Surface-to-bed heat transfer in fluidised beds: Effect of surface shape

Powder Technology 174 (2007) 75 – 81 www.elsevier.com/locate/powtec

Surface-to-bed heat transfer in fluidised beds: Effect of surface shape Francesco Di Natale ⁎, Amedeo Lancia, Roberto Nigro Dipartimento di Ingegneria Chimica, Università di Napoli “Federico II”, P.le Tecchio, 80, 80125 Napoli, Italy Received 9 December 2005; received in revised form 3 January 2007; accepted 9 January 2007 Available online 20 January 2007

Abstract In recent times, the possible application of fluidisation technologies to the surface treatments of engineering materials becomes a subject of growing interest both for manufacturing and chemical industries. Heat and mass transfer rates between the surface and the fluidised bed strongly influence the performance of the surface treatment. Experimental results of heat transfer between a submerged surface and a fluidised bed are presented in this article. This work is focused on the influence of bed material properties and surface geometry on heat transfer coefficient. Experimental tests show that the heat transfer coefficient is notably affected by the shape of the immersed surface resulting higher for surfaces with better aerodynamic shape. An interpretative model, based on the dimensional analysis, has been used for the description of the experimental results. © 2007 Elsevier B.V. All rights reserved. Keywords: Heat transfer; Bubbling fluidised bed; Bed material properties; Exchange surface shape

1. Introduction Surface treatments are used to improve the functions and service lives of engineering materials controlling friction and wear, increasing corrosion resistance, changing physical properties (e.g., conductivity, resistivity, and reflection), dimensions and appearance (e.g., colour and roughness) also obtaining a costs reduction. Surface treatments can be roughly schematized as a series of elemental steps involving heat and mass transfer processes. The overall efficiency of a superficial treatment is related both to the improvement of the surface properties and to the degree of homogeneity of the treated surface. This last is a crucial parameter since a non-uniform quality of the treatment may lead to the creation of weak points on the surface. This problem is more relevant when the process is carried out by immersion of the surface in a flowing fluid. In this case, differences in the fluid dynamic field around the surface alter the local heat and mass transfer rates and reduce the uniformity of the superficial treatment. Surface geometry directly influences the treatment efficiency.

⁎ Corresponding author. Tel.: +39 81 7682246; fax: +39 81 5936936. E-mail address: [email protected] (F. Di Natale). 0032-5910/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2007.01.010

Fluidised beds are characterised by high values of heat and mass transfer rates and solid mixing [1] which may suggest the use of these reactors for surface treatments. Classical applications of fluidisation technologies to surface coating and decoating are available in literature [1–5] and, in recent times, examples of more complex surface treatments have been reported [6–9]. For example, fluidised beds have been used for the Thermal Reactive Deposition [6], a hard coating technology used to enhance the tool life, while fluidised bed plasma reactors have been used to modify the surface of fine alumina powders [7] and to alter the superficial properties of polymers, such as wettability and adhesion, without changing their bulk properties [8]. Finally, fluidised bed reactors have been used for surface pre-treatments required by film and solid covering depositions [9]. Accurate estimations of the heat and mass transfer coefficient between the fluidised bed and the immersed surface are crucial to an efficient reactor design and operation. However, at this moment, the prediction of heat and mass transfer rates in different working conditions is still not addressed. Only few experiments exist on the mass transfer rate which is mainly related to gas phase dynamics near the immersed surface and may be qualitatively described by classical models [1,10]. On the contrary, heat transfer coefficient has been widely studied [11–22] and its features have been mainly related to the so-

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This work concerns the effect of surface shape on the heat transfer rate from a bubbling and slugging fluidised bed and an immersed object. In particular, the heat transfer coefficient has been studied for different bed materials and several objects of elemental shape (cone, sphere, cylinder, parallelepiped, frustum of cone) which are chosen to obtain a good simplification of the different typologies of complex shaped objects which has to be treated in industrial applications. 2. Experimental apparatus

