Agitation Laboratory Report

University of San Carlos School of Engineering Talamban, Cebu City, Philippines

CHE 422L Chemical Engineering Laboratory 1

Agitation of Liquids Agitation of Water in a Cylindrical Tank

A laboratory report submitted to

Camila Flor Y. Lobarbio, PhD CHE 422L Instructor

by

Carl John Louie G. Navalta

February 06, 2017

1. Introduction Agitation is by far the most common and one of the oldest unit operations used in the field of chemical engineering. It is often interchanged with mixing, but the two are not synonymous. Mixing is random distribution of two separate phases into one another and agitation is an induced motion of a material in a specified pattern inside a container (McCabe and Smith, 1993). There are many purposes upon which liquids are agitated. These are based on the objectives and the processing steps that liquids will undergo. These purposes includes suspension of solid particles, blending of two miscible liquids, dispersion of gas in liquid in a form of bubbles, formation of emulsion and to promote heat transfer. All these can be done when a turbulent motion within the fluid is present, and this will be accomplished with the use of mechanical devices such as impellers (flat blade turbines and marine propeller) which are attached to a shaft and the shaft is then mechanically driven by an electric motor which gives the shaft work that is necessary to create the specified flow pattern (usually circular motion) in the liquid system. The fluid motion is created with the use of an impeller, and each impeller type has a specific fluid motion created. But in general, impellers are classified into two types: axial-flow and radial flow impellers. Axial-flow impellers are impellers that generate flow currents that are parallel to the axis of the shaft and radial-flow impellers are those that generates currents that are tangential or radial. Axial-flow impellers include propellers which are commonly used for low viscosity liquids. The flow currents in an axial flow is transferred from the impeller to the liquid and will continue to the wall and to the floor of the tank where it is deflected. On the other hand, for example turbines, give a radial and tangential flow wherein currents travel outward of the walls of tank and with almost no vertical motion. As an effect, vortices and swirls can be generated, specially when the impeller speed is high enough. As mentioned, agitation of liquids are done inside a container – a tank or vessel. The tank is usually in cylindrical form, and the top portion of it can be closed or open to air. The design of the tank must promote effectiveness by eliminating sharp corners and dead zones, or regions in which flow currents cannot penetrate. With this, tanks used in agitation have round bottoms and usually added with baffles which works as an additional resistance to the flow of of the liquid inside the tank, and thereby increasing turbulence in the system manifested by the presence of eddies. But as a consequence, additional resistance means higher power requirement to agitate the fluid. Power requirement specifies an agitation tank. This power is required to overcome all the resistances present in agitation, the skin and form drag associated with the motion of the fluid inside the tank. Power is dependent on the flow pattern, impeller types, properties of the fluid being studied, tank dimensions and the height of the fluid inside the tank. It can be analyzed by a mechanical energy balance: 𝑊" =

𝐹

(1) 2



wherein the work done by the shaft of the agitator is equal to the total fluid friction. This fluid friction is produced by the agitating fluid inside the tank. This is true for a batch and continuous (the magnitude of the flow terms – inflow and outflow, are negligible compared to the fluid friction) agitation operations (Foust et al., 1960). In deriving the working equation for the power requirement for agitation, an analysis is made from a baffled tank. As a consequence of the rotational speed, the impeller blade and the resulting fluid motion past the baffles and the wall of the tank is associated with skin friction and form drag. In which for similar systems the drag coefficient is a function of the Reynolds number. The drag coefficient for agitation is called the power number. Empirical correlations of power number and Reynolds number (and other variables in the agitation system, e.g. Froude number) is utilized to estimate the power requirement to rotate the impeller at a specified rotational speed. Dimensional analysis is made to acquire the form of the semi-empirical equation (equation 2) that is useful in solving the power requirement for agitation systems. With this analysis, the dimensions of the tank, baffles if used, and the depth of the fluid inside the tank are specified. Specification on the fluid properties such as the density and viscosity are also important. % & ' ( )* +

=𝑓

( )- &+ ( ) & - (1 2 .

