detectors was 72 cm long. Two ‘sentry’ detectors were fixed at the top and bottom levels of the zone to determine precisely the instants of entry and exit of the tracer particle into the zone. Prior to tracking the tracer particle, the detectors were calibrated by placing the tracer particle manually, manipulating it through the column wall, at several hundred known locations. The average error in tracer position reconstruction found at any flow condition was less than 5mm. The actual CARPT results are
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interpreted only with in the central 48 cm long zone, where the resolution is even better. 2.2. Computed Tomography (CT) A gamma ray computed tomography (CT) for probing phase volume fractions in multiphase reactors had been developed and discussed by Kumar et al. [21,22]. For this work, the existing setup was modified and mounted on the gas–solid riser system for studying the time-averaged solids volume fraction distribution. For the 6 in. riser column, an array of 7 detectors was placed to span the fan beam of the source, which yields a total of 17,500 projections (radiation attenuation measurements). This results in a significant improvement in the spatial resolution over the previous reported studies of γ-ray tomography on risers of Martin et al. [17] and Azzi et al. [18]. For image reconstruction, the iterative alternating-minimization (AM) algorithm [27] was used, the implementation of which for the CREL scanner has been discussed by Bhusarapu et al. [28]. The average theoretical spatial resolution for the CREL scanner is better than 2 mm. 3. Results and discussion The solids velocity field obtained from CARPT experiments is discussed first. The solids holdup from CT experiments is shown later. Comparative and symbiotic analysis of these two results is used to understand the complex flow structure of the solids in two different flow regimes; Fast Fluidization (FF) and Dilute Phase Transport (DPT). 3.1. Solids velocity field 3.1.1. Instantaneous positions and velocity calculations The knowledge of the tracer particle trajectory provides insight into the solids dispersion and mixing. Fig. 2 shows the instantaneous particle position trace during a single passage through the riser visualized in three different planes — x–z, y–z and x–y planes. As the tracer particle moves around the CFB loop, it periodically resides in the zone of interrogation in the riser (Fig. 1). During each passage through the riser, completely independent tracer particle trajectories are obtained. Two such trajectories were picked for understanding in Fig. 2. Clearly in some instances the tracer particle passes through the section straight, while in others it undergoes internal recirculation in the section. In both cases, the tracer particle takes a tortuous path undergoing acceleration at times and deceleration at other times. The tracer positions when the axial velocity is negative (Fig. 2b) are indicated in red. It can be observed that the tracer has acquired negative axial velocity starting near the center (core region) and maintains a negative axial velocity as it moves towards the wall (annulus region). So during this episode the tracer particle falls both with in the core as well as in the annular region. Analyzing many such trajectories shows that few times the tracer particle passed through the zone of interrogation straight with very little or no backmixing, while many times it underwent internal recirculation with the tracer falling down. Also, it was observed that the span of the tracer residence time
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(b) 37.4
37.4
37.4
36.7
36.7
36.7
36.7
36.1
36.1
36.1
36.1
35.4
35.4
35.4
35.4
34.7
34.7
34.7
34.7
34.1
34.1
34.1
34.1
33.5
33.5
33.5
33.5
32.8
32.8
Z/D
37.4
Z/D
Z/D
(a)
32.8
32.8
-1 -.5 0 .5 1
-1 -.5 0 .5 1
-1 -.5 0 .5 1
-1 -.5 0 .5 1
x/R
y/R
x/R
y/R
No. of Occurences = 55 (Positions) Residence time = 0.275 sec
No.of Occurrences = 207 (positions) Residence Time = 1.035 sec
Fig. 2. Examples of traces of particle instantaneous positions in the x–z, y–z and x–y planes during two different passages through the CARPT section: a) tracer passed through the section without recirculation; b) tracer underwent internal recirculation inside the section. The operating conditions were in the Fast Fluidization regime at Uriser = 3.2 m s− 1 and Gs = 26.6kg m− 2 s− 1. g
within the zone of interrogation varied widely from 0.1 to 100s. Such large residence time variation (without stagnation) explains why the solids mixing in the axial direction or the axial dispersion coefficients are very large in riser reactors. The accuracy of tracer position reconstruction is influenced by the way detectors are packed around the column [12,26]. Since near the lowest and highest axial levels in the CARPT section there will be fewer number of detectors, the position reconstruction near these axial levels is bound to be worse compared to the section in between. This can indeed be observed from the cluttering of the tracer positions (Fig. 2) near the axial planes of z / D = 32.8 and 37.4. Hence, to reduce the position error propagation to velocity calculations, the zone of interrogation was reduced to the section between the axial planes of z / D = 33.5–36.7. This translates to an interrogation zone of 48 cm between the axial heights of z = 5.1–5.6 m. All the subsequent CARPT results reported are within this zone of interrogation. Fig. 3 shows the evolution of the tracer axial and radial position, with time. Fig. 3b shows the radial position time series, which indicates that the solids motion in the horizontal plane is
principally random (dispersive). However, the actual mechanism of the lateral movement of the solids can be understood only once the radial mixing parameters are evaluated. It can also be noted from Fig. 3b that the particle occurrences near the wall are more numerous than near the center or core region. The tracer particle axial position trace in time shown in Fig. 3a indicates extensive internal recirculation. Also, the axial flow seems like a typical wall bounded flow, although there is no physical wall. The same result of wall-boundedness in the axial direction can also be reached by looking at the auto-correlation function of the Lagrangian velocity. Also, in the axial direction, the motion seems to be ultimately directed upward with the particle tumbling up and down during a single passage through the riser section. Hence, the large scale internal recirculation, superimposed with the fine scale fluctuations contributes to the axial backmixing. A time derivative of the tracer particle position yields the instantaneous Lagrangian velocity of the tracer. Now, by invoking ergodicity, we convert the velocity trace of the single tracer particle to the time-averaged Eulerian velocity field that is representative of the entire ensemble of particles. To perform this
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
105
Tracer passage
(a) 36.7 36.4
Z/D
35.7
35.1
34.4
33.5
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
Time (sec)
(b) 1.0 0.93
r/R
0.8
0.53
0.27 0 1419
1420
1421
1422
1423
1424
1425
1426
Time (sec) Fig. 3. Tracer position with time visualized for a small period a) axial b) radial positions. The operating conditions were in the Fast Fluidization regime at Uriser = g 3.2m s− 1 and Gs = 26.6kg m− 2 s− 1.
calculation, we assume an imaginary grid in the 3D space in the riser section. For any two successive tracer positions, the velocity is calculated by time-differencing and assigned to the compartments of the grid, where the velocity vector falls. Thus, one can build a histogram (i.e. probability density function (PDF)) of the instantaneous velocities in each compartment of the grid, given that the tracer particle visits these compartments a sufficient number of times. Hence, by claiming that the system is ergodic and stationary, one asserts that the moments of the histogram, calculated from the ensemble of observations for long enough time, are the same as those that would be obtained by analysis of time series of solids particle velocity at the given point (such as obtainable by a probe). Post facto validation of the ergodicity of the system was performed by checking for occurrence independence of the velocity and turbulence profiles (not shown for brevity). Details on occurrence independence can be found in Bhusarapu [29]. To obtain the time-averaged Eulerian velocity field, one needs to compartmentalize the section of the riser and count the velocity statistics. Three different compartment sizes as stated in Table 3 ranging from coarse to fine grid were considered to obtain mesh independent profiles. It was observed that the velocity and turbulent profiles from Mesh 2 and 1 are approximately the same (not shown for brevity), indicating that the
velocity and turbulent quantities from Mesh 1 are grid independent. Further details on mesh independence can be found in Bhusarapu [29]. Note that in Mesh 3 volumes of the cells are three times those of cells in Mesh 1 and a similar proportional increase in the number of particle occurrences in each compartment. Hence, for further analysis, Mesh 1 was employed, where the nominal grid size was Δr = 0.95cm, Δz = 2 cm, and Δθ was varied so that all the cells have equal volume of about 5.7 cm3. 3.1.2. FF versus DPT regimes Earlier studies on riser flow established that in a timeaveraged sense, solids flow upwards in the center or core region and downward near the wall, or annulus region, at conditions characteristic of the fast fluidized and heterogeneous dilute flow regimes (e.g. [7,23,30,31,73]). The typical characteristics of the solids flow in the fast fluidized and dilute phase regimes were Table 3 Details of the three different mesh evaluated to check for mesh independence
Mesh 1 Mesh 2 Mesh 3
Nr
Nθ (max)
Nz
Total grids
% of volume
8 7 5
15 13 9
24 24 20
1536 1176 500
0.065 0.085 0.2
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
r / R = 0.063
r / R = 0.438
= 407
n
0.1
0.1 σv = 382.66
0.18 σv = 169.41
σv = 340.11
0.09
0 0
5
0.18
-5
0
= 336
0.13
σv = 415.86
0
100
0
20
0
50
0.21 n
= 168.07
0 -100
5
0.17 n
= 2208
= -9.84
0.05
0.05
-5
Probability
n
= 384
= 147.02
0
= 469
n
= 126.32
0.16
σv = 349.41
0.09
0.1
0.04
0.05
= 960
= -60.63 σv = 239.2
0.06
0
0 -5
0
5
0.17 0.13
-5
0
= 463
0.28 n
= 205.8
0.13
σv = 375.64
0.09
0.09
0.04
0.05
0 -20
5
0.18 n
Probability
0.27
= 447
n = 2186
= 125.85
= -19.08
σv = 347.15
Z / D = 33.7
Probability
n
= 190.25
0.12
r / R = 0.938
0.16
Z / D = 36
0.14
Z / D = 35
106
0.18 σv = 185.35
0.09
0
0 -5
0
5
-5
0
5
0 -50
v/, Dimensionless axial velocity n - Particle Occurences in the voxel(#); - Mean axial velocity(cm/s); σv - Standard deviation of axial velocity (cm/s)
Fig. 4. Spatial variation of the solids axial velocity histograms illustrated at three different axial and radial locations for the FF regime at Ug = 3.2m s− 1 and Gs = 26.6kg m− 2 s− 1.
summarized by Bi and Grace [23,32]. In the fast fluidization regime, axial solids segregation exists, resulting in a dense lower region and dilute upper region. Particle streamers form close to the riser wall, leading to a core-annulus structure in the upper dilute region [32]. While in the heterogeneous dilute phase flow, average solids flux in the annular region is downward with little axial segregation of particles. In this regime too, particles streamers form close to riser wall leading to a core-annulus structure [32]. However, there are only few studies (with intrusive techniques) that presented the velocity histograms [33] or turbulent stresses [34–36]. There are no studies presenting the full velocity field that show the components of turbulent stresses, turbulent kinetic energy, eddy diffusivities, solids residence time distribution and the solids holdup maps. In this section, local velocity histograms (PDFs), time-averaged velocity vector plots and turbulent stress profiles are compared in the two operating regimes to quantify the local solids flow structure. 3.1.3. Velocity PDFs One acquires PDFs of the local velocity components in each of the compartments of the grid as discussed earlier. Fig. 4 shows the PDFs of the axial solids velocity at three different radial positions (r / R = 0.063, 0.438, 0.938) and at three different axial planes (Z / D = 33.7, 35, 36; z = 5.12, 5.32, 5.47m) at a
particular angular position. The operating conditions for this experiment are in the FF regime with Ugriser = 3.2 m s− 1 and Gs = 26.6 kg m− 2 s− 1. Also indicated in each of the PDF plots are the number of particle occurrences in the given compartment, the mean and standard deviation of the axial velocity. Fig. 4 leads to the following conclusions: a) large radial gradients in the axial solids velocity; b) ensemble averaged axial slip velocity (assuming plug flow for gas phase) in the center or core region is much larger than the particle terminal velocity, while the ensemble average axial velocity near the wall is negative (downfall), which is an order of magnitude higher than the minimum fluidization velocity; c) very small axial variations within the zone of interrogation; d) two prominent axial velocities at the centerline — one negative and one positive, with the ensemble average being positive. Similar conclusions were drawn from the axial velocity PDFs at another operating condition in the FF regime (Ugriser = 3.2 m s− 1; Gs = 30.2kg m− 2 s− 1). One possible explanation for the appearance of negative velocities at the centerline in the FF regime (Fig. 4), which are absent in the DPT regime (Fig. 5), could be due to the enhanced formation of clusters, which tend to fall down. Based on the same argument, the prominent negative solids velocity at the center can be associated with the cluster terminal velocity and an approximate
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r / R = 0.063
σv = 378.3
Probability
0.14
0 -1
0
1
2
σv = 158.6
0.28
0.06
0 -2
-1
0
1
2
-10
0.3
n = 143 = 481
0.21
-5
0
5
10
n = 678 = 16.73 σv = 169.1
σv = 151.6
σv = 158.5
0.14
0.15
0.08 0.07 0 -2
0.23
Probability
σv = 202.1
0.12
n = 131 = 550
0.15
n = 1427 = 66.43
Z / D = 36
n = 168 = 566.9
n = 96 = 593
0.05
0 -2
r / R = 0.938 0.42
Z / D = 35
0.1
r / R = 0.438 0.18
0 0
1
2
-1
n = 178 = 522.1
0.16 = 489.4
n
σv = 145.6
σv = 152.7
0.11
0 -2
-2
0
1
0.31
= 123
0
1
2
0 -2
-10 0 10
50
n = 6373 = 0.77 σv = 113.4
0.16
0.08
-1
0 -5 0
2
Z / D = 33.7
Probability
0.16
107
-1
0
1
2
0 -800
0
800
v/, Non-dimensional axial velocity n - no. of occurrences in the voxel (#); - mean axial velocity (cm/s); σv - standard deviation of axial velocity (cm/s)
Fig. 5. Spatial variation of the solids axial velocity histograms illustrated at three different axial and radial locations in the DPT regime at Ug = 4.5m s− 1; Gs = 36.8kg m− 2 s− 1.
cluster size can be estimated. Also, the prominent positive velocities at the centerline can be interpreted to be representative of the tracer particle which passed through the riser straight up with very little backflow. This bimodal PDF in the FF regime seems to gradually change to a single modal one as one moves towards the wall. Hence, the existence of clustering phenomenon, inferred from the negative axial velocities, seems to be prevalent throughout the riser cross-section (more likely near the wall) in the FF regime. In the DPT regime, with the operating conditions at Ugriser = 4.5 m s− 1 and Gs = 36.8 kg m− 2 s− 1, Fig. 5 shows the spatial variation of axial solids velocity PDFs at the same compartments. In contrast to the FF regime, PDFs at the centerline have a single peak with no negative velocities. Also, the ensemble average solids velocity is positive near the wall even though one can note some negative instantaneous velocities. Hence, in the DPT regime no clustering occurs in the core. However, the radial particle exchange is still pronounced as suggested by the nonhomogeneous particle segregation (interpreted from the number of occurrences) and the radial velocity profiles. Similar conclusions were also drawn with regard to the absence of clustering in the central core from the axial velocity PDFs in the DPT regime at other operating conditions. Note that all the flow conditions in DPT regime are actually in the heterogeneous or core-annular dilute flow regime.
Each of the axial velocity PDFs shown in Figs. 4 and 5 was obtained based on the statistics from a single compartment at a particular angular position. Now one can also collect the statistics from every angular compartment at each radial location to construct axial velocity PDFs. Comparing the velocity PDFs from a single compartment to that obtained from the perimeter (not shown for brevity), we noticed that the functions do not change much (less than 7%) with the increase in the statistics. Such small variation indeed reflects axisymmetric flow. Further details can be found in Bhusarapu [29]. The variation of solids radial velocity PDFs was found to be similar in both flow regimes, in FF and DPT. Although the ensemble averaged values reveal that the velocity component is directed towards the wall, negative instantaneous radial velocities were observed. Also, the mean radial velocities are an order of magnitude smaller than the mean axial velocities. However, the standard deviation of the radial velocities was much higher (one order of magnitude) than their corresponding means. This result was established earlier using LDV measurements in a very dilute riser [35]. 3.1.4. FF versus DPT — velocity vector plots In this section, velocity vector plots representing the timeaveraged solids velocities are presented to check for axisymmetry in the solids flow pattern in the 3D risers in the two
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regimes — FF and DPT. Both the vertical and horizontal plane projections are given to interpret all the three components of the velocity vectors. The vertical planes are sliced through the center of the column at four different angles — 0–180°, 45– 225°, 135–315°, 90–270°, while the horizontal cross-sectional views are obtained at two different axial elevations. The display of the vector plots is accomplished using MATLAB. Fig. 6 displays the velocity vectors for the flow condition in the FF regime at Ugriser = 3.2 m s− 1 and Gs = 26.6 kg m− 2 s− 1. As evident from these figures, the flow pattern seems to
be axi-symmetric. In addition, Fig. 6a indicates that the solids flow upwards in the center and downwards near the wall in the FF regime, an observation frequently reported (e.g. [7,23,30,31,73]). However, in the DPT regime, the flow near the wall is also upwards (Fig. 7). This difference in the flow pattern (compared to the FF regime) could be due to the decrease in the solids cross-sectional concentration, resulting in the decrease of the clustering effect. With the decreased cluster formation, the downflow of solids is also reduced. Such upward flow near the wall was also observed by few
Fig. 6. Visualization of the ensemble averaged solids velocity vectors in the zone of interrogation in a) r–z plane at different angles; b) r–θ plane at different axial heights. The operating conditions are in FF regime at Ug = 3.2m s− 1; Gs = 26.6kg m− 2 s− 1.