Fig. 1. Fluidisation column and heat transfer probes (spherical exchange surface).

called particle convective heat transfer mechanism, which accounts for the unsteady contact between the fluidised particles and the exchange surface. However, no definite mechanistic models for the determination of heat transfer coefficient are available and empirical correlations for the prediction of heat transfer coefficient are limited to the range of working conditions represented by the existing data. In this sense it is worth noticing that experimental evaluations of the surface-to-bed heat transfer coefficient are commonly available for cylindrical surfaces, while only a few examples exist for spheres [13,14] or plane slabs [15]. Experimental results [13–17] have pointed out that heat transfer coefficient decreases by increasing surface dimensions mainly due to a longer particle-to-surface contact time. Nonetheless, the differences in experimental apparatus and in fluidisation conditions do not allow the evaluation of the effect of probe shape on heat transfer rate starting from the existing data. Recent studies on the heat transfer coefficient at different angular position on a horizontal cylindrical surface [18,19] have clearly pointed out that the heat transfer coefficient is the highest on the lateral surface of the cylinder and the lowest on the portions of surface pointing downward and upward, when the solid mixing is less pronounced. Qualitative analyses on the fluid dynamic field near differently shaped surfaces have been reported in Buyevich et al. [23]. These results clearly show the considerable dependence of heat transfer phenomena on the fluid dynamic field near the exchange surface and that it can be reasonably expected that the surface averaged value of heat transfer coefficient has to depend on the shape of exchange surface. This result is of primary importance for an appropriate design of surface treatment processes in fluidised bed reactors since the treated surface commonly presents a complex shape.

The experimental rig consists of a Plexiglas column 0.1 m ID and 1.8 m height with a porous plate distributor at its base (Fig. 1). Dry air is used as fluidising gas and the gas flow rate can be risen up to about 25 Nm3/h. The settled bed height is of 600 mm. The column is equipped with a gas flow-meter (Micro motion Elite sensor CMF050) and a differential pressure transducer (Druck PMP4110) for the measurement of the pressure drop within the fluidised bed. To analyze the effect of the object shape, six different exchange surfaces have been used: a sphere, a cone, a frustum of cone, a square base parallelepiped and two cylinders with the same height but different diameters. Their characteristic dimensions are reported in Table 1 while the construction details are resumed in Fig. 1 for the spherical surface. The generic exchange surface (Fig. 1) consists of an aluminium shell of the desired shape in which is centrally inserted a 150 W cylindrical heater cartridge (diameter 8 mm, height 25 mm). A K-type thermocouple is fixed in a small cavity on the surface. The heat transfer probe is completed by an 80 mm thermal insulating PTFE support screwed on one side into the upper side of the exchange surface and then fastened to a PET hollow rod which is fixed on the top of the column. The PTFE support assures an almost complete elimination of heat losses by conduction along the heater support, which results to be less than the 3% of the total energy supply. The heat transfer probe is positioned vertically, directed downwards, and placed along the longitudinal axis of the bed, 300 mm above the gas distributor. At the same height a second thermocouple is placed in the bed to measure the bulk temperature. The heat transfer coefficient is calculated at constant surface temperature, through the measures of the probe power input and the time-averaged temperature difference between the external surface of the heat transfer probe and the bulk of the bed. It has to be noted that all the exchange surfaces are made of aluminium (thermal conductivity Kp ∼ 204 W/m K) and the Table 1 Geometrical characteristics of the exchange surfaces Probe

Geometry

H, mm

L, mm

l, mm

Deq, mm

1 2 3 4 5 6

Sphere Cone Frustum of cone Cylinder #1 Cylinder #2 Parallelepiped

28 31 31 30 30 30

28 30 30 20 30 14

– – 15 – – –

16.2 17.3 23.7 20.0 30.0 15.8

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Table 2 Physical properties of fluidised solids Solid material

dp, μm

Ar

Umf, cm/s

Uslug, cm/s

εmf

Geldart's [24] type

ρp, kg/m3

cp, J/(kg K)

