iffichanically agitated gas-liquid contactors by a …

EFFECT OF HORIZONTAL BAFFLES ON THE PERFORIIANCE OF

IffiCHANICALLY AGITATED GAS-LIQUID CONTACTORS

by

HIMANSHU ZINZUWADIA, B. of Ch.E.

A THESIS

IN

CHEMICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

CHEMICAL ENGINEERING

Approved

Accepted

May, 1987

%06

' ' ' ACKNOWLEDGEMENTS

The author wishes to express his deep appreciation to Dr. Uzi

Mann for his support and encouragement during the course of this

work and his assistance in writing this thesis.

The author would like to thank Dr. P.E. Fischer and Dr. R.R.

Rhinehart for serving on the thesis committee and for giving

valuable suggestions.

Special thanks are due to Mr. R.M. Spruill for his help and

suggestions in constructing the experimental system. The author

sincerely appreciates the constant support and help of fellow

students Mr. Vijay Shirsat and Mr. Rajiv Doshi.

Financial support from the National Science Foundation and a

donation of some equipment by Mixing Equipment Company is

gratefully acknowledged.

11

TABLE OF C0NTENT5

ACKNOWLEDGEMENTS

ABSTRACT

LISTOF FIGURES

LIST OF SYMBOLS vi

LISTOFTABLES

CHAPTER

1. INTRODUCTION

1.1 Background

1.2 Literature Review

2. THEORETICAL CONSIDERATIONS :

2.1 Determination of Volumetric Mass-Transfer Coefficient and Interfacial Area :

2.2 Measurement of Power Requirement

3. EQUIPMENT AND PROCEDURE

3.1 Descríption of the Equipment

3.2 Operating Procedure

3.3 Analytical Procedure

4. RESULTS ANDDISCUSSION

4.1 Presentation of Data

4.2 Normalîzation of Data

4.3 Validity of the Model and the Accuracv of Experimental Data

iii

4.4 Comparison of Results for Horízontal and Vertical Baf f les 60

4.5 Analysis of Results 77

5. CONCLUSIONS AND RECOMMENDATIONS 87

5.1 Conclusions 87

5.2 Recommendations 88

LITERATURECITED 93

APPENDICES

A. A SAMPLE CALCULATION OF

MASS-TRANSFER COEFFICIENT 93 B. EXPERIMENTAL DATA 100 C. STRAIN MEASUREMENT WITH

A RESISTANCE STRAIN GAUGE 1 1 0

IV

ABSTRACT

The objective of this investigation was to study the effect of

horizontal baffles on the performance of a mechanically agitated

gas-liquid contactor in comparison to its performance with vertical

baff les. The performance cr i ter ia were: the overall average

volumetric mass-transfer coefficient, k^a, and the agitation power.

The investigation was conducted on a lab-scale tank 1 f t . in

diameter and 2 f t . height agitated with a 3" Rushton Turbine. Air

was injected into a 0.25M Sodium Sulfite solution, and the oxygen

consumption rate was determined. The primary independent

variables were the impeller speed (changed from 500 to 1450 rpm.)

and the rate of air injection (changed from zero to 0.67 l./sec).

The horizontal baffles improved the contactor performance

over that when vertical baffles were used. The values of kjâ were

80% tol30% higher, while the agitation power required was as much

as 33% lower at certain operating conditions. The improvement was

more pronounced at impeller speeds of 800-1450 rpm.

The experimental data indicated that the improvement in kjâ

was identical to the increase of the gas holdup in the liquid. It was

seen that the horizontal baffles induce entrainment from the upper

surface of the liquid (surface aeration) and the increase of k a is

due to a higher entrainment of gas in the liquid and not due to

smaller size bubbles.

The results of this investigation suggested that there is a

potential for using horizontal baffles on an industrial scale.

LISTOFFIGURES

1.1 Schematic of a Mechanically Agitated Gas-Liquid Contactor

1.2 Power Curves for non-Aerated Liquid (Rushton [ 1950])

1.3 Development of Cavities with Increasing Aeration Number

1.4 Appearance of Different Cavity Regimes in an Agitated Contactor wíthout Recirculation (Van't Reit et al.. [ 1976])

1.5 Reduction in Power of Agitatíon with and without Gas

Recirculation (Van't Reit et a l . í l976] )

2. l Concentration Profiles near the Interface

2.2 Stress and Strain Relations in a Shaft

3.1 Schematic Diagram of the Experimental System

3.2 Tank Assembly with Vertical Baffles

3.3 Tank Details

3.4 Details of Vertical Baffles and Tank Lid

3.5 Details of Horizontal Baffles

3.6 Tank Assembly with Horizontal Baffles

3.7 Rushton Turbine Impeller (R-100) of 3" Size

4.1 Average Interfacial Area for Vertical Baffles

4.2 Average Interfacial Area for Horizontal Baffles

4.3 Effect of Gas Flow Rate on Average Interfacial Area

for Vertical Baffles

4.4 Effect of Gas Flow Rate on Average Interfacial Area

for Horízontal Baffles

4.5 Correlation of Average Interfacial Area for

Vertical Baffles

vi

4.6 Correlation of Average Interfacial Area for Horizontal Baffles

4.7 Comparison of Average Interfacial Area for Vertical and Horizonta) Baffles

4.8 Gas Holdup for Vertical Baffles

4.9 Gas Holdup for Horizontal Baffles

4.10 Comparison of Power of Agitation without Aeration for Vertical and Horizontal baffles

4.1 1 Plots of Pg versus Ny for Vertical and Horizontal Baf fles (20 rps.)

4.1 2 Plots of P3 versus N^ for Vertical and Horizontal Baffles (21.7 rps.)

4.1 3 Plots of Pg versus N/ for Vertícal and Horizontal Baffles (23.3 rps.)

4.14 Power of Agitation with Aeration to Gas Holdup Ratio for Vertical and Horizontal Baffles

4.15 Mean Bubble Diameter for Vertical Baf f les

4. l 6 Reduction in Power for Vertical Baffles as a Function of Effectíve Aeration Number

4.17 Rates of Gas Recirculation in the Contactor without Gas Injection for Horizontal Baffles

Vll

LISTOF SYMBOLS

a Average gas-Liquid interfacial area per unit volume of

dispersion, mVm^

a' Average gas-Liquid interfacial area per unit volume of liquid.

mVm^

â'i Average gas-Liquid interfacial area per unit volume of liquid

f o rH /T= l

C Concentration

C/ j Concentration of gaseous solute at the gas-liquid interface,

kmole/m ^

C^b Concentration of gaseous solute in the bulk of the liqid,

kmole/m^

d Mean bubble díameter, m.

D Impeller diamter, m

D Diffusivity of the solute gas, mVsec.

E Modulus of elasticity, N/m^

g Acceleration due to gravity, m/sec^

H Liquid height,m.

H/ Dispersion height, m.

Hj Impeller height of f the bottom of the tank, m.

He Henry's law constant, kPa.mVkmole.

k Pseudo-first order reaction constant, sec-1.

k| Mass transfer coefficient, m/sec.

ki° Mass transfer coefficient for absorption without chemical

reaction, m/sec.

viii

kjâ Overall average volumetric mass transfer coefficient, sec"

n Rotational speed, rps.

Ny Aeration number.

Ny ^ Effective aeration number.

Npp Froude number.

Np Power number.

Npø Reynolds number.

NQ Impeller discharge coefficient in liquid.

NQ(J Impeller díscharge coefficient in dispersion.

P3 Power of agitation under aerated condition, Watts.

Po Power of agitation under non-aerated condition, Watts.

PAO. PA

Partial pressure of gaseous solute, kPa.

P/ j Partial pressure of gaseous solute at the interface, kPa.

Qp Rate of gas entrainment from surface or surface aeration,

mVsec

Qq FI0W rate of sparged gas, mVsec.

Qp Pumping rate of the impeller, mVsec.

r^ Local Rate of reaction of gaseous solute A, kmoles/mVsec.

r^ Overall Rate of reaction of gaseous solute A, kmol/mVsec.

R Universal gas law constant

T Tank diameter, m.

V5 Linear or superficial velocity of the gas, m/sec.

V Volume , m^

IX

Greek svmbols:

e Temperature, °K.

f Tensile strain along the principal axis of the shaft,

S Film thickness according to film theory, m.

e Gas hold-up, m gas/m^ of dispersion.

[1 Viscosity of the liquid, kg.m/sec.

p Density of the liquid, kg/m^

SubscriDts:

L,l Liquid

G,g Gas

d Dispersion

LISTOFTABLES

1.1 Correlations for Reduction in Power Consumption in Presence of a Gas f or a Rushton Turbine

1.2 Mass-Transfer Correlations

3.1 Summary of Important Contactor Dimensions and Ratios 4

4.1 Scheme of Experiments 5

4.2 Reproducibility of Experimental Data 5

B. 1 Inlet Conditions and Other Data for Set 2 to Set 7 1C

B.2 Power of Agitation without Gas Injection for Vertical Baffles IC

B.3 Power of Agitation without Gas Injection for Horizontal Baffles

B.4 Observations and Calculations for Set 2






XI

CHAPTER 1

INTRODUCTION

1.1 Backaround

Many chemical processes involve contacting a gas and a liquid.

For good contacting, the gas must be very well dispersed in the

liquid. Such a dispersion can be achieved by injecting the gas into

the liquid through one or several orifices (spargers, perforated

rings, perforated plates, etc.) placed under a mechanical agitator

which breaks the gas bubbles into smaller ones and disperses them

throughout the liquid phase. Because of the increase in the surface

area due to bubble breakage and better dispersion of the bubbles,

the mass-transfer rate between the gas and liquid is greatly

improved with mechanical agitation. Such an arrangement for

contacting gas and liquid is generally called "Mechanically Agitated

Gas-Liquid Contactor" and will be referred to as an agitated

contactor throughout this thesis.

Agitated contactors are generally used for processes involving

an absorption of a slightly soluble gas which undergoes a chemical

reaction in the liquid phase. In such processes the reaction rate is

usually much faster than the absorption rate. These contactors are

commonly used in biological fermentations (e.g., manufacture of

penicillin), hydrogenations (e.g., manufacture of margarine from

vegetable oils), and oxidations (e.g., biological oxidation of chemical

and municipal waste). The design of such contactors is reliable and

they can be operated under wide range of operating conditions. In

1

most applications, the design of agitated contactors involves two

major considerations: (i) the overall gas-liquid mass-transfer rate

and, (ii) the agitator power requirement. Besides these, there are

secondary considerations such as, blending of the reactor contents,

heat-transfer, and solids suspension, which are usuaHy not critical

because they are automatically provided for when the design is

satisf actory f or mass transf er consideration (Uhl and Gray [ 1966] ).

The aim of a good design then is to obtain maximum mass-transfer

rate, and at the same time keep the power consumption to a

minimum.

A schematic diagram of a typical agitated contactor is shown

in Fig.1.1. Major dimensions are shown relative to the tank

diameter (T). The important internal elements are; a flat bladed

disk turbine impeller for agitation (also referred to as a Rushton

turbine), a sparger ring below the impeller to inject the gas and,

four vertical baffles extending throughout the depth of liquid. It

may be noted that the vertical baffles are offset from the tank waV

to minimize formation of stagnant zones near the baffles.

The four vertical baffles serve to convert rotational motion oi

the liquid to vertical motion and hence prevent the formation of Í

vortex. It is necessary to prevent the formation of a vortex in ar

agitated contactor because, when a vortex develops the fluid swirl^

around as one element and there is no turnover of the 1iqui(

contents and the dispersion of the gas in the liquid is poor.

The use of such a design sometimes leads to high values o

shear rates in the vicinity of the impeller and hence high powe

Gas Outlet-

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Figure 1.1. Schematic of a Mechanically Agitated Gas-Liquid Contactor

4

requirement for agitation. For reducing the power requirement to

get the same or higher mass-transfer rates, a different type of

baffle arrangement called horizontal baffles was examined. From

preliminary visual observations with this type of baffles it was

seen that they served effectively to prevent the formation of a

vortex and the power requirement for agitation was much less

compared to that f or vertical baf f les.

The objective of this investigation then was to determine

whether an improvement in the performance of an agitated

gas-liquid contactor could be achieved by using horizontal baffles

instead of the commonly-used vertical baffles. The performance

criterion to be examined was overall mass-transfer rate for a given

power input.

For these purposes an experimental system of the type shown

in Fig.1.1 was constructed. Experimental methods for determining

the power of agitation and the gas-liquid interfacial area were

devised. The details of the system configuration and the

experimental procedure are given in Chapter 3.

1.2 Literature Review

1.2.1 Dimensionless Numbers Used in Mixing Analysis

Agitation Revnolds Number (NR^). This group represents the

ratio of inertial forces to viscous forces. It is commonly defined as

pvL/|JL, where, p is the density of the liquid, \i is the viscosity of

the liquid, v denotes a characteristic velocity and L denotes a

characteristic length. For agitation L is taken as the diameter of

the impeller, D, and v is taken as the tip speed of the impeller, nD,

where n is the rotational speed of the impeller. Substitution gives,

D np N Re

M-

Agitation Reynolds number determines whether the flow is laminar

or turbulent and hence it is a critical group in correlating power.