,

0

,

(

, ,… (

(2)

The denominator term on the left side of equation is the power number 𝑁%5 . The first term on the right hand side of the equation is the Reynolds number 𝑁67 , followed by the Froude number 𝑁89 , and the last two terms are shape factors in which they cancel out for geometrically similar systems. The flow of the fluid inside the tank, whether laminar or turbulent, is described by the 𝑁67 . In agitation, when the flow is laminar (𝑁67 < 10 ), 𝑁%5 is inversely proportional to the 𝑁67 , and when the flow is turbulent (𝑁67 > 300) 𝑁%5 is constant. To define, 𝑁%5 is proportional to the ratio of drag force acting on the impeller and inertial stress – related to flow of the momentum associated with the fluid’s bulk motion. 𝑁89 on the other hand is the measure of the ratio of the inertial stress to the gravitational force acted on the fluid (McCabe, Smith, & Harriott, 1993). In the design for an upscale agitation tank, the power requirement and the size of the equipment is conducted initially in a small-scale tank. In order to achieve the same mixing motion, the geometric, kinematic and dynamic similarities are maintained. The design of an upscale tank is based on the ratio of the volume of the fluid in the upscale and the volume of the small-scale tank, and this is reflected in the equation below. B

𝑅=

A- ' AB

(3)

3

2. Objectives of the Experiment a) Compare visually the fluid motion in a baffled and an unbaffled tank agitated by a mechanical impeller. b) Investigate the effect of the impeller speed on the power requirement for agitation. c) Calculate the theoretical power requirements for agitation and compare with experimentally determined values. d) Determine the time required to achieve complete mixing in a baffled or unbaffled tank using an electrolyte tracer. e) Design a large scale mixer using data obtained from the small scale agitation experiments. 3. Methodology 3.1. Methodological Framework Objective 1: Compare visually the fluid motion in a baffled and an unbaffled tank agitated by a mechanical impeller. • • •

The fluid motion obtained in a baffled and unbaffled agitating tank is visually observed. The type of fluid motion is observed by using different types of impellers. Types of fluid motion includes axial, tangential or radial flow. Fluid motions are compared by varying the speed and type of impeller, and observations are in a set of photos of the fluid motion. Observations

Recording – Taking photos

Photos

Objective 2: Investigate the effect on the impeller speed on the power requirement for agitation. • •

The temperature of the water, dimensions of the impeller per impeller type, dimensions of baffles and the composition of the fluid are set constant. The speed and type of impeller is varied to a setting assigned by the instructor. CONSTANTS

•

Twater

•

Impeller dimensions (diameter, elevation, width) Baffle dimensions (length, width) Fluid composition

• •

INDEPENDENT VARIABLE • Impeller speed (rotational)

DEPENDENT VARIABLE

•

Impeller type

Power Requirement

•

Type of tank (baffled or unbaffled)

4

N

D’

ρ

µ

Impeller Type

Determine Reynold’s Number NRe

ρ

Obtain power from Reynold’s Number NPo

N

D’

Obtain power from NPo

P

Objective 3: Calculate theoretical power requirements for agitation and compare with experimentally determined values. •

NPo value is obtained from the graphical correlations of NPo vs NRe from literature for a specific type of impeller.

•

Power requirement is determined from NPo given by the equation 𝑁%5 =

•

Experimentally determined power requirements are compared with theoretical power requirements by calculating the percent difference. N

ρ

D’

Impeller Type Use Power No. correlations

NPo F

Calculate experimental power requirement.

d N

.

µ

Determine Reynolds number

NRe

% & ' (D* +

P (expt)

N

D’

ρ

Obtain power from NPo

P (theoretical)

Compare theoretical and experimental power requirements.

Comparison

5

Objective 4: Determine the time required to achieve complete mixing in a baffled or unbaffled tank using an electrolyte tracer. • • •

Calibrate the conductivity meter with a 0.1N KCl solution. Measure conductivity of the fluid as well as the time elapsed for agitation using a conductivity meter and a stopwatch for a specified impeller speed Plot conductivity versus time and determine the percent difference of the conductivity for the respective time. The mixing time is the time that corresponds to the point at which the conductivity reading is stable within 1 percent (when the sinusoidal curve flattens out).

Conductivity reading Conductivity, λ Time, [m2/cm] t (s) Baffled Unbaffled

λ λ t

tmix t

Objective 5: Design a large scale mixer using data obtained from the small scale agitation experiments. •

Estimate the scale-up ratio by determining the volume of the lab-scale cylinder tank and the full-size agitator by the equation 𝑅 =

• •

AAB

E

F

.

Obtain data on the tank dimensions, impeller dimensions, and the type of tank whether baffled or unbaffled. Calculate the rotational speed and the power requirements for the full-size agitator. ρ

DT

V2

EstimateVscale-up 1 ratio

μ

Calculate the power requirements of the full-size tank.

Determine the volume of liquid in the lab-scale cylinder tank.