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
Axial velocity (cm/s)
600 FF regime
400 DPT regime
200 0 -200
0
0.2
0.4
0.6
0.8
1
60 40 20 0
0
0.2
0.4
0.6
0.8
-20 1
Radial velocity (cm/s)
Nondimensional radius ( ξ )
Azimuthal velocity (cm/s)
Nondimensional radius ( ξ ) 15
5 0 -5
-15
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ ) Fig. 7. Azimuthally and axially averaged ensemble-averaged solids velocity components compared in two different regimes — FF (Uriser = 3.2m s− 1; g = 4.5m s− 1; Gs = 36.8kg m− 2 s− 1). Gs = 26.6kg m− 2 s− 1) and DPT (Uriser g
other researchers ([73,83]), but under very high solids flux conditions, termed as dense phase suspension by Grace et al. [37]. Note that the flow conditions investigated in this work are quite different from the dense phase suspension regime. The axial variation of the velocity is small (less than 11%) within the zone of interrogation in both the flow regimes (as seen in Fig. 6 for the FF regime). The radial and azimuthal components of the velocity are very small compared to the axial component indicating that the time-averaged flow pattern is basically representative of a close to fully developed flow within the zone. Similar observations were seen for other flow conditions investigated. However, fully developedness of the solids flow inferred from Fig. 6 cannot be taken in a strict sense, since the radial velocities are only relatively small and are numerically not equal to zero. The vector plots establish that even though the passage of individual solid particles through the zone of interrogation is tortuous (Figs. 2 and 3), the time-averaged velocity field is structured with a clear pattern (Fig. 6). Although, the local variations (instantaneous velocities) can never be reproduced by any number of experiments, the time-averaged developed velocity profiles are reproducible. The time-averaged solids velocity components in the two flow regimes — FF and DPT are compared in Fig. 7. In the plots of Fig. 7, the velocities are circumferentially and axially
109
averaged. In the FF regime, the axial solids velocity component exhibits negative values near the wall, while in the DPT regime, such negative axial solids velocities are not observed. An estimate of annulus boundary can be taken as the ‘cross over’ point of the time-averaged axial velocity. While such a definition of the annulus seem to suggest no annulus in the DPT regime, the axial solids velocity profiles in both the regimes seem roughly parabolic. Within the spatial resolution of the velocity reconstruction, the inversion point of the axial velocity profile (corresponding to the annulus thickness) in all the cases in the FF regime is found to be in the same compartment (with r / R = 0.81). Hence, the downflow of solids at the wall in the FF regime is expected to cause considerable backmixing of the solids phase. It can be observed that both the solids axial and radial components of the time-averaged velocity in the DPT regime are higher in magnitude compared to the values in the FF regime, while azimuthal profiles in both seem to be negligible and close to zero. This result once again confirms axi-symmteric flow pattern of the solids in the riser. Values that deviate from zero in the central part may be caused by the poor statistics in the region with fewer particle occurrences. The time-averaged radial velocity profile in both the regimes seems to be always positive (Fig. 7). Thus, positive timeaveraged radial velocities indicate that the flow is still not fully developed (in a strict sense) and that the solids in the core have a tendency to move radially outward. The core seems to feed the solids to the annulus even at these elevations. However, the instantaneous radial velocities (from radial velocity PDFs) do exhibit negative velocities. Hence, the radial velocity profiles suggests that the movement of solids from core to annulus seems to be governed by the time-averaged velocity profiles, while the movement of solids from annulus to core (if prevalent) is governed by the fluctuating velocity profiles in the fully developed zone. 3.1.5. FF versus DPT — turbulent stresses and kinetic energy CARPT technique provides turbulent stresses and kinetic energy in the entire three dimensional flow field [15,19]. It is known that turbulence is characterized by random fluctuations and statistical characterization of the flow parameters leads to important information about the flow [38,39]. The instantaneous flow information is usually obtained from higher order correlations of the fluctuation quantities that represent the turbulent interactions. Turbulent stress is one such interaction which represents the transport of momentum due to the turbulent velocity fluctuations. The main diagonal terms in a turbulent stress tensor contribute to the pressure at a point in the flow, while the non-diagonal terms are the tangential or shear stress components. The energy associated with the fluctuating quantities called the turbulent kinetic energy is the sum of the three normal stress components. Turbulence kinetic energy (per unit bulk density) in granular flows is also called granular temperature. Sinclair and Jackson [40] were the first to analyze fully developed riser flow using the kinetic theory of granular flow. The primary aim in this section is to present the detailed experimental study on the turbulent quantities required for the CFD model verification. Experimental data on turbulent
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quantities is very limited and is available only for dilute, low flux riser flows. This data is usually obtained by imaging techniques such as PIV or LDV and/or by probes. Imaging techniques, as discussed earlier, have limitations that CARPT technique can overcome. Fig. 8 shows the comparison of the turbulent kinetic energy per unit bulk density in the two regimes. The turbulent kinetic energy can be scaled with a constant to obtain the granular temperature. A clear demarcation between a core and an annulus in the turbulent energies is observed in the FF regime (Fig. 8a). However, in the DPT regime, the turbulent kinetic energy is more uniform (Fig. 8b) in the radial direction, although it decreases near the wall. Very small axial variation of the turbulent kinetic energy is seen in both flow regimes. Fig. 9 shows the contours of the particle occurrences per unit volume in the FF and DPT regimes. With an assumption of ‘wellperfusedness’, or no stagnation in the zone of interrogation, one
can interpret the solids volume fraction to be proportional to the ratio of the particle occurrences (in a compartment) to the total number of occurrences. Similar interpretation of the particle occurrences was done in other multiphase systems [10,11,15,41]. In other words, the contours shown in Fig. 9 are those of the solids volume fraction, whose magnitude needs to be scaled appropriately. To do the scaling one needs an independent measurement (like tomography) of the solids concentration. Such analysis is done later while discussing the results from tomography. The solids concentration in Fig. 9a (FF regime) clearly shows a concentrated annulus layer near the wall and a dilute core in the center. One can interpret the annulus wall layer thickness based on these contours. This is another way of obtaining the annulus thickness, methods reported in the literature are based on the axial velocity and flux profile's ‘cross over’ points [42]. It can also be observed from Fig. 9 that there are some concentrated +
(a)
+ -
-
+ -
+
-
36.5
40
36.1
36 32
Z/D
35.5
28 24
34.8 20 16
34.2
12 33.5
-5
0
5
-1 -.5 0
X/R
.5
1
X/R
-1 -.5 0
.5 1
X/R
-1 -.5 0
.5
1
X/R
8 (m 2/s 2)
(b) 36.5
40
36.1
36 32
35.5
28 24
34.8 20 16
34.2
12 33.5 -1 -.5 0
.5
X/R
1
-1 -.5 0
.5
X/R
1
-1 -.5 0
X/R
.5 1
-1 -.5 0
.5
X/R
1
8 (m 2/s 2)
Fig. 8. Comparison of the contour plots of the turbulent kinetic energy per unit bulk density a) FF regime (Uriser = 3.2m s− 1; Gs = 30.2kg m− 2 s− 1) and, b) DPT g −1 −2 −1 (Uriser = 3.9m s ; G = 33.7kg m s ). g s
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
111 +
(a)
-
+ -
+ -
+
-
36.7
300
36.1
250
200
Z/D
35.5
150 34.8 100 34.2 50 33.5 -1 -.5 0
.5
1
-1 -.5 0
X/R
.5
-1 -.5 0
1
.5
1
-1 -.5 0
X/R
X/R
.5
0
1
X/R
(b) 36.7
3000
36.1
2500
2000
Z/D
35.5
1500 34.8 1000 34.2 500 33.5 -1 -.5 0
.5
X/R
1
-1 -.5 0
.5
1
X/R
-1 -.5 0
.5
X/R
1
-1 -.5 0
.5
1
0
X/R
Fig. 9. Comparison of the contour plots of the particle occurrences per unit volume a) FF regime (Uriser = 3.2m s− 1; Gs = 30.2kg m− 2 s− 1) and, b) DPT (Uriser = 3.9 m s− 1; g g Gs = 33.7kg m− 2 s− 1).
pockets of solids near the wall and a few in the core region. These concentrated pockets cannot be directly interpreted as ‘clusters’ considering that the lifetime of the clusters is very small and that these contours are derived from several particle trajectories observed over hours of experiment. If one makes an ergodic assumption (validated earlier) that observing several independent single particle trajectories is equivalent to observing all the trajectories of the ensemble of particles in the system, then the concentrated pockets can be interpreted as ‘clusters’. Hence, the message is that there is a definite probability of the ‘cluster’ formation in these regions of concentrated pockets. Thus, Fig. 9 a) and b) convey the message that the clustering phenomenon is significant near the wall region and can also occur in the core of the riser. In contrast, in the DPT regime, the solids concentration is more uniform (both radially and axially) and the intensity of clustering much less compared to that in the FF regime. Notably, the contours in both regimes seem to be nearly axi-symmetric. Based on the symmetry in most of these
observations, the 3D velocity data were azimuthally and axially averaged to obtain the one-dimensional variation of the velocity and turbulent fields along the radial direction. 3.1.6. FF versus DPT — radial variation of velocity and turbulent fields Further analysis is restricted to the discussion of the azimuthally, axially and time-averaged quantities of the velocity and turbulence profiles. All the quantities were axially averaged from Z / D = 33.5–36.7 (z = 5.1–5.6 m) and the error bars on each profile represent the range of values encountered for all z levels. In order to show generality in the comparison of FF and DPT regimes, the flow conditions presented in the radial profile plots are different from those compared in the contour plots (Figs. 8 and 9). The variation of radial profiles of the time-averaged velocity was discussed earlier with reference to Fig. 7. A substantial increase in the mean axial velocity was observed in the center of
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the solids mass flux and/or superficial gas velocity under ‘dilute conditions’. A similar decreasing trend in the solids velocity fluctuations with the increase in solids holdup was observed by Benyahia et al. [95]. This finding also substantiates our comparison between the FF and DPT regimes. Note that increasing the solids mass flux at constant gas superficial velocity, or decreasing the gas superficial velocity at constant mass flux, increases the solids holdup (tomography results). Fig. 10 shows a decay of axial velocity fluctuations radially in both the FF and DPT regimes following the same trend as the mean values (minimum reached at the wall). The low variations of the axial solids velocity (fluctuation velocity being very close to the mean values) reveal the great agitation of the solids along the flow direction. The radial solids velocity fluctuation profile in both the FF and DPT regimes interestingly show a peak near r / R = 0.7 (Fig. 10). This radial position, according to the radial particle occurrence profile, corresponds to the transition from a flat solids holdup profile to a drastically increasing one. Hence, the peak in the radial solids velocity fluctuation profile corresponds to the transition from a lean core with nearly constant solids density to a dense zone with increasing solids density. All these results show the predominance of the fluctuations over the mean particle motions. In Fig. 11 the ratio of the axial to the radial solids velocity fluctuation profiles in the FF and DPT regimes are presented. As it can be seen, the axial solids velocity fluctuations are always greater than the radial ones but not by much. In the FF regime, the anisotropy is significant decaying slightly from 2.5 near the center to 1.5 near the annulus, while in the DPT regime the anisotropy is nearly uniform around 1.2. Thus, the dilute risers in the DPT regime tend towards isotropic turbulence. Note the clear distinction in the ratio values across the flow regimes. Hence, the conclusion is that fluctuating motion is principally directed along the main axis of the multiphase flow. There is experimental evidence that the particle turbulence in risers is not isotropic for both Group A and B particles [30,34– 36]. The normal stresses in the axial direction are much larger
the flow when superficial gas velocity and mass flux were increased from the FF to DPT regime (Fig. 7). Also, the mean radial velocity showed the same trend. A significant velocity variation was indicated between the central core and annulus zone near the wall. Near to the transition between these two zones, the axial and radial components of the mean velocity are of the same order revealing a particle motion principally directed toward the riser walls. However, axial and radial velocity fluctuation profiles in Fig. 10 show an opposite trend (to that of mean profiles) for comparison between FF and DPT regimes. The axial velocity fluctuations are of the same order of magnitude as the mean values. On the other hand, the radial velocity fluctuations are significant and are always greater than the measured mean values. This observation is in agreement with the earlier experimental studies by Van den Moortel et al. [35] and Godfroy et al. [11]. Fig. 10 suggests that with the increase in solids concentration, particle fluctuating velocities also increase. Note that the flow condition in the FF regime (Ugriser = 3.2m s− 1; Gs = 26.6kg m− 2 s− 1) has a higher solids holdup compared to the DPT condition (Ugriser = 4.5 m s− 1; Gs = 36.8 kg m− 2 s− 1) as observed from the particle occurrence plots and the tomography results (discussed later). However, this is contrary to the commonly reported simulation results [43,44] and experimental data [11,35]. With the increased solids concentration, the mean free path of the solids is reduced, resulting in the reduction of velocity fluctuations. However, there is a competing mechanism for increasing the particle velocity fluctuations due to the increase in particle collision frequency. As reported by Gidaspow and Huilin [45], collision frequency increases with particle concentration, which increases the velocity fluctuations with solids holdup under ‘dilute conditions’ (solids holdup less than 5–10%). Note that ‘dilute conditions’ need not imply the DPT regime of operation. All the flow conditions investigated in this study had a solids holdup less than 10% (tomography results). Hence, the above argument leads to the conclusion that although the mean velocity increases, the velocity fluctuations decrease with the increase in
(a)
(b) 450
200 FF regime DPT regime
Radial RMS velocity (cm/s)
Axial RMS velocity (cm/s)
400 350 300 250 200
180
160
140
120
150 100
0
0.2
0.4
0.6
0.8
Nondimensional radius ( ξ )
1
100
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ )
Fig. 10. Comparison of the azimuthally and axially averaged radial profiles of the RMS fluctuating velocity components in a) axial and, b) radial in the FF regime (Uriser = 3.2m s− 1; Gs = 26.6kg m− 2 s− 1) and, b) DPT (Uriser = 4.5 m s− 1; Gs = 36.8kg m− 2 s− 1). g g
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123 4
Ug Gs m/s kg/m2/s FF; 3.2 30.2 DPT; 3.9 33.7 FF; 3.2 26.6 DPT; 4.5 36.8
3.5
Ratio (Vz' / Vr')
3 2.5 2 1.5 1 0.5 0
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ ) Fig. 11. Ratio of the axial to radial RMS fluctuating velocity profiles.
involving the angular fluctuating velocities, τzθ and τrθ, are negligible and can be considered to be zero. Similar to the RMS velocity fluctuation profiles, the axial and radial solids normal stresses are found to be higher in the FF regime than in the DPT regime (Fig. 12). The reason could be due to the higher solids concentration in the FF regime, leading to significantly higher number of particle collisions. Hence, particle collisions are the controlling mechanism for momentum transfer due to the fluctuating velocities or are the turbulent Reynolds stresses. However, one can note that the shear stresses were comparable in magnitude in both regimes, indicating that the changes in solids turbulent viscosity (as given by Eq. (1)) are mainly governed by the gradients in the mean velocities. Since the solids phase turbulence was found to increase with solids holdup, the data and trends are consistent with those of Tartan and Gidaspow [36]. Although the angular and radial normal stresses are about the same order of magnitude, the radial normal stress was always higher than the angular normal stress. A distinct feature for conditions in the DPT regime is that angular normal stress peaks at the center of the column. This suggests that the vertical structures spiraling up the column have a tendency to cross over the axis, especially at high superficial gas velocities. This behaviour of vortex structures rules out the possibility of performing a transient simulation using 2D axi-symmetric conditions.
20
4.8
16
4 2 2 τrr (m / s )
τzz (m2 / s2)
than in the radial and angular directions. Fig. 12 compares the radial profiles of the spatially averaged turbulent Reynolds stresses (per unit bulk density) in the FF and DPT regimes. It can be clearly observed that the axial normal stresses are about 3 to 5 times higher than the radial and azimuthal normal stresses. This is due to the high gradient in the axial solids velocity. In addition, the radial and tangential solids velocities are quite small and, hence, their gradients are also small. The Reynolds shear stress, τrz, is much lower than the radial and angular normal stresses (about 1 / 2 to 1 / 3), while the shear stresses
12 8 4 0
3.2 2.4 1.6
0
0.2
0.4
0.6
0.8
.8
1
0
2.4
3.2
1.6
2.8
.8 0 -.8
0.6
0.8
1
2 1.6
0
0.2
0.4
0.6
0.8
1.2
1
0
1.6
.8
.8
.4
0 -.8
0
0.2
0.4
0.6
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ )
2 2 τzθ (m / s )
τzθ (m2 / s2)
0.4
2.4
Nondimensional radius ( ξ )
-1.6
0.2
Nondimensional radius ( ξ )
2 2 τθθ (m / s )
τrz (m2 / s2)
Nondimensional radius ( ξ )
-1.6
113
0.8
1
Nondimensional radius ( ξ )
0 -.4 -.8
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ ) 2
- FF regime (Ug = 3.2 m/s; Gs = 26.6 kg/m /s)
2
- DPT regime (Ug = 4.5 m/s; Gs = 36.8 kg/m /s)
Fig. 12. Comparison of the azimuthally and axially averaged radial profiles of the turbulent Reynolds stress components in the FF and DPT regimes.
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Imposing a zero gradient at the centerline, as done in axi-symmetric conditions, would contradict the measured flow structure. The relationship between the shear stress, τrz, and the gradient of the mean axial velocity can be obtained using Bossinesq's hypothesis as shown by Eq. (1). P
lturbulent ¼ s
es qs vr Vvz V Avz =Ar
ð1Þ
The validity of the Bossinesq's theory is questionable since the hypothesis was originally proposed for single phase flows with isotropic turbulence. However, such closure is often used in the two-fluid modeling of granular flows [43] due to lack of a proper anisotropic closure. Also, the same hypothesis was employed to calculate the turbulent shear viscosity of liquid in bubble column flows [25,46]. Hence, Eq. (1) was employed to obtain the solids phase viscosity profiles. The solids holdup values required for the calculations were estimated from the radial profiles of the particle occurrences (per unit volume). The ratio of the particle occurrences in a compartment to the total occurrences was taken to be proportional to the solids volume fraction. The proportionality constant was estimated for each flow condition by comparing the crosssectional average holdup to that obtained from tomography. The viscosity profiles obtained did not make physical sense. Two peaks were observed in the FF regime, one in the core near the center and one near the wall cannot be realized with any physical flow structure. Also, for the flow conditions in DPT regime, negative solids viscosities were observed near the wall. Hence, the only explanation is that the Bossinesq's hypothesis does not hold for solids flow in a riser and yields physically unrealizable viscosity values. Based on the kinetic theory of granular flows (isotropic), a constitutive relation for the solids viscosity was derived relating it to the granular temperature (turbulence kinetic energy) and solids holdup ([47,48,96]). The following expressions describe the closure relations that are typically used in a kinetic theory based model. Solid phase shear viscosity (μs): rffiffiffiffiffiffi 2 2ls;dil 4 4 Hs ls ¼ 1 þ g0 es ð1 þ eÞ þ es qs dp ð1 þ eÞg0 5 5 ð1 þ eÞg0 p
e is the restitution coefficient, taken to be 0.89 based on the reported measured values by Foerster et al. [49] and recommendation by Tartan and Gidaspow [36]. The above expressions were used, along with the measured granular temperatures (turbulence kinetic energy per unit bulk density), and the solids holdup profiles derived from the CARPT data to calculate the viscosity profiles. Fig. 13 presents the solids viscosity profiles for different flow conditions in the FF and DPT regimes. In contrast to the previous calculations, it can be seen that the viscosity values and trends do make physical sense. The solids viscosity was found to be decaying monotonically in the radial direction in the FF regime, but in the DPT regime it shows a hump around r / R = 0.7. The reason for such a hump can be explained based on the solids holdup profile (cross-sectional view). At the radial position (r / R = 0.7) the solids concentration starts to increase rapidly (particle occurrence profiles) and represents the approximate interface between the lean core and a dense phase annulus. Thus, the particle exchange at this interface is frequent and vigorous, thereby decreasing the easy movement of the solids phase, which increases the solids viscosity. Although, the same argument holds in the case of the FF regime, but the axial fluctuations of the particles dominate (compared to radial) resulting in a higher turbulent transport of particles axially. Thus, in the FF regime, the decrease in the axial fluctuations (radially) dominates the peak in radial fluctuations, resulting in a smooth gradient of solids viscosity. The solids viscosity in each of the flow conditions exhibits similar radial trends as that of the granular temperature, indicating that the viscosity is almost independent of the solids holdup in the range of the measurements studied. This result is in agreement to that of Tartan and Gidaspow [36], who estimated solids viscosities in relatively dilute 3 in. riser using ‘PIV with probe’ technique. With the same Group B particles and a larger mean particle diameter (3.5 times) Tartan and Gidaspow [36] found nearly constant viscosities in the core (for all the flow conditions investigated). The viscosity values reported by them were lower, possibly due to the lower solids holdup, resulting in lower velocity fluctuations (under ‘dilute conditions’). Besides, the use of an intrusive imaging technique with a 0.5cm diameter probe to measure the velocity fluctuations is questionable. Hrenya and Sinclair [50] in their simulations reported higher
ð2Þ
ls;dil
pffiffiffiffiffiffiffiffiffi 5q dp Hs p ¼ s 96
ð3Þ
g0 is the radial distribution function which becomes very large as the solids holdup approaches the maximum packing (εs,max = 0.64 for the glass beads used) and is given by: 3 es 1 −1 3 g0 ¼ 1− 5 es;max
ð4Þ
Solids Viscosity (g/cm-s)
where Θs is the granular temperature, dp is the sauter mean size of the solids distribution, ρs is the density of the solids (glass beads), εs is the local solids holdup and the solids phase dilute viscosity (μs,dil) is given by:
1.5
1
0.5 0
Ug m/s FF; 3.2 FF; 3.2 DPT; 3.9 DPT; 4.5
Gs kg/m2/s 26.6 30.1 33.7 36.8
0.2
0.4
0.6
0.8
1
Nondimensional radius( ξ ) Fig. 13. Radial profiles of the solids viscosity calculated from kinetic theory based expressions.
