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Hydrodynamic and heat transfer characteristics of liquid—solid suspensions in horizontal turbulent pipe flow
The Chernwal
Engmeermg
Journal,
38 (1988)
111
111 - 122
Hydrodynamic and Heat Transfer Characteristics in Horizontal Turbulent Pipe Flow TULAY
A OZBELGE
Chermcat
Engmeermg
(Received
December
and TARIK Department,
East
Technrcal
1 INTRODUCTION
The understandmg of heat transfer to liquid-sohd suspensions 1s important m chemical engmeermg The mam apphcatlons of heat transfer to liquid-sohd suspensions are m power plants usmg slurries as fuels or as heat transfer media [l, 21 and m slurry transport reactors In the design of a slurry transport reactor, it is necessary to know the flow and heat transfer characterlstlcs of the hquld-sohd suspension since the overall of Ankara 50
~lnwerslty,
Ankara
(Turkey)
9, 1987)
Hydrodynamic and heat transfer characterlstlcs of water-feldspar suspensrons flowmg m a horzzontal copper pipe of 41 5 mm internal diameter have been rnvestzgated Consistency (concentratron) dutrrbutlons of solid part&es over a pipe cross-sectron for various operatmg condltlons are presented The feldspar particles used m the expenmen ts had mean diameters of 0 081, 0 161 and 0 227 mm The operating range of Reynolds numbers was from 14 000 to 115 000, and of volume fraction of soltds from 0 005 to 0 03 Experimental results of the heat transfer study mdlcate that for a given llqurd-sohd suspension in turbulent flow, there exuts a specrflc combmatlon of particle size, Reynolds number and inlet solid consistency for optimum enhancement of heat transfer rate This combmatlon 1s found to occur at a particle size of 0 161 mm, at a Reynolds number of 26500 and at an inlet solid consistency of around 0 01 volume fraction of solids for water-feldspar suspensions flowing m a horizontal pipe
0300.9467/881$3
Suspensions
G SOMER* hllddle
ABSTRACT
*President
of Liquid-Solid
Unwerslty.
Ankara,
Turkey
reaction rate will be greatly affected by transport phenomena A number of studies on flow and heat transfer characterlstlcs of liquid-sohd twophase flows have been conducted m the past Toda et al [ 31 measured the radial consistency dlstrlbutlon of particles m a vertical tube as well as m a horizontal tube They showed that the dlstrlbutlons were related to the size and the density of particles as well as to the liquid velocity Scarlett and Grlmley [4] reported measurements of solid velocltles and conslstencles m a horizontal pipe using high speed motion pictures of coloured marker particles They used a dlffuslonal mechanism to explam the various regimes of conveying which were possible m a hydraulic conveying system Furuta et al [5] measured the radial consistency dlstrlbutlon of particles m a vertical downward flow as well as m an upward fully developed turbulent flow They classlfled the patterns of the consistency dlstrlbutlon of solids by means of the particle Reynolds number (D,u,/v) and the Reynolds number for the liquid (DuJv) Ohashl et al [6] determined the dlstrlbutlons of concentration and velocity of solid particles for hquld-solid horizontal flow and vertical upflow using a conventional photographic method, and also by two newly developed laser methods. They calculated the average particle velocity from the local values of particle concentration and velocity; then they correlated the average particle velocity with a modfiled Froude number and particle Reynolds number. The solid materials used were ion-exchange resin particles and glass beads with diameters of 0 321 - 1 84 mm and densities of 1190 - 2500 kg rne3. The pipe diameters were 19 2, 30 and 54 2 mm Toda et al [7] studied the transition velocltles of horizontal sohd-liquid two-phase flow expenmentally They reported correlations for the @ Elsewer
Sequola/Prmted
m The Netherlands
112
tlansition velocity from asymmetric suspension to moving-bed-type flow, for the velocity correspondmg to the mmlmum pressure drop and for the hmltmg velocity for deposltlon at which a fured bed forms A good review of the previous work on heat transfer to non-newtonlan sloes was given by Quader and Wllkmson [8] They studied experimentally the heat transfer to pseudoplastic tltanlum dioxide suspensions m pipes and discussed the lunltatlons of the analogy between heat and momentum transfer Zenz and Othmer [9] and Thomas [ 101 mvestlgated heat transfer to concentrated suspensions; they suggested the use of conventional heat transfer relations, employing the physlcal properties of the suspension Brandon and Thomas [ll] measured the heat transfer rates to water suspensions of glass microspheres with mean diameters from 0 020 to 0 86 mm which were used III concentrations of less than 0 02 volume fraction of solids m both the horizontal and the vertical upward transport The Reynolds number was varied from 20 000 to 90 000 A peak m the relative heat transfer enhancement was observed for the constant value of the product 11’16. Konno et al [12,13] (&lD)(Rel) Investigated the heat transfer characterlstlcs of downward and upward flowing suspensions of water -glass bead or water-ion exchange resin particles m vertical pipes The pipe diameters were 8, 12 8 and 19 mm. Harada et al [ 141 measured the rates of heat transfer between the pipe wall and the suspension flow m horizontal pipes using water suspensions of glass beads (0.06 to 10 mm m diameter) at concentrations up to 0.1 volume fraction of solids and at Reynolds numbers varying from 3000 to 50 000 They observed that the heat transfer coefficient of an asymmetric suspension flow was always higher than that of a sunple water flow They correlated their data on the basis of the Sleder -Tate equation [ 151 and reported an emplrlcal equation for heat transfer to asymmetric suspension flow In spite of these studies mentioned above, the flow and heat transfer characterlstlcs of a horizontal hquld-solid suspension flow have not been understood well enough owing to the complex behavlour of the suspension flow The purpose of this study 1s therefore to produce new experimental data m order to
determine the relatlonshlps among the consistency dlstrlbutlons of solid particles, their flow patterns and the heat transfer behavlour of the suspension flow 2 EXPERIMENTAL
DETAILS
The experiments consist of two parts (1) Measurement of consistency dlstrlbutlons of solid particles over a cross-sectlon of the horizontal pipe as the suspension flows turbulently m the fully developed region, (u) Measurement of heat transfer coefhclents for horizontal flow of hquld-sohd suspensions under different operatmg condltions A schematic diagram of the experimental apparatus 1s shown m Fig. 1 The horizontal test section IS a copper pipe of 41 5 mm I d The details of the experimental set-up are given elsewhere [ 161 A samphng probe was deslgned and constructed to measure the transport conslstencles of solids at different pomts along the vertical, the horizontal and the 454dlrected diameter of the pipe at an axial distance of 2820 mm from the pump outlet Photographs of the samphng probe and the closed-loop flow system are given m Fig. 2 and Fig 3 respectively The samphng probe could be moved across the pipe diameter by a screw mechanism The posltlon of the probe tip m the pipe was mdlcated with good accuracy by a needle on the scale (Fig 2). The dlrectlon of the probe was ahgned parallel with the streamhnes of flow and every precaution was taken to keep this alignment durmg the expenment The probe (D,, = 2 mm and D,, = 4 mm) was inserted mto the flow with the opening facing the dlrectlon of flow The entire assembly of the sampling probe was clamped tightly on the pipe In order to change the orientation of the dlameter, across which the probe tip travelled, the pipe was rotated between the end flttmgs, together with the samphng probe assembly The angle of onentatlon, the angle between the probe length and the horizontal, was accurately measured at each settmg The dlrectlons of sampling using the mserted probe are shown m Fig 4 The physical properties of the sohd particles used m this work are listed m Table 1 The gram sizes of the particles were
36cm
27cm
t
Hg -Monometer
48cm
I -
Fig
1
SchematIc
dlai gram
of the experlmental
Condensate
apparatus
i Ftg 2 Samphng
probe
Fig -I Dwectlons of samplmg (AIBI, Al&, A3B3)
by Inserted
probe
The scope of the flow experiments and that of the heat transfer experiments are given III Tables 2 and 3 respectively 2 1 Expenmen experlmen
Fig 3 Photograph
of the apparatus
made uniform by usmg a series of Tyler’s standard sieves Arlthmetlc average diameters between the sieves were taken as the average diameter for each set of particles
tal procedure
for flow
ts
A slurry, of the required consistency, and with a umform particle size, was prepared m the head tank The required velocity of the slurry was set The coolmg water was started to maintam a constant slurry temperature durmg the flow experunents The slurry would otherwlse heat up during the cu-culatlon through the pump m a closed-loop system To measure the solid conslstencles at various points along the chosen diameter, a gravlmetrlc method was employed A set
