Power consumption and mixing time for newtonian and non-newtonian liquids mixing in a ribbon mixer

The Chemacal Engzneermg

Jaurnal,

52 (1993)

13-17

13

Power consumption and mixing time for newtonian and non-newtonian liquids mixing in a ribbon mixer S. Masmk and H Eqcki Department

of Chemzcal

Engwwerzng,

Technacal

Unzverszty

of Szczeczn,

Al Pzastbw

42, 7X-065 Szczeczn

(Poland..

(Received June 11, 1992)

Abstract The purpose of tlus mvestlgatlon was to select the lowest energy-consummg configuration of a nbbon agtator The cnterion of the selection was nuxmg energy The mteraction between power consumption, nuxmg tune and the geometnc parameters of a non-typxal hehcal nbbon wtator was also mvestlgated

1. Introduction Various types of mixer are used for nuxing of hqmds, but helical ribbon mixers are most appropriate for the homogenization of high viscosity hqmds The high rotational capacity of this type of mixer reduces undesirable variations m composition, temperature or other properties m the bulk of the hquid. The shear stresses generated by a hehcal mixer are generally lower than those which result from other types of agitators and this is particularly important for biotechnologmal processes. The configuration of a ribbon mixer, as exammed m this mvestigation, 1s determmed by the system of outer and inner ribbons, the output quantities are power consumption and murmg time In a mlxmg vessel the power consumption for lammar flow 1s given by PoRe = C1

(I)

The dependence of the muung tune on other quantities may be expressed m a similar way by mtroducmg the dimensionless group nt [ 1, 21 nt =C,Re-’

5

(2)

An agitator which has low power consumption and a long mlxmg tune is usually as undesirable as an agitator which requires a short nuxmg tune but very high power consumption. For assessmg the capability of a given mixer to homogenize hquid it is not suflicrent to take mto consideration these quantities separately; better selection results are obtamed by considenng the mixmg energy values Knowledge of this energy value 1s also very useful dunng the design of nbbon

0923-0467/93/$6

00

mixers. The relationship of the mlxmg energy, as a product of, the power consumption and mixmg tune Pt may be written m the form [l] Pt = C,Re*

(3)

2. Experimental

details

The mlxmg equipment used m this mvestlgation consisted of a 1 1 kW d.c. electric motor with a variable-speed dnve and electrical and thermal mstrumentation to measure power mput to the liquid and nuxmg tune (Fig. 1). The vertical cylmdncal vessel, with a liquid height to tank diameter ratio equal to 0.97, had a 0 345 m diameter with a shghtly dished bottom. The vessel was cooled by water on its cylmdncal surface Mlxmg was carried out with a non-typical helical mixer. The different configurations of this type of mixer are given in Fig 2 and the dimensions are summarized m Table 1 Glycerol and a freshly prepared aqueous solution of the commercial product of CMC were used as the newtoman and non-newtoman liquids, respectively. In the experiments, in all cases the nuxer rotated m a clockwise direction so that the mner nbbon pumped m one direction (downwards) and the outer ribbon pumped m the reverse du-ection (upwards) The electrical isothermal method was used for measurmg the torque produced by the rotating agitator. Equations for calculation of the power consumption are given m ref 3. To determine the mixmg tune, the thermal-response technique was used [ 1, 41 Detailed descnptions of the procedures

0 1993 - Elsemer Sequoia All r&s

reserved

S Maszuk, H Eqckz / Power consumptwn

Fkg 1 Expenmental set-up (1) d c electnc motor, (2) batch meter, (3) IN(er, (4) a@tator, (5) recorder, (6) measunng system, T,T,, thermocouples

for measurmg power consumption and mlxmg tune appear m refs. 1 and 3. The bulk liquid temperature, mltlally about 20 “C, rose to about 21 “C after the addltlon of the heated sample and complete nuxmg Durmg the power measurements the temperature m the bulk of nuxed liquid was stabilized usmg a contmuous flow of water through the coolmg Jacket of the nuxer The vlscoslty of the hqulds was evaluated at the mean hquld temperature

