Pump Capacity and Power Consumption of Two Commercial In-lineHigh Shear MixersQin Cheng, Shuangqing Xu, Jintao Shi, Wei Li, and Jinli Zhang *
School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China
ABSTRACT: Two main commercial in-line high shear mixer (HSM) configurations, including the dual rows ultrafine teethedand the single-row blade-screen in-line units, were investigated under the pump-fed mode in order to disclose the pump capacity and power consumption characteristics. Results indicate that the pump capacity of the teethed in-line HSM is rather poor, withmaximum pumping heads of 2.31−2.72 m and a maximum pumping efficiency of 1.5%. By contrast, the blade-screen in-lineHSM demonstrates maximum heads around 4.33−4.76 m and a maximum pumping efficiency of 7.3%. The power number dataof both units with the bearing loss subtracted can be correlated by the Froude number modi fied power consumption model. Thepredicted power numbers show good agreement with the experimental data for both in-line HSMs. The results obtained here arefundamental for the performance assessment as well as the design and selection of in-line HSMs.
1. INTRODUCTION
As a promising equipment to develop novel processintensification techniques, high shear mixers (HSMs) haveattracted increasing attention in chemical , biochemical,agricultural, and food-processing industries.1−14 HSMs havegreat potential to intensify chemical reactions with fast inherentreaction rates but relatively slow mass transfer due to theirlocally intense turbulence and shear.14−17 The applications of HSMs have been broadened from typical physical processesincluding homogenization, dispersion, emulsification, grinding,dissolving, and cell disruption to the chemical reactionprocesses. Patented fine chemical productions using HSMs
have been booming recently.18−25
However, the currentunderstanding of HSMs still needs to be advanced in orderto predict or assess the device performance. The processdevelopment, scale-up, and operation of HSMs are mostly relied on engineering judgments and trial-and-errors other thansound engineering principles, which lead to high developmentcosts, start-up problems, lost time to market, and considerablematerial waste.1 ,26 ,27
HSMs can be generally categorized into batch and in-lineunits. Compared with batch units, in-line HSMs have theadvantages of continuous operation, short residence time, andhigh throughput.2 ,28 Commercial in-line HSMs are usually designed as either the teethed or blade-screen configuration.The presence of blades on the rotor is a significant feature
aff
ecting the device performance.
1,2 ,29
In-line HSMs with blades, such as Silverson series, can simultaneously pump anddisperse materials. While for the teethed in-line units, anexternal pump is often needed for feeding.1 In practice, it isoften convenient and preferable to use a separate pump toadjust the residence time of the materials for dispersion andreactive mixing by controlling the flow rate independently,
while varying the rotor speed controls the level of energy inputand the resulting turbulence and shear instead.
Power consumption, which is an important parameter for theperformance assessment and motor selection of an in-lineHSM, can be measured by the electric,30 calorimetric,29 ,31 ortorque method.28 ,32,33 The electric method directly measures
the apparent voltage and current (assuming alternating currentmotors used) but suff ers from the problem caused by the v ariedmotor efficiency and power factor with respect to load.30 Thecalorimetry technique, which insulates the system and measuresthe temperature rise over time, is not so reliable in accuracy dueto the eff ectiveness of the insulation and the changes of fluidphysical properties with temperature.34 The method based onmeasuring the torque is preferred and believed to be moreaccurate in the open literature.28 ,32,33
In an in-line HSM, the flow rate can be controlledindependently of the rotor speed. Experimental results show that power consumptions of in-line HSMs depend on not only
the rotor speed but also the processing flow rate.28−33
Sparks32
studied the power consumption of several single-row teethedand blade-screen in-line HSMs using water, where the axially straight teeth slots and the round screen holes were rathercoarse (with opening percentages over 50%). On the basis of the kinetic energy of a fluid element on the rotor tip, a powerconsumption correlation in proportion to ρQN 2 D2 wasobtained, where ρ is the density (kg/m3), Q is the volumetricflow rate (m3/s), N is the rotor speed (s−1), and D is the rotordiameter (m). However, as criticized by Hall et al.31 andKowalski et al.,28 this expression predicted incorrect zero powerconsumption at zero flow rate. Kowalski30 proposed that thetotal power consumption of an in-line HSM consisted of threeparts: the power required to rotate the rotor against the liquid
in the gap (“tank term” , P T); the power requirements from theflow of fluid through the gap (“flow term” , P F); and the powerloss by vibration and noise, kinetic energy losses at the entranceand exit, and the accuracy of measurements, etc. (“losses term” ,
P L). As shown in eq 1 , the “tank term” P T is analogous to thepower consumption in a stirred vessel, while the “flow term” P Faccounts for the pumping action of the in-line mixer.