114 TABLE
1
Physlcal
propertles
ot sohds Den&y
Alaterral
Feldspar (K20-A120~
TABLE Scope
pP
Diameter
D,
Calculated
(kg mP3)
(mm)
(m s-‘)
1698
0 061 0 161 0 227
0 0025 0 0099 0 0152
6&O:)
termmal
velocrty
Specific heat C, [ 1 i] (kcal kg-’ “C-l) 02
2 of the flow experiments
(a) Inlet sohd consistency Sifeed (volume fraction sohds) (b) SolId particle size D, (mm) (c) Flow
Reynolds
number
Rel =
0061 D-r, fi,,,P,,
022’;
1 4 A lo4 < Rel C 5 X lo4
IJI (d) Temperature of the suspension T (“C) (e) Orlentatron of the (probe-pipe diameter) dlrectlon to the horizontal ~9(deg)
TABLE Scope
3 of the heat transfer
experiments
(a) Inlet solld consistency c;feed (volume fraction sollds) (b) Sohd particle size D, (mm) fc)
T=205% 8 = O’, 45-, 90
Flow
Reynolds
number
Rel =
DTI ~tnike
0 005
G Cfeed < 0 03
0 081
< D, < 0 227
25000
< Re, < 110000
Fl
(d) Suspension veloclty Urn (m s-‘) (e) Pipe-wall temperature Tis, ( C)
02
of lOO-ml Erlenmeyer flasks were washed, dried and weighed to be used m the experlments During the clrculatlon of the slurry m the system, the samples of any volume were collected m the Erlenmeyer flasks, each of which corresponded to a mixture of water and solids at a defmlte distance from the centre-line of the pipe This distance was read from the scale on the probe assembly. Keeping the same flow Reynolds number, the same consistency of sohds and the same particle size, the pipe was rotated around its horizontal axis, together with the probe assembly. This operation provided a change m the orlentatlon of the probe-diameter dlrectlon of 45” or 90” The Erlenmeyer flasks containing the collected samples were tightly closed with their correspondmg corks Just after the samples were taken, and were
then weighed These samples were carefully dried, preventing splashmg, overnight m an oven at around 110 “C, they were cooled m a desiccator and then weighed agam with a sensltlve balance to an accuracy of ?O 001 g This procedure was repeated for four different solid conslstencles (0 5%, 1 OS, 2 0% and 3 0% by volume of solids m the system) with each particle size of solids At each solid consistency, experunental runs for four different Reynolds numbers (around 14 000, 24 000, 38 000, and 50 000) were performed At each Reynolds number, the data were obtained along the diameters for three orlentatlons Altogether, 144 runs were performed m the determmatlon of the solid conslstencles For each run, an average consM.ency of solids m the liquid phase was obtamed by
115
simultaneously opening the valve on the samplmg lme and closing the vslve on the mam closed-loop system After this operation, these valves were agam set to their previous posltlons, the slurry which was collected m a bucket, durmg the sampling procedure, was returned to the head tank to keep the hquld level constant For each consistency, Just before adJustmg the flow to a new value of the Reynolds number, a weighed amount of solids of that particle size and some water were added to the head tank to keep the hquld level the same and to compensate for the loss of material due to sampling At the end of a day of experlmentatlon, the sohds were washed out of the system to prevent their settlmg m the pump, tank and pipes, and then the pump was turned off 2 2 Experimental expenmen ts
procedure
technique previously described,, on a sample of the slurry obtained at the steady state from the sampling lme At the end of each day of expenmentatlon, the sohds were washed out of the system and the pump was turned off The details for the temperature measurements are given elsewhere [16,18] 2 3 Calculation of heat transfer coefflclent The heat flow rate through the wall of the test section was calculated from the followmg equation
(1) where UAave =
I
+ lleT,/DT,)
1
’
/ h,nD,,
L
(-’
k,,2nL
(2)
\
for heat transfer
After the flow experiments were completed, the thermocouples were put m place and the test section was msulated with flbreglass The operation of the system and the reproduclbllIty of the results were checked by performmg several runs with water only Then the expenments with sohd particles m water were started The procedure for these experiments was as follows The slurry, of the required consistency, and with a uniform particle size, was prepared m the head tank The required velocity of the slurry was set The steam and the coolmg water rates were adJusted so that the slurry would be heated by about 5 - 7 C This temperature difference and the approach of the system to the steady state were checked by means of the thermocouple readmgs Actual data were taken after reaching the steady state, which required at least 1 5 h after the start of each experiment Wlthm 10 mm, after reaching the steady state, the thermocouple readmgs of the wall and of the Inlet and the outlet slurry temperatures, the condensate temperature and Its flow rate at this temperature, the steam temperature m the steam Jacket around the test sectlon, and the pressure drop caused by the flow of the slurry through the orlflce meter were all recorded The average solid consistency for each run was determmed usmg the gravlmetrlc
and A ate = nD,,L
(4)
q 1s also equal to rnCPabeT, which can be wrltten as
_ -
T&l2
Q = UrnPa,, -
4
GaJTSO - T,,)
(5)
where
ii,,, 1s the slurry velocity, p,,, and are the volume-averaged density and Le weight-averaged heat capacity respectively of the slurry at the bulk mean steady-state slurry temperature It was assumed that the thermal conductivity and vlscoslty of the dilute hquld-sohd suspension were equal to those of water at the bulk mean temperature Therefore the dunenslonless groups were defmed as m the following formulae Nu,=
hn,D-r, -
Pr, =
kl
FIG,,, k, (6)
Re, =
DT,
fim i&we Pl
Fr, =
Ut WA,)’
’
The heat transfer coefflclent was calculated by means of eqns (1) - (5), usmg a value of 326 kcal m-’ h-’ ‘C-’ for the thermal conductlvlty of the copper pipe k, Cl71
116
3 EXPERIMENTAL
RESULTS
AND
DISCUSSION
The local sohd conslstencles along the pipe diameter, for three orlentatlons of the probediameter dlrectlon (0’, 45”, 90’) and for three ddferent slzesof feldspar particles (0 081 mm, 0 161 mm and 0 227 mm) were measured at different flow Reynolds numbers From the data, lsoconslstency lmes for solids distributed m the flowing suspension were plotted, but only some of these figures have been presented here as representative samples of the other cases (Figs 5 - 11) The value given for each lme 1s the local solid consistency pS as wt R The value m parentheses 1s the local solid consistency divided by the average sohd consistency (p,/Ct,,) of the suspension flow during each run
y-ax.6
I
(cm) I4
% WI
IO 991
m)
Fig 7 Isoconslstency lines for sollds of_slze 0 081 mm Rel = 13 780, ii,,, = 32 26 cm SC’, Cfed = 1 0 vol s (1 7 wt %), c,, = 0 831 volo1 (1 411 wt %) y-axis
A.
(cm) 2 4 % II
II
15)
34
44
(I631
19931 70
Fig 5 Isoconslstency lmes for sohds of size 0 161 mm Rel = 13 890, ti,,, = 33 39 cm SC’ ~c+d = 1 0 vol~(17wt%),C;tr=0261\~ol~(0143wt~)
(3
35)
Fig 8 Isoconslstenc\ lmes for sohds of sue 0 081 mm Rel = 13 82G ,_&, = 32 96 cm s-’ , Cfed = 2 0 \Ol “c (3 35 wt “c). CL, = 1 21 vol c; (2 39 wt “c) y-0x1s (cm)
)
y-axis
t
(cm)
10%
.I I6
70
2 0
10 231 IO 371 561
(I 601
(cm)
Fig 6 Isoconslstency lines for sohds of size 0 227 mm Re, = 13 940 ,j,,, = 33 39 cm s-l, ~?fd = 2 0 vol Y- (3 35 wt T)? c,, = 0 i37 vol p: (1 248 wt %)
60
II
39)
Fig 9 Isoconslstencq lanes tor sollds of size 0 161 mm Re~=21340,ti,=5685cm~-‘,~~~~=20 vol % (3 35 wt “c), c,, = 2 59 \Ol 0: (-I 321 at Tj
I2 1043) /20 10721
Ftg 10 Isoconslstencq lmes for solids of size 0 227 mm Re~=23900,tim=5665cms-‘,C~ee~=23 vol 0; (3 35 wt ‘), c,, = 1 65 vol P; (2 772 wt %)
Fig 11 Isoconslstency lines for sollds of size 0 161 mm Rel = 52 660,-G, = 123 80 cm S-', cfed = 2 0 vol 0: (3 35 wt “c). Ct, = 3 43 vol % (5 703 wt S)
Calculations have been performed with the present data to determine the various tranwtlon velocltles (e g the velocity at which asymmetric suspension flow changes over to a moving-bed-type flow, and the hmltmg velocity for depoatlon, at which a sohd deposit begms to build up m the bottom of the pipe), according to the defmltlons and correlations reported by Toda et al [7] The results of the calculations were m agreement with the experimentally obtained lsoconslstency lmes, both mdlcatmg the same type of flow pattern These flow patterns under the various operating condltlons are
summarized m Table 4, where they are classified by means of the particle Reynolds number
TABLE
Re, =
number
D,, k, pave
PI and the inlet solid consistency m each run As can be observed from Figs 5 - 11 and Table 4, the flow behavlour of llquld-sohd suspensions m a horizontal pipe 1s highly
4
Chart of flow patterns
(hvdrodynamlc
DP
Cfeecl
(mm)
the flow Reynolds
RelJ
study)
_ (vol?)
