Effects of Agitation on Gas Fluidization of Solids

ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT

Effects of Agitation on Gas T. M. REED, Ill',

AND

M. R. FENSKE

The Pennsylvania Sfofe University, Sfafe College, Pa.

G

AS film heat transfer coefficients ordinarily range from 1 to 10 B.t.u. per (hour) (square foot) ( " F,). In fluidized solid-

gas systems these coefficients may be raised to values approaching those attained in liquid films. Coefficients of 100 may easily be attained. Values as high as 300 have been reported (IS) for an industrial installation. The literature contains some data and several discussions on heat exchange between gases and fluidized granular solids (6) and between gases and extended surfaces immersed in fluidized beds in laboratory units (3, 6, 8, 11, 12). Some typical results (11) show that the fluidization of 1- and 4-inch-diameter beds of glass beads of uniform sizes ranging from 0.0016 inch (40 microns) t o 0.0178 inch (450 microns) in diameter by air flow alone produced heat transfer coefficients between the flowing gas and the vessel walls varying from 10 B.t.u. per (hour) (square foot) ( O F . ) with the larger particles and high air velocities to 120 B.t.u. per (hour) (square foot) ( O F . ) with the smallest particles and low air velocities. Superficial air velocities were in the range 2 to 13 feet per second. These data indicate that the coefficient is inversely proportional to the 0.7 or 0.8 power of the particle diameter. Coefficients as high as 200 B.t.u. per (hour) (square foot) ( O F.) have been obtained (12) between fluidized beds of silicone carbide and vessel walls. The gas in this case was helium and the particles were 120 microns in diameter. The gas flow rate was 0.15 foot per second superficial velocity. Particle conductivity is practically of no significance in determining the rate of heat transfer between gases and extended surfaces in fluidized beds ( 3 ) . The fluidizing action of mechanical stirrers has been utilized to aid in handling particulate solids in various processes. Oscillating] rotating] and impeller-type agitators have been used to blend various solid components in cement manufacturing (8, 7 , 14-16). Rotating stirrers have been used in laboratory cracking catalyst activity evaluation ( 1 ) . A patent (18) has been issued revealing the use of vibrators immersed in beds of solids as an aid in fluidization a t low gas rates. The studies discussed in this paper show that agitation can be used to advantage to increase the rate of heat transfer between air and extended surfaces in contact with fluidized beds in a small scale rectangular vessel. Such devices may be of value in heat transfer in large scale apparatus where restrictions on gas flow rates limit the condition in beds of granular solids. Aerated bed i s agitated by specially designed oscillating stirring elements

The apparatus used for heat and temperature measurements in aerated, agitated beds of granular solids is shown in Figure 1. The apparatus was in the form of a box of rectangular cross section, 10.75 x 4 inches inside. The height of the test chamber 1

Present address, University of Florida, Gainesville, Fla.

February 1955

was 31 inches. A section, not shown on Figure 1, 3 feet long of larger cross section was provided above the test chamber to reduce solids entrainment. The two opposite walls of the t e a t chamber, 10.75 inches long by 31 inches high, were made of 0.25inch steel, while the other two wallsi 4 inches long by 31 inches high, were made of 0.375-inch Transite. Thermocouple wells were bored horizontally to varioua locations in the heated and cooled walls. Copper-constantan thermocouple junctions were peened flush with the inside surfaces of the walls through small holes drilled into the walls.

RANSITE WALL

U

HEATING

ELEMEkTS

.75" SQUARE

SHAFT ABOVE T H I S P O I N T

GAS

DISTRl0UTOR

B E A R I N G G A S PURGE

4-

OSCILLATING ROTATING

SHAFT

CAM

SIDE E L E V A T I O N - S E C T I O N A-A

Figure 1. Test chamber One of the end Transite walls had a 1 X 15 inch plate glass window. The opposite end Transite wall carried nine thermocouple probes for examining the temperature pattern in the unit. Five thermocouples were in a vertical plane midway between the heated wall and cooled wall. Four thermocouples were 0.8 inch apart in a horizontal plane midway between the top and bottom ends of the heated and cooled length. Each thermocouple was adjustable and could be located at any distance along a line between the middle regions of the unit and the Transite wall. The box rested upon a bottom assembly. Stirring in an upand-down direction was imparted to beds of particulate solids

INDUSTRIAL AND ENGINEERING CHEMISTRY

275

ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT contained in the unit through a vertical shaft which was connected to a rotary eccentric cam located beneath the unit. The eccentric @am was operated by a hydraulic motor. The designs of the stirring elements used in these experiments are shown in Figures 2 and 3. 8-MES? SCREEN

Figure 2.

Screen plate agitator element

of sizes, the size was given as all passing through a certain mesh screen and all retained on a certain smaller mesh screen. The average of these two mesh sizes was taken as the particle diameter. The free fall velocity in air for the individual particle in each case was calculated according to well-known methods ( 4 ) . The values for the minimum air velocity for fluidization were calculated by an equation of Miller and Logainuk ( I d ) . This equation is valid only in the streamline region where the Reynolds number, based on the individual particle diameter, is less than 10 and the particle diameter is greater than about 20 to 40 microns. Consequently, the fluidization velocity calculated for particles smaller than this (where agglomeration is influential) and for the larger materials, where the Reynolds number may exceed 10, is no doubt incorrect and too low.