H

D’

R

P

Determine the required rotational speed of the N2 full-size tank. N1 n

6

3.2. Materials The table below shows the materials used in the experiment. Table 1. List of Materials And Apparatus Material Water Salt Solution KCl Solution Apparatus Graduated cylinders Steel Tape Beakers Large Pail Wrench Thermometer Stopwatch Equipment Agitator Conductivity Meter

Quantity 7L 350 mL 50 mL Size 100 mL 100 mL -

Quantity 1 1 5 2 1 1 1 Specifications Armfield Jenco

3.3. Equipment The set-up used in the experiment consists of a cylindrical mixing vessel over which is an electric motor (agitator) with a shaft and detachable impeller is mounted, which in this case, a size 4 flat blade turbine and a marine propeller. The mixing vessel has a drain tap and a removable set of baffles. The motor on the top of the agitation tank was coupled to a torque arm wherein it is connected to a dynamometer balance by a cord. Force and mass readings are measured by the balance. The impeller speed is displayed in the RPM meter, and the speed is varied by turning the control knob counterclockwise and clockwise to decrease and increase the speed respectively. Another apparatus was used to determine the mixing time of the vessel. A conductivity meter was used, and was initially calibrated using a 0.1N KCl for the range of 0 to 20 mS. After calibration, the probe was then installed to the tank for the conductivity measurements. The figure on the next page are the equipment and apparatus used in the experiment.

7

Motor

Shaft Control Knob

RPM Meter Dynamometer

Agitation tank

Impellers

Drain tap

Conductivity meter

Torque arm

Probe

Baffles

Figure 1. Equipment and apparatus used in the agitation experiment. 8

3.4. Procedures For the preliminary steps, the cord between the cord and the balance was detached before removing the motor. Same thing was done if baffles were installed. The dimensions of the impeller used were measured and was attached to the shaft assembly. Relevant dimensions such as the width, diameter, and height of the tank and baffles were recorded. The ratio of the impeller elevation above the tank bottom to the diameter of the impeller was made sure that it is within the range specified in relevant literature on power number correlations. The baffles are then placed inside the tank, and were tightened using a screw. The cord was attached to the torque arm and the dynamometer balance was checked for a correct setting. Next, the tank was filled with water, ensuring that the discharge valve was closed. The liquid height to impeller diameter ratio was within the range, and the liquid height was made sure not to exceed 35 cm. The temperature of the water was recorded and water properties (density and viscosity) was determined using literature data available. It was made sure that the control knob was set to zero and then, the support screw was released and the balance came to rest. The support screw was tightened again when the balance was its on rest position and the initial reading was recorded. To study the power requirements and flow pattern by visual observation, the agitator was switched on and ensured that the red indicator lit. The agitator’s RPM was increased using the knob and the speed was recorded. Since the actual RPM differs from the indicated RPM in the range of 50 to 160, it was noted and corrected using the following equation: 𝐴𝑐𝑡𝑢𝑎𝑙 𝑅𝑃𝑀 = 1.26 𝑅𝑃𝑀 𝑅𝑒𝑎𝑑𝑖𝑛𝑔 − 40.84

(4)

The resulting force balance, in grams and in Newtons, was recorded for every set impeller speed. Visual observations were done for the presence of vortex, turbulence strong eddy currents, etc. When the torque arm has already reached the most backward position, the speed was not further increased, and the the speed was set to zero before turning off the power. The same procedure was repeated for an unbaffled tank. In the determination of the mixing time, first the conductivity meter was calibrated using the 0.1N KCl solution. The meter was digital, so the calibration was not rigorous, it was done by pressing the calibrate button that says and wait for a minute to have a reading of 12.9mS. After calibrating, the probe was installed at the agitation tank. The depth of the probe was made sure that it was less than 4 cm when the impeller was running at the required RPM setting. The set-up was checked by the laboratory personnel before turning on the agitator. For the tracer, two portions of 80-mL salt solution was prepared and placed in a separate container. The first 80-mL of tracer was for the agitation for an unbaffled tank, and the other one is for the baffled. At the start of the trial at the desired impeller speed, the initial conductivity of the liquid inside the tank were determined (without tracer), and conductivity readings were taken every 5 seconds. After 10 measurements, an average of the readings was taken and noted as the initial conductivity reading. With the tracer, in one go the salt solution (first 80-mL) was added into the tank that is opposite to the tracer probe/cell and at the same time the stopwatch was started. Readings were taken every 3 seconds during the first 2 minutes of agitation and then the interval was increased to every 10 9

seconds until 5 minutes or until the reading was stable. Then the agitator speed was turned to zero and was switched off. The liquid inside the tank was drained, and the tank was cleaned out of the salt solution, and filled again with water for the next trial with baffles. The same procedure was done for the second run. In shutting down, the impeller and baffles from the tank were taken out to be cleaned and were placed in their designated area. The outer sleeve of the force balance was positioned at its up-most position and was locked so that there is no tension on the cord or in the balance.