Froude Number (Npp). This group represents the ratio of

inertial to gravitational forces and is defined as vVLg, where g is

the gravitational acceleration. Substituting the characteristic

length and velocity for agitation as before the Froude number for

agitation becomes,

n D Ncn = Fr =

g

In most fluid flow problems, gravitational effects are unimportant

and the Froude number is not a significant factor. The reason it is

included in the dimensional analysis of agitated tanks is that most

agitation operations are carried out with a free liquid surface in the

tank. The shape of the surface and, therefore, the flow pattern in

the vessel, are affected by the gravitational field. This is

particularly noticeable in unbaffled tanks where vortex formation

occurs; the shape of the vortex represents a balancing of

gravitational and inertial forces.

Power Number (Np). The power number is the ratio of the

power applied by agitation (P) to the pumping produced by the

rotat ing impeller and is defined as P/mv^ where P is the power

applied by mechanical agitation, m is the mass of the liquid

displaced by the impeller per unit time and v is a characteristic

velocity. The quantity m can be expressed as pnD^ As before, the

characteristic velocity is the impeller tip speed nD. Thus power

number for agitation can be writ ten as.

Np = 3 n 5 pn^D

The physical significance of the Power number is similar to the drag

coefficient in fluid flow analysis.

Aeration Number (N/v ). This dimensionless number is the ratio

of the gas flow rate, Qg, to the impeller pumping capacity which is

proportional to nD^ Hence the Aeration number for agitation is

defined as,

Qg

nD'

Aeration number comes into play only in the case where a gas is

introduced into the liquid. It is useful in correlating the reduction

in power consumption in gas-liquid dispersion.

Weher Number (N\A/^). Weber number represents the effect of

surface forces on the bubbles size. It is the ratio of inertial

7

forces to surface tension forces and is defined as pv^L/cj.

Substituting for v and L as before, the Weber number for agitation

can be wri t ten as,

pN^D' Nwe = •

o

It appears in many correlations where the surface tension effects

are important.

1.2.2 Agitation Power for Contactors in Absence of Gas Injection

The subject of power requirement in agitated contactors with

Newtonian liquids is extensively covered in the chemical engineering

l i terature. A comprehensive analysis was prepared by Rushton £t.

a]., (1950 a,b). More recently, the subject was reviewed by Holland

and Chapman (1966), Uhl and Gray (1966), Nagata (1975), and

Midoux and Charpentier (1 984).

The power requirement is usually expressed as curves of the

power number, Np, versus the Reynolds number, Np^. Each

combination of impeller type and vessel geometry has i ts unique

power curve; however, the same power curve can be used for

di f ferent size vessels if the geometric similarity is preserved.

Some typical curves for the Rushton turbine impeller that is used in

this investigation are shown in Figure. 1.2. When the vessel does

not have baffles or has inadequate baffling, a vortex is formed, and

Froude number, Npp, must be introduced for Np^ greater than 300.

Most power curves available in the l i terature were developed for

Newtonian liquids.

8

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1.2.3 Hydrodynamics and Agitation Power for Contactor in Presence of Gas Injection

When gas is introduced into an agitated contactor the power

requirement is reduced. In a comprehensive investigation of

hydrodynamic conditions, Van't Reit et a1.. (1973,1974,1976) and

Bruij in et a!.. (1974) have found that the formation of stable

cavities behind the impeller reduces form drag and hence the power

requirement.

Various regimes of cavity formation for a six blade Rushton

turbine operating with increasing aeration number are shown in

Fig.1.3. According to Van't Reit et al.,(1976) the appearance of

cavit ies wi th increasing Aeration number follows the following

order:

a. Six pairs of vortex cavities; one pair of cavity on each blade.

b. Six clinging or adherent cavities.

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three clinging cavities, the 3-3 configuration.

d. Two groups of three large cavities with larger and smaller on

successive blades.

e. Three bridging cavities arranged symmetrically and fiHing the

space between alternate blades, which is also called the flooding of

the impeller.

According to Rruijin et al.. (1974), it is possible to isolate the

effect of cavities on the agitation power if the recirculation of the

gas at the agitator level is prevented, (this was done by placing the

impeller in a large square vessel where the gas was sparged below

10 lOi

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(a) 5 Vortex Cavities (b) 6 Clinging Cavities

(c) 3 Clinging and 3 Large Cavities

(d) 6 Large Cavities of different size

(e) Brídging Cavities or flooding

Figure 1.3. Development of Cavities with Increasing Aeration Number

11

the impeller, passed through the impeller only once and then

escaped to the surface). In that case the reduction in power,

Pa^^o, with increasing aeration number depends only on the type and

size of the agitator. Fig.1.4 shows the appearance of various

cavity regimes on the plot of Pg/Po vs. Aeration Number, N^. On the

other hand if recirculation of the gas at the agitator level is

permitted, which is usually the case in the operation of most

agitated contactors, then the relationship of Pa/Po vs. N^ not only

depends on the impeller type but also on various other factors such

as tank geometry, baffle type, and on the speed of rotation of the

impeller. Power reduction curves for a typical agitated contactor

of the type shown in Fig. 1.1 are shown in Fig. 1.5.

According to Roustan (1978), these curves can be brought

together to give a unique power reduction curve for a given impeller

by the following considerations: The recirculating flow of gas, 0^',

can be expressed as the product of the pumping flow from the

impeller, Qp, and the holdup of the gas in the tank as below:

Qc' = Qp.e. (1.1)

Then, an effective aeration number, N/^^, can be defined as,

Qg + Qc' N A ^ = —r- = NA - N Q ^ . C . (1.2)

where NQ^J is defined as,

Qp NQH = — — . (1.3)

^^ nD^

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the presence of a gas. Since it is difficult to measure the

velocity and flow rates of a dispersion, the value of \^Q^ has not

been found for gas-liquid dispersions by any investigator so far, but

according to the hypothesis of Cooper and Wolf (1958), which

assumes that the presence of gas does not appreciably modify the

pumping flow from the impeller, the discharge coefficient of the

impeller in presence of gas remains the same as the discharge

coefficient of the impeller, NQ, in liquid alone. Fairly accurate

values of NQ for a11 the common impellers are given in the

literature. The value of NQ for a Rushton turbine can be estimated

according to the following relation (See for example, Uhl and Gray

[1955]);

NQ = 0.98 (T/D) (1.4)

Using the approach outlined above, the relations between the

impeller power reduction and Aeration number for a given impeller

rotating in vessels of different geometry can be brought together

on a common basis. Though the above approach is the most

fundamental one available to date, the understanding of

hydrodynamic mechanism was expanded only during the last ten

years.

It is a common practice in the existing literature to correlate

the reduction in power in the form of empirical dimensional

correlations. Several investigators have correlated the ratio of

power of agitation with gas injection, P^, and the power of

agitation without gas injection, Po, with various parameters such as

15

impeller diameter, D, impeller speed, n, and volumetric gas flow

rate, Qg. The usual group used for correlation is the Aeration

number, N^. Some correlations also include dimensionless groups of

the physical properties of the two phases. Table 1.1 gives the

summary of correlations and their range of applicability. In Table

1.1, T is the tank diameter, D is the impeller diameter, H is the

liquid height, \-\^ is the impeller height off the bottom of the tank,

and Vg is the linear or the superficial gas velocity and is

obtained by dividing the volumetric gas flow rate, Qg, by the tank

cross sectional area.

Hughmark (1980) made a stat ist ical analysis of most of the

reported data and correlations and found the correlations of Michael

and Miller (1952) and Luong and Volesky (1979) to be the most

suitable for correlating the aerated power data over a wide range of

variables. Hughmark's analysis indicates that the effect of surface

tension is not significant in correlating the reduction in power

consumption to the system variables. Calculated values from

correlation of Loung and Volesky (1979) show a i21 .4% from the

experimental data. Hughmark (1980) has also revised the

correlation of Loung and Volesky (1979), and showed that using the

liquid volume, V^, in the contactor in place of D in the correlation

improves the correlation coefficients. He also used a modified

Froude number to obtain a correlation that showed an average

deviation of i8.5% between calculated and reported experimental

data.

16

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i ^ 0 0 ,

1 c c

< <

"O

cr> in 2 c Qj r

0 0 _ _ ) > >.

' j i í_ "O 0 =;

>— - ^ • ^ • -

^ S 0 g II t c ^

- ^

cr

0 II

0

00' ^~

d 1 II

Ol

û . c

- 1

^

^ \

'—

D

t :

cr>

c

CL

c 0

r

17

Based on statistical analysis of reported data, the correlation

of Hughmark (1980) is the most recommended one for Newtonian

liquids (Joshi et al.. [ 1982] ).

1.2.4 Gas-Liquid Mass-Transfer

Mass-transfer rate (r) in agitated tanks is usually expressed

as the amount of gas absorbed per unit volume of the gas-liquid

dispersion per unit time. This quantity depends on the gas-liquid

in ter fac ia l area per unit volume of dispersion, 3_, and the

concentration driving force (CQ-C|_)- The overall mass-transfer

coefficient, K|_, is defined by the relationship;

r = Ki_a . (CQ-C[_)

where CQ denotes the concentration of a solute A in the gas phase

and C|_ denotes the concentration of the solute A in the bulk of the

absorbing liquid. Thus, the mass-transfer coefficient is defined as

the rate of mass transfer per unit driving force per unit interfacial

area. It has the units of m/sec. The gas-liquid interfacial area can

be estimated by using physical methods which involve actually

observing the bubble sizes and their distribution, but the physical

methods are tedious and expensive. By using a chemical method in

which rate of absorption of a gas is measured for a known value of

driving force, the product K|_a can be estimated. This is a

convenient quantity and it is extensively used to characterize

mass-transfer rate. This product is commonly referred to as

volumetric average mass-transfer coefficient. Usually it is diff icult

to estimate the interfacial area per unit volume in most chemical

18

methods; however, under some conditions the value of 3 can be

deduced from the measurements of a chemical method. One such

method is used in this investigation and is described in Chapter 2.

When a chemical method is used for calculating K^a. or a.,

information on the behavior of the gas phase is needed to calculate

the average driving force. In most applications, the gas phase is

assumed to be backmixed. Mehta and Sharma (1971) showed that

the gas phase can be considered fully backmixed under the usual

operating conditions in a laboratory-scale mixer.

Most correlations of mass-transfer involve either the overall

mass transfer coefficient, K^â, or the effective interfacial area, a.

All these correlations are in the form of empirical dimensional

relationships between the relevant variables. All the correlations

are of the following general type:

K[_aora is proportional to,

Vs^.nPor v s " . [ ^ ^

In Table 1.2 therefore, the values of the exponents a , p and y for a

turbine wi th six f lat blades are given, together wi th the most

important dimensions of the vessels investigated. The large

variations of the exponent values for different vessel geometries

and different systems indicates that this correlation is not general,

and depends on vessel geometries and the type of gas-liquid

system.

Another correlation method was proposed by Westerterp ei.

al., (1953). They found that the effect of v^ is significant only at a

19

CD C L > >

CZL

£

CD C

j Q C_

o -I—» CD

O i5 O

CD C

O (_

o - » — > <D

O

o

CD C

o c_ o

-t—'

CD

o i5 o

O o (\) C L

<D

o 03

LO

cn c o

- t — »

i5 CD c_ c_ o (_J c_ < D

»<—

cn c ( ^ c_ ^7 cn cn ( ^

21

C l (^ h-

o > c o

- l — »

i5 CD C_ í_ o (-J CD

cn -i_» c CD c o CL X

^-

CÛ_

b

CD O

c CD c_

CD

CD

cn

d LO

d

LD

q CsÍ

co

d

-i—' L_ ^ <D ^

cr> o

<D O

' c co

~ LD I , " O^

o d IT)

d

d

o CN

d

CD Q C

> O

OJ

d ro

d ro d

o

d

o LT)

d

o c

Q CD C P ^ r5 >. o X cû

O IT) O cj> fO —

00

d ro

LO ro

o

d

( l

>

CÛ

c CD <D

20

low value of n. Above a certain value of n (called critical impeiler

speed) they found that Ki_a is independent of v^. This critical

impeller speed, n^, found by considering the circulation of the gas

bubbles and bubble coalescence, is given as,

noD ÍT = A + B —

(a g / p)0-25 l D

where A and B are correlation coefficients with values of 1.22 and

1.25 for a turbine impeller with six flat blades. In the regime above

the critical impeller speed the specific interfacial area is

correlated as follows:

aH = C (n-n^) D vTpTTã')

(1-e) where,

C = (0.79 1 0 . 1 6 ) [i i[i\n cP)

1.2.5 Surface Aeration

Entrainment of the gas into the liquid from the freeboard liquid

surface is called surface aeration. Several types of agitated

contactors, particularly in fermentation industry, are specifically

designed to enhance surface aeration. Calderbank (1959) has

pointed out that surface aeration leads to an increase in the

hold-up of the gas in the contactor and hence to an increase in the

gas-liquid interfacial area. For this reason, surface aeration is an

important consideration in the design of an agitated contactor. The

correlations discussed in the preceding sections ignore the effect

of surface aeration. Very few studies on the effects of surface

2

aeration on mass-transfer and power requirement have been

published.

