Transcript
Ryerson University
Department of Chemical Engineering
CHE 415 Unit Operations II
Lab Report
Experiment #8
Agitation
Experiment Performed on 9 November 2009
Report Submitted to
Dr.
By Group # 3 Section # 3 1 (Leader)
2. (Data Reporter)
3. (Safety Officer)
Submitted on: 16 November 2009
Marking Scheme
Formatting Used all 6 writing points in each section of the report / 10
General Appearance; Grammar and Spelling / 5
Complete and Informative Tables and Graphs / 15
Contents Calculation of Accuracy and of Precision of Results / 20
Comparison with Literature Data (expected results) / 10
Discussion on Influence of Procedural Design on Results / 10
Logic of Argumentation / 20
Sample Calculations / 10
_____ Total: / 100
Table of Contents
Introduction 3
Theoretical Background 4
Experimental Procedure 8
Results and Discussion 10
Error Analysis 14
Safety Concerns 15
Conclusions 16
Appendix 17
Bibliography 20
List of Figures and Tables
Figure 1: Agitator flow patterns with respect to baffles 4
Figure 2: Power number against Reynolds number for different impellers 6
Figure 3. Schematic of the Agitation Laboratory Apparatus 8
Figure 4: Effect Diameter on Power at Constant RPM Setting 11
Figure 5: Effects of RPM on Power at Constant Impellor Diameter of 2.5 inch 11
Figure 6: Power Number vs. Reynolds Number 12
Table 1. Results and Calculated Parameters 10
Table A.1. Straight Blade Impeller 17
Table A.2. Curved Blade Impeller 17
Table A.3. Slanted Blade Impeller 17
Table A.4. Raw Data 17
Introduction
There were three objectives that were to be achieved by completing this experiment. The first was to determine the relationship between the power required for mixing and various impeller shapes. The second objective was to determine the effect that diameter of the agitator impeller, as well as the rotations per minute, had on the power required for mixing. The final objective was to determine the power needed if the mixing operation was scaled up to 5000 litres while maintaining the geometry of the tank. The scale up factors that were needed to accomplish this were calculated and evaluated.
In order to achieve the objectives of this experiment, three different types of impellers were used to mix a tank filled with water. The impeller types used were a straight blade, a curved blade and a slanted blade. Also, three different diameters for each impeller type were employed. The impeller was inserted into the motor and then lowered into the tank. The motor was then activated and the system was allowed to reach equilibrium. Different RPM values were chosen and recorded using a tachometer and for each RPM value, also, the torque experienced by the motor was observed using a torque meter. Using the values obtained for power, RPM and impeller diameter, relationships between these values was found using linear regression. These relationships were compared to values from theory. Also, using the impeller type and diameter that showed the closest relationship to theoretical equations, scaling up of the mixer was then completed using formulas from theory.
It was determined that the power required for mixing increase with increasing impeller diameter. Impeller power consumption was observed to be distributed as follows (starting with the highest): straight impeller, slanted impeller, curved impeller. Curved blade at a power setting of 30 was determined to be the most effective for scale up.
Theoretical Background
Agitation generally refers to forcing a fluid by mechanical means to flow in a circulatory or other pattern inside a vessel. Agitation and mixing are widely used in industry because it can blend miscible liquids, disperse immiscible liquids or gases in liquids, mix suspension of solid particles in a slurry, and enhance heat exchange between the fluid and mass transfer between dispersed phases. A typical example is the CSTR reactor, where its contents have to be perfectly mixed to be able to use steady state equations to evaluate the performance of the reaction. In most cases, agitation is achieved by an impeller mounted on a shaft driven by an electric motor. Also, the liquid is normally contained in a cylindrical tank with the liquid height equal to the tank diameter.
For all agitation processes, the type of impeller used is very important, and is chosen based on several factor, one important one being fluid viscosity. They type of impeller used has implications on the flow patterns of the agitated fluid, and on the required power for agitation. Three common types of impellers are three-blade, paddle, and turbine agitators. Each of these impellers has an optimum operating range depending on the viscosity of the fluid.