8-mesh screen

Agitation increases resistance to bed of solids

gas flow through

Figure 3.

Perforated aluminum plate agitator element 0.25-inch plate

The construction of one of the hollow plates used to measure heat transfer rates between the gas floxving through fluidized beds of solids and extended oscillating surfaces in contact with the beds is shown in Figure 4. A second hollow element was similar to the one shon-n, but it did not have the eight 1-inch holes cut in the surfaces. The second hollow plate had plane surfaces with no holes. Both units were made of brass. In each case the cavity through which mater or air flowed as coolant was 0.125 inch thick. Thermocouples were also located in the fluid streams entering and leaving the plate. The effective heat transfer areas of these plates used in calculating the coefficients between the plate surface and the gas floving through the beds of granular solid in contact Rith the plate included only the large area sides of the plate. The stirring elements mere mounted in the heat transfer unit on the vertical square shaft extending up the center of the unit. These plates were spaced by means of pieces of square tubing fitting over the square shaft. Materials. The particulate materials used in the experimental work, together with their physical properties and size parameters. are given in Table I. The particle size parameter taken as that representing the size of the granules was the number arithmetic average diameter. For the smaller sized materials the distribution was obtained by measuring the size of about 200 particles under the microscope. For the larger particles containing a range

Table 1.

The agitation of the oscillating or vibrating plates was observed to have an interesting series of effects on the resistance to gas flow through the beds of solids. In general, the agitation by the particular stirrers used in these experiments increased the pressure drop over that found in the unstirred beds. This is particularly true a t the lower gas velocities. At the higher velocities this increase in pressure drop arising from agitation is usually not measurable. Figure 5 shows that vibration produces the fluidized state where gas flow alone is insufficient. This plot shows the simultaneous changes that occur in the bed height and the pressure drop for flow of air through a bed of the carbon powder, material 5, as COOLANT IN OUT

I N t SECTION B-8

A

-. f

1"DIA.

E

3

SECTION

Figure

4.

A-A

Hollow brass plate heat transfer element

Particulate Materials

Heat Particle Heat Conductivity, Particle Size P a r a m ? ? ? ? Capacity D a y . b, ( 2 0 3 to 1000 C ) B.t.u./(Hr.) Density, Dy Material NO. Material CaI./(G.)(O C.) ' (Sq.Ft.)(O F./Ft.) G./Cc. micrdns rgQ m~crons 56 2.28 40 1.45 0.19; 0.27 DA-1 compound 2 4.3 .. 1.0 0.03 0.18 Carbon powder 5 26 1:91 21 8.9 33 0.12 Nickel powder 6 63 1.58 57 1.45 0.19d 0.23 SA Microspheres 41 1.41 38 1.45 0.19d 0.23 Microspheres 8B 3.9 2.4 2.3 8.2 220 0.094 Copper powder 10 .. 550 .. 1.0 0.03e 0.30 Carbon granules 11 7.8 880 . . .. 25 0.12 Steel wire shot 12 38 .. 11.3 .. 20 0.034 Lead uowder 13 a Ratio of diameter, Do,below which 50% of particles lie t o diameter below which 15.9% of particles lie. b Arithmetic average diameter. 4 At looo C. and 1 atmosphere pressure. d Value for sand. * Value for charcoal.

276

ql6" B R A S S ?MET

Shape Irregular

Irregular Spherical Spherical Irregular Irregular Cylinders Irregular


Free Fall Velocity in Air0 Ft./Seo: 0.11 0.00086 0.25 0.24 0.10 0.005 19 24 0.7

Minimum Air Velocity for Fluidizationc, Ft./Scc. 0.003 0,000002 0.005 0.006 0,002 0.0001 0.3 5.4 0.014

Vol. 4'2, No. 2

ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT the vibration frequency of horizontal 8-mesh screen elements is changed. The air flow was 0.05-foot-per-second superficial velocity, and the vibration stroke was 0.313 inch. A constant total mass of 2400 g r a m was present in the bed. Both pressure drop and bed height increase from low values at zero frequency t o the flat maximum between 800 and 1200 cycles per minute. The premure drop a t this maximum is equal t o 2300 grams of solid, approximately the true mass in the bed. Once the fluidized condition has been attained in beds of carbon powder, the pressure drop is essentially independent of gas flow rate and vibration frequency. 35

a e w

I U

30

2.5

Table J I presents some average temperature gradients obtained in an aerated agitated bed of the nickel powder material. In these particular observations the thermocouples were located 4.3 inches from one of the end Transite walls of the apparatus. If the bed were a solid block of nickel, a temperature gradient of about 3" C. per om. would be required to move 0.35 t o 0.4calorie per (second) (square cm.), which is the heat flux obtained a t the cooled wall in these runs. Since the net direction of heat flow is horizontal, it is to be expected that horizontal gradients should be higher than the vertical gradients. I n addition, the two mixing influences] the air flow and the agitation, are in the vertical direction, so that there is no dircct effect in the horizontal dircct ion.