Matsumara et al.. (1977) have studied surface aeration rates

wi th a Rushton turbine in a tank with four vertical baffles. They

have proposed the following implicit correlation for estimating the

rate of surface aeration (Q^);

-2.2 -n

(l-Tl)

where

= 1.913x10"^ InD

z\ nD

\^ J

0.1 ^n^D^pA

V

1.38 0.07 6.4 n^D'i f D ^

T.

Ti = 0^/(0^+0^)

where Qg is the volumetric flow rate of sparged gas, and Q^ is the

volumetric flow rate of entrained gas. Matsumara et al..( 1978)

have also measured the power consumption in the presence of

surface aeration using a Rushton turbine impeller. The following

correlation has been proposed.

= 0.25 ívo inDj

-0.2 r n D"* 0-05

ig ;

There is not much information in the l i terature about

mass-transfer coefficients in the presence of surface aeration.

Mehta (1970) has obtained the values of effective interafacial area,

a, and liquid side mass transfer coefficient, k|_â, using a six-bladed

disk turbine as the impeller. The values of a and k^â were found to

vary between 125-325 mVm^ and 0.08-0.2 sec" ^ respectively,

when Pa/V|_ was varied in the range of 0.017 to 41.1 1 kW/m^

CHAPTER 2

THEORETICAL C0N5IDERATI0NS

As stated above, the objective of this investigation is to

compare the performance of an agitated contactor with horizontal

baff les to one wi th vert ical baff les. The cr i ter ia used for

comparing the performance are, the mass-transfer rate and the

agitat ion power requirement. In the following sections the

theoretical basis for the experimental methods and the calculation

procedure used in this investigation are developed.

2.1 Determination of Volumetric Mass-Transfer Coefficient and Interfacial Area

A chemical method for determining overall volumetric

mass-transfer coefficient, K\_3, and interfacial area, 3, is used in

this investigation. Below it is shown how these quantities can be

determined from measurable quantities. For a complete analysis,

refer to the original publications on theory of mass-transfer with

chemical reaction by Danckwerts and Sharma (1966,1970). This

theory is a commonly-accepted theory for chemical methods of

measurement of Ki_i and 3.

Consider a system of a gaseous solute A being absorbed in a

liquid B. The concentration profile near the gas-liquid interface at

steady state is shown schematically in Figure 2.1 . In this figure P3

and PAJ denote the partial pressure of the gaseous solute A (which

is a measure of concentration in the gas phase) in the bulk of the

22

»3

gas and that at the interface respectively, whereas, C|_ and C^^

denote the concentration of A in the bulk of the liquid, and at the

interface, respectively.

Now according to the theory of Lewis and Whitman (1923), the

interface is always saturated; therefore, the liquid concentration

and gas concentration at the interface are related by.

^A i = PA

RøHe (2.1)

<D d O o. E o o

cn

cz o -i—>

(^

d OJ <-)

o (_;

C L

Liquid Phase

Distance

Figure2.1. Concentration Profiles near the Interface

24

where He is the Henry's law constant which represents the

equilibrium constant between concentration in the gas phase and in

the liquid phase (when the solubility of the gaseous solute is small

[e.g. oxygen in water] and ideal gas law applies), ø denotes the

temperature, and R denotes the gas law constant. Several

mass- t ransfer coeff ic ients can be defined depending on the

concentrat ions used for the driving force. Mass-transfer

coefficients for the gas side (kQ°) and for the liquid side (k^^) are

defined as the ratios of flux, Ny , of gaseous species A and the

respective driving forces; (PG"PAÍ^ ^^^ ^^^ 9^^ side, and (C/!^J-CL)

for the liquid side. An overall mass-transfer coefficient K^ is

defined based on the overall driving force from gas to liquid

expressed in terms of concentration units. Then at steady state,

the flux of A can be expressed in terms of these different driving

forces as follows;

N A = ^G ° (PG-PAÍ ) = ki ° ( C A Í - C L ) = KL (CG-CL) . (2.2)

Using the equalities in (2.2), i t can be shown that overall

mass-transfer coefficient based on liquid side, K^, is related to

individual mass-transfer coefficients on the gas and the liquid side

as,

1 1 1 (2.3)

KL He kG° kL°

For relatively insoluble gases the value of He is very high and hence

the f i r s t term on the right hand side in (2.3) may be considered

negligible in comparison to the second term. In that case the

25

overall resistance to mass-transfer can be considered to be

entirely in the liquid phase and the flux of A can be wri t ten as.

NA = kL°(CArCL)- (2.4)

The physical significance of the mass-transfer coefficient k ^ is

discussed in the following paragraphs.

According to the well known fi lm theory of mass-transfer

developed by Hiegbie (1935), the resistance to mass-transfer from

gas to liquid can be located in a gas film and liquid film surrounding

the interface. This means that any drop in concentration due to

mass-transfer occurs in a narrow region around the interface. Also

the concentration profiles near the interface are approximated as

straight lines which are shown as dotted lines in Fig. 2.1 above.

Assuming that the gaseous solute A is transfered in the liquid

phase by diffusion, the flux of A in the liquid is expressed as,

dCA NA =-D

dx x = 0. (2.5)

where, D is the d i f fus iv i ty of the gas and dC^/dx is the

concentration gradient at the interface. If the concentration

prof i le in the f i lm is assumed to be linear and a depth of

penetration, 5, defined by Hiegbie's film theory, then the slope of

the concentration profile at steady state is constant and is given

as. dCA

dx

CAI - C L

x = 0 (2.6)

Substituting this result in (2.5),

26

N A = D ^Ai - ^L

(2.7)

From (2.4) and (2.7), it can be seen that according to the film

theory the mass-transfer coeff ic ient, k^^, is the ratio of the

diffusivity to the depth of penetration. Therefore,

k, ° = D

(2.8)

Consider now, a situation where the gaseous solute A reacts

wi th the liquid B to form a liquid product C according to the

reaction,

A(g) + B(L) - C(L).

The reaction is a f i r s t order reaction with a rate constant, k,

defined as,

(-r^)] = kC^. (2.9)

where (-rA)] is the rate of disappearance of A per unit volume of

the liquid. Now if the reaction is much faster compared to

absorption rate so that most of the diffusing gas A is consumed

inside the liquid fi lm then the concentration profi le near the

interface can no longer be considered as a straight line as before.

Danckwerts and Sharma (1963) derived the equation for

concentration profile for absorption accompanied by a fast chemical

reaction, using the film theory, they found the value of the slope of

the concentration profile at x = 0 to be.

dCA

dx x = 0

^Ai - C

VÔTk L

(2.10)

27

Substituting (2.10) into (2.5), an equation for rate of absorption of

gas in presence of a fast f i rs t order chemical reaction is,

H^ = 4W ( C A J - C L ) = kL° VkD / kL° (CAÍ - CL) . (2.11)

Comparing (2.1 1) to (2.4), the term VkD may be considered as the

mass- t ransfer coeff ic ient for gas absorption wi th chemical

reaction and is denoted as k^. Thus,

NA = kL(CAi - C L ) , (2.12)

where, k^ = VkD.

Note that the derivation given above for the mass-transfer

coefficient with a fast chemical reaction in the liquid film applies

only when the following condition is satisfied;

ki VkD (0 = — ^ = > 2 . (2.13)

kL° kL°

In the above equation, cp is commonly called the enhancement

factor. It is the ratio of mass-transfer coefficient with chemical

reaction to mass-transfer coefficient without chemical reaction.

Now, when the reaction rate is much faster than the

absorption rate, the concentration of the solute in the bulk of the

liquid, CL, is very small in comparison to C^j. Therefore, (2.1 2) can

be wr i t ten as,

NA = k L . C A i - (2.14)

For a weak solute and assuming the gas phase behaves as ideal gas,

Henry's law can be used to relate the concentration at the interface

to the partial pressure of the gaseous solute. Equation 2.14 then

J

28

becomes,

NA = k 'Ai

L R eHe

(2.15)

It was shown above (following Equation 2.3) that the partial

pressure of the gaseous solute at the interface, Py j, is equal to its

partial pressure in the bulk of the gas, P^, for negligible gas phase

resistance.

The above analysis is now extended to a gas-liquid reaction in

an agitated contactor in which gas carrying the solute A is

dispersed in a pool of liquid B. The mixture of gas bubbles and liquid

wi1l be referred to as the "dispersion".

Consider a small element of volume dVp in the contactor as

shown below.

This element consists of gas bubbles carrying solute gas A,

dispersed in liquid B. The fractional volume of bubbles is denoted by

£. Thus the volume of the liquid, dV^, in the volume dVp is

(1 -c)dVp. The interfacial area per unit volume of the dispersion is

denoted by a. At steady state, using (2.14), the rate of absorption

in the volume element is therefore.

29

NA a dVn = f P

'A R 1 A

,R GHe, a dV R. (2.16)

As discussed earlier, the local rate of absorption of A is equal to

the local rate of reaction of A. Since the local rate of reaction of

A, ( - P A ) ] , is expressed on the basis of liquid volume, Equation 2.16

can be wr i t ten as,

(-rA)i ( l -£ ) dVp = kL

Upon rearrangement (2.17) becomes.

'A

, ReHe , a dV R-

(-rA)i dVp = k^a

(1-c)

'A

ReHe dV R'

(2.17)

(2.18)

The above equation can be integrated over the entire tank.

/ (- ^ A ) ! dVR VR

1 Í P

(l-£)He VR

A

. Rô kia dV R, (2.19)

The left hand side of (2.19) is the overall rate of reaction of the

gas which is a measurable quantity. To integrate on the right hand

side, the variation of all the quantities inside the integral with the

volume should be known. In an agitated contactor, He is a constant

for isothermal operation. The value of k] for a fast chemical

reaction is given by VkD . For constant temperature, both k and D

are constants. Also, the gas phase is assumed to be fully mixed,

i.e., the concentration of A in the gas is uniform throughout the

tank. It has been shown by Mehta and Sharma (1971) that under

30

usual operating conditions in the laboratory, there is considerable

recirculation of the gas inside the tank and therefore the gas phase

can be considered backmixed. Therefore, a representative gas

phase concentration within the contactor can be taken as a

constant referred to as (PA^^^âv- "^^^^ ef fect ive average

concentration is calculated by considering the oxygen material

balance and the variation of pressure from the bottom of the tank

to the top. (See next section). Under the above assumptions (2.19)

can be wr i t ten as;

/ ,(-rÂ)ldVR VR

•1 ^ P A ^

He L R e J av V

(1-e) dVp. (2.20)

R Dividing both sides of the above equation by dispersion volume VR

J- /,(-rA)ldVR VR VR

(P.

He Re av V R V

(1-e) dVR . (2.21)

R Now defining an average interfacial area per unit volume of liquid as

a' = - / k dV VD V D ( 1 - £ )

R (2.22) R R

Eqn. (2.21) reduces to.

( -Âh kiâ'

He

'A

l R e J (2.23)

av

In the above equation (-rA^d is the overall average rate of

uptake of oxygen per unit volume of the dispersion which is a

measurable quantity. Furthermore, when data are available for the

chemical reaction rate constant, k, and diffusion coeff icient, D,

31

then the constant k^ can be computed as VkD (see Equation 2.11).

The value of He is known for the system used. In that case the

value of 3 is given by.

He (-rA)H ^ ^ . (2.24)

ki (PA/RT)av

Equation 2.24 is the basis for calculating the average interfacial

area per unit volume of the liquid which is used to characterize the

mass-transfer performance.

The reaction system chosen for this investigation was

oxygen-sodium sulfite solution because the reactants are readily

available and inexpensive. This system is commonly used in studies

of this type. (See for example Westerterp et al..í 19631). Sodium

sulfite is oxidized to sodium sulfate in presence of a cupric ion

catalyst according to,

2 S 0 3 ~ + O2 - 2 S 0 4 ~ .

Westerterp et a1., (1963) have shown that this reaction is a fast

chemical reaction of second order in the liquid film with the rate

given by,

( T A ) I = ^' [O2] [503~] . (2.25)

Note that in a solution this second order reaction can be

approximated as a pseudo first order reaction because the sulfite

concentration is in excess of the oxygen concentration and

therefore [SO3--] can be assumed constant. Thus, the overall

average rate of reaction per unit volume of liquid can be written as,

32

(-Â)I = 1 d[C5o-- ]

V L dt = kÔ^]. (2.26)

The rate of change of concentration of sulphite is measured

experimentally. If this rate is denoted by d^Cô —]/dt then the

overall average rate of reaction of O^, (~A)d ' ^^ defined before, is

given by.

dC ( - rA)d = - 1 / 2

SO.

dt

^ L

VR (2.27)

Note that here the basis for rate of reaction was changed from unit

volume of the liquid to unit volume of the dispersion. The procedure

for measurement of sulfite oxidation rate is described in Chapter 3.

