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Study of wear characteristics and solid distribution in constant area and erosion-resistant long-radius pipe bends for the flow of multisized particulate slurries
WEAR ELSEVIER
Wear 217 (1998) 297-306
Study of wear characteristics and solid distribution in constant area and erosion-resistant long-radius pipe bends for the flow of multisized particulate slurries Rakesh
M i s h r a ~, S . N . S i n g h b, V . S e s h a d r i b . ,
Department of Applied Mechanics. MNREC. Allahabad. India h Department of Applied Mechanics. Indian Institute of Technolog)~ New Delhi. India
Received 18 July 1997:accepted 9 January 1998
Abstract The wear characteristics of three types of long radius pipe bends in the flow of multisizcd particulate slun'ics have been extensively ~udied. Conventional long radius bend, and two types of diverging-convergingbends are investigated. MeasuremenLs have been made over a range of solid concentrations and flow velocities. The results have shown that diverging-convergingbend with an area ratio 2 exhibiLs reduced wcm-. and in fact can even be expected to have a longer life than a straight pipe. Furlber, measurement of solid di.qribmion in the three bends has given some insight into the causes tbr the reduced wear in these modified bends. It h0s also been demonstrated that the diverging-converging bends even with enlarged cross-sections are not prone to choking when the pipeline is operating near critical d e , ilion velocity. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Slurry pipelines: Pipe bends: Erosion wear: Solid distribution
I. Introduction Bends are an integral part of any pipeline network system. In solid-liquid pipeline systems, bends are prone to excessive wear and their failure leads to excessive loss of time and money. Concerted efforts have not been made to improve the constant-area long-radius hencks commercially available for their suitability to solid-liquid flows. Toda et al. [ I ] were the first to investigate the flow characteristics in pipe bends for slurry flows. They observed that the particles are forced towards the outer wall as a result of centrifugal force generated in the bends. Nasr-EI-Din and Shook 12 ] measured the slurry velocity and concentration downstream o f bends with short and long radii. They observed that the distribution of particles was skewed lot long radius bend. whereas particles retained the original distribution for the short radius bend. Ahmed et al. [ 31 measured the concentration in the horizontal and vertical planes o f a conventional bend (radius ratio = 4.0) at the mid-section. They concluded that particles migrated from the vertical plane perpendicular to the plane * Correspondingauthor. Dept. of Applied Mechanics.Indian Institute of Technology. Hauz Khas. New Delhi I I0 016. India. Fax: +91-11-6862037. 0043-1648/98/$19.00 © 1998ElsevierScience S.A. All right~reserved. PII S0043-1648 ( 98 )00147- I
of the bend towards the diagonal planes. Gup4a [41 has reported the concentration distribution in a 55-mm pipe bend ( radius ratio = 5.5). He observed the concentration o f coarser particles to be higher near the bottom portton o f the outer wall whereas, the filler particles were more or less uniformly distributed. His measurements support the observatio~¢ o f earlier investigators [ 1,21. Wear studies in bends for solid-liquid mixtures are limited. Seshadri et at. [ 5 ] have measured overall wear in long-radius 9 0 ° bends and compared it with straight pipe. They observed wear in bends to be approximately double that in the straight pipe. Murakami et at. [ 6] have reported wear measurements along the periphery o f a 9 0 ° bend and observed the wear to he more in the first half o f the bend. Widenroth [ 7 ] hascarried out wear rate studies in a 90 ° bend by measuring the wall thickness at different locations. He observed that wear rate increases in the first half o f the Lend and then gradually
reduces. Wear studies in bends for pneumatic conveying systems have been reported by .several researchers 18-111. Horii et al. [ I I ] developed a Lend with a diverging and a converging portion upstream and downstream o f the bend. They observed considerable reduction in wear in this Lend as compared to the constant area bend. The studies in bends for solid-liquid
298
R. Mislm] et aL / Wear 21711998) 297-306
mixtures and gas-solid system have clearly established the excessive wear in bends, but have not been able to identify the basic mechanism, in the pre~nt study, an attempt has been made to measure the erosive wear at the mid-plane of a 90 ° bend for solid-liquid mixture along with complete mapping of the solid distribution. The study has been carried out on three bends, namely, a 90 ° constant area bend and two diverging-converging bends with area ratios of 1.5 and 2.0.
2. Design and development of diverging-converging bends Investigations on bends in solid-liquid flows have shown that the primary reasons lor erosive wear in bends are migration of larger-size particles [4.12] and velocity-related effects. The solid particles directly impact against the outer wall of the bend leading to larger deformation wear. Hence, it is expected that reduction in the impact velocity of particles will reduce erosive wear in the bends. In order to exploit this mechanism, the modified geometry for the bends was envisaged. The basic philosophy in the development of diverging and converging bends was to initially reduce the flow ~,elocity and then create a favourable pressure gradient in the downstream, in these bends (Fig. I ), the radius of curvature of the inner wall was kept the same ( R / r = 3) as the constant area bend. This was done to have a reduction in velocity, as well as particle migration towards the outer wall. The area ofcross~ction of the modified bends was increased linearly from inlet to the middle of the bend to enhance diffusion, then the area was reduced linearly up to the outlet at the same rate. The cross-section of the bend was always kept circular along its length. The maximum cross-sectional area of the two fabricated bends was kept at 1.5 and 2 times the original pipe area. and this occurred at the mid-section ( see Fig. I ). This
/, I Fig. I. Plan ,Jew ol ihc three I~:ndsinvc'~titzalcdalong with the imporlant din~nsi~m~..
design leads to reduced velocity and enhanced intensity of secondary flows. It is further expected that the reduction in velocity and change in radius of curvature will reduce the effect of centrifugal forces on the flow field. It is envisaged that all the three mechanisms described above lead to more uniform distribution of the particles in the bend which, in turn, should result in the reduction of erosive wear. A somewhat similar concept was used by Horii et al. [ I I ] in pneumatic conveying systems.
3. Experimental set-up and measurement methods The test bends having fixtures for the measurement of wear and concentration field at the mid-plane of the bends are fitted in the pilot plant test loop as shown in Fig. 2a. Sufficient upstream and downstream lengths were incorporated before and after the bends to ensure undisturbed flow at the inlet. The solid distribution in the bends was measured along 4 diametrical planes, as shown in Fig. 2b, at the middle crosssection using sampling tubes ( Fig. 2c). Out of the tour planes. one was vertical (plane 2-2) and another was horizontal (plane 4-4). The remaining two planes were ( I-I and 3-3) at an angle of +_45 ° with vertical. The closest point to the wall at which concentration was measured along different pla,)es was 5 mm from the wall. Sampling tubes were traversed along the identified planes, and samples were collected under near iso-kinetic conditions. Concentration at any measurement point was evaluated from the measured density of the collected slurry sample. The concentration along each plane was measured at seven points to adequately cover the total cross-section of the bend. In line with the aims of the present study, arrangements were made for the determination of wear rate in the bends. Rajat [ 41 has shown that the primary reason for the enhanced wear in bends is the impact of the particles on the outer wall. He has also shown that bulk of the solids move towards the outer wall increasing the local concentration, which also tends to increase the wear in bends. Thus, the bottom quarter of the outer wall of the bend was considered critical for studies of the wear rate in bends. Hence. three locations were selected in each of the three bends for determination of wear as shown in Fig. 3a. At all the three locations brass (composition- 70% Cu, 30c~ Zn. sp. gr.: 8.5 and Rockwell hardness: 94 (.scale B ) ) w0ar pieces having surface area of 25 mmX 15 mm and thickness equal to that of the mild steel pipe wall were fitted as shown in Fig. 3b. The whole fixture consisted of mild steel cover plate, rubber packing, fixing screws, aligning screws and adjustable holding screw. The brass wear piece was held to the cover plate by adjustable holding screw. The cover plate was fixed to the bend surface after placing the rubber packing with fixing screws. Two aligning ~ r e w s were provided on the mild steel cover plate for aligning the wear piece flush with the inner surface of the bend. All t h e ~ fixtures ensured the exact positioning of the wear pieces in the bends
R. Mishra e! .It / Wear 217 (19Q8) 297-306
(a)
_'299
Stirrer
FLov
div.tir ~ .
/ • [ t~
]
1
/Oen~ityum0ttw
~.~)f.I /._9end(inherizontotptone
:',I'?I17/""
)
+ i ?. . . . . .". . ,. . . . . . " ,'I
,'
4
.. -
i ~ o . to.gl
W e l test rig
- " -- ~ : ~ $ i . r r l li.,I.li 1-IpllneI hid• 1.0 2-2Plane2 3-3 ......... PIine3 h/Dh/O~~~" 1.0 122~.// hiD• 1.0
+> ,==
(C)~~~TOSAMII[N ~.
;o.odS,+: I
h/O
~/hid
• O.O
• O.O
Fig. 2. (a) Schematicdiagramof the pih)t planl: ( b ) Planesof me~,~uremcnzstit concentration profile in Ibe mid-sectionof Ibe bends: (c) Clmcenlrali~m samplingprabe. to avoid discontinuity in the pipe and wear piece surfaces. For the purpose of comparison, the wear in the straight pipe was also measured at the three locations, namely, bottom of the pipe "A'. middle of the pipe "B" and topmost point "C" on a given cross-section of the pipe (Fig. 3a). The pilot plant test loop (Fig. 2a) u ~ d in the pre~nt study consisted of a closed pipe test loop of 105 mm NB pipe having a length of 60 m. a mixing tank. a measuring tank and other test fixtures [ 13 ]. To monitor the efflux concentration, a density sampler was provided in the vertical portion of the pipe loop. Efflux concentrations, for different flow conditions, were calculated from the measured density of the efflux samples.
concentrations (approximately 30% and 40% by weight). The concentration lields were al,q) determined along the four planes for all the above combinations ofefflux concentrations and flow velocities. Solid distribution in the bends was also investigated at different efflux concentrations near the deposition velocity in the straight pipe. This wa~ done to detect the occurrence of particle deposition in the bends under conditions when bed formation is beginning to lake place in the straight pipe.