Figure 1: Agitator flow patterns with respect to baffles
When analyzing power consumption for an agitation process, power number, NP, and agitator/impeller Reynolds Number, NRe,I, are two necessary parameters to consider. The Impeller Reynolds Number describes the type of flow near the impeller and helps to characterize the presence/absence of turbulence in an agitation process. Turbulence allows for optimal mixing conditions, and is therefore normally required in an agitation system. The Impeller Reynolds Number can be calculated as follows :
(1)
where Da = the diameter of the impeller (m)
N = rotational speed (rev/s)
? = fluid density (kg/m3) – changes with temperature
? = fluid viscosity (kg/m/s) – changes with temperature
The flow of the liquid is laminar if NRe,I <10; the flow of the liquid is turbulent if NRe,I > 104.
The power number, Np, describes the ability of the impeller to transport mechanical power with specific rotation speed to a fluid. It is a commonly used dimensionless number relating the resistance force to the inertia force. The following formula can be used to determine the power number (Walas, 1990):
(2)1
where P = power consumption of the system (J/s)
The greater the power number, the more power that can be transported to the fluid and agitation is thus more efficient. It is important to realize that the exponents for N and Da will be treated as theoretical values. It will be the main objective of this experiment to determine if the experimental data correlates to this equation via regression analysis. The relationship between power number and Reynolds number is shown in Figure 2 on a logarithmic graph :
Figure 2: Power number against Reynolds number for different impellers
A final calculation that takes place in process industries is the scaling up of agitator systems. Experimental data is often available on a laboratory or pilot-plant scale and this data is used to create a full scale production process. Based on the assumption that the new process will have geometric similarity to the experimental process, scale-up is a method to translate a process or model to larger sizes using scale up ratio. Therefore, if the geometry of the tank is maintained, the scale up ratio equation is given by:
(3)
Where V1 = volume of experimental vessel
V2 = volume of scaled up vessel
D1 = diameter of experimental vessel
D2 = diameter of scaled up vessel
This equation is derived from the fact that the volume of a tank is ?D3/4 and we are looking at V2/V1. The parameters of the scaled up system, such as the propeller diameter, can be calculated by multiplying the experimental value by the scale up ratio.
Finally, the agitator speed of the scaled up process can be calculated using the following formula:
(4)
where N1 = rotation speed of experimental process
N2 = rotational speed of scaled up process
n = 1 for equal liquid motion
n = 2/3 for equal rates of mass transfer
n = 3/4 for equal suspension of solids
The value for n for this process is 1 due to the fact that the system is an example of equal liquid motion.
Experimental Procedure
Figure 3. Schematic of the Agitation Laboratory Apparatus
Before starting the experiment the safety check was performed. All the switches on all the equipment were checked if they are in the off position. Also the equipment was verified if it is in working order; it was checked for any damages and/or leaks. Also proper safety standards were kept while performing the experiment; safety precautions were taken when handling the rotating equipment such that loose clothing or hair would not get into the equipment and cause severe injury . First the tank was filled to about 75%. A 2.5” straight blade was fastened to the shaft and the assembled item was attached to the motor located above the plastic tank. It was ensured that the set screw is facing the flat part of the shaft. The baffles were installed inside the tank and checked that the baffle ring cleared the shaft. The motor was disconnected from the torque meter and turned on. While the motor was on it was reconnected to the torque meter when the apparatus was ready for operation. Initially the speed of the impeller was set to 10 using the speed dial on the motor. The necessary readings, such as rpm and torque were recorded into the data tables and the same procedure was repeated for speed settings of 20 and 30. Once completed, the device was turned off and the procedure was repeated for the 3” and then 4” straight blades. Once this was accomplished the same process was duplicated for the curved and slanted blades. Once the experiment was completed the tank was emptied and all the equipment was safety checked and secured in a safe and proper manner.