5 0

Figure 5. Effect of mechanical stirring on pressure drop and bed height of carbon powder

The carbon powder is a particularly difficult material to fluidize by gas flow alone. Mechanical agitation imparted by stirring the bed or by shaking the vessel holding the particles is necessary to counteract the tenacity with which such small particles cling together in large aggregates. The stirring action disperses the gas throughout the interstice causing the bed t o expand and become very fluid even a t very low gas rates of 0.01-foot-per-second superficial air velocity. The expansion of the bed caused by oscillating screens is apparent in Figure 5. The high air velocities required to supply this agitation are beyond the maximum velocity at which a dense fluidized bed of the light carbon particles can exist. Under various conditions, beds of these small carbon particles may expand under the influence of the mechanical stirring as much as 30% or t o 1.3 times the volume occupied by the bed a t a given air rate without the agitation. Heavier materials, such as the nickel powder, material 6, may be expanded by the stirring action to about 1.1 times the volume without mechanical stirring. On the other hand, the pressure drop in beds of the nickel powder is profoundly influenced by the agitation, as shown in Figure 6. The results of Figure 6 were measured using an agitator composed of plates shown in Figure 3 spaced 0.5 inch apart on the vertical oscillator shaft. The plane of each plate was perpendicular to the shaft. Similar results were obtained with the screen plate elements of Figure 2. At low air flow rates from 0.2- to about 0.6-foot-per-second superficial velocity the agitation increases the pressure drop not only to that value corresponding t o the total weight of solid in the bed, but to values ranging up to 1.4 times that required to support the fluidized bed. This behavior may indicate unusual friction in flow around each individual particle. It may also be interpreted as the result of channeling of the gas stream into streams of effective total cross section less than that prevailing in the entire bed without the agitation, or as an indication of slugging tendencies (9). A similar abnormally high pressure drop behavior was observed with the microsphere particles, material SA. Since the pressure drop in the beds of the small particles never was observed t o exceed the suspended weight of the material, the abnormally high pressure drop behavior may be characteristic of massive particles.

February 1955

Vertical and horizontal temperature gradients are higher in plate-obstructed beds

Table II.

Temperature Gradients in Aerated and Agitated Bed of Nickel Powder

[Agitating element 8-mesh #screenplates (Figure 2) spaced 0.5 inch apart on cisciliated shaft. Oscillation stroke, 0.313 inch] Av. Temperature Gradient C./Cm,, a t Frequency of Oscillation, bycles/Min. 0 600 1000 1500 Hor- Verti- Hor- VertiAir Flow, Hor- VertiHor- Vertiisontal c a l izontal cal izontal cal ieontsl cal Ft./Sec. 0.2 1.8 1.3 0.9 0.39 1.1 0.06 0.3 2.2 0.78 2.4 0:ZQ 0.9 0.40 1.6 0.23 0.4 1.9 0.48 1.8 0.15 1.1 0.23 2.8 0.12 0.6 1.5 0.21 0.7 0.10 0.6 0.19 0.2 0.13 0.7 1.0 0.08 0.7 0.15 1.7 0.16

..

/ 4

0

(Of1

0.e

40

AIR FLOW,

Figure 6.

1

80

4

[

0.70 [FT,/JEC. I

120

..

I 160

/HR.X SQ CM.

Pressure drop in aerated agitated bed of nickel powder

Vertical gradients in beds unobstructed by the horizontal plate elements are very low compared t o those in beds segmented by the plates. The horizontal gradients are also smaller in unobstructed fluidized beds. Figures 7A, B, and C show vertical and horizontal temperature traverses when the total heat input was at the bottom section of the hot wall (lower 6 inches of bed), and the only section cooled on the cold wall was the top 6 inches. The total bed height wai about 20 inches. The heat input in this case and in that of Figure 8 was 1000 watts. Each figure shows a series of four traverses, each of which was taken a t a different distance] in centimeters, into the bed from the Transite end wall. The temperatures in parentheses are the wall temperatures. As the vertical temperature gradient decreases from around 0.3' t o about 0.1' C. per cm., the horizontal gradients decreased from around 0.3" to about 0.2' C. per cm.


277

ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT HORI Z O N T A L

VERTICAL TRAVERSES

TRAVERSES A. N O AGII T A T ION

a0 75

70 65

60 .55

Y. ~

6

8. 1000 CYCLE

5

d

60 U

2n 55

COOLED

HEATED

I 50 c 80 8 01

1

,

I

C . 1500 C Y C L E S / M I N . l I ! ,

I

I

I

I

75 f0

1 I I I I 1 2

"0

4

8

6

0

CM FROM C O L D W A L L

Figure

7.

