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Particle slip surfaces in bubbling gas-fluidised beds
Short commtulicatiolts
Par&de slipsnrfacesin
bubblinggas-flnidkedbeds
Two-dimensional beds have heen widely used in studying the bubbles which are an important and characteristic feature of gas-fluidised systems’-‘. We have taken X-ray photographs of a twodimensional air-fluidised bed 30 cm wide by 30 cm deep and 1.4 cm thick in the direction of the X-ray beam. The distance of the X-ray source from the front face of the bed was 1 m, a 14 in. by 14 in. X-ray cassette containing Kodak Blue Brand film and Ilford X-ray screens was placed 5 cm behind the back face and spanned most of the bed area The X-ray generator was a Philips Maximus DLX sixpulse unit ; the totalX-ray tube filtration was equivalent to 2 mm of ahuninium and no anti-scatter grid was used. The X-ray exposure was 1/3OOth of a second using X-rays from a tungsten target and at 60-92 peak kV depending upon the absorption TABLE
1 T PROPERTIES
Panicle
Mcterial
characteristics of the particulate material used in the bed_ Prints from the X-ray films taken with each of five different materials in the bed are shown in Fig I- The properties of the five particulate materials used are given in Table 1 and photomicrographs are shown in Fig 2 In each experiment the bed was bubbling freely and in Fig. 1 the bubbles, which are essentially empty of solids, are seen as black areas as a result of the increased X-ray penetration. The front and back faces of the bed were made of $ in-thick plate glass and gave a uniform bed thickness over the whole of the bed The plate glass itselfwas responsible for a significant, but uniform, attenuation of the X-ray beam and the black disc visible in the photographs of Fig 1 results from an increased X-ray penetration through two Perspex inserts fitted in the faces for other experimental work. Because of the high X-ray
OF THE MATERIALS
IXED
shape
Minimum jluidiulxion r;elociry
Mean roihge
d-
of
phase
Angle of repose
(dw)
(c&s sup.)
184 /.m Ballotini
193 _ _ _ 74.792 164 _ _. 23.2% 136___ 21%
37 pm Ballotini
37...965% ts... 2272 23_.. 13%
sand
5%6_._37_5% 472__.565% 385. _ _ 6.0%
95 /.un Crushed sand
136-e. 3.7% 113...35.1% 96.._255% 82_..32.2% 71__. 3_5%
480 m
Natural
96 pm Millscalc
Ponder
Temfogy
164... 12% 136... 13.1% 113__.245% 96.._212% 82...34_8% 71... 4.7% .59___ OS%
- ElsEvia
sequoia %A_,
spherical
z93
3.50
O-43
24
spherical
x33
0.24
0.46
25
irregular,
255
19.0
O-47
35
263
24
0.60
37
537
43
059
39
SW
irregular.
sharp and panly plate-like
Lausannc
-
printed
in the
Netherlarlds
30’
SHORT
COU\IUWC.\TIO~S
in tilt 1SI .mu lead-glrtxi Ballotini and in thcdcnsc ~~illscaletheintcnsit~ oftheX-ray beam in regions xx-ithout solids. ix. in bubbles and above the hcd surface_ ga\c rise to some local scatter of rhc hcam in the hacl. fact of the htd. in the intensif\ins screen and in the S-m> film itseif and this results i.1 the darkening obscr\rd around these regions in Fip. l(a)_ (c) and (f)_ This should not ho
atIsnu:xtion
mistaken as et-idcnce for an increased ~oidagc in the dense phase around the bubble boundary_ In Fig_ 1 particular attention is drawn to photographs (d). (e) and (f) which re\eal patterns of line. curved lines which correspond to surfaces of IOU particle concentration (Cc. increased voidage) within the dense phase of each bubbling bed. It is seen that thcsc surfaces are quite sharply dcfmed and this
(a)
Poufcr
7-c&noL,
2 (1968169)
301-305
SHORT
COVMUSICATIOSS
means that they must be parallel to the X-ray beam and that they probably span the thickness of the bed. Scxcral sizes of spherical $ass Ballotini within the range 500 io 37 grn diameter wcrc cxamincd and all but the 37 Jcrn material ga\c X-ray photographs shoxing the particulate phase to ha\c a uniform appearance. as show-r for the IS4 /cm material in Fig. l(a). With the 37 Jtrn material no surfaces of low particle concentration \\erc obscrvcd but larger scale areas of increased voidage xcrc apparent. althoqh some of these may have been caused by the presence of tiny bubbles which x\-cre too small to span the thickness of the bed. The irregularly shaped. but rounded, 180 ?cm natural sand also demonstrated a uniform dense phase but the more angular crushed sand and PI-lillseale both shoxved surfaces of low particle concentration and also larger scale areas of increased voidage. The surfaces of reduced particle concentration appear to be surfaces of particle slip that result from the stresses placed upon the dense phase as bubbles rise through it. Ideally, the particles ahcad of a risin_g bubble must moxe away from it. slip around the srdes as it passes and then follow up into its wake. their paths thus following the ‘-elasticas‘- dcscribed by Darwin3 for the streamline flow of fluid around a circular body_ Experiments using coloured