Rcl
13700 14300 urn = 0 335 (m s-‘)
23700 24500 um - 0 56.5 (m s-‘)
37500 39500 l’rn * 0905 (m s-’ )
51500 53200 Ll, 2 1 235 (m s-‘)
0 081
02
05 10 20 30
MBF hlBF FB FB
hqBF hlBF hlBF bIBF
ASYM ASYiU ASI-hl ASYhl
ASYM ASYhI ASYM XSYM
0 161
16
05 10 20 30
FB FB FB FB
hlBF hlBF hIBF MBF
‘GYM MBF hIBF hlBF
GYM ASYM ASEW ASYM
0 227
35
05 10 20 30
FB FB FB FB
MBF hlBF hlBF MBF
AS Yhl MBF hlBF MBF
ASYLI ASYM ASYM ASYhI
FB, flxed bed, MBF, moving-bed
flow,
ASnl,
asymmetric
flow
118
dependent on the inlet solid consistency of solids, the particle size and the flow Reynolds number Along the vertical diameter, the solid consistency profiles show a common trend m that the particles are dlstrlbuted contmuously with a mu-umum consistency near the upper wall and the maximum solid consistency at the lower wall This IS as expected because of gravity The lsoconslstency lines are sharply convex m the lower half of the circular pipe crosssection at low Reynolds numbers (I c around 14 000) for particles of size 0 161 mm and 0 227 mm because the terminal velocltles of these particles are higher than those of 0 081 mm particles, the effect of gravity IS also slgnlflcant (Figs 5 and 6) These convex lines are observed under condltlons where a futed bed forms For small particles of size 0 081 mm, lsoconslstency lines are concave at low and medium conslstencles for low Reynolds numbers as can be seen m Fig 7 This corresponds to the existence of a moving bed In the lower part of the pipe while the upper part IS fllled with an asymmetric suspension For any one size of particles, at low Reynolds numbers, the convex lines are observed only at high solid conslstencles mdlcatmg the formation of a futed bed (Fig 8), but these convex lines are curved up from both sides in the lower regions between the 45’dlrected diameter and the horizontal diameter of the pipe as m Figs 5,7 and 8 The same curving up cannot be observed for 0 227 mm particles m Fig 6 This shows that only the smaller particles can be carried up easily by the turbulent eddies, so the lateral movement of particles becomes slgnlflcant at low Reynolds numbers The lateral movements may also be enhanced by the agitation created from the particle-particle and particle-wall mteractlons caused by the surface u-regularities on the particles and on the pipe wall The lsoconslstency lmes for 0 161 and 0 227 mm particles, at Reynolds numbers of around 24 000, are slightly concave m the lower half of the circular pipe cross-section (Figs 9 and lo), because the particle eddy ddfuslvlty increases with increasing flow Reynolds number Therefore the lsocons1stency lines tend to be smoothed over the pipe cross-section as the particle eddy dlffuslvlty
increases [ 51 These cases correspond to the existence of a moving bed below the asymmetric suspension flow (Table 4) At high flow velocltles and at medium or high solid consistencies, asymmetric suspension alone fills the pipe cross-sectlon for all the particle sizes (Table 4) The lsoconslstency lines for such a flow case are shown m Fig 11, as an example of 0 161 mm particles m water, at 2 vol % solid consistency and at a flow velocity of around 1 24 m s-’ Figure 12 shows the enhancement ratio (h,/h,, ) which 1s the convective heat transfer coefflclent of the hquld-solid suspension divided by the convective heat transfer coefficient of water under the same operating condltlons, plotted with respect to the mlet solid consistency for the different particle sizes and Reynolds numbers The heat transfer coefflclent of water without sohds h,, was determined m several runs to check the accuracy of the expenmental system The well-known Sleder and Tate equation [ 151 was used to calculate h, under exactly the same operating condltlons for each run
4-
z’
P
I
e-
Fig 12 Effect of particle we and Reynolds on enhancement of convectwe heat transfer clent (12,/h, t’s‘ ?feed)
number coeffl-
119
h, = 0 023 +
(Re,)O 8(Pr,)1,3( ;)O Tl
I4
(7)
U’
where the Reynolds number and the Prandtl number are calculated using the propertles of water at the average bulk temperature for each run From Fig 12, It appears that there is greater heat transfer enhancement with 0 081 and 0 161 mm particles than with 0 227 mm particles This may be due to the greater momentum gam by large particles m the dlrectlon of motion, preventing these particles from moving (or vlbratmg) m the lateral dlrectlon The small magnitude of such lateral motions would prevent the mductlon of turbulence mto the boundary layer close to the wall Smaller particles, however, should possess greater freedom to move towards the walls since the resultant of two momenta, one m the dlrectlon of motion and the other perpendicular to this, 1s directed at a greater angle towards the walls Furthermore low Reynolds numbers favour the lateral movement of solid partrcles, and this contributes to the thmnmg of the viscous boundary layer, thus the heat transfer 1s enhanced In Figs 5. 7 and 8, these lateral movements of solids are indicated by the lsoconslstency lines being curved up from both sides of the convex lines, for 0 081 and 0 161 mm particles at low Reynolds numbers, whereas this 1s not so for the 0 227 mm particles m Fig. 6 In Fig 12, ior all the particle sizes, the enhancement ratio increases with decreasing Reynolds number, but it shows a mmlmum at 0 01 volume fraction sohd consistency for all the runs except those m which 0 161 mm particles were transported at Reynolds numbers of 35 000 and 26 500 In the latter case, a highest peak value for the enhancement ratio 1s reached, then the addition of solids to greater than 0 01 volume fraction solids produces a defmlte decrease In all the other cases, the small peaks for the enhancement ratio, the values of which are inversely proportional to the Reynolds number, are observed at 0 005 volume fraction sohds, then, after the mmlmum values of the enhancement ratio at 0 01 volume fraction sohds, the so-called barrier solid consistency for these specific cases, the addition of more solids gradually increases the enhancement ratio [ 181
The heat transfer coefficients of the waterfeldspar suspension flows are lower than those of a sunple water flow under the same operatmg condltlons at around 0 01 - 0 03 volume fraction solids and at very high Reynolds numbers (I e around 88 000 - 115 000) for 0 081 and 0 161 mm particles, but for 0 227 mm particles, the heat transfer coefficients are extremely low at all the Reynolds numbers, the experimental range being approximately 26 500 - 115 000, and at medium to high solid conslstencles (I e at around 0 01 - 0 03 volume fraction solids) The small peak values m the enhancement ratlo can be explained by reasoning that particle-particle and particle-wall mteractlons may be occurring at a high rate because of the high degree of freedom of solid particles at low solid conslstencles At a medium conslstency of 0 01 volume fraction solids, the number of particles m the system ~111increase, but they may start to have less freedom to move As a result, the heat transfer coefficient may decrease because of the reduction m particle-wall mteractlons However, Fig 12 indicates that there exists a particular combination of particle size, flow Reynolds number and inlet solid consistency of particles which gives optimum heat transfer Obviously, some change m the flow pattern of sohds occurs with 0 161 mm particles at 0 01 volume fraction solid consistency m the suspension for flow Reynolds numbers of 35 000 and 26 ZOO, which gives rise to the maximum values of the enhancement ratio, the latter number giving the highest peak value of the enhancement ratio This is most probably due to the combmatlon of two phenomena, namely, the lateral motion of particles at low Reynolds numbers and the suitablllty of an intermediate particle size for thinning the boundary layer This explanation was also supported by Lee and Durst [19] Brandon and Thomas [ll] also obtained an optimum heat transfer enhancement m studying the heat transfer to dilute (less than 0 02 volume fraction solids) hquld-solid suspension flows They concluded that a critical particle size should exist which would Interact most effectively with the contmuousphase turbulence to enhance the heat transfer At 3 vol 7c solid consistency, higher enhancement ratios than those at lower solid
120
conslstencles might have been expected because of the mcreasmg effect of partlcleparticle and particle-pipe-wall mteractlons, but there IS a contradictory factor which 1s that the heat capacity of feldspar particles 1s only about one-ftith that of water Therefore as the solid consistency increases, the heat capacity of the mixture becomes even lower than that of water As a result of these two competing effects (I e the particle-wall lnteractlons and the relative heat capacltles of the phases) the enhancement ratio increases or decreases with increasing inlet solid consistency of the water-feldspar suspension flow, m the manner shown m Fig 12 [ 16,181 The correlations given by Toda et al [7] for calculatmg the transItIon velocltles, which determine the flow patterns m a suspension flow, were also used for the heat transfer experunents The results are given m Table 5 When Tables 4 and 5 are compared, it can be seen that, In the low velocQ~ ranges, the changes m the flow patterns m the heat transfer experiments take place wlthm almost the same velocity ranges as do the changes m the flow patterns m the flow experiments In contrast, at the higher velocltles, this parallehsm IS not observed m most of the experunental runs The reason for this may be the higher terminal velocltles of the particles m the heat transfer experiments or the expenmental errors and the shortcommgs of the empu-lcal correlations This pomt 1s not completely understood TABLE Chart
patterns
(heat
transfer
_
ut
Cfeed
(mm)
(m SC’)
(vol %)
11,
(Re,
0 227
(8) where 14 000 < Re, < 140 000 34<
-Clt4ll < 12 7 121
282 < ;
0 53 < 2
009<
< 10 500
< 583
$022
P
A comparison of the present data with eqn (8) showed poor agreement, because all of the experu-nental (C, /_fm/h,) values were smaller than Its correlation hmlt of 3 4 It was only
study)
(m s-‘)
0 ‘?4
0161
Nu, = 0 131 Relo 62
5 of flow
4
0081
Optimum heat transfer, m this work, corresponds to a case where there IS a stationary (fured) bed m the bottom of the pipe With stationary bed flow, the heat transfer rate increases greatly because the fluid velocity IS much higher than that of a simple water flow m the upper part of the pipe, owmg to the smaller cross-sectional area available for flow, since the bottom part 1s occupied by the futed bed This is m agreement with the results obtained by Harada et al [14] Salamone and Newman [20] proposed the following empirical equation for a fine particle-water suspension
2:
26,joo)
0 32 (RE,
686x10-3 630/10-”
05 10
FB FB
FB FB
647/10-3
30
FB
154~10-~
OS
FB
1 51 Y lo-’ 1 49 x10-?