Results and Discussion
Table 1. Results and Calculated Parameters
Diameter
(Inch)
Rotation Setting
Torque (ftlb)
RPM
RPS
Power (Hp)
Power (J/s)
Power Number (Np)
Reynolds Number (Re)
Straight Blade
2.5
10
0.05
373
6.22
0.00148
1.08854
4.39
22371
20
0.12
750
12.5
0.00714
5.25147
2.61
44957.79
30
0.23
1070
17.83
0.01952
14.35696
2.46
64127.79
3.0
10
0.1
375
6.25
0.00298
2.19179
3.5
32369.61
20
0.28
750
12.5
0.01666
12.25343
2.44
64739.21
30
0.55
1070
17.83
0.04669
34.3405
2.36
92344.01
4.0
10
0.32
365
6.08
0.00927
6.818085
2.8
55980.72
20
1.32
730
12.17
0.07645
56.22898
2.88
112053.5
15
0.72
555
9.25
0.0317
23.31535
2.72
85168.03
Curved Blade
2.5
10
0.03
375
6.25
0.00089
0.654595
2.6
22478.89
20
0.04
750
12.5
0.00238
1.75049
0.87
44957.79
30
0.07
1077
17.95
0.00598
4.39829
0.74
64559.38
3.0
10
0.04
364
6.07
0.00116
0.85318
1.49
31437.36
20
0.07
745
12.42
0.00414
3.04497
0.62
64324.88
30
0.1
1078
17.97
0.00855
6.288525
0.42
93069.09
4.0
10
0.09
374
6.23
0.00267
1.963785
0.75
57361.82
20
0.18
747
12.45
0.01067
7.847785
0.38
114631.6
30
0.3
1075
17.92
0.02559
18.82145
0.3
164995.8
Slanted Blade
2.5
10
0.04
375
6.25
0.00119
0.875245
3.48
22478.89
20
0.09
750
12.5
0.00536
3.94228
1.96
44957.79
30
0.14
1079
17.98
0.01198
8.81129
1.47
64667.28
3.0
10
0.1
350
5.83
0.00278
2.04469
4.02
30194.37
20
0.22
730
12.17
0.01274
9.37027
2.03
63030.1
30
0.4
1070
17.83
0.03395
24.97023
1.72
92344.01
4.0
10
0.21
352
5.87
0.00586
4.31003
1.97
54047.17
20
0.82
720
12
0.04684
34.45082
1.84
110488.3
30
1.66
950
15.83
0.12511
92.01841
2.14
145752.4
Figure 4: Effect Diameter on Power at Constant RPM Setting
Analyzing figure 2 shows that increasing the diameter of the impellor at a constant RPM increases the power consumed, but it can also be seen that the three prong curved blades result in the lowest increase in power and that the general trend is less exponential. Figure 3 shows the same trend. Increasing the RPM at constant impellor diameters increases the amount of power consumed, but the curved blades result in much less power use.
Figure 5: Effects of RPM on Power at Constant Impellor Diameter of 2.5 inch
Figure 6: Power Number vs. Reynolds Number
Figure 4 was graphed to show the change in the Power number with respect to Reynolds number for each type of impellor. Comparing these results to the text reference is can be seen that both the straight and slanted follow exactly the same behaviour. All graphs show that as Reynolds increases the power number levels of. The three prong curved blade is not graphed in the reference text of figure 2. The Power Number taken for the scale up is from this figure.
Scale Up
The requirement of scaling for a 5000 L vessel and determining the most appropriate impellor is based on several factors. The most important measure is to achieve proper mixing. The higher the Reynolds’s number the better the mixing, but more power is consumed. The lower the power number is at a certain Reynolds number the less power consumed. From the analysis of Table 1 it can seen that the curved blade at setting 30 is most effective with a power number 0.3 and Reynolds number of 164995. For the scale up of a 5000 litre vessel with this impellor, a motor running at 1.05 Hp is needed. This makes sense because at this scale the RPM is 166 and the diameter Is 0.659 m.
The difference between an analytical relationship and expression is that a relationship is an equation which is determined experimentally and is fit over a specific range of data points while and expression is a group of characters or symbols representing a quantity or operation. To obtain the required analytical relationship the independent variables use where the impeller sizes and shapes. The Froude number is dimensionless variable that in tanks is describes the formation of surface vortices when the impeller agitates the liquid surface. It is based on rotational frequency and is negligible at low angular velocities. That is for systems with low Reynolds number it can be abandoned when completing the design.
