analysis and design of heat exchanger

8/10/2019 Analysis and Design of Heat exchanger

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HEAT TRANSFER TESTING AND

HEAT EXCHANGER DESIGN

Faculty Advisor: Dr. Guo-Xiang Wang

Teaching Assistant: Mr. Troy Snyder

Written by: Spencer Fulmer

Group Members: Pat D., Mitch, Adam G., Joe K.


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10/1/2014

TABLE OF CONTENTS

PART 1....3

Test Facility.3

Experimental Procedure...4

Analytical Background..7

Data Reduction..9

Validation12

Conclusions..13

Appendix. ...13

PART 2..18

Design strategy and methodology.....18

Analytical Background..18

Implementation of strategy.19

Description of Optimization.21

Sample Calculations...21

Conclusion and recommendations..23

Appendix23

Technical Drawing24


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Test Facility:

The heat transfer testing and heat transfer design lab took place in ASEC 1B. Thesetup, shown in figure 1, consists mainly of a duct in which air is forced through via

a blower motor. The flow rate is an

unknown constant value in which we can

obtain from experimental data. In

addition, seen in figure 2, vertical and

inclined manometers are included tomeasure Static Pressure Drop and the

Centerline Velocity Pressure. A throttle valve on the flow exit stack allows flow

control from 10%-100% flow. The test section shown consists of an arrangement of

18 glass tubes as shown in figure 3. These tubes represent a staggered tube bank

which is found in many heat exchangers. Finally, the heater allows for a

thermocouple equipped copper rod to be heated to specific temperatures. The

following section describes how we

used this apparatus to obtain

experimental data and design our own

heat exchanger with.


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Experimental Procedure:

Pressure Measurements:

Fill all test section openings with the glass tubes provided.

With the throttle valve closed turn on the blower.

Open the throttle valve to 100% flow area.

Verify two or three velocity pressures listed in the table provide to you

(Table 1).

Record the static pressure drop and the velocity pressure at the geometric

centerline for the following flow areas: 100, 80, 60, 40, 30, 20, and 10

percent.

Table-1 Above, shows the obtained manometer measurements.

Temperature Measurements:

Turn on the computer. From the windows desktop, double click on the icon

labeled Wind Tunnel Temperature Acquisition. This will load the program

that can be used to acquire temperature data.

In the temperature acquisition program, set the number of samples per

channel to 100, and the scan rate to 1000 scans/sec.

Open the throttle valve to 100% flow area.

After wind tunnel has run for a couple minutes (to allow for the wind tunnel

entrance temperature to stabilize), begin data acquisition. This can be done

by selecting the run icon, which looks like an arrow (left-hand corner of the computer screen.

Once data acquisition has begun, heat the copper rod in the heater until it

reaches a temperature between 35

Remove the copper rod from the heater, and place it into the wind tunnel at

position #3. (Remove the glass rod first.)


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Allow the temperature of the copper rod to cool until it reaches (or nearly

reaches) the ambient temperature of the air entering the wind tunnel.

Hit the bright red STOP button to end the data acquisition. The computer

will prompt the user to save the acquired data. Specify the location (A:\

drive), and the file name (***.xls), and save.

The data can then be opened up in Microsoft Excel for further analysis. It is

best to open the excel file from the Windows Explorer (The alternative is to

open it from Microsoft Excel, but it will require that you import the data).

In the Excel file, the time in seconds, the copper rod temperature, and the

ambient temperature will be contained in the first, second, and third

columns, respectively.

Remove the copper rod and replace the glass rod in location #3.

Repeat Steps 9 through 14 for the following tube locations: 2, 4, 7, 8, 11, 12,13, 16, and 17.

Repeat steps 9 through 14 for location #17 with the following throttle valve

openings: 80, 60, 40, 30, 20, and 10 percent.

Exit out of the temperature acquisition program, and make sure to press the

no to all button when prompted whether to save changes to subVIs.

The following Graph, figure 4, shows experimental data obtained in the

temperature measurements section. This graph shows how the rate of temperaturedecay is dependent on the rate of flow in the duct. This data is important in order

for a correlation of Flow rate vs. temperature decay to be assessed:


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The following graph, figure 5, plots experimental data obtained to provide a visual

representation of how the time decay of heat transfer is also dependent on the

position of tube in the tube bank. This data is most important to be considered in

task two where a heat exchanger has been designed using correlations from this

collected data. Referring back to figure 3, notice how position 17 is further

downstream of flow as opposed to position 2. Now looking at the plot below, we see

how position 17 transfers heat at a more effective rate then position 2. This

phenomenon is caused by turbulent wake emanating from the first three rows of

tubes.


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Analytical Background:

Heat transfer of a body in a simple fluid flow is governed by the equation:

This equation will be primarily used in Part 2, the design portion. It may be used to

obtain the transfer of heat transfer per unit area. We will know the h value and

design a heat exchanger to suit by picking a surface temp. This is seen in Part 2.