Received: August 30, 2012Revised: November 25, 2012 Accepted: December 12, 2012Published: December 12, 2012
where P shaft is the shaft power (W), P fluid is the net power
delivered to fluid including the contributions by P T and P F (W), Poz is the power number at zero flow rate, and k 1 is the modelconstant. Experimental results from sev eral recent publicationshave shown the rationality of this model.28,29 ,31,33 However, it is
worth noting that, the in-line HSMs investigated in thesestudies all have blades on the rotors providing positive pumpingefficiencies, e.g., either the typical blade-screen configuration, orthe modification from the typical teethed unit to include anadditional “pumping wheel”.
In this paper, two main commercial in-line HSMs, includingthe teethed and the blade-screen configurations, wereinvestigated under the pump-fed mode in order to study thepump capacity and power consumption characteristics. By ananalogy with a centrifugal pump, the pump capacity of the in-
line HSMs was characterized by the pumping head andpumping efficiency. The Froude number adjusted powerconsumption model was utilized for the power prediction.
2. EXPERIMENTAL SECTION
2.1. Experimental Apparatus. The experimental in-lineHSM is a custom-built pilot-scale unit of FDX series provided
by FLUKO. The rotor and stator of the mixer are designed asinterchangeable so that the two main commercial rotor−statordesigns can be expediently tested in the same model. Originally,the mixer is a rotor−stator teethed design, where the rotorconsists of two rows of 52 teeth (axially straight; with outerdiameters of the inner and outer teeth rows of 47 and 59.5
mm) with 1 mm slots; while the stator has two rows of 30 teeth(15° backward inclined; with outer diameters of the inner andouter teeth rows of 53.5 and 66 mm) with 2 mm slots. Theshear gap width (i.e., the annular space between the assembled
rotor and stator) is 0.5 mm; and the tip-to-base clearance (i.e.,the axial space from the rotor tip to the stator base or that fromthe stator tip to the rotor base) is 1 mm. Geometric details of the stator and rotor teeth are shown in Figure 1a and b.
Alternatively, the mixer can be assembled into a blade-screenconfiguration, where the rotor has a single row of 6 blades (15°
backward inclined; with the same rotor outer swept diameter of 59.5 mm) while the single-row stator screen (with the samestator outer swept diameter of 66 mm) has two rows of 3 mm× 3 mm square holes with 30 holes in each row. The shear gap
width and tip-to-base clearance are kept the same as those of the teethed design, i.e., 0.5 mm and 1 mm, respectively. Theopening areas are calculated as both 23.6% of the outer circularface for the teethed and screen stators. Figure 1c and d show
the geometric details of the blades and screen holes.2.2. Materials and Properties. The Newtonian fluids of
pure water and glycerin (Sinopharm Chemical Reagent Co.,Ltd.) aqueous solutions and the non-Newtonian fluids of carboxymethyl cellulose (CMC, Tianjin Bodi Chemical Co.,Ltd.) aqueous solutions were used. The densities of all fluids
were measured by the pycnometer method. A viscometer(LVDV-II+Pro, Brook field) and a rheometer (MARS III,Thermo Scientific) were utilized for the rheology measure-ments of the Newtonian and non-Newtonian fluids, respec-tively.
For the Newtonian working fluids, the viscosities anddensities were measured at temperatures from 20 to 50 °C
Figure 1. Geometric details of (a and c) the stator and (b and d) the rotor in (a and b) the teethed and (c and d) the blade-screen in-line high shearmixers.