Glass beads

210 280 500 630 930 290 670 310 590 300 590

980 2080 12,710 24,036 87,500 2492 30,733 4138 28,529 3229 24,563

6.2 9 22 35.6 51 9 30 18 50 13 40

12.5 15.2 34 42.0 60 16.2 36.2 26.3 60.2 20.2 45.4

0.44 0.44 0.44 0.44 0.44 0.315 0.4 0.52 0.53 0.56 0.57

B B B B D B B B D B D

2540

765

0.9

2700

840

1.9

3670

780

10.6

3160

780

16

Silica sand Corundum Carborundum

maximum thickness between the internal heater cartridge and the external surface is of around 8 mm. Hence, considering the typical values of heat transfer coefficients in fluidised beds (100–1000 W/m2 K), the Biot number of the exchange surface is always well below unity and the surface temperature can be assumed to be almost uniform. This condition allows simple and reliable measures of heat transfer coefficient but also represents one of the limits of this technique as only its surface averaged values can be determined. Experimental tests have been conducted with 11 different bed materials whose physical properties are listed in Table 2. Minimum fluidisation and minimum slugging velocities, evaluated by pressure drop measures and visual observations, have been also reported. Gas flow rate has been varied between 0 and 22 Nm3/h in order to cover the whole bubbling and a wide part of the slugging regime. Gas pressure and temperature have been fixed at ambient conditions. 3. Experimental results Experimental results consist of plots of heat transfer coefficient, h, in function of the gas velocity, U. Typical experimental results are reported in Fig. 2 for the case of 310 μm corundum particles.

The general trend of experimental results is always the same regardless the bed material and the surface shape: for fixed bed conditions, heat transfer coefficient presents an almost constant value, hmf, between 50 and 150 W/m2 K. At incipient fluidisation, heat transfer coefficient shows a rapid growth up to an almost constant value, hmax, at least three times higher than hmf. Experimental results show that the spherical surface usually presents the highest heat transfer coefficient, while the minimum value is obtained for the two cylinders. On the contrary, the heat transfer coefficient at incipient fluidisation is almost constant with the probe shape. Finally, the sphere, the cone and the frustum of cone present a steeper increase of heat transfer coefficient from minimum fluidisation condition to the asymptotic value, hmax. The same results have been obtained for each of the other bed materials. To resume the typical experimental curve of heat transfer coefficient in function of gas velocity, the values of hmf and hmax, the minimum fluidisation velocity and the velocity at which heat transfer approach the value of hmax (denoted Umax) are required. However, it is worth noticing that the value of Umax chiefly depends on the bubbles characteristics, which determine the solid mixing in bubbling/slugging fluidised beds and are strictly related to the experimental set up (e.g., distributor design, column diameter and presence of internal surfaces [1,24]). On the contrary, the values of Umf, hmf, and hmax are physical properties of the fluidised bed and the exchange surface are therefore used to summarize the experimental results for all the investigated conditions (Table 3). A more interesting analysis of experimental results is obtained with the representation of heat transfer coefficient in terms of surface Nusselt number, Nu = hDeq/Kg. The surface characteristic length, Deq, is defined as the diameter of a circumference whose area, Seq, is equivalent to the average cross sectional area of the exchange surface perpendicular to the main gas flow direction (the horizontal one in typical fluidised beds): rffiffiffiffiffiffiffiffiffi  0:5 Z H 4Seq 4 Deq ¼ S ð yÞdy ¼ pH 0 p

Fig. 2. Heat transfer coefficient in function of gas velocity for 310 μm corundum particles.

Kp, W/m K

ð1Þ

In Eq. (1), y represents the vertical position on the exchange surface of height H. The values of Deq for each exchange surface are reported in Table 1.