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
viscosities for FCC particles compared to Gidaspow and Huilin [45], who employed the same ‘PIV with probe’ technique. The solids viscosity in Fig. 13 increases with the solids concentration (from DPT to FF regime). This can be explained with the following interpretation of Eq. (2) [51]. kinematic viscosity ¼ mean free path random oscillating velocity
(with solids holdup) enforces the above trend for the granular temperature. With the solids holdup increasing from DPT to FF regime, the increase in the collision frequency seems to be dominant compared to the decrease in the mean free path. However, with the solids holdup increasing radially in each of the regimes, the decrease in the mean free path becomes dominant (at different magnitude for each of the regimes) compared to the increase in the collision frequency. This effect is less pronounced in the DPT regime (compared to FF) as suggested by a relatively flat radial profile of the granular temperature. The observations from Fig. 14 suggest that the granular temperature is strongly correlated to the solids holdup. Also, the above arguments suggest that the peak in the granular temperature may occur around a solids holdup value of 1–6%, in contrast to that reported by Gidaspow and Huilin [45] of 5–10%. Considering the fact that Gidaspow and Huilin [45] and Tartan and Gidaspow [36] employed imaging techniques like PIV or ‘PIV with probe’, the reliability of the velocity measurements away from the walls is questionable. Also, in their granular temperature calculations, angular velocity fluctuations were assumed equal to the radial component. In addition, the densitometry technique employed had a coarse resolution (N1.27cm) and yields only line-averaged solids holdups. In view of the above uncertainities, the position of the peak in the granular temperature reported by Gidaspow's group at 5–10% is uncertain. It is noted here that due to the data acquisition frequency of 200 Hz for CARPT experiments, the maximum range of frequencies tracked by the tracer particle is up to 100Hz. Therefore, the present measurements represent only scales up to 100Hz of the turbulent structures. However, since the large scales contain the most energy, it is expected that what remains due to small scales is not very significant in magnitude. There are several studies reporting the dominant frequencies of oscillation of particles in the dense and dilute zones for a wide variety of operating conditions ([51–55,96]). Typical macroscopic frequency range reported was up to 4 Hz.
14 2
2
2
Turbulent kinetic energy per unit bulk density (m /s )
The mean free path decreases with increasing solids concentration, while the velocity fluctuations increase due to the increase in the collision frequency under ‘dilute conditions’. Hence in dilute risers (εs b 0.05–0.1), the increase in the collision frequency dominates the decrease in the mean free path, while it is vice versa in dense risers. Also, Gidaspow and Huilin [45], based on experimental data, showed that, for different particles, the dimensionless viscosity calculated based on Eq. (2) shows a minimum at solids holdup of 0.057 and increases beyond that. It can also be observed from Fig. 13 that with the decrease in the solids concentration, tending towards more dilute flow conditions, the viscosity profile tends to become flat. This is due to the fact that the granular temperature and the solids holdup profiles tend to be nearly flat in a dilute riser. Both these profiles are presented subsequently. An unusual hump in the viscosity profile can be noted for the flow condition of Ugriser = 3.9 m s− 1 and Gs = 33.7kg m− 2 s− 1 compared to the other three profiles. This is possibly because the flow condition is close to the regime transition boundary between FF and DPT (type A choking velocity). Fig. 14 compares the radial profiles of the granular temperature in the FF and DPT regimes. Based on the earlier discussion, the velocity fluctuations and hence the granular temperature increases with the solids holdup for ‘dilute conditions’ and decreases for higher solids holdups. The relative dominance of the increase in the collision frequency over the decrease in the mean free path
115
FF, Ug = 3.2 m/s; Gs = 26.6 kg/m /s 2
DPT,Ug = 4.5 m/s, Gs = 36.8 kg/m /s
12
2 2 2 KE = 1/2 (u' +v' +w' )
10
8
6
4
2 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Nondimensional radius ( ξ ) Fig. 14. Radial profiles of the turbulent kinetic energy (per unit bulk density) in FF and DPT regimes.
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3.2. Solids holdup measurements
CT scanner setup were stationary. Hence, the dynamic bias in these phantom scans arises only from the stochastic nature of the emissions from a γ-ray source. However, during the actual riser scan, solids holdup fluctuations also contribute to the bias. If the sampling time is small enough, then the variation of the holdup within the time interval is small allowing one to assume an approximately static holdup. Hence, the sampling frequency should be at least twice the macroscopic oscillation frequencies of the solids in order to assume a static holdup within each pixel (imaginary grid assumed for image reconstruction). There is a vast experimental and modeling evidence of the dominant frequency range for riser flow to be up to 4Hz (for example Ref. [55]). Another constraint in selecting a high sampling frequency is the need to obtain adequate statistics in the photon counting process. For the CT scanner in our laboratory, a sampling frequency of 20Hz is low enough for statistical counting errors to be small. In fact, AM reconstruction algorithm models the photon emission and detection to be of Poisson, yielding good image estimates even at low counts [56]. Also, note that it is not intended to capture the small time scale fluctuations in the flow. An inherent approximation involved is that these small time scale fluctuations lead to solids movement within the spatial resolution. Therefore a sampling frequency of 10 Hz was considered to be sufficiently high for making static holdup approximation. The main factors that determine the imaging capabilities of a CT scanner are its achievable spatial, temporal and density
Significant experimental evidence is available which show radial segregation of the solids in gas–solid risers (refer to Table 2). According to Sinclair and Jackson [40], the central problem in constructing a satisfactory model for riser systems is to understand the mechanism that gives rise to lateral particle segregation. The intent in this section is to study the solids holdup distribution to complement the CARPT data in providing valuable insight into the physics of the complex hydrodynamics. To achieve these objectives, accurate estimation of solids holdup is required. Hence, the accuracy of estimating the solids holdup via γ-ray tomography is discussed before presenting the riser holdup profiles. Improvements in the image reconstruction by implementing an Alternating-minimization (AM) algorithm were discussed by Bhusarapu et al. [28]. The AM algorithm was found to improve the image quality near the high attenuation (high holdups) regions. The CT scanner setup was validated with a phantom scan of a beaker filled with water. The reconstructed image showed that the flat distribution of the single phase (water) was reconstructed with the mean total attenuation coefficient of 0.085cm− 1. The discrepancy with the theoretical mass attenuation value of water at the photo peak of Cs-137 (660keV) was found to be less than 2.3%. The phantom scans that illustrated the improvements shown by AM algorithm and the validation of the
Radius (cm)
(a)
(b) 7.5
7.5
5.4
5.4
2.7
2.7
0
0
-2.7
-2.7
-5.4
-5.4
-7.5 -7.5 -5.4
-7.5 -7.5 -5.4
0.14 0.12 0.1 0.08 0.06 0.04 0.02
-2.7 0 2.7 Radius (cm)
5.4 7.5
(c)
-2.7 0 2.7 Radius (cm)
5.4 7.5
(d) 7.5
7.5
5.4
5.4
2.7
2.7
0
0
-2.7
-2.7
-5.4
-5.4
-7.5 -7.5 -5.4
-7.5 -7.5 -5.4
0.14 0.12 0.1 0.08 0.06 0.04 0.02
-2.7 0 2.7 Radius (cm)
5.4 7.5
-2.7 0 2.7 Radius (cm)
5.4 7.5
Fig. 15. Contour plots of the solids holdup at Z / D = 33 (z = 5 m) in the riser under the operating conditions: a) Uriser = 3.2m s− 1; Gs = 26.6kg m− 2 s− 1, FF; b) g −1 −2 −1 −1 −2 −1 −1 riser riser Uriser = 3.2 m s ; G = 30.1kg m s , FF; c) U = 3.9m s ; G = 33.7kg m s , DPT; d) U = 4.5m s ; G = 36.8kg m− 2 s− 1, DPT. g s g s g s
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
resolutions [22]. A measure of the spatial resolution is the point spread function which is the extent to which an image of a point object will be blurred. The effective detector aperture width is taken to be the spatial resolution of the scanner and the expression to calculate it was derived by Yester and Barnes [57]. The spatial resolution for the CT scanner in our laboratory was found to be 1.7mm at the center of the column. The resolution employed for reconstructing the solids holdup tomograms in the riser was 2.7 mm. The single important factor that determines the density resolution is the random fluctuations in the photon counts. De Vuono et al. [58] derived an expression for the density resolution obtainable from all the measurements in an entire scan as follows: rU n pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ q 2lw qw Di mCT Md
ð5Þ
where n is the number of beams in each view, m is the number of views, Md is the average number of photon detected per beam, μw is the mass attenuation of water, ρw is the density of water and di is the inside diameter of the column. The density resolution for the designed CT scanner in our laboratory for a 6 in. column was found to be 8.1 × 10− 3 g cm− 3. Hence, the holdup resolution with glass beads in the riser is 3.2 × 10− 3. Fig. 15 shows the tomograms of the riser at the operating conditions of investigation. Qualitatively all the scans reveal increased solids holdup near the walls and with nearly same relative increase from their means. The distributions seem to disclose nearly axi-symmetric flow as predicted from the velocity distributions (Fig. 6). In the FF regime, solids holdup seems to exhibit a three layer stratification with gradual gradient, while in the DPT regime there seems to be a smooth gradient, which is less than that in the FF regime. Also, there is an overall reduction in the solids volume fraction in the DPT regime with the corresponding increase seen in the velocity
117
PDFs (Figs. 4 and 5). Albeit, there seems to be large radial solids segregation towards the wall in both cases. Radial migration of solids is a complex phenomenon and is not properly understood [59]. The effect of increasing the solids mass flux at constant gas superficial velocity increases the solids holdup (Fig. 15). This increase arises because more solids are fed into the riser section for the same gas superficial velocity (and hence the energy input) to the system. The effect of increasing the gas superficial velocity at constant mass flux can be understood to decrease the solids holdup due to the increase in the solids velocity. Since the gas injected is the only source of energy that drives the solids circulation, constant solids mass flux with higher gas flow drives more solids out of the riser. Consequently, solids holdup decreases. Unfortunately, such a trend can be verified only by comparing one pair of conditions (Ugriser = 3.2 and 3.9m s− 1; Gs = 30.1 kg m− 2 s− 1). The qualitative findings presented above can be quantitatively verified by circumferentially averaging the solids holdup distributions. Fig. 16 shows such a plot of the radial profiles under all the operating conditions investigated. The two profiles in the FF regime show distinctly higher holdups (relatively) and also higher radial gradients. Clearly, three distinct slopes in the profiles can be identified (FF regime) illustrating a three layer stratification observed in the tomograms (Fig. 15). The solids concentration was nearly zero in the center (up to r / R = 0.27, 0.5 for high and low fluxes, respectively), increases linearly up to r / R = 0.8, 0.85 for high and low fluxes, respectively, and later increases linearly with a higher slope. However, in the DPT regime, the density profiles seem to be relatively flat and show very little variation (within 20%) among the different operating conditions. Nevertheless, the relative (with respect to mean) radial increase of the solids holdup seems to be high and is comparable to that in the FF regime illustrating similarity profiles.
0.08 Ug, Gs m/s kg/m2/s
0.07
3.2, 3.9, 4.5, 3.2, 3.9, 4.5,
Solids Holdup
0.06 0.05 0.04
30. 1 33. 7 36. 8 26. 6 30. 1 32. 1
-
FF DPT DPT FF DPT DPT
0.03 0.02 0.01 0 0
0.13
0.27
0.4
0.53
0.67
0.8
Non-dimensional radius ( ξ ) Fig. 16. Azimuthally averaged radial profiles of the solids holdup.
0.93
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S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
Table 4 Correlation fits for the radial holdup profiles r m i mþ2 h 1þc m þ 2 þ 2c R
Operating conditions
Mean from CT
(m s− 1) Uriser g
Gs (kg m− 2 s− 1)
〈εs〉CT (%)
〈εs〉 (%)
m
c
D (%)
3.2, 3.2, 3.9, 3.9, 4.5, 4.5,
30.1 26.6 33.7 30.1 36.8 32.1
2.9 0.85 0.48 0.45 0.61 0.4
3.24 0.97 0.53 0.51 0.67 0.43
3 3.9 4 7 5.1 3.9
13.5 12 9.5 4.2 2.5 3.8
12 14 11 12 10 8
Discrepancy, D ¼
hes i−hes iCT hes iCT
es ¼ hes i
Rhodes et al. [79]
Patience and Chaouki [60]
Wang et al. [80]
F
〈εs〉
β
D (%)
〈εs〉
k
D (%)
〈εs〉
D (%)
0.1 0.037 0.019 0.019 0.017 0.011
3.23 0.98 0.53 0.51 0.67 0.44
1.98 2.1 1.7 1.36 1.14 1.44
11 15 10 12 10 10
3.1 0.94 0.5 0.51 0.67 0.42
1.32 1.26 1.15 1.13 1.1 1.12
7 10 4 14 10 5
2.65 0.73 0.41 0.44 0.59 0.36
−9 − 14 − 15 −2 −3 − 10
100.
F — Steepness factor. m, c, β, k — Regressed constants. r 6 h 2 i es −hes ik Rhodes et al. [79] — es ¼ hes i 1−b=2 þ b Rr ; Patience and Chaouki [60] — ¼4 ; k R hes i−hes i r h r i es es r 19 for 1.5% b 〈εs〉 b 5%; Wang et al. [80] — ¼ 0:82 þ 48 1− d exp −22 1− ¼ 0:905 þ for 〈εs〉 b 1%. R R R hes i hes i
The reduced holdup profiles are typically correlated with the radial position to be incorporated in a phenomenological flow model. Patience and Chaouki [60] and Schlichthaerle and Werther [61] employed the following form of correlation: es ðrÞ−es ð0Þ m þ 2 r m ¼ : hes i−es ð0Þ 2 R
ð6Þ
A more general form of Eq. (6) was employed to model the radial profiles of gas holdup in bubble columns [22,46]. es ¼ hes i
r m i mþ2 h 1þc : m þ 2 þ 2c R
ð7Þ
In the above equations, 〈εs〉 is the cross-sectional average solids holdup, constant m is related to the steepness of the
profile, and constant c is related to the extent of solids present in the local wall region. Eq. (7) was employed to correlate the solids holdup data. Table 4 provides the results of fitting the above functional form to the solids holdup profiles. It is clear from the available data (Table 4) that the cross-sectional average solids holdup shows trends with both the superficial gas velocity and solids mass flux. However, the effect on the curvature parameters m and c is not so evident. To facilitate such understanding, Fig. 17 shows the relative holdup profiles for all the flow conditions from the fitted parameters. Parameter c seems to be very high in the FF regime (greater than 10) and decreases with the change of regime to DPT (less than 5). In contrast, exponent m was found to be lower in the FF regime as compared to that in DPT regime, indicating a steeper profile in the FF regime. However, for the operating condition with Ugriser = 3.9 m s− 1 and Gs = 33.7 kg m− 2 s− 1, which is close to the regime transition, a c value of 9.5 is bound intermediate between FF and DPT regimes. Also, the m value was found to
3 Ug Gs m/s kg/m2/s
3.2, 3.2, 3.9, 3.9, 4.5, 4.5,
2.5
ε(ξ) 2
---Relative holdup
<ε>
1.5
30.1-FF 26.6-FF 30.1-DPT 33.7-DPT 36.8-DPT 32.1- DPT DPT regime
1
0.5
FF regime
0 0
0.13
.27
.4
.53
.67
.8
Nondimensional radius ( ξ ) Fig. 17. Relative holdup profiles obtained from the holdup correlation.
.93
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
Similar stratification can be observed in the tomograms (Fig. 15). Note that for the flow condition at Ugriser = 3.9 m s− 1 and Gs = 33.7kg m− 2 s− 1, close to regime transition, indicate a mixed behavior with FF characteristics near the core transiting slowly to DPT characteristics near the wall. Although it is difficult to generalize the findings with the limited experimental data available, one can observe from Fig. 17 that in the FF regime the solids concentration in the core is insensitive to the averaged holdup 〈εs〉. On the other hand in the DPT regime, averaged holdup influences the core solids concentration and is insensitive to the wall concentration. Similar trend with two distinctive variational regions in the radial profiles was reported by Xu et al. [63] for FCC particles. However, none of the studies (within the literature reviewed in Table 2) reported the three characteristic layers in the FF regime conditions. Most of the studies, covering a wide range of operating conditions (including DPT and FF), reported only a two layer structure with a nearly constant core in the center transiting to a steep increasing holdup near the wall ([17,55,63–65,97]). The reason could be that the employed techniques in the studies have a poor spatial resolution (5–10 holdup data across the radius). Also, the wall effects influence most of the sensing techniques employed. The results with X-ray tomography from Wirth's group [66,67], with a spatial resolution as good as 6 mm, also could not capture such three layer stratification. As a matter of fact, such three layer stratification could not be captured in the velocity fields from CARPT results (Figs. 6–9) for the same reason that the spatial resolution (for Eulerian averaging) is poor. The radial profiles of the granular temperature (Fig. 14) seem to have similar shape as that of the gas holdup (1 − εs) profiles. In order to understand their relationship and to obtain a functional form for the granular temperature, Θs, the reduced profiles of the two measured quantities were plotted in Fig. 18. Considering the fact that the granular temperature was obtained from CARPT data with low spatial resolution, there seems to be a fair comparison of the reduced profiles in both the regimes. Hence
be low (4), indicating abnormalities near the regime transition conditions. It can be observed from Eq. (7) that the exponent m alone is not representative of the gradient of the solids holdup. The radial steepness of the solids holdup profile can be assessed with a parameter F given by: Z 1 des des F¼ ¼ 2 n d dn dn average dn 0 average 2hes icmðm þ 2Þ : ¼ ðm þ 1Þðm þ 2 þ 2cÞ
ð8Þ
Table 4 lists the values of the steepness factor F for the each of the operating conditions. It can be observed that F increases with the solids mass flux at constant superficial gas velocity both in FF and DPT regimes. Although not conclusive enough, comparing the F values at operating conditions with the constant mass flux Gs = 30.1 kg m− 2 s− 1 shows that F decreases with increase in superficial gas velocity. Both trends are inline with that reported by Zhang et al. [62]. Table 4 also lists the various available correlations for the radial profiles of solids holdup. The regressed constants and the mean holdup values are indicated for each of the correlations. The correlation by Patience and Chaouki [60] seems to give the least discrepancy of 8% (averaged for all the operating conditions). Relative holdup profiles in Fig. 17 reveal distinctive flow behavior in the FF and DPT regimes. In the central core region, the relative holdup is distinctively lower in the FF regime compared to DPT, although both are flat. The uniformly flat region in FF seems to extend until r / R = 0.27 (approximately), while in DPT it extends until r / R = 0.45 (approximately). Beyond that, the relative holdup increases with close to similar slopes in FF and DPT regimes. While in the DPT regime, such radial gradients prevail till the wall, FF regime indicates a higher radial gradient starting from r / R = 0.8 (approximately). Hence, the above trends reveal three different characteristic layers in the FF regime, while the DPT regime has two characteristic layers.