$. Results and discussion 5. I. W e a r cbaraewristics a f bend.~
4. Materials used and range of parameters The tailing material (waste material after the extraction of zinc from the ore) collected from a zinc processing plant has been used in the pre~nt study to prepare the slurry by mixing it with water. The physical properties of the material are given in Table I. It is ~ e n that 55% particles are Icss than 75/.tin and only 2% particles are larger than 0.3 ram. The specific gravity of the solid particles was 2.85 and static-~ttled concentration was 60% by weight. The range of efflux concentrations covered was from 9.82% to 41.21% by weight. Wear was determined by measuring the loss in weight over a fixedtime interval at one flow velocity (2.25 m / s ) for two lower efflux concentrations ( 9.82% and 20.32% by weight), and at two velocities (2.25 m / s and 2.89 m / s ) for higher efflux
Wear in different bends has been measured at different efflux concentrations and flow velocities. Wear was determined by measuring the weight loss of the brass specimen after running the pilot plant for I0 h at a given flow velocity. Measurement of particle size distribution before and after any experimental run did not exhibit any appreciable attrition of the particles. The data on wear for bends and straight pipeline is given in Table 2. 5. I.I. W e a r in ctmslaat area b e n d
Table 2 gives the variation of wear at all the locations for the constant area bend ( R / r = 3) ( I ARB). It is ~ e n that the wear inerea~s with increase in efflux concentration at location I at any flow velocity. The wear increases gradually up
R. Mishra et al. / Wear 217 (19Q8) 297-306
300
Table I Physicalpropertiesof the zinc tailings slurry Inner
w
a
l
~
u
t
e
r will
LOCATION 2
Panicle size (ran;)
% finer
0.85 0.30 0.21 0.15
100.0 96.26 85.9 I 78.57 63.67 .51.39
0.106
0.075
(a) Overall specificgravity of the solid material: 2.85. (b) Static settling concentralion:60.21 ( ¢/~by wt.). (e) Panicle size distribution.
e,nu LOCATION C
LOCATION A (a) St ¢=hil~.L~p£ ttotOln9
~,c few
namely, 26.73% and 36.83% by weight, and it is ~ e n that the increase in the flow velocity causes only marginal increase in the wear at both the efflux concentrations (Table 2). The trend also supports the steep increase between these concentrations as seen at lower velocity. The variation o f weight Joss in constant area bend, at location 2, is seen to be similar to location I. The maximum weight loss for this location was measured as O.O117 g for 41.21% efflux concentration for lower velocity, and 0.0121 g for higher velocity at an efflux concentration of 36.83%. The weight loss at location 3 for the same bend also seems to be similar, i.e., wear increases with increase in the efflux concentration. The measured wear is maximum at the highest efflux concentration tested. A comparison of the wear at different locations in the constant area bend suggests that up to efflux concentration c l o ~ to 30% maximum wear is associated with location I, whereas the minimum wear is associated with location 3. At an efflnx concentration close to 40%, maximum wear is associated with location 2, whereas the minimum wear is still associated with location 3. This may be because o f predominance of deformation wear at location 3. whereas at kv,:ations I and 2, both deformation and cutting wear are dominant. The steep increase in the wear beyond an efflux concentration of 30% at all three locations could be due to substantial increase in the contribution of cutting wear to the overall wear. 5.1.2. W e a r in b e n d with area ratio 1.5
/
~1
L
i
j
T
Fig. 3. (a) I~Jtails of the hx:atlonof .,-earpicot.., in hendsand ~.traightpipe: t b) Detailsof the lest |ixlure for tixingand aligningof the brass wear pieces in the straight pipe and bends. to a concentration of 28.73% and the further increase is steep at high efflux concentnltion. The maximum wear was 0.008 I g at 41.21% efflux concentration. At higher vekx:ity of 2.89 m / s . the wear was measured at two efflux concentrations.
Table 2 also gives the variation o f wear for the bend with area ratio 1.5. The variation of wear indicates that at lower flow velocity ( 2.25 m / s ) , wear increases with an increase in el'flux concentration. At 41.21% efflux concentration, wear shows a significant increase. It is also seoa that an increase in vek)city increases the wear significantly at an efflux concentration close to 30%. A similar effect is .seen even at higher concentration. A comparison of corresponding data with constant area bend shows that up to 30% ¢fflux concentration for lower flow velocity, the wear in the I..5 area ratio bend is less than the constant area bend. At higher efflux concentration (close to 40% ) there is not much change in wear characteristics in the two bends as far as bottom o f the bends is concerned. Even the trends and magnitudes of wear are similar. At location 2 in 1.5 ARB, the effect of efflux concentration
R. Mishra et aL I Wear 217 ( 1998~ 297-306
Table 2 Wearcharacteristicsin the bends and the straight pipes Bend or straight pipe
Constant area bend
Locations
I 2 3
Diverging-convergingbend witharea ratio 1.5
I 2 3
Velocity (m/s)
Wear (g) Cw, =9.82%
Cw: = 20.32~ Cw, = 27.73ch Cw~= 39.112t,~ ( 28.73c/,([email protected] ) 36.83ch )
2.25 2.89 2,..?5 2.89 2.25 2.8t.)
a.lXt29 O.(X)30
n.n4D6
U.IXII2
n.lx)21
2.25 2.89 2.25 2.89
O.(IIX)t)
O.IX)I2
().iX) 12
0.(1015
2. ")5
O.(XX)8
().(X)14
().1X134
2.89 Diverging--convergingbend with area ratio 2.0
l 2 3
Straight pipe
Bom)raof pipe. location "A"
2.25 2.89 2.25 2.80 2.25 2.89
O.IXI05
O.IN;II
().txx)o
n.lX)l2
n.txx)6
n.tx)14
2.25
0.(X123
1k0032
2.89
and flow velocity on wear is .seen to he similar to location I with marginal fall in the values of wear. A similar trend is seen for wear at location 3 also. An analysis of wear at different locations in 1.5 ARB suggests that maximum wear is associated with location 2 at an efflux concentration of 36.83% for the higher flow velocity. A comparison of wear at different locations at corresponding efflux concentration and flow velocities in the constant area bend and 1.5 ARB suggests marginally reduced wear in 1.5 ARB. 5.1.3. W e a r in the b e n d n'ith area ratio 2 Table 2 also gives the wear data for bend with area ratio 2.0 ( 2 ARB). At location I. wear increases with the increase in efflux concentration, but the values are much smaller as compared to other two bends. The maximum value of 0.0047 g of weight loss for an efflux concentration of 41.21% at a velocity of 2.25 m / s is only 60% of the weight loss measured in the constant area bend. The rate of increase in wear is seen to rise steeply between efflux concentrationsof30% and40%. a trend which is similar to the other two bends. An increase in velocity increases the wear, but the effect is only marginal. Similar features are seen tbr wear at h)cation 2 in the :ame bend. The effect of velocity appears to he somewhat more pronounced at this location with other features remaining the same as at location I. The maximum wear at this location is 0.0041 g for an efflux concentnltion of 41.21% at lower velocity (2.25 m / s ) . and is only 35% of the constant area bend. The wear at the higher velocity ( 2.89 m / s ) is 0.0049
0.OO41 0 (X)51 O.(X)41 o.on5 0.1X132
11.0o8i U.IX)~) O.O117 0.012 I U.O061
n.oo51
0.01164
0.0021 1).11n5 1).0n2_7 11.0048
11.11082 11.n079 n.o I I U.(l12
O.(X)17
0.0074
0.1X132
(t.f1076
U.0017 U.(X)26 {).Ill)17 n.ix)26 ().(X)16 n.iN)28
().01M.7
n.00.~;7
u.lxt5 I
(1.0n3,I
U.IXK) l
0.11046
O.(X)41 0.(N)46 0,1X142 U.iX)51
g. and is only 40c,~ of the wear in constant area bend at the same concentration. Similar effecLs are also observed for location 3 in 2 ARB. An overall comparison of wear at different locations in 2 ARB demonstrates that the wear is almost uniform at the three locations at which wear has been measured. The effect of increasing efflux concentration and flow velocity on wear is also similar at all three locations. A comparison of wear at the three locations for the three bends suggests that minimum wear is associated with the 2 ARB. The reduction in the wear of this bend could he attributed to the geometry used. In the 2 ARB. velocities at the mid-section are half as compared toconstant area bend, which result.,; in considerable reduction in the centrifugal force. This. along with diffusion and generation of secondary flow. would he causing the particles to move toward.,; the inner wall. This brings about considerable reduction in wear in 2 ARB.
5 . Z Relative w e a r hi bends
It is known that wear in bends is more than thai in a straight pipe. In order to quantitatively analyze the wear in bends visa-vis that in straight pipe. relative wear has been calculated. The wear in the straight pipe is maximum at the bottom. Thus. the relative wear for any location in a bend is presented with respect to the wear at bottom of the straight pipe. Table 2 al.,a) gives the variation of wear measured at the bottom of the straight pipe.