4. Results and Discussions 4.1 Fluid Motion in a Baffled and an Unbaffled Tank Table 2. Visual Observation for Fluid Motion at Varying RPM in a Baffled Tank Using Size 4 Flat Blade Impeller

Impeller speed, RPM

Visual Description Side view Top view Eddies are not yet visible, slow radial flow, no vortex formed

50

75

Radial flow is observed, turbulence (swirling) starts to be evident near the baffles

10

Radial flow was evident near the shaft; eddy currents were clearly seen; fluid motion is turbulent

100

150

fluid motion is characterized to be more turbulent (high degree of eddies); moment arm reached backward most position

11

Table 3. Visual Observation for Fluid Motion at Varying RPM in an Unbaffled Tank Using Size 4 Flat blade impeller

Impeller speed, RPM

Visual Description Side view Top view No vortex formation, very slow fluid motion is seen

50

100

eddy currents can be seen; a narrow and shallow vortex (3.95 cm) was developed

12

vortex continues to develop; vortex grew wider and deeper (11 cm); tangential and radial flow is evident, rapid fluid flow

150

200

vortex grew much more wider and deeper (21.5 cm); the tip of the vortex is not sharp; it resembled that of a truncated cone; circular motion is very evident

13

Vortex (28.5 – cm tall) reached the impeller, very turbulent flow

250

Swirling below the impeller is observed (30 – cm vortex), very turbulent flow (vigorous flow pattern)

14

300

Table 4. Visual Observation for Fluid Motion at Varying RPM in a Baffled Tank Using a Marine-type Propeller

Impeller speed, RPM

Visual Description Side view

Top view No fluid motion is observed

50

100

No fluid motion is observed

15

No fluid motion is observed

150

200

Fluid motion is starting to be visible. Specific flow patterns are not yet recognizeable.

16

Fluid motion becomes more evident. Axial flow starts to be recognizeable.

250

Axial flow is dominantly observed with radial flow. Fluid motion intensifies.

17

300

Fluid motion intensifies compared to the previous RPM. Axial and radial flows become more evident. Swirling starts to appear below the propeller.

350

400

Eddies become visible. Swirling intensifies below the propeller. Higher degree of turbulence in the fluid motion.

18

Stronger eddies. Swirling increases in size. Even higher degree of turbulence and eddies compared to the previous RPM.

450



19

Table 5. Visual Observation for Fluid Motion at Varying RPM in an Unbaffled Tank Using a Marine-type Propeller

Impeller speed, RPM

Visual Description Side view Top view No fluid motion is observed. No vortex formation.

50

Fluid motion starts to be visible.

100

150

Fluid motion starts to be visible. Vortex formation starts to appear, with a height of 0.5cm.

20

200

The fluid motion becomes more evident. Vortex increases its height to 1.5cm.

250

The vortex height increases to 3.8cm.

21

Vortex height lengthens to 5.5cm. The width doesn’t almost change. Small swirling appears below the propeller.

300

350

Vortex height increases to 9cm. The fluid motion at the top of the liquid is smooth. Swirling becomes more visible. Vortex reaches the propeller. Increase in vortex width

22

Vortex height increases to 14cm and exceeds the propeller level. Swirling intensifies. Fluid motion becomes rigorous.

400

The presence of eddies and turbulent currents indicates fluid motion and can be clearly observed at higher impeller speed. The type of flow in an agitated vessel is dependent on the impeller being used, the characteristics of the fluid and the specification of the tank, baffles and agitator. The flow pattern observed in the fluid is due to the variation of velocity components from point to point. These three velocity components are radial, tangential and longitudinal or axial. Radial flow acts in the direction perpendicular to the axis of the shaft. Longitudinal, on the other hand, acts in the direction parallel to the shaft’s axis. Lastly, tangential, also known as rotational, acts in a direction tangent to a circular path around the shaft. 23