,b

IrHEATED

IO

COOLED

IO '40 CM,FROM FLOOR

'

Temperatures in aerated agitated bed of nickel powder

Bottom section heated, top section cooled kpertlcial air flow = 0.2 ft./sec. Agitator stroke = 0.31 3 inch

VERTICAL

HORIZONTAL TRAVERSES A

TR AV E R S E S NO

AGI T A T I O N

Accompanying these decreases in temperature gradients there is a shift in the relative positions of the traverses for each distance into the bed. It is probable that the reversal of the relative positions of the traverses of Figure 7 with increase in f r e quency occurs because the bulk of the air stream changes path with frequency. At zero vibration it appears that the bulk of the air is flowing up the central portions of the bed. (Uniform gradients exist a t the center traverses.) At 1500-cycles-perminute vibration frequency the bulk of the air flows up the outer portions of the bed near the walls. (Uniform gmclienth and higher temperatures in the traverses exist a t points closer t o the end wall.) Temperature gradients obtained when the heat is applied at the top section and extracted at the bottom section of the bed are shown in Figure 8. Much steeper vertical gradients are obtained with the source of heat a t the top of the bed rather than a t the bottom a t zero vibration. The steeper gradient9 correspond to the net heat flow in a direction opposite to the air flow. It appears, however, that a more uniform distribution of heat in the horizontal plane is obtained when the source of hest is at the top of the bed rather than a t the bottom. In the counter directional flow of heat and air, the heat is more uniformly mixed with the solid by the time it reaches the middle of the bed (between the top and bottom) than when the heat and air flow in the same direction. The application of vibration ai 1000 cycles per minute (Figures 7 B and 8 R ) eliminates these differences in gradient magnitudes. Some typical traverses found 2.3 incher in from the Transit(. wall in beds of the 20-gage steel wire shot heated by a stationary vertical wall and cooled by an oscillating vertical plane area in the form of the hollow plate of Figure 4 are plotted in Figure 9 The horizontal traverses on one side of the cooled plate f,uther from the heated wall are continuations of the temperature leveb on tho other side closer to the heat source, even though the cold plate is a t 20' to 25" C. and the bed temperatures are around 60" to 70" C. Shading on Figure 9 is the cooled plate location A very uniform temperature may be maintained in beds of such la1 ge particles as the 880-micron-diameter steel particle6 by the high gas flow rate of 7 5 feet per second, as shown in Figure 9. The vibration stirring has some smoothing influence on the vertical gradient a t 3.8 feet per second in Figure 9. If the air rate is reduced t o 1.6 feet per second and 50% t ) ~ weight of lead powder, 38 microns average particle diameter, is added to the steel shot, a fluidized bed of very uniform temprrature is obtained even without mechanical stirring.

VERT IC A L TRAVERSES

HORIZONTAL TRAVERSES

A . 3.8 I:

80

-

70 V'

60 n

W

5

c 0

75

50

1000 CI'CL- E S / M I N 4

8. 7.5 FT./SEC.

w a 70

70

0.

2 60

w

65

I-

50 0

2 4 6 8 1 CM. FROM C O L D W A L L

0

0

10

20

40 C M . FROM FLOOR

30

40

2 4 6 8 IO C M . FROM U N H E A T E D W A L L

0

Figure 8.

Temperatures in aerated agitated bed of nickel powder Top section heated, bottom section cooled Superficial air flow = 0.1 9 ft./sec. Agitator stroke = 0.31 3 inch

Figure

9.

0

IO 20 30 4 0 CM. FROM FLOOR

Temperatures in aerated agitated bed of steel wire shot Agitator stroke = 0.31 3 inch


Vol. 41, No. 2

ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT The carbon powder, material 5, so difficult t o fluidize without agitation, shows high horizontal temperature gradients on the order of 2" to 3" C. per cm. and vertical gradients of 1' to 2' C. per cm. in the unagitated obstructed beds. With the application of agitation, a t frequencies above 400 cycles per minute and a stroke of 0.313 inch, by means of the perforated plates spaced 2 inches apart these gradients are reduced essentially to zero throughout the bed of carbon powder. Heat transfer to stationary vertical wall i s improved by baffling

In the cases of heat transfer to the stationary wall the heat picked up by the cooled sections per unit wall area was essentially the same for each section. The effects of various types of baffle arrangements and bed Agitation on the wall heat transfer coefficients with nickel powder in the apparatus are shown in Figure 10. Curve 1 for the completely unbaffled or unobstructed bed shows the poorest coefficient, although the temperature uniformity throughout was found to be excellent. Curve 2 for the horizontal stationary perforated plates shows the best coefficient improvement with increase in air rate. A coefficient of 90 is obtained a t 0.7 foot per second. This arrangement probably gives the gas a horizontal component directed toward the walls and causes the bulk of the gas to flow up through the bed in the immediate region of the wall. When these plates are oscillated a t 1000 and 1500 cycles per minute (curves 3 and 4 ) the coefficient becomes less dependent upon the gas rate. The maximum coefficient under these conditions is 70 B.t.u. per [hour)[square foot)(" F.). When horizontal wall baffles 0.5 inch wide, lying in a plane perpendicular t o and up against the wall and spaced 2 inches

j I

0

LUPERFICIM

t i '

03

2

20

40 A I R FLOW,

AiR

VELOClTl,

II/SCc 0.05

0 55

0.

c.