302
R. Mishra el al. / Wear 217 f 1998) 297-306
Fig. 4 shows the relative wear calculated at the bottommost point in different bends. The relative wear in the constant area bend is always more than I, indicating higher wear in the bend as compared to that at bottom of the straight pipe. The variation of relative wear up to efflux concentration of 28.73% by weight at lower flow velocity is marginal, but beyond this concentration, the relative wear increases steeply, indicating enhanced wear in bend as compared to a straight pipe. At higher flow velocity of 2.89 m / s . the effect of increase in concentration on relative wear is marginal. Similar features are noticed for the other two bends with area ratio 1.5 and 2.0 also. However, minimum relative wear at any efflux concentration and flow velocity is always associated with 2 ARB, whereas, maximum relative wear is associated with constant area bend except at highest efflux concentration o f 41.21 ~ and flow velocity of 2.25 m / s , at which relative wear in 1.5 ARB is marginally higher than that o f conventional bend. It is also seen that for 1.5 and 2.0 area ratio bends. the relative wear value is around 0.5 for efflux concentrations less than 30% for lower velocity. For 2 ARB. the relative wear values are less than 1.0 even at higher velocity and highest efflux concentration. This implies that bends with an area ratio of 2.0 will have a life span equal to or more than the straight pipe. Fig. 5 shows the relative wear in different bends at location 2. The relative wear in the constant area bend is always more than I at this location also. indicating higher wear in the bend as compared to straight pipe. The variation of relative wear at this location is similar to the one observed at location I. Similar features are noticed for wear for the other two bends. The minimum relative wear at any efflux concentration and flow velocity is always associated with 2 ARB even at this location, whereas maximum relative wear is associated with constant area bend. It is also seen that for 1.5 and 2.0 area ratio bends, the relative wear value is close to 0.5 for efflux concentrations less than 30ch for lower velocity. For 2 ARB, the relative wear values are less than 1.0 even at higher velocity and highest efflux concentration. This implies that local wear in 2 ARB will always be less than that at the bottom in straight pipe. Fig. 6 depicts the relative wear at the location 3 in different bends. This figure has similar features. At this location for I ARB and 1.5 ARB relative wear is less than I at the lower velocity of 2.25 m / s up to efflux concentration of 28.73ch ; however, at 41.21ch efflux concentration, relative wear is more than I. indicating su~eptibility of these bends to earlier failure compared to the straight pipe. For 2 ARB. relative wear is always less than I. indicating increased wear rcsislance of this bend. A comparison of Figs. 4 - 6 suggests that higher relative wears at different locations are always associated with either I ARB or 1.5 ARB irrespective of the flow velocity and efflux concentration. Further. maximum wear in these bends is eitber at location I or location 2. The 2 ARB shows minimmn wear for all locations. This proves that bend with area ratio 2
Relative Weflt
2
e
× An-1
o o
+
V , 2 2 5 role
A~I,I v . 2 8 a m / s An.1.5 V , 2 2 5 rn/l
× o
AR=15 v.2 Bn rots
x
An,2
v.2gsm/s
0 An.2 v,2snm/m Fig. 4. Variation of relative wear ( w e i g h t loss at location I in bend/weight loss in straight pipe at location A ) as a function of efflux concentrationand flow velocities. Relative wear
2,5
15 c,
1
+
o~
20
30
V.2.2~ rn/s
AR.1
v,2.et)nv=
Aa.l.5 V.22S r*l=
05
lo
ARol
40
a
,n.~.5 v . 2 m l m,'s
x
AR"=.O V"'Z.Z6 m,'=
50
Cw (%)
Fig. 5. Variationof relative wear ( weight loss at location "2' in rend/weight loss in straight pipe at location "A' ) as a function of efflux concentration and llow vehv,:ities. Relative Wear
't ',~
÷
%
o 06
&
r)4
4,
e. +
9
~
kn.l AR.I
02
lo
20 Cw
30 (%)
40
m,5
o
.,m.ls v.2 s~ m,s
×
AR'2 Am=
o
v,225m/s v.2S{~mts
AR-~ 5 V . ~ 5
v.225mt= v . 2 s o m,=
50
Fig. 6. Variationof relative wear ( weight loss at location 3 in I~nd/weight loss in straight pipe at location A) as a functionof e[flgx concentrationand flow vek~ities. has better wear resistive characteristics compared to constant area bend and bend with area ratio 1.5. 5.3. Crmcentration field in bends
To have more insight into the mechanism of wear in the three bends, the concentration field was measured along four
g Mi.~hra et al. / Wear 217 (199~;)297-306
planes in each of them. The overall concentration distribution in the three bends for selected combinations are presented in Figs. 7-9 in the form of iso-concentration contours. These contours have been drawn using a software package "Surfer'. The package uses cubic spline fit and a very fine interpolation routine. The number on each contour represents the ratio of local solid concentration to the efflux concentration. 5.3. I. Iso-concentration contours in conventional b e n d
Fig. 7a shows the concentration contours at a flow velocity of 2.25 m / s and an efflux concentration of 9.82% in the constant area bend. The figure clearly shows the effect of centrifugal force in the upper portion of the bend where concentration shows increasing trend towards the outer wall: however, in the bottom portion, there is clear indication of movement of particles towards the inner wall. The observed distribution of the solid particles is indicative of predominance of centrifugal force in the upper part of the bend, whereas that of secondary flows, on the lower portion of the bend. Similar features are also seen in Fig. 7b for an efflux concentration of 28.73% at the same flow velocity. This figure indicates increased homogeneity vis-a-vis Fig. 7;), which may be because of increased particle-particle interactions. The effect of flow velocity on isc~concentration contours can be ~ e n by comparing Fig. 7c which shows iso-concentration contours at an efflux concentration of 26.73% at a flow velocity of 2.89 m / s with Fig. 7b. With an increase in flow velocity, the area of predominance of centrifugal force has increased marginally. A similar trend is seen at the higher concentration ( Fig. 7d), but the homogeneity has increased further. The measured wear under different conditions of flow can be explained now from the information available from the
£Wl,9.1~ "/. V.Z.IS,w, lS
m ¢w,,~-7~% V.~g~nqS
i~) c w ~ i ..n °1. votqHin~'s
calc~un,'/. v.a4h,/s
Fig. 8. Iso-conccntrationcontour~in arc-..Iratio 1.5 bend.
v,,.j.~l$ nltlr,
Icl Cw, 2 l , r ~ "I, v = z41') ml~, Fig. 9. Iso-concentralion contours in area
to) Cw .z6.73 % vlz41g,W*
[d) Cw • ~I.83"/, v.z.ltm/l
Fig. 7. ]so-concentration contours in area ratio I bend.
v=2-2Sm/s
( ~ Cw,~,-13*t* v = ~ , N mrs
ratio 2.0 bend.
iso-concentration field. At the lowest efflux concentration of 9.82% for a flow velocity of 2.2.5 m/s, the maximum wear was noticed at location I followed by location 2 and location 3. As seen in iso-concentration contours, the maximum concentration of the solid particles are observed at location I out of the three locations at which wear was measured, followed by location 2 and location 3. Furthermore, at locations I and 2. wear will he primarily due to both deformation and cutting;
31)4
R. Mishra et aL / W,,ar 217 t 1998) 297-306
whereas, at location 3. it will be primarily due to deformation. E.arlier studies 1141 have shown that wear is maximum at the locations at which both the phenomenon of wear work together. At higher efflux concentration of 28.73% at the same flow velocity, a consequent increase in the wear at different points can be attributed to an increase in the local concentration values near the points of wear measurement. resulting in higher cutting and deformation wear. The Variation of wear along the bend periphery at the three locations is similar to the one observed at lower efflux concentration. Across the bend surface, at locations I and 2, wear is almost similar, with the minimum wear being at the location 3. The measured wear at the higher flow velocity nearly at the same concentration and at higher concentrations indicate higher wear at location 2 and minimum at location 3. The reason for higher wear at location 2 as compared to i,.,.a;.k~ I l':ay be due to increased con;dbutioa of deformation wear at this location as compared to location I. with the effect of cutting wear remaining same ( Fig. 7c,d ). 5.3.2. Iso-c¢mcentrathm contours bz 1.5 A R B
Fig. 8 shows iso-conceatration contours at various efflux concentrations and flow velocities. Fig. 8a shows iso-concentratiou contours for an efflax concentration of 9.82% and flow velocity of 2.25 :n/s. It is clearly evident from the figure that panicles move clearly along the inner wall. which shows that the influence of secondary flows close to the bottom wall visa-vis that of centrifugal force. The maximum concentration anywhere in the section is noticed at the inner wall along the plane I-I. A comparison of this figure v.ith Fig. 7a brings out the effect of area ratio on the distribution pattern. As compared to constant area bend, in 1.5 ARB, iso-concentration contours are tilted upwards along the inner wall even above the middle plane. This indicates that more and more particles are travelling upwards along the inner wall. This may be because of increased secondary effects and reduced centrif ugal forces, which is insufficient to displace panicles outward. The reduction in centrifugal fo,rce has been mainly brought about by reduction in flow velocity due to increased area of cross-section. Similar trends are seen in Fig. 8c. which shows iso-concentration contours at increased efflux concentration of 28.73c~ at the same flow velocity of 2.25 m/s. The only notable difference is a reduced range of concentration values indicating increased homogeneity in the flow field with increasing el'flux concentration. The iso-concentration contours at a higher flow velocity of 2.89 m / s at efllux concentrations of 26.73~ and 36.83"h are depicted in Fig. 8c,d. Comparison of Fig. 8c with Fig. 8b indicates that the increase in the flow velocity has increased the effect ~ff centrifugal force on the flow. In the upper half of the bends, concentration contours are tilted upwards towards the outer wall zone in around 70c/, of the portion. Similar effects are seen in Fig. 8d at higher concentration and velocity. The wear ob.~rved under different flow conditions in 1.5 ARB can also be explained on the basis of concentration lield observed. The reduction in we~u in this bend as compared to
constant area bend at smaller efflux concentration (below 40oh) is primarily due to reduction in local concentration values near the points of wear measurement. This change is brought about by the reduction in flow velocity and centrifugal force, thereby increasing the influence of secondary flow. Generally, wear in this bend is maximum at the location 2 and minimum at location 3. This may have been again brought about by relative importance of cutting and deformation wear at different locations.