303
trxcrsJ-C have shown that bubbles in hcds oi spherical particks or in the more rounded irregular material such as the 40 Icm natural sand used hcrc$1~ rise IO a motion which is close to this idcal and the present observations indicate that the motion can occur xxithout recourse to a dcgrcc of locai slip v.hich is detcctablc by the tcchniquc used. Howxcr_ it seems that in Icry- anpular materials the interfcrcncc bctwccn adjacent la>crs of parxiclcs is such that particle flow- can onI> occur with the formation of slip surfaces. The phenomenon is chxiously related to the natural art&z of repose of the particuiatt material and in the prcscnt \\orL has arisen in materials xx-ith an angle of repose g-cater than about 36 degrees. Slip surfaces ha\c been observed b> .-\thc>_ Cutress and Pulfcr” (set also Cutrcss and Pulfcr ) in the flow of granular materials from hoppers and the remarks of these authors stem to bc directly rclcx ant here. They obscn ed by cinc-photozgaphythat shear occurred at any instant only- oxcr a I?\\of the many slip surfaces visible in the X-m> photograph. They suggested that the slip surfaces moved down with the flowing powder for some distance and that an X-ray- photograph thcreforc rcvcals all the surfaces o\cr which slip has occurred during some previous period. This is indeed apparent in (e) and (f) of Fi_r. I where bubbies are seen to hale
30-t
SHORT
COMSIMUNICATIOSS
of the materials used.
left interleaving patterns of slip surfaces marking the paths of their movement through the bed_ It is aiso seen that a bubble leaves a band of generally increased voidage in these regions. When it is remembered that the streamlines of the particle flow observed, as in the present techniclue, by a camera at rest would have the appearance
of a dipole centred on the bubble centre and s_\-mmetrical about its vertical axisa, the slip surfaces are seen to correspond approximately to the local direction of the solids movement_ The picture is complicated, however, by the fact that the surfaces persist within the solids after a bubble has passed. It is cleariy seen in Fig. l(e) that the irregularities &n,der
Technoi.. -7 (1968169) 301-305
SHORT
often observed in the upper boundary of a bubble are points from which slip surfaces run into the dense phase. It may be that the effects observed here are influenced by the fact that the particle flow has been constrained to only two dimensions. However, it seems certain that such behaviour will also occur in the gas-fluidisarion of very irreguIar particks in conventional three-dimensional beds. B. A.
PARTRIDGE,
E. LYALL
Chemical Engineering DiL2sionS. Health
Physics
AXD
and Process
and Medical
H.
E. CROOKS
Teclmolog>
Division,
Atomic Energy Research Establishment. Hansell, Didcot (G?. Britain j
Heat
305
COMMLJUNICATIOSS
and momentum transfer analogy in dense aerosols flowing turbulently in ducts
In a one-phase fluid it is well known’ that the mechanism of the turbulent transfer of heat, momentum and mass resemble each other closely. In many accurate calculations the “turbulent diffusivities* of heat, matter and momentum have merely been considered equal, although the accuracy of this simple assumption depends on interaction between turbulence and molecular dispersion and remains an issue which is still unresolved’. It appears from new experimental data given in the present communication that there are grounds for considering similar analogies to exist in a llowing gas, even when it contains an appreciable conteni of tine particles. It is believed that these are the only existing data where turbulent dispersion of momentum, heat and mass have all been examined for the same experimental conditions in a flowing aerosol. The aerosol used’ was air at near-atmospheric conditions, flowing vertically upwards in tubes and containing line zinc spheres with diameters in the range 04004 cm_ The flow was fully-developed, and experimental data for tubes of diameter (0) 1,2 and 3 in. are summarized in Fig. 1 (a)-(c) for various values of the pipe Reynolds number (i5DpJp) and solids/gas mass-flow ratios (WJWJ_ The gas has mean flow velocity D, density pr, and viscosity JL in the pipe The results are for: (1)fJ’c which is the fractional increase in the wall
REFERESCES 1 P. F. WACE AXXJS. J. BLRX~. Tronr. INI. Chcnz Engrs.. 3Y (1961) 16% 1 P. N. ROWE. B. A. PARTRIDGE AXD E. LYALL. Chum. Eng. Sri.. 19 (1964) 973. 3 C. DARWIS. Proc.Can& Phil. Ser.. 49 (1953) 342. J P.N.Rou’F.Ax?,B.A. P~RIRIDGE in P.A. Ro-E~RG(c~.). l3e InreracrionBrrxrecn Ruidr and Parxiclcx insr. Chem. En_ms. London. 1961. p_ 135 5 P. N. ROW-E EZal.. Trans. INI Chmr. Engrs_ 33 (1965) T171. 6 J. D. ATHEI-_ J. 0. Ctxitm \?rD R. F. PULFEX. Cim?z. Enq. Sri.. ‘I (1966) 535. 7 J. 0. CLXRESS A\D R. F. P~XFER. Ponder Tcchnnl.. I (1967) 213.