/HR

60

00

x sa.^^.

100

10

I20

apart vertically, are placed along the wall, thc coefficient follows curve 5. At higher air rates, above 0.2 foot per second, these baffles improve the heat transfer over that obtained in the unbaffled bed, curve 1. At 0.2 foot per second the wall baffles decrease the coefficient. Small horizontal perforated plates, similar to those of Figure 3, inserted between the wall baffles and attached to the vibrator shaft produce the results shown in curves 6, 7, and 8 for zero, 1000-, and 1500-cycles-per-minute vibration frequency, respectively. Except a t 0.2 foot per second these plates are of no value in improving the Coefficient unless they are vibrated. Even a t 1500 cycles per minute these plates cannot improve the heat transfer to the extent which the larger plates are able a t the lower air flow rates. It appears as though the agitator should extend throughout most of the bed cross section to be of maximum benefit.

0 , L - I

' 500 '

'

"

1000

'ABRASION FREQUENCY,

1500 CYCLES/MIN

2000

Figure 1 1 . Effects of air flow rate and vibration frequency on heat transfer to plane surface oscillating parallel to direction of air flow

The 8-mesh screen elements of Figure 2 spaced 2 inches apart on the vibrator shaft produced essentially the same effects, qualitatively and quantitatively, on the heat transfer coefficient a t the cold wall as those produced by the perforated plate elements of Figure 3 spaced 0.5 inch apart. Heat transfer a t the cooled wall in contact with fluidized bed6 of the carbon powder way poor. Coefficients ranged from about 1 to 40 B.t.u. per (hour)(square foot)(' F.) when air passed through a t superficial velocities from 0.05 t o 0.3 foot per second. The stirring action of the 8-mesh screens spaced 2 inches apart oscillating a t 2000 cycles per minute over a stroke length of 0.313 inch raised this coefficient from a value of 1 to a value of about 15 B.t.u. per (hour)(square foot). At the higher air rates the agitation decreased the coefficient by as much as 50% of the values obtained without the mechanical stirring action. I n the case of larger particles, such as the microsphere catalysts, the agitation was found to improve the heat transfer a t the cooled wall a t the higher gas rates [around 0.2 foot per second) as well as a t the lower gas rates (around 0.04 foot per second).

Figure 10. Effect of baffling and agitation on heat transfer between vertical cold wall and heated beds of nickel powder

Motion of heat transfer surface increases heat transfer coefficient

1 . Unbatfled and unagitated 2. Baffled with perforated plates 3. Agitated, 1000 cycles/min., perforated plates 4. Agitated, 1500 cycler/min., perforated plater 5. W a l l baffles, 0.5 inch, 2 inches apart 6. W a l l baffles, 0.5 inch and 2.25 X 8.25 inch perforated plates, 0 cyctes/min. 7 . W a l l baffles, 0.5 inch and 2.25 X 8.25 inch perforated plater, 1000 cycles/rnin. 8. W a l l baffler, 0.5 inch and 2.25 X 8.25 inch perforated plates, 1500 cycles/min.

In an effort to attain the maximum heat transfer at a surface in a fluidized bed a t low gas flow rates the cooled hollow plates were attached to the oscillated shaft in the rectangular box apparatus in the manner of the agitator plates. By means of an adapter these plates were also mounted on the shaft with the large areas parallel to the gas flow direction. In these runs horizontal plates of the type shown in Figure 3 were also present on the shaft, By motion of the extended surface of the hollow plates relative to the granular material and to the gas phase a greater disturb-

February 1955


279


w

5 BO [L

,ul" 6 0 3 8 FT/SLC(.)

CAREON

20

--0

550 N I C R O N S

GRANULES,

0 17

I 500 VI0RArlON

n/

5LC

I

I

low

1500

FREOUENCY,

CYCLES/

2000

250C

MIN

Figure 12. Effect of air flow rate on heat transfer coefficient vs. vibration frequency curve