1 0 3 0
229 110-Z 2 13 Alo2 15 x10-2
05 10 3 0
aOptlmum Table 4)
heat
transfer
2
0 -55
0 90
,350OO) (Re, - 58000)
(Rel
I 19
* 88000)
fRe1
FB
hlBF hIBF MBF
hIBF MBF hlBF
ASYhl ASYhl hlBF
FB= FB
FB FB FB
hlBF RlBF hlBF
blBF hlBF hlBF
MBF hlBF hlBF
FB FB FB
FB FB FB
MBF hlBF MBF
MBF hlBF hlBF
hlBF MBF hlBF
and the highest
peak
value
of the enhancement
ratlo
occur
2
m this run (abbrevlatlons
115000)
see
121
for some of the experimental runs, m which the values of (Cl~,/kl) approached 3 4, that the correlation fitted the data to within +20% Another correlation was proposed by Harada et al [14] for an asymmetric suspension flow Only nme of the runs m this mvestlgatlon seemed to cover the condltlons given m then work Although the experlmental parameters were within the given hmlts, m each of these runs, the flow pattern was not that of an asymmetric flow, but was a combmatlon of a fured-bed or moving-bed flow with an asymmetric flow Therefore it was not suitable for estlmatmg the heat transfer coefflclents for the water-feldspar suspension flow and the accuracy of the fit was poor Quantitative studies are under way to obtain an emplrlcal equation which gives the best fit to the present data, and this will be presented m a future pubhcatlon
1 CONCLUSIONS The hydrodynamic and heat transfer characterlstlcs of water-feldspar suspensions m horizontal transport were studled expertmentally, under turbulent flow condltlons In the determination of solid consistency profiles m water-feldspar systems, a gravlmetric method applied together with a specially designed sampling probe served the purpose successfully The maximum expenmental error was around 27% In the horizontal flow of hquld-solid muctures, the solid particles were dlstrlbuted contmuously with a mlmmum density at the upper wall and a maxunum density at the lower wall owing to the slgmflcance of the gravity effect The smaller the particle size and solid conslstency, and the larger the Reynolds number, the more uniformly distributed were the solids across the cross-sectional flow area The ddferent shapes of the lsoconslstency lmes were related to the different flow patterns These flow patterns could be classlfled by takmg particle size, flow Reynolds number, inlet solid consistency and particle Reynolds number as parameters For low velocltles, the changes m the flow patterns in both the flow and the heat transfer experiments took place wlthm almost the same velocity ranges The same phenom-
enon was not observed at high velocltles This point could not be explamed completely The heat transfer study mdlcated the existence of a particular combmatlon of the particle size, the flow Reynolds number, and the mlet solid consistency of particles m each specific hquld-solid system which would give the highest heat transfer enhancement. In this study, for the water-feldspar system, the highest enhancement of heat transfer occurred at an mtermedlate particle size of 0 161 mm, at a low Reynolds number of about 26 500, and at an intermediate inlet sohd consistency of around 0 01 volume fraction of solids As the solid consistency increased, the particle-wall mteractlons and the physical properties of the system became unportant factors m determining the heat transfer to two-phase flows For water-feldspar systems, the particle-wall mteractlons and especially the heat capacity of the system were competmg factors m heat transfer No expertmental equation for heat transfer coefflclents m water-feldspar suspension flow has been developed here This will be the subJect of a future publication REFERENCES 1 V
F Kustov, Fuel Suspensions Academy of Sciences of the U S S R , 1942 2 Ch Bomlla, Heat Transtcr m Nuclear Engmeerrng, State Publlshmg House tor Atomic Literature, New York, 1961 3 hl Toda, T Shnnlzu, S Salto and S hlaeda, Preprint for ,37th Ann Meet Japan, Tokyo 1972, p B-310
Sot
Chem
Eng
B Scarlett and A Crlmley, Hydrotransport 3. Proc 3rd fnt Conf on the Hydraulw Transport of Sohds rn Prpes, Golden CO, 1974, Paper no D3, pp 23 - 3: 5 T Furuta, S TsuJImoto, hl Toshlma, M Okazakt and R Toel, Kagahu Kogaku Ronbunshu, -I (1978) 105 H Ohashl, T Sugawara, K Klhuchl and hl Ise, J Chem Eng Jpn, 13 (5) (1980) 343 - 339 hl Toda, d Yonehara, T Klmura and S hlaeda, Int Chem Eng, 19 (1979) 145 A K hl A Quader and W L WIlkInson, Int d Multzphase Flow, 12 (:981) 545 F A Zenz and D E Othmer, FlwdrzatIon and Flurd-Partwle Systems, Remhold, New York, 1960 10 D G Thomas, 4IChE J, 6 (1960) 631 - 639 11 C A Brandon and D G Thomas, Transport characterlstlcs of suspensions, Proc 4th Int Heat Transfer Conf, Parls, 1970, Paper no CT-2 : 12 H Konno, E Harada, hl Toda, hl Kurlvama and hl Asano, Kagahu Kogahu Ronbunshu. 5 (1979) 464
122 13
H Konno, E Harada, hl Toda, hl Kurlyama and S Saruta, Kagakrc Kogaku Ronbunshu 6 (1980) 308
14
E Harada,
M Toda, M Kurlyama and H Konno, Jpn, 18(1)(1985)33-38 15 E N Sleder and G E Tate, Ind Eng Chem , 28 J
Chem
(1936)
kl
Eng
kP
1429
16 T
A Ozbelge, Hydrodynamic and heat transfer characterlstws of gas-solld and Iquld-solid systems In turbulent flow, Ph D Thesls, Chetnrcal Engmeermg Department, hllddle East TechnIcal LJnwersltJ, Ankara, Turkey Handbook, 17 J H Perry, C’hemrcat Engmeers hlcCraa-Hdl. New York, 1911, 2nd edn 18 T 4 Ozbelge and T G Somer, Heat transfer to slurries m horizontal transport, Proc 16th Ann Meet phase
k CU
Fine Partrcle Sot on Particulate Processes, .Illanu Beach, 1985,
L
In m Nul Prl
and hlultl Vol 3,
Hemisphere Pub1 Corp 1 Washrngton, 1987, pp 271 279 19 S L Lee and F Durst, Int J Multiphase Flow 8 13) (1982) 125 146 20 J J Salamone and Rl Newman, Ind Eng C’hem , 47 (1955) 283 APPENDIX
A_a\
e
c feed Cl GN
Gr
41
D PO DP D-r,vD
D
FrT,D g
A NOMENCLATURE
surface area for heat transfer ( m2) inlet solid consistency (wt % or vol 70) heat capacity of hquld (kJ kg-’ K-‘) weight-average heat capacity of hquld-sohd suspension depending on the solid consistency m the liquid (kJ kg-’ K-‘) average sohd consistency m each run (wt lo) inside diameter of sampling probe (mm) outside diameter of sampling probe (mm) solid particle size (mm) inside pipe diameter outslde pipe diameter particle Froude number acceleration due to gravity (9 81 m S-2)
h,
h,
mdlvldual convective heat transfer coefflclent for heat transfer to hquldsolid suspensions (W me2 K-‘) heat transfer coefficient wlthout sohds m water (W me2 K-*)
thermal conductlvlty of copper -1 K-1 (Wm ) thermal conductlvlty of liquid -1 K-1 (Wm 1 thermal conductlvlty of feldspar partxles (W m-’ K-‘) length of test section (m) natural logarithm mass flow rate (kg s-‘) Nusselt number for hquld-solid suspension flow Prandtl number for hquld-solid suspension flow rate of heat flow (W) Reynolds number for hquld-solid suspension flow particle Reynolds number inlet temperature of hquld-solid suspension to the test section (K or ‘C) outlet temperature of llquld-sohd suspension from the test section (K or ‘CT) pipe-wall temperature (K or “c) average velocity of llquld-solid suspension (m s-’ or cm s-‘) free-fall or termmal velocity of a single particle (m s-’ or cm s-l) overall heat transfer coefflclent -2 K-1 (Wm )
Greek symbols
AT =L~I
PI Pm
l-&V 1)
Pa\ e
PI PP
PS
T,, - T,, , temperature difference (K or %) logarlthmlc mean temperature dtiference vlscoslty of liquid (kg m- ’ s-‘) vlscoslty of suspension (kg m-’ s-‘) vlscoslty of hquld at wall temperature (kg m-' s-l) kmematlc vlscoslty (m2 s-‘) volume-averaged denslty of liquidsolid suspension (kg m-“) den&y of hquld (kg me3) solid density (kg m-3) local sohd consistency m hquldsolid suspension (wt ‘7,)
Engmeermg
Journal,
38 (1988)
111
111 - 122
Hydrodynamic and Heat Transfer Characteristics in Horizontal Turbulent Pipe Flow TULAY
A OZBELGE
Chermcat
Engmeermg
(Received
December
and TARIK Department,
East
Technrcal
1 INTRODUCTION
The understandmg of heat transfer to liquid-sohd suspensions 1s important m chemical engmeermg The mam apphcatlons of heat transfer to liquid-sohd suspensions are m power plants usmg slurries as fuels or as heat transfer media [l, 21 and m slurry transport reactors In the design of a slurry transport reactor, it is necessary to know the flow and heat transfer characterlstlcs of the hquld-sohd suspension since the overall of Ankara 50
~lnwerslty,
Ankara
(Turkey)
9, 1987)
Hydrodynamic and heat transfer characterlstlcs of water-feldspar suspensrons flowmg m a horzzontal copper pipe of 41 5 mm internal diameter have been rnvestzgated Consistency (concentratron) dutrrbutlons of solid part&es over a pipe cross-sectron for various operatmg condltlons are presented The feldspar particles used m the expenmen ts had mean diameters of 0 081, 0 161 and 0 227 mm The operating range of Reynolds numbers was from 14 000 to 115 000, and of volume fraction of soltds from 0 005 to 0 03 Experimental results of the heat transfer study mdlcate that for a given llqurd-sohd suspension in turbulent flow, there exuts a specrflc combmatlon of particle size, Reynolds number and inlet solid consistency for optimum enhancement of heat transfer rate This combmatlon 1s found to occur at a particle size of 0 161 mm, at a Reynolds number of 26500 and at an inlet solid consistency of around 0 01 volume fraction of solids for water-feldspar suspensions flowing m a horizontal pipe
0300.9467/881$3
Suspensions
G SOMER* hllddle
ABSTRACT
*President
of Liquid-Solid
Unwerslty.