Rcceivcd
January 7. 1969 Ponder
Tcchnol.. 2 (3968,69)
301-305
frictional shear stress due to the aerosol compared with the value experienced when solids are absent Thwe results have been published more comprehensively’. (2) NzrS/Nzcowhich is the fractional increase in the heat transfer coefficient caused by the presence of the solids expressed in terms of the Nusselt numbers for constant heat-flux conditions_ These results are new_ (3) s/c0 which is the fractional increase in the eddy diffusivity of the gas itself- These data are also published in detai13. Comparison of Fig 1 (a), (b) and (c) shows that suspensions flowing in pipes of different diameter may eshibit strongly contrasting transport properties_ An explanation of these observations involves the important time-scale parameter and has been discussed elsewhere3-;_ Despite these differences. however, it is noted (for pipes of the same size where this time-scale parameter is the same) that heat, momentum and the gaseous phase have similar overall transport characteristics. For instance: (1) There are corresponding minima for IF&, iVuJ_Wu, and .sJ.sOin the 2 in. pipe. It is seen that the minima occur when the densities of the phases are approximately equal (W,/iQ=l) and there is a large stabihsing effect of the solids on the carrier fluid turbulence which seems to change its characteristics as more solids are added”. (2) There is a tendency for fdy,, NuJNu, and .s&-, all to have larger values in the 3 in. pipe than Powder Tedmol..
Z (1968;69)
305-307
Par&de slipsnrfacesin
bubblinggas-flnidkedbeds
Two-dimensional beds have heen widely used in studying the bubbles which are an important and characteristic feature of gas-fluidised systems’-‘. We have taken X-ray photographs of a twodimensional air-fluidised bed 30 cm wide by 30 cm deep and 1.4 cm thick in the direction of the X-ray beam. The distance of the X-ray source from the front face of the bed was 1 m, a 14 in. by 14 in. X-ray cassette containing Kodak Blue Brand film and Ilford X-ray screens was placed 5 cm behind the back face and spanned most of the bed area The X-ray generator was a Philips Maximus DLX sixpulse unit ; the totalX-ray tube filtration was equivalent to 2 mm of ahuninium and no anti-scatter grid was used. The X-ray exposure was 1/3OOth of a second using X-rays from a tungsten target and at 60-92 peak kV depending upon the absorption TABLE
1 T PROPERTIES
Panicle
Mcterial
characteristics of the particulate material used in the bed_ Prints from the X-ray films taken with each of five different materials in the bed are shown in Fig I- The properties of the five particulate materials used are given in Table 1 and photomicrographs are shown in Fig 2 In each experiment the bed was bubbling freely and in Fig. 1 the bubbles, which are essentially empty of solids, are seen as black areas as a result of the increased X-ray penetration. The front and back faces of the bed were made of $ in-thick plate glass and gave a uniform bed thickness over the whole of the bed The plate glass itselfwas responsible for a significant, but uniform, attenuation of the X-ray beam and the black disc visible in the photographs of Fig 1 results from an increased X-ray penetration through two Perspex inserts fitted in the faces for other experimental work. Because of the high X-ray
OF THE MATERIALS
IXED
shape
Minimum jluidiulxion r;elociry
Mean roihge
d-
of
phase
Angle of repose
(dw)
(c&s sup.)