The two useful flow patterns in agitation, which facilitates mixing, are the radial and axial flow. In this experiment, where the shaft is oriented vertically at the center, the tangential flow is disadvantageous. The tangential motion of the liquid follows a circular swirling pattern around the shaft and creates a vortex in the liquid. Vortex formation is unfavourable because the circulatory currents produced by the tangential component, tend to throw particles to the outside of centrifugal force from which they are drawn to the bottom of the impeller. Hence, leading to poor mixing of components in the agitated vessel and can also cause air entrainment near the impeller. In unbaffled tanks, fluid motion is generally indicated by the formation of a vortex with the rotating shaft as its axis of rotation. As the rotational speed is increased, the vortex region also increased in width and depth. Swirling is another undesirable effect in agitation. The swirling perpetuates stratification at the various levels without accomplishing longitudinal flow between levels. The presence of baffles disrupts the tangential component without impeding the radial or longitudinal flow of the fluid. Thus, no swirling motion and vortex formation is observed. The baffles suppress the formation of a vortex by developing eddy currents or eddies in the fluid as what can be seen from the visual observations presented, which enhance mixing. A turbulent (formation of random waves) fluid motion was also observed especially at higher RPM readings or impeller speed. At higher RPM, the fluid velocity increases which causes the fluid to hit the walls of the baffles at higher velocity. This causes greater interruption and leads to an increased turbulence within the tank. 4.2 Effect of impeller Speed on Power Requirements As the impeller speed of the agitator is varied, the force exerted by the fluid (water) also varies. And the amount of force exerted is measured by a dynamometer which is attached to the moment arm of the agitator. This force is needed to compute for the experimental power requirement, using the equation below. 𝑃 = 𝐹𝑟𝑁

(5)

The power exerted by the motor or the agitator is a function of the speed and diameter of impeller, as well as the tank dimensions (diameter and height), and also the properties of the fluid (viscosity and density). It can also be a function of other factors such as the shape factors (ratios of different tank parameters). However in this experiment, all variables are kept constant except for the impeller speed.

24

9 8 7

Power, W

6 5 4 3 2 1 0 0

50

100

150

200

250

300

Impeller Speed, rpm Baffled

Unbaffled

Figure 2. Power requirement as a function of impeller speed - for baffled and unbaffled tank. Impeller type: size 4 flat blade.

From equation 5, the power required to agitate the fluid inside the tank is directly proportional to the impeller speed N. As the impeller speed increases, the power also increases. This trend is shown in the figure above. Regardless of the type of impeller used and the presence of a baffle, the power required for agitation is increasing with respect to impeller speed.

25

9 8 7

Power, W

6 5 4 3 2 1 0 0

50

100

150

200

250

300

350

400

450

Impeller Speed, rpm Baffled

Unbaffled

Figure 3. Power requirement as a function of impeller speed – baffled and unbaffled tank. Impeller type: marine propeller.

Another type of impeller (marine propeller) was used. The power requirement for this type of impeller was also calculated using equation 5, and the trend of the plot of the power versus impeller speed was the same with that of the size 4 flat blade as shown in figure 2. In the case of the presence of baffles, the power requirement is relatively higher than that of an unbaffled tank. This is true for both impeller types.

4.3 Experimental and Theoretical Power Requirements for Agitation For baffled tanks 𝑁%5 is a function of the 𝑁67 only. In the case of the unbaffled tank, where vortices can form at higher impeller speed, the fluid force is associated with the gravitational force so that 𝑁%5 is a function of both the 𝑁67 and 𝑁89 , because 𝑁89 accounts for the effect of the gravitational force on the fluid. The plot found in p. 507 in the book Unit Operations by Brown (1973), also shown in the annex, presents the curves for the power number as a function of both the 𝑁67 and 𝑁89 and the curves are specified for each impeller type. The plot is used to get the value of 𝑁%5 graphically. Using the equations and correlation, the theoretical power requirement is calculated for each impeller speed and type, together with the calculations for baffled and unbaffled tank. Sample calculations are presented in the annex. These theoretical power requirements are then compared 26

to the experimentally determined power requirement using two types of impeller and is shown in the annex. To visually compare the theoretical and experimental power requirements for each type of impeller and as well as the effect of the presence of baffles in the tank, the power is plotted versus the impeller speed in the figures 4 and 5. 40 35 30

Power, W

25 20 15 10 5 0 0

50

100

150

200

250

300

Impeller Speed, rpm Baffled - Theo (Flat Blade)

Unbaffled - Theo (Flat Blade)

Baffled - Exptl (Flat Blade)

Unbaffled - Exptl (Flat Blade)

Figure 4. Theoretical and experimental power requirements as a function of impeller speed - for baffled and unbaffled tank. Impeller type: size 4 flat blades.