Industrial & Engineering Chemistry Research Article
and found to fit well using eqs 2 and 3 , respectively, where μ isthe viscosity from 0.001 to 0.4 Pa·s, ρ the density from 988 to1252 kg/m3 , T is the absolute temperature from 293 to 323 K,and a1 ∼ a3 and b1 ∼ b3 are the fitted constants as shown inTable 1.
μ = + +a a T a
T ln 1 2
3
(2)
ρ = + +b b T b T 1 2 32
(3)
μ γ γ = =− + + −
K en a a T a T n
a av
1 /
av
11 2 3
(4)
For the non-Newtonian working fluids, the physical properties were measured at temperatures from 15 to 30 °C. The densitiesdemonstrated relatively small diff erence from 1008 to 1017 kg/m3 and were also fitted by eq 3. The rheologies of the CMCsolutions were found to obey power law as indicated by eq 4 ,
where μa is the apparent viscosity (Pa·s), K is the consistency index from 0.227 to 1.360 Pa·sn , γ av the average shear rate (s−1),and n the power law index. The temperature dependency of K
was expressed in the similar form as eq 2 and the smalldiff erence of n was averaged out within the temperatureranges.33 The values of the constants for fitting the physicalproperties of the non-Newtonian fluids were also listed in Table1.
2.3. Experimental Procedure. The pump capacity of theteethed in-line HSM was rather poor,1 therefore the mixer wasfed by a centrifugal pump. The blade-screen HSM was alsooperated under the pump-fed mode. The in-line HSM wasinstalled in the recirculation loop of a 60 L storage tank, wheretwo brass coil pipes were utilized in parallel for heat removaland temperature control. Under the pump-fed mode, the
volumetric flow rates of the working fluids were controlled by a valve downstream of the pump and measured by a rotameter.The temperatures and pressures at the inlet and outlet of thein-line HSM were monitored via temperature probes andprecision pressure gauges, respectively. The rotor speed of theHSM (up to ∼3500 rpm) was controlled by an inverter. Theshaft torque and the rotor speed were measured on the drive
shaft using an AKC-215 transducer (China Academy of Aerospace Aerodynamics) and recorded by the data-loggingsystem at a frequency of 1 Hz. The actual volumetric flow ratesof the fluids other than water from the rotameter reading werecarefully calibrated by measuring the volume and flow timeunder the same temperature ranges as those during the powermeasurements.
The bearing losses were measured at zero flow rate by rotating the shaft at diff erent rotor speeds without the rotorsattached. The underlying assumption is that the powerconsumption by drag on the shaft should be negligibly smallcompared to the bearing loss. Therefore, the measured power
without rotors when using pure water as the working fluid was
utilized to account for bearing losses in this paper. It was foundthat, when using the low viscous water as working fluid, thetype of the fitted stator (i.e., the teethed or screenconfiguration) showed no obvious influence on the measured
bearing loss.2.4. Data Processing. The head of the experimental in-line
HSM was calculated as
∑ ρ
= − +−
+−
+H h h p p
g
u u
g H ( )
22 1
2 1 22
12
f (5)
where H is the head of the mixer (m), h is the mounting heightof the pressure gauge (m), p is the measured pressure (Pa), u isthe mean flow velocity calculated from the corrected volumetricflow rate and the inlet or outlet tube diameter (m/s) (d 1 = 25mm, d 2 = 20 mm), ΣH f is the head loss by friction and localresistance in the inlet and outlet tubes35 (m), ρ is the density of the working fluid (kg/m3), g is the gravitational acceleration (=9.81 m/s2). Subscripts 1 and 2 denote the inlet and outletconditions, respectively.
The shaft power and net power delivered to fluid wereexpressed as
π = P NM 2shaft (6)
π π = − P NM NM 2 2fluid n (7)
where P shaft is the shaft power (W), N is the rotor speed (s−1),and M is the torque (N·m). P fluid is the net power delivered tofluid (W), and M n is the torque for the bearing loss correction,measured using water with no rotor attached (N·m).