Ankara,
Turkey
reaction rate will be greatly affected by transport phenomena A number of studies on flow and heat transfer characterlstlcs of liquid-sohd twophase flows have been conducted m the past Toda et al [ 31 measured the radial consistency dlstrlbutlon of particles m a vertical tube as well as m a horizontal tube They showed that the dlstrlbutlons were related to the size and the density of particles as well as to the liquid velocity Scarlett and Grlmley [4] reported measurements of solid velocltles and conslstencles m a horizontal pipe using high speed motion pictures of coloured marker particles They used a dlffuslonal mechanism to explam the various regimes of conveying which were possible m a hydraulic conveying system Furuta et al [5] measured the radial consistency dlstrlbutlon of particles m a vertical downward flow as well as m an upward fully developed turbulent flow They classlfled the patterns of the consistency dlstrlbutlon of solids by means of the particle Reynolds number (D,u,/v) and the Reynolds number for the liquid (DuJv) Ohashl et al [6] determined the dlstrlbutlons of concentration and velocity of solid particles for hquld-solid horizontal flow and vertical upflow using a conventional photographic method, and also by two newly developed laser methods. They calculated the average particle velocity from the local values of particle concentration and velocity; then they correlated the average particle velocity with a modfiled Froude number and particle Reynolds number. The solid materials used were ion-exchange resin particles and glass beads with diameters of 0 321 - 1 84 mm and densities of 1190 - 2500 kg rne3. The pipe diameters were 19 2, 30 and 54 2 mm Toda et al [7] studied the transition velocltles of horizontal sohd-liquid two-phase flow expenmentally They reported correlations for the @ Elsewer
Sequola/Prmted
m The Netherlands
112
tlansition velocity from asymmetric suspension to moving-bed-type flow, for the velocity correspondmg to the mmlmum pressure drop and for the hmltmg velocity for deposltlon at which a fured bed forms A good review of the previous work on heat transfer to non-newtonlan sloes was given by Quader and Wllkmson [8] They studied experimentally the heat transfer to pseudoplastic tltanlum dioxide suspensions m pipes and discussed the lunltatlons of the analogy between heat and momentum transfer Zenz and Othmer [9] and Thomas [ 101 mvestlgated heat transfer to concentrated suspensions; they suggested the use of conventional heat transfer relations, employing the physlcal properties of the suspension Brandon and Thomas [ll] measured the heat transfer rates to water suspensions of glass microspheres with mean diameters from 0 020 to 0 86 mm which were used III concentrations of less than 0 02 volume fraction of solids m both the horizontal and the vertical upward transport The Reynolds number was varied from 20 000 to 90 000 A peak m the relative heat transfer enhancement was observed for the constant value of the product 11’16. Konno et al [12,13] (&lD)(Rel) Investigated the heat transfer characterlstlcs of downward and upward flowing suspensions of water -glass bead or water-ion exchange resin particles m vertical pipes The pipe diameters were 8, 12 8 and 19 mm. Harada et al [ 141 measured the rates of heat transfer between the pipe wall and the suspension flow m horizontal pipes using water suspensions of glass beads (0.06 to 10 mm m diameter) at concentrations up to 0.1 volume fraction of solids and at Reynolds numbers varying from 3000 to 50 000 They observed that the heat transfer coefficient of an asymmetric suspension flow was always higher than that of a sunple water flow They correlated their data on the basis of the Sleder -Tate equation [ 151 and reported an emplrlcal equation for heat transfer to asymmetric suspension flow In spite of these studies mentioned above, the flow and heat transfer characterlstlcs of a horizontal hquld-solid suspension flow have not been understood well enough owing to the complex behavlour of the suspension flow The purpose of this study 1s therefore to produce new experimental data m order to
determine the relatlonshlps among the consistency dlstrlbutlons of solid particles, their flow patterns and the heat transfer behavlour of the suspension flow 2 EXPERIMENTAL
DETAILS
The experiments consist of two parts (1) Measurement of consistency dlstrlbutlons of solid particles over a cross-sectlon of the horizontal pipe as the suspension flows turbulently m the fully developed region, (u) Measurement of heat transfer coefhclents for horizontal flow of hquld-sohd suspensions under different operatmg condltions A schematic diagram of the experimental apparatus 1s shown m Fig. 1 The horizontal test section IS a copper pipe of 41 5 mm I d The details of the experimental set-up are given elsewhere [ 161 A samphng probe was deslgned and constructed to measure the transport conslstencles of solids at different pomts along the vertical, the horizontal and the 454dlrected diameter of the pipe at an axial distance of 2820 mm from the pump outlet Photographs of the samphng probe and the closed-loop flow system are given m Fig. 2 and Fig 3 respectively The samphng probe could be moved across the pipe diameter by a screw mechanism The posltlon of the probe tip m the pipe was mdlcated with good accuracy by a needle on the scale (Fig 2). The dlrectlon of the probe was ahgned parallel with the streamhnes of flow and every precaution was taken to keep this alignment durmg the expenment The probe (D,, = 2 mm and D,, = 4 mm) was inserted mto the flow with the opening facing the dlrectlon of flow The entire assembly of the sampling probe was clamped tightly on the pipe In order to change the orientation of the dlameter, across which the probe tip travelled, the pipe was rotated between the end flttmgs, together with the samphng probe assembly The angle of onentatlon, the angle between the probe length and the horizontal, was accurately measured at each settmg The dlrectlons of sampling using the mserted probe are shown m Fig 4 The physical properties of the sohd particles used m this work are listed m Table 1 The gram sizes of the particles were
36cm
27cm
t
Hg -Monometer
48cm
I -
Fig
1
SchematIc
dlai gram
of the experlmental
Condensate
apparatus
i Ftg 2 Samphng
probe
Fig -I Dwectlons of samplmg (AIBI, Al&, A3B3)
by Inserted
probe
The scope of the flow experiments and that of the heat transfer experiments are given III Tables 2 and 3 respectively 2 1 Expenmen experlmen
Fig 3 Photograph
of the apparatus
made uniform by usmg a series of Tyler’s standard sieves Arlthmetlc average diameters between the sieves were taken as the average diameter for each set of particles
tal procedure
for flow
ts
A slurry, of the required consistency, and with a umform particle size, was prepared m the head tank The required velocity of the slurry was set The coolmg water was started to maintam a constant slurry temperature durmg the flow experunents The slurry would otherwlse heat up during the cu-culatlon through the pump m a closed-loop system To measure the solid conslstencles at various points along the chosen diameter, a gravlmetrlc method was employed A set
114 TABLE
1
Physlcal
propertles
ot sohds Den&y
Alaterral
Feldspar (K20-A120~
TABLE Scope
pP
Diameter
D,
Calculated
(kg mP3)
(mm)
(m s-‘)
1698
0 061 0 161 0 227
0 0025 0 0099 0 0152
6&O:)
termmal
velocrty
Specific heat C, [ 1 i] (kcal kg-’ “C-l) 02
2 of the flow experiments
(a) Inlet sohd consistency Sifeed (volume fraction sohds) (b) SolId particle size D, (mm) (c) Flow
Reynolds
number
Rel =
0061 D-r, fi,,,P,,
022’;
1 4 A lo4 < Rel C 5 X lo4
IJI (d) Temperature of the suspension T (“C) (e) Orlentatron of the (probe-pipe diameter) dlrectlon to the horizontal ~9(deg)
TABLE Scope
3 of the heat transfer
experiments
(a) Inlet solld consistency c;feed (volume fraction sollds) (b) Sohd particle size D, (mm) fc)
T=205% 8 = O’, 45-, 90
Flow
Reynolds
number
Rel =
DTI ~tnike
0 005