The heat transfer coefficient is a complex variable dependent on many factors and

is most easily obtained by experimental data. The following equation shows it s

dependent factors:


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The Buckingham Pi process is used to obtain further unit-less quantities which will

aid in our design and data analysis. The Nusselt number is now obtained:

By taking the Log of each side of the latter Nusselt equation, we are able to obtain

an equation with correlates Nusselt number and the Reynolds number. This

equation is used to graphically represent the relation and find the first unknown, C:

The maximum velocity of the specific flow rates of Table-1 are calculated using:

Now the Reynolds number of the duct is calculated using the velocities obtained

and known parameters using:

The following equations show how from the experimental data, the heat transfer

coefficient, h, is found for each location in the duct:

The second unknown, C, can be found from data of the heat transfer coefficient as

the position in the duct increases:


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Data Reduction:

The first step to analyze this data was plotting the temperature time decay of

position 17 as the flow ranged from 10% flow to 100% flow. Figure 4 is pictured

again below and shows this data:


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Table-2 shown below is a conversion of Table-1 which displays the pressures in

Pascals as flow changes:

Table-2

Table-2 is then used to find centerline velocity, maximum velocity, Reynoldsnumber, the heat transfer coefficient, and the Nusselt Number. Results are shown

in Table-3:


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Table-3

Table-4

Table 4, shown above, documents the Log of each the Reynolds number and the

Nusselt number taken at position 17 for all the flows 10-100%. These values areplotted below:

Using the graph data from Figure 6, and the equation:

Figure-6


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We obtain a correlation of Reynolds number to Nusselt number that has the form

created from the slope and intersect of the above graph: Nu=5Re^.351.

Next, to find a relationship between the Nusselt Number and the depth of the

tube bank, the following Table was obtained from recorded data and then andNusselt number vs tube depth was plotted:

Table-5

All of the above collected and interpreted data will aid in the following heat

exchanger design portion, and may be referred back to.

Validation & Uncertainty:


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This experiment relies on three main terms which form the important correlations

used in Part 2:

The Prandtl, the Nusselt, and the Reynolds number are all goning to be considered

in uncertainty analysis, however since we treated the Prandtl number as a constant

during this experiment, we only must consider the Reynolds and the Nusselt

number:

The Reynolds number:

The Reynolds number consists of velocity, tube diameter, and the dynamic viscosity

of air. Dynamic viscosity is a constant, and the tube diameter was given, so the

uncertainty here comes from the measured and calculated velocity using

manometer readings.

Pressure Resolution: Velocity Uncertainty: =

Reynolds Uncertainty:

The Nusselt Number:

The Nusselt number consists of the heat transfer coefficient, the diameter, and

the thermal conductivity of air. The diameter is given, the thermal conductivity is

a constant, and the heat transfer coefficient. Thus, the experimental procedure to

obtain the heat transfer coefficient is the only factor which contributes

uncertainty:

Time is the only variable here which has an uncertainty of +/- 1 second, thus the

uncertainty is

. So: Nusselt uncertainty = .

Conclusions:


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While performing this experiment and analyzing the data, it has been proven to us

how the heat transfer coefficient increases with the depth inside a tube-bank

style heat exchanger. It also has been proven how the flowrate directly relates to

the rate of heat transfer. I would recommend this experiment to following senior

mechanical engineer students because it shows how such hard to find variables

such as the heat transfer coefficient can be easily obtained experimentally and

used to design an actual heat exchanger.

Appendix:


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Figure - 7


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Eq 1-3:

Eq 7-9:

Eq 10-

12:

Eq 13-

15:

Eq 4-6:


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PART 2

Design Strategy and Methodology:

With collected and interpreted data, the next task was to design and optimize aheat exchanger which would heat air from room temperature to 200C at a rate of

18m/min. My strategy was derived from the heat transfer coefficient vs tube

depth relation that was solved for in Part 1. First a duct size was picked, this

governed the flow velocity. Next, a tube size was picked as a staggered

arrangement. Finally using the data trends found, this problem was analyzed and

optimized for the material volume of the duct.

Analytical Background:

Figure 7 shows the earlier obtained

graph which will be used to iterate for

an appropriate heat exchanger design.

Other equations used include:

(Where is the time flow contacts each tube)

(Where is Joules transferred per tube)I used simple therdynamic properties and laws to break the heat transfer down

nodally per tube and per each specific column. This can be dont using the linearNusselt number trend found in figure 7 and basic knowledge of properties. Then

the data was iterated until a conclusion was reached and a design was created.

