Heat transfer in jacketed agitated vessels equipped with non-standard baffles

THE CHEMICAL ENGINEERING JOURNAL The Chemical

Heat transfer

Engineering

Journal

58 (1995) 135-143

in jacketed agitated vessels equipped standard baffles Joanna Technical

Karcz, Fryderyk

with non-

Strgk

University of Szczecin, Al. Piastdw 42, 71-065 Szczecin, Poland

Abstract The effects of the geometrical parameters of non-standard baffles on heat transfer coefficient were experimentally studied for agitated vessels equipped with a Rushton disc turbine, pitched-blade turbine and propeller. The following geometrical parameters of the baffles were tested: number J, width B, length L and distance p between the lower edge of the baffle and the bottom of the vessel. Measurements were carried out in accordance with a second-order rotatable experimental design. The results of the investigations have been approximated analytically.. Keywords:

Agitation;

Heat

transfer;

Liquid

mixing;

Newtonian

fluid; Stirred-tank

1. Introduction Mixing has found wide application in chemical and biochemical processing. Many agitated chemical reactors and bioreactors require precise control of both mixing and heat transfer [1,2]. Heat transfer in agitated vessels is important because fluid temperature in the reactor is one of the most significant factors for controlling the outcome of chemical and biochemical processes. Usually, agitated vessels have a heat transfer surface, in the form of a jacket or internal coils, for addition or removal of the heat. The intensity of heat transfer during mixing of fluids depends on the type of the agitator, the design of the vessel and conditions of the process. The transfer of heat from the fluid to the heat transfer area at the vessel wall (jacket or coil) can be characterized by a film heat transfer coefficient (Y.Because heat transfer in agitated vessels is complex, an empirical approach based on dimensionless analysis has been used to predict the average heat transfer coefficients at the jacketed wall or at the helical coil surface. Hence, the results of many heat transfer studies are frequently correlated using a dimensionless equation

Nu= $

=C ReA PrB ViE

(1)

where C = C, PI(&). . . ?I$(&) 0923~0467/95/$09.50 0 1995 Elsevier SSDI 0923-0467(94)02945-S

(2) Science

S.A. All rights

reserved

reactor

The functions qj describe the effect of the geometrical parameters of the agitated vessel on the heat transfer coefficient. Reviews of such correlations for various geometries of the agitated vessels have been presented in monographs [3-51 and papers [6,7]. In the 1990s experimental studies of heat transfer in agitated vessels have been continued. The results of the investigations concerned non-newtonian fluids [8] and multiphase systems, such as gas-liquid [g-15] and solids suspensions [16]. Various types of multiple agitators [17,18] and constructions of coils, i.e. helical [19] or vertical tubular baffles [18,20,21], have been also tested. Distributions of the heat transfer coefficient at the vessel wall have been measured using thermal [14,22,23] or electrochemical [9,10,24] methods. The influence of different geometrical parameters of the agitated vessel on the heat transfer coefficient can be determined using a modern experimental method in which the measurements are mathematically planned, for example, in the form of the rotatable design of second order. The results of such experiment are approximated as a quadratic polynomial i--k

i-k

C=zy==bo+ Xbb,x,+ Cb&+ i-l

i=l

i, ‘-k

k

i.j-l.i+j

b,jx,xi

(3)

where C is a constant, xi are independent variables in code, and bo, bi, bii, bij are numerous coefficients. The rotatable design was applied in the studies of the effect of the geometrical parameters on the coefficient a for jacketed, baffled agitated vessels equipped with disc turbine [25,26], pitched blade turbine [27,28]