184 /.m Ballotini
193 _ _ _ 74.792 164 _ _. 23.2% 136___ 21%
37 pm Ballotini
37...965% ts... 2272 23_.. 13%
sand
5%6_._37_5% 472__.565% 385. _ _ 6.0%
95 /.un Crushed sand
136-e. 3.7% 113...35.1% 96.._255% 82_..32.2% 71__. 3_5%
480 m
Natural
96 pm Millscalc
Ponder
Temfogy
164... 12% 136... 13.1% 113__.245% 96.._212% 82...34_8% 71... 4.7% .59___ OS%
- ElsEvia
sequoia %A_,
spherical
z93
3.50
O-43
24
spherical
x33
0.24
0.46
25
irregular,
255
19.0
O-47
35
263
24
0.60
37
537
43
059
39
SW
irregular.
sharp and panly plate-like
Lausannc
-
printed
in the
Netherlarlds
30’
SHORT
COU\IUWC.\TIO~S
in tilt 1SI .mu lead-glrtxi Ballotini and in thcdcnsc ~~illscaletheintcnsit~ oftheX-ray beam in regions xx-ithout solids. ix. in bubbles and above the hcd surface_ ga\c rise to some local scatter of rhc hcam in the hacl. fact of the htd. in the intensif\ins screen and in the S-m> film itseif and this results i.1 the darkening obscr\rd around these regions in Fip. l(a)_ (c) and (f)_ This should not ho
atIsnu:xtion
mistaken as et-idcnce for an increased ~oidagc in the dense phase around the bubble boundary_ In Fig_ 1 particular attention is drawn to photographs (d). (e) and (f) which re\eal patterns of line. curved lines which correspond to surfaces of IOU particle concentration (Cc. increased voidage) within the dense phase of each bubbling bed. It is seen that thcsc surfaces are quite sharply dcfmed and this
(a)
Poufcr
7-c&noL,
2 (1968169)
301-305
SHORT
COVMUSICATIOSS
means that they must be parallel to the X-ray beam and that they probably span the thickness of the bed. Scxcral sizes of spherical $ass Ballotini within the range 500 io 37 grn diameter wcrc cxamincd and all but the 37 Jcrn material ga\c X-ray photographs shoxing the particulate phase to ha\c a uniform appearance. as show-r for the IS4 /cm material in Fig. l(a). With the 37 Jtrn material no surfaces of low particle concentration \\erc obscrvcd but larger scale areas of increased voidage xcrc apparent. althoqh some of these may have been caused by the presence of tiny bubbles which x\-cre too small to span the thickness of the bed. The irregularly shaped. but rounded, 180 ?cm natural sand also demonstrated a uniform dense phase but the more angular crushed sand and PI-lillseale both shoxved surfaces of low particle concentration and also larger scale areas of increased voidage. The surfaces of reduced particle concentration appear to be surfaces of particle slip that result from the stresses placed upon the dense phase as bubbles rise through it. Ideally, the particles ahcad of a risin_g bubble must moxe away from it. slip around the srdes as it passes and then follow up into its wake. their paths thus following the ‘-elasticas‘- dcscribed by Darwin3 for the streamline flow of fluid around a circular body_ Experiments using coloured
303
trxcrsJ-C have shown that bubbles in hcds oi spherical particks or in the more rounded irregular material such as the 40 Icm natural sand used hcrc$1~ rise IO a motion which is close to this idcal and the present observations indicate that the motion can occur xxithout recourse to a dcgrcc of locai slip v.hich is detcctablc by the tcchniquc used. Howxcr_ it seems that in Icry- anpular materials the interfcrcncc bctwccn adjacent la>crs of parxiclcs is such that particle flow- can onI> occur with the formation of slip surfaces. The phenomenon is chxiously related to the natural art&z of repose of the particuiatt material and in the prcscnt \\orL has arisen in materials xx-ith an angle of repose g-cater than about 36 degrees. Slip surfaces ha\c been observed b> .-\thc>_ Cutress and Pulfcr” (set also Cutrcss and Pulfcr ) in the flow of granular materials from hoppers and the remarks of these authors stem to bc directly rclcx ant here. They obscn ed by cinc-photozgaphythat shear occurred at any instant only- oxcr a I?\\of the many slip surfaces visible in the X-m> photograph. They suggested that the slip surfaces moved down with the flowing powder for some distance and that an X-ray- photograph thcreforc rcvcals all the surfaces o\cr which slip has occurred during some previous period. This is indeed apparent in (e) and (f) of Fi_r. I where bubbies are seen to hale
30-t
SHORT
COMSIMUNICATIOSS
of the materials used.
left interleaving patterns of slip surfaces marking the paths of their movement through the bed_ It is aiso seen that a bubble leaves a band of generally increased voidage in these regions. When it is remembered that the streamlines of the particle flow observed, as in the present techniclue, by a camera at rest would have the appearance
of a dipole centred on the bubble centre and s_\-mmetrical about its vertical axisa, the slip surfaces are seen to correspond approximately to the local direction of the solids movement_ The picture is complicated, however, by the fact that the surfaces persist within the solids after a bubble has passed. It is cleariy seen in Fig. l(e) that the irregularities &n,der
Technoi.. -7 (1968169) 301-305
SHORT
often observed in the upper boundary of a bubble are points from which slip surfaces run into the dense phase. It may be that the effects observed here are influenced by the fact that the particle flow has been constrained to only two dimensions. However, it seems certain that such behaviour will also occur in the gas-fluidisarion of very irreguIar particks in conventional three-dimensional beds. B. A.