iiiwsimum is only 120. At the lower gas velocity the iiiereasc, 1)ngins practically with the beginning of the plate motion, while at the higher gas velocities the oscillation is not effective until frequencies around 400 cycles per minute are attained. At 1.0 and 1.2 feet per second the coefficient increases to a niaxiniuni at which the curves are flat. At 1.0 foot per second there i h indicated a slight decrease in coefficient above a frequency of 1900 cycles per minute. K i t h the lead powder the vibration is not as effective, at least i n the range of frequencies below 1500 cycles per minute that were studied. The maximum coefficient obtained with the lead POLYder is only 70 B.t.u. per (hour)(square foot)(" F.) at l.O-foot,per-second superficial air velocity. A further increase at frequencies above 1500 cycles per minute is indicated by the data. At high gas rates the estra velocity of the plate cannot increase the relative velocity hetween the gas and t.he plate surface, while at low gas rates the relative velocity is increased by the oscillation. Where the velocity of the gas is always greater than that of the plate, the oscillation mill have little or no effect on the heat transfer coefficient. Thus, the coefficient with the large steel shot is not improved by the vibration since gas velocities of 4 to 7 feet per second are far above the range of 0.1 to 1 foot per second for the averagc velocity of t,he plate motion. Figure 12 also illustrat,es that the lower maximum coefficients are obtained with beds of solids of the larger particle size. Figure 13 shows data obtained wit8hhollow element of Figure 4 i n the horizontal positioii using granular materials of average particle diameter below 100 microns. The coefficients with the plate in this position are only slightly better than when the plate i, in the vertical position. At the 0.0625-inch stroke of Fizure 138, the coefficient in nickel powder (curves 6 and 7) and i n t h e carbon powder at lower gas rates (curves 1 and 2) is greatly improved by the oscillation of the heat transfer surface. The larger particles of DA-1 compounds do not show such rapid increase with frequency (curves 4 and 5 ) . At the higher air rate of 0.2 foot per second in the carbon povder (curve 3), t.he motion of the plate is also not as effective as at the lower air flow rates of 0.07 and 0.02 foot per second. At the larger stroke of 0.313 inch (Figure 13B) the coefficient increases rapidly with frequency of oscillation under all these eontlit'ions. The difference in the range of values of the coefficient obtained between nickel powder and tho other solids arises from differences in particle size and particle density. Studies previously reported in the literature demonstrated that the heat transfer coefficient increases with decrcaeing particle size. This is true for paiticles above about 20 microns in diameter. When the diameter is below this valuc the particles no longer behave as individuals

ance may be generated in the gas film on the surface at low gas rates than by the gas flow alone. Figure 11shows that the oscillating motion of the hollow element without holes oriented and vibrating with the extended surface parallel to the gas flow has a slight enhancing effect on the heat exchange rate between the gas stream and the cooled element even without granular material in the unit. Gas ve1oeit.y also has an effect. The effects of oscillation frequency a t 0.313-inch st,rolreand of superficial air velocity in various fluidized beds are illustrated in Figure 12 for the hollow elements arranged parallel to the gas flow. Data from the two plates check. Nickel poxder is represented in Figure 12-4, lead powder in 12B, steel shot in 12C, and carbon granules in 120. These materials are. of 26-, 35-, 880-, and 550-micron average particle diameter, respectively. 4 t zero frequency of oscillation, the coefficients obtained w i t h the nickel powder are essentially those previously obtained at the cold wall of the rectangular A , V l B R A T I O N STROKE = 0.0625 IN. a \/:BRATION STROKE c 0.3'3 IN. box without the stirring influence operating. It is apparent from the plots of Figure 12 that a t gas rates at and below about 1 foot per second the motion of the plate is effective in enhanc160 ing the coefficient between the gas and the exI40 tended plate surface. This is true to a pronounced extent for the nickel powder particles, I20 somewhat less for the lead powder, and still less 100 for the large carbon granules. A t the high gas rates of 3.8 and 7.5 feet per second used to 80 fluidize the steel shot the motion of the plate BO has essentially no effect on the coeflicient. The increase in coefficient with vibration is less at 40 high air rates than at low ones. 20 At 0.2 foot per second wit8h nickel powder 0 the coefficient is raised from 60 with no vibra1000 2000 3000 4000 0 1000 20W 3000 4000 tion t o 100 B.t.u. per (hour)(sqiiare foot)(' F.) VIBRATION FREQUENCY, C Y C L E S / MIN. a t 800 to 2000 cycles per minute. At 1.0 foot per second the increase is from 100 to 130. At Figure' 13. Heat transfer coefficients between vibrated plate and beds of fluidized solids the higher velocity of 1.2 feet per second the 280


Vol. 47, No. 2


e

but appear t o be agglomerated into particles of much larger effective size. Particle conductivity is certainly not an important factor determining the heat exchange rate, since the nickel powder (curves 5 and 6) and the copper powder (curve 7 of Figure 12B) give essentially the same maximum coefficients of 150 B.t.u. per (hour)(square foot)( " F.) although nickel has a conductivity of 33 and copper of 220 B.t.u. per (hour)(square foot)(' F. per foot) A comparison of coefficients obtained with the large particles of the steel wire shot of average diameter 880 microns (Figure 12C) and the carbon, material 11, af average diameter 550 microns (Figure 1 2 0 ) also indicates that particle properties other than size and density are of little significance in governing the rate of heat transfer provided the bed is fluidized. Except for differences easily attributed to the gas velocity and t o particle density, these materials produce essentially the same coefficient although they differ considerably in particle heat capacity and conductivity. A calculation of the temperature change experienced by the mass of material contacting the oscillating plates from the heat transfer rate and the heat capacity of the materials involved shows that the amount of heat carried by the particle is not a limiting or controlling factor. The temperature change experienced on the average by a hot particle per contact with the cold surface is around 0.01" to 0.1" C. The mass of solid contacting the plate per unit time may be calculated in these experiments from the volume swept out by the plate in the horizontal position per unit time and the measured bed density or solids concentration.

plate region appreciably lower than the average in the bed. At such a large stroke value and at the higher frequencies the plate probably sweeps out 8 volume sufficiently large and sufficiently rapidly so that the particles do not immediately fill a space left by the motion of the plate.