Westerterp el_al.,( 1963) have also estimated the value of kj

and i ts variation with temperature for the oxygen-sodium sulphite

system to be.

k = 4467.63 f -16500

exp Re

0.5 sec -1 (2.28)

where R is in ca1/gmo1e/°K and e in °K.

2.1.1. Calculation of the Average

Driving Force

The average driving force in the contactor is calculated by

assuming a well mixed gas phase and using a material balance over

oxygen. Consider molar balance of oxygen over the control volume

shown in the diagram on below.

At steady state, an oxygen molar balance over the control

volume gives.

33

îontrol Volume

g in

(rate of O^ in)- (rate of O^ out) = rate of consumption of Oo inside the control volume.

n symbolic form this may be wri t ten as.

n, in • 0,1 out (-^o)dVR. (2.29)

Note here that the subscript A in the previous equations is now

change to denote oxygen. The molar flow rate, n^ ,on the left hand

side of the above equation can be expressed as a product of

volumetric flow rate Q^ and molar concentration CQ . Also the gas

concentration can be expressed in terms of partial pressure of the

gas by using ideal gas law; In that case, (2.29) becomes.

Q gin ^02

, Rø J in + Q gout . Re J out

= (-r^o)dVR. (2.30)

In thisequation the outlet concentration may be taken as the

average concentration in the tank because the assumption that the

gas phase is well mixed. Therefore, the outlet concentration can be

expressed as.

34

í ô^] (^gin iôA . (- o,_)d^R (^.31) in í ^02 \ ^ i Re Jin Re Jav Qgo^t l Re j in Qgo^t

Equation 2.31 gives the method for calculating the average driving

force as follows: Here the absorption rate per unit volume of the

dispersion, (-ro^^d, is determined experimentally. Both the

dispersion volume, VR, and the inlet gas flow rate, Qgin, ai e

measured experimentally. The outlet flow rate, Qgout' ^^^ ê

calculated from the knowledge of inlet flow rate by considering the

change in pressure from inlet to outlet due to hydrostatic head and

change in number of moles due to water evaporation into the gas

and the change of oxygen concentration due to reaction. The

diff iculty here is that the concentration of oxygen at the outlet

cannot be calculated without knowing the outlet flow rate. A trial

and error procedure is used in which the outlet flow rate is f irst

guessed as being equal to the inlet flow rate and the concentration

of oxygen at the outlet is calculated. The outlet flow rate is then

corrected by using this concentration of oxygen. The trial and

error is repeated until a constant value of oxygen concentration is

obtained. A summary of a typical calculation is given in Appendix A.

7 9 Measurement of Power pfiquirement

The agitation power is determined by measuring the shaft

torque and its rotational speed. The following equations summarize

the relationships used in this work. A detailed discussion may be

35

found in the book by Oldshue (1966). The power delivered to a

rotating shaft is given by the following equation.

2TmTe P = =- .

33,000

Where P is the power in horsepower, T^ is the torque in 1bf-in and n

is the rotational speed in rpm. Torque of a circular shaft can be

calculated from the knowledge of shear stress perpendicular to the

axis of the shaft by the foHowing relation;

16To f = r s

TTd^

Here, fg is the maximum shear stress in the cross section of the

shaft and d is the shaft diameter.

The shear stress, f^, is the average of the tension and

compression stresses introduced along the principal axes of the

shaft. The tension and compression stresses are in turn related to

the strains along the principal axes via the elastic relation. These

relationships are;

fg = 1/2 (Tensile stress + Compressive stress)

= 1/2(E. e - E.(ve)).

where E denotes the Modulus of Elasticity, v denotes the Poisson's

ratio, and f denotes the tensile strain along the principal axis.

Figure 2.2. shows these stresses and strains in a rotating shaft.

To determine f^ a measure of the strain is needed. This is

done by using a resistance strain gauge attached to the shaft. They

work on the principle that the resistance of a thin metallic wire

36

<r

Compressive strain

t

Shear stresses

Tensile strain

Figure 2.2. Stress and Strain Relations ín a Shaft

37

varies linearly with the strain acting on it. The details regarding

the construction and use of strain gauges are given in Appendix C.

CHAPTER 3

EQUIPMENT AND PRQCEDURE

The experimental system used in this investigation was

designed to allow measurements of the mass-transfer coefficients

and power requirements under various conditions of mechanical

agitation. The system was designed under two cirteria: (i) to

employ existing equipment and, (ii) ease of operation. The design of

the system was based on the configuration for Mechanically

Agitated Contactors recommended by Qldshue (1966).

3 • 1 DescriDtion of the Eauipment

Fig. 3.1 shows a schematic diagram of the experimental

system. For ease of description the system is divided into three

main sections:

• contactor (or tank),

• agitator assembly, and

• gas supply.

The heart of the system is the contactor. A diagram of the

contactor with drive assembly is given Fig. 3.2. For convinience,

identification codes are given in parenthesis for each part.

A detailed drawing of the tank (TA), is shown in Fig. 3.3. The

tank was constructed of a polyacrylic tube 30.5 cm diameter and

3.2 mm thickness. The bottom of the tank was closed by a

polyacrylic sheet of 6.4 mm thickness. A flange was mounted on

the top of the tank to support the cover (C) which was fastened to

38

39

CD í_ <D d Û -cn o E

•*->

( 3

<

Á

<

c (\3

CO

<D C

cc

CD 4-J <D

E (\3

O

cr

T >

<D >

(^ >

TD <D <D

î

<D

E (\3 C_ cn (\î •.— O CJ

- i —

- » — » (V3

i-<D C. ( ) co

'

ro <D í_ Z5 CD

E <D

-t—'

cn • ^ co , (\1

4—»

c <D

F i _ CD C L X

LU

CL a. Z3

co

<

40

r .^r^ ' i lLUL'A<UH(LUlUlkUULUlÚ(.CT

Figure 3.2 Tank Assembly with Vertical Baffles

12.7 mm |

A

E E o LD

340 mm

__

í E E

vû

Figure 3.3 Tank Details

42

the tank by means of six C-clamps. A sample line (SL) was mounted

near the bottom on the side wall of the tank. A rubber gasket (G)

was used to seal the space between the flange and the cover. The

top cover (C) shown in Fig. 3.4 was made of a polyacrylic sheet of

1 2.7 mm thickness. A bush bearing (BB) was mounted in the center

of the top cover through which the shaft (S) entered the tank. The

cover also had openings for entry of the sparge tube (SP) and

venting the gas. The cover supported four vertical baffles, as

shown in Fig. 3.4, set at ninety degrees to one another. The Four

vertical baffles were made of polyacrylic strips of 25 mm width and

2 mm thick and were suspended from the top cover by means of

screws. The baffles hung from the top cover wi th a 25 mm

clearance from the wall, and extended to the bottom of the tank.

The baff les were fastened to each other at the bottom by

connecting diametrically opposite baffles wi th polyacrylic resin

strips of 3.2 mm thickness.

A set of the horizontal baffles (H) used in this study are shown

in Fig. 3.5. It consisted of four baffles connected to a central hub

to form a cruciform shape, and they extended radially to the tank

walls. The impeller shaft (S) passed through the hub in the center.

The whole unit of horizontal baffles slipped very closely in the tank

and could be supported at any height by means of two set screws

(SS). Fig. 3.6 shows the assembly of the contactor with horizontal

baffles in place.

The agitator assembly was a LIGHTNIN model CV-3 (See Fig.

3.2). The motor (M) had a power of 1 / 4 hp rated at maximum speed

43

12.5 mm

2 mm •#• <^^-

25 mm :^

I •'A'.i. ' . ' ." . ' . ' . . . ." ' U ' "•' " ' " ' " " • ' • ' • •' •.•.'.'.•••••.'.'.'.'•.'.'.'.'.'.?r?j i

o

290 mm

Figure 3.4 Details of Vertical Baffles and Tank Lid

44

SS

(a) Top View

305 mm •

• V ,

r

49 mm 7

(b) Cross Section A-A

Figure 3.5 Details of Honzontal Barfles

Horizontal Baffles

Figure 3.6 Tank Assembly with Horizontal Baffles

46

of 1700rpm. Its maximum rated current was 4 amps. The agitator

drive (A) was a direct drive provided with a ball bearing and a chuck

to connect the impeller shaft. The impeller shaft (S) was a 1 /2 inch

diameter solid circular shaft. The impeller (I) was a six-blade

Rushton turbine impeller (LIGHTNIN type R-100). A detailed

drawing of the impeller is shown in Fig. 3.7.

The power consumption was measured by a resistance strain

gauge (SG) mounted on the shaft below the drive. (See Fig. 3.2). A

MICRO-MEASUREMENTS strain gauge (CEA-1 3-1 87UV-1 20) was

used. It was pasted on the shaft with a special adhesive supplied

by the manufacturer.

The strain gauge was connected to the external circuit by

means of slip rings (SB) made of Inconel alloy and spring loaded

carbon brushes of the type used in small electric motors. (See Fig.

3.2 ).

Air was supplied to the system f rom a central air line. The air'

passed through a pressure reducer (PR) along wi th a pressure

indicator (P) ( U.S.Gage Co. Model N l -1 1 ). Further downstream a

needle valve (V) was used to control the flow rate. (See Fig. 3.1 ).

The flow rate was measured by a previously-caliberated rotameter

(R) (Brooksmodel 1 1 10-06 FIA).

The air was injected into the tank through a copper sparge

tube (SP), one end of which was made into a sparger ring right

underneath the impeller. The sparger ring had a diameter of 5

inches and ten 1/16" diameter holes were dri l led along the

periphery of the sparger ring.

Top View

0.3 mm

2 mm R 19.1 mm^

U . ^ ^ M . l . L i A . ^ ^ ^ ^ ^ ^ ^ L H L > ^ V ^ V k ^ ^ ^ ^ i . k ^ V V V ^ ^ . U A . ^ . ^ ^ g g

56.2 mm

ssa J'

47

2.7 mm

76.2 mm

Section A-A

Figure 3.7 Rushton Turbine Impeller (R-100) of 3" Size

48

3.2 Oneratinn Prorfidurft

Several runs were made to determine the power requirement

and mass-transfer coefficients for different tank configurations.

For each run, the tank configuration, i.e., the baffle arrangement,

impeller height, and liquid height, were selected in advance. Table

3.1> summarizes the important dimensions in the contactor

configuration.

Once the contactor was set up to the desired configuration,

the following procedure was foHowed for each run:

The strain gauge was connected to a bridge circuit for torque

determination and initial reading for value of voltage across the

bridge circuit was taken. (Refer Appendix C).

A known amount of sodium sulphite was then dumped into the

liquid in the tank so as to get a 0.25M solution. The agitation was

started slowly and continued ti l l a11 the sodium sulphite dissolved.

The rpm of the agitator was then adjusted to the desired value.

Once again, the reading for voltage across the bridge circuit under

strained conditions was taken. From the values of these voltage

readings, and the rpm, agitation power without gas injection could

be calculated.

The gas flow was started and the flow rate was adjusted to

the desired value. Since the motor of the agitator was not of

constant-torque type, the rpm of the agitator increased upon

sparging of the gas. The agitator speed was brought down to the

desired value by adjusting the speed controller on the motor. The

voltage across the bridge circuit was measured for operation with

49

Table 3.1 Summary of Important Contactor Dimensions and Ratios

Important Dimensions

Tank diameter, T (m)

Impeller diameter, D (m)

Impeller Height off the tank bottom, H Í (m)

Liquid height, H (m)

0.305

0.0762

0.15

0.45

Vertical baffle dimensions

Baffle width, B (m)

Baffle clearance from the wall, B^ (m)

0.025

0.025

Horizontal baffle dimensions

Height of each baffle, H^ (m)

Distance from the tank bottom to the middle of a horizontal baffle , B j (m)

0.05

0.45

Important Ratios

D/T

Hi /H

B/T

Hp/H

Bd/H

0.25

0.33

0.08

0.1 1

1

50

gas injection. From this va1ue the agitation power requirement with

gas injection was calculated.

The reaction was started by adding a known amout of cupric

sulphate catalyst so as to have a concentration of 10"^ M. The

color of liquid in the tank f i rs t turned turbid and then deep green.

About 10 minutes were allowed to elapse for steady state to be

reached. This time for steady state was decided from experience

on rate measurements under different conditions. The steady state

was decided based on constant value of the rate of reaction. The

mass-transfer coefficient determination was then commenced by

withdrawing the f i rs t sample from the tank via the sampling line

(SL). About 30 m1 of liquid was allowed to run to waste before the

actual sample was taken. The sample analysis was started

immidiately a f ter withdrawing the sample. Five samples at

intervals of 5 to 10 minutes were taken.