G Cfeed < 0 03
0 081
< D, < 0 227
25000
< Re, < 110000
Fl
(d) Suspension veloclty Urn (m s-‘) (e) Pipe-wall temperature Tis, ( C)
02
of lOO-ml Erlenmeyer flasks were washed, dried and weighed to be used m the experlments During the clrculatlon of the slurry m the system, the samples of any volume were collected m the Erlenmeyer flasks, each of which corresponded to a mixture of water and solids at a defmlte distance from the centre-line of the pipe This distance was read from the scale on the probe assembly. Keeping the same flow Reynolds number, the same consistency of sohds and the same particle size, the pipe was rotated around its horizontal axis, together with the probe assembly. This operation provided a change m the orlentatlon of the probe-diameter dlrectlon of 45” or 90” The Erlenmeyer flasks containing the collected samples were tightly closed with their correspondmg corks Just after the samples were taken, and were
then weighed These samples were carefully dried, preventing splashmg, overnight m an oven at around 110 “C, they were cooled m a desiccator and then weighed agam with a sensltlve balance to an accuracy of ?O 001 g This procedure was repeated for four different solid conslstencles (0 5%, 1 OS, 2 0% and 3 0% by volume of solids m the system) with each particle size of solids At each solid consistency, experunental runs for four different Reynolds numbers (around 14 000, 24 000, 38 000, and 50 000) were performed At each Reynolds number, the data were obtained along the diameters for three orlentatlons Altogether, 144 runs were performed m the determmatlon of the solid conslstencles For each run, an average consM.ency of solids m the liquid phase was obtamed by
115
simultaneously opening the valve on the samplmg lme and closing the vslve on the mam closed-loop system After this operation, these valves were agam set to their previous posltlons, the slurry which was collected m a bucket, durmg the sampling procedure, was returned to the head tank to keep the hquld level constant For each consistency, Just before adJustmg the flow to a new value of the Reynolds number, a weighed amount of solids of that particle size and some water were added to the head tank to keep the hquld level the same and to compensate for the loss of material due to sampling At the end of a day of experlmentatlon, the sohds were washed out of the system to prevent their settlmg m the pump, tank and pipes, and then the pump was turned off 2 2 Experimental expenmen ts
procedure
technique previously described,, on a sample of the slurry obtained at the steady state from the sampling lme At the end of each day of expenmentatlon, the sohds were washed out of the system and the pump was turned off The details for the temperature measurements are given elsewhere [16,18] 2 3 Calculation of heat transfer coefflclent The heat flow rate through the wall of the test section was calculated from the followmg equation
(1) where UAave =
I
+ lleT,/DT,)
1
’
/ h,nD,,
L
(-’
k,,2nL
(2)
\
for heat transfer
After the flow experiments were completed, the thermocouples were put m place and the test section was msulated with flbreglass The operation of the system and the reproduclbllIty of the results were checked by performmg several runs with water only Then the expenments with sohd particles m water were started The procedure for these experiments was as follows The slurry, of the required consistency, and with a uniform particle size, was prepared m the head tank The required velocity of the slurry was set The steam and the coolmg water rates were adJusted so that the slurry would be heated by about 5 - 7 C This temperature difference and the approach of the system to the steady state were checked by means of the thermocouple readmgs Actual data were taken after reaching the steady state, which required at least 1 5 h after the start of each experiment Wlthm 10 mm, after reaching the steady state, the thermocouple readmgs of the wall and of the Inlet and the outlet slurry temperatures, the condensate temperature and Its flow rate at this temperature, the steam temperature m the steam Jacket around the test sectlon, and the pressure drop caused by the flow of the slurry through the orlflce meter were all recorded The average solid consistency for each run was determmed usmg the gravlmetrlc
and A ate = nD,,L
(4)
q 1s also equal to rnCPabeT, which can be wrltten as
_ -
T&l2
Q = UrnPa,, -
4
GaJTSO - T,,)
(5)
where
ii,,, 1s the slurry velocity, p,,, and are the volume-averaged density and Le weight-averaged heat capacity respectively of the slurry at the bulk mean steady-state slurry temperature It was assumed that the thermal conductivity and vlscoslty of the dilute hquld-sohd suspension were equal to those of water at the bulk mean temperature Therefore the dunenslonless groups were defmed as m the following formulae Nu,=
hn,D-r, -
Pr, =
kl
FIG,,, k, (6)
Re, =
DT,
fim i&we Pl
Fr, =
Ut WA,)’
’
The heat transfer coefflclent was calculated by means of eqns (1) - (5), usmg a value of 326 kcal m-’ h-’ ‘C-’ for the thermal conductlvlty of the copper pipe k, Cl71
116
3 EXPERIMENTAL
RESULTS
AND
DISCUSSION
The local sohd conslstencles along the pipe diameter, for three orlentatlons of the probediameter dlrectlon (0’, 45”, 90’) and for three ddferent slzesof feldspar particles (0 081 mm, 0 161 mm and 0 227 mm) were measured at different flow Reynolds numbers From the data, lsoconslstency lmes for solids distributed m the flowing suspension were plotted, but only some of these figures have been presented here as representative samples of the other cases (Figs 5 - 11) The value given for each lme 1s the local solid consistency pS as wt R The value m parentheses 1s the local solid consistency divided by the average sohd consistency (p,/Ct,,) of the suspension flow during each run
y-ax.6
I
(cm) I4
% WI
IO 991
m)
Fig 7 Isoconslstency lines for sollds of_slze 0 081 mm Rel = 13 780, ii,,, = 32 26 cm SC’, Cfed = 1 0 vol s (1 7 wt %), c,, = 0 831 volo1 (1 411 wt %) y-axis
A.
(cm) 2 4 % II
II
15)
34
44
(I631
19931 70
Fig 5 Isoconslstency lmes for sohds of size 0 161 mm Rel = 13 890, ti,,, = 33 39 cm SC’ ~c+d = 1 0 vol~(17wt%),C;tr=0261\~ol~(0143wt~)
(3
35)
Fig 8 Isoconslstenc\ lmes for sohds of sue 0 081 mm Rel = 13 82G ,_&, = 32 96 cm s-’ , Cfed = 2 0 \Ol “c (3 35 wt “c). CL, = 1 21 vol c; (2 39 wt “c) y-0x1s (cm)
)
y-axis
t
(cm)
10%
.I I6
70
2 0
10 231 IO 371 561
(I 601
(cm)
Fig 6 Isoconslstency lines for sohds of size 0 227 mm Re, = 13 940 ,j,,, = 33 39 cm s-l, ~?fd = 2 0 vol Y- (3 35 wt T)? c,, = 0 i37 vol p: (1 248 wt %)
60
II
39)
Fig 9 Isoconslstencq lanes tor sollds of size 0 161 mm Re~=21340,ti,=5685cm~-‘,~~~~=20 vol % (3 35 wt “c), c,, = 2 59 \Ol 0: (-I 321 at Tj
I2 1043) /20 10721
Ftg 10 Isoconslstencq lmes for solids of size 0 227 mm Re~=23900,tim=5665cms-‘,C~ee~=23 vol 0; (3 35 wt ‘), c,, = 1 65 vol P; (2 772 wt %)
Fig 11 Isoconslstency lines for sollds of size 0 161 mm Rel = 52 660,-G, = 123 80 cm S-', cfed = 2 0 vol 0: (3 35 wt “c). Ct, = 3 43 vol % (5 703 wt S)
Calculations have been performed with the present data to determine the various tranwtlon velocltles (e g the velocity at which asymmetric suspension flow changes over to a moving-bed-type flow, and the hmltmg velocity for depoatlon, at which a sohd deposit begms to build up m the bottom of the pipe), according to the defmltlons and correlations reported by Toda et al [7] The results of the calculations were m agreement with the experimentally obtained lsoconslstency lmes, both mdlcatmg the same type of flow pattern These flow patterns under the various operating condltlons are
summarized m Table 4, where they are classified by means of the particle Reynolds number
TABLE
Re, =
number
D,, k, pave
PI and the inlet solid consistency m each run As can be observed from Figs 5 - 11 and Table 4, the flow behavlour of llquld-sohd suspensions m a horizontal pipe 1s highly
4
Chart of flow patterns
(hvdrodynamlc
DP
Cfeecl
(mm)
the flow Reynolds
RelJ
study)
_ (vol?)