(a)
(b) 4
3
ϕ=Θs ϕ=εs
ϕ(ξ)-ϕ(0) 3
2.5
<ϕ>-ϕ(0) Reduced profiles
119
2 2
FF regime
1.5
DPT regime
1
1
0.5 0
0 0
0.2
0.4
0.6
0.8
Non-dimensional radius ( ξ )
1
0
0.2
0.4
0.6
0.8
1
Non-dimensional radius ( ξ )
Fig. 18. Reduced profiles of the granular temperature, Θs and the solids holdup, εs in: a) DPT (Uriser = 4.5m s− 1; Gs = 36.8kg m− 2 s− 1); b) FF (Uriser = 3.2 m s− 1; g g Gs = 30.1kg m− 2 s− 1).
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one can assume an approximate functional form for granular temperature as: Hs ðrÞ−Hs ð0Þ es ðrÞ−es ð0Þ c Z Hs ðrÞcaes ðrÞ þ b: hHs i−Hs ð0Þ hes i−es ð0Þ
ð9Þ
Such a functional form can be employed to derive the dependence of solids viscosity (Eq. (2)) variation with solids holdup, which can be used as an input in a two-fluid approach of a CFD model. One should note that the relationship given in Eq. (9) is limited to dilute flow in risers. The riser was investigated only under ‘dilute conditions’ where solids fluctuations increase with the solids holdup, while it is known that beyond a certain limit (1–6%) fluctuations decrease with the solids holdup. 3.2.1. Axial variation of solids holdup It was established in the earlier section that the axial variation of solids velocity within the zone of investigation was negligible. To check for the ‘fully developed’ flow in the zone of investigation the radial profiles of the solids holdup at two different axial planes were compared for all the operating conditions under investigation. Although there are slight variations in the holdup profiles at the two different axial planes, the differences are within the density resolution of scanner. Hence, the axial gradients of the solids holdup are negligible in the zone of investigation.
CT. Comparison in both FF and DPT regimes seems to be fair with the CARPT derived profiles over predicting the averaged reduced holdups. Similar trends were observed for all the operating conditions under investigation. Again the reason for such over prediction could be due to the low spatial resolution for Eulerian averaging in the CARPT technique. Considering the fact that the profiles were derived from two independent experimental techniques, this comparison serves as a validation of results for both the techniques. 4. Summary Single radioactive particle tracking in the gas–solid riser yielded a wealth of solids instantaneous and time-averaged flow information. Added to it the γ-ray tomography provided detailed time-averaged volume fraction profiles of the two phase riser flow enabling some insights into the complex phenomena. Following are the key conclusions with regards to the solids flow in risers: i. Instantaneous particle traces reveal occasional downflow in the core region (near center) only in the FF regime at the operating conditions investigated. Both large scale internal recirculation superimposed by fine scale fluctuations contribute to axial backmixing, while in the horizontal plane solids mixing is principally dispersive. ii. Solids flow is nearly axi-symmteric and is close to fully developed (within the zone of interrogation) revealed from both the velocity and holdup profiles. iii. The movement of solids from core to annulus seems to be governed by the time-averaged velocity profiles, while the movement of solids from annulus to core (if prevalent) is governed by the fluctuating velocity profiles in the fully developed zone. iv. Contour plots of turbulent kinetic energy and particle occurrences reveal a clear core-annular flow structure with FF regime, while the profiles are uniform under DPT regime.
3.2.2. Comparison of CT versus CARPT derived holdup profiles By assuming ‘well-perfusedness’ [10,11,15,41], particle occurrences per unit volume obtained from CARPT data can be related to solids holdup as follows: Occurrences ðper unit volumeÞ ~es : ð10Þ Total Occurrences CS Fig. 19 presents the typical comparison of the reduced holdup profiles derived from CARPT and that obtained from
(a)
(b)
ε(ξ)—ε(0)
------<ε>—ε(0)
4
3.5 CT CARPT
3.5
3
3 2.5
Reduced Holdup
2.5
DPT regime
2
2
FF regime
1.5
1.5
1
1
0.5
0.5
0 0
0.2
0.4
0.6
0.8
Nondimensional radius ( ξ )
1
0
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ )
Fig. 19. Comparison of the reduced holdup profiles derived from CARPT and CT at: a) FF (Uriser = 3.2 m s− 1; Gs = 26.6kg m− 2 s− 1); b) DPT (Uriser = 3.9 m s− 1; g g Gs = 33.7kg m− 2 s− 1).
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v. Clustering phenomena exists throughout the riser crosssection (more likely near the wall) along with the particle exchange between core and annulus. vi. Although the mean velocity increases, the velocity fluctuations decrease with the increase in the solids mass flux and/or superficial gas velocity under ‘dilute conditions’. vii. Flow in the riser is anisotropic with the fluctuating motion principally directed along the main axis of flow. viii. The relative dominance of the increase in the collision frequency over the decrease in the mean free path (with solids holdup) dictates the trends for the granular temperature and solids viscosity. ix. Tomograms reveal three different characteristic layers in the FF regime, while the DPT regime has two characteristic layers. x. Steepness in the radial profiles of solids holdup increases with the solids mass flux at constant superficial gas velocity both in the FF and DPT regimes. xi. Reduced holdup profiles derived from CARPT and CT match fairly well. Notation c parametric constant (–) dp particle diameter (m) D diameter of the column (m) E coefficient of restitution (–) F steepness parameter (–) Gs mass flux (kg m− 2 s− 1) g0 radial distribution function (–) k parametric constant (–) m parametric constant (–) mCT number of views (#) Md average number of photons detected per beam (#) n number of beams in each view(#) r radial position (cm) R riser radius (cm) Ugriser superficial gas velocity (m s− 1) v′ fluctuating velocity (m s− 1) bvN time-averaged velocity (m s− 1) z axial distance (m) Greek letters ε holdup (–) bεN cross-sectional averaged holdup (–) ρ density (kg m− 3) σ standard deviation μ viscosity (g cm− 1 s− 1) μw mass attenuation coefficient of water (m2 kg− 1) τ stress tensor per unit bulk density (m2 s− 2) Θs granular temperature (m2 s− 2) ξ dimensionless radius (–) β parametric constant (–) Subscripts and Superscripts g gas s solid phase
p i z r θ ρ cs
121
particle inside axial radial azimuthal density cross-sectional average
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Solids flow mapping in a gas–solid riser: Mean holdup and velocity fields Satish Bhusarapu 1 , Muthanna H. Al-Dahhan, Milorad P. Duduković ⁎ Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Campus Box 1198, 1 Brookings Drive, Washington University, St. Louis, MO 63130-4899, USA Available online 4 April 2006
Abstract In this study, solids flow dynamics has been investigated in a 6 in. “cold-flow” circulating fluidized bed riser using non-invasive flow techniques. Gamma ray Computed Tomography (CT) has been used to measure the time-averaged cross-sectional solids holdup distribution. The time-averaged mean and fluctuating solids velocity fields have been quantified using the Computer Automated Radioactive Particle Tracking (CARPT) technique. Details of the experimental techniques, protocol of implementation and data analysis are discussed. The experimental studies examine operating conditions in fast fluidization and dilute phase transport regimes. Comparative and symbiotic analyses of the results obtained from CARPT and CT have been used to develop a coherent picture of the solids flow field. In addition, this work also demonstrates the power of CARPT and CT as flow mapping techniques in studying highly turbulent and opaque multiphase systems. © 2006 Elsevier B.V. All rights reserved. Keywords: Riser; Solids; Fluid dynamics; Computed tomography; Radioactive particle tracking
1. Introduction Contacting solid particles with gases is often a necessity in chemical processes, in the pharmaceutical and metallurgical industries, in mineral processing, energy related processes, etc. The Circulating Fluidized Bed (CFB) is one of the widely employed reactors for gas–solid systems because of its efficiency, operational flexibility, and overall profitability [1]. Fluid catalytic cracking (FCC) and circulating fluidized bed combustion (CFBC) are by far the largest technologies that utilize CFBs. Other applications have been investigated, and some have been developed commercially or are under development. Further details and use of CFB technology can be found in Berruti et al. [1] and Grace and Bi [2]. Risers, which are an important part of CFBs, pose a considerable challenge in design and scale-up because it is not yet possible to produce ab initio predictions of their complex fluid dynamics, which impairs reactor modeling. In particular, quantification of solids holdup and velocity field is important. Existing models describing this complex flow often lack ⁎ Corresponding author. E-mail address: [email protected] (M.P. Duduković). 1 Present address: Harper International Corp., West Drullard Ave, Lancaster, NY 14086, United States. 0032-5910/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2006.01.013
relevant experimental data needed for model validation and refinement [3]. Moreover, many of the phenomenological and Computational Fluid Dynamic (CFD) models require empirical inputs, and their quality depends on the availability and accuracy of the measurement techniques and data. Hence, to properly understand and quantify the solids flow inside risers, it is first necessary to map the solids flow field inside a riser. Almost all the experimental techniques used to characterize CFB systems are intrusive (probe techniques), with measured variables having appreciable errors in large scale, high mass flux systems [1,4]. Moreover, CFB systems are opaque due to high solids mass fluxes and holdups, and, hence, one cannot “see” into the risers. Therefore, commonly used, sophisticated and nonintrusive, optical techniques such as Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV) cannot be used for investigation of solids flow and mixing in such opaque systems. At best, these techniques provide some Eulerian measurements, in a very local region of the riser close to the outside wall. The solids flow structure in CFB risers is inherently complex. Risers exhibit axial solids holdup distribution, with a certain degree of densification at the bottom of the column where the solids are introduced from the downcomer. The solids holdup decreases along the riser as the solids are accelerated by the high velocity gas stream [5,6]. Provided the riser is long enough, fully developed flow conditions are reached beyond a certain height,
Table 1 Sources of experimental data for solids velocity in gas–solid risers Reference
Measurement technique
Invasive techniques Bader et al. [7] Pitot tube Fiedler et al. [33] Harris et al. [68] Hartge et al. [69]
CCD based spatial filter Pitot tube/isokinetic probe Optical fiber probe
Herbert et al. [70] Optical fiber probe Optical fiber probe Optical fiber probe Optical fiber probe/ dynamic pressure Extraction probe
Miller and Gidaspow [30] Parssinen and Zhu Optical fiber probe [73] Wang et al. [74] Particle dynamic anlyser (phase/Doppler) Zhou et al. [75] Optical fiber probe
Non-invasive techniques Cody et al. [76] Acoustic shot noise (ASN) excitation Donsi and Osseo Laser Doppler [77] anemometer Godfroy et al. [11] Radioactive particle tracking Li and Tomita Photographic imaging [78] technique
Solids material/ diameter
30.5 × 12.2, abrupt exit 40 × 15.6, abrupt 14 × 5.1, abrupt exit
FCC, 76μm Sand, 120μm FCC, 60μm
40 × 8.4, abrupt exit
FCC, CFBC ash; 85, 120μm 41 × 8.5, abrupt exit FCC, glass beads; 42–300μm 5 × 2.79, smooth exit FCC, 60μm 5 × 2.79, smooth exit FCC, 60μm 7.5 × 10, – FCC, 54μm 7.5 × 6.58, smooth FCC, 75μm exit 7.6 × 10, smooth exit FCC, 67μm 22.2 × 22.2 × 300 Sand, 530μm cm3, elbow exit 14.6 × 14.6 × 914cm3, Sand, 213μm abrupt exit
Operating conditions
Measurement region
Measured solids velocity
Comments
3.7; 98
H = 4, 9.1 m
4–6; 28 2.6, 3; 26–52
H = 1.7, 10.7m H = 4.4m
Mean radial profile of axial velocity Particle velocity distribution Mean radial profile of ax. vel
Core-annulus flow structure with parabolic profile Two phase flow Wavy annular structure
3.8–5.4; 27–70
H = 0.9–4.7 m
Two phase flow
≤13; ≤250
H = 4, 4.2 m
1.17, 1.29; 11.7, 11.25 H = 0.36, 1.06, 1.63m 1.29; 10.7 H = 0.36. 1.06, 1.63 2.5; 62 H = 6.5m
Mean radial profile of axial velocity Mean radial profile of axial velocity Mean radial profile of ax. vel Mean radial profile (clusters) Instantaneous and mean radial
Core-annulus with the influence of particle diameter Annular flow with clusters Cluster velocity profiles Radial profiles
2.61–3.84; 12–32.8
H = 1.86–5.52m
Mean radial profile
Core-annulus flow structure
5.5, 8, 10; 100, 300, 400, 550 5.85; 25.4
H = 1.53–9.42m
S-shaped, linear, parabolic in 4 longitudinal sections Core-annulus flow structure
5.5, 7; 20, 40
H = 5.13, 6.2, 8.98m
Mean radial and averaged axial profiles 3 components of particle velocities, TKE Vertical and lateral profiles of particle vel.
H = 5–40 ft. (from feed Average axial velocities, RMS Granular temperature variation with Ug injection) acceleration (at the wall) H = 270cm
Mean radial profiles
H = 4–5m (above distributor) 20 cm regions at 0.7, 5.7, 11.7 m from feed
3-D Eulerian and Lagrangian Clusters with core-annulus, dispersion velocity field (of a large particle) coefficients variation Mean radial profile Uniform profiles (swirling and axial)
0.1 × 0.1 m2 at 3.5m from the distributor 0.1 × 0.1 × 0.1 m3
Downward velocity of particle swarms near the wall 3-D Eulerian and Lagrangian velocity field
Three flow forms — dilute, dense and swarm were found near the riser wall Presence of small vortex in both the beds
H = 4–6m 2.5 × 10− 4 mm3 volume at H = 1.5–6.2m H = 6, 14 m
Mean radial profile Radial mean and RMS fluctuating profiles Mean radial profile, PDD curves of particle velocity
Radial profile obeys 1/7 power law Core-annulus with radial profiles as parabolic and Boltzman function Dispersed particle and cluster two phase flow
Gs Ug (m s− 1) (kg m− 2 s− 1)
61–274 × –
FCC, 60μm
4 × 10 × 460 cm3, smooth exit 8.2 × 7, elbow exit
Glass, 94μm
Q = 233–1333kg s− 1 Gs = 152– 1247kg m− 2 s− 1 10–25; 50–350
Sand, 150μm
4; 23–75
Polyethylene, 3.2 mm, 946kg m− 3 Alumina, 75μm
9–25; O (0.01)
8 × 12, elbow exit
Rhodes et al. [79] High speed video camera 30.5 × 6.6
3–5; 2–80 Ug = 0.972 m s− 1 Q = 0.121kg s− 1
Wang et al. [80] Wei et al. [81]
Positron Emission 10 × 10 × 10cm3 Glass, 700μm Particle Tracking (PEPT) (interconnected fluidized beds) LDV 14 × 10.4, abrupt exit FCC, 36μm LDV 18.6 × 8, abrupt exit FCC, 54μm
Zhang et al. [82]
LDV
2.7–3.7; 29.7–44
Stellema [10]
41.8 × 18, abrupt
FCC, 77μm
3.49–4.78; 2.6–78.3 2.3–6.2; 18–200
H = 1.19–2.24m
Core-annulus flow structure
Turbulent profile with no downflow
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Horio et al. [71] Ishii et al. [16] Qian and Li [72]
Riser geometry (Dia × height, cm × m)
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corresponding to a solids holdup which is approximately invariant with height. Some of the early studies provided some experimental evidence that the riser flow structure consists of two characteristic regions: a dilute gas–solid suspension preferentially traveling upward in the center (core) and a dense phase of particle clusters, or strands, moving downward along the wall (annulus) (e.g. [7–9]). Such an annulus-core structure is usually assumed by those that model the riser reactor. Thus it is important to quantify solids distribution, velocity and mixing in the riser. Table 1 lists the sources of experimental data on solids velocity in gas–solid risers. The experimental techniques employed are invasive and non-invasive. Invasive methods are optical fiber probes, extraction probes, pitot tubes, isokinetic probes, and spatial filter processes. The advantages of using such probes are the ease of use at industrially relevant high flux conditions. However, the disadvantages, apart from intrusiveness, are: a) complicated calibration procedure, b) need for manual probe positioning and, c) fouling effects due to the ports on the walls. Moreover, only point measurements are obtained, and thus only the mean radial profile of axial velocity can be derived. The non-invasive methods are either based on optical techniques such as PIV, LDV, and high-speed cameras, on electrical and magnetic field measurements and on the use of radioisotopes, such as the Positron Emission Particle Tracking (PEPT) employed by Stellema [10], and the gamma emitting Radioactive Particle Tracking (RPT) used by Godfroy et al. [11]. The RPT technique developed by Larachi et al. [12] and applied by Godfroy et al. [11] in a CFB riser is similar to that of previous researchers [13–15] who used the RPT technique in fluidized beds. In the open literature, the study of Godfroy et al. [11] is the only work that presents the particle trajectories in a CFB riser in a full 3-D field and gives particle velocities. They indicated that the solids velocity and solids dispersion coefficient in the longitudinal direction decrease with increasing solids circulation rates due to a decrease in the turbulent axial velocities. Annulus diameter increases with increasing solids circulation rate. However, there are a few shortcomings of their study: a) The radioactive tracer used is approximately 27 times larger in volume (dp = 500 μm) than the solids used, which had mean particle size of dp = 150μm. Due to higher inertia of the tracer particle, the results represent the motion of a large particle among the smaller solids; this large particle has smaller fluctuating velocity components; b) The data acquisition frequency used by Godfroy et al. [11] was 100 Hz, which might not provide a good temporal resolution; c) It is difficult to validate a CFD or mechanistic model for the velocity profiles using the results of Godfroy et al. [11] because there is no reliable model to predict the behavior of a large tracer particle surrounded by smaller particles. Table 1 reveals that no experimental study provides all the information on solids velocity field that one requires for CFD model validation. Most of the studies either provide only the time-averaged velocity profiles at few axial locations, or at best provide 2-D velocity components in 3-D columns. None of the experimental studies report turbulence stresses, turbulent kinetic energy (granular temperature), diffusivity (axial, radial), return length distributions, circulation time distributions. All these flow and mixing parameters are required to understand the mecha-