3. Results

and discussion

The effects on power consumption, nuxmg tnne and, therefore, mlxmg energy of the geometrical shape of the ribbons and the mdth of outer and mner ribbons were mvestlgated m a total of 290 runs carned out m the lammar region The effect of nbbon shape on power consumption and mlxmg tune was mvestlgated wth five nuxers (Fig 2) using glycerol as a nuxmg hquld The mfluence of the dunenslonless moduh w/d and w’ld (representmg the geometric parameters of mixer III) on these quantltles was mvestlgated usmg CMC-water so-

l3g

2

TABLE

and mzmng

tame

Schematic view of the nbbon ag&ators 1 Geometrical

vanables

of the nbbon agtators

Aatator

nb

n;,

Dfd

Did’

hld

I II III N V

2 2 2 2 2

2 2 2

103 103 103 1 03 103

2 06 2 06 2 06

0871 0871 087 0 87 0 87

sid

s’ld

wld

w’id

1 1 1

2 2 2

009 009 009 0 09 0 09

0 09 0 09 0 09

lutlons The flow properties K and m were measured at 20 5 “C with a “Rheotest 2” vlscometer. AU experunental data for power consumption and murmg tune were correlated by usmg eqns (1) and (2) descnbmg power and nuxmg tune charactenstlcs respectively From the power consumption and mlxmg tune measurements the mlxmg energy was calculated and the value of Pt was plotted on a log-log graph agamst Reynolds number (Fig 3) In Elg 3 the calculated pomts approach straght lmes urlth a slope 0 5 glvmg the exponent Avalue of the Reynolds number m eqn (3) This type of correlation for sectioned helical nbbon mxers was proposed by the authors of ref 1 The values of the constants

15

S Maszuk, H Eqckz / Power cansumptaon and mzxzng tzme

obtamed from the mrxer usmg ditferent moduli wl d and w’ld values are shown m Pigs. 4 and 5. Each set of crosses m Fig. 4 lies on a straight lme m a system of co-ordmates PO VS. Re, w/d =constant (not presented m this report). Figure 4 also compares the results of our mvestigations with studies reported m refs 5-7 the conclusions of which are discussed m detarl m ref. 8. Prom Fig. 4 it can be seen that values of PoRe obtamed m this work are higher than those reported m refs 5-7. These differences could be explamed by the different desrgn of the helical mixer and the fact that the mixer had an mner ribbon system mstalled between the shaft and outer ribbons

1

The work 700 200 Fig

Glu

1030

600

f+

t

3 Influence of nbbon shape on the nuxmg energy

TABLE 2 Values of the constant C1, C, and C, Agitator

C,

c2

G

I II III IV V

620 460 528 570 720

400 375 305 420 450

3 2 45 22 3 65 6 95

C1, C, and C, (eqns. (l)-(3)) are established from the expenmental data. Table 2 illustrates the drfferent values of these constants for five ribbon mixers with different outer ribbon shapes. The optunal shape for the nbbons can be deduced by comparmg the values of the constant C, (i = 1, 2, 3) Table 2 shows that m the lammar region configuration III is the most advantageous; rt exhibits the lowest mixing time value, but somewhat greater value of power consumption 1s given for this configuration However, this shape of mixer has advantages for homogemzation because it exhibits the lowest mrxmg energy value (see Pig. 3 inset) These results suggest that mixer III should be used for the expenmental mvestigation of the miluence of some other geometrical parameters on power consumption and nuxmg time. In the first stage of the mvestigations the mfluence of ribbon width on power consumption was mvestigated usmg a CMC-water solution (K= 1 82 and m=0.769). The results of power measurements

1

1

I

I

004

006

012

I

I

016

Wb

of our results of power consumption measurements vvlth those of other authors fig

4 Companson

4 30

20

10 8

I 4

6

4

20

fig

5

nbbons

LO

Power charactenstx

60

80

100

140

Re,

for various urldth of the mner

S Maszuk, H tqcka / Power consumptum

16

The data from our mvestigations (collected 111 E’lgs 4 and 5) mdlcate the effect of both dunensionless moduh, w/d and w’ld, on power consumption. After some trial and error, a prediction equation was found which fits the data with an average deviation of about it 10%. PoRe,-1464($)nllX(

I+

5)

Equation (4) 1s valid for the followmg geometrical parameters w/d w’ld

0.045-0.179 o-o 179

Re,

16-160

g -05X

80 -

o-Nag& et ai [ 9 1 A -Hagendorn and Hartq

ranges of

x-Ffleger

a04

Re,

008

012

et a

T---T---

O2

---

14

I

I II I

0.16

Fig 6 Comparison of our results of nuxmg tie wth those of other authors

! i

w/d

measurements

i

(5) 3t

Equation (5) LS vahd for wld

tzme

(4)