Rcl
13700 14300 urn = 0 335 (m s-‘)
23700 24500 um - 0 56.5 (m s-‘)
37500 39500 l’rn * 0905 (m s-’ )
51500 53200 Ll, 2 1 235 (m s-‘)
0 081
02
05 10 20 30
MBF hlBF FB FB
hqBF hlBF hlBF bIBF
ASYM ASYiU ASI-hl ASYhl
ASYM ASYhI ASYM XSYM
0 161
16
05 10 20 30
FB FB FB FB
hlBF hlBF hIBF MBF
‘GYM MBF hIBF hlBF
GYM ASYM ASEW ASYM
0 227
35
05 10 20 30
FB FB FB FB
MBF hlBF hlBF MBF
AS Yhl MBF hlBF MBF
ASYLI ASYM ASYM ASYhI
FB, flxed bed, MBF, moving-bed
flow,
ASnl,
asymmetric
flow
118
dependent on the inlet solid consistency of solids, the particle size and the flow Reynolds number Along the vertical diameter, the solid consistency profiles show a common trend m that the particles are dlstrlbuted contmuously with a mu-umum consistency near the upper wall and the maximum solid consistency at the lower wall This IS as expected because of gravity The lsoconslstency lines are sharply convex m the lower half of the circular pipe crosssection at low Reynolds numbers (I c around 14 000) for particles of size 0 161 mm and 0 227 mm because the terminal velocltles of these particles are higher than those of 0 081 mm particles, the effect of gravity IS also slgnlflcant (Figs 5 and 6) These convex lines are observed under condltlons where a futed bed forms For small particles of size 0 081 mm, lsoconslstency lines are concave at low and medium conslstencles for low Reynolds numbers as can be seen m Fig 7 This corresponds to the existence of a moving bed In the lower part of the pipe while the upper part IS fllled with an asymmetric suspension For any one size of particles, at low Reynolds numbers, the convex lines are observed only at high solid conslstencles mdlcatmg the formation of a futed bed (Fig 8), but these convex lines are curved up from both sides in the lower regions between the 45’dlrected diameter and the horizontal diameter of the pipe as m Figs 5,7 and 8 The same curving up cannot be observed for 0 227 mm particles m Fig 6 This shows that only the smaller particles can be carried up easily by the turbulent eddies, so the lateral movement of particles becomes slgnlflcant at low Reynolds numbers The lateral movements may also be enhanced by the agitation created from the particle-particle and particle-wall mteractlons caused by the surface u-regularities on the particles and on the pipe wall The lsoconslstency lmes for 0 161 and 0 227 mm particles, at Reynolds numbers of around 24 000, are slightly concave m the lower half of the circular pipe cross-section (Figs 9 and lo), because the particle eddy ddfuslvlty increases with increasing flow Reynolds number Therefore the lsocons1stency lines tend to be smoothed over the pipe cross-section as the particle eddy dlffuslvlty
increases [ 51 These cases correspond to the existence of a moving bed below the asymmetric suspension flow (Table 4) At high flow velocltles and at medium or high solid consistencies, asymmetric suspension alone fills the pipe cross-sectlon for all the particle sizes (Table 4) The lsoconslstency lines for such a flow case are shown m Fig 11, as an example of 0 161 mm particles m water, at 2 vol % solid consistency and at a flow velocity of around 1 24 m s-’ Figure 12 shows the enhancement ratio (h,/h,, ) which 1s the convective heat transfer coefflclent of the hquld-solid suspension divided by the convective heat transfer coefficient of water under the same operating condltlons, plotted with respect to the mlet solid consistency for the different particle sizes and Reynolds numbers The heat transfer coefflclent of water without sohds h,, was determined m several runs to check the accuracy of the expenmental system The well-known Sleder and Tate equation [ 151 was used to calculate h, under exactly the same operating condltlons for each run
4-
z’
P
I
e-
Fig 12 Effect of particle we and Reynolds on enhancement of convectwe heat transfer clent (12,/h, t’s‘ ?feed)
number coeffl-
119
h, = 0 023 +
(Re,)O 8(Pr,)1,3( ;)O Tl
I4
(7)
U’
where the Reynolds number and the Prandtl number are calculated using the propertles of water at the average bulk temperature for each run From Fig 12, It appears that there is greater heat transfer enhancement with 0 081 and 0 161 mm particles than with 0 227 mm particles This may be due to the greater momentum gam by large particles m the dlrectlon of motion, preventing these particles from moving (or vlbratmg) m the lateral dlrectlon The small magnitude of such lateral motions would prevent the mductlon of turbulence mto the boundary layer close to the wall Smaller particles, however, should possess greater freedom to move towards the walls since the resultant of two momenta, one m the dlrectlon of motion and the other perpendicular to this, 1s directed at a greater angle towards the walls Furthermore low Reynolds numbers favour the lateral movement of solid partrcles, and this contributes to the thmnmg of the viscous boundary layer, thus the heat transfer 1s enhanced In Figs 5. 7 and 8, these lateral movements of solids are indicated by the lsoconslstency lines being curved up from both sides of the convex lines, for 0 081 and 0 161 mm particles at low Reynolds numbers, whereas this 1s not so for the 0 227 mm particles m Fig. 6 In Fig 12, ior all the particle sizes, the enhancement ratio increases with decreasing Reynolds number, but it shows a mmlmum at 0 01 volume fraction sohd consistency for all the runs except those m which 0 161 mm particles were transported at Reynolds numbers of 35 000 and 26 500 In the latter case, a highest peak value for the enhancement ratio 1s reached, then the addition of solids to greater than 0 01 volume fraction solids produces a defmlte decrease In all the other cases, the small peaks for the enhancement ratio, the values of which are inversely proportional to the Reynolds number, are observed at 0 005 volume fraction sohds, then, after the mmlmum values of the enhancement ratio at 0 01 volume fraction sohds, the so-called barrier solid consistency for these specific cases, the addition of more solids gradually increases the enhancement ratio [ 181
The heat transfer coefficients of the waterfeldspar suspension flows are lower than those of a sunple water flow under the same operatmg condltlons at around 0 01 - 0 03 volume fraction solids and at very high Reynolds numbers (I e around 88 000 - 115 000) for 0 081 and 0 161 mm particles, but for 0 227 mm particles, the heat transfer coefficients are extremely low at all the Reynolds numbers, the experimental range being approximately 26 500 - 115 000, and at medium to high solid conslstencles (I e at around 0 01 - 0 03 volume fraction solids) The small peak values m the enhancement ratlo can be explained by reasoning that particle-particle and particle-wall mteractlons may be occurring at a high rate because of the high degree of freedom of solid particles at low solid conslstencles At a medium conslstency of 0 01 volume fraction solids, the number of particles m the system ~111increase, but they may start to have less freedom to move As a result, the heat transfer coefficient may decrease because of the reduction m particle-wall mteractlons However, Fig 12 indicates that there exists a particular combination of particle size, flow Reynolds number and inlet solid consistency of particles which gives optimum heat transfer Obviously, some change m the flow pattern of sohds occurs with 0 161 mm particles at 0 01 volume fraction solid consistency m the suspension for flow Reynolds numbers of 35 000 and 26 ZOO, which gives rise to the maximum values of the enhancement ratio, the latter number giving the highest peak value of the enhancement ratio This is most probably due to the combmatlon of two phenomena, namely, the lateral motion of particles at low Reynolds numbers and the suitablllty of an intermediate particle size for thinning the boundary layer This explanation was also supported by Lee and Durst [19] Brandon and Thomas [ll] also obtained an optimum heat transfer enhancement m studying the heat transfer to dilute (less than 0 02 volume fraction solids) hquld-solid suspension flows They concluded that a critical particle size should exist which would Interact most effectively with the contmuousphase turbulence to enhance the heat transfer At 3 vol 7c solid consistency, higher enhancement ratios than those at lower solid
120
conslstencles might have been expected because of the mcreasmg effect of partlcleparticle and particle-pipe-wall mteractlons, but there IS a contradictory factor which 1s that the heat capacity of feldspar particles 1s only about one-ftith that of water Therefore as the solid consistency increases, the heat capacity of the mixture becomes even lower than that of water As a result of these two competing effects (I e the particle-wall lnteractlons and the relative heat capacltles of the phases) the enhancement ratio increases or decreases with increasing inlet solid consistency of the water-feldspar suspension flow, m the manner shown m Fig 12 [ 16,181 The correlations given by Toda et al [7] for calculatmg the transItIon velocltles, which determine the flow patterns m a suspension flow, were also used for the heat transfer experunents The results are given m Table 5 When Tables 4 and 5 are compared, it can be seen that, In the low velocQ~ ranges, the changes m the flow patterns m the heat transfer experiments take place wlthm almost the same velocity ranges as do the changes m the flow patterns m the flow experiments In contrast, at the higher velocltles, this parallehsm IS not observed m most of the experunental runs The reason for this may be the higher terminal velocltles of the particles m the heat transfer experiments or the expenmental errors and the shortcommgs of the empu-lcal correlations This pomt 1s not completely understood TABLE Chart
patterns
(heat
transfer
_
ut
Cfeed
(mm)
(m SC’)
(vol %)
11,
(Re,
0 227
(8) where 14 000 < Re, < 140 000 34<
-Clt4ll < 12 7 121
282 < ;
0 53 < 2
009<
< 10 500
< 583
$022
P
A comparison of the present data with eqn (8) showed poor agreement, because all of the experu-nental (C, /_fm/h,) values were smaller than Its correlation hmlt of 3 4 It was only
study)
(m s-‘)
0 ‘?4
0161
Nu, = 0 131 Relo 62
5 of flow
4
0081
Optimum heat transfer, m this work, corresponds to a case where there IS a stationary (fured) bed m the bottom of the pipe With stationary bed flow, the heat transfer rate increases greatly because the fluid velocity IS much higher than that of a simple water flow m the upper part of the pipe, owmg to the smaller cross-sectional area available for flow, since the bottom part 1s occupied by the futed bed This is m agreement with the results obtained by Harada et al [14] Salamone and Newman [20] proposed the following empirical equation for a fine particle-water suspension
2:
26,joo)
0 32 (RE,
686x10-3 630/10-”
05 10
FB FB
FB FB
647/10-3
30
FB
154~10-~
OS
FB
1 51 Y lo-’ 1 49 x10-?