nism of mixing (e.g. lateral segregation) and its variation with the operating parameters. Several experimental methods of characterizing the solids concentration distribution in a cross-section of the riser are listed in Table 2. The key observations regarding the experimental results of each researcher are also presented in Table 2. Strong radial suspension density gradients have been experimentally found and reported, with a maximum at the wall and a minimum at the center, which agree well with the core-annulus approximate description of the solids flow field. A critical examination of the experimental results for radial solids concentration distribution suggests that neither the core-annular theory [9] nor the clustering approach [16] alone can fully describe the riser dynamics. For example, instantaneous data indicate intermittent passage of solids clusters, while time-averaged data, obtained at several radial locations, suggest core-annulus flow structure. It is evident that both phenomena coexist and that a rigorous interpretation should take into consideration both clusters and core-annulus flow. Tomography proved to be a valuable tool for determining the solids concentration distribution non-invasively and was used by several researchers, as indicated in Table 2. In contrast to electrical capacitance tomography (ECT) and X-ray tomography, γ-ray tomography, with proper source shielding, can be used in dense flows, but the weight of the experimental setup reduces the attainable temporal resolution and restricts its applicability to selected positions along the riser length. Martin et al. [17] and Azzi et al. [18] are the only studies that presented 2-D concentration maps using γ-ray tomography in CFB risers. However, both studies used relatively few projections (27 and 21 projections, respectively), which result in a coarse reconstruction. The main improvement in this work is the use of a large number of projections, which improves the spatial resolution. The motivation for this study was provided by the availability of specialized gamma ray based techniques in our Chemical Reaction Engineering Laboratory (CREL) and the need of the community for improved and more detailed data base for solids flow in risers. We utilized the Computer Automated Radioactive Particle Tracking (CARPT) technique [19,20] to obtain the complete Lagrangian description of solids flow in the riser including ensemble average and statistical properties of the flows. Gamma ray computed tomography (CT) [21,22] is used to obtain the solids holdup distribution in cross-section of the riser. The objective was to generate the data base for an improved phenomenological model of the riser to be coupled with the appropriate kinetic studies and to provide data for CFB models of the riser that include novel turbulence closures. Our effort was part of the work conducted by the Multiphase Fluid Dynamics Research Consortium (MFDRC) funded by the Department of Energy (DOE), Office of Industrial Technology (OIT). 2. Experimental setup The gas–solid CFB shown in Fig. 1a was used. The total height of the glass riser is 26ft. (7.9 m) and the internal diameter is 6in. (15.2 cm). The solids are soft, approximately spherical, glass beads with a mean diameter (dp) of 150 μm and particle
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Table 2 Sources of experimental data for solids concentration in gas–solid risers Reference
Measurement technique
Riser Solids geometrya material/ (Dia × height, diameter cm × m) 14 × 5.1, abrupt exit 40 × 8.4, abrupt exit
Herbert et al. [70]
Pitot tube/ isokinetic probe Capacitance probes/optic fiber probe Optical fiber probe
41 × 8.5, abrupt exit
Horio et al. [71] Issangya et al. [83,65]
Optical fiber probe Optical fiber probe
5 × 2.79, smooth exit 7.6 × 6.1, smooth exit
Kato et al. Optical [84] fiber probe Parssinen and Zhu Optical [85] fiber probe Schlichthaerle and Optical probe, Werther [61] γ-ray densitometry Schuurmans [86] γ-ray absorption Tanner et al. [87] Optical fiber probe Wang et al. [80] Optical density sensor Wei et al. [81] Optical fiber probe Xu et al. [63] Optical probe
Invasive techniques Harris et al. [68] Hartge et al. [69]
Operating conditions Gs Ug (m s− 1) (kg m− 2 s− 1)
Measurement regionb
Measured parameters
Comments
Mean radial profile Mean radial and axial profiles
Wavy annular structure
Core-annulus with the influence of particle diameter Annular flow with clusters
FCC, 60μm
2.6, 3; 26–52
H = 4.4m
Sand, FCC, CFBC ash; 56, 85, 120 FCC, glass beads; 42–300μm FCC, 60μm
3.8–5.4; 27–100
H = 0.6–4.7m
≤13; ≤250
H = 4, 4.2m
Mean radial and axial profile
FCC, 70μm
1.17, 1.29; 11.7, 11.25 4–8; 14–425
H = 0.36, 1.06, 1.63m H = 0.97– 5.23m
15 × 3, abrupt exit 7.6 × 10, smooth exit
FCC, 74μm
2.4–4; 9–53
H = 70–230cm
FCC, 67μm
5.5, 8, 10; 100, 300, 400, 550
H = 1.53– 9.42m
40 × 15.6, abrupt exit
Sand, 200μm 3–5; 5–50
H = 0.29–1m
Mean radial profile Mean and standard deviation profile Mean radial profiles Mean radial and averaged axial profiles Mean radial and averaged axial
Cracking unit 41.1 × 8.5, smooth exit 14 × 10.4, abrupt exit 18.6 × 8, abrupt exit 9 × 11, elbow exit
–
–
–
Glass beads, 110μm FCC, 36μm
2.5, 4.5, 6.5; 30, 79, 107 2.6, 3; 26–52
–
FCC, 54μm
3.8–5.4; 27–100
FCC, 54μm
0.11–3.15; 0–65
2.5 × 10− 4 H = 1.5–6.2m H = 3m
H = 4–6m
Zhang et al. [82]
Optical density probe
41.8 × 18, abrupt exit
FCC, 77μm
2.7–3.7; 29.7–44
H = 6, 14m
Zhang et al. [62]
Optical probe
FCC, HGB, ALO
1–4; 5–300
H = 1.27, 4.27, 3.77m
Zhu et al. [88]
Optical probe
3.2, 9, 30 × 2.8, 10, 12, abrupt exit 7.6 × 3, –
Non-invasive techniques Azzi et al. [18] γ-ray densitometry Berker and Tulig γ-ray camera [89] Du and Fan [90], ECT Du et al. [91] Grassler and X-ray tomography Wirth [67] Jaworski and ECT Dyakowski [92] Li and Tomita [78] Photographic imaging technique Malcus et al. [55]
ECT
Two phase flow
Core-annulus structure in ‘dense suspension’ and FF regimes Core-annulus in turbulent and FF Constant in the center and decreasing near the wall with height Presence of local acceleration effects
Mean radial profile Mean radial and averaged axial Mean radial profiles Radial mean profiles Radial profiles of mean and fluctuations Mean radial profile, PDD curves of conc. Mean radial profiles and wave forms in 3 regimes
Near parabolic profile
Radial profile independent of Ug, Gs, if CS averaged voidage is constant Ring internals result in uniform profiles
Gas and slip velocity profiles estimated Three kinds of profiles: dense, ring and aggregative Similar profile given Boltzman function Two distinctive regions of lateral profiles Dispersed particle and cluster two phase flow
Sand, 169μm 6, 8; 71, 214
H = 1.61–2m
Mean radial and axial profiles
19 × 11.7; 70 × – 17.8 × –
FCC, 75μm
6.1, 21; 150, 1080
H = 3.1–4.8m
Mean radial profile 2-D concentration map
FCC, –
9.4, 15.3; 122, 310
H = 5.34m
Mean radial profile k–ε turbulence model
10 × 6.3, abrupt exit 19 × 15
Glass; FCC 0.97–3.4; 1.32–35.7 240; 60μm Glass, 60μm 2.7, 5.6; 195, 415
Instantaneous 3D profiles 2-D holdup maps
3m vertical channel 8 × 12, elbow exit
Polyamide, 1–5; Q ≤ 900kg s− 1 3 3 × 3 × 1mm Polyethylene, 9–25; O (0.01) 3.2mm, 946kg m− 3 FCC, 89μm 3.7–4.7; 148–302
H = 0.4–0.6m 4.4–6.3m H = 4.4, 6.8, 11.6m –
14 × 7, smooth exit
Choking flow structures Core-annulus structure
Instantaneous Train of plugs with 2D profiles downflow at the wall Mean radial profile Symmetric profiles (swirling and axial)
20 cm regions at 0.7, 5.7, 11.7m from feed H = 1.55, 2.1 m Radial, PDD, standard deviation profiles
Core-annulus structure
(continued on next page)
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Table 2 (continued) Reference
Solids Riser material/ geometrya (Dia × height, diameter cm × m)
Measurement technique
Non-invasive techniques Martin et al. [17] γ-ray tomography 19 × 11.7 Miller and Gidaspow [30] Rhodes et al. [64]
X-ray densitometry ECT
Saxton and Worley [93] Weinstein et al. [94]
γ-ray absorption X-ray absorption
7.5 × 6.58, smooth exit 9 × 7.2, smooth exit – 15.2 × 8.5, abrupt exit
62 μm, 1560kg m− 3 FCC, 75μm
Operating conditions Gs Ug (m s− 1) (kg m− 2 s− 1)
4.2, 6.3; 114, 308, 202 2.61–3.84; 12–32.8
Measurement regionb
Measured parameters
H = 4m
Mean radial 2-D concentration maps, and axial profiles core-annulus flow Mean radial profile Core-annulus flow structure
H = 1.86–5.52m
Sand, 100μm 4; 150
H = 2.8–4.3 m
–
–
–
HFZ-33, 59 um
1.1–5; 12–154
H = 1.64m
Contours of constant conc. Mean radial profiles Mean radial profiles
Comments
Core-annulus, annulus width decreases height Dense wall, dilute core 3rd order polynomial radial profile
Ug — gas superficial velocity (m s− 1). Gs — overall solids mass flux (kg m− 2 s− 1). Q — overall solids flow rate (kg s− 1). ‘–’ indicates data not reported. a Risers with circular cross-section are defined by diameter × height, while the ones with rectangular are defined by length × width × height; 90° exits are termed as elbow exits, risers with increased diameter at the exit (disengagement section) are termed as smooth exits and others are termed as abrupt exits. No attempt is made to quantify the smoothness of the riser exit. b H — height from the distributor, where measurements are reported.
density (ρs) of 2550 kg m− 3, which fall into Group B of Geldart's classification. The secondary fluid (air) enters the system at the base of the riser, and flow is regulated by a standard air flow meter. The two phase gas–solid suspension in the riser exits into an axi-symmetric disengagement section. Air exits from the disengagement section to a cyclone, connected to the hopper at its bottom. Air from the top of the cyclone exits into a dust collector. The hopper is connected by a flexible pipe to the return leg (downcomer), and the solids return to the base of the riser
through the downcomer. The glass downcomer is 18ft. tall with a 2in. (5.1 cm) internal diameter. The base of the downcomer is connected to the base of the riser with a 45° angled standpipe of 2in. (5.1 cm) diameter, made of glass. To regulate the flow of solids into the riser, a mechanical ball valve was placed between the base of the downcomer and the 45° standpipe. The experimental conditions included three different superficial gas velocities varying from 3.2 to 4.5 m s− 1 and two different solids loading of 140 and 190lbs at ambient
Fig. 1. a) Schematic of CFB setup; b) Photograph of the zone of investigation for CARPT.
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pressure and temperature. This spans from fast fluidization (FF) to dilute phase transport (DPT) operating regimes. The regimes of operation were obtained from the flow regime maps of Bi and Grace [23]. To determine the regime, one needs along with the superficial gas velocity in the riser, which is directly measured, the value of the overall solids mass flux. Our earlier published work [24] reports the method and the data obtained for the overall solids mass flux at each gas velocity. 2.1. Computer Automated Radioactive Particle Tracking (CARPT) Computer Automated Radioactive Particle Tracking (CARPT) is an advanced non-invasive technique for measuring solids (in gas–solid, liquid–solid and gas–solid–liquid systems) or liquid (in gas–liquid systems) flow field and turbulent parameters (e.g. [12,14,19,20,25]). In CARPT we track the motion of a single particle as a marker of the solids phase, if the flow field of solids needs to be measured (e.g. gas–solid riser), or of a neutrally buoyant particle, if the flow field of the liquid phase needs to be measured (e.g. bubble column). Further details regarding the CARPT technique and its ability to provide time-averaged velocities (3-D solids flow field) and turbulence parameters (kinetic energy, shear stress, turbulent eddy diffusivities) can be found elsewhere [12,15,19,25]. For the gas–solid riser study, the challenge is to implement CARPT on a pilot-plant scale, which has never been accomplished before. The scale of the system and the continuous nature of the solids flow, with high velocities and heavy attrition, gave rise to many implementation issues. These include: a) selecting the radioactive particle, b) devising a method for the detector calibration, c) selecting data sampling frequency, d) best positioning of the detectors, e) selecting a safe procedure for introduction and recovery of radioactive tracer, f) post-processing method for the data. A single radioactive particle (46Sc) was used as a tracer. It was tailored by coating a layer of polymer (Parylene N) on the Scandium particle to achieve the same density as the solids used (glass beads) and the same diameter (150 μm) as the mean particle size of glass beads. By tracking this single radioactive tracer at a data acquisition frequency of 200Hz, instantaneous solids velocity field in a developed flow section was measured. A total of 20NaI(Tl) scintillation detectors were positioned around the column and Fig. 1b shows the photograph of such configuration. 18 detectors were positioned close to the column wall (yet far enough to ensure that the detectors do not get saturated) with 3 detectors at each level to determine the position of the tracer particle. This was shown by Roy et al. [26] to lead to good sensitivity and resolution. The zone of interrogation of the detectors was 72 cm long. Two ‘sentry’ detectors were fixed at the top and bottom levels of the zone to determine precisely the instants of entry and exit of the tracer particle into the zone. Prior to tracking the tracer particle, the detectors were calibrated by placing the tracer particle manually, manipulating it through the column wall, at several hundred known locations. The average error in tracer position reconstruction found at any flow condition was less than 5mm. The actual CARPT results are
103
interpreted only with in the central 48 cm long zone, where the resolution is even better. 2.2. Computed Tomography (CT) A gamma ray computed tomography (CT) for probing phase volume fractions in multiphase reactors had been developed and discussed by Kumar et al. [21,22]. For this work, the existing setup was modified and mounted on the gas–solid riser system for studying the time-averaged solids volume fraction distribution. For the 6 in. riser column, an array of 7 detectors was placed to span the fan beam of the source, which yields a total of 17,500 projections (radiation attenuation measurements). This results in a significant improvement in the spatial resolution over the previous reported studies of γ-ray tomography on risers of Martin et al. [17] and Azzi et al. [18]. For image reconstruction, the iterative alternating-minimization (AM) algorithm [27] was used, the implementation of which for the CREL scanner has been discussed by Bhusarapu et al. [28]. The average theoretical spatial resolution for the CREL scanner is better than 2 mm. 3. Results and discussion The solids velocity field obtained from CARPT experiments is discussed first. The solids holdup from CT experiments is shown later. Comparative and symbiotic analysis of these two results is used to understand the complex flow structure of the solids in two different flow regimes; Fast Fluidization (FF) and Dilute Phase Transport (DPT). 3.1. Solids velocity field 3.1.1. Instantaneous positions and velocity calculations The knowledge of the tracer particle trajectory provides insight into the solids dispersion and mixing. Fig. 2 shows the instantaneous particle position trace during a single passage through the riser visualized in three different planes — x–z, y–z and x–y planes. As the tracer particle moves around the CFB loop, it periodically resides in the zone of interrogation in the riser (Fig. 1). During each passage through the riser, completely independent tracer particle trajectories are obtained. Two such trajectories were picked for understanding in Fig. 2. Clearly in some instances the tracer particle passes through the section straight, while in others it undergoes internal recirculation in the section. In both cases, the tracer particle takes a tortuous path undergoing acceleration at times and deceleration at other times. The tracer positions when the axial velocity is negative (Fig. 2b) are indicated in red. It can be observed that the tracer has acquired negative axial velocity starting near the center (core region) and maintains a negative axial velocity as it moves towards the wall (annulus region). So during this episode the tracer particle falls both with in the core as well as in the annular region. Analyzing many such trajectories shows that few times the tracer particle passed through the zone of interrogation straight with very little or no backmixing, while many times it underwent internal recirculation with the tracer falling down. Also, it was observed that the span of the tracer residence time
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(b) 37.4
37.4
37.4
36.7
36.7
36.7
36.7
36.1
36.1
36.1
36.1
35.4
35.4
35.4
35.4
34.7
34.7
34.7
34.7
34.1
34.1
34.1
34.1
33.5
33.5
33.5
33.5
32.8
32.8
Z/D
37.4
Z/D
Z/D
(a)
32.8
32.8
-1 -.5 0 .5 1
-1 -.5 0 .5 1
-1 -.5 0 .5 1
-1 -.5 0 .5 1
x/R
y/R
x/R
y/R
No. of Occurences = 55 (Positions) Residence time = 0.275 sec
No.of Occurrences = 207 (positions) Residence Time = 1.035 sec
Fig. 2. Examples of traces of particle instantaneous positions in the x–z, y–z and x–y planes during two different passages through the CARPT section: a) tracer passed through the section without recirculation; b) tracer underwent internal recirculation inside the section. The operating conditions were in the Fast Fluidization regime at Uriser = 3.2 m s− 1 and Gs = 26.6kg m− 2 s− 1. g
within the zone of interrogation varied widely from 0.1 to 100s. Such large residence time variation (without stagnation) explains why the solids mixing in the axial direction or the axial dispersion coefficients are very large in riser reactors. The accuracy of tracer position reconstruction is influenced by the way detectors are packed around the column [12,26]. Since near the lowest and highest axial levels in the CARPT section there will be fewer number of detectors, the position reconstruction near these axial levels is bound to be worse compared to the section in between. This can indeed be observed from the cluttering of the tracer positions (Fig. 2) near the axial planes of z / D = 32.8 and 37.4. Hence, to reduce the position error propagation to velocity calculations, the zone of interrogation was reduced to the section between the axial planes of z / D = 33.5–36.7. This translates to an interrogation zone of 48 cm between the axial heights of z = 5.1–5.6 m. All the subsequent CARPT results reported are within this zone of interrogation. Fig. 3 shows the evolution of the tracer axial and radial position, with time. Fig. 3b shows the radial position time series, which indicates that the solids motion in the horizontal plane is
principally random (dispersive). However, the actual mechanism of the lateral movement of the solids can be understood only once the radial mixing parameters are evaluated. It can also be noted from Fig. 3b that the particle occurrences near the wall are more numerous than near the center or core region. The tracer particle axial position trace in time shown in Fig. 3a indicates extensive internal recirculation. Also, the axial flow seems like a typical wall bounded flow, although there is no physical wall. The same result of wall-boundedness in the axial direction can also be reached by looking at the auto-correlation function of the Lagrangian velocity. Also, in the axial direction, the motion seems to be ultimately directed upward with the particle tumbling up and down during a single passage through the riser section. Hence, the large scale internal recirculation, superimposed with the fine scale fluctuations contributes to the axial backmixing. A time derivative of the tracer particle position yields the instantaneous Lagrangian velocity of the tracer. Now, by invoking ergodicity, we convert the velocity trace of the single tracer particle to the time-averaged Eulerian velocity field that is representative of the entire ensemble of particles. To perform this
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Tracer passage
(a) 36.7 36.4
Z/D
35.7
35.1
34.4
33.5
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
Time (sec)
(b) 1.0 0.93
r/R
0.8
0.53
0.27 0 1419
1420
1421
1422
1423
1424
1425
1426
Time (sec) Fig. 3. Tracer position with time visualized for a small period a) axial b) radial positions. The operating conditions were in the Fast Fluidization regime at Uriser = g 3.2m s− 1 and Gs = 26.6kg m− 2 s− 1.