The pumping efficiency, η , and the power number, Po , werethen determined by
η ρ
=Q gH
Pshaft (8)
ρ= Po
P
N D
fluid3 5
(9)
The power-law Reynolds number of the non-Newtonian
CMC solutions, Repl , was given by ρ
=
−
ReN D
K
n
pl
2 2
(10)
In this paper, calculations of the power number Po and theReynolds number Re (= ρ ND2/ μ) or Repl were based on therotor outer swept diameter of 59.5 mm. The corrected fluidphysical properties based on the averaged inlet and outlettemperatures were utilized in data processing.
3. RESULTS AND DISCUSSION
3.1. Pump Capacity. The head, by an analogy with acentrifugal pump, is characteristic for the pump capacity of an
Table 1. Values of the Constants to Correct Viscosity (or Apparent Viscosity) and Density under Diff erent Temperatures
in-line HSM. Figure 2 shows the head of the teethed in-lineHSM when processing diff erent working fluids. The headincreases with rotor speed and decreases with flow rate. Atlower rotor speeds of 500−1000 rpm, the teethed unit mostly causes a pressure drop rather than a pumping action at almostall fluid flow rates investigated here (see the negative heads inFigure 2), confirming the poor pumping capacity of the teethdesign. At the maximum flow rate of each fluid, the mixerdemonstrates negative head under a broad range of rotorspeeds (even up to 2500 rpm). The maximum pumping heads
of the mixer are just 2.31−2.72 m at the maximum rotor speedof 3500 rpm and zero flow rate of each fluid.
As shown in Figure 3 , the pumping efficiencies of the teethedunit at lower rotor speeds of 500−1000 rpm are predominantly negative and decrease with flow rate to even lower than −20%.
A peak pumping efficiency of 1.5% is observed at 3500 rpm when processing water at 1000 L/h or CMC no. 2 at 889.77 L/h. In comparison, Sparks32 reported a peak pumping efficiency of 6.7% at 3500 rpm and the water flow rate of 1800 L/h for anin-line teethed HSM of similar scale (with the rotor outer sweptdiameter of 61.44 mm), where the rotor and stator had single
Figure 2. Head of the teethed in-line high shear mixer.
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rows of 18 coarse, axially straight teeth. Therefore, the dualrows and ultrafine teethed design (with the stator teeth backward inclined) in the custom-built teethed HSM breaks thealready-poor pumping action and should be responsible for thelow pumping efficiency here. It deserves mention that the low pumping efficiency is no longer a problem when using aseparate pump for feeding. Furthermore, the custom-built in-line teethed HSM studied in this article can avoid thechanneling and/or short circuiting defects that may occur inthe single-row, coarse teethed units,1 ,27,36 which is of morepractical importance in the reactive mixing processes.
The pumping head of the blade-screen HSM, as shown inFigure 4 , also increases with rotor speed but decreases less
significantly or remains relatively stable with flow rate. At thelower rotor speeds of 500−1000 rpm, the blade-screen unitdoes not pump fluids well, either. The maximum pumpingheads of the blade-screen unit are 4.33−4.76 m at 3500 rpm,over 60% higher than those of the teethed unit. As presented inFigure 5 , the pumping efficiency of the blade-screen HSMshows an increase with the flow rate at higher rotor speeds as
well as with the fluid viscosity (or apparent viscosity), which isan obvious diff erence from that of the teethed HSM. A peak pumping efficiency of 7.3% is observed at 3500 rpm and waterflow rate of 2000 L/h. By contrast, Kowalski et al.28 reported apumping efficiency of 11.5% at 5000 rpm and water flow rate of 2000 L/h for a double-row blade-screen Silverson in-line unit of
Figure 3. Pumping efficiency of the teethed in-line high shear mixer.
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similar scale (with the rotor outer swept diameter of 63.5 mm)and opening percentage on the screen (∼21%). This pumping
effi
ciency diff
erence can be reasonably attributed to confi
gura-tional diff erence of the blades (e.g., rows, total numbers,orientations and axial heights, etc.), considering the weak dependence of pumping efficiency on the rotor speed higherthan 3000 rpm (see Figure 5d).