PARTRIDGE,
E. LYALL
Chemical Engineering DiL2sionS. Health
Physics
AXD
and Process
and Medical
H.
E. CROOKS
Teclmolog>
Division,
Atomic Energy Research Establishment. Hansell, Didcot (G?. Britain j
Heat
305
COMMLJUNICATIOSS
and momentum transfer analogy in dense aerosols flowing turbulently in ducts
In a one-phase fluid it is well known’ that the mechanism of the turbulent transfer of heat, momentum and mass resemble each other closely. In many accurate calculations the “turbulent diffusivities* of heat, matter and momentum have merely been considered equal, although the accuracy of this simple assumption depends on interaction between turbulence and molecular dispersion and remains an issue which is still unresolved’. It appears from new experimental data given in the present communication that there are grounds for considering similar analogies to exist in a llowing gas, even when it contains an appreciable conteni of tine particles. It is believed that these are the only existing data where turbulent dispersion of momentum, heat and mass have all been examined for the same experimental conditions in a flowing aerosol. The aerosol used’ was air at near-atmospheric conditions, flowing vertically upwards in tubes and containing line zinc spheres with diameters in the range 04004 cm_ The flow was fully-developed, and experimental data for tubes of diameter (0) 1,2 and 3 in. are summarized in Fig. 1 (a)-(c) for various values of the pipe Reynolds number (i5DpJp) and solids/gas mass-flow ratios (WJWJ_ The gas has mean flow velocity D, density pr, and viscosity JL in the pipe The results are for: (1)fJ’c which is the fractional increase in the wall
REFERESCES 1 P. F. WACE AXXJS. J. BLRX~. Tronr. INI. Chcnz Engrs.. 3Y (1961) 16% 1 P. N. ROWE. B. A. PARTRIDGE AXD E. LYALL. Chum. Eng. Sri.. 19 (1964) 973. 3 C. DARWIS. Proc.Can& Phil. Ser.. 49 (1953) 342. J P.N.Rou’F.Ax?,B.A. P~RIRIDGE in P.A. Ro-E~RG(c~.). l3e InreracrionBrrxrecn Ruidr and Parxiclcx insr. Chem. En_ms. London. 1961. p_ 135 5 P. N. ROW-E EZal.. Trans. INI Chmr. Engrs_ 33 (1965) T171. 6 J. D. ATHEI-_ J. 0. Ctxitm \?rD R. F. PULFEX. Cim?z. Enq. Sri.. ‘I (1966) 535. 7 J. 0. CLXRESS A\D R. F. P~XFER. Ponder Tcchnnl.. I (1967) 213.
Rcceivcd
January 7. 1969 Ponder
Tcchnol.. 2 (3968,69)
301-305
frictional shear stress due to the aerosol compared with the value experienced when solids are absent Thwe results have been published more comprehensively’. (2) NzrS/Nzcowhich is the fractional increase in the heat transfer coefficient caused by the presence of the solids expressed in terms of the Nusselt numbers for constant heat-flux conditions_ These results are new_ (3) s/c0 which is the fractional increase in the eddy diffusivity of the gas itself- These data are also published in detai13. Comparison of Fig 1 (a), (b) and (c) shows that suspensions flowing in pipes of different diameter may eshibit strongly contrasting transport properties_ An explanation of these observations involves the important time-scale parameter and has been discussed elsewhere3-;_ Despite these differences. however, it is noted (for pipes of the same size where this time-scale parameter is the same) that heat, momentum and the gaseous phase have similar overall transport characteristics. For instance: (1) There are corresponding minima for IF&, iVuJ_Wu, and .sJ.sOin the 2 in. pipe. It is seen that the minima occur when the densities of the phases are approximately equal (W,/iQ=l) and there is a large stabihsing effect of the solids on the carrier fluid turbulence which seems to change its characteristics as more solids are added”. (2) There is a tendency for fdy,, NuJNu, and .s&-, all to have larger values in the 3 in. pipe than Powder Tedmol..
Z (1968;69)
305-307