calculation, we assume an imaginary grid in the 3D space in the riser section. For any two successive tracer positions, the velocity is calculated by time-differencing and assigned to the compartments of the grid, where the velocity vector falls. Thus, one can build a histogram (i.e. probability density function (PDF)) of the instantaneous velocities in each compartment of the grid, given that the tracer particle visits these compartments a sufficient number of times. Hence, by claiming that the system is ergodic and stationary, one asserts that the moments of the histogram, calculated from the ensemble of observations for long enough time, are the same as those that would be obtained by analysis of time series of solids particle velocity at the given point (such as obtainable by a probe). Post facto validation of the ergodicity of the system was performed by checking for occurrence independence of the velocity and turbulence profiles (not shown for brevity). Details on occurrence independence can be found in Bhusarapu [29]. To obtain the time-averaged Eulerian velocity field, one needs to compartmentalize the section of the riser and count the velocity statistics. Three different compartment sizes as stated in Table 3 ranging from coarse to fine grid were considered to obtain mesh independent profiles. It was observed that the velocity and turbulent profiles from Mesh 2 and 1 are approximately the same (not shown for brevity), indicating that the
velocity and turbulent quantities from Mesh 1 are grid independent. Further details on mesh independence can be found in Bhusarapu [29]. Note that in Mesh 3 volumes of the cells are three times those of cells in Mesh 1 and a similar proportional increase in the number of particle occurrences in each compartment. Hence, for further analysis, Mesh 1 was employed, where the nominal grid size was Δr = 0.95cm, Δz = 2 cm, and Δθ was varied so that all the cells have equal volume of about 5.7 cm3. 3.1.2. FF versus DPT regimes Earlier studies on riser flow established that in a timeaveraged sense, solids flow upwards in the center or core region and downward near the wall, or annulus region, at conditions characteristic of the fast fluidized and heterogeneous dilute flow regimes (e.g. [7,23,30,31,73]). The typical characteristics of the solids flow in the fast fluidized and dilute phase regimes were Table 3 Details of the three different mesh evaluated to check for mesh independence
Mesh 1 Mesh 2 Mesh 3
Nr
Nθ (max)
Nz
Total grids
% of volume
8 7 5
15 13 9
24 24 20
1536 1176 500
0.065 0.085 0.2
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
r / R = 0.063
r / R = 0.438
= 407
n
0.1
0.1 σv = 382.66
0.18 σv = 169.41
σv = 340.11
0.09
0 0
5
0.18
-5
0
= 336
0.13
σv = 415.86
0
100
0
20
0
50
0.21 n
0 -100
5
0.17 n
= 2208
0.05
0.05
-5
Probability
n
= 384
0
= 469
n
0.16
σv = 349.41
0.09
0.1
0.04
0.05
= 960
0.06
0
0 -5
0
5
0.17 0.13
-5
0
= 463
0.28 n
0.13
σv = 375.64
0.09
0.09
0.04
0.05
0 -20
5
0.18 n
Probability
0.27
= 447
n = 2186
σv = 347.15
Z / D = 33.7
Probability
n
0.12
r / R = 0.938
0.16
Z / D = 36
0.14
Z / D = 35
106
0.18 σv = 185.35
0.09
0
0 -5
0
5
-5
0
5
0 -50
v/
Fig. 4. Spatial variation of the solids axial velocity histograms illustrated at three different axial and radial locations for the FF regime at Ug = 3.2m s− 1 and Gs = 26.6kg m− 2 s− 1.
summarized by Bi and Grace [23,32]. In the fast fluidization regime, axial solids segregation exists, resulting in a dense lower region and dilute upper region. Particle streamers form close to the riser wall, leading to a core-annulus structure in the upper dilute region [32]. While in the heterogeneous dilute phase flow, average solids flux in the annular region is downward with little axial segregation of particles. In this regime too, particles streamers form close to riser wall leading to a core-annulus structure [32]. However, there are only few studies (with intrusive techniques) that presented the velocity histograms [33] or turbulent stresses [34–36]. There are no studies presenting the full velocity field that show the components of turbulent stresses, turbulent kinetic energy, eddy diffusivities, solids residence time distribution and the solids holdup maps. In this section, local velocity histograms (PDFs), time-averaged velocity vector plots and turbulent stress profiles are compared in the two operating regimes to quantify the local solids flow structure. 3.1.3. Velocity PDFs One acquires PDFs of the local velocity components in each of the compartments of the grid as discussed earlier. Fig. 4 shows the PDFs of the axial solids velocity at three different radial positions (r / R = 0.063, 0.438, 0.938) and at three different axial planes (Z / D = 33.7, 35, 36; z = 5.12, 5.32, 5.47m) at a
particular angular position. The operating conditions for this experiment are in the FF regime with Ugriser = 3.2 m s− 1 and Gs = 26.6 kg m− 2 s− 1. Also indicated in each of the PDF plots are the number of particle occurrences in the given compartment, the mean and standard deviation of the axial velocity. Fig. 4 leads to the following conclusions: a) large radial gradients in the axial solids velocity; b) ensemble averaged axial slip velocity (assuming plug flow for gas phase) in the center or core region is much larger than the particle terminal velocity, while the ensemble average axial velocity near the wall is negative (downfall), which is an order of magnitude higher than the minimum fluidization velocity; c) very small axial variations within the zone of interrogation; d) two prominent axial velocities at the centerline — one negative and one positive, with the ensemble average being positive. Similar conclusions were drawn from the axial velocity PDFs at another operating condition in the FF regime (Ugriser = 3.2 m s− 1; Gs = 30.2kg m− 2 s− 1). One possible explanation for the appearance of negative velocities at the centerline in the FF regime (Fig. 4), which are absent in the DPT regime (Fig. 5), could be due to the enhanced formation of clusters, which tend to fall down. Based on the same argument, the prominent negative solids velocity at the center can be associated with the cluster terminal velocity and an approximate
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
r / R = 0.063
σv = 378.3
Probability
0.14
0 -1
0
1
2
σv = 158.6
0.28
0.06
0 -2
-1
0
1
2
-10
0.3
n = 143
0.21
-5
0
5
10
n = 678
σv = 151.6
σv = 158.5
0.14
0.15
0.08 0.07 0 -2
0.23
Probability
σv = 202.1
0.12
n = 131
0.15
n = 1427
Z / D = 36
n = 168
n = 96
0.05
0 -2
r / R = 0.938 0.42
Z / D = 35
0.1
r / R = 0.438 0.18
0 0
1
2
-1
n = 178
0.16
n
σv = 145.6
σv = 152.7
0.11
0 -2
-2
0
1
0.31
= 123
0
1
2
0 -2
-10 0 10
50
n = 6373
0.16
0.08
-1
0 -5 0
2
Z / D = 33.7
Probability
0.16
107
-1
0
1
2
0 -800
0
800
v/
Fig. 5. Spatial variation of the solids axial velocity histograms illustrated at three different axial and radial locations in the DPT regime at Ug = 4.5m s− 1; Gs = 36.8kg m− 2 s− 1.
cluster size can be estimated. Also, the prominent positive velocities at the centerline can be interpreted to be representative of the tracer particle which passed through the riser straight up with very little backflow. This bimodal PDF in the FF regime seems to gradually change to a single modal one as one moves towards the wall. Hence, the existence of clustering phenomenon, inferred from the negative axial velocities, seems to be prevalent throughout the riser cross-section (more likely near the wall) in the FF regime. In the DPT regime, with the operating conditions at Ugriser = 4.5 m s− 1 and Gs = 36.8 kg m− 2 s− 1, Fig. 5 shows the spatial variation of axial solids velocity PDFs at the same compartments. In contrast to the FF regime, PDFs at the centerline have a single peak with no negative velocities. Also, the ensemble average solids velocity is positive near the wall even though one can note some negative instantaneous velocities. Hence, in the DPT regime no clustering occurs in the core. However, the radial particle exchange is still pronounced as suggested by the nonhomogeneous particle segregation (interpreted from the number of occurrences) and the radial velocity profiles. Similar conclusions were also drawn with regard to the absence of clustering in the central core from the axial velocity PDFs in the DPT regime at other operating conditions. Note that all the flow conditions in DPT regime are actually in the heterogeneous or core-annular dilute flow regime.
Each of the axial velocity PDFs shown in Figs. 4 and 5 was obtained based on the statistics from a single compartment at a particular angular position. Now one can also collect the statistics from every angular compartment at each radial location to construct axial velocity PDFs. Comparing the velocity PDFs from a single compartment to that obtained from the perimeter (not shown for brevity), we noticed that the functions do not change much (less than 7%) with the increase in the statistics. Such small variation indeed reflects axisymmetric flow. Further details can be found in Bhusarapu [29]. The variation of solids radial velocity PDFs was found to be similar in both flow regimes, in FF and DPT. Although the ensemble averaged values reveal that the velocity component is directed towards the wall, negative instantaneous radial velocities were observed. Also, the mean radial velocities are an order of magnitude smaller than the mean axial velocities. However, the standard deviation of the radial velocities was much higher (one order of magnitude) than their corresponding means. This result was established earlier using LDV measurements in a very dilute riser [35]. 3.1.4. FF versus DPT — velocity vector plots In this section, velocity vector plots representing the timeaveraged solids velocities are presented to check for axisymmetry in the solids flow pattern in the 3D risers in the two
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regimes — FF and DPT. Both the vertical and horizontal plane projections are given to interpret all the three components of the velocity vectors. The vertical planes are sliced through the center of the column at four different angles — 0–180°, 45– 225°, 135–315°, 90–270°, while the horizontal cross-sectional views are obtained at two different axial elevations. The display of the vector plots is accomplished using MATLAB. Fig. 6 displays the velocity vectors for the flow condition in the FF regime at Ugriser = 3.2 m s− 1 and Gs = 26.6 kg m− 2 s− 1. As evident from these figures, the flow pattern seems to
be axi-symmetric. In addition, Fig. 6a indicates that the solids flow upwards in the center and downwards near the wall in the FF regime, an observation frequently reported (e.g. [7,23,30,31,73]). However, in the DPT regime, the flow near the wall is also upwards (Fig. 7). This difference in the flow pattern (compared to the FF regime) could be due to the decrease in the solids cross-sectional concentration, resulting in the decrease of the clustering effect. With the decreased cluster formation, the downflow of solids is also reduced. Such upward flow near the wall was also observed by few
Fig. 6. Visualization of the ensemble averaged solids velocity vectors in the zone of interrogation in a) r–z plane at different angles; b) r–θ plane at different axial heights. The operating conditions are in FF regime at Ug = 3.2m s− 1; Gs = 26.6kg m− 2 s− 1.
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
Axial velocity (cm/s)
600 FF regime
400 DPT regime
200 0 -200
0
0.2
0.4
0.6
0.8
1
60 40 20 0
0
0.2
0.4
0.6
0.8
-20 1
Radial velocity (cm/s)
Nondimensional radius ( ξ )
Azimuthal velocity (cm/s)
Nondimensional radius ( ξ ) 15
5 0 -5
-15
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ ) Fig. 7. Azimuthally and axially averaged ensemble-averaged solids velocity components compared in two different regimes — FF (Uriser = 3.2m s− 1; g = 4.5m s− 1; Gs = 36.8kg m− 2 s− 1). Gs = 26.6kg m− 2 s− 1) and DPT (Uriser g
other researchers ([73,83]), but under very high solids flux conditions, termed as dense phase suspension by Grace et al. [37]. Note that the flow conditions investigated in this work are quite different from the dense phase suspension regime. The axial variation of the velocity is small (less than 11%) within the zone of interrogation in both the flow regimes (as seen in Fig. 6 for the FF regime). The radial and azimuthal components of the velocity are very small compared to the axial component indicating that the time-averaged flow pattern is basically representative of a close to fully developed flow within the zone. Similar observations were seen for other flow conditions investigated. However, fully developedness of the solids flow inferred from Fig. 6 cannot be taken in a strict sense, since the radial velocities are only relatively small and are numerically not equal to zero. The vector plots establish that even though the passage of individual solid particles through the zone of interrogation is tortuous (Figs. 2 and 3), the time-averaged velocity field is structured with a clear pattern (Fig. 6). Although, the local variations (instantaneous velocities) can never be reproduced by any number of experiments, the time-averaged developed velocity profiles are reproducible. The time-averaged solids velocity components in the two flow regimes — FF and DPT are compared in Fig. 7. In the plots of Fig. 7, the velocities are circumferentially and axially
109
averaged. In the FF regime, the axial solids velocity component exhibits negative values near the wall, while in the DPT regime, such negative axial solids velocities are not observed. An estimate of annulus boundary can be taken as the ‘cross over’ point of the time-averaged axial velocity. While such a definition of the annulus seem to suggest no annulus in the DPT regime, the axial solids velocity profiles in both the regimes seem roughly parabolic. Within the spatial resolution of the velocity reconstruction, the inversion point of the axial velocity profile (corresponding to the annulus thickness) in all the cases in the FF regime is found to be in the same compartment (with r / R = 0.81). Hence, the downflow of solids at the wall in the FF regime is expected to cause considerable backmixing of the solids phase. It can be observed that both the solids axial and radial components of the time-averaged velocity in the DPT regime are higher in magnitude compared to the values in the FF regime, while azimuthal profiles in both seem to be negligible and close to zero. This result once again confirms axi-symmteric flow pattern of the solids in the riser. Values that deviate from zero in the central part may be caused by the poor statistics in the region with fewer particle occurrences. The time-averaged radial velocity profile in both the regimes seems to be always positive (Fig. 7). Thus, positive timeaveraged radial velocities indicate that the flow is still not fully developed (in a strict sense) and that the solids in the core have a tendency to move radially outward. The core seems to feed the solids to the annulus even at these elevations. However, the instantaneous radial velocities (from radial velocity PDFs) do exhibit negative velocities. Hence, the radial velocity profiles suggests that the movement of solids from core to annulus seems to be governed by the time-averaged velocity profiles, while the movement of solids from annulus to core (if prevalent) is governed by the fluctuating velocity profiles in the fully developed zone. 3.1.5. FF versus DPT — turbulent stresses and kinetic energy CARPT technique provides turbulent stresses and kinetic energy in the entire three dimensional flow field [15,19]. It is known that turbulence is characterized by random fluctuations and statistical characterization of the flow parameters leads to important information about the flow [38,39]. The instantaneous flow information is usually obtained from higher order correlations of the fluctuation quantities that represent the turbulent interactions. Turbulent stress is one such interaction which represents the transport of momentum due to the turbulent velocity fluctuations. The main diagonal terms in a turbulent stress tensor contribute to the pressure at a point in the flow, while the non-diagonal terms are the tangential or shear stress components. The energy associated with the fluctuating quantities called the turbulent kinetic energy is the sum of the three normal stress components. Turbulence kinetic energy (per unit bulk density) in granular flows is also called granular temperature. Sinclair and Jackson [40] were the first to analyze fully developed riser flow using the kinetic theory of granular flow. The primary aim in this section is to present the detailed experimental study on the turbulent quantities required for the CFD model verification. Experimental data on turbulent
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S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
quantities is very limited and is available only for dilute, low flux riser flows. This data is usually obtained by imaging techniques such as PIV or LDV and/or by probes. Imaging techniques, as discussed earlier, have limitations that CARPT technique can overcome. Fig. 8 shows the comparison of the turbulent kinetic energy per unit bulk density in the two regimes. The turbulent kinetic energy can be scaled with a constant to obtain the granular temperature. A clear demarcation between a core and an annulus in the turbulent energies is observed in the FF regime (Fig. 8a). However, in the DPT regime, the turbulent kinetic energy is more uniform (Fig. 8b) in the radial direction, although it decreases near the wall. Very small axial variation of the turbulent kinetic energy is seen in both flow regimes. Fig. 9 shows the contours of the particle occurrences per unit volume in the FF and DPT regimes. With an assumption of ‘wellperfusedness’, or no stagnation in the zone of interrogation, one
can interpret the solids volume fraction to be proportional to the ratio of the particle occurrences (in a compartment) to the total number of occurrences. Similar interpretation of the particle occurrences was done in other multiphase systems [10,11,15,41]. In other words, the contours shown in Fig. 9 are those of the solids volume fraction, whose magnitude needs to be scaled appropriately. To do the scaling one needs an independent measurement (like tomography) of the solids concentration. Such analysis is done later while discussing the results from tomography. The solids concentration in Fig. 9a (FF regime) clearly shows a concentrated annulus layer near the wall and a dilute core in the center. One can interpret the annulus wall layer thickness based on these contours. This is another way of obtaining the annulus thickness, methods reported in the literature are based on the axial velocity and flux profile's ‘cross over’ points [42]. It can also be observed from Fig. 9 that there are some concentrated +
(a)
+ -
-
+ -
+
-
36.5
40
36.1
36 32
Z/D
35.5
28 24
34.8 20 16
34.2
12 33.5
-5
0
5
-1 -.5 0
X/R
.5
1
X/R
-1 -.5 0
.5 1
X/R
-1 -.5 0
.5
1
X/R
8 (m 2/s 2)
(b) 36.5
40
36.1
36 32
35.5
28 24
34.8 20 16
34.2
12 33.5 -1 -.5 0
.5
X/R
1
-1 -.5 0
.5
X/R
1
-1 -.5 0
X/R
.5 1
-1 -.5 0
.5
X/R
1
8 (m 2/s 2)
Fig. 8. Comparison of the contour plots of the turbulent kinetic energy per unit bulk density a) FF regime (Uriser = 3.2m s− 1; Gs = 30.2kg m− 2 s− 1) and, b) DPT g −1 −2 −1 (Uriser = 3.9m s ; G = 33.7kg m s ). g s
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
111 +
(a)
-
+ -
+ -
+
-
36.7
300
36.1
250
200
Z/D
35.5
150 34.8 100 34.2 50 33.5 -1 -.5 0
.5
1
-1 -.5 0
X/R
.5
-1 -.5 0
1
.5
1
-1 -.5 0
X/R
X/R
.5
0
1
X/R
(b) 36.7
3000
36.1
2500
2000
Z/D
35.5
1500 34.8 1000 34.2 500 33.5 -1 -.5 0
.5
X/R
1
-1 -.5 0
.5
1
X/R
-1 -.5 0
.5
X/R
1
-1 -.5 0
.5
1
0
X/R
Fig. 9. Comparison of the contour plots of the particle occurrences per unit volume a) FF regime (Uriser = 3.2m s− 1; Gs = 30.2kg m− 2 s− 1) and, b) DPT (Uriser = 3.9 m s− 1; g g Gs = 33.7kg m− 2 s− 1).