5.3.3. Iso-concentration contours h~ 2.0 A R B
Iso-eoncentration contours lbr area ratio 2 bend are shown in Fig. 9. Fig. 9a shows the iso-concentration contours for tbe efflux concentration of 9.82% at a flow velocity of 2.25 m / s. This figure indicates that bulk flow .............; ......... i;~,:, aloi~g ;.i,,~ inner wall of the bend, and there are lesser number of particles near the outer wall. The effect of centrifugal force is limited to outer upper quarter of the bend, and in the remaining area, strong movement of the solid particles towards the inner wall is seen. The pattern of solid distribution observed here clearly establishes the effect of modified geometry of the bend on the flow structure. A comparison of this figure with Fig. 7aFig. 8a shows that, as the area of cross-section of bends at the 45 ° plane increases, particles are forced towards the inner wall of the bend. This phenomenon has been brought about by the reduction in centrifugal force, owing to reduced velocity along with the induced diffusion along the outer wall of the bend. Thus, the geometry of the bends are serving the purpose for which they were envisaged. A similar pattern is seen at the efflux concentration of 28.73% at the same flow velocity (Fig. 9b) with solid particles being more or less unilormly distributed. The effect of flow velocity on the solid particle distribution can be seen from the comparison of Fig. 9b.c. The increase in velocity from 2.25 m / s to 2.89 m / s has increased the area of predominance of centrifugal force along the outer portion of the bend. At an higher efflax concentration ( Fig. 9d }, an increase in velocity causes vigorous mixing of the particles making distribution much more homogeneous. The wear measured at different locations in area ra;io 2 bend show uniformity in their values, i.e.. at any given velocity and efflux concentration, wear is almost the same at all the points of wear measurement. This may be due to almost uniform distribution of solid panicles across the bend crosssection. The increase in wear with an increase in concentration of solid panicles at all the locations is due to the increase in local concentration value at the points of wear measurement. The increase in the wear with increase in flow velocity may be due to increased impact of the particles. In the overall sense, minimum wear was observed in bend with area ratio 2 as compared to other bends (area ratio 1 and 1.5}. This is clearly due to: ( I ) diffusion along outer wall, (2) reduced flow velocity. ( 3 } reduced centrifugal force. ( 4 } the presence
R. Mishra et aL / Wear 217 (1998) 297-306
of secondary flow, and action.
(6)
305
increased particle-particle inter-
I ~ c.. ~.,on
3.3
4-
5.4. Flow behavioar in bends near depositional veloci~, in the straight pipe
Cw " 27~
4K C w " 4 8 4 g e&
2e
23
It has been seen that modified bends are comparatively less prone to wear compared to constant area bends, and hence will have a longer life. The effect of increa.se in the area of cross-section of modified bends will, however, result in reduced velocity of flow in them as compared to flow velocity in straight pipe and constant area bend. Thus. it is important to ascertain that, whether deposition in modified bends will take place before or after the deposition in straight pipe because lower flow velocities may cause earlier bed formation in pipe bends and may lead to choking. Generally, in constant area bends, deposition of particles takes place at a much lower velocity as compared to straight pipe, because of the presence of secondary flows that tend to make the particle distribution more uniform, resulting in the suppression of deposition in bends as compared to a straight pipe [ 12 ]. However. the same cannot be said with confidence about the deposition pattern in modified bends due to the reduction in the a b ~ l u t e values of local velocity. Thus, experiments were specifically conducted to ascertain this aspect in all the three bends. It has been proved earlier [ 15 ] that at the point of deposition, the local concentration of solids at the bottom are approximately 80% of the static-settled concentration value. Thus, the local concentrations at the likely points of deposition in different bends would be :he true indicators of deposition behaviour of different bends. Experiments were thus conducted by measuring concentration in straight pipe, as well as in different bends at points where deposition was likely to hake place, over a wide range of efflux concentrations ( 12.78% to 48.49% by weight). The flow velocity selected was 1.54 m/s, which is very close to the deposition velocity in straight pipe ( 1.50 m / s ) . Fig. 10 depicts normalized bottom concentration ( ratio of local to efflux solid concentration) 5 mm from the bottom of pipe (BOP) for straight pipe. as well as the three bends at different efflux concentrations. At the lowest efflux concentration (12.78%). the normalized bottom concentration is close to 3. I in straight pipe. where as, in constant area bend tile value observed was close to 1.70. In modified bend with area ratio 1.5, normalized bottom concentration value was 1.3; whereas, in area ratio 2 bend, it was 1.14. This indicates that, in all the bends, local concentration at bottom points is much smaller than that in straight pipe. Thus, it can be concluded that deposition in bends will take place much later than that in straight pipe. At the next efflux concentration of 27.69%. similar trends were observed, except that difference between concentrations in straight pipe and bends has been reduced. Similar trends continue at the highest efflux concentration of 48.49%.
1.8
m ÷
1
o
08
lip. ~ ,m-*.o h.m m.n.s ~ ~a..ei Fig. IO. Variationof m~rraalisedhonom concentration(at 5 mm from bottom) in straight pipe and bends at different efflux concentrationand an ::~'crag~P.owvclot:ltyof t.54 m/s. 6. C o l l u d i n g r e m a r k s Detailed studies on three hems. namely, constant areahend and two diverging-converging bends have been reported in terms of wear. concentration and deposition velocity. Studies on wear characteristics have shown that minimum wear is always associated with diverging-converging bend with area ratio 2. and it is even less than the wear at the bottom of a straight pipe. Hence. the diverging-converging bend with area ratio 2 can be expected to have a longer life than both the constant area bend and even straight pipe. Measurements of concentration field in different bends have shown that solid particles are more uniformly distributed in modified bends as compared to the constant area bend, and is nearly uniform for area rado 2 bend. This coutd be the reason for the observed uniform wear in the area ratio 2 bend at the points of wear measurement. The uniform distribution of solid particles in this bend is ~ne to the interaction of strong .secondary flows and centrifugal forces. Another important feature observed is that, in spite of increase in the area of cross-section, deposition does not take place in bends near the deposition velocity in straight pipe. Based on the above findings, it can be concluded that diverging-converging bend with area ratio 2 offers many attractive features and can be used in practice for slurry pipelines.
7. Nomenclature
AR C~,.,,m Cw C+c.. D ,~
Area ratio Concentration at y/D = 0.05 ( % ) Concentration by weight (%) Efflux concentration by weight (%) Diameter of the pipe (m) Distance along any diametrical planc from the lower surface of the pipe (m) ( for horizontal plane, the distance is from the outer surface)
R. Mi.~hra et aL / Wear 217 (1998) 297-306
31)6 r R V 3'
Pipe radius ( m ) Radius o f curvature o f the inner surface o f the bends ( m ) Local flow velocity ( m / s ) Distance along the vertical diameter from the bottom o f the pipe ( m )
1141 AJ. Karabelas. An experimental study of pipe erosion by turbulent slurry flow. Prne. HT 5, BHRA Fluid Eng., Crainfield, UK. Paper E2. 1978, pp. EI5-24. 1151 D.R. Kaushal. V. Seshadri, S.N. Singh, R.C. Malhotra, Estimatlon of deposition velocity in the flow of multisized particulate slurries based on concentration protile prediction, Prnc. 12th Natl. Conf on FMFP. Madras. India, 1995. pp. 438-444.
Biographies References [ I I M. Tt~la. N. Karm)ri.S. Salt. S. Maeda. Hydraulic conveying of solids through pipe bend, J. Chem. Engg. Japan ( 19711 5. 121 H- Nasr-EI-Din. C.A. Shook, Effect of 90° bend on slurry velocity and concentration distribution, J. Pipelines 6 (1987) 239-252. 131 M. Ahmed. S.N. Singh. V. Seshadri. Distribution of solid particles in mutli-sized slun"y flow through 90° pipe bend in horizontal plane, Bulk Solids Handling 13 t 2 ) ( 1993) . 141 G. Rajat, Erosion wear in pipelines, PhD Thesis. Indian Institute of Technology, Delhi, 1994. 151 V. Seshadri, R.C. Malhotra. S. Chander. Pilot plant study ti)r the hydraulic transportation of bauxite ore. Internal report prepared fi)r Engim.'ersIndia, Department of Applied Mechanics, liT. Delhi, India, 1976. [ 61 S. Murakami. T. Kawa_shima.S. Tsukahara. T. Okada. Wear test on pipelines for hydraulic transport of dam delx)sit. HT 7. BHRA Fluid Eng.. Cranlield. England. 1980, pp. 315-330. 171 W. Wideuroth. Wear tests executed with a 125-ram ID pipe-hmp and a model dredge pump. HT 9. BHRA Fluid Eng.. Cmntield, England. 1984, pp. 317-330. 181 J.S- Maim. B.Y. Smith. Powder Technol. O ( 1972) 323-335. 191 D. Mills. J.S. Ma-~m, Particle size effects in bend erosion. Wear 44 t 1977) 311-328. I till D. Mills. J.S. Mason, Conveying ",elt~ity effects in bend erosion, J. Pipelines I ( 1981 ) 69-81. I 111 K. Horii. Y. Matsumae. X.M. Cheng, M. Takei. E. Yasukawa. B. Ha..,ia~to. Trans. ASME. J. Fluids Eng. 113 ( 1991 ) 149-15 I. 1121 A. Mukhtar. lnvestigation oftheflow ofmultisizedslurriesin straight pipe and pipe bends, PhD Thesis. liT. Delhi, 1991. 1131 R. Mishra. A study on the flow (~f muhisized particulate solid-liquid mixtures in horizontal pipelines. PhD Thesis, liT, Delhi. 1996.
Dr. Rakesh Mishra Received his PhD degree from Indian Institute o f Technology, Delhi. He has 10 years o f teaching and research experience. He has published 10 research p a p e ~ and guided 7 ME theses. At present he is Senior Lecturer in the Department o f Applied Mechanics, M N R E C , Allahabad, India. Currently, he is working in the field o f optimisation and reliability based studies o f hydraulic and capsule transportation o f solids. Prof. Dr. S.N. Singh Received his PhD degree from Indian Institute o f Technology, Delhi. He has 20 years o f teaching and research experience. He has published 148 research papers and has also been a consultant to m a n y industries. Currently, he is Professor in the Department o f Applied Mechanics, lIT, Delhi. He has guided 25 M T e c h and 6 PhD theses in the area o f aerodynamics and pipeline slurry transportation. Prof. Dr. V Seshadri Received his PhD degree from Brown University. Providence. USA. He has 30 years o f teaching and research experience. He has published o v e r 150 research papers and also has been a consultant to a large n u m b e r o f industrial/consuhancy organisations. He is at present Professor in the Department o f Applied Mechanics and Chairman, Estate and Works. liT, Delhi. He has s u p e r v i ~ d 18 PhD and m a n y M T e c h theses, in the area o f fluid mechanics and slurry pipeline transporfadou.