27

7 6

Power, W

5 4 3 2 1 0 0

50

100

150

200

250

300

350

400

450

500

Impeller Speed, rpm Baffled - Theo (Propeller)

Unbaffled - Theo (Propeller)

Baffled - Exptl (Propeller)

Unbaffled - Exptl (Propeller)

Figure 5. Theoretical and experimental power requirements as a function of impeller speed – for baffled and unbaffled tank. Impeller type: marine propeller.

Power requirement for agitation is directly proportional to the impeller speed. As the speed increases, the power also increases. This trend is shown in the plots above. Although two types of impeller was used, the power requirement for both cannot be compared because the maximum rotational speed for the marine propeller was not achieved during the experiment. This is because for a reason that the diameter of the marine propeller used was very small compared to the diameter of the tank, which results to a lesser force that is applied to the fluid. One solution would be to lower the liquid height inside the tank, but from the experiment, the liquid height was lowered but the same output was achieved – maximum rpm was not reached. The presence of baffles inside the tank adds to the resistances already present in the tank. With this additional resistance to fluid flow, the power required to agitate the liquid should be greater in order to overcome all the resistances. This is observed in the figures 4 and 5, wherein for each type of impeller, the power required for a baffled tank is higher compared to unbaffled tank. This occurs at higher impeller speeds starting from 100 rpm. Say, at 150 rpm using the size 4 flat blade impeller, the power consumed is approximately 10 W for baffled and approximately 2 W. But from an rpm of 50 to less than 100 rpm, the power requirement for both baffled and an unbaffled tank is almost the same. Previous experiments in literature suggests that for low 𝑁67 , the power requirement for baffled and unbaffled tank is identical (McCabe et al., 1993). 28

Large differences in the values of the experimental and theoretical power requirement were calculated and is shown in the annex. It is expected that the experimental power requirement is greater than the theoretical power requirement because of the fact that the energy supplied to motor is dissipated and considered as energy loss (heat loss to the environment) and transmission losses in the parts of the agitator (gear box, motor, bearings, etc.). It could be that at the gear box, the friction in the gears reduces the energy as it flows through the shaft and into the impeller (Coulson & Richardson, 1999). As the plots suggest, say at an impeller speed of 75 rpm, the experimental power calculated is 0.7161 which is greater than the theoretical calculated power of 0.4081 W. Of the two impeller type used, marine propellers gives almost the same power requirement for a baffled and an unbaffled tank as shown in figure 5. As suggested in the study of Kato et al. (2009), the correlation of the power number and the Reynolds’ number using a propeller, is approximately the same for an unbaffled and a fully baffled condition. With this, the power offered by a marine propeller in a baffled and an unbaffled tank would be similar. One factor could be is that the diameter of the marine propeller used in the experiment is very small compared to the diameter of the tank, that the axial flow it produces does not reach the baffles at the side of the tank, and thus the power it requires to agitate the fluid is similar to the power it requires when the tank is unbaffled. 4.4 Complete Mixing Time in a Baffled and Unbaffled Tank Using an ElectrolytTracer One of the main aim of measurements of the single-phase mixing behavior in a stirred tank is to obtain a mixing time for the system under investigation. The mixing time is the time taken for a volume of fluid added to a fluid in mixing vessel to blend throughout the rest of the mixing vessel to a pre-chosen degree of uniformity. Before making measurements of the mixing time for a given process, it is necessary to perform a number of flow visualization studies. These tests are designed not only to help decide how the mixing time should be measured, but also to provide information on flow and to highlight regions of poor fluid motion and flow compartmentalization within the mixing system. Mixing time techniques all work on the principle of adding material to the vessel which has different properties from the bulk. Measurements are then made (usually in a controlled volume within the vessel) that show the presence of the added material. The decay of material property fluctuations is used to measure the mixing time for the system. In this experiment, electrical conductivity was the criterion used in determining the complete mixing time in an agitation tank, both baffled and unbaffled. The conductivity probe mixing time technique uses an electrolyte in the added liquid as the marker. NaCl solution was added to the water in the tank to be used as the tracer to observe the changes in conductivity as a function of time. A plot of electrical conductivity versus time is constructed. The point at which the conductivity reading is stable with 0% difference is determined to be the mixing time. The mixing time is determined using the following equation: 29

[5\]^_`aba`c 97d]a\0e[5\]^_`aba`c 97d]a\0fgh [5\]^_`aba`c 67d]a\0

≤ 1%

(6)

If equation 6 is satisfied, that the percent difference between the present conductivity and the conductivity reading at t=∞ is less than or equal to 1, then the mixing time is determined. The figures below show the plot of conductivity reading versus time in a baffled and unbaffled tank using two impeller types: two-flat blade impeller, and marine-type propeller.