The better pump capacity is certainly an advantage of the blade-screen configuration over the teethed one; however, it is worth noting that, in-line HSMs are basicall y designed fordispersion and mixing rather than pumping.32 The pumpingefficiencies of the teethed and blade-screen in-line HSMs are
both much lower than those of conventional centrifugal pumps.In the in-line HSMs, the tangential velocities resulting fromrotor rotation are redirected radially as the fluid passes through
the stator slots or holes to counteract the pumping action.Howev er, it is the dissipation of this energy that promotes
mixing.
1
As a matter of fact, the dispersing performance of theteethed in-line HSMs is never inferior to the blade-screen units, which explains their widespread applications and their survivalafter decades of developments. As for the industrial applicationsinvolving large flow rates and/or high viscosities of the fluids,even the blade-screen in-line HSMs cannot provide sufficientpump capacity, considering the upper limit of the industrialoperating rotor speed. Therefore, the external pump-fed modeis essential for both the teethed and blade-screen in-line HSMsin practice.
3.2. Power Consumption. The input shaft power into themixer is an important parameter for motor selection. Figure 6presents the shaft power of the teethed in-line HSM as a
Figure 4. Head of the blade-screen in-line high shear mixer.
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function of the rotor speed when processing diff erent workingfluids. The shaft power shows an increase with the rotor speed,flow rate and fluid viscosity (or apparent viscosity). Forexample, the shaft power ranges from 166 to 258 W at N =3500 rpm when the water flow rate increases from 0 to 2000 L/h (see Figure 6d). The shaft power at N = 2000 rpm, Q =1218.48 L/h for Gly no. 3 is 120 W; while at N = 2000 rpm andan approximate flow rate of Q = 1213.64 L/h for Gly no. 2, thisincreases to 199 W (see Figure 6 b and c). The shaft power at N = 3000 rpm and zero flow rate is 199 and 160 W for CMC nos.1 and 2, respectively (see Figure 6e and f). Under the same flow rate for each working fluid, the shaft power demonstrates an
exponential increase with the rotor speed. Power law fits werethen conducted between the shaft power and the rotor speedfor each flow rate of each working fluid. The indexes are found
varied with the working fluid, i.e, 1.2−1.3 for Gly nos. 1 and 2and 1.5−1.6 for Gly no. 3, water, and CMC nos. 1 and 2.
Figure 7 shows the normalized shaft power (not powernumber) P shaft/ ρ N 3 D5 as a function of the Reynolds number inthe double logarithmic coordinate. A linear relationship isobserved between the logarithms of P shaft/ ρ N 3 D5 and Re (orRepl) for all working fluids. Regressions show that P shaft/ ρ N 3 D5
is proportional to Re−1.5 for Newtonian fluids and to Repl−1.2 for
non-Newtonian CMC solutions. The net power delivered to
Figure 5. Pumping efficiency of the blade-screen in-line high shear mixer.
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fluid, obtained with the bearing loss subtracted, presents similar variations as the shaft power and is therefore not shown here.Power law fits of the net delivered power versus rotor speedgive indexes of 1.1−1.2 for Gly nos. 1 and 2 and 1.6−2.0 forGly no. 3, water, and CMC nos. 1 and 2. The index near 2 forthe working fluid of water is consistent with earlier results fromthe pump-fed teethed HSMs reported by Sparks.32
The power curve, usually expressed as the relationship between the power number and the Reynolds number, is oftenused to predict the power requirements for given fluidproperties, impeller dimensions, and operation parameters.
The power number data of the teethed in-line HSM with the bearing loss subtracted are presented as a function of theReynolds number in Figure 8. The data exhibit exponentialdecrease at lower Reynolds number and approach to constantat higher Reynolds number. The constant power number of theteethed in-line HSM approximates Poz(t ) = 0.147 under theReynolds number above 8.3 × 104. The flow is considered asturbulent when processing water in the Reynolds numberranges from 2.7 × 104 to 2.1 × 105. The constant of k 1 inKowalski’s power consumption model can be obtained by fitting the turbulent power data. It deserves to note that the
Figure 6. Shaft power of the teethed in-line high shear mixer as a function of the rotor speed.