pockets of solids near the wall and a few in the core region. These concentrated pockets cannot be directly interpreted as ‘clusters’ considering that the lifetime of the clusters is very small and that these contours are derived from several particle trajectories observed over hours of experiment. If one makes an ergodic assumption (validated earlier) that observing several independent single particle trajectories is equivalent to observing all the trajectories of the ensemble of particles in the system, then the concentrated pockets can be interpreted as ‘clusters’. Hence, the message is that there is a definite probability of the ‘cluster’ formation in these regions of concentrated pockets. Thus, Fig. 9 a) and b) convey the message that the clustering phenomenon is significant near the wall region and can also occur in the core of the riser. In contrast, in the DPT regime, the solids concentration is more uniform (both radially and axially) and the intensity of clustering much less compared to that in the FF regime. Notably, the contours in both regimes seem to be nearly axi-symmetric. Based on the symmetry in most of these
observations, the 3D velocity data were azimuthally and axially averaged to obtain the one-dimensional variation of the velocity and turbulent fields along the radial direction. 3.1.6. FF versus DPT — radial variation of velocity and turbulent fields Further analysis is restricted to the discussion of the azimuthally, axially and time-averaged quantities of the velocity and turbulence profiles. All the quantities were axially averaged from Z / D = 33.5–36.7 (z = 5.1–5.6 m) and the error bars on each profile represent the range of values encountered for all z levels. In order to show generality in the comparison of FF and DPT regimes, the flow conditions presented in the radial profile plots are different from those compared in the contour plots (Figs. 8 and 9). The variation of radial profiles of the time-averaged velocity was discussed earlier with reference to Fig. 7. A substantial increase in the mean axial velocity was observed in the center of
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S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
the solids mass flux and/or superficial gas velocity under ‘dilute conditions’. A similar decreasing trend in the solids velocity fluctuations with the increase in solids holdup was observed by Benyahia et al. [95]. This finding also substantiates our comparison between the FF and DPT regimes. Note that increasing the solids mass flux at constant gas superficial velocity, or decreasing the gas superficial velocity at constant mass flux, increases the solids holdup (tomography results). Fig. 10 shows a decay of axial velocity fluctuations radially in both the FF and DPT regimes following the same trend as the mean values (minimum reached at the wall). The low variations of the axial solids velocity (fluctuation velocity being very close to the mean values) reveal the great agitation of the solids along the flow direction. The radial solids velocity fluctuation profile in both the FF and DPT regimes interestingly show a peak near r / R = 0.7 (Fig. 10). This radial position, according to the radial particle occurrence profile, corresponds to the transition from a flat solids holdup profile to a drastically increasing one. Hence, the peak in the radial solids velocity fluctuation profile corresponds to the transition from a lean core with nearly constant solids density to a dense zone with increasing solids density. All these results show the predominance of the fluctuations over the mean particle motions. In Fig. 11 the ratio of the axial to the radial solids velocity fluctuation profiles in the FF and DPT regimes are presented. As it can be seen, the axial solids velocity fluctuations are always greater than the radial ones but not by much. In the FF regime, the anisotropy is significant decaying slightly from 2.5 near the center to 1.5 near the annulus, while in the DPT regime the anisotropy is nearly uniform around 1.2. Thus, the dilute risers in the DPT regime tend towards isotropic turbulence. Note the clear distinction in the ratio values across the flow regimes. Hence, the conclusion is that fluctuating motion is principally directed along the main axis of the multiphase flow. There is experimental evidence that the particle turbulence in risers is not isotropic for both Group A and B particles [30,34– 36]. The normal stresses in the axial direction are much larger
the flow when superficial gas velocity and mass flux were increased from the FF to DPT regime (Fig. 7). Also, the mean radial velocity showed the same trend. A significant velocity variation was indicated between the central core and annulus zone near the wall. Near to the transition between these two zones, the axial and radial components of the mean velocity are of the same order revealing a particle motion principally directed toward the riser walls. However, axial and radial velocity fluctuation profiles in Fig. 10 show an opposite trend (to that of mean profiles) for comparison between FF and DPT regimes. The axial velocity fluctuations are of the same order of magnitude as the mean values. On the other hand, the radial velocity fluctuations are significant and are always greater than the measured mean values. This observation is in agreement with the earlier experimental studies by Van den Moortel et al. [35] and Godfroy et al. [11]. Fig. 10 suggests that with the increase in solids concentration, particle fluctuating velocities also increase. Note that the flow condition in the FF regime (Ugriser = 3.2m s− 1; Gs = 26.6kg m− 2 s− 1) has a higher solids holdup compared to the DPT condition (Ugriser = 4.5 m s− 1; Gs = 36.8 kg m− 2 s− 1) as observed from the particle occurrence plots and the tomography results (discussed later). However, this is contrary to the commonly reported simulation results [43,44] and experimental data [11,35]. With the increased solids concentration, the mean free path of the solids is reduced, resulting in the reduction of velocity fluctuations. However, there is a competing mechanism for increasing the particle velocity fluctuations due to the increase in particle collision frequency. As reported by Gidaspow and Huilin [45], collision frequency increases with particle concentration, which increases the velocity fluctuations with solids holdup under ‘dilute conditions’ (solids holdup less than 5–10%). Note that ‘dilute conditions’ need not imply the DPT regime of operation. All the flow conditions investigated in this study had a solids holdup less than 10% (tomography results). Hence, the above argument leads to the conclusion that although the mean velocity increases, the velocity fluctuations decrease with the increase in
(a)
(b) 450
200 FF regime DPT regime
Radial RMS velocity (cm/s)
Axial RMS velocity (cm/s)
400 350 300 250 200
180
160
140
120
150 100
0
0.2
0.4
0.6
0.8
Nondimensional radius ( ξ )
1
100
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ )
Fig. 10. Comparison of the azimuthally and axially averaged radial profiles of the RMS fluctuating velocity components in a) axial and, b) radial in the FF regime (Uriser = 3.2m s− 1; Gs = 26.6kg m− 2 s− 1) and, b) DPT (Uriser = 4.5 m s− 1; Gs = 36.8kg m− 2 s− 1). g g
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123 4
Ug Gs m/s kg/m2/s FF; 3.2 30.2 DPT; 3.9 33.7 FF; 3.2 26.6 DPT; 4.5 36.8
3.5
Ratio (Vz' / Vr')
3 2.5 2 1.5 1 0.5 0
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ ) Fig. 11. Ratio of the axial to radial RMS fluctuating velocity profiles.
involving the angular fluctuating velocities, τzθ and τrθ, are negligible and can be considered to be zero. Similar to the RMS velocity fluctuation profiles, the axial and radial solids normal stresses are found to be higher in the FF regime than in the DPT regime (Fig. 12). The reason could be due to the higher solids concentration in the FF regime, leading to significantly higher number of particle collisions. Hence, particle collisions are the controlling mechanism for momentum transfer due to the fluctuating velocities or are the turbulent Reynolds stresses. However, one can note that the shear stresses were comparable in magnitude in both regimes, indicating that the changes in solids turbulent viscosity (as given by Eq. (1)) are mainly governed by the gradients in the mean velocities. Since the solids phase turbulence was found to increase with solids holdup, the data and trends are consistent with those of Tartan and Gidaspow [36]. Although the angular and radial normal stresses are about the same order of magnitude, the radial normal stress was always higher than the angular normal stress. A distinct feature for conditions in the DPT regime is that angular normal stress peaks at the center of the column. This suggests that the vertical structures spiraling up the column have a tendency to cross over the axis, especially at high superficial gas velocities. This behaviour of vortex structures rules out the possibility of performing a transient simulation using 2D axi-symmetric conditions.
20
4.8
16
4 2 2 τrr (m / s )
τzz (m2 / s2)
than in the radial and angular directions. Fig. 12 compares the radial profiles of the spatially averaged turbulent Reynolds stresses (per unit bulk density) in the FF and DPT regimes. It can be clearly observed that the axial normal stresses are about 3 to 5 times higher than the radial and azimuthal normal stresses. This is due to the high gradient in the axial solids velocity. In addition, the radial and tangential solids velocities are quite small and, hence, their gradients are also small. The Reynolds shear stress, τrz, is much lower than the radial and angular normal stresses (about 1 / 2 to 1 / 3), while the shear stresses
12 8 4 0
3.2 2.4 1.6
0
0.2
0.4
0.6
0.8
.8
1
0
2.4
3.2
1.6
2.8
.8 0 -.8
0.6
0.8
1
2 1.6
0
0.2
0.4
0.6
0.8
1.2
1
0
1.6
.8
.8
.4
0 -.8
0
0.2
0.4
0.6
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ )
2 2 τzθ (m / s )
τzθ (m2 / s2)
0.4
2.4
Nondimensional radius ( ξ )
-1.6
0.2
Nondimensional radius ( ξ )
2 2 τθθ (m / s )
τrz (m2 / s2)
Nondimensional radius ( ξ )
-1.6
113
0.8
1
Nondimensional radius ( ξ )
0 -.4 -.8
0
0.2
0.4
0.6
0.8
1
Nondimensional radius ( ξ ) 2
- FF regime (Ug = 3.2 m/s; Gs = 26.6 kg/m /s)
2
- DPT regime (Ug = 4.5 m/s; Gs = 36.8 kg/m /s)
Fig. 12. Comparison of the azimuthally and axially averaged radial profiles of the turbulent Reynolds stress components in the FF and DPT regimes.
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Imposing a zero gradient at the centerline, as done in axi-symmetric conditions, would contradict the measured flow structure. The relationship between the shear stress, τrz, and the gradient of the mean axial velocity can be obtained using Bossinesq's hypothesis as shown by Eq. (1). P
lturbulent ¼ s
es qs vr Vvz V Avz =Ar
ð1Þ
The validity of the Bossinesq's theory is questionable since the hypothesis was originally proposed for single phase flows with isotropic turbulence. However, such closure is often used in the two-fluid modeling of granular flows [43] due to lack of a proper anisotropic closure. Also, the same hypothesis was employed to calculate the turbulent shear viscosity of liquid in bubble column flows [25,46]. Hence, Eq. (1) was employed to obtain the solids phase viscosity profiles. The solids holdup values required for the calculations were estimated from the radial profiles of the particle occurrences (per unit volume). The ratio of the particle occurrences in a compartment to the total occurrences was taken to be proportional to the solids volume fraction. The proportionality constant was estimated for each flow condition by comparing the crosssectional average holdup to that obtained from tomography. The viscosity profiles obtained did not make physical sense. Two peaks were observed in the FF regime, one in the core near the center and one near the wall cannot be realized with any physical flow structure. Also, for the flow conditions in DPT regime, negative solids viscosities were observed near the wall. Hence, the only explanation is that the Bossinesq's hypothesis does not hold for solids flow in a riser and yields physically unrealizable viscosity values. Based on the kinetic theory of granular flows (isotropic), a constitutive relation for the solids viscosity was derived relating it to the granular temperature (turbulence kinetic energy) and solids holdup ([47,48,96]). The following expressions describe the closure relations that are typically used in a kinetic theory based model. Solid phase shear viscosity (μs): rffiffiffiffiffiffi 2 2ls;dil 4 4 Hs ls ¼ 1 þ g0 es ð1 þ eÞ þ es qs dp ð1 þ eÞg0 5 5 ð1 þ eÞg0 p
e is the restitution coefficient, taken to be 0.89 based on the reported measured values by Foerster et al. [49] and recommendation by Tartan and Gidaspow [36]. The above expressions were used, along with the measured granular temperatures (turbulence kinetic energy per unit bulk density), and the solids holdup profiles derived from the CARPT data to calculate the viscosity profiles. Fig. 13 presents the solids viscosity profiles for different flow conditions in the FF and DPT regimes. In contrast to the previous calculations, it can be seen that the viscosity values and trends do make physical sense. The solids viscosity was found to be decaying monotonically in the radial direction in the FF regime, but in the DPT regime it shows a hump around r / R = 0.7. The reason for such a hump can be explained based on the solids holdup profile (cross-sectional view). At the radial position (r / R = 0.7) the solids concentration starts to increase rapidly (particle occurrence profiles) and represents the approximate interface between the lean core and a dense phase annulus. Thus, the particle exchange at this interface is frequent and vigorous, thereby decreasing the easy movement of the solids phase, which increases the solids viscosity. Although, the same argument holds in the case of the FF regime, but the axial fluctuations of the particles dominate (compared to radial) resulting in a higher turbulent transport of particles axially. Thus, in the FF regime, the decrease in the axial fluctuations (radially) dominates the peak in radial fluctuations, resulting in a smooth gradient of solids viscosity. The solids viscosity in each of the flow conditions exhibits similar radial trends as that of the granular temperature, indicating that the viscosity is almost independent of the solids holdup in the range of the measurements studied. This result is in agreement to that of Tartan and Gidaspow [36], who estimated solids viscosities in relatively dilute 3 in. riser using ‘PIV with probe’ technique. With the same Group B particles and a larger mean particle diameter (3.5 times) Tartan and Gidaspow [36] found nearly constant viscosities in the core (for all the flow conditions investigated). The viscosity values reported by them were lower, possibly due to the lower solids holdup, resulting in lower velocity fluctuations (under ‘dilute conditions’). Besides, the use of an intrusive imaging technique with a 0.5cm diameter probe to measure the velocity fluctuations is questionable. Hrenya and Sinclair [50] in their simulations reported higher
ð2Þ
ls;dil
pffiffiffiffiffiffiffiffiffi 5q dp Hs p ¼ s 96
ð3Þ
g0 is the radial distribution function which becomes very large as the solids holdup approaches the maximum packing (εs,max = 0.64 for the glass beads used) and is given by: 3 es 1 −1 3 g0 ¼ 1− 5 es;max
ð4Þ
Solids Viscosity (g/cm-s)
where Θs is the granular temperature, dp is the sauter mean size of the solids distribution, ρs is the density of the solids (glass beads), εs is the local solids holdup and the solids phase dilute viscosity (μs,dil) is given by:
1.5
1
0.5 0
Ug m/s FF; 3.2 FF; 3.2 DPT; 3.9 DPT; 4.5
Gs kg/m2/s 26.6 30.1 33.7 36.8
0.2
0.4
0.6
0.8
1
Nondimensional radius( ξ ) Fig. 13. Radial profiles of the solids viscosity calculated from kinetic theory based expressions.
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
viscosities for FCC particles compared to Gidaspow and Huilin [45], who employed the same ‘PIV with probe’ technique. The solids viscosity in Fig. 13 increases with the solids concentration (from DPT to FF regime). This can be explained with the following interpretation of Eq. (2) [51]. kinematic viscosity ¼ mean free path random oscillating velocity
(with solids holdup) enforces the above trend for the granular temperature. With the solids holdup increasing from DPT to FF regime, the increase in the collision frequency seems to be dominant compared to the decrease in the mean free path. However, with the solids holdup increasing radially in each of the regimes, the decrease in the mean free path becomes dominant (at different magnitude for each of the regimes) compared to the increase in the collision frequency. This effect is less pronounced in the DPT regime (compared to FF) as suggested by a relatively flat radial profile of the granular temperature. The observations from Fig. 14 suggest that the granular temperature is strongly correlated to the solids holdup. Also, the above arguments suggest that the peak in the granular temperature may occur around a solids holdup value of 1–6%, in contrast to that reported by Gidaspow and Huilin [45] of 5–10%. Considering the fact that Gidaspow and Huilin [45] and Tartan and Gidaspow [36] employed imaging techniques like PIV or ‘PIV with probe’, the reliability of the velocity measurements away from the walls is questionable. Also, in their granular temperature calculations, angular velocity fluctuations were assumed equal to the radial component. In addition, the densitometry technique employed had a coarse resolution (N1.27cm) and yields only line-averaged solids holdups. In view of the above uncertainities, the position of the peak in the granular temperature reported by Gidaspow's group at 5–10% is uncertain. It is noted here that due to the data acquisition frequency of 200 Hz for CARPT experiments, the maximum range of frequencies tracked by the tracer particle is up to 100Hz. Therefore, the present measurements represent only scales up to 100Hz of the turbulent structures. However, since the large scales contain the most energy, it is expected that what remains due to small scales is not very significant in magnitude. There are several studies reporting the dominant frequencies of oscillation of particles in the dense and dilute zones for a wide variety of operating conditions ([51–55,96]). Typical macroscopic frequency range reported was up to 4 Hz.
14 2
2
2
Turbulent kinetic energy per unit bulk density (m /s )
The mean free path decreases with increasing solids concentration, while the velocity fluctuations increase due to the increase in the collision frequency under ‘dilute conditions’. Hence in dilute risers (εs b 0.05–0.1), the increase in the collision frequency dominates the decrease in the mean free path, while it is vice versa in dense risers. Also, Gidaspow and Huilin [45], based on experimental data, showed that, for different particles, the dimensionless viscosity calculated based on Eq. (2) shows a minimum at solids holdup of 0.057 and increases beyond that. It can also be observed from Fig. 13 that with the decrease in the solids concentration, tending towards more dilute flow conditions, the viscosity profile tends to become flat. This is due to the fact that the granular temperature and the solids holdup profiles tend to be nearly flat in a dilute riser. Both these profiles are presented subsequently. An unusual hump in the viscosity profile can be noted for the flow condition of Ugriser = 3.9 m s− 1 and Gs = 33.7kg m− 2 s− 1 compared to the other three profiles. This is possibly because the flow condition is close to the regime transition boundary between FF and DPT (type A choking velocity). Fig. 14 compares the radial profiles of the granular temperature in the FF and DPT regimes. Based on the earlier discussion, the velocity fluctuations and hence the granular temperature increases with the solids holdup for ‘dilute conditions’ and decreases for higher solids holdups. The relative dominance of the increase in the collision frequency over the decrease in the mean free path
115
FF, Ug = 3.2 m/s; Gs = 26.6 kg/m /s 2
DPT,Ug = 4.5 m/s, Gs = 36.8 kg/m /s
12
2 2 2 KE = 1/2 (u' +v' +w' )
10
8
6
4
2 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Nondimensional radius ( ξ ) Fig. 14. Radial profiles of the turbulent kinetic energy (per unit bulk density) in FF and DPT regimes.