Wear 217 (1998) 297-306
Study of wear characteristics and solid distribution in constant area and erosion-resistant long-radius pipe bends for the flow of multisized particulate slurries Rakesh
M i s h r a ~, S . N . S i n g h b, V . S e s h a d r i b . ,
Department of Applied Mechanics. MNREC. Allahabad. India h Department of Applied Mechanics. Indian Institute of Technolog)~ New Delhi. India
Received 18 July 1997:accepted 9 January 1998
Abstract The wear characteristics of three types of long radius pipe bends in the flow of multisizcd particulate slun'ics have been extensively ~udied. Conventional long radius bend, and two types of diverging-convergingbends are investigated. MeasuremenLs have been made over a range of solid concentrations and flow velocities. The results have shown that diverging-convergingbend with an area ratio 2 exhibiLs reduced wcm-. and in fact can even be expected to have a longer life than a straight pipe. Furlber, measurement of solid di.qribmion in the three bends has given some insight into the causes tbr the reduced wear in these modified bends. It h0s also been demonstrated that the diverging-converging bends even with enlarged cross-sections are not prone to choking when the pipeline is operating near critical d e , ilion velocity. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Slurry pipelines: Pipe bends: Erosion wear: Solid distribution
I. Introduction Bends are an integral part of any pipeline network system. In solid-liquid pipeline systems, bends are prone to excessive wear and their failure leads to excessive loss of time and money. Concerted efforts have not been made to improve the constant-area long-radius hencks commercially available for their suitability to solid-liquid flows. Toda et al. [ I ] were the first to investigate the flow characteristics in pipe bends for slurry flows. They observed that the particles are forced towards the outer wall as a result of centrifugal force generated in the bends. Nasr-EI-Din and Shook 12 ] measured the slurry velocity and concentration downstream o f bends with short and long radii. They observed that the distribution of particles was skewed lot long radius bend. whereas particles retained the original distribution for the short radius bend. Ahmed et al. [ 31 measured the concentration in the horizontal and vertical planes o f a conventional bend (radius ratio = 4.0) at the mid-section. They concluded that particles migrated from the vertical plane perpendicular to the plane * Correspondingauthor. Dept. of Applied Mechanics.Indian Institute of Technology. Hauz Khas. New Delhi I I0 016. India. Fax: +91-11-6862037. 0043-1648/98/$19.00 © 1998ElsevierScience S.A. All right~reserved. PII S0043-1648 ( 98 )00147- I
of the bend towards the diagonal planes. Gup4a [41 has reported the concentration distribution in a 55-mm pipe bend ( radius ratio = 5.5). He observed the concentration o f coarser particles to be higher near the bottom portton o f the outer wall whereas, the filler particles were more or less uniformly distributed. His measurements support the observatio~¢ o f earlier investigators [ 1,21. Wear studies in bends for solid-liquid mixtures are limited. Seshadri et at. [ 5 ] have measured overall wear in long-radius 9 0 ° bends and compared it with straight pipe. They observed wear in bends to be approximately double that in the straight pipe. Murakami et at. [ 6] have reported wear measurements along the periphery o f a 9 0 ° bend and observed the wear to he more in the first half o f the bend. Widenroth [ 7 ] hascarried out wear rate studies in a 90 ° bend by measuring the wall thickness at different locations. He observed that wear rate increases in the first half o f the Lend and then gradually
reduces. Wear studies in bends for pneumatic conveying systems have been reported by .several researchers 18-111. Horii et al. [ I I ] developed a Lend with a diverging and a converging portion upstream and downstream o f the bend. They observed considerable reduction in wear in this Lend as compared to the constant area bend. The studies in bends for solid-liquid
298
R. Mislm] et aL / Wear 21711998) 297-306
mixtures and gas-solid system have clearly established the excessive wear in bends, but have not been able to identify the basic mechanism, in the pre~nt study, an attempt has been made to measure the erosive wear at the mid-plane of a 90 ° bend for solid-liquid mixture along with complete mapping of the solid distribution. The study has been carried out on three bends, namely, a 90 ° constant area bend and two diverging-converging bends with area ratios of 1.5 and 2.0.
2. Design and development of diverging-converging bends Investigations on bends in solid-liquid flows have shown that the primary reasons lor erosive wear in bends are migration of larger-size particles [4.12] and velocity-related effects. The solid particles directly impact against the outer wall of the bend leading to larger deformation wear. Hence, it is expected that reduction in the impact velocity of particles will reduce erosive wear in the bends. In order to exploit this mechanism, the modified geometry for the bends was envisaged. The basic philosophy in the development of diverging and converging bends was to initially reduce the flow ~,elocity and then create a favourable pressure gradient in the downstream, in these bends (Fig. I ), the radius of curvature of the inner wall was kept the same ( R / r = 3) as the constant area bend. This was done to have a reduction in velocity, as well as particle migration towards the outer wall. The area ofcross~ction of the modified bends was increased linearly from inlet to the middle of the bend to enhance diffusion, then the area was reduced linearly up to the outlet at the same rate. The cross-section of the bend was always kept circular along its length. The maximum cross-sectional area of the two fabricated bends was kept at 1.5 and 2 times the original pipe area. and this occurred at the mid-section ( see Fig. I ). This
/, I Fig. I. Plan ,Jew ol ihc three I~:ndsinvc'~titzalcdalong with the imporlant din~nsi~m~..
design leads to reduced velocity and enhanced intensity of secondary flows. It is further expected that the reduction in velocity and change in radius of curvature will reduce the effect of centrifugal forces on the flow field. It is envisaged that all the three mechanisms described above lead to more uniform distribution of the particles in the bend which, in turn, should result in the reduction of erosive wear. A somewhat similar concept was used by Horii et al. [ I I ] in pneumatic conveying systems.
3. Experimental set-up and measurement methods The test bends having fixtures for the measurement of wear and concentration field at the mid-plane of the bends are fitted in the pilot plant test loop as shown in Fig. 2a. Sufficient upstream and downstream lengths were incorporated before and after the bends to ensure undisturbed flow at the inlet. The solid distribution in the bends was measured along 4 diametrical planes, as shown in Fig. 2b, at the middle crosssection using sampling tubes ( Fig. 2c). Out of the tour planes. one was vertical (plane 2-2) and another was horizontal (plane 4-4). The remaining two planes were ( I-I and 3-3) at an angle of +_45 ° with vertical. The closest point to the wall at which concentration was measured along different pla,)es was 5 mm from the wall. Sampling tubes were traversed along the identified planes, and samples were collected under near iso-kinetic conditions. Concentration at any measurement point was evaluated from the measured density of the collected slurry sample. The concentration along each plane was measured at seven points to adequately cover the total cross-section of the bend. In line with the aims of the present study, arrangements were made for the determination of wear rate in the bends. Rajat [ 41 has shown that the primary reason for the enhanced wear in bends is the impact of the particles on the outer wall. He has also shown that bulk of the solids move towards the outer wall increasing the local concentration, which also tends to increase the wear in bends. Thus, the bottom quarter of the outer wall of the bend was considered critical for studies of the wear rate in bends. Hence. three locations were selected in each of the three bends for determination of wear as shown in Fig. 3a. At all the three locations brass (composition- 70% Cu, 30c~ Zn. sp. gr.: 8.5 and Rockwell hardness: 94 (.scale B ) ) w0ar pieces having surface area of 25 mmX 15 mm and thickness equal to that of the mild steel pipe wall were fitted as shown in Fig. 3b. The whole fixture consisted of mild steel cover plate, rubber packing, fixing screws, aligning screws and adjustable holding screw. The brass wear piece was held to the cover plate by adjustable holding screw. The cover plate was fixed to the bend surface after placing the rubber packing with fixing screws. Two aligning ~ r e w s were provided on the mild steel cover plate for aligning the wear piece flush with the inner surface of the bend. All t h e ~ fixtures ensured the exact positioning of the wear pieces in the bends
R. Mishra e! .It / Wear 217 (19Q8) 297-306
(a)
_'299
Stirrer
FLov
div.tir ~ .
/ • [ t~
]
1
/Oen~ityum0ttw
~.~)f.I /._9end(inherizontotptone
:',I'?I17/""
)
+ i ?. . . . . .". . ,. . . . . . " ,'I
,'
4
.. -
i ~ o . to.gl
W e l test rig
- " -- ~ : ~ $ i . r r l li.,I.li 1-IpllneI hid• 1.0 2-2Plane2 3-3 ......... PIine3 h/Dh/O~~~" 1.0 122~.// hiD• 1.0
+> ,==
(C)~~~TOSAMII[N ~.
;o.odS,+: I
h/O
~/hid
• O.O
• O.O
Fig. 2. (a) Schematicdiagramof the pih)t planl: ( b ) Planesof me~,~uremcnzstit concentration profile in Ibe mid-sectionof Ibe bends: (c) Clmcenlrali~m samplingprabe. to avoid discontinuity in the pipe and wear piece surfaces. For the purpose of comparison, the wear in the straight pipe was also measured at the three locations, namely, bottom of the pipe "A'. middle of the pipe "B" and topmost point "C" on a given cross-section of the pipe (Fig. 3a). The pilot plant test loop (Fig. 2a) u ~ d in the pre~nt study consisted of a closed pipe test loop of 105 mm NB pipe having a length of 60 m. a mixing tank. a measuring tank and other test fixtures [ 13 ]. To monitor the efflux concentration, a density sampler was provided in the vertical portion of the pipe loop. Efflux concentrations, for different flow conditions, were calculated from the measured density of the efflux samples.
concentrations (approximately 30% and 40% by weight). The concentration lields were al,q) determined along the four planes for all the above combinations ofefflux concentrations and flow velocities. Solid distribution in the bends was also investigated at different efflux concentrations near the deposition velocity in the straight pipe. This wa~ done to detect the occurrence of particle deposition in the bends under conditions when bed formation is beginning to lake place in the straight pipe.