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measured power with and without rotors are rather close atzero water flow rate. Consequently, the power numberscalculated using the net delivered power show fluctuation anddo not conform to the turbulent power model well.Fortunately, this zero water flow rate is not important inpractice, since the in-line HSMs are usually utilized forprocessing more viscous fluids,1 or operated at higher flow rates aiming for high throughputs.2 ,28 Therefore, the powernumber data under zero water flow rate are excluded in themodel constant fitting, and this yields k 1 = 14.49.
Cooke et al.33 suggested the power requirement at zero flow
rate in the transition regime consisting of the contributions by alaminar and a turbulent part, with the laminar Poz inversely proportional to the Reynolds number while the turbulent Poz
almost constant. However, discontinuity of the power curve inFigure 8 indicates that P oz is not a sole function of the Reynoldsnumber. Myers et al.37 reported similar discontinuity in themeasured power curve for a batch HSM and the Froudenumber (Fr = N 2 D/ g ) adjusted method was introduced inorder to yield a smooth correlation. Similar treatment isconducted in this article and the laminar Poz is presented as afunction of both the Reynolds number and Froude number.
According to Kowalski’s power consumption model (see eq 1),the power numbers at zero and nonzero flow rates can then be
expressed in dimensionless forms as eqs 11 and 12 , respectively, where Fl is the flow number defined as Fl = Q / ND3.
= + = + Po Po Po K Re Fr Pol t z z( ) z( ) Pc c
z(t)1 2
(11)
= + + Po K Re Fr Po k Flc c zP (t) 1
1 2(12)
The power number data at zero flow rate for the three
Newtonianfl
uids other than water arefi
tted using eq 11 , whichgives K P = 322.57, c1= −0.39, and c2= −0.65. While for the non-Newtonian CMC solutions, the power-law Reynolds numberRepl is used instead of Re in data fitting. With the fi xed values of c1 , c2 , Poz(t ) , and k 1 in eq 12 , the K P values of 40.43 and 25.16are obtained from regressions for the teethed HSM whenprocessing CMC nos. 1 and 2, respectively.
It is expected that eq 12 should be capable of predicting thepower numbers from the laminar, transition to turbulentregime. However, the exponent of −0.39 on the Reynoldsnumber is not low enough to diminish the laminar term on theright of eq 12 for a smooth transition to the power numberexpression in the fully turbulent regime as eq 13.
= + Po Po k Flt z( ) 1 (13)
Therefore, eq 13 was utilized for the power predictions in thefully turbulent regime with Re ranging from 2.7 × 104 to 2.1 ×
105; while in the laminar to transition regime with Re from 105to 7.3 × 103 or Repl from 46 to 2.0 × 103 eq 12 was used. Thepower data from Gly no. 3, with Re ranging from 1.4 × 104 to1.0 × 105 , is found to be better fitted by eq 12. This is probably
because the flow may not be fully turbulent away from therotor−stator head in the bulk region of the mixer chamber. Asshown in Figure 9 , the calculated power numbers from this
“zonal correlation” approach show good agreement with theexperimental results, with an overall average error of 20.1%.The few inaccurate predictions are observed only for the caseunder the lowest rotor speed of 500 rpm.
Shown in Figure 10 , the shaft power of the blade-screenHSM presents similar variations as those of the teethed unit,i.e., an increase with rotor speed, flow rate, and fluid viscosity (or apparent viscosity). In comparison, the shaft power of the
blade-screen and teethed in-line HSMs are relatively close whenprocessing the fluids of water, Gly nos. 2 and 3 and CMC no. 2;
Figure 7. Normalized shaft power of the teethed in-line high shearmixer as a function of the Reynolds number.
Figure 8. Power number of the teethed in-line high shear mixer as afunction of the Reynolds number.
Figure 9. Comparison between the experimental and predicted powernumbers for the teethed in-line high shear mixer.