:.I 9 160

-Vl6RATION

2

t

I

0.2 1.0

STROKE, INCH

OPEN SYMBOLS H W - S H A D E D SYMBOLS 0.125 FULL-SHADED SYMBOLS 0.313

40

I

5 0 1

'

loo '

'

200 1

'

'

MO

'

'

400

'

I

500 J

FREQUENCY X STROKE PRODUCT. INCHES/MIN '

Figure 15. Heat transfer between vibrated plate and beds of aerated nickel powder as function of frequency-stroke product

Effective gas velocity at heat transfer surface in fluidized bed i s limiting gas velocity

At 1.0 foot per second the points for all strokes fall on one curve. This curve is shown as a dashed line in Figure 15 and For all practical purposes the velocity of the surface oscilis distinct from those obtained at 0.2-foot-per-second air flow. Nevertheless, the coefficients obtained at 1.0-foot-per-second lated in the manner of these experiments is the average for a sine wave velocity, 2FL, where F is the oscillation frequency and superficial air velocity are not far different from those obtained L is the oscillation stroke length equal to twice the sine wave amat 0.2 foot per second. One explanation of this behavior is obviously t o be found in heterogeneous gas flow distribution. plitude. Figure 14 shows the various lines obtained a t several stroke It may be assumed that the relative velocity between the plate lengths when the coefficient is plotted against oscillation freand the air stream is the velocity variable determining the rate quency for one of the hollow elements oriented perpendicular to of heat transfer. For two reasons this relative velocity may not the air flow in beds of nickel powder. These lines are brought be the total superficial velocity measured in these experiments. more or less together when the frequericy-stroke product, FL, is From mass transfer data McCune and Wilhelm (IO)concluded used as abscissa, as in Figure 15. Two superficial air velocities that the particles in a fluidized bed occupy, on the average, regions are represented4.2 and 1.0 foot per second. The data a t 0.2 of low velocity. Perhaps the particles tend to remain in regions foot per second and the two stroke lengths, 0.0625 a s d 0.125 or to produce zones where the actual linear gas velocity is apinch, are coincident on the F L product plot. The 0.313-inch proximately the free fall v locity of the particles. This actual stroke line a t this air rate falls below the curve obtained a t the gas velocity around the particles will be termed the "effective" lower strokes. This may be attributed to a bed density a t the gas velocity. If it is assumed that this effective gas velocity is the gas velocity at the oscillating plate, the relative velocity between plate and gas must include the velocity of motion of the plite $180 x It may be shown ( 1 7 ) that when the maximum Cleo oscillator velocity, TFL, is less than or equal to 5:A40 the effective gas velocity-Le., the gas velocity d a t the plate-the relative velocity between gas . . 1$ and plate surface is the effective gas velocity G- 100 value alone. U7hen the maximum oscillator velocity, aFL, is greater than the effective gas $80 VIBRATION STROKE, INCH velocity, the relative velocity is the average k OPEN SYM6OL s" 60 HALF.SHADED SYMBOL 0.125 oscillator velocity, 2FL. I n the follo~ring disFULL-WADED SYMBOL 0.313 cussion it is shown that the maximum agitator A I R FLOW, FT / SEC. velocity must be greater than the effective gas ii40 CALLY BECOMES EFFECTIVE 0 2 20 FT/SEC AIR FLOW. velocity in order that the plate motion influence 5 0 the heat transfer. I O 500 1000 1500 2000 2500 3WO 3500 In Figure 14 the curves for each of the three V I B R A T I O N FREQULNCY, CYCLES/ M I N stroke lengths a t 0.2-foobper-second superficial Figure 14. Heat transfer between vibrated plate and beds of air velocity begin to rise above the heat transfer aerated nickel powder as function of frequency and stroke of vibration coefficient of 50 B.t.u. per (hour)(square foot)February 1955


281

ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT ( " F.) a t the frequencies of oscillation tabulated as observed values of Table 111. The theoretical minimum frequencies

U/TL(in which u is the effective gas velocity) where the oscillation should begin to effect the relat,ive velocity, are listed as theoretical frequencies. The value of u is taken as 0.2 foot per second. Apparently 0.2 foot, per second is essent,iallp the effective gas velocity.

Table 111.