Standard agitation is conventional agitation that takes place when a set of design ratios is met. These design ratios are based on the impeller diameter, tank diameter, vertical width of the impeller and horizontal and height from the bottom of the tank. After careful analysis it was determined that the experiment variables do not meet the set specification ratios and therefore this experiment does not follow standard agitation.
Placing more than one impeller in a tank would be required for large tanks in which allows for better mixing and reduces mixing times. They are also used to reduce dead mixing zones in tanks because a single impeller may only produce certain mixing in certain regions of the tank. Installing multiple impellers changes the aspect ratio used in the design of angular velocity and therefore a change of scale up calculation would be needed; the impellers would have to model as mixing stages.
Error Analysis
Errors in the experiment stemmed from a number of sources:
Fluctuations of the torque meter. Due to mechanical nature of the torque meter, high rpm resulted in fluctuating reading which contributed to the error.
RPM meter was laser based and was varying slightly during the measurements.
There is an error incorporated in the scale up assumption. Impellers are assumed to be linearly scalable, and be able to retain the mixing properties obtained at lab scale.
Another source of error dealt with the spring that was used to connect the motor to the torque meter. The spring was old and had been stretched passed its elastic limit and was permanently deformed. The spring’s tension can be related to Hooke’s law if and only if the spring hasn’t undergone appreciable plastic deformation. Because plastic deformation of the spring had taken place, the torque values observed are based on the spring’s tension force which is no longer defined by Hooke’s law. This would cause inaccuracies in the torque meter readings and this would contribute to the inaccuracies observed in the experimental data.
Safety Concerns
The main areas of safety concern in this lab were the mixing blade and the motor. Caution was taken when attaching the blades to the shaft and the shaft to the motor. It was verified that this was completed correctly. During operation, the moving parts of the shaft/blade system could have grabbed any loose clothing or hair. Care was taken to avoid such an incident. Also, this lab dealt with water and this combined with the electricity from the motor could cause electrocution. These three reasons were the most important safety concerns that were monitored.
In the industry, mixers are commonly used. Without adequate mixing, complete uniformity cannot be achieved. This is an issue due to the quality standards imposed on businesses. Due to the size of shaft and blades, mixers are often not run continuously. They are shut down once the tank is opened to prevent danger to the workers. This will not be a fatal issue in our lab due to the relatively small size of the equipment. Loose clothing catching the blade would more likely damage the motor than cause harm to the experimenter.
Conclusions
In summary, the objectives of this experiment were successfully accomplished. It was determined that the power required for mixing increase with increasing impeller diameter. Impeller power consumption was observed to be distributed as follows (starting with the highest): straight impeller, slanted impeller, curved impeller. Curved blade at a power setting of 30 was determined to be the most effective for scale upIn order to increase the accuracy of this experiment, the following actions are recommended:
Replace the plastically deformed spring with a new spring. This will help to reduce some of the error associated with the torque meter readings.
Either re-calibrate the old torque meter or employ the use of a new torque meter. An offset from the zero mark was apparent which would cause errors in the readings taken from it.