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while for Gly no. 1 and CMC no. 1, the teethed HSM drawsmore shaft power than the blade-screen unit under all rotorspeeds and flow rates. The shaft power of the blade-screenHSM shows similar power law relationship with rotor speed,
with indexes of 1.1−1.3 for Gly nos. 1 and 2 and 1.4−1.6 forGly no. 3, water, and CMC nos. 1 and 2. The normalized shaftpower of the blade-screen HSM is also plotted versus theReynolds number in the double logarithmic coordinate, asshown in Figure 11. Similar trends to those for the teethed unitare observed, i.e., the proportionality of P shaft/ ρ N 3 D5 to Re−1.5
for Newtonian fluids and to Repl−1.2 for non-Newtonian CMC
solutions.Power-law fits of the net delivered power to fluid by the
blade-screen HSM versus rotor speed give indexes of 1.1−1.3for Gly nos. 1 and 2 and 1.6−2.0 for Gly no. 3, water, and CMCnos. 1 and 2, similar to those of the teethed unit. Figure 12shows the power curve of the blade-screen HSM. The constantturbulent power number is found to be Poz(t ) = 0.241 under theReynolds number above 1.4 × 105. With the power numberdata at zero water flow rate excluded, k 1 = 8.38 is obtained by fitting the turbulent power data from the working fluid of water
Figure 10. Shaft power of the blade-screen in-line high shear mixer at diff erent rotor speeds.
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(Re = 2.8 × 104−2.0 × 105). Due also to the discontinuity in
the power curve, eq 11 is adopted for correlating the powernumber data at zero flow rate for the three Newtonian fluidsother than water, which yields K P = 624.81, c1= −0.53, and c2=−0.56. With the fi xed values of c1 , c2 , Poz(t ), and k 1 in eq 12 , the
K P values of 39.42 and 54.33 were obtained from regressionsfor the blade-screen HSM when processing CMC nos. 1 and 2,respectively. The “zonal correlation” approach, as previously described for the power prediction of the teethed HSM, is alsoadopted for the estimation of the power consumption of the
blade-screen HSM. As shown in Figure 13 , good agreement isobserved between the measured and predicted power numbers,
with an overall average error of 16.3%.Table 2 lists the values of the turbulent power consumption
model constants for both the teethed and blade-screen HSMs,along with those reported in the literature for comparisonpurpose. The turbulent power number Poz(t ) of 0.147 for theultrafine teethed in-line HSM is very close to 0.145 for theSilverson 150/250 MS in-line mixer fitted with dual finescreens. Whereas the k 1 value of 14.49 is much higher than 8.79for the dual fine Silverson,33 indicating a more significantdependence of the power consumption on the processing flow rate for the ultrafine teethed unit. Under the fully turbulentregime with the same flow number, the ultrafine teethed HSMdraws over 60% higher power than the dual fine Silverson. On
the other hand, for the single-row blade-screen HSM, the Poz(t )
value of 0.241 is equal to that for the Silverson 150/250 MS in-line mixer fitted with dual standard screens; while the k 1 valueof 8.38 is slightly higher than 7.75 for the dual standardSilverson.33 Considering the fact that the flow number is rathersmall in the high Re turbulent regime, the contribution by the“flow term” to the power consumption is small. Therefore, the
blade-screen HSM in this article draws similar power as thatfrom the dual standard Silverson.
4. CONCLUSIONS
The pump capacity and power consumption of the dual rowsultrafine teethed and the single-row blade-screen in-line HSMs
were investigated under the pump-fed mode. Both HSMconfigurations do not pump well at lower rotor speeds of 500−1000 rpm. The heads of both HSMs increase with the rotorspeed. As the flow rate increases, the head of the teethed unitdrops more significantly than that of the blade-screen unit. Thepump capacity of the teethed HSM is rather poor, withmaximum pumping heads of 2.31−2.72 m and a maximumpumping efficiency of 1.5%. At the maximum flow rate of each
fluid, the teethed unit demonstrates negative heads andpumping efficiencies under a broad range of rotor speed. By contrast, the blade-screen HSM presents maximum headsaround 4.33−4.76 m and a maximum pumping efficiency of 7.3%.