3.9

Conductivity, mS

3.4

2.9

2.4

1.9

1.4

0.9 0

50

100

150

200

250

300

350

400

450

Time, s Baffled

Unbaffled

Figure 6. Conductivity versus time plot at 22.3oC and 50RPM for mixing time determination using a two-flat blade paddle.

From Figure 6, it can be observed that for the baffled tank, the conductivity reading starts to reach a percent difference of less than 1% at t=180s, and t=21s for the unbaffled tank. After these time intervals, the readings begin to stabilize but still fluctuate. From the processed data found in the annex, the conductivity fully stabilizes (≤1% difference) at t=240s for the baffled tank and 300s for the unbaffled tank, and these quantities represent the mixing time. It can be noted that the baffled tank approaches uniformity sooner than the unbaffled tank. Furthermore, it can also be noted that the final conductivity readings of the two plots are almost equal, with a very small difference of 0.013mS, despite having different mixing time. 30

The two plots showed that for baffled tanks, a shorter time is needed for it to reach complete mixing. Based from this, we can infer that the presence of baffles serves as an aid in hastening the time for mixing. Without the presence of baffles, a swirling motion is induced which enables the fluid to follow a tangential flow pattern. The said pattern is undesirable because it induces the formation of a vortex which in turn does not promote mixing of the salt solution in the solvent. In principle, the presence of baffles lessened the formation of swirls and converted the fluid motion into a flow pattern that would allow mixing to occur. 4.5 Design of a Large-scale Mixer The power requirement of the tank is a function of the shear stress, inertial stress and the drag force present in the system. These are dependent on the tank dimensions and fluid characteristics (e.g. µ and ρ). It is necessary to identify the effect of the said characteristics in a scale-up process because the scale-up criteria is dependent on the said process specifications. In designing a large-scale mixer from experimental data gathered, the scale-up ratio must be firstly determined in order to have estimate measurements of the dimensions of the large-scale fluid mixing vessel. It is important to establish geometric similarity in designing scale-up designs. Geometric similarity exists between two systems of different sizes if all counterpart length dimensions have a constant ratio. Aside from geometric similarity, it is also essential that both kinematic and dynamic similarities be established between the two systems in order for effective scale-up to happen where fluid motion, velocities and significant forces are all taken into account. Presented below are the estimated equipment dimensions of the large-scale fluid mixing vessel. Table 6. Large-scale Equipment Dimensions of the Fluid Mixing Vessel Equipment Dimensions

Baffles

Diameter, DB [cm] Width, w [cm]

245.9212

Diameter, D’ [cm] Elevation above tank bottom, Zi [cm]

190.0300

Height of the Stirrer Blade, HS [cm]

70.3297

Diameter, DT [cm] Height, H [cm]

267.3461

Width [cm] Height [cm]

21.8907

Length, B [cm]

100.6041

22.3565

Impeller 122.0291

Tank 388.9094

Blade 70.3297

Torque Arm

31

Geometric similarity is generally the basis of the dimensions between the small tank and the large tank. This was emphasized as the dimensions between the two have a constant ratio. This includes that the tank and impeller dimensions to have a constant ratio. The Scale Ratio, R, was obtained using the data from the volume of the tank from the experiment and the given volume of the large-scale mixer. Three different cases have been identified: (a) the power to volume ratios of the lab scale and the large-scale tank are equal, (b) the maximum liquid velocities are equal and (c) the Froude numbers are equal, in designing a large – scale mixer having a holding capacity of 15 m3 of water. Using the experimental impeller speeds, the new agitator speed must be determined. The new agitator speed is then used to obtain the power requirement and mixing time of this large-scale tank. 𝑁k = 𝑁E

E \

(7)

6

where n is based on empirical and theoretical considerations. n=1 for equal liquid motion, n=0.75 for equal suspension of solids or constant Froude number and n=2/3 for equal rates of mass transfer or equivalent power per unit volume. A commonly-mentioned scale-up parameter is the power input per unit volume of a material to be mixed. Power per unit volume is equivalent to the mass transfer rate in a given system. Mass transfer includes dissolving solids or gases or mass transfer between two liquid phases. This scale-up parameter is usually used for gas-liquid systems carrying out fermentations and for liquid-liquid extraction systems. For these types of systems, the power input per unit volume is a main factor affecting mass transfer and extraction efficiency. When equal power to volume ratio is assumed for systems other than those stated above, it can result to serious error in the scale-up design. Another scale-up parameter is the maximum liquid velocity of the fluid. When equal liquid motion is assumed, kinematic similarity is maintained. This scale-up approach is suggested for processes that are termed “flow sensitive”. Another scale-up parameter is the solids suspension. For an assumption of equal solids suspension or equal Froude Number, the level of solids suspension is maintained. For conservative scale-up designs, this assumption is commonly used. Table 7. Power Requirement and Mixing Time for Scaled-up Agitator

