melab ht fall2015

ME-Lab 4 Heat Exchanger Experiment – Fall 2015 1/16

MECHANICAL ENGINEERING

LABORATORY

4600:484

EXPERIMENT #4

HEAT TRANSFER TESTING

1. Testing Of Heat Transfer Characteristics Of A

Triangular-Pitch Cross-Flow Type Air Heater In

A Wind-Tunnel

2. Open Design Of An Efficient Cross-Flow Air

Heater Based On Heat Transfer Coefficients And

Curves Obtained In Item 1

Faculty Supervisor: Prof. M.J. Braun (ASEC 325)

([email protected])

Teaching Assistant:

Troy Snyder, ASEC 324 ([email protected])

Location: ASEC Rm. 15B

Fall 2015

mailto:[email protected]


Interoffice Correspondence

Date: October 4, 2012

To: Test Engineering

From: Dr. J.E. Drummond, Chief Engineer

Subject: Testing of the Triangular-Pitch Tube Bundle cross-flow air heater

1. FIRST TASK: (100 points); weight in final grade: 65%:

Note: that means that if you get 100 points the contribution to the final grade is 65.

The new triangular-pitch cross-flow air heater (heat exchanger) that will be marketed in the

near future will be part of an effort to develop a code to predict performance of our heat

exchangers. The software group has requested an experimental correlation(s) for the new tube

bundle that will enable them to reach this objective. They need this correlation(s) in order to

further design a full scale cross-flow air heater

The new correlation for a given single rod will, I presume, be of the form

nm

DD Ck

DhNu PrRe

In addition you are requested to

(1) Determine the velocity profiles in the duct and determine the nature of the flow (laminar,

turbulent or inviscid ?)

(2) Determine based on temperature and pressure measurements if the Prandtl number should

be considered or can be assumed not to be essential to the correlation.

(3) Acquire the pressure drop data across the bundle from the test.

(4) Provide customers with an uncertainty for the correlation above and indicate how the

errors are propagating in the final results from the individual measurement errors. If that

means more data is to be collected, then feel free to do that. It is not true, as some of our

colleagues believe, that collecting a paucity of data is best and always save resources.

(5) Obtain a correlation of NuD with respect to the depth in the tube bundle

For this Task 1, the report should document the following:

1. Description of the test facility

2. Experimental procedure


3. Analytical background (including the governing equations, assumptions, solutions)

4. Data reduction for temperature, pressures and flow velocities, interpreting and obtaining

C, m and n and velocities profiles throughout the test section

5. Uncertainty analysis

6. Conclusions and recommendations

7. Appropriate appendices (if necessary) to fully support your analysis.

IMPORTANT:

Both oral presentations and written reports will be graded based on the completeness of

the report/presentation and soundness of the analysis with supporting material

equations, plots, discussion)

2. SECOND TASK (100 points); weight in the final grade 35% Note: that means that if you get 100 points the contribution to the final grade is 35.

This is an open design task that requires that you now design a scaled up cross-flow air heater to

heat process air from room temperature to a process air temperature of 200oC.

You are required to use the information you obtained for Nu as a function of tube depth and use

it in the process of design. All heating tubes are powered electrically at a voltage of 480V, 3-

phase.

Design the cross flow air heater heat exchanger for maximum efficiency, using the minimum

amount of power and tube rows to accomplish the task.

For this Task 2, the report should document the following:

1. A 3-D solid model with appropriate 2-D cross sections of the proposed facility

2. Design strategy and methodology

3. Analytical background (including the governing equations, assumptions, solutions)

4. Implementation of the methodology and calculations Flowchart of information

5. Description of the optimization procedure and its results

6. Conclusions and recommendations

7. Appropriate appendices (if necessary) to fully support your analysis and design.

IMPORTANT:

Each one of the items above will be graded as shown on the second grading sheet.

Please use as titles in the report, the items from 1-7 as you progress through the report.

The written report will be graded on the basis of justifications and completeness of each

titled section.


Recommended references for this task:

1. Your current heat transfer book

2. Nellis, G., Klein S., Heat Transfer, Chap 8: Heat Exchangers, Cambridge Univ Press

3. Cengel et al, Heat and Mass Transfer 4th Ed. Chap 11 (or other Cengel edition)

4. Incropera et al, Introduction to Heat Transfer, 4th Ed. Chap 11 (or other any other

Incropera edition)

5. Any other literature (books, design papers, scientific papers) that you may find useful for

your design process


FOR TASK 1

1. EXPERIMENTAL PROCEDURE – suggested:

Pressure Measurements:

1. Fill all test section openings with the glass tubes provided.

2. With the throttle valve closed turn on the blower.

3. Open the throttle valve to 100% flow area.

4. Verify two or three velocity pressures listed in the table provided to you (Table 1).

5. 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.

Temperature Measurements:

6. Open Labview temperature acquisition vi.

7. In the temperature acquisition program, set the number of samples per channel to 100,

and the scan rate to 1000 scans/sec.