136

J. ffircz, F. Strqk f 7he Chemical Engineeting Journal 58 (1995) 135-143

and conical turbine [29,30]. The results given by Eq. (3) were compared with the conventional function (2). Studies of heat transfer in the agitated vessel can be carried out more easily in small equipment, but then the problem of scale-up occurs. Experimental results [31], obtained for jacketed, baffled agitated vessels of inner diameters D=O.15 m, 0.45 m and 0.9 m, equipped with a Rushton disc turbine, propeller and turbine, are presented in Fig. 1. As the experimental data in Fig. 1 show, the effect of the vessel diameter D on the heat transfer coefficient has no importance in the range studied. Baffled agitated vessels are usually equipped with four baffles of width B = O.lD and length L =H (Fig. 2). In the literature [3,4], such dimensions of the baffles correspond to the geometry of the so-called “standard baffles”. Therefore, shorter baffles (L O) from the bottom of the agitated vessel (Fig. 2) can be determined as “nonstandard” baffles. Experimental studies have shown that

= d’

2.8

a’ .!z

2.6

2.2 4.0 Fig. 1. The dependence

&.L

4.2

4.6

lg Re Nu/Pr033Vi”-‘4=f(Re) for agitated vessels

of various inner diameters

D (311: curve I, standard disc turbine; curve 2, standard turbine (/3=90”); curve 3, standard propeller.

n J=4

the use of shorter than “standard” baffles in the agitated vessel can be advantageous for the production of the suspension [32] and the heat transfer process [33]. However, difficulties in design calculations of the heat transfer for agitated vessels equipped with short baffles result from the lack of relevant correlations.

2. Experimental

The purpose of the investigation was to determine experimentally the influence of geometrical parameters of the non-standard baffles on the heat transfer coefficient (Yfor jacketed, agitated vessels equipped with different types of high speed agitators. The following geometrical parameters of the baffles were taken into account as variables: number J, width B, length L and distance p between the lower edge of the baffle and the bottom of the vessel (Fig. 2). The measurements were carried out in an agitated vessel of inner diameter D = 0.45 m and liquid height H=D, equipped with a single agitator: disc turbine of diameter d = 0.330 or d = 0.5D (radial flow), pitched-blade turbine (mixed flow) or propeller (axial flow). In all the experiments, the propeller and pitched-blade turbine worked in an upward pumping mode. The detailed geometrical parameters of the agitators used in the investigation (Fig. 3) are given in Table 1. A rotatable design [34,35] represented by a quadratic function was used in the investigations, in which the relevant parameters were selected as follows: number k of variables, 4; number IZ,,of measurements at the centre point of the plan, 7; characteristic distance a = 2; total number N of experiments, 31. The experiments performed in the factor design correspond to combinations of variables at levels + 1 and - 1, at the centre point of zero level (i.e. (0, 0, 0, 0)) and, at the characteristic distance a, the combinations (i-u, 0, 0, 0), . . *> (0, 0, 0, +a). The matrix of the rotatable design is shown in Table 2. The investigated geometrical parameters of the baffles were varied within the following ranges: 2~5~10;

0.067
0
j

Fig. 2. Geometrical parameters of the baffles for the agitated vessel.

details

O.l
wherep+L
Values of the geometrical parameters attributed to each level of the rotatable design are shown in Table 3. The measurements were carried out in the turbulent flow regime of a newtonian liquid, mixed in the agitated vessel (Re E ( 104; 6 x 104)). The physical properties of the machine oil used as the liquid phase, i.e. density and viscosity, have been described by the equations p = 881.66 - 0.62t,

for t (“C) E (50; 100)

1. Karcz, F. Stqk

I The Chemical

Engineering Journal 58 (1995) 135-143

137

0C Y

Fig. 3. Types Table 1 Geometrical

of agitators

parameters

used

in the study:

(a) propeller;

(b) pitched-blade

turbine;

of the agitators

Agitator

dlD

ald

bld

Z

1 2 3 4

Propeller Disc turbine Disc turbine Pitched-blade turbine

0.33 0.33 0.5 0.5

0.25 0.25

0.2 0.2 0.13

3 6 10 8

Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

=_r

(c) disc turbine.