1 0 3 0
229 110-Z 2 13 Alo2 15 x10-2
05 10 3 0
aOptlmum Table 4)
heat
transfer
2
0 -55
0 90
,350OO) (Re, - 58000)
(Rel
I 19
* 88000)
fRe1
FB
hlBF hIBF MBF
hIBF MBF hlBF
ASYhl ASYhl hlBF
FB= FB
FB FB FB
hlBF RlBF hlBF
blBF hlBF hlBF
MBF hlBF hlBF
FB FB FB
FB FB FB
MBF hlBF MBF
MBF hlBF hlBF
hlBF MBF hlBF
and the highest
peak
value
of the enhancement
ratlo
occur
2
m this run (abbrevlatlons
115000)
see
121
for some of the experimental runs, m which the values of (Cl~,/kl) approached 3 4, that the correlation fitted the data to within +20% Another correlation was proposed by Harada et al [14] for an asymmetric suspension flow Only nme of the runs m this mvestlgatlon seemed to cover the condltlons given m then work Although the experlmental parameters were within the given hmlts, m each of these runs, the flow pattern was not that of an asymmetric flow, but was a combmatlon of a fured-bed or moving-bed flow with an asymmetric flow Therefore it was not suitable for estlmatmg the heat transfer coefflclents for the water-feldspar suspension flow and the accuracy of the fit was poor Quantitative studies are under way to obtain an emplrlcal equation which gives the best fit to the present data, and this will be presented m a future pubhcatlon
1 CONCLUSIONS The hydrodynamic and heat transfer characterlstlcs of water-feldspar suspensions m horizontal transport were studled expertmentally, under turbulent flow condltlons In the determination of solid consistency profiles m water-feldspar systems, a gravlmetric method applied together with a specially designed sampling probe served the purpose successfully The maximum expenmental error was around 27% In the horizontal flow of hquld-solid muctures, the solid particles were dlstrlbuted contmuously with a mlmmum density at the upper wall and a maxunum density at the lower wall owing to the slgmflcance of the gravity effect The smaller the particle size and solid conslstency, and the larger the Reynolds number, the more uniformly distributed were the solids across the cross-sectional flow area The ddferent shapes of the lsoconslstency lmes were related to the different flow patterns These flow patterns could be classlfled by takmg particle size, flow Reynolds number, inlet solid consistency and particle Reynolds number as parameters For low velocltles, the changes m the flow patterns in both the flow and the heat transfer experiments took place wlthm almost the same velocity ranges The same phenom-
enon was not observed at high velocltles This point could not be explamed completely The heat transfer study mdlcated the existence of a particular combmatlon of the particle size, the flow Reynolds number, and the mlet solid consistency of particles m each specific hquld-solid system which would give the highest heat transfer enhancement. In this study, for the water-feldspar system, the highest enhancement of heat transfer occurred at an mtermedlate particle size of 0 161 mm, at a low Reynolds number of about 26 500, and at an intermediate inlet sohd consistency of around 0 01 volume fraction of solids As the solid consistency increased, the particle-wall mteractlons and the physical properties of the system became unportant factors m determining the heat transfer to two-phase flows For water-feldspar systems, the particle-wall mteractlons and especially the heat capacity of the system were competmg factors m heat transfer No expertmental equation for heat transfer coefflclents m water-feldspar suspension flow has been developed here This will be the subJect of a future publication REFERENCES 1 V
F Kustov, Fuel Suspensions Academy of Sciences of the U S S R , 1942 2 Ch Bomlla, Heat Transtcr m Nuclear Engmeerrng, State Publlshmg House tor Atomic Literature, New York, 1961 3 hl Toda, T Shnnlzu, S Salto and S hlaeda, Preprint for ,37th Ann Meet Japan, Tokyo 1972, p B-310
Sot
Chem
Eng
B Scarlett and A Crlmley, Hydrotransport 3. Proc 3rd fnt Conf on the Hydraulw Transport of Sohds rn Prpes, Golden CO, 1974, Paper no D3, pp 23 - 3: 5 T Furuta, S TsuJImoto, hl Toshlma, M Okazakt and R Toel, Kagahu Kogaku Ronbunshu, -I (1978) 105 H Ohashl, T Sugawara, K Klhuchl and hl Ise, J Chem Eng Jpn, 13 (5) (1980) 343 - 339 hl Toda, d Yonehara, T Klmura and S hlaeda, Int Chem Eng, 19 (1979) 145 A K hl A Quader and W L WIlkInson, Int d Multzphase Flow, 12 (:981) 545 F A Zenz and D E Othmer, FlwdrzatIon and Flurd-Partwle Systems, Remhold, New York, 1960 10 D G Thomas, 4IChE J, 6 (1960) 631 - 639 11 C A Brandon and D G Thomas, Transport characterlstlcs of suspensions, Proc 4th Int Heat Transfer Conf, Parls, 1970, Paper no CT-2 : 12 H Konno, E Harada, hl Toda, hl Kurlvama and hl Asano, Kagahu Kogahu Ronbunshu. 5 (1979) 464
122 13
H Konno, E Harada, hl Toda, hl Kurlyama and S Saruta, Kagakrc Kogaku Ronbunshu 6 (1980) 308
14
E Harada,
M Toda, M Kurlyama and H Konno, Jpn, 18(1)(1985)33-38 15 E N Sleder and G E Tate, Ind Eng Chem , 28 J
Chem
(1936)
kl
Eng
kP
1429
16 T
A Ozbelge, Hydrodynamic and heat transfer characterlstws of gas-solld and Iquld-solid systems In turbulent flow, Ph D Thesls, Chetnrcal Engmeermg Department, hllddle East TechnIcal LJnwersltJ, Ankara, Turkey Handbook, 17 J H Perry, C’hemrcat Engmeers hlcCraa-Hdl. New York, 1911, 2nd edn 18 T 4 Ozbelge and T G Somer, Heat transfer to slurries m horizontal transport, Proc 16th Ann Meet phase
k CU
Fine Partrcle Sot on Particulate Processes, .Illanu Beach, 1985,
L
In m Nul Prl
and hlultl Vol 3,
Hemisphere Pub1 Corp 1 Washrngton, 1987, pp 271 279 19 S L Lee and F Durst, Int J Multiphase Flow 8 13) (1982) 125 146 20 J J Salamone and Rl Newman, Ind Eng C’hem , 47 (1955) 283 APPENDIX
A_a\
e
c feed Cl GN
Gr
41
D PO DP D-r,vD
D
FrT,D g
A NOMENCLATURE
surface area for heat transfer ( m2) inlet solid consistency (wt % or vol 70) heat capacity of hquld (kJ kg-’ K-‘) weight-average heat capacity of hquld-sohd suspension depending on the solid consistency m the liquid (kJ kg-’ K-‘) average sohd consistency m each run (wt lo) inside diameter of sampling probe (mm) outside diameter of sampling probe (mm) solid particle size (mm) inside pipe diameter outslde pipe diameter particle Froude number acceleration due to gravity (9 81 m S-2)
h,
h,
mdlvldual convective heat transfer coefflclent for heat transfer to hquldsolid suspensions (W me2 K-‘) heat transfer coefficient wlthout sohds m water (W me2 K-*)
thermal conductlvlty of copper -1 K-1 (Wm ) thermal conductlvlty of liquid -1 K-1 (Wm 1 thermal conductlvlty of feldspar partxles (W m-’ K-‘) length of test section (m) natural logarithm mass flow rate (kg s-‘) Nusselt number for hquld-solid suspension flow Prandtl number for hquld-solid suspension flow rate of heat flow (W) Reynolds number for hquld-solid suspension flow particle Reynolds number inlet temperature of hquld-solid suspension to the test section (K or ‘C) outlet temperature of llquld-sohd suspension from the test section (K or ‘CT) pipe-wall temperature (K or “c) average velocity of llquld-solid suspension (m s-’ or cm s-‘) free-fall or termmal velocity of a single particle (m s-’ or cm s-l) overall heat transfer coefflclent -2 K-1 (Wm )
Greek symbols
AT =L~I
PI Pm
l-&V 1)
Pa\ e
PI PP
PS
T,, - T,, , temperature difference (K or %) logarlthmlc mean temperature dtiference vlscoslty of liquid (kg m- ’ s-‘) vlscoslty of suspension (kg m-’ s-‘) vlscoslty of hquld at wall temperature (kg m-' s-l) kmematlc vlscoslty (m2 s-‘) volume-averaged denslty of liquidsolid suspension (kg m-“) den&y of hquld (kg me3) solid density (kg m-3) local sohd consistency m hquldsolid suspension (wt ‘7,)