$. Results and discussion 5. I. W e a r cbaraewristics a f bend.~
4. Materials used and range of parameters The tailing material (waste material after the extraction of zinc from the ore) collected from a zinc processing plant has been used in the pre~nt study to prepare the slurry by mixing it with water. The physical properties of the material are given in Table I. It is ~ e n that 55% particles are Icss than 75/.tin and only 2% particles are larger than 0.3 ram. The specific gravity of the solid particles was 2.85 and static-~ttled concentration was 60% by weight. The range of efflux concentrations covered was from 9.82% to 41.21% by weight. Wear was determined by measuring the loss in weight over a fixedtime interval at one flow velocity (2.25 m / s ) for two lower efflux concentrations ( 9.82% and 20.32% by weight), and at two velocities (2.25 m / s and 2.89 m / s ) for higher efflux
Wear in different bends has been measured at different efflux concentrations and flow velocities. Wear was determined by measuring the weight loss of the brass specimen after running the pilot plant for I0 h at a given flow velocity. Measurement of particle size distribution before and after any experimental run did not exhibit any appreciable attrition of the particles. The data on wear for bends and straight pipeline is given in Table 2. 5. I.I. W e a r in ctmslaat area b e n d
Table 2 gives the variation of wear at all the locations for the constant area bend ( R / r = 3) ( I ARB). It is ~ e n that the wear inerea~s with increase in efflux concentration at location I at any flow velocity. The wear increases gradually up
R. Mishra et al. / Wear 217 (19Q8) 297-306
300
Table I Physicalpropertiesof the zinc tailings slurry Inner
w
a
l
~
u
t
e
r will
LOCATION 2
Panicle size (ran;)
% finer
0.85 0.30 0.21 0.15
100.0 96.26 85.9 I 78.57 63.67 .51.39
0.106
0.075
(a) Overall specificgravity of the solid material: 2.85. (b) Static settling concentralion:60.21 ( ¢/~by wt.). (e) Panicle size distribution.
e,nu LOCATION C
LOCATION A (a) St ¢=hil~.L~p£ ttotOln9
~,c few
namely, 26.73% and 36.83% by weight, and it is ~ e n that the increase in the flow velocity causes only marginal increase in the wear at both the efflux concentrations (Table 2). The trend also supports the steep increase between these concentrations as seen at lower velocity. The variation o f weight Joss in constant area bend, at location 2, is seen to be similar to location I. The maximum weight loss for this location was measured as O.O117 g for 41.21% efflux concentration for lower velocity, and 0.0121 g for higher velocity at an efflux concentration of 36.83%. The weight loss at location 3 for the same bend also seems to be similar, i.e., wear increases with increase in the efflux concentration. The measured wear is maximum at the highest efflux concentration tested. A comparison of the wear at different locations in the constant area bend suggests that up to efflux concentration c l o ~ to 30% maximum wear is associated with location I, whereas the minimum wear is associated with location 3. At an efflnx concentration close to 40%, maximum wear is associated with location 2, whereas the minimum wear is still associated with location 3. This may be because o f predominance of deformation wear at location 3. whereas at kv,:ations I and 2, both deformation and cutting wear are dominant. The steep increase in the wear beyond an efflux concentration of 30% at all three locations could be due to substantial increase in the contribution of cutting wear to the overall wear. 5.1.2. W e a r in b e n d with area ratio 1.5
/
~1
L
i
j
T
Fig. 3. (a) I~Jtails of the hx:atlonof .,-earpicot.., in hendsand ~.traightpipe: t b) Detailsof the lest |ixlure for tixingand aligningof the brass wear pieces in the straight pipe and bends. to a concentration of 28.73% and the further increase is steep at high efflux concentnltion. The maximum wear was 0.008 I g at 41.21% efflux concentration. At higher vekx:ity of 2.89 m / s . the wear was measured at two efflux concentrations.
Table 2 also gives the variation o f wear for the bend with area ratio 1.5. The variation of wear indicates that at lower flow velocity ( 2.25 m / s ) , wear increases with an increase in el'flux concentration. At 41.21% efflux concentration, wear shows a significant increase. It is also seoa that an increase in vek)city increases the wear significantly at an efflux concentration close to 30%. A similar effect is .seen even at higher concentration. A comparison of corresponding data with constant area bend shows that up to 30% ¢fflux concentration for lower flow velocity, the wear in the I..5 area ratio bend is less than the constant area bend. At higher efflux concentration (close to 40% ) there is not much change in wear characteristics in the two bends as far as bottom o f the bends is concerned. Even the trends and magnitudes of wear are similar. At location 2 in 1.5 ARB, the effect of efflux concentration
R. Mishra et aL I Wear 217 ( 1998~ 297-306
Table 2 Wearcharacteristicsin the bends and the straight pipes Bend or straight pipe
Constant area bend
Locations
I 2 3
Diverging-convergingbend witharea ratio 1.5
I 2 3
Velocity (m/s)
Wear (g) Cw, =9.82%
Cw: = 20.32~ Cw, = 27.73ch Cw~= 39.112t,~ ( 28.73c/,([email protected] ) 36.83ch )
2.25 2.89 2,..?5 2.89 2.25 2.8t.)
a.lXt29 O.(X)30
n.n4D6
U.IXII2
n.lx)21
2.25 2.89 2.25 2.89
O.(IIX)t)
O.IX)I2
().iX) 12
0.(1015
2. ")5
O.(XX)8
().(X)14
().1X134
2.89 Diverging--convergingbend with area ratio 2.0
l 2 3
Straight pipe
Bom)raof pipe. location "A"
2.25 2.89 2.25 2.80 2.25 2.89
O.IXI05
O.IN;II
().txx)o
n.lX)l2
n.txx)6
n.tx)14
2.25
0.(X123
1k0032
2.89
and flow velocity on wear is .seen to he similar to location I with marginal fall in the values of wear. A similar trend is seen for wear at location 3 also. An analysis of wear at different locations in 1.5 ARB suggests that maximum wear is associated with location 2 at an efflux concentration of 36.83% for the higher flow velocity. A comparison of wear at different locations at corresponding efflux concentration and flow velocities in the constant area bend and 1.5 ARB suggests marginally reduced wear in 1.5 ARB. 5.1.3. W e a r in the b e n d n'ith area ratio 2 Table 2 also gives the wear data for bend with area ratio 2.0 ( 2 ARB). At location I. wear increases with the increase in efflux concentration, but the values are much smaller as compared to other two bends. The maximum value of 0.0047 g of weight loss for an efflux concentration of 41.21% at a velocity of 2.25 m / s is only 60% of the weight loss measured in the constant area bend. The rate of increase in wear is seen to rise steeply between efflux concentrationsof30% and40%. a trend which is similar to the other two bends. An increase in velocity increases the wear, but the effect is only marginal. Similar features are seen tbr wear at h)cation 2 in the :ame bend. The effect of velocity appears to he somewhat more pronounced at this location with other features remaining the same as at location I. The maximum wear at this location is 0.0041 g for an efflux concentnltion of 41.21% at lower velocity (2.25 m / s ) . and is only 35% of the constant area bend. The wear at the higher velocity ( 2.89 m / s ) is 0.0049
0.OO41 0 (X)51 O.(X)41 o.on5 0.1X132
11.0o8i U.IX)~) O.O117 0.012 I U.O061
n.oo51
0.01164
0.0021 1).11n5 1).0n2_7 11.0048
11.11082 11.n079 n.o I I U.(l12
O.(X)17
0.0074
0.1X132
(t.f1076
U.0017 U.(X)26 {).Ill)17 n.ix)26 ().(X)16 n.iN)28
().01M.7
n.00.~;7
u.lxt5 I
(1.0n3,I
U.IXK) l
0.11046
O.(X)41 0.(N)46 0,1X142 U.iX)51
g. and is only 40c,~ of the wear in constant area bend at the same concentration. Similar effecLs are also observed for location 3 in 2 ARB. An overall comparison of wear at different locations in 2 ARB demonstrates that the wear is almost uniform at the three locations at which wear has been measured. The effect of increasing efflux concentration and flow velocity on wear is also similar at all three locations. A comparison of wear at the three locations for the three bends suggests that minimum wear is associated with the 2 ARB. The reduction in the wear of this bend could he attributed to the geometry used. In the 2 ARB. velocities at the mid-section are half as compared toconstant area bend, which result.,; in considerable reduction in the centrifugal force. This. along with diffusion and generation of secondary flow. would he causing the particles to move toward.,; the inner wall. This brings about considerable reduction in wear in 2 ARB.
5 . Z Relative w e a r hi bends
It is known that wear in bends is more than thai in a straight pipe. In order to quantitatively analyze the wear in bends visa-vis that in straight pipe. relative wear has been calculated. The wear in the straight pipe is maximum at the bottom. Thus. the relative wear for any location in a bend is presented with respect to the wear at bottom of the straight pipe. Table 2 al.,a) gives the variation of wear measured at the bottom of the straight pipe.