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Table 3 Experimental values of the averaged maximum surface-to-bed heat transfer coefficient Ar

Glass beads

Silica sand Corundum Carborundum

980 2100 12,710 24,036 87,500 2459 30,733 4138 28,529 3229 24,563

hmf, W/m2 K 70 85 90 97 105 83 95 92 105 75 98

hmax, W/m2 K Sphere

Cone

Frustum of cone

Cylinder #1

Cylinder #2

Parallelepiped

360 ± 5 325 ± 7 260 ± 5 230 ± 7 190 ± 5 316 ± 5 240 ± 5 325 ± 5 239 ± 7 295 ± 8 244 ± 6

325 ± 6 330 ± 5 250 ± 4 240 ± 5 200 ± 4 320 ± 6 232 ± 7 302 ± 8 225 ± 9 294 ± 9 230 ± 5

327 ± 5 290 ± 6 250 ± 5 215 ± 7 170 ± 5 300 ± 8 220 ± 6 270 ± 10 218 ± 10 278 ± 7 215 ± 6

333 ± 3 300 ± 5 230 ± 6 190 ± 5 161 ± 6 284 ± 7 196 ± 6 230 ± 10 178 ± 8 278 ± 6 195 ± 6

266 ± 6 240 ± 4 200 ± 4 160 ± 6 140 ± 5 255 ± 8 155 ± 4 200 ± 6 160 ± 8 220 ± 7 150 ± 6

325 ± 4 320 ± 5 240 ± 6 210 ± 5 190 ± 5 300 ± 7 197 ± 6 250 ± 8 212 ± 8 282 ± 7 218 ± 7

The use of dimensionless numbers makes possible the direct comparison of surfaces with different sizes and shapes. Fig. 3 reports the value of the asymptotic Nusselt number in function of particle Archimedes number. The Nusselt number monotonically decreases with Archimedes number with a similar functional dependency for all the exchange surfaces. The effect of surface shape results in an almost constant vertical shift of each curve with maximum differences of the order of 100. Moreover, regardless the wide variation of this parameter, heat transfer coefficient is almost unaltered by particle thermal conductivities. This result has been described in Fig. 4 which reports the particle Biot number in function of particle thermal conductivity for four bed materials with similar average particle diameter (280–310 μm). The independence of heat transfer coefficient from particle thermal conductivity is assured by the inverse proportionality between Biot number and Kp, as observed in Fig. 4. This evidence can be ascribed to a gas resistance controlling mechanism, which leads to a limited interparticle heat exchange and, finally, to a negligible effect of particle thermal conductivity. 4. Discussion

bed material properties, global fluidisation conditions, pressure and temperature [25]. A classical interpretation [1,15], considers the amount of heat transfer due to the flow of interstitial gas and to the conduction mechanism between the solid and the gas phase as a whole. This is defined as “gas convective component” of heat transfer coefficient, hgc, and resumes all the features of the heat exchange through a fixed bed. Its order of magnitude is around the value of the heat transfer coefficient in minimum fluidisation condition, hmf [20]. Radiative contributions to heat transfer coefficient, usually denoted as hr occur at temperatures above 600 °C [15] both in fixed and fluidised states. In fluidised beds, two more heat transfer mechanisms take place due to the presence of gas voidages and to the motion of particles near the surface. The former mechanism is usually denoted as hb while the last is defined as “particle convective” component, hpc. According to this definition, the heat transfer coefficient, h, can be written as: h ¼ fb hb þ ð1  fb Þðhgc þ hpc Þ þ hr ;

ð2Þ

The four heat transfer coefficients are usually assumed to be independent.

The heat transfer rate between a fluidised bed and an immersed surface is a function of several parameters; first of all

Fig. 3. Surface Nusselt number in function of particle Archimedes number.

Fig. 4. Particle Biot number in function of the particle thermal conductivity.