Number

Table 2 Matrix for rotatable

d

design

of second

XI -1 +1 -1 -1 +1 +1 -1 +1 -1 +1 -1 -1 +1 -1 +1 +1

x2 -1 -1 -1 +1 +1 -1 +1 +1 -1 -1 +1 -1 +1 +1 -1 +1

B 0

hlD

S/d 1

45

0.33 0.33 0.5 0.33

order *3 -1 +1 +1 -1 -1 -1 +1 +1 -1 -1 -1 +1 +1 +1 +1 -1

x4 -1 -1 +1 +1 -1 +1 -1 +1 +1 -1 -1 -1 -1 +1 +1 +1

~=(6.1~10-~t-0.239)-‘x10-~, for t (“C) E (75; 100) The measurements were repeated five times at different Re numbers for each baffle geometry at a given plan point. The heat transfer coefficients determined under steady state conditions [36] were measured in the

Number 17 18 19 20 21 22 23 24 25 26 21 28 29 30 31

Xl -2 +2 0 0 0 0 0 0 0 0 0 0 0 0 0

X2

x4

x3 0 0

-2 +2 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 -2 +2 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 -2 i-2 0 0 0 0 0 0 0

experimental set-up sketched in Fig. 4. The agitated vessel (1) was equipped with a jacket (2), baffles (3) an agitator (4) and a flat non-heated bottom. The vertical wall of the vessel of thickness 5 mm was made of copper. The agitator (4) was driven, via belt transmission (6) by an electric motor (5) coupled with a control unit (10). The revolution frequency of the agitators was measured by means of an electronic impulse counter (13),

138

J. K&z,

F. Stqk

/ The Chemical

Table 3 Values in code and real values of variables Level of variable

-2 -1 0 +1 +2

Engineering Journal 58 (1995) 135-143

3. Results and discussion

Variables X1 J

X2 B (ml

X3 L (m)

P (m)

2 4 6 8 10

0.030 0.045 0.060 0.075 0.090

0.045 0.114 0.184 0.253 0.323

0 0.064 0.128 0.191 0.255

X,

Fig. 4. Experimental set-up: 1, agitated vessel; 2, jacket; 3, baffle; 4, agitator; 5, electric motor; 6, belt transmission; 7, circulating pump; 8, intermediate vessel; 9, liquid cooler; 10, control unit; 11, reed relay; 12, magnet; 13, electronic counter; 14, rotameter; 15, condenser pot; 16, thermocouple; 17, point recorder; 18, thermostat; 19, manometer.

The influence of the distance f between the wall of the vessel and the baffle was evaluated in the preliminary series of the experiments (0
C 0.7

0.6

0.5

with reed relays (11) as sensors being placed above the magnet (12). The liquid was recirculated in the system via an overflow of the agitated vessel (1) the intermediate vessel (8), liquid cooler (9), circulating pump (7), a rotameter (14) and a pipe in the bottom of the agitated vessel. The heating jacket (2) was filled with steam and the condensate was collected in the condenser pots (15). All temperatures were measured with thermo-. couples (16) and mercury thermometers.

OX

0:.-

ox

0.8

1.2

)(_

Z(B+f) D-d

Fig. 5. The dependence of coefficient C on the distancef vessel equipped with disc turbine.

for agitated

J. tircz,

F. Strgk I The Chemical

Engineering Joumal 58 (1995) 135-143

139

Table 4 Results of factor analysis for coefficient C Number

Pitched blade turbine, d/D = 0.5

Propeller, d/D = 0.33

2

/ JBP

J

XI

Statistically

3

JB

P

X4

significant

4

LP B

JP B

x1-G

effects

5 6

JLP

EL

7

JPP L \

JL

1

8 9

L

b

10 --------11

BP JBL L ---------JL

12

BLp EL

14

JBLp

1.5

P

I _I

\ L.