3.3 Analvtical Procedure

Elseworth et_ai.,( 1957) described the foHowing procedure for

determination of sulf i te concentration. For any sample a measured

excess (usually 20 m1.) of 0.1 N-iodine was added to 50 ml of boiled

disti l led water and 5 m1 of 30% by volume glacial acetic acid in a

500-m1 conical flask. The sample (10 m1. usually) was pipetted into

the iodine solution by immersing the tip below the liquid surface and

swir l ing the f lask. The excess iodine was t i t ra ted wi th 0.1

N-thiosulfate using starch as an indicator.

The values of the thiosulfate t i t rat ion reading (TT m1) were

plotted against time and a straight line drawn to f i t the points. If p

is the slope of this line, then, the suphite oxidation rate

(dCso^—/dt) is given by 150 x p. The derivation is as follows,

Let T j be the volume of lodine neutralized, and TT^ be the

Thiosulfate t i ter at a time point t p Then, if excess lodine used is

20 ml we may wr i te, for t i t rat ion with thiosulphate,

N,^x(20-T i ) = NThiosu1fateXTTi,

where, Ni^^Njhiosulfate = 0-lN.

Therefore, (20-T1) = TTp

or, Ti = 2 0 - T T | .

From Scott and Furman (1965), 100 ml. of 0.1 N lodine neutralized

= 0.6303 grams of Sodium Sulfite

Concentration of Sodium Sulfite at time t ] for a sample size of 10

m1 is then given by

0.6303 X (20-TT i ) grams/liter

Therefore molar concentration of Sodium Sulfite is then given by,

0.6303 X (20-TT | ) /126 gram moles/liter

The concentrat ion of Sul f i te ion therefore is half of the

concentration of Sodium Sulfite (Na^SOs). The concentration of

Sulfite ion at time t ] is therefore,

Ci = 0.31515 x (20 -TT i ) / 126

= 0.0025 X (20-TTi) gram moles/liter

= 2 .5x (20 -TT i ) milimoles/liter

Similarly the concentration of Sulfite ion at another time t^ , when

the t i t rat ion reading is TT^, can be wr i t t ten as.

52

C2 = 2.5 X (20 -TT^)

Then, if t is in minutes, the rate of change of concentration is given as,

(C2-C 1 ) / ( t2- t 1) = 2.5 X (TT i -TT^^/^t^ - 11)

= 150x(TT1-TT2) / ( t2 - t l )

= 150xp milimoles/lit/hr.

The quantity (TT^ -TT^^ / ^ t ^ - t i ) is the slope of the plot of

Thiosulfate titration reading (TT m1.) vs. time (t min).

CHAPTER 4

RESULTS AND DISCU5SI0N

The use of horizontal baffles instead of vertical baffles proved

to be beneficial in terms of lesser power requirement and higher

mass-transfer rates under the range of conditions investigated. In

this chapter the results for horizontal and vertical baffles are

compared and discussed.

The investigation was divided into eight sets of experiments

listed in Table 4.1. For each set, the baffle type and the injected

gas flow rate were kept constant. Six runs for each set were made

with different impeller speeds. For each run in which gas was

injected from the sparger, the rate of oxygen uptake, the gas

holdup, and the power of agitation were measured. The power of

agitation and the gas holdup were also measured for the runs

without gas injection. From the measured oxygen uptake rates, the

values of volumetric average mass-transfer coefficient, and the

values of average interfacial area per unit volume of the liquid were

calculated according to the procedure described in Chapter 2. The

observations and results are shown in Appendix B.

4.1 Presfintation of Data

The mass-transfer rates in this investigation can be

characterised by the average interfacial area per unit volume of the

liquid, a'. As discussed in Section 1.2.4, the mass-transfer rate in

agitated contactors is usually reported in terms of the volumetric

53

Table 4.1 Scheme of Experiments

54

Set Number

1

2

3

4

5

6

7

8

Gas Flowrate

mVs

0

1.54E -04

3.68 E -04

6.81 E -04

1.54E -04

3.68 E -04

6.81 E -04

0

Baffle Type

Vertical

Vertical

Vertical

Vertical

Horizontal

Horizontal

Horizontal

Horizontal

55

average mass-transfer coefficient, k^a, which is the product of the

average interfacial area per unit volume of the dispersion, 3, and

the mass-transfer coefficient, kj. As shown in Chapter 2, for a

fast chemical reaction, like the oxidation of sulfite used in this

investigation, the value of k is VkD (Eqn. 2.1 1), where k is the

reaction rate constant and D is the molecular diffusivity of oxygen

in the liquid. Both these quantities are physical properties which

are independent of agitation conditions. Hence kj is constant at a

given temperature. Consequentially, the average interfacial area,

a, can be used to evaluate the mass-transfer rate.

Two types of average interfacial area may be defined; one

defined on the basis of area per unit volume of the dispersion, 3,

and the other on the basis of area per unit volume of the liquid, 3.

They are related according to.

a = l -£

where e is the fractional gas holdup. An examination of the

experimental data revealed that when 3 was correlated with the

impeller speed and the gas flow rate, the spread was smaller

compared to the case when a was correlated. Thus it was decided to

report the experimental results in terms of a'.

It is common to report the data of mass-transfer performance

in terms of dimensionless correlations. A dimensional analysis

indicated that a.' can be correlated according to the following

dimensionless relation.

56

â'D = f (NR^, Npp, N^e, N^, H/To, Hi/H.. other geometric ratios).

The values of a11 the geometric ratios except H/T were constant for

all the runs, so their effect could not be considered. The same fluid

type was used in all the runs, therefore the fluid physical

properties (e.g., viscosity, surface tension, density) were fixed and

their effect could not be studied independently. Therefore, the

effect of Reynolds number and Weber number which involve fluid

physical properties could not be studied. Also, the impeller

diameter was constant, so the effect of Froude number could not be

considered. This left only the impeller speed and the gas flow rate

as the two independent variables. Thus in this investigation, the

results of mass-transfer rates are reported in terms of the

impeller speed and the gas flow rate directly.

4.2 Normalization of Data

During different runs in a set, the liquid volume in the

contactor diminished gradually due to sample taking and therefore

the liquid height H varied from one run to another. Because the

values of interfacial area depend on the liquid height, before

attempting to compare and discuss the results of different runs,

this effect of differing liquid height had to be considered.

According to Westerterp et a1.. (1963), the relation between a' and

H/T is given by,

H (a*)H/T=i = a' — = a'i

57

This relationship was tested in order to bring the results to a

common basis of H / T = l . A procedure similar to the one used by

Westerterp et a1. ( l 963) was foHowed.

In each set, one run was selected to investigate the influence

of H/T. This was done by varying the liquid height while keeping a11

the other conditions (i.e. gas flow rate, rotational speed, and the

contactor configuration) constant, calculating the values of a' at

di f ferent H/T values, and plotting them against H/T on a log-log

paper. A linear regression line was drawn through the points and

the value of the slope, q, was determined. The individual values of

q varied between -0.7 and -1.2 with an average value of about - 1 .

Dependency of q on the gas flow rate, Qg, or the rotational speed,

n, could not be determined due to the limited data.

Taking q = - 1 , the values of 3 were then converted to a common

basis of H/T = 1. These values are denoted by â ' i , and are given by

H a'i = (a " )H /T= i = a' — •

Most of the data in l i terature are reported on this basis (See for

example, Midoux and Charpentier [ 1984]).

4.3 Validity of the Model and the Accuracv of Experimental Data

Before discussing the results, it is important to address the

issues of experimental data reproducibility and the validity of

di f ferent assumptions used in the calculation procedure described

in Chapter 2.

58

To check the reproducibility, six randomly-selected runs

were reproduced. Table 4.2 shows the results of these runs.

The dâta indicate that the values of â'i were reproducible within

115% accuracy.

Now the validity of the assumptions made in developing the

calculation procedure is examined. Recall here that following main

assumptions were made in the derivation 1n Chapter 2:

• Henry's law relates the interfacial concentration of gaseous

solute in the gas phase and the liquid phase.

• Resistance to mass-transfer on the gas side is negligible.

• Film theory applies.

• The gas in the liquid is fully mixed.

The maximum partial pressure of oxygen in the inlet air was

22.09 kPa (See Table B. 1 in Appendix B). For these conditions,

Henry's law can be used for predicting the equilibrium solubility of

oxygen, in water and electrolytic solutions, in this range of oxygen

partial pressure. (See for example, Hougen, Watson and Ragatz

[1970]).

The assumptions of negligible mass transfer resistance in the

gas side and the applicability of film theory are Justified by the fact

that the experimental results obtained by different investigators

using the chemical method same as the one used in this

investigation, were within ±20% accuracy of the results of

interfacial area obtained from physical methods. (See for example

Midoux and Charpentier [ 1 980].)

59

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The assumption of fuHy mixed gas phase in the liquid for runs

wi th vertical baffle configuration can be Justified based on the

experimental results of Mehta and Sharma (1971) who used agitated

tanks of similar scale and geometry to the one used in this

investigation operated at similar conditions. They compared their

results wi th measurements of interfacial area by physical methods

and showed that the assumption of a fully mixed gas phase gives

close agreement (within i 15%) between the results from chemical

method and those of physical methods. Also, in this investigation,

visual observations indicated that there was a very high

recirculation of the gas within the contactor. This also suggests

that the gas phase was close to being fully mixed. The assumption

of fu l ly mixed gas phase for runs wi th horizontal baff le

configuration was tested from independent measurements of power

of agitation the details of which can be found in Section 4.5.

4.4 Comparison of Results for Horizontal and Vertical Baffles

4.4.1. Average Interfacial Area

Figure 4.1 shows the plots of the average interfacial area per

unit volume of liquid, a' i , vs. impeller speed , n, wi th, the injected

gas flow rate, Qg, as a parameter for vertical baffle configuration.

Two dist inct regions could be identified: One at impeller speed

lower than 13.3 rps. and another at impeller speed greater than

1 3.3 rps. The former (n < 13.3 rps.) is a region with l i t t le agitation

e f f ec t ; where the average inter facia l area increases w i th

increasing gas flow rate and increases very slightly with impeller

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62

speed. The latter (n >13.3 rps.) is a region with strong agitation

effect; where the average interfacial area seems to be independent

of gas flow rate and increases linearly with increasing impeller

speed.

These observations are consistent with those reported by

Westerterp et_al.,(1963), Mehta and Sharma (1971), and others. It

is generally agreed that there is no effect of agitation on the

interfacial area below a certain critical speed, and therefore, there

is no sense in operating an agitated contactor below this critical

impeller speed.

No attempt was made in this investigation to determine the

exact crit ical speed, because in practice most agitators are

operated at much higher speeds in the region with strong agitation

effect. Therefore, the effect of gas flow rate, Qg, and impeHer

speed, n, in that region was examined in more detail for both

horizontal and vertical baff 1e configurations.

Figure 4.2 shows the plots of 3\ vs. n at different gas flow

rates for horizontal baffle configuration. Here too, two distinct

regions are identified with critical speed between 13.3 rps. and 20

rps.

Figure 4.3 shows the plots of a'i vs. Qg with n as a parameter

for vertical baffle configuration. It is seen from these plots that

there is l i tt le effect of Qg on a'i above the impeller speed of 13.3

rps. Unfortunately, there are too few data points to conduct a

meaningful statistical analysis. Figure 4.4 shows the plots of a'|

63

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66

vs. Qg for horizontal baffle configuration. Here too litt le effect of

Qg on â' 1 could be observed for impeller speed above 1 3.3 rps.

Based on the results above, it was assumed that for impeller

speed above the critical speed, a'i is independent of Qg. In that

case a linear regression line was drawn through all the data points

with n > 13.3 rps. for vertical baffle configuration. Figure 4.5

shows these points and the line obtained by linear regression. The

correlation of Westerterp et a1.. (1963) is also shown for

comparison. Figure 4.6 shows the data points with n > 13.3 rps. and

the f i t ted line for horizontal baffle configuration.

The lines for the two cases are compared in Figure 4.7. It is

seen that for an impeller speed in the range of 20 to 24.2 rps. (a

range of practical importance) the measured values of a.'i when

horizontal baffles were used were 80% to 130% higher than the

values when vertical baffles were used.

4.4.2 Gas Holdup

Figure 4.8 shows the plots of gas holdup, e, vs. impeller speed

at different gas flow rates for vertical baffle configuration.

Figure 4.9 shows these plots for horizontal baffle configuration. It

is seen by comparing Figs. 4.8 and 4.9 that the percent improvement

in the gas holdup for horizontal baffles over vertical baffles

corresponds very nearly to that observed in average interfacial

area, a' i . Also, a closer examination of the trend of e vs. n in each

case (vertical and horizontal) shows that each is very similar to the

trend of â'i vs. n. (Compare 4.1 with 4.8 and 4.2 with 4.9). These

67 7 7

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69

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72

indicators wil l be examined in detail in the section on analysis of

results.