In the second stage of the investigation, the mfluence of the dimensionless modulus w/d on the power consumption and mixing tune was mvestigated usmg a CMC-water solution (K= 1 26 and m= 0 689) The relationship between the dunensionless groups ti and ReB, and dimensionless modulus w/d may be generalized by eqn. (1) written m the form -05

nt=68XRe

and rnwaw

i

/

i

0.045-O 179 90-420

wnh an average deviation of about f6% A comparison of murmg tune data from this work with that of other researchers [4, 9-l 1 ] 1s shown m lQg 6 for Re= 100 Early papers referring to murmg tune studies have been reviewed m detail m refs 2 and 4 The different results may be explamed by the use of another type of helical nuxer and by the different nuxmg time measurements used After analyzmg Fig. 6 we conclude that the nuxmg time value was smaller by a factor of approximately two than that of a typical helical ribbon mixer After analyzmg other results obtamed for mixer III usmg a different width of mner ribbon (not given m this report) we conclude that the measured nuxmg tune was almost mdependent of the parameter w’l d Hence, the parameter w’ was not mcluded m eqn (5) The power characteristic is suitable for design purposes, but it gives no mdicatron of the optnnum width of the outer ribbon required to achieve nuxmg with the smallest energy expenditure The nuxmg energy value should be adopted as the optimization criterion to represent the relationship between power

201

/ % I 80 MO

/ 200

I 300

,

I Reg

Elg 7 Influence of nbbon width on the nuxmg energy

input and nuxmg time. The effect of the width of the outer ribbon on the product F’t is shown m E’lg 7. By fittmg straight lmes to the results this alternative correlation may be expressed m the form of eqn (3) The equation for calculation of the energy may be written m the following form -1

Pt = Rego 6 22;

01

+0 125 ;

(6)

The generahzed eqn (6) is valid for the range of the parameters given for the eqn. (5), with an average deviation of about + 9% It follows from eqn (6) and the inset to I+g 7 that the lowest murmg energy to achieve a suitable

S Masauk, H Eqcka / Power consumptwn and mzxwg tame

degree of homogemzation requires the use of the mixer with a modulus w/d value equal to 0.09.

4. Conclusions Several sign&ant conclusions may be drawn from the material presented m this report. (1) It has been shown that the shape of the ribbon agitator has a sigmilcant mfluence on the mixing energy required for nuxmg the liquid. Agitator III 1s the most satisfactory type of non-typical hehcal ribbon agitator. (2) From the results presented here it follows that the best mixmg efficiency is obtamed with agitator III and an outer ribbon width of w = 0 09d. This geometry exhibits a lower mixmg energy than ag&ators which have a modulus w/d ZO.09 The above result was found in the nuxmg of non-newtoman hquids. (3) For practical purposes the general design correlations shown m eqns. (4)-(6) have been proposed for the calculation of power consumption, nuxmg tune, and nnxmg energy when nuxmg viscous hqmds.

8 P A Shamloy and M F Edwards, Chem Eng Scz, 40 (1985) 1773 9 S Nagata, T Yokogama and M Yaragunoto, J Chem. Eng Jpn, 21 (1957) 278 10 B Gray, C?sxsn. Eng Progr, 5 (1963) 55 11 F Beger, V Novak and D Havelkova, Chem. Eng J, 33 (1986) 143 12 K Takahash, T Yokota and H Konno, J Chem Eng Jpn , 17 (1984) 657

Appendix A: Nomenclature

W’

clearance between the agitator and the wall of the vessel (m) diameter of agitator (m) diameter of mner ribbons (m) mside diameter of the vessel (m) height of agitator (m) height of liquid level in the vessel (m) agitator shear rate constant [ 12 ] k, = 11.4(c/d)-’ 411x (s/d)-’ 361x (w/d-)’ 164 consistency (Pa s”> power law exponent speed of agitator (s-l) number of outer ribbons number of mner ribbons power consumption (W) power number; PO = P/pn3d 6 Reynolds number; Re = nd”p/q generahzed Reynolds number [ 51; Re, = d2n2-“h?‘lK pitch of outer ribbons (m) pitch of inner ribbons (m) tune of homogenization (mixing tune) (s) width of outer ribbons (m) vvldth of inner nbbons (m)

Greek

letters

17

viscosity (N s mV2) density (kg m- 3,

c

d d' D h

H

k, K m

n nb , ?

References 1 S Masnxk, H Lqclo and F Strgk, Chem Eng , J ,48 (1992) 135 2 V Novak and F fieger, Z%wzs Inst Chmrz Eng ,47(1969) 335 3 S Masluk, Powder TechmL, 51 (1987) 217 4 C J Hagendoom and A P den Hartog, Chem. Eng Sa , 22 (1967) 1689 5 K R Hall and J Godfrey, Trans Inst Chem. Eng, 48 (1970) 201 6 H Brauer and H Snndt-Traub, Chxsn. 1~ Techa., 44 (1972) 1237 7 H Biastiln and E Rzyslo, Chem. Eng J, 19 (1980) 157

17

PO Re Re&! S S’ t W

P