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3.2. Solids holdup measurements
CT scanner setup were stationary. Hence, the dynamic bias in these phantom scans arises only from the stochastic nature of the emissions from a γ-ray source. However, during the actual riser scan, solids holdup fluctuations also contribute to the bias. If the sampling time is small enough, then the variation of the holdup within the time interval is small allowing one to assume an approximately static holdup. Hence, the sampling frequency should be at least twice the macroscopic oscillation frequencies of the solids in order to assume a static holdup within each pixel (imaginary grid assumed for image reconstruction). There is a vast experimental and modeling evidence of the dominant frequency range for riser flow to be up to 4Hz (for example Ref. [55]). Another constraint in selecting a high sampling frequency is the need to obtain adequate statistics in the photon counting process. For the CT scanner in our laboratory, a sampling frequency of 20Hz is low enough for statistical counting errors to be small. In fact, AM reconstruction algorithm models the photon emission and detection to be of Poisson, yielding good image estimates even at low counts [56]. Also, note that it is not intended to capture the small time scale fluctuations in the flow. An inherent approximation involved is that these small time scale fluctuations lead to solids movement within the spatial resolution. Therefore a sampling frequency of 10 Hz was considered to be sufficiently high for making static holdup approximation. The main factors that determine the imaging capabilities of a CT scanner are its achievable spatial, temporal and density
Significant experimental evidence is available which show radial segregation of the solids in gas–solid risers (refer to Table 2). According to Sinclair and Jackson [40], the central problem in constructing a satisfactory model for riser systems is to understand the mechanism that gives rise to lateral particle segregation. The intent in this section is to study the solids holdup distribution to complement the CARPT data in providing valuable insight into the physics of the complex hydrodynamics. To achieve these objectives, accurate estimation of solids holdup is required. Hence, the accuracy of estimating the solids holdup via γ-ray tomography is discussed before presenting the riser holdup profiles. Improvements in the image reconstruction by implementing an Alternating-minimization (AM) algorithm were discussed by Bhusarapu et al. [28]. The AM algorithm was found to improve the image quality near the high attenuation (high holdups) regions. The CT scanner setup was validated with a phantom scan of a beaker filled with water. The reconstructed image showed that the flat distribution of the single phase (water) was reconstructed with the mean total attenuation coefficient of 0.085cm− 1. The discrepancy with the theoretical mass attenuation value of water at the photo peak of Cs-137 (660keV) was found to be less than 2.3%. The phantom scans that illustrated the improvements shown by AM algorithm and the validation of the
Radius (cm)
(a)
(b) 7.5
7.5
5.4
5.4
2.7
2.7
0
0
-2.7
-2.7
-5.4
-5.4
-7.5 -7.5 -5.4
-7.5 -7.5 -5.4
0.14 0.12 0.1 0.08 0.06 0.04 0.02
-2.7 0 2.7 Radius (cm)
5.4 7.5
(c)
-2.7 0 2.7 Radius (cm)
5.4 7.5
(d) 7.5
7.5
5.4
5.4
2.7
2.7
0
0
-2.7
-2.7
-5.4
-5.4
-7.5 -7.5 -5.4
-7.5 -7.5 -5.4
0.14 0.12 0.1 0.08 0.06 0.04 0.02
-2.7 0 2.7 Radius (cm)
5.4 7.5
-2.7 0 2.7 Radius (cm)
5.4 7.5
Fig. 15. Contour plots of the solids holdup at Z / D = 33 (z = 5 m) in the riser under the operating conditions: a) Uriser = 3.2m s− 1; Gs = 26.6kg m− 2 s− 1, FF; b) g −1 −2 −1 −1 −2 −1 −1 riser riser Uriser = 3.2 m s ; G = 30.1kg m s , FF; c) U = 3.9m s ; G = 33.7kg m s , DPT; d) U = 4.5m s ; G = 36.8kg m− 2 s− 1, DPT. g s g s g s
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
resolutions [22]. A measure of the spatial resolution is the point spread function which is the extent to which an image of a point object will be blurred. The effective detector aperture width is taken to be the spatial resolution of the scanner and the expression to calculate it was derived by Yester and Barnes [57]. The spatial resolution for the CT scanner in our laboratory was found to be 1.7mm at the center of the column. The resolution employed for reconstructing the solids holdup tomograms in the riser was 2.7 mm. The single important factor that determines the density resolution is the random fluctuations in the photon counts. De Vuono et al. [58] derived an expression for the density resolution obtainable from all the measurements in an entire scan as follows: rU n pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ q 2lw qw Di mCT Md
ð5Þ
where n is the number of beams in each view, m is the number of views, Md is the average number of photon detected per beam, μw is the mass attenuation of water, ρw is the density of water and di is the inside diameter of the column. The density resolution for the designed CT scanner in our laboratory for a 6 in. column was found to be 8.1 × 10− 3 g cm− 3. Hence, the holdup resolution with glass beads in the riser is 3.2 × 10− 3. Fig. 15 shows the tomograms of the riser at the operating conditions of investigation. Qualitatively all the scans reveal increased solids holdup near the walls and with nearly same relative increase from their means. The distributions seem to disclose nearly axi-symmetric flow as predicted from the velocity distributions (Fig. 6). In the FF regime, solids holdup seems to exhibit a three layer stratification with gradual gradient, while in the DPT regime there seems to be a smooth gradient, which is less than that in the FF regime. Also, there is an overall reduction in the solids volume fraction in the DPT regime with the corresponding increase seen in the velocity
117
PDFs (Figs. 4 and 5). Albeit, there seems to be large radial solids segregation towards the wall in both cases. Radial migration of solids is a complex phenomenon and is not properly understood [59]. The effect of increasing the solids mass flux at constant gas superficial velocity increases the solids holdup (Fig. 15). This increase arises because more solids are fed into the riser section for the same gas superficial velocity (and hence the energy input) to the system. The effect of increasing the gas superficial velocity at constant mass flux can be understood to decrease the solids holdup due to the increase in the solids velocity. Since the gas injected is the only source of energy that drives the solids circulation, constant solids mass flux with higher gas flow drives more solids out of the riser. Consequently, solids holdup decreases. Unfortunately, such a trend can be verified only by comparing one pair of conditions (Ugriser = 3.2 and 3.9m s− 1; Gs = 30.1 kg m− 2 s− 1). The qualitative findings presented above can be quantitatively verified by circumferentially averaging the solids holdup distributions. Fig. 16 shows such a plot of the radial profiles under all the operating conditions investigated. The two profiles in the FF regime show distinctly higher holdups (relatively) and also higher radial gradients. Clearly, three distinct slopes in the profiles can be identified (FF regime) illustrating a three layer stratification observed in the tomograms (Fig. 15). The solids concentration was nearly zero in the center (up to r / R = 0.27, 0.5 for high and low fluxes, respectively), increases linearly up to r / R = 0.8, 0.85 for high and low fluxes, respectively, and later increases linearly with a higher slope. However, in the DPT regime, the density profiles seem to be relatively flat and show very little variation (within 20%) among the different operating conditions. Nevertheless, the relative (with respect to mean) radial increase of the solids holdup seems to be high and is comparable to that in the FF regime illustrating similarity profiles.
0.08 Ug, Gs m/s kg/m2/s
0.07
3.2, 3.9, 4.5, 3.2, 3.9, 4.5,
Solids Holdup
0.06 0.05 0.04
30. 1 33. 7 36. 8 26. 6 30. 1 32. 1
-
FF DPT DPT FF DPT DPT
0.03 0.02 0.01 0 0
0.13
0.27
0.4
0.53
0.67
0.8
Non-dimensional radius ( ξ ) Fig. 16. Azimuthally averaged radial profiles of the solids holdup.
0.93
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Table 4 Correlation fits for the radial holdup profiles r m i mþ2 h 1þc m þ 2 þ 2c R
Operating conditions
Mean from CT
(m s− 1) Uriser g
Gs (kg m− 2 s− 1)
〈εs〉CT (%)
〈εs〉 (%)
m
c
D (%)
3.2, 3.2, 3.9, 3.9, 4.5, 4.5,
30.1 26.6 33.7 30.1 36.8 32.1
2.9 0.85 0.48 0.45 0.61 0.4
3.24 0.97 0.53 0.51 0.67 0.43
3 3.9 4 7 5.1 3.9
13.5 12 9.5 4.2 2.5 3.8
12 14 11 12 10 8
Discrepancy, D ¼
hes i−hes iCT hes iCT
es ¼ hes i
Rhodes et al. [79]
Patience and Chaouki [60]
Wang et al. [80]
F
〈εs〉
β
D (%)
〈εs〉
k
D (%)
〈εs〉
D (%)
0.1 0.037 0.019 0.019 0.017 0.011
3.23 0.98 0.53 0.51 0.67 0.44
1.98 2.1 1.7 1.36 1.14 1.44
11 15 10 12 10 10
3.1 0.94 0.5 0.51 0.67 0.42
1.32 1.26 1.15 1.13 1.1 1.12
7 10 4 14 10 5
2.65 0.73 0.41 0.44 0.59 0.36
−9 − 14 − 15 −2 −3 − 10
100.
F — Steepness factor. m, c, β, k — Regressed constants. r 6 h 2 i es −hes ik Rhodes et al. [79] — es ¼ hes i 1−b=2 þ b Rr ; Patience and Chaouki [60] — ¼4 ; k R hes i−hes i r h r i es es r 19 for 1.5% b 〈εs〉 b 5%; Wang et al. [80] — ¼ 0:82 þ 48 1− d exp −22 1− ¼ 0:905 þ for 〈εs〉 b 1%. R R R hes i hes i
The reduced holdup profiles are typically correlated with the radial position to be incorporated in a phenomenological flow model. Patience and Chaouki [60] and Schlichthaerle and Werther [61] employed the following form of correlation: es ðrÞ−es ð0Þ m þ 2 r m ¼ : hes i−es ð0Þ 2 R
ð6Þ
A more general form of Eq. (6) was employed to model the radial profiles of gas holdup in bubble columns [22,46]. es ¼ hes i
r m i mþ2 h 1þc : m þ 2 þ 2c R
ð7Þ
In the above equations, 〈εs〉 is the cross-sectional average solids holdup, constant m is related to the steepness of the
profile, and constant c is related to the extent of solids present in the local wall region. Eq. (7) was employed to correlate the solids holdup data. Table 4 provides the results of fitting the above functional form to the solids holdup profiles. It is clear from the available data (Table 4) that the cross-sectional average solids holdup shows trends with both the superficial gas velocity and solids mass flux. However, the effect on the curvature parameters m and c is not so evident. To facilitate such understanding, Fig. 17 shows the relative holdup profiles for all the flow conditions from the fitted parameters. Parameter c seems to be very high in the FF regime (greater than 10) and decreases with the change of regime to DPT (less than 5). In contrast, exponent m was found to be lower in the FF regime as compared to that in DPT regime, indicating a steeper profile in the FF regime. However, for the operating condition with Ugriser = 3.9 m s− 1 and Gs = 33.7 kg m− 2 s− 1, which is close to the regime transition, a c value of 9.5 is bound intermediate between FF and DPT regimes. Also, the m value was found to
3 Ug Gs m/s kg/m2/s
3.2, 3.2, 3.9, 3.9, 4.5, 4.5,
2.5
ε(ξ) 2
---Relative holdup
<ε>
1.5
30.1-FF 26.6-FF 30.1-DPT 33.7-DPT 36.8-DPT 32.1- DPT DPT regime
1
0.5
FF regime
0 0
0.13
.27
.4
.53
.67
.8
Nondimensional radius ( ξ ) Fig. 17. Relative holdup profiles obtained from the holdup correlation.
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Similar stratification can be observed in the tomograms (Fig. 15). Note that for the flow condition at Ugriser = 3.9 m s− 1 and Gs = 33.7kg m− 2 s− 1, close to regime transition, indicate a mixed behavior with FF characteristics near the core transiting slowly to DPT characteristics near the wall. Although it is difficult to generalize the findings with the limited experimental data available, one can observe from Fig. 17 that in the FF regime the solids concentration in the core is insensitive to the averaged holdup 〈εs〉. On the other hand in the DPT regime, averaged holdup influences the core solids concentration and is insensitive to the wall concentration. Similar trend with two distinctive variational regions in the radial profiles was reported by Xu et al. [63] for FCC particles. However, none of the studies (within the literature reviewed in Table 2) reported the three characteristic layers in the FF regime conditions. Most of the studies, covering a wide range of operating conditions (including DPT and FF), reported only a two layer structure with a nearly constant core in the center transiting to a steep increasing holdup near the wall ([17,55,63–65,97]). The reason could be that the employed techniques in the studies have a poor spatial resolution (5–10 holdup data across the radius). Also, the wall effects influence most of the sensing techniques employed. The results with X-ray tomography from Wirth's group [66,67], with a spatial resolution as good as 6 mm, also could not capture such three layer stratification. As a matter of fact, such three layer stratification could not be captured in the velocity fields from CARPT results (Figs. 6–9) for the same reason that the spatial resolution (for Eulerian averaging) is poor. The radial profiles of the granular temperature (Fig. 14) seem to have similar shape as that of the gas holdup (1 − εs) profiles. In order to understand their relationship and to obtain a functional form for the granular temperature, Θs, the reduced profiles of the two measured quantities were plotted in Fig. 18. Considering the fact that the granular temperature was obtained from CARPT data with low spatial resolution, there seems to be a fair comparison of the reduced profiles in both the regimes. Hence
be low (4), indicating abnormalities near the regime transition conditions. It can be observed from Eq. (7) that the exponent m alone is not representative of the gradient of the solids holdup. The radial steepness of the solids holdup profile can be assessed with a parameter F given by: Z 1 des des F¼ ¼ 2 n d dn dn average dn 0 average 2hes icmðm þ 2Þ : ¼ ðm þ 1Þðm þ 2 þ 2cÞ
ð8Þ
Table 4 lists the values of the steepness factor F for the each of the operating conditions. It can be observed that F increases with the solids mass flux at constant superficial gas velocity both in FF and DPT regimes. Although not conclusive enough, comparing the F values at operating conditions with the constant mass flux Gs = 30.1 kg m− 2 s− 1 shows that F decreases with increase in superficial gas velocity. Both trends are inline with that reported by Zhang et al. [62]. Table 4 also lists the various available correlations for the radial profiles of solids holdup. The regressed constants and the mean holdup values are indicated for each of the correlations. The correlation by Patience and Chaouki [60] seems to give the least discrepancy of 8% (averaged for all the operating conditions). Relative holdup profiles in Fig. 17 reveal distinctive flow behavior in the FF and DPT regimes. In the central core region, the relative holdup is distinctively lower in the FF regime compared to DPT, although both are flat. The uniformly flat region in FF seems to extend until r / R = 0.27 (approximately), while in DPT it extends until r / R = 0.45 (approximately). Beyond that, the relative holdup increases with close to similar slopes in FF and DPT regimes. While in the DPT regime, such radial gradients prevail till the wall, FF regime indicates a higher radial gradient starting from r / R = 0.8 (approximately). Hence, the above trends reveal three different characteristic layers in the FF regime, while the DPT regime has two characteristic layers.
(a)
(b) 4
3
ϕ=Θs ϕ=εs
ϕ(ξ)-ϕ(0) 3
2.5
<ϕ>-ϕ(0) Reduced profiles
119
2 2
FF regime
1.5
DPT regime
1
1
0.5 0
0 0
0.2
0.4
0.6
0.8
Non-dimensional radius ( ξ )
1
0
0.2
0.4
0.6
0.8
1
Non-dimensional radius ( ξ )
Fig. 18. Reduced profiles of the granular temperature, Θs and the solids holdup, εs in: a) DPT (Uriser = 4.5m s− 1; Gs = 36.8kg m− 2 s− 1); b) FF (Uriser = 3.2 m s− 1; g g Gs = 30.1kg m− 2 s− 1).
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S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
one can assume an approximate functional form for granular temperature as: Hs ðrÞ−Hs ð0Þ es ðrÞ−es ð0Þ c Z Hs ðrÞcaes ðrÞ þ b: hHs i−Hs ð0Þ hes i−es ð0Þ
ð9Þ
Such a functional form can be employed to derive the dependence of solids viscosity (Eq. (2)) variation with solids holdup, which can be used as an input in a two-fluid approach of a CFD model. One should note that the relationship given in Eq. (9) is limited to dilute flow in risers. The riser was investigated only under ‘dilute conditions’ where solids fluctuations increase with the solids holdup, while it is known that beyond a certain limit (1–6%) fluctuations decrease with the solids holdup. 3.2.1. Axial variation of solids holdup It was established in the earlier section that the axial variation of solids velocity within the zone of investigation was negligible. To check for the ‘fully developed’ flow in the zone of investigation the radial profiles of the solids holdup at two different axial planes were compared for all the operating conditions under investigation. Although there are slight variations in the holdup profiles at the two different axial planes, the differences are within the density resolution of scanner. Hence, the axial gradients of the solids holdup are negligible in the zone of investigation.
CT. Comparison in both FF and DPT regimes seems to be fair with the CARPT derived profiles over predicting the averaged reduced holdups. Similar trends were observed for all the operating conditions under investigation. Again the reason for such over prediction could be due to the low spatial resolution for Eulerian averaging in the CARPT technique. Considering the fact that the profiles were derived from two independent experimental techniques, this comparison serves as a validation of results for both the techniques. 4. Summary Single radioactive particle tracking in the gas–solid riser yielded a wealth of solids instantaneous and time-averaged flow information. Added to it the γ-ray tomography provided detailed time-averaged volume fraction profiles of the two phase riser flow enabling some insights into the complex phenomena. Following are the key conclusions with regards to the solids flow in risers: i. Instantaneous particle traces reveal occasional downflow in the core region (near center) only in the FF regime at the operating conditions investigated. Both large scale internal recirculation superimposed by fine scale fluctuations contribute to axial backmixing, while in the horizontal plane solids mixing is principally dispersive. ii. Solids flow is nearly axi-symmteric and is close to fully developed (within the zone of interrogation) revealed from both the velocity and holdup profiles. iii. The movement of solids from core to annulus seems to be governed by the time-averaged velocity profiles, while the movement of solids from annulus to core (if prevalent) is governed by the fluctuating velocity profiles in the fully developed zone. iv. Contour plots of turbulent kinetic energy and particle occurrences reveal a clear core-annular flow structure with FF regime, while the profiles are uniform under DPT regime.
3.2.2. Comparison of CT versus CARPT derived holdup profiles By assuming ‘well-perfusedness’ [10,11,15,41], particle occurrences per unit volume obtained from CARPT data can be related to solids holdup as follows: Occurrences ðper unit volumeÞ ~es : ð10Þ Total Occurrences CS Fig. 19 presents the typical comparison of the reduced holdup profiles derived from CARPT and that obtained from
(a)
(b)
ε(ξ)—ε(0)
------<ε>—ε(0)
4
3.5 CT CARPT
3.5
3
3 2.5
Reduced Holdup
2.5
DPT regime
2
2
FF regime
1.5
1.5
1
1
0.5
0.5
0 0
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0.8
Nondimensional radius ( ξ )
1
0
0
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Nondimensional radius ( ξ )
Fig. 19. Comparison of the reduced holdup profiles derived from CARPT and CT at: a) FF (Uriser = 3.2 m s− 1; Gs = 26.6kg m− 2 s− 1); b) DPT (Uriser = 3.9 m s− 1; g g Gs = 33.7kg m− 2 s− 1).
S. Bhusarapu et al. / Powder Technology 163 (2006) 98–123
v. Clustering phenomena exists throughout the riser crosssection (more likely near the wall) along with the particle exchange between core and annulus. vi. Although the mean velocity increases, the velocity fluctuations decrease with the increase in the solids mass flux and/or superficial gas velocity under ‘dilute conditions’. vii. Flow in the riser is anisotropic with the fluctuating motion principally directed along the main axis of flow. viii. The relative dominance of the increase in the collision frequency over the decrease in the mean free path (with solids holdup) dictates the trends for the granular temperature and solids viscosity. ix. Tomograms reveal three different characteristic layers in the FF regime, while the DPT regime has two characteristic layers. x. Steepness in the radial profiles of solids holdup increases with the solids mass flux at constant superficial gas velocity both in the FF and DPT regimes. xi. Reduced holdup profiles derived from CARPT and CT match fairly well. Notation c parametric constant (–) dp particle diameter (m) D diameter of the column (m) E coefficient of restitution (–) F steepness parameter (–) Gs mass flux (kg m− 2 s− 1) g0 radial distribution function (–) k parametric constant (–) m parametric constant (–) mCT number of views (#) Md average number of photons detected per beam (#) n number of beams in each view(#) r radial position (cm) R riser radius (cm) Ugriser superficial gas velocity (m s− 1) v′ fluctuating velocity (m s− 1) bvN time-averaged velocity (m s− 1) z axial distance (m) Greek letters ε holdup (–) bεN cross-sectional averaged holdup (–) ρ density (kg m− 3) σ standard deviation μ viscosity (g cm− 1 s− 1) μw mass attenuation coefficient of water (m2 kg− 1) τ stress tensor per unit bulk density (m2 s− 2) Θs granular temperature (m2 s− 2) ξ dimensionless radius (–) β parametric constant (–) Subscripts and Superscripts g gas s solid phase
p i z r θ ρ cs
121
particle inside axial radial azimuthal density cross-sectional average
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