Observed and Theoretical Minimum Vibration Frequencies

Stroke, dnch

47.0625

Q. 125

0.313

Min. Effective Vibration Frequency, Cycles/Min. Observed Tlieoretical Air Flow, 0.2 Ft./Sec. >60 734 350 366 150

1413

Air k'low, 1.0 Ft./Sec. 0.0628 0.125 0.313

600 450

36fiO

1830 730

0.125-inch stroke is probably not the maximum that could be attained under other conditions with respect to particle size and density. The curves for the carbon powder at 0.02 and 0.07 foot per second (Figure 13) as well as that for nickel powder a t 0.042 foot per second (Figure 12) show no trend to leveling off even though 1-hecoefficients attained at these air rates with oscillation of the heat transfer surface were 100 B.t.u. per (hour)(square foot)( F.). Even the larger particles of microspheres (Figure 13B, curve 4) and DA-1 compound, rurve 3, were able t,o produce coefficients of 100 to 120 a t 2000 cycles per minut,r and 0.313-inch stroke a t air rates of 0.2 foot per second. The existence of an effective gas velocity a t the moving heat transfer surfaces which is on the order of the free fall velocity of the fluidized particles a t both 0.2 and 1.0 foot per second total air flow indicates that, in ordinary fluidized beds where t>hetransfer surface is stationary, the limiting gas velocity is this effective gas velocity. The extra gas flowing as bubbles through the bed a t higher total rates may raise the coeficieiit. somewhat above the value attained when t,he total rate is equal to the effective velocity. Acknowledgment

By assuming that u equalb 1.0 foot per second when the total superficial velocity is I .O foot per second, the corresponding data from Figure 14 show that the frequency of initial influence of the oscillation is far below that expected for this total superficial velocity. In fact, the effective gas velocity is about 0.2 foot per second a t this higher total air flow rate also. The value 0.2 foot per year is about equal to the free fall vclocity of 0.25 foot per second for the average nickel particle The total superficial of 0.2 foot per second corrected for the volume occupied by the particles is about 0.3 foot per second This value is then, according t o the suggestion of McCune and Rilhelm, equal to the effective gas velocity a t all total gas rates greater than this in all regions of the bed wheie partioles are concentrated. Conclusions

The effect of rnechanioal agitation on the pressure drop through beds of solids fluidized by air show that immersed stirrers can improve the fluidization throughout the volume of a vessel of rectangular cross section. The heat transfer data from the hollow moving plates show, by coincidence a t high oscillation frequency values a t different air rates, that the total air flow may be eliminated as the limit. ing factor in attaining higher heat transfer coefficients. The fact that particles composed of materials so vaiied as nickel, copper, carbon, and siIica-alumina may give heat transfer coefficients approaching one another in magnitucie is indioative that the governing effects are external to the particles when the diameter and density are fixed. The upper limit of 170 B.t.u. per(hour)(square foot)(' F.) obtainrd with thr nickel powder at

282

R. A . Husk and R-. L. Brouse of the Petroleum IlrfiIiirlg Laboratory constructed and improved on the designs of the apparatus used in this xork. I n obtaining and interpreting the experimeiital results the assistance of R. H. Criswell has been invaluable. Literafure Cited

(I) Beck, It. A , , INL).EKG.CHESI.,41, 1242 (1949). (2) Brady, E. J. (to United Gay Improvement Co., Phila., Pa,), I,:. S . P a t e n t 1,731,223 (Oct,. S, 1929). (3) Campbell. .J. It., and Rumford, F., J . SOC.Cherrr. fnd. ( I ; ( J ? L ~ o ~ ) , 69, 373 (1050). (4) Chemical Engineers Handbook (J. t i . Perry, editor), XIcGrawHill Book Co., h-ew York, 1941. (5) Gamuon, B. W., Chem. Eng. Progr., 47, 19 (1951). ( 6 ) Kettenring, K. N., Ihid.. 46, 139 (1950). (7) Lepersonne, AI., and Hastert, E. (to iSoci(.t(. Anonyme des cimeiits Luxembourgrois, Luxemburg), U. 9 . P a t e n t 1,806,068 ( M a y 19. 1931). (8) Leva, 51.,and coworkers, Chrni. Enu. Prugr., 45, 563 (1049). (9) Lewis, W. K., Gilliland, E. R.. and Bailer, W. C., IN). ENR. c:HEhi., 41, 1104 (1949). (10) hlcCune, L. K., and Wilhelm. It. ET., Ibid.,41, 1124 (1949). (11) blickley, €I. S.. a n d Trilling, C. A , Ibid., p. 1135. (12) Miller, C:. O., and Logwinuk, &4.K., Ibid., 43, 1220 (1951). (13) Xicholson, E. W.. Noise, J . E., and H a r d y , R. L., Ihid.,40, 2033 (1948). (14) Sielsen, N. (to F. L. Binidtli 8: (20.. S e w York. S . Y . ) ,TT. M. P a t e n t 2,027,697 ( J a n . 1 4 , 1936). (15) [[Jid.,2,292,897 (AUg. 11. 1942). (16) Pontoppidan, C. (to F. L. Smidth & C'o.. ?;ex Y o r k , S . Y,), M d . , 1,616,547 (Feb. 8 , 1927). (17) Reed, T . 11..P h . D . thesis, T h e Peniinyl\-unia State ( h l l e p e , 1952. (18) Smith, R. 13.. I,?. S. P a t e n t 2,542,587 (1951). HE:(,EIVFID for review June 1 5 . 1954.


.!.ccErTEn Sertternber 20. 1954,

Vol. 41, No. 2

Effects of Agitation on Gas Fluidization of Solids

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