4.4.3 Power of Agitation

Power of agitation, PQ, for runs without gas injection for both

horizontal baffle configuration and the vertical baffle configuration

is shown as commonly used curves of Power number, Np , vs.

Reynolds number, NR^ , in Fig. 4.10. It is seen that at the same

value of impeller speed, the same fluid and impeller, the Power

number when horizontal baffles are used was 25% to 31% lower

than that when vertical baffles are used.

The power of agitation when gas is injected from the sparger,

Pg, depends on the impeller speed and the flow rate of the injected

gas. It is common to present this dependency in the form of curves

of P3 vs. the Aeration number, N^. These curves for the vertical

baff le configuration and the horizontal baffle configuration are

shown in Figs. 4.1 1 to 4.13. In general it is seen that at low values

of gas flow rate (0.154 1/sec) and high values of impeller speed

(23.3 rps.) the Pg is 33% lower for horizontal baffle configuration

than that for vertical baffle configuration. At increasing values of

injected gas flow rate and decreasing values of rotational speed,

the d i f ference in P^ for ver t ica l and horizontal baf f le

configurations becomes smaller until at injected gas flow rate of

0.68 1/sec. and the impeller speed of 20 rps. the difference is

hardly 3%. It is obvious from the above discussion, that the

dependency of Pg on N ^ is not unique but differs from one impeller

73

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77

speed to another. The way to bring these curves together is to

somehow incorporate the gas holdup, e, in the relation. This is

commonly done by plotting P^/{]-e) vs. the Aeration number, N^.

However, it was found that when P^/e was plotted vs. N^ the

spread of the data points was smaller.

The physical significance of Pa/(l-£) is that it is the power

input per unit volume of the liquid; whereas, the physical

significance of P^/e is that it is the ratio of power input per unit

volume of liquid to the volume of the gas in the contactor per unit

volume of liquid.

P^/e = 'Pa ] / (e ^ L 1 - £ . [\-e}

Thus the power of agitation in tank with injection of gas is

represented as curves of Pg/e vs. Aeration Number (Qg/nD^).

Figure 4.1 4 shows the plots of Pg/e vs. N/ and their corresponding

linear regression f i ts for tanks vertical and horizontal baffles. It

is seen from figure 4.14 that the power for an agitated contactor

with horizontal baffles to have the same gas holdup as in the case

of vertical baffles is 50 to 57% less than that required for vertical

baffles at a given Aeration number.

4.5 AnaJvsis of Results

It has been indicated above that when horizontal baffles were

used the average interfacial area, â'i / was 80% to 130% higher

than when vertical baffles were used. Also, it was found that the

power of agitation for runs without gas injection was 25-31% lower

78

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79

for horizontal baffle configuration than that for vertical baffle

configuration. It was also seen that for runs with gas injection,

the power of agitation per unit gas holdup, Pg/e, was 50 to 57%

lower for horizontal baffle configuration than that with vertical

baffles. In this section an attempt is made to identify the causes

of these results.

It was indicated in section 4.4.2. that the gas holdup, e, in the

horizontal baffle configuration and that in the tank with vertical

baffles change with rotational speed in a manner similar to the

variation of 3, in the respective cases (see Fig. 4.1 and 4.8 and 4.2

and 4.9). This observation was scrutinized further by the following

analysis:

Since â'i snd e are measured independently, then from these

measurements a mean gas bubble diameter can be deduced from the

following relation.

_ 5 e d =

a' 1 1 -e

Fig. 4.15 shows plots of d vs. n for vertical baf f 1e configuration. 11

is seen that for n > 13.3 rps., the mean bubble diameter remains

essentially constant. A linear regression line was drawn through

a11 the points for n > 13.3 rps. and the slope of this line was found.

to be close to zero. This suggests that the mean bubble diameter,

d, is independent of n. The average value of bubble diameter for

vertical baffle configuration was found to be 2.53 x 10"^ m.

Similar analysis for horizontal baffle configuration indicated that

80

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81

the bubble diameter remained constant in this case too. The

average value of bubble diameter was f ound to be 2.51x10"^.

From this analysis, it can be concluded that the mean bubble

diameter is the same for vertical and horizontal baffles. This

implies that the increase in average interfacial area observed when

horizontal baf f les were used was probably due to a higher number of

gas bubbles in the dispersion and not due to smaller gas bubbles.

Next the plausible causes of a higher number of bubbles in the

dispersion and the lower agitator power requirement when

horizontal baffles are used are examined. It appears that the main

reason is surface aeration when horizontal baffles were used. In

the runs with horizontal baffles when no gas was sparged it was

observed visually that gas bubbles penetrated into the liquid from

the liquid surface and circulated in the liquid. This is called surface

aeration. No surface aeration was observed in runs with vertical

baffles. Below an attempt is made to analyze this phenomenon in

some detail.

The rates of gas recirculation in the tank are related to the

power of agitation as discussed in Section 1.2.3. Recall that

Roustan (1978) developed a technique for getting a unique power

reduction curve for a given impeller by plotting the ratio of power in

presence of gas to power in absence of gas, Pa/Po, vs. the effective

Aeration Number, H^^. Values of N^^ were calculated by Eqns. 1.2

and 1 -4. The curve developed in this manner is unique for a given

impeller and does not depend on the tank geometry or the baffle

arrangement. Figure 4.16 shows a plot of Pg/Po vs. N/^^ for

82

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83

vertical baffles and a third order polynomial regression curve

through the points.

Consider the scheme of gas flow rate in the contactor shown in

the diagram on below:

Here Q^ denotes the surface aeration rate, Q^ the internal gas

recirculation rate (i.e gas recircualting within the liquid), Qc' is the

total gas recirculation rate (Q^ + Q^). The total gas recirculation

rate, Q^', in absence of gas injection can be estimated from

experimentally measured quantities (Power of agitation and Gas

Holdup) as follows:

Q E QE+Qg ^

?# <b

Q: i wT"wwtmw

P tttWWTWfH IHiMM oo

fcllMINIIMIMIMIMIIIIIIimilllMMIIII ^ s V s s • • .w.y.;:

^^táÊÊÊiitÊtmHtiÊiáiiiíiliii

g

To estimate the rates of total gas recirculation, QQ', in the

absence of gas injection, it was assumed that the decrease in the

Power number with increasing Reynolds number observed for

horizontal baffles in Fig. 4.10, was solely due to surface aeration.

If there had been no surface aeration, the Power number for

84

horizontal baffles would have remained constant at a value of 5.5,

which is the extrapolated value from the Np -Np^ curve for

horizontal baffle configuration in Fig. 4.10. Using this value of

Power number the value of an hypothetical power requirement, PQ',

without surface aeration was calculated for each run with

horizontal baffle configuration. The power reduction PQ/PO' was

then obtained for each run using the value of PQ' calculated above

and the observed values of the power of agitation without gas

injection, PQ.

Now as discussed above, the curve of P /Po vs. N^^ shown Fig.

4.16 does not depend on the baffle configuration. Therefore, it is

assumed that this curve can also be used for operation with

horizontal baffle configuration. tJsing the curve in Fig. 4.16 the

effective Aeration Number, N^^, required to obtain a given power

reduction can be obtained. Now noting that,

N A " = nD

then, when Qg = 0, which is the case here,

Qc' = ^A^ ^^^'^

Figure 4.1 7 shows the values of OQ' thus obtained as a function

of impeller speed. It is seen from fig. 4.17 that the total rates of

gas recirculation are 2 to 15 times higher than the rates of injected

gas flow rates, Qg, which were in the common range (0.1 to 0.7

1/sec.) of operating conditions for the range of impeller speeds

used. This observation supports the assumption of fully mixed gas

phase for horizontal baff 1e configuration.

85 co C\í

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or

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=> T

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cn — (\3 - ^

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86

The rates of gas recirculation, QQ', thus obtained are related

to surface aeration rates, Q^, as follows: The recirculation of the

gas in an agitated contactor can occur either within the contactor,

QQ, or the exit gas may be reincorporated by surface aeration, Q ,

as shown in the diagram on the page before, which means that Q ' =

Qc - QE-

No method was available in this investigation to measure either

QQ or Q^ individually. Therefore the value of Q^ cannot be calculated

directly. However, in the extreme case when Qc = 0, 0£ = QQ. This

of course represents the highest limit on the value of Q .

CHAPTER 5

CQNCLU5I0NS AND RECOMMENDATIONS

5.1 Condusions

The ef fect of horizontal baff les on the performance of

mechanically agitated contactor was tested. The results indicated

that under the range of conditions investigated, the horizontal

baffles proved to be better compared to the conventional vertical

baffles in terms of lesser power requirement and higher values of

average interfacial area per unit liquid volume. The following list

summarises the conclusions:

1. Under the range of conditions investigated, the values of

average interfacial area are 80-130% higher when horizontal

baffles were used than when vertical baffles were used.

2. Power of agitation without gas sparging was 20-30% less

for operation wi th horizontal baffles than that wi th vert ical

baffles.

3. Power of agitation to gas holdup ratio for agitation in

presence of gas sparging was 50-57% less for operation wi th

horizontal baffles than that with vertical baffles. This implies

that the power of agitation required for a given value of gas holdup

at agiven impeller speed and gas flow rate, is 50-57% less for

operation with horizontal baffles than that with vertical baffles.

4. It is shown that the increase in average interfacial area

observed for horizontal baffle configuration over that with vertical

87

88

baffle configuration is due to higher gas holdup in the system rather

than smaller size of bubbles.

5. Visual observations indicate that in operation wi th

horizontal baffle configuration, the gas penetrates into the liquid

from its surface. This is also called surface aeration.

6. A methodology to make rough estimates of the rates of

total gas recirculation, QQ', within the liquid, based on the power

reduction curve f or the given impeller was proposed.

5.2 Recommendations

Based on the the results and experience of this investigation,

the foHowing recommendations are made:

1. Additional experiments should be carried out over a wider

range of impeller speeds and gas flow rates than is used in this

investigation. It is particularly important to carry out experiments

at higher impeller speeds because in industrial practice values of

impeller speeds as high as 2000 rpm. are used. This will require a

drive with higher power than the one used in this investigation.

2. Effect of fluid properties such as viscosity, density and

surface tension should be studied to get more insight into the

results of this investigation.

3. Experiments should be carried out w i th larger size

contactors to develop scale-up relations.

4. Surface aeration was observed in the operation of the

contactor with horizontal baffle configuration and was suspected to

be the main cause of the increased average interfacial area and

89

lower power requirement the operation with vertical baffles. In

this investigation, means were not available to measure the rates

of surface aeration directly. It is strongly recommended that the

rates of surface aeration be measured independently. A possible

technique to measure rates of surface aeration has been suggested

by Matsumara et a1.. (1977).

5. Different configurations of horizontal baffles should be

examined for further improvement in the contactor performance.

These may include:

• Number of baffles.

• Location of baffles relative to the liquid surface.

• Pitch of the baffles.

• A combination of horizontal and vertical baffles.

6. The most promising potential application of horizontal

baffles appears to be in Fermentation processes. Therefore, it is

suggested that the performance of an agitated contactor with

horizontal baffles be tested for fermentation broths or simulated

fermentation broths. A possible system that simulates the

rheological behavior of fermentation broths is a paper pulp

suspension as suggested by Loucaides and McManamey (1973).

LITERATURE CITED

Brui j in, V/., van"t Reit, K.,and Smith, J.M., Trans. Instn. Chem.

Enanrs.. (London). 52, 99 (1974).

Calderbank, P. H.. Trans. Instn. Chem. Engnrs.. (London). 36, 443

(1958).

Calderbank, P. H., Trans. Instn. Chem. Engnrs. (London). 37. 173

(1959).

Cooper, R.D., and Wolf, D., Canad. J. Chem. Ena.. 94, 46 (1968).

Danckwerts, P. V., and Sharma, M. M.. Br. Chem. Enanr.. J ^ , 522

(1970).

Danckwerts, P. V., and Sharma, M. M., Chem. Enana. Sci.. 3 1 , 767

(1976).

Elseworth, R., Vv'illiams, V., and Harris-Smith, R., J. ADDI. Chem.. 7,

261 (1957).

Hassan, I. T. M., and Robinson, C. W., A.I.ChE.J.. 23, 48 (1 977).

Hiegbie, R., Trans. A.I.ChE. 12,365 (1935).

Holland, F. A., and Chapman, F.S., "Liquid Mixing and Processing,"

Reinhold, NewYork, (1966).

Hughmark, fí Ind. Enann Chem.. Proc. Des. Dev.. i 9 , 638 (1980).

Hyman, D., and Van Den Bogaerde, J. M., Ind. Engng. Chem., 52, 757

(1960).

Joshi, J.B., Pandit, A.B., and Sharma, M.M., Chem. Engng. Sci., 27

(6),813(1980)

Lewis, W.K., andWhitman, W., Ind. Engng. Chem., 16, 1215(1924).

Loung, H. T. and Volesky, B., AJ.ChE.J., 25, 893 (1979).