C decreases with increasing value of a given variable. The effects of the statistically significant factors are also shown in Table 4. The results indicate that linear effects of the variables x3, x, and X, are the greatest for agitated vessels equipped with a propeller (dl D= 0.33) and the variable x1 exerts the strongest influence on the heat transfer coefficient for agitated

x3

h

X2 L

x2x3

Aa

XIX3

x1x3& JLP___-__--_---__--_--------

_-___ l

I

13

I

Remarks

BP

x2x4

BLP

*2x3%

JBP JB \

x1-Q.Q

JBL

Xl.w3

LP JBLp

X3%

vessels

XIX2

\

Statistically insignificant

\1

Xl%?w2

equipped

--

effects b

with a pitched-blade

D=OS). The results obtained

on the basis design were expressed as a quadratic (3)). The following equations describe geometries of the agitated vessels: for d/D = 0.5,

turbine

(dl

of the rotatable polynomial (Eq. the investigated the disc turbine,

C= 0.7692 + 3.2541 x lo-‘x, -t 1.9791 x 10-*x, + 1.3875 x lo- ‘x3 + 1.1875 x lo-“x, + 7.7536 x 1O-3x,2 +1.3753x1O-~,2-9.4963x1O-3x32-l.3246x1O-2x~2+1.1938x1O-2x~x~+1.O313x1O-2x~x3 +9.8131x 10-3x,xz,+8.4380x

10-3xx,~,-2.1188x

(4)

1O-2x3x,

for the disc turbine, dlD=O.33, C=O.7167+3.875

x lO-3x, +6.125x lo-‘x2 -6.7083x

10-3x3- 1.4541 x 1O-2x,- 1.1376~ lo-‘x,*

-8.1266x1O-3x22+1.2126x1O-2x32-l.2251x1O-2x~2-4.O627x1O-3x~x~-5.9378x1O-3x~x3 -3.8127x

(5)

1O-3x,x,

for the pitched blade turbine, d/D=0.5, C=O.5817+ 1.3958x lo-‘x, +7.7917x 1O-3~,+3.5416x -1.2212x - 5.8128

1O-3x3- 1.2712x 1O-2~,2-7.O879x

~O-?X,~- 1.2587x 1O-2x,2+8.O63Ox 10-3x,x,+4.8128x x

10-3q2

1O-3xx,x,+2.9376x 1O-3x,x,

(6)

lO-3x,x,

for the propeller, d/D =0.33, C=O.3119+3.3333~

1O-3x, + 1.75x 1O-3x,-6.8333x

1O-3x3+2.3333

x

lo-‘x,

-2.2223 x lO-3x32- 3.0973 x 1O-3x,2+ 1.6251 x 1O-3x,x3 + 2.5001 x 1O-3x,x, - 1.8751 X 10-3xzx3

(7)

Here Nu

c= and x,=

J-6 - 2

B - 0.06 x2= 0.015

x3

= L-O.184 0.0694

x = p-O.128 4 0.0638

-2
+2

i= 1, 2, 3 or 4

(8)

140

J. Karcz, F. Strgk f YI7zeChemical

The variables B, L andp in Eq. (8) should be substituted in metres. Eqs. (4)-(7) approximate results of the measurements with mean relative error f4%, l&3%, + 5% and + 3% respectively. Values of the coefficient C calculated from Eqs. (4)-(7) are compared with that from experiments in Figs. 6-9. The effects of the geometrical parameters of the nonstandard baffles on the heat transfer coefficient are presented graphically in Figs. 10-13. The functions C=&) are drawn for constant values of the other independent variables corresponding to the centre point level of the experiment design. In general, the heat transfer process in the agitated vessels equipped with non-standard baffles is more intensive when radial flow agitators are used instead of axial flow agitators. The pitched blade turbine is clearly a mixed-flow impeller; probably because of this fact its results fall between

Engineering Journal 58 (1995) 135-143

C talc 0.6

0.5

0x5

+ 0x5

0.5

0.55

0.6

c

exP

Fig. 8. Comparison of the experimental values of coefficient those calculated from Eq. (6) (pitched-blade turbine).