8. Open the throttle valve to 100% flow area.

9. 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 (), located in the upper left-hand corner of the

computer screen.

10. Once data acquisition has begun, heat the aluminum rod in the heater until it reaches a

temperature between 35 C and 40 C.

11. Remove the aluminum rod from the heater, and place it into the wind tunnel at position

#3. (Remove the glass rod first.)

12. Allow the temperature of the aluminum rod to cool until it reaches (or nearly reaches) the

ambient temperature of the air entering the wind tunnel.

13. Hit the bright red “STOP” button to end the data acquisition. The computer will prompt

the user to save the acquired data.

14. The data is saved as an ASCII text file with the time in seconds, the aluminum rod

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

columns, respectively. The data may be imported into excel or other software for

analysis.

15. Remove the aluminum rod and replace the glass rod in location #3.

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

17.

17. Repeat steps 9 through 14 for location #17 with the following throttle valve openings: 80,

60, 40, 30, 20, and 10 percent.

18. Exit out of the temperature acquisition program, and make sure to press the “no to all”

button when prompted whether to save changes to subVI’s.


2. DESCRIPTION OF THE EXPERIMENTAL SYSTEM:

Figure 1. Photo of the experimental apparatus (Located at Rm#15B).

System Information:

Dimensions:

Working section: 12.5 cm by 12.5 cm (nominal)

Glass Elements (dia.) 12.5 cm (nominal)

Transverse Pitch: 2.5 cm (nominal)

Longitudinal Pitch: 2.875 cm (nominal)

Specimen:

Material: Aluminum

Diameter: 12.46 mm

Length: 95.0 mm

Weight: 107.30 gm

Thermocouples:

Type T (Copper and Constantan)


Figure 1: Schematic of the Experimental Apparatus

Figure 2: Manometer Setup

Figure 3: Tube Locations


Table 1. Velocity pressure distribution at 100% flow (mmH2O) for calibration.

Vertical

Location

(mm)

Horizontal Location

1 2 3 4 5

0 12 12 12 12 12

10 15 18 18 18 18

20 15 18 19 19 18

30 15 18 19 19 19

40 18 18 20 19 19

50 18 19 20 19 19

60 18 19 20 19 19

70 18 19 20 20 19

80 18 19 19 19 19

90 18 19 19 19 19

100 18 19 18 18 18

110 18 18 18 17 16

116 15 17 17 17 15


3. THEORY AND ANALYSIS (suggested approach)

In heat transfer problems, generally the engineer is interested in either how much heat is being

transferred per unit time (q), or what the relevant temperatures (T) are, or both. In convective

heat transfer problems, these two features are related via the convection heat transfer coefficient

“h”, and Newton’s law of cooling:

)( TThq surf (1)

Where Tsurf is the surface temperature of the body and T∞ is the fluid temperature of free stream

away from the surface.

Generally, one is interested in determine the heat transfer coefficient (h) for a given set of

conditions, so that the rate of heat transfer (q) can be computed. The following paragraph

reviews how one obtains the heat transfer coefficient (h).

Consider the flow of a cold fluid over a hot body. If the body has a cylindrical shape, it can be

shown that the value of the heat transfer coefficient can be expressed as follows:

),,,,,( kcdVfh p (2)

Where d is a characteristic length of the body (here the diameter), V is the freestream velocity of

the fluid away from the body, and , cp, and k are the density, specific heat, dynamic viscosity,

and thermal conductivity of the fluid, respectively. Generally, one is interested in determining

the function “f” in Eq. (2), so that a value of the heat transfer coefficient (h) can be determined at

any set of operating conditions (V, d, etc.). Keep in mind that in order to obtain an accurate

expression for f, we would have to measure h under a variety of flow conditions (i.e., turbulent,

laminar), different sizes of the body, and various fluid properties. Alternatively (and hopefully),

someone may have already determined an expression for “f” for circumstance similar to your

own, and published a correlation such as Eq. (2), that applies to your specific circumstance. Now

let’s consider how this correlation may be performed.

Recall the principle that three points are necessary to generate a line. In order to adequately

determine “f” in Eq. (2), we would thus have to conduct tests at 3 different values of each of the

parameters on the right hand side of Eq. (2) – for a total of 36 tests! The expression for “f”

clearly would be complicated, if it could be found at all. However (and fortunately), the art of

dimensional analysis1 can be used to reduce the number of variables involved in “correlating” h.

Using dimensional analysis for our problem (which Eq. (2) pertains to), one arrives at the

following expression:

Pr)(Re,fk

hdNu (3)

Where Nu, Re, and Pr are the Nusselt, Reynolds, and Prandtl numbers appropriately defined for

the specific application2. Since h is directly proportional to Nu, the problem of determining h

becomes a problem of determining Nu. Comparison of Eqs. (2) and (3) reveals that the function

“f” in Eq. (3) will be much simpler to obtain that the “f” in Eq. (2) – far fewer tests are needed to

obtain the “f” in Eq. (3). Thus, the utility of dimensional analysis is obvious. Once someone has

made measurements of h