90

91

Loucaides, R., and McManamey, W. J . , Chem. Enana. Sci.. 28, 21 65

(1973).

Mann, U., and Rubinowitch, M., Ind. Ena. Chem.. Proc. Des. Dev.. 22.

545 (1983).

Matsumara, M., Masunga, H., and Kobayashi, J . , J. Ferm. Tech.. 55,

388 (1977).

Mehta, V. D., and Sharma, M. M., Chem. Engng. Sci.. 26. 461 (1 971).

Mehta, V. D., Ph.D.(Tech.) Thesis, Univ. Bombay, (1970).

Michael, B. J . , and Miller, S. A., A.I.ChE. J.. 8, 262 (1962).

Midoux, N., and Charpentier, J. C. Int. Chem. Enana.. 24 (2). 249

(1984).

Nagata, S., "Mixing", Wiley, New York (1966).

Nagata, S., Yamamoto, K., Hashimoto, K., Naruse, Y., Chem.Ena.

(Jaoan). 23. 565(1959).

Oldshue, J . Y., "Fluid Mixing Technology", McGraw-Hill, NewYork

(1966).

Preen, B. V., Ph.D. Thesis, University of Durham, South Afr ica

(1961).

Roustan, M., Thesis, Univ. de Toulouse, France (1978).

Rushton, J . H., Costich, E. W., and Everette, H. J . , Chem. Engng.

Proar.. 46. 395 (1950 a).

Rushton, J . H., Costich, E. W., and Everette, H. J. . Chem. Enana.

Progr.. 4^ . 467 (1950 b).

Scot t , W.W., and Furman, N.H., "Analytical Chemistry", D.Van

Nostrand Corp, New York, (1965).

92

Snijder, R.J., Hagerty, P.F., and Molstad, M.C., Ind. Enana. Chem..

49, 689(1957)

Uhl, V. W., and Gray, J. B., "Mixing, Theory and Practice", Academic

Press, New York (1966).

Van't Reit, K., Boom, J. M., and Smith, J. M.. Trans. instn. Chem.

Enars.(London). 54, 124(1976).

Van't Reit, K., and Smith, J. M., Chem. Enana. Sci.. 28, 1 031 (1973).

Van't Reit, K., and Smith, J. M., Chem. Engng. Sci.. 28, 1 093 (1974).

Westerterp, K.R., Van Dierendonck, L.L., and De Kraa, J.A., Chem.

Enana. Sci.. 18. 157(1963).

APPENDIX A

A SAMPLE CALCULATIQN OF MASS-TRANSFER COEFFICIENT

93

94

The procedure for calculation of mass-transfer coefficient

from experimental observations is shown below. The calculations

are carried out for Run Number 5 of Set 1 (Appendix B). For

convinience the contactor configuration, the experimental

conditions and the pertinent observations for this particular run are

also shown below.

Contactor Confiauration

• Impeller Diameter, D (m) = 0.0762.

• Tank Diameter, T(m) = 0.305.

• Impeller Height off the Bottom of the Tank, Hi (m) = 0.15.

Liquid Height, H (m) = 0.45. •

Experimental Conditons

• Gas Flow Rate at inlet, Og^p^, (mVs) = 0.000154.

• Rotational Speed, n (rps) = 23.33.

• Ambient Temperature, T (°K) = 295.522.

Atmospheric Pressure, Pgi-pn (kPa) = 100.88. •

• Moisture Content of ambient air, X^ (kmole water/kmole dry air)

= 0.0064.

Observations

• Dispersion Height, H^ (m) = 0.47.

• Sample Analysis

The samples withdrawn were anlysed according to the

procedure described under Section 3.2. Thiosulfate titration reading

(TT) varied with time interval according to the table below.

95

Time, t , (min) Thiosulfate Titration reading, TT (m1)

5 16.4

10 22.3

15 28.1

20 34.0

A plot of TT vs. t was prepared and the slope of the best

s t ra ight line through the points was determined by linear

regression.

• Slope of theTT vs. t Plot, p, = 1.174.

Calculations

Sten A: Calculation of Inlet

/Mr romnosition

Total pressure at inlet, P (kPa), 0.45 X 1.096x10'x 9.8

= Patm ^ Hpg/1000 = 100.88 — •

P = 105.71 kPa.

Molar gas flow rate at inlet, nøin' (kmol/sec),

p. Q^. 105.71 X 0.000154. ^ ^ ^in^Gin ^ = 6.626 X 1 0 - ^

RT 8.314 X 295.522

nøir^ = 6.626 x 1 0 " ' kmoles/sec.

Molar Flow Rate of Dry Air at Inlet , kmole/sec

nrin 6.626 X 1 0 " ' ^ ^^ , Giri ^ 6.584 X 1 0 - ^

(1 ^ X ^ ) (1 + 0.0064)

96

Knowing the composition of dry air (21% Oxygen and 79% Nitrogen),

the composition of inlet air was calculated and is shown below.

Component

Qxygen

Nitrogen

Water

Molar flow rate

kmole/sec

1.3826 X 10-6

5.2014X 10-6

4.2 X 10-8

Steo B: Calculation of Liauid Volume and Hold-HJU

Mole Fraction

0.2087

0.7850

0.0063

Partial Pressure kPa

22.06

82.98

0.67

Liquid Volume, V|_ (m^)

= T T / 4 X ( T O ) ' X H = 0.25 XTTX (0.305) 2 = 0.033

Vi_ = 0.033 m^

Hold-up of Gas, e ( void fraction)

H = ] - _ = 0.053.

HA

e = 0.053.

StPn C: Ca1riil?>tionof Rate of

frhsorntion of Oxvaen

According to the Analytical Procedure shown in Section 3.2, the

Rate of Reaction of Sulfite was found to be equal to;

—^ ( mmole/l i t /hr) dt

= -150 X (Slope of TT (m1) vs. t (min) plot) = -150 x p = - 1 76.1

97

According to Equation 2.26,

Rate of absorption of oxygen, i-r^)^ (mmole/dit.hr)),

1 dCso Vi = - — -— = 88.05 = 2.45 X 1 0 - ^ kmo1e/(m^sec),

2 dt VR

^"•Â^d "" 2.45 X 10-^kmo1e/(m^sec).

Step D: Calculation of Outlet Flow Rate and Average Concentration

Average gas concentration at the outlet is calculated by trial

and error procedure discussed in Section 2.1.1. The calculation

steps are as follows:

(i) Outlet flow rate Qoout âs guessed as equal to the inlet flow

rate, QQ,^^^

(ii) [RT J

was calculated using Equation 2.29, as follows; av

^RT Jav QGoutVRTj in

(-rÂ^dVR

Q Gout

22 06 2.45 X 1 0 ' X 0.033 - = 0.00373.

8.31 4 X 295.522 0.000154

(ii i) Composition of air at the outlet was calculated as follows;

Partial pressure of oxygen at outlet, (Po^) av, kPa

98

/ Po. PO2 " X R XT = 0 .00373x8.314x295.522 = 9.1645

RT J av

Total pressure at the outlet, (kPa),

Atmospheric pressure, Pgj-pp = 100.88.

Mole fraction of oxygen at the outlet,

(Po2)av = 0.09084.

atm

It was assumed that the air left the contactor saturated with

water vapor; therefore, the partial pressure of water vapor at

outlet was taken as vapor pressure of water at the constnat gas

temperature of 295.522 °K.

Partial pressure of water vapor at outlet, (kPa)

= 2.68.

Mole fraction of water vapor at outlet,

= 0.0266.

Mole fraction of inert was therefore, by difference,

= 1-0.09084-0.0266 = 0.8754.

(iv) The total molar flow rate at the outlet was found by inert

balnce; since, the number of moles of inert remained constant.

Molar flow rate at outlet, nøout' (knnoles/sec),

Molar FI0W Rate of inert at inlet 5.2014 x 1 0 - ' = = 5.942 X 1 0 - ^

Mole Fraction of inert at outlet 0.8754

99

Volumetric flow rate at the outlet, Qoout' (i^Vsec),

•^Gout X R X T 5.942 x 1 0 " ' x 8.3 1 4 x 295.522

atm 100.88 = 0.000145,

(v) Steps (ii) to (iv) were repeated with the new value of Qgout

until constant value of average concentration at the outlet was

obtained. The results of the tr ial are shown below:

Trial f P 0 2 ^

,R T J av

kmole/m^

Mole Fraction 0 Q Gout

(mVsec)

1

2

3

0.00373

0.00396

0.00397

0.09084

0.0964

0.0967

The average concentration of oxygen is therefore,

( ^ l = 0.00397 kmoles/m^ av

0.000146

0.000144

0.000144

Sten F: Calculation of Avearae

Interfacial area

According to Equation 2.24, the quantity a' is given as.

He (-rA)d

ki (Po/RT)av = 93.07 mVm^

APPENDIX B

EXPERIMENTAL DATA

100

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^-"

Û

<l; I D (^

l ^ 4--> <D C/) o

•i->

(N 4 - > <1) co

o **— (^

4-.» (^ Q L-<1> CT

4-» ( ^

r

KD

l O

^

ro

CN

Set

Num

ber

296.6

29

7.7

29

6.1

29

6.6

294.

4 29

5.5

Tem

pera

ture

, T

°K

no

i

100.

7 10

0.6

101

100.

1 10

0.9

Atm

osph

eric

P

ress

ure,

P,

kPa

0.0

068

0.00

71

0.0

056

0.

0077

0.

0075

0.

0064

M

oist

ure

Con

tent

, ,m

ol

of w

ate

r/m

ol

dry

aír

105.

9 10

5.6

105.

4 10

5.8

105.

9 10

5.7

.t—>

cu c

J—>

CL> ro

(T) C

CL -

0.0

00

68

1 0.0

00368

0.0

00

15

4 0

.00

06

81

0.00

0368

0

.00

01

54

Gas

ílo

w r

ate

at

inle

t ,

Qg,

mV

s

22.0

9 2

2.0

1 22

.05

22.0

5 22

.08

22.0

6

4_>

03 ^ u' (^;^ o Q-<_ C Jxí

Q L CU CT> -

(\3 > ^ C

t::°o~

ro 'o

X

CM r-ro

ro ' o

X

CN cr> ro

ro •o

X

ro vO ro

ro 1 o

X

00 vû ro

ro 1 O

X

ro ro

ro ' o

X

00

ro

na

ss t

ran

sfe

r co

eff

icie

nt,

k ,

, m

/s

'

62

.23

65.3

2 6

4.4

3 6

3.2

3 5

9.0

8 6

0.8

3 H

enry

's l

av;

con

sta

nt,

He

02

•D O r~

4 - *

^

c o

4 - >

4 - ^

O^ < V— O c_ <D :^

o (^.

(N •

CÛ

<D

r^ 03

\ -

(f) Oí <•—

CD __

ica

4 - > c (1)

> c_ o H—

c o

4—» (J (D "•"" c cn Cs5 iD

o Q.

t_" 4_) (\3

o CL

C_" o o û .

o cr

2 t_" o C!

E 2 co

"ô c >> o

n rps

5.92

9.65

41000

8.33

6.08

40.58

65000

13.33

5.92

133.35

98000

o CM

5.95

151.48

102000

20.83

6.05

173.28

106000

21.67

6.13

196.61

1 10000

22.5

5.89

210.67

114000

23.33

5.86

232.89

118000

24.17

10

(T) CO iD 4—>

13 o r 4—'

^

c o

4-> •— o> < V -

o c_ <D ^ o a.

ro

cn OJ —

«•— < 4 —

CÛ , c

4—»

o N (_

o X í_ o « « - • c o

4->

í ) (D

CÛ £

<D

o CL

2 L." O

E 2 L. <I) ^ O

CL

<n 4-> 4_>

ra

o Q.

t_ O

o Q.

O

<_'

o

E

co "C o c >-o c:

n rp

s

5.5

8.

95

41

00

0 8.

33

5.25

35

.01

65

00

0

13.3

3

4.5

10

1.4

00086

o CM

4.47

1 1

3.75

10

2000

2

0.8

3

4.37

12

5.1

1060

00

21

.67

4.27

13

6.95

00

00

11

22.5

4.2

150.

2 1

1 40

00

2

3.3

3

4.17

16

5.72

1

1800

0 2

4.1

7

Table B.4 Observations and Calculations for Set 2

104

Set Number:2 Baf fle Type: Vertlcal Gas Flow Rate: 0.000154 m

Run No

Rotational speed, n.rps

Rate of oxygen uptake, - r ^

A -r kmol/mVs x 10~*

Partial Pressure of oxygen ín outlet gas, P02 out, kPa

Gas Flow rate out, -r Qg out, mVs x 10

^ l ^ . ^ 3 { \ - e )He '' ' ^

( l - Ê )

H/T

Interracial area for H/T=l

1

3] , mVm'

Gas holdup, £

Power of Agitaticn.Pg Watts.