Appendix
Table A.1. Straight Blade Impeller
Torque Setting
Torque (ftlb)
RPM
Impeller Diameter (in)
10
20
30
10
20
30
2.5
0.05
0.12
0.23
373
750
1070
3.0
0.1
0.28
0.55
375
750
1070
4.0
0.32
1.32
0.72
(Setting 15 due to limit of operation)
365
730
555 (15)
Table A.2. Curved Blade Impeller
Torque Setting
Torque (ftlb)
RPM
Impeller Diameter (in)
10
20
30
10
20
30
2.5
0.03
0.04
0.07
375
750
1077
3.0
0.04
0.07
0.1
364
745
1078
4.0
0.09
0.18
0.3
374
747
1075
Table A.3. Slanted Blade Impeller
Torque Setting
Torque (ftlb)
RPM
Impeller Diameter (in)
10
20
30
10
20
30
2.5
0.04
0.09
0.14
375
750
1079
3.0
0.1
0.22
0.4
350
730
1070
4.0
0.21
0.82
1.66
352
720
950
Table A.4. Raw Data
Diameter
(Inch)
Rotation Setting
Torque (ftlb)
RPM
RPS
Power (Hp)
Power (J/s)
Power Number (Np)
Reynolds Number (Re)
Straight Blade
2.5
10
0.05
373
6.22
0.00148
1.08854
4.39
22371
20
0.12
750
12.5
0.00714
5.25147
2.61
44957.79
30
0.23
1070
17.83
0.01952
14.35696
2.46
64127.79
3.0
10
0.1
375
6.25
0.00298
2.19179
3.5
32369.61
20
0.28
750
12.5
0.01666
12.25343
2.44
64739.21
30
0.55
1070
17.83
0.04669
34.3405
2.36
92344.01
4.0
10
0.32
365
6.08
0.00927
6.818085
2.8
55980.72
20
1.32
730
12.17
0.07645
56.22898
2.88
112053.5
15
0.72
555
9.25
0.0317
23.31535
2.72
85168.03
Curved Blade
2.5
10
0.03
375
6.25
0.00089
0.654595
2.6
22478.89
20
0.04
750
12.5
0.00238
1.75049
0.87
44957.79
30
0.07
1077
17.95
0.00598
4.39829
0.74
64559.38
3.0
10
0.04
364
6.07
0.00116
0.85318
1.49
31437.36
20
0.07
745
12.42
0.00414
3.04497
0.62
64324.88
30
0.1
1078
17.97
0.00855
6.288525
0.42
93069.09
4.0
10
0.09
374
6.23
0.00267
1.963785
0.75
57361.82
20
0.18
747
12.45
0.01067
7.847785
0.38
114631.6
30
0.3
1075
17.92
0.02559
18.82145
0.3
164995.8
Slanted Blade
2.5
10
0.04
375
6.25
0.00119
0.875245
3.48
22478.89
20
0.09
750
12.5
0.00536
3.94228
1.96
44957.79
30
0.14
1079
17.98
0.01198
8.81129
1.47
64667.28
3.0
10
0.1
350
5.83
0.00278
2.04469
4.02
30194.37
20
0.22
730
12.17
0.01274
9.37027
2.03
63030.1
30
0.4
1070
17.83
0.03395
24.97023
1.72
92344.01
4.0
10
0.21
352
5.87
0.00586
4.31003
1.97
54047.17
20
0.82
720
12
0.04684
34.45082
1.84
110488.3
30
1.66
950
15.83
0.12511
92.01841
2.14
145752.4
Sample Calculations
Density Water ? = 999 kg/m3
Viscosity Water = 1.12 x 10-3 N*s/m2
? = 1
Sample Data for Straight Blade Impeller at Setting “20”
Diameter = 2.5 inch
Torque = 0.12 ftlb
RPM = 750
Power:
= (5 x 750 x 0.12) /63025)
= 0.00714 Hp x (735.5 W/Hp)
= 5.25 W
Angular Velocity
= 750/60
= 12.5 Hz
Reynolds Number
Power Number
Scale Up Calculations
For 4.0 inch curved impellor at 1075 RPM.
Scale up volume: 5000 L
= 5 m3
Parameters of Mixing Drum:
D = 0.281m
H = 0.293 m
= (0.1405 2)?(0.293)
= 0.0182 m3
= [5m3/0.0182 m3]1/3
= 6.49
Diameter:
Da2 = 6.49*4.0in
= 25.96 in
Angular Velocity:
?2 = (1075/6.49)/60
= 2.76 Hz
Reynolds Number
Power
From Figure 4 the Power number Np for a curved impellor at the new Re:
Np = 0.3
=0.3(999)(2.76)3(0.659)5
= 1.07 hp
Bibliography
F. Incropera, D. DeWitt. Heat and Mass Transfer. New York: John Wiley & Sons, 2002.
G.Turcotte. "Agitation." CHE-415 Laboratory Manual, 2009.
Paul, E. L., and V. A Atiemo-Obeng. Handbook of Industrial Mixing: science and practice. New Jersey: John Wiley and Sons, 2004.
Perry, R. H, and D. W Green. Perry's Chemical Engineers' Handbook, 7th ed. McGraw-Hill, 1999.