302
R. Mishra el al. / Wear 217 f 1998) 297-306
Fig. 4 shows the relative wear calculated at the bottommost point in different bends. The relative wear in the constant area bend is always more than I, indicating higher wear in the bend as compared to that at bottom of the straight pipe. The variation of relative wear up to efflux concentration of 28.73% by weight at lower flow velocity is marginal, but beyond this concentration, the relative wear increases steeply, indicating enhanced wear in bend as compared to a straight pipe. At higher flow velocity of 2.89 m / s . the effect of increase in concentration on relative wear is marginal. Similar features are noticed for the other two bends with area ratio 1.5 and 2.0 also. However, minimum relative wear at any efflux concentration and flow velocity is always associated with 2 ARB, whereas, maximum relative wear is associated with constant area bend except at highest efflux concentration o f 41.21 ~ and flow velocity of 2.25 m / s , at which relative wear in 1.5 ARB is marginally higher than that o f conventional bend. It is also seen that for 1.5 and 2.0 area ratio bends. the relative wear value is around 0.5 for efflux concentrations less than 30% for lower velocity. For 2 ARB. the relative wear values are less than 1.0 even at higher velocity and highest efflux concentration. This implies that bends with an area ratio of 2.0 will have a life span equal to or more than the straight pipe. Fig. 5 shows the relative wear in different bends at location 2. The relative wear in the constant area bend is always more than I at this location also. indicating higher wear in the bend as compared to straight pipe. The variation of relative wear at this location is similar to the one observed at location I. Similar features are noticed for wear for the other two bends. The minimum relative wear at any efflux concentration and flow velocity is always associated with 2 ARB even at this location, whereas maximum relative wear is associated with constant area bend. It is also seen that for 1.5 and 2.0 area ratio bends, the relative wear value is close to 0.5 for efflux concentrations less than 30ch for lower velocity. For 2 ARB, the relative wear values are less than 1.0 even at higher velocity and highest efflux concentration. This implies that local wear in 2 ARB will always be less than that at the bottom in straight pipe. Fig. 6 depicts the relative wear at the location 3 in different bends. This figure has similar features. At this location for I ARB and 1.5 ARB relative wear is less than I at the lower velocity of 2.25 m / s up to efflux concentration of 28.73ch ; however, at 41.21ch efflux concentration, relative wear is more than I. indicating su~eptibility of these bends to earlier failure compared to the straight pipe. For 2 ARB. relative wear is always less than I. indicating increased wear rcsislance of this bend. A comparison of Figs. 4 - 6 suggests that higher relative wears at different locations are always associated with either I ARB or 1.5 ARB irrespective of the flow velocity and efflux concentration. Further. maximum wear in these bends is eitber at location I or location 2. The 2 ARB shows minimmn wear for all locations. This proves that bend with area ratio 2
Relative Weflt
2
e
× An-1
o o
+
V , 2 2 5 role
A~I,I v . 2 8 a m / s An.1.5 V , 2 2 5 rn/l
× o
AR=15 v.2 Bn rots
x
An,2
v.2gsm/s
0 An.2 v,2snm/m Fig. 4. Variation of relative wear ( w e i g h t loss at location I in bend/weight loss in straight pipe at location A ) as a function of efflux concentrationand flow velocities. Relative wear
2,5
15 c,
1
+
o~
20
30
V.2.2~ rn/s
AR.1
v,2.et)nv=
Aa.l.5 V.22S r*l=
05
lo
ARol
40
a
,n.~.5 v . 2 m l m,'s
x
AR"=.O V"'Z.Z6 m,'=
50
Cw (%)
Fig. 5. Variationof relative wear ( weight loss at location "2' in rend/weight loss in straight pipe at location "A' ) as a function of efflux concentration and llow vehv,:ities. Relative Wear
't ',~
÷
%
o 06
&
r)4
4,
e. +
9
~
kn.l AR.I
02
lo
20 Cw
30 (%)
40
m,5
o
.,m.ls v.2 s~ m,s
×
AR'2 Am=
o
v,225m/s v.2S{~mts
AR-~ 5 V . ~ 5
v.225mt= v . 2 s o m,=
50
Fig. 6. Variationof relative wear ( weight loss at location 3 in I~nd/weight loss in straight pipe at location A) as a functionof e[flgx concentrationand flow vek~ities. has better wear resistive characteristics compared to constant area bend and bend with area ratio 1.5. 5.3. Crmcentration field in bends
To have more insight into the mechanism of wear in the three bends, the concentration field was measured along four
g Mi.~hra et al. / Wear 217 (199~;)297-306
planes in each of them. The overall concentration distribution in the three bends for selected combinations are presented in Figs. 7-9 in the form of iso-concentration contours. These contours have been drawn using a software package "Surfer'. The package uses cubic spline fit and a very fine interpolation routine. The number on each contour represents the ratio of local solid concentration to the efflux concentration. 5.3. I. Iso-concentration contours in conventional b e n d
Fig. 7a shows the concentration contours at a flow velocity of 2.25 m / s and an efflux concentration of 9.82% in the constant area bend. The figure clearly shows the effect of centrifugal force in the upper portion of the bend where concentration shows increasing trend towards the outer wall: however, in the bottom portion, there is clear indication of movement of particles towards the inner wall. The observed distribution of the solid particles is indicative of predominance of centrifugal force in the upper part of the bend, whereas that of secondary flows, on the lower portion of the bend. Similar features are also seen in Fig. 7b for an efflux concentration of 28.73% at the same flow velocity. This figure indicates increased homogeneity vis-a-vis Fig. 7;), which may be because of increased particle-particle interactions. The effect of flow velocity on isc~concentration contours can be ~ e n by comparing Fig. 7c which shows iso-concentration contours at an efflux concentration of 26.73% at a flow velocity of 2.89 m / s with Fig. 7b. With an increase in flow velocity, the area of predominance of centrifugal force has increased marginally. A similar trend is seen at the higher concentration ( Fig. 7d), but the homogeneity has increased further. The measured wear under different conditions of flow can be explained now from the information available from the
£Wl,9.1~ "/. V.Z.IS,w, lS
m ¢w,,~-7~% V.~g~nqS
i~) c w ~ i ..n °1. votqHin~'s
calc~un,'/. v.a4h,/s
Fig. 8. Iso-conccntrationcontour~in arc-..Iratio 1.5 bend.
v,,.j.~l$ nltlr,
Icl Cw, 2 l , r ~ "I, v = z41') ml~, Fig. 9. Iso-concentralion contours in area
to) Cw .z6.73 % vlz41g,W*
[d) Cw • ~I.83"/, v.z.ltm/l
Fig. 7. ]so-concentration contours in area ratio I bend.
v=2-2Sm/s
( ~ Cw,~,-13*t* v = ~ , N mrs
ratio 2.0 bend.
iso-concentration field. At the lowest efflux concentration of 9.82% for a flow velocity of 2.2.5 m/s, the maximum wear was noticed at location I followed by location 2 and location 3. As seen in iso-concentration contours, the maximum concentration of the solid particles are observed at location I out of the three locations at which wear was measured, followed by location 2 and location 3. Furthermore, at locations I and 2. wear will he primarily due to both deformation and cutting;
31)4
R. Mishra et aL / W,,ar 217 t 1998) 297-306
whereas, at location 3. it will be primarily due to deformation. E.arlier studies 1141 have shown that wear is maximum at the locations at which both the phenomenon of wear work together. At higher efflux concentration of 28.73% at the same flow velocity, a consequent increase in the wear at different points can be attributed to an increase in the local concentration values near the points of wear measurement. resulting in higher cutting and deformation wear. The Variation of wear along the bend periphery at the three locations is similar to the one observed at lower efflux concentration. Across the bend surface, at locations I and 2, wear is almost similar, with the minimum wear being at the location 3. The measured wear at the higher flow velocity nearly at the same concentration and at higher concentrations indicate higher wear at location 2 and minimum at location 3. The reason for higher wear at location 2 as compared to i,.,.a;.k~ I l':ay be due to increased con;dbutioa of deformation wear at this location as compared to location I. with the effect of cutting wear remaining same ( Fig. 7c,d ). 5.3.2. Iso-c¢mcentrathm contours bz 1.5 A R B
Fig. 8 shows iso-conceatration contours at various efflux concentrations and flow velocities. Fig. 8a shows iso-concentratiou contours for an efflax concentration of 9.82% and flow velocity of 2.25 :n/s. It is clearly evident from the figure that panicles move clearly along the inner wall. which shows that the influence of secondary flows close to the bottom wall visa-vis that of centrifugal force. The maximum concentration anywhere in the section is noticed at the inner wall along the plane I-I. A comparison of this figure v.ith Fig. 7a brings out the effect of area ratio on the distribution pattern. As compared to constant area bend, in 1.5 ARB, iso-concentration contours are tilted upwards along the inner wall even above the middle plane. This indicates that more and more particles are travelling upwards along the inner wall. This may be because of increased secondary effects and reduced centrif ugal forces, which is insufficient to displace panicles outward. The reduction in centrifugal fo,rce has been mainly brought about by reduction in flow velocity due to increased area of cross-section. Similar trends are seen in Fig. 8c. which shows iso-concentration contours at increased efflux concentration of 28.73c~ at the same flow velocity of 2.25 m/s. The only notable difference is a reduced range of concentration values indicating increased homogeneity in the flow field with increasing el'flux concentration. The iso-concentration contours at a higher flow velocity of 2.89 m / s at efllux concentrations of 26.73~ and 36.83"h are depicted in Fig. 8c,d. Comparison of Fig. 8c with Fig. 8b indicates that the increase in the flow velocity has increased the effect ~ff centrifugal force on the flow. In the upper half of the bends, concentration contours are tilted upwards towards the outer wall zone in around 70c/, of the portion. Similar effects are seen in Fig. 8d at higher concentration and velocity. The wear ob.~rved under different flow conditions in 1.5 ARB can also be explained on the basis of concentration lield observed. The reduction in we~u in this bend as compared to
constant area bend at smaller efflux concentration (below 40oh) is primarily due to reduction in local concentration values near the points of wear measurement. This change is brought about by the reduction in flow velocity and centrifugal force, thereby increasing the influence of secondary flow. Generally, wear in this bend is maximum at the location 2 and minimum at location 3. This may have been again brought about by relative importance of cutting and deformation wear at different locations.