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Usually the contribution to heat transfer due to the rising bubbles is insignificant and, at low temperatures, also the radiative one can be neglected [1,15,25]. Experimental results show that the heat transfer coefficient at minimum fluidisation velocity is almost independent on surface shape. On the contrary, it significantly varies for a fully bubbling fluidised bed (Table 3) where particle convective component prevails [1,15,26,22]. Particle convective heat transfer mechanism is strictly related to the particle motion field near the exchange surface whose properties are usually described by means of a particle residence time distribution [17–19] and a surface bed voidage [12,18,23]. As a general rule, the surface-to-bed heat transfer coefficient increases by decreasing the averaged particle-to-surface contact time and increasing the solid volume fraction near the exchange surface [15–18,21,27]. In bubbling and slugging regimes, the increase of fluidisation velocity generates a higher solid mixing which reduces the particle-to-surface contact time [15–18,21,27]. On the other hand, a corresponding increase of bubble fraction is observed, leading to a consequent decrease of solid volume fraction near the exchange surface [11,23,27]. As a consequence, there is usually an optimal gas velocity at which the heat transfer coefficient is the highest, as critically described by Molerus and Mattmann [22]. Experimental evidences [11,12,17–19,23] clearly pointed out that the arrangement of the fluidised particles near an immersed surface derives from the peculiar characteristics of the gas flow field in its proximity, following the general rule that the presence of shear rate (produced by the gas flow near the immersed surface) leads to a higher bed voidage due to the socalled Reynolds dilatancy [28]. Moreover, the particle-tosurface contact time decreases with the surface size [14,27]. X-ray images [23] and numerical simulations [12] highlight that the surface flow field appears like a jet of homogeneous fluid impacting against a surface. Experimental results show the existence of a layer of higher gas velocity and bed voidage in proximity of the lateral and the lower surfaces of the object (on which is eventually present a stagnation point). The extension of the gas layer increases with the vertical position of the surface [23] and may also give rise to the so-called indigenous bubbles [29], mainly depending on the surface geometry and the gas velocity. These features severely affect the intensity of solid mixing and the particle convection can be realistically considered the predominant mechanism for this fraction of the exchange surface. On the contrary, several authors [12,18,19,23] pointed out that the upper part of the surface usually present an almost defluidised region. The extension of this area mainly depends on the collapse of the gas layer on the lateral surface and to the following creation of vortexes and indigenous bubbles. At this moment a quantitative estimation of the properties of the defluidised region is not still available, but it is reasonable that the most important heat exchange mechanism for this area is the gas convective one. As a consequence, the bed structure near the exchange surface is not defined by global fluidisation regime only but

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depends on the peculiar, shape dependent, fluid dynamic field near the surface. This feature is at the basis of the observed shape dependence on the surface-to-bed heat transfer coefficient (Fig. 3). Furthermore, the lower solid fraction near the immersed surface [11,12,17,23] leads to a higher effect of the gas phase resistance on the wall-to-particle and the interparticle exchange mechanisms which determines the negligible effect of particle thermal conductivity on the heat transfer coefficient (Fig. 4). Several models have been developed in the past to evaluate the maximum value of heat transfer coefficient [14,21,30,31]. In particular, Prins et al. [14] analysed the heat transfer coefficient between a 103 μm FCC fluidised bed and spherical exchange surfaces of different size (6–30 mm). The authors proposed the following equation for the description of their experimental data: Nup;max ¼