Basis Assumption Equal power to

n 0.6667

Scale Up N2 (rad/s) 0.1882 0.3206 0.7529

Unbaffled Theoretical Power Mixing (MW), Time (s) Ptheo 0.27 1.32 17.11

106.12 62.30 26.53

Scale Up N2 (rad/s)

Baffled Theoretical Power (MW), Ptheo

0.1882 0.3206 0.4391

0.27 1.32 3.40

Mixing Time (s) 106.12 62.30 45.48 32



volume ratio Equal maximum liquid velocities Equal Froude number

0.75

1

1.1293

57.75

17.69

0.5647

7.22

35.37

0.1563 0.2662 0.6251 0.9377 0.0895 0.1524 0.3578 0.5368

0.15 0.76 9.80 33.06 0.03 0.14 1.84 6.20

127.80 75.03 31.95 21.30 223.26 131.08 55.81 37.21

0.1563 0.2662 0.3646 0.4689 0.0895 0.1524 0.2087 0.2684

0.15 0.76 1.94 4.13 0.03 0.14 0.36 0.78

127.80 75.03 54.77 42.60 223.26 131.08 95.69 74.42

From the data presented, both baffled and unbaffled mixing system show a similar trend. As the impeller speed increases, the power requirement increases as well however mixing time decreases. Also for increasing values of n, theoretical power requirement decreases and mixing time increases.

5. Conclusions With increased impeller speed in an agitated unbaffled tank, evident vortex formation can be observed; the water draws away from the center of rotation, inducing the vortex. Axial flow is not observable for the unbaffled system. On the other hand, no vortex formation can be observed for the baffled mixing system in this experiment but the formation of eddies was present and the flow is found to be more turbulent compared to the unbaffled system. The energy consumption and mixing effectiveness are influenced by how liquids move and approach homogeneity. Based on experimental results from equal impeller speed settings, the power required for baffled mixing is higher compared to that of the system without baffles which is verified by principle that addition of baffles would induce higher resistance needed to be overcome and thus require a larger amount of power. For both baffled and unbaffled mixing systems, the actual power requirement for agitation is relatively larger than its corresponding theoretical power requirements. The duration to reach complete mixing or a specific mixing intensity is determined by the mixing time. Mixing time was obtained using an electrolyte tracer. Based on the processed data, it takes a shorter period of time to achieve complete mixing for the baffled system compared to an unbaffled one. Maintaining geometric similarity between the small-scale model and the large-scale mixer is important for scale – up design of a large mixer. Geometric similarity is attained by maintaining constant the ratio of all counterpart length dimensions for the small-scale and large-scale system. Aside from constant ratio of length dimensions, another important factor to consider in scaling up is the objective of the agitation process. For scale-up designs, the major problem is not usually in the scale-up calculation, but rather in obtaining a true relationship between the desired 33

performance and the controlling variables or variable-groups. Generally for both baffled and unbaffled systems, impeller speed is directly proportional to the power requirement for agitation and is inversely proportional to the time to achieve complete mixing. (Kato, Tada, Takeda, Hirai, & Nagatsu, 2009) References Brown, G. G. (1993). Unit Operations. New Delhi, India: CBS Publishers & Distributors. Coulson, J. M., & Richardson, J. F. (1999). Coulson & Richardson's Chemical Engineering: Fluid Flow, Heat Transfer and Mass Transfer (6th ed., Vol. 1). Woburn: Butterworth Heinemann. Foust, A. S., Wenzel, L. A., Clump, C. W., Maus, L., & Andersen, L. (1960). Principles of Unit Operations (2nd ed.). Toronto, Canada: John Wiley & Sons. Kato, Y., Tada, Y., Takeda, Y., Hirai, Y., & Nagatsu, Y. (2009). Correlation of Power Consumption for Propeller and Pfaudler Type Impellers . Nagoya Institute of Technology Repository . McCabe, W. L., Smith, J. C., & Harriott, P. (1993). Unit Operations of Chemical Engineering (5th ed.). New York: McGraw Hill.

ANNEX Data Processing & Analysis Report Please see attachment.

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