Power reauction, f^/ PQ

Aeration number,

M X lO^

Reynolds number, x 10

Npe

1

8.33

0.002

18.74

0.161

0.342

5.99

1.5

8.93

0.0037

8.5

0.88

42

0.408

2

13.33

0.006

17.66

0.159

0.860

15.04

1.46

21.96

0.0091

32.37

0.81

26

0.653

3

20

0.019

12.52

0.149

3.96

69.42

1.^4

99.97

0.04

106.63

0.8

17

1.273

4

21.67

0.022

1 1.95

0.148

4.55

79.37

1.43

1 13.5

0.045

135.16

0.78

16

1.379

5

23.33

0.025

9.75

0.144

6.15

93.07

I.4I

151.6

0.053

153.79

0.73

15

I 485

Vs

6

22.5

0.023

1 1.55

0.147

4.54

79.33

1.4

1 1 1.07

0.044

-

-

15.5

I 432


105

SetNumber:3 Baffle Type: Vertical Gas Flow Rate: 0.000368 mVs

Run No

Rotatlonal speed, n.rps

Rate of oxygen uptake, - r ,

kmol/mVs x 10-^

Partial Pressure of oxygen in outlet gas, P02 out, kPa

Gas FIow rate out, -r Qgout .mVs x 10

\ã 3 (1 - e )he

a

(1-e)

H/T

Interfacial area for H/T=l

1

3 1 , mVm^

Gas holdup. £

Power of Agitatíon.Pg Watts.

Power reductlon, p / p„ a °

Aeration number,

N X 10"^ A

Reynolds number, x I0~^ NRe 1

1

8.33

0.005

18.91

0.388

0.66

1 1.81

1.5

17.71

0.0069

6.76

0.7

10

0.408

2

13.33

0.007

18.45

0.386

0.97

17.29

1 46

25.25

0.0095

26.33

0.65

62

0.653

3

20

0.024

16.07

0.375

3.76

67.31

1 44

96.93

0.039

92.01

0.69

42

1.273

4

21.67

0.027

15.64

0.373

4.25

87.74

1.43

121.18

0.043

109.17

0.63

39

1.379

5

23.33

0.030

15.31

0.371

4.31

93.26

1.41

131.5

0.052

126.4

0.6

36

1 485

6

20.83

0.032

14.96

0.370

5.26

77.23

1.4

103.2

0.043

-

-

40

1.326


06 6

SetNumber:4 Baff le Type: Vertlcal Gas Flow Rate: 0.000681 mVs

Run No

Rotational speed, n,rps

Rate of oxygen uptake, - r .

A -r kmo l /mVs x 10 ^

Part ial Pressure of oxygen in out let gas, P02 out , kPa

Gas Flovy rate out, -r Q g o u t , m V s x 10

lá 3 V 1 n

(1 - £ )he

a

( l - £ )

H/T

Inter facia l area for H / T = l a i , m^/m'

Gas holdup, £

Power of Agi ta t ícn,^^ Wat ts .

Power reduct ion, p^/ p„

Aerat ion number,

N X lO^ A

Reynolds number, x 10~^

NRe

1

8.33

0.007

19.39

0.710

1.02

17 45

1.5

26.18

0.01 1

5.69

0.59

13.5

0.403

2

13.33

0.010

19.21

0.709

1.36

23.32

1.46

34.05

0.012

22.32

0.55

1 1.5

0.653

3

20

0.029

17.73

0.696

4.13

71.01

1.44

102.26

0.041

72

0.54

3

1.273

4

21.67

0.032

17.52

0.694

4.56

73.2

1 4Z

1 1 1.33

0.045

90.1 1

0.52

7

1.379

5

23.33

0.037

17.07

0.690

5.46

93.76

1.41

132.2

0.052

101.12

0.43

6.6

1.485

6

24.17

0.039

17.01

0.639

5.63

97.64

1 4

136.7

0.054

-

-

6.4

1.53


SetNumbenS Baf fle Type: Horlzontal gas Flow Rate: 0.000154 mVs

Run No

Rotatlonal speed, n,rps

Rate of oxygen uptake, - r .

A -r kmol/mVs x 10 ^

Partial Pressure of oxygen in outlet gas, P02 out, kPa

Gas FIow rate out, -, Qgout ,mVs x 10

lá 3 (1 - £ )H? "" ' ^

( l - £ )

H/T

Interfacial area rcr H/T=I

1

a| , mVm^

Gas holdup. £

Power cf Agitaticn^Pg Watts.

Power reducticn, P^/ p. a -'

Aeration number,

N X 10- A

Reynolds number, x I0~^ NRe

1

8.33

0.003

19.26

0.163

0.398

7.03

1.5

10.62

0.0044

3.51

0.95

42

0.408

2

13.33

0.01

16.37

0.157

1.536

27.23

1.46

39.33

0.016

32.56

0.93

26

0.653

3

20

0.025

9.26

0.145

6.341

121.69

1 44

175.23

0.063

92.33

0.916

17

1.273

4

21.67

0.029

7.27

0.141

10.01

177.15

1 43

253.33

0.091

93.2

0.735

16

1.379

5

23.33

0.031

6.63

0.140

I 1.33

201 99

1 41

234.8

0.107

102.74

0.684

15

1.435

6

22.5

0.030

6.77

0.141

1 1.07

196.57

1.4

275.2

O.I

-

-

15.5

1.432


108

Set Number:6 Baf f le Type: Horizontal gas Flow Rate: 0.000368 mVs

Run No

Rotational speed, n.rps 8.33 3.33 20 21.67 23.33 20.83

Rate of oxygen uptake, - r ^

A -, kmol/mVs x 10~^

0.006 0.013 0.038 0.047 0.052 0.048

Partial Pressure of oxyaen in outlet aas, P02 out, kPa

Gas Flow rate out, 3 Qgout ,mVs x 10

kJJ (1 - £ )He

X 10

( l - £ )

H/T

Interracial area for H/T= l ai , mVm^

Gas holdup. £

Power of Agitaticn,^2 Watts.

Power reaucmcn, 9 / p

Aeration number,

N. X 'O^ A

9.49 18.33 13.93 12.03 1.08 1 1.93

0.395 0.339 0.369

0.334

.91

1.5

20.37

.793 6.762

29.33

I ^ô

43.63

0.C037

3.15

Reynolds number, x 10

NRe

r5

0.9

0

0.403

2.92

.44

0.362

9.747

161.97

.43

0.357

1 1.753

95.96

0.360

10.066

17971

62.6

0.013 0.063

~j 0.3

0.33

62

37.75

231.61

41

276.3

0.033

90.47

0.365

42

0.653 273

0.103

1 4

251.6

0.095

95.68

0.723 0.637

39

.379

36 40

1.435 1.326


109

Set Number: 7 Baf f le Type: Horizontal

Run No

Rotational speed, n,rps

Rate of oxygen uptake, - r ,

A -r kmo l /mVs x lO- '

Part ial Pressure of oxvgen in out let gas, P02 out , kPa

Gas Flow rate out, -r Qg cut , mVs x 10

k 1 a 3 Y 1 n

(1 - £ )^* '' ' ^

a

( l - £ )

H/T

Inter facia l area ror H / T = l

1

a i , mVm^

Gas holdup. £

Power of Agitation^Pg Wat ts .

Power reGuction, f^/ p^

Aerat ion number,

N X lO^ A

Reynolds number, x 10~^

NRe

1

8.33

0.008

19.33

0.721

I.OI

13.87

1.5

28.31

0.012

7.1

0.79

13.5

0.403

2

13.33

0.016

19.17

0.714

2.16

37.12

1.46

54.2

0.022

26.6

0.76

1 1.5

0.653

gas FIow Rate: 0.00068

3

20

0.022

18.86

0.71 1

2.67

46.04

1.44

66.3

0.065

73.92

0.681

3

1.273

4

21.67

0.061

14.95

0.673

9.99

171.24

1.43

244.33

0.102

85.19

0.73

7

1.379

5

23.33

0.073

13.39

0.669

12.61

216.52

1.41

305.3

0.127

92.37

0.613

6.6

1 435

mVs

6

24.17

0.075

13.44

0.666

13.32

237.5

1.4

332.5

0.133

-

—

6.4

1.53

APPENDIXC

STRAIN MEASUREMENT WITH A RESISTANCE STRAIN GAUGE

1 10

11

In Section 2.3, we developed the relations for determining the

torque from measurements of strain along the principal axes of the

impeller shaft. The strain measurements are carried out using a

device called a Resistance Strain Gauge. A brief discussion about

the construction and the use of this gauge is given below. For a

detailed discussion please consult the "Pressure and Strain

Measurement Handbook and Encyclopedia" published by Omega

Engineering, Inc. This reference manual is available free .of charge

from Omega Engineering.

As mentioned cursorily in Section 2.3, Resistance Strain Gages

operate on the principal that electrical resistance of a thin metallic

wire varies in proportion to the strain applied to it. These devices

are further classified into different catogories depending on the

material of the resistance. These catagories are; (i) Piezoresistive

or Semiconductor Gauge, which is made from a semiconductor

material like Germanium or Silicon; (ii) Carbon Resistor Gauge; and

(iii) Bonded Metallic Foil Resistance Gauge.

The Bonded Metallic Foil Gauge, referred to as strain gauge

henceforth, is shown in the diagram below. This type of strain

gauge was used in this investigation because it offered ease of

handling and durability, and it is not sensitive to changes in

temperature or humidity. It consists of a grid of very thin metallic

foi l , bonded to a thin insulating backing called a carrier matrix. In

use the carrier matrix is attached to the test specimen with an

adhesive.

1 12

Foil

Carrier Matrix

Leads to connect grid in circuit

When the specimen is loaded, the strain on i ts surface is

transmitted to the grid material by the adhesive and carrier system.

The strain in the specimen can be found by measuring the change in

the electrical resistance of the grid material. It may be noted here

that the strain gauge used in this investigation actually had two

resistances aligned at right angle to each other and at a 45 ° angle

to the principal axes of the shaft. One resistance was subjected to

tensi le s t ra in (^), and the other resistance was subject to

compression strain (vf). (See Section 2.3).

Before we go on to describe the pract ica l s t ra in

measurements, it is necessary to explain a term closely associated

wi th strain gauge applications. This term is called the GAUGE

FACTOR, GF. It is defined as the ratio of the fractional change in

resistance to the fractional change in length. Expressed in equation

form as;

GF = AR/R

AL/L

AR/R

e

1 13

where f denotes the strain. It is a measure of the resistance

change with strain. Gauge Factor is a dimensionless quantity and

the larger the value the more sensitive the strain gauge. It should

be noted here that the change in resistance with strain is not just

due to the dimensional changes in the conductor, but that the

restivity of the metallic foil also changes with strain: The term

Gauge Factor applies to the strain gauge as a whole, complete with

the carrier matrix, not just to the metallic foil. The gauge factor

for each resistance of the Bonded Metallic Foil gauge used in our

investigation was 2.

From the gauge factor equation we see that it is the fractional

change of in resistance that is the important quantity rather than

absolute value of the gauge resistance. For the 120 ohm Bonded

Metallic Foil gauge with a gauge factor of 2 used in this

investigation, the gauge factor equation suggested that for 1 | i f

(microstrain, 1 x 10 '^) the change in resistance would be 240

micro-ohms. This meant that we needed to have micro-ohm

sensitivity in the measuring instrumentation.

Direct measurement of resistance was rendered very difficult

due to the high sensitivity requirement. An alternate way was to

use a Wheatstone bridge circuit, which is a sensitive way of

measuring small changes in resistance.

For our application, the strain gauge with its two resistances,

formed what is referred to as a Half Bridge Configuration in the

Pressure and Strain Measurement Handbook referenced at the

1 ,1

begining of this appendix. The circuit for this configuration is

shown in the diagram below. In the circuit below, R and R^ denote

two resistances used to complete the bride circuit. Rg denotes a

gauge resistance and R] denotes the line resistance. The bridge

cirduit was excited by a d.c. voltage equal to y^^. The output

voltage, VQy from the bridge circuit was amplified by the amplifier,

R, and measured by a voltmeter. For this configuration the strain,

Rg (^e)

Rg (-ve)

f, is given by the foHowing equation. (See "Pressure and Strain

Measurement Handbook and Encyclopedia" page no. E-59).

-4V e = R

G F [ ( 1 + V ) - 2 V R ( V - 1 ) ]

R i l 1 +

l R g^

n the above equation VR is given by the equation below

^ out '

strained VR =

[Vout^ LVin I unstrained

Thus, by measuring the ratio of Vout under strained condition, when

1 15

the shaft is rotating, and under unstrained condition, when the shaft

was at rest, the value of Vp was calculated. The line resistances

were measured by a sensitive ohmmeter.

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requirements for a master's degree at Texas Tech University, I agree

that the Library and my major department shall make it freely avail-

able for research purposes. Permission to copy this thesis for

scholarly purposes may be granted by the Director of the Library or

my major professor. It is understood that any copying or publication

of this thesis for financial gain shall not be allowed without my

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