C and

C catc 0.9

C talc 0.325

0.8 0.3

0.7

0.6 /

5

0.7

08

1

0.275

OQ c -P

Fig. 6. Comparison of the experimental values of coefficient those calculated from Eq. (4) (disc turbine, d = OSD).

C and

7

C catc

0.25

I

3

0.325

p

Lexp

Fig. 9. Comparison of the experimental values of coefficient those calculated from Eq. (7) (propeller).

C and

0.75

0.7

0.65

0.6

0.6

0.65

0.7

o.75

Cexp

Fig. 7. Comparison of the experimental values of coefficient those calculated from Eq. (5) (disc turbine, d=0.330).

C and

the two extreme cases of axial and radial flow impellers. Moreover, the agitators of diameter d = OSD and blade number Z> 6 are more. advantageous than those with d=0.330 and ZG 6. The strongest effects of the geometrical parameters of non-standard baffles on the heat transfer coefficient characterize the agitated vessel equipped with the disc turbine of diameter d =0.5D, whereas the least effects correspond to the agitated vessel equipped with the propeller of diameterd = 0.330. It results from the diagrams in Figs. 12 and 13 that the values of the length L of baffle and distance p, the best from the point of view of the heat transfer process, can be found for all the investigated geometries of the agitated vessels.

J. Karcz, F. Strck I The Chemical

Engineeting Journal 58 (1995) 135-143

0.6

Fig. IO. The plots C=f(.rr) for agitated vessels equipped with nonstandard baffles: curve 1, disc turbine (d = 0.5D); curve 2, disc turbine (d= 0.330); curve 3, pitched blade turbine (d=0.5D); curve 4, propeller (d = 0.330).

0.6

Fig. 12. The plots C=f(x,) for agitated vessels equipped with nonstandard baffles (symbols as in Fig. 10).

0.6 0.6

0.4 0.4

0.2 0.2 Fig. 11. The plots C=f(x2) for agitated vessels equipped with nonstandard baffles (symbols as in Fig. 10).

The values of the coefficients C for certain geometries of the non-standard baffles are comparable with the experimentally obtained values C for standard baffles presented in Table 5. However, power numbers for agitated vessels with the non-standard baffles are less than those with the standard baffles [38], and therefore the efficiency of the heat transfer process is greater in agitated vessels equipped with the short baffles. For example, if the agitated vessels equipped with the disc turbine of diameter d =OSD is analysed then the geometry of the baffles defined by J=8, BID =0.17, L,/ H=0.25 and plH= 0.37 is better than that with J= 4,

Fig. 13. The plots C=f(Q for agitated vessels equipped with nonstandard baffles (symbols as in Fig. 10).

Table 5 Values of coefficient C for agitated vessel equipped with standard baffles and different types of agitators (D=O.45 m) Number

Agitator

C

1 2 3 4

Disc turbine, d = 0.5D Pitched-blade turbine, d = 0.5D Disc turbine, d = 0.330 Propeller, d = 0.330

0.88 0.55 0.73 0.30

BID =0.17, LIH= 1 and plH = 0 from the point of view

of the efficiency of the heat transfer

[33].

142

J. Knrcz, F.

I The

4. Conclusions

Engineering Journal

agitator speed (s-l) number of measurements at the centre point of the plan distance from bottom of vessel to lower edge of baffle (m) ml tan& agitator pitch (m) temperature (“C) independent variable in code number of blades

n no

The results of the investigations, including 620 experimental data obtained in the planned experiments, can be summarized as follows. (1) Geometrical parameters of the non-standard baffles ,exert a significant effect on the heat transfer coefficient in jacketed agitated vessels equipped with the high speed agitators. (2) Advantageous conditions for the heat transfer were found for the agitated vessel equipped with the disc turbine and non-standard baffles with the following system geometrical parameters:

P s t x Z

Greek symbols

heat transfer coefficient (W m-* K-l) angle of blade pitch to horizontal (deg) dynamic viscosity of liquid (kg m-’ s-l) thermal conductivity (W m-l K-l) density of liquid (kg rnv3) function in Eq. (2)

HID = 1; d/D = 0.5; ald = 0.25; bld = 0.2; Z = IO; h/D = 0.5; J= 8; BID = 0.17; L/H= 0.25; p/H = 0.37

For such a geometry, the coefficient C=O.90 in Eq. (4) is approximately 20% greater than that for standard geometry of the agitated vessel with a Rushton disc turbine. (3) Non-standard, short baffles may be preferable for bioreactors considering their low energy requirement obtained without compromising the heat transfer parameters. These improvements could be coupled with the case of production of solid suspension reported in the literature for such systems [32]; however, the real benefits should also be assessed in real fermentation broths of different rheologies.

Dimensionless

A, B, E a B b

c C0 2 f” H h

fr k L

I N

A: Nomenclature

Pr Re Vi

References

f21 [31

exponents in Eq. (1) characteristic distance in the experiment design; length of agitator blade (m) baffle width (m) width of agitator blade (m) constant in Eq. (1) constant in Eq. (2) specific heat (J kg-l K-l) inner diameter of the agitated vessel (m) diameter of the agitator (m) distance between the wall of the vessel and the baffle (m) liquid height in the vessel (m) distance from bottom of the vessel to the agitator (m) invariant of geometric similarity number of baffles number of variables baffle length (m) linear dimension number of experiments

numbers

cQIA, Nusselt number cp q/A, Prandtl number nd*plq, Reynolds number q/r],, viscosity simplex

Nu

111 J.Y. Appendix

(1995) 135-143

[41 [51 161

[71

PI

[91

WI

illI

Oldshue, Fluid Miring Technology McGraw-Hill, New York, 1983. N. Harnby, M.F. Edwards and A.W. Nienow, Mixing in the Process Industries, Buttenvorths, London, 1985. S. Nagata, Miring, Principles and Applications, Halsted, New York, 1975. F. Strgk, Miring and Agitated VesseLs, WNT, Warsaw, 2nd edn., 1981 (in Polish). P. Kurpiers, Waermeuebergang in Ein- und Mehrphasenreaktoren, VCH, Weinheim, 1985. R. Poggeman, A. Steiff and P.M. Weinspach, Waermeuebergang in Ruehrkesseln mit einphasigen Fluessigkeiten, Chem. Ing. Tech., 51 (10) (1979) 948959. A. Steiff, R. Poggeman and P.M. Weinspach, Waermeuebergang in Ruehrkesseln mit mehrphasigen Systemen, Chem. Zng. Tech., 52 (6) (1980) 492-503. K. Wang and S. Yu, Heat transfer and power consumption of non-newtonian fluids in agitated vessels, Chem. Eng. Sci., 44 (1) (1989) 33-40. J.R. Boume, 0. Dossenbach and T. Post, Local and average mass and heat transfer due to turbine impellers, 5th Eur. Co@ on Mixing, Wuenburg, 1985, BHRA Fluid Engineering, Cranfield, Paper 21. K.L. Man, A study of local heat transfer coefficients in mechanically agitated gas-liquid vessels, 5th Eur. Conj on Miring, Wuerzburg, 1985, BHRA Fluid Engineering, Cranfield, Paper 23. J. Karcz, J. Vlcek, V. Machon and F. Stqk, Mass and heat transfer in gas-liquid system for stirred tank equipped with two stirrers, Technol. Today, 3 (1990) 176182.

J. Karcz, F. Strck / The Chemical

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[I71

PI

WI WI

(1987) 61-64. G. Havas, A. Deak and J. Savinsky, Heat transfer coefficients in an agitated vessel using vertical tube baffles, Chem. Eng. J., 23

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