Figure - 7


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Implementation of strategy:

In order to optimize a design, I used an excel spreadsheet which iterated for 5

different tube sizes. The cross-section of the designed heat exchanger was the

first thing that had to be picked. So in order to optimize the volume of the heat

exchanger, I chose a 0.25m by 0.25m size which almost mimics the experimental

duct size so that we may use the same Nusselt correlation. Also I picked an

arbitrary value of 210C as the temperature of the cross tubes. The size and the

specific diameter of the tube governed the number of tube per column as shown

below:

TABLE 6.25m by .25m with flow rate of 18m/min (0.3615kg/s)

Tube Dia. .75cm 1cm 1.25cm 1.75cm 2.25cm

Tubes per

Column

16 12 10 7 5

Now the number of tubes per column is important because I will analyze the

heat transfer per tube and then iterate to solve for how many rows are required to

reach a temperature of 200C. The Excel spreadsheet starts out with column count

going from 1-40 (an arbitrary value which I didnt want to surpass). Next the

Nusselt number was calculated at each specific column using the slope of the

linear-fit line seen in Figure 7. The nusselt number is witnessed to increase with

every increasing row.

Next five columns were created to solve for the heat transfer coefficient

with the specific tube diameter and the specific Nusselt for that row.

Following that, five more columns were created in Excel which will display

the amount of heat transfer to the fluid at a specific instant in time. At this point

I found it necessary to create a variable called. This is the amount of Joulestransferred to the fluid, air, per tube at a specific instant in time:


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(Where is Joules transferred per tube)The amount of heat transfer to the fluid at a specific instant in time is calculated

by:

( ) Where N = number of tubes per column and

Next, a series of 5 columns were created which display the temperature of

air after it has passed one column of heating tubes. This temperature is calculated

by:

The theoretical background to this method is obtained with the variable

and the knowledge that this is the amount of Joules per Kilogram to raise the

temperature of air one degree Kelvin. After iterations, I have found with the

following parameters that 11 columns with 0.75cm tubes at 210C will be

appropriate for this design:

Duct Area = 0.25m by 0.25m

Cross-tube diameter = 0.75cm

Tubes per column = 16

Number of columns = 11

Tube arrangement: Staggered

Cross-tube temperature = 210C

Temperature in = 22C

Flow rate = 18m/min = 0.3615 Kg/sec

Flow velocity = 960 cm/sec Temperature out = 200.77C

Time contact = .001227sec

= 1005 J/Kg*KNote: Air is assumed at constant pressure in order to use


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Optimization of design:

During consideration of the design process I concluded that the volume of

material is usually the more expensive aspect. If the volume of the design is

minimized, it can also be implemented in applications where space is limited. First

the duct size was chosen as .25m by .25m which is a very reasonable size for this

design. Next I found that the smaller the cross-tube size we use, the better the

overall heat transfer, this is due to the fact that more heating tubes can be placed

in the cross flow to efficiently transfer more heat. Thus, the cross-tube size was

chosen to optimize the efficiency of the heat transfer, also this size will be able

to heat up at a faster rate than a larger cross-tube. This mean the heat exchanger

will be able to properly function quicker this way once turned on.

Sample Calculations:

Column in H.E. Nu h q (J per

column)

New temp

1 149.13 521.7 11.34 47.44

2 171.53 600.1 11.28 72.75

3 193.93 678.5 10.76 96.91

4 216.33 756.866 9.89 119.11

5 238.73 835.236 8.77 138.80

6 261.13 913.60 7.52 155.68

7 283.53 991.97 6.23 169.65

8 305.93 1070.34 4.99 180.85

9 328.33 1148.71 3.87 189.54

10 350.73 1227.08 2.90 196.0511 373.13 1305.45 2.10 200.77

You can see that as the air heats up, less heat is able to transfer due to the

surrounding air increasing in temperature with respect to the cross-tubes. The

above table is backed by the following calculations and explanations:


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A Nusselt number is solved for depending on the column number, depth, in

the tube bank.

Then the heat transfer coefficient is solved with respect to the found Nu.

Next the constant for the time of contact of each tube is solved.

Next the amount of heat transferred for the first column is calculated

( ) Next the parameter I created is solved. It is a constant which will help us

solve for the temperature exiting each column in the tube bank.

Next the temperature of the exiting air from the first column in the tube

bank is found.

Finally this process is iterated until the nex temperature is above 200C. It is

found to take only 11 iterations with these set design parameters.


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Conclusions:

While performing this experiment and analyzing the data, it has been proven to us

how the heat transfer coefficient increases with the depth inside a tube-bank

style heat exchanger. It also has been proven how the flowrate directly relates to

the rate of heat transfer. I would recommend this experiment to following senior

mechanical engineer students because it shows how such hard to find variables

such as the heat transfer coefficient can be easily obtained experimentally and

used to design an actual heat exchanger.

Appendix:

Table 7

analysis and design of heat exchanger

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