 0:278 hmax dp D ¼ 4:175Arn dp Kg

ð3Þ

 0:128 D n ¼ 0:087 dp

ð4Þ

Eq. (3) shows that the heat transfer coefficient is inversely proportional to D/dp and directly proportional to Ar. In this model the characteristic surface length D, which for a sphere corresponds to the diameter, is compared to the particle diameter which is chosen as the characteristic length scale for the solid mixing. This model can not be directly extended to different bed material as well as to different shaped exchange surfaces. Experimental results reported in Fig. 3 shows that the maximum Nusselt number is a decreasing power law function of the Archimedes number with exponent between − 0.13 and − 0.15, while the surface shape gives rise to a vertical shift of the values of Numax. The dependence on Archimedes number seems to fully characterize the correlation between bed material properties and heat transfer coefficient. On the contrary, to describe the effect of surface shape an appropriate shape factor is required. A possible shape factor is represented by the ratio between the surface height and the equivalent diameter, H/Deq. This ratio is a geometric index of how slender is a surface and also represents the ratio between the characteristic length for heat transfer phenomena [32], H, which is directly proportional to the duration of particle-to-surface contact, and that of the fluid dynamic field, Deq, which addresses the particle mixing near the surface. Table 4 Parameter estimation for Eq. (5) Parameters

a

b

c

Mean value Standard error % Correlation factor R2 = 0.89

837.2 6.69

− 0.141 5.38

− 0.572 7.36

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for the different fluid dynamic field around the exchange surface. The shape factor is higher for slender surface for which a lower solid mixing occurs due to the reduced tendency to form indigenous bubbles. As a consequence, for higher values of H/Deq, longer particle-to-surface contact times are achieved and lower values of the heat transfer coefficient are consequently observed.

Fig. 5. Comparison of calculated heat transfer coefficient (Eq. (5)) with the experimental data.

Following this approach, the following equation is proposed to describe the experimental results:  c hmax Deq H b Numax ¼ ¼ aAr ð5Þ Deq Kg Regression analysis of experimental data (Table 3) with Eq. (5) has been carried out with the statistic software Sigma Plot V9.0 for Windows (SPSS Inc.). The values of the regression parameters and their standard errors have been reported in Table 4. The precision of data fitting is described by the correlation factor R2 which results equal to 0.89. The comparison between experimental results and model prediction is reported in Fig. 5 in terms of surface Nusselt number in function of Archimedes number, parametric with the shape factor. The model predicts an inverse proportionality between the maximum Nusselt number and the shape factor. Slender surfaces present a more stable surface gas layer [23,32] and a less tendency to form indigenous bubbles which induced an additional particle mixing. As a consequence, a lower particle mixing is obtained for slender surfaces respect to blunt or bluff ones. Accordingly, these surfaces show higher values of the average particle-to-surface contact times which determine the lower value of heat transfer coefficient.

Notation a model parameter b model parameter c model parameter cp specific heat (J/g K) dp particle diameter (μm) Deq probe characteristic dimension (m) fb bubble fraction within the bed g acceleration of gravity (9.81 m/s2) h heat transfer coefficient (W/m2 K) H vertical probe dimension (mm) K thermal conductivity (W/m K) L horizontal probe diameter or side length (mm) l horizontal lower diameter for frustum of cone probe (mm) μ dynamic viscosity (kg/m s) n parameter for Prins model Eq. (4) ν kinematic viscosity (m2/s) ρ density (kg/m3) U gas velocity (m/s) Dimensionless numbers Ar = ρg(ρp − ρg)dp3g/μ2, Archimedes number Nu = hDeq/Kg, surface Nusselt number Subscript b bubble eq equivalent g gas gc gas convective max averaged maximum mf minimum fluidisation p particle pc particle convective r radiative

5. Conclusions This paper deals with the surface-to-bed heat transfer with different shaped surfaces by varying bed material properties and fluidising gas velocity. Experimental results pointed out that the heat transfer coefficient is strongly influenced by surface shape with variations up to 40% while it is almost independent on particle thermal conductivity. Both the effects may be justified as a result of local perturbation of fluid dynamic field around the surface which consists in a layer of higher gas velocity and bed porosity on the lateral and lower surface of the object and an almost defluidised area on its upper surface. A simple dimensional model is able to describe all the experimental data by means of an appropriate shape factor, H/Deq, which accounts

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