5.3.3. Iso-concentration contours h~ 2.0 A R B
Iso-eoncentration contours lbr area ratio 2 bend are shown in Fig. 9. Fig. 9a shows the iso-concentration contours for tbe efflux concentration of 9.82% at a flow velocity of 2.25 m / s. This figure indicates that bulk flow .............; ......... i;~,:, aloi~g ;.i,,~ inner wall of the bend, and there are lesser number of particles near the outer wall. The effect of centrifugal force is limited to outer upper quarter of the bend, and in the remaining area, strong movement of the solid particles towards the inner wall is seen. The pattern of solid distribution observed here clearly establishes the effect of modified geometry of the bend on the flow structure. A comparison of this figure with Fig. 7aFig. 8a shows that, as the area of cross-section of bends at the 45 ° plane increases, particles are forced towards the inner wall of the bend. This phenomenon has been brought about by the reduction in centrifugal force, owing to reduced velocity along with the induced diffusion along the outer wall of the bend. Thus, the geometry of the bends are serving the purpose for which they were envisaged. A similar pattern is seen at the efflux concentration of 28.73% at the same flow velocity (Fig. 9b) with solid particles being more or less unilormly distributed. The effect of flow velocity on the solid particle distribution can be seen from the comparison of Fig. 9b.c. The increase in velocity from 2.25 m / s to 2.89 m / s has increased the area of predominance of centrifugal force along the outer portion of the bend. At an higher efflax concentration ( Fig. 9d }, an increase in velocity causes vigorous mixing of the particles making distribution much more homogeneous. The wear measured at different locations in area ra;io 2 bend show uniformity in their values, i.e.. at any given velocity and efflux concentration, wear is almost the same at all the points of wear measurement. This may be due to almost uniform distribution of solid panicles across the bend crosssection. The increase in wear with an increase in concentration of solid panicles at all the locations is due to the increase in local concentration value at the points of wear measurement. The increase in the wear with increase in flow velocity may be due to increased impact of the particles. In the overall sense, minimum wear was observed in bend with area ratio 2 as compared to other bends (area ratio 1 and 1.5}. This is clearly due to: ( I ) diffusion along outer wall, (2) reduced flow velocity. ( 3 } reduced centrifugal force. ( 4 } the presence
R. Mishra et aL / Wear 217 (1998) 297-306
of secondary flow, and action.
(6)
305
increased particle-particle inter-
I ~ c.. ~.,on
3.3
4-
5.4. Flow behavioar in bends near depositional veloci~, in the straight pipe
Cw " 27~
4K C w " 4 8 4 g e&
2e
23
It has been seen that modified bends are comparatively less prone to wear compared to constant area bends, and hence will have a longer life. The effect of increa.se in the area of cross-section of modified bends will, however, result in reduced velocity of flow in them as compared to flow velocity in straight pipe and constant area bend. Thus. it is important to ascertain that, whether deposition in modified bends will take place before or after the deposition in straight pipe because lower flow velocities may cause earlier bed formation in pipe bends and may lead to choking. Generally, in constant area bends, deposition of particles takes place at a much lower velocity as compared to straight pipe, because of the presence of secondary flows that tend to make the particle distribution more uniform, resulting in the suppression of deposition in bends as compared to a straight pipe [ 12 ]. However. the same cannot be said with confidence about the deposition pattern in modified bends due to the reduction in the a b ~ l u t e values of local velocity. Thus, experiments were specifically conducted to ascertain this aspect in all the three bends. It has been proved earlier [ 15 ] that at the point of deposition, the local concentration of solids at the bottom are approximately 80% of the static-settled concentration value. Thus, the local concentrations at the likely points of deposition in different bends would be :he true indicators of deposition behaviour of different bends. Experiments were thus conducted by measuring concentration in straight pipe, as well as in different bends at points where deposition was likely to hake place, over a wide range of efflux concentrations ( 12.78% to 48.49% by weight). The flow velocity selected was 1.54 m/s, which is very close to the deposition velocity in straight pipe ( 1.50 m / s ) . Fig. 10 depicts normalized bottom concentration ( ratio of local to efflux solid concentration) 5 mm from the bottom of pipe (BOP) for straight pipe. as well as the three bends at different efflux concentrations. At the lowest efflux concentration (12.78%). the normalized bottom concentration is close to 3. I in straight pipe. where as, in constant area bend tile value observed was close to 1.70. In modified bend with area ratio 1.5, normalized bottom concentration value was 1.3; whereas, in area ratio 2 bend, it was 1.14. This indicates that, in all the bends, local concentration at bottom points is much smaller than that in straight pipe. Thus, it can be concluded that deposition in bends will take place much later than that in straight pipe. At the next efflux concentration of 27.69%. similar trends were observed, except that difference between concentrations in straight pipe and bends has been reduced. Similar trends continue at the highest efflux concentration of 48.49%.
1.8
m ÷
1
o
08
lip. ~ ,m-*.o h.m m.n.s ~ ~a..ei Fig. IO. Variationof m~rraalisedhonom concentration(at 5 mm from bottom) in straight pipe and bends at different efflux concentrationand an ::~'crag~P.owvclot:ltyof t.54 m/s. 6. C o l l u d i n g r e m a r k s Detailed studies on three hems. namely, constant areahend and two diverging-converging bends have been reported in terms of wear. concentration and deposition velocity. Studies on wear characteristics have shown that minimum wear is always associated with diverging-converging bend with area ratio 2. and it is even less than the wear at the bottom of a straight pipe. Hence. the diverging-converging bend with area ratio 2 can be expected to have a longer life than both the constant area bend and even straight pipe. Measurements of concentration field in different bends have shown that solid particles are more uniformly distributed in modified bends as compared to the constant area bend, and is nearly uniform for area rado 2 bend. This coutd be the reason for the observed uniform wear in the area ratio 2 bend at the points of wear measurement. The uniform distribution of solid particles in this bend is ~ne to the interaction of strong .secondary flows and centrifugal forces. Another important feature observed is that, in spite of increase in the area of cross-section, deposition does not take place in bends near the deposition velocity in straight pipe. Based on the above findings, it can be concluded that diverging-converging bend with area ratio 2 offers many attractive features and can be used in practice for slurry pipelines.
7. Nomenclature
AR C~,.,,m Cw C+c.. D ,~
Area ratio Concentration at y/D = 0.05 ( % ) Concentration by weight (%) Efflux concentration by weight (%) Diameter of the pipe (m) Distance along any diametrical planc from the lower surface of the pipe (m) ( for horizontal plane, the distance is from the outer surface)
R. Mi.~hra et aL / Wear 217 (1998) 297-306
31)6 r R V 3'
Pipe radius ( m ) Radius o f curvature o f the inner surface o f the bends ( m ) Local flow velocity ( m / s ) Distance along the vertical diameter from the bottom o f the pipe ( m )
1141 AJ. Karabelas. An experimental study of pipe erosion by turbulent slurry flow. Prne. HT 5, BHRA Fluid Eng., Crainfield, UK. Paper E2. 1978, pp. EI5-24. 1151 D.R. Kaushal. V. Seshadri, S.N. Singh, R.C. Malhotra, Estimatlon of deposition velocity in the flow of multisized particulate slurries based on concentration protile prediction, Prnc. 12th Natl. Conf on FMFP. Madras. India, 1995. pp. 438-444.
Biographies References [ I I M. Tt~la. N. Karm)ri.S. Salt. S. Maeda. Hydraulic conveying of solids through pipe bend, J. Chem. Engg. Japan ( 19711 5. 121 H- Nasr-EI-Din. C.A. Shook, Effect of 90° bend on slurry velocity and concentration distribution, J. Pipelines 6 (1987) 239-252. 131 M. Ahmed. S.N. Singh. V. Seshadri. Distribution of solid particles in mutli-sized slun"y flow through 90° pipe bend in horizontal plane, Bulk Solids Handling 13 t 2 ) ( 1993) . 141 G. Rajat, Erosion wear in pipelines, PhD Thesis. Indian Institute of Technology, Delhi, 1994. 151 V. Seshadri, R.C. Malhotra. S. Chander. Pilot plant study ti)r the hydraulic transportation of bauxite ore. Internal report prepared fi)r Engim.'ersIndia, Department of Applied Mechanics, liT. Delhi, India, 1976. [ 61 S. Murakami. T. Kawa_shima.S. Tsukahara. T. Okada. Wear test on pipelines for hydraulic transport of dam delx)sit. HT 7. BHRA Fluid Eng.. Cranlield. England. 1980, pp. 315-330. 171 W. Wideuroth. Wear tests executed with a 125-ram ID pipe-hmp and a model dredge pump. HT 9. BHRA Fluid Eng.. Cmntield, England. 1984, pp. 317-330. 181 J.S- Maim. B.Y. Smith. Powder Technol. O ( 1972) 323-335. 191 D. Mills. J.S. Ma-~m, Particle size effects in bend erosion. Wear 44 t 1977) 311-328. I till D. Mills. J.S. Mason, Conveying ",elt~ity effects in bend erosion, J. Pipelines I ( 1981 ) 69-81. I 111 K. Horii. Y. Matsumae. X.M. Cheng, M. Takei. E. Yasukawa. B. Ha..,ia~to. Trans. ASME. J. Fluids Eng. 113 ( 1991 ) 149-15 I. 1121 A. Mukhtar. lnvestigation oftheflow ofmultisizedslurriesin straight pipe and pipe bends, PhD Thesis. liT. Delhi, 1991. 1131 R. Mishra. A study on the flow (~f muhisized particulate solid-liquid mixtures in horizontal pipelines. PhD Thesis, liT, Delhi. 1996.
Dr. Rakesh Mishra Received his PhD degree from Indian Institute o f Technology, Delhi. He has 10 years o f teaching and research experience. He has published 10 research p a p e ~ and guided 7 ME theses. At present he is Senior Lecturer in the Department o f Applied Mechanics, M N R E C , Allahabad, India. Currently, he is working in the field o f optimisation and reliability based studies o f hydraulic and capsule transportation o f solids. Prof. Dr. S.N. Singh Received his PhD degree from Indian Institute o f Technology, Delhi. He has 20 years o f teaching and research experience. He has published 148 research papers and has also been a consultant to m a n y industries. Currently, he is Professor in the Department o f Applied Mechanics, lIT, Delhi. He has guided 25 M T e c h and 6 PhD theses in the area o f aerodynamics and pipeline slurry transportation. Prof. Dr. V Seshadri Received his PhD degree from Brown University. Providence. USA. He has 30 years o f teaching and research experience. He has published o v e r 150 research papers and also has been a consultant to a large n u m b e r o f industrial/consuhancy organisations. He is at present Professor in the Department o f Applied Mechanics and Chairman, Estate and Works. liT, Delhi. He has s u p e r v i ~ d 18 PhD and m a n y M T e c h theses, in the area o f fluid mechanics and slurry pipeline transporfadou.