The normalized shaft power P shaft/ ρ N 3 D5 of both in-lineHSMs shows the proportionality to Re−1.5 for the Newtonianfluids and to Repl
−1.2 for the non-Newtonian CMC solutions.The power number data of both units with the bearing losssubtracted can be correlated with a Froude number modifiedpower model. The predicted power numbers from the “zonalcorrelation” approach show good agreement with theexperimental data for both in-line HSMs. The power
Figure 11. Normalized shaft power of the blade-screen in-line highshear mixer as a function of the Reynolds number.
Figure 12. Power number of the blade-screen in-line high shear mixer
as a function of the Reynolds number.
Figure 13. Comparison between the experimental and predictedpower numbers for the blade-screen in-line high shear mixer.
Table 2. Turbulent Power Consumption Model Constants
for the Teethed and Blade-Screen In-line High Shear Mixersin-line high shear mixers Poz(t ) k 1
dual ultrafine teethed 0.147 14.49
single row blade-screen 0.241 8.38
dual fine Silverson33 0.145 8.79
dual standard Silverson33 0.241 7.75
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consumption of the dual rows ultrafine teethed HSM showsmore significant dependence on the flow rate than the dual fineSilverson unit of the similar scale. In the high Re turbulentregime with the same flow number, the ultrafine teethed HSMdraws over 60% higher power than the dual rows Silverson withfine screen; while the single-row blade-screen HSM drawssimilar power as that from the dual rows Silverson withstandard screen.
For a successful design and scale-up of the high shearprocess, one should take into consideration both the pumpcapacity and power consumption characteristics of the in-lineHSMs together. For the applications where the materials arerelatively easy to disperse and the throughput is not very large,the blade-screen HSMs with optimized pumping capacity
would be good choice due to their simultaneous pumping anddispersing capability. While for the applications where highenergy inputs are required (e.g., high viscosity, largethroughput, some multiphase systems, etc.), the in-line HSMs
with optimized mixing capability are needed and the pump-fedoperation mode is preferred, whether the teethed or blade-screen configuration is chosen.
The authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
This work is financially supported by NSFC (20836005,21076144) and the Special Funds for Major State BasicResearch Program of China (2012CB720300). The authorsgratefully acknowledge FLUKO Equipment Shanghai Co., Ltd.,for providing the custom-built in-line high shear mixer of FDX
series and off ering technical support. The authors also wish tothank associate professor Lvhong Zhang and Miss Jing Zhangfrom Tianjin University for the kind assistance and usefuldiscussion and colleagues from Chemical Engineering Exper-imental Center (CEEC) of Tianjin University for thedebugging of the data-logging system.
■ NOMENCLATURE
a1−a3 , b1−b3 , c1−c2 , K P , k 1 = constants, − D = outer diameter, md = inner diameter of the inlet or outlet tube, m
g = gravitational acceleration, m/s2
H = head, mh = mounting height, m
K = consistency index, Pa·sn
M = torque, N·m M n = torque measured without the rotor, N·m N = rotational speed, s−1
n = power-law index, − P F = power requirements from the flow of liquid through thegap, W
P fluid = net delivered power to fluid, W P L = power loss, W P shaft = shaft power, W P T = power required to rotate the rotor against the fluidresistance, W
Poz = power number at zero flow rate, −
Poz(l) = laminar power number at zero flow rate, − Poz(t ) = turbulent power number at zero flow rate, − p = pressure, PaQ = volumetric flow rate, (m3/s)T = absolute temperature, K u = mean flow velocity, m/s
ΣH f = head loss by friction and local resistance, m
Subscripts
1 = inlet conditions2 = outlet conditions
Dimensional GroupsFl = Q / ND3 = flow numberFr = N 2 D/ g = Froude number
Po = P fluid/ ρ N 3 D5 = power number
Re = ρ ND2/ μ = Reynolds numberRepl = ρ N 2−n D2/ K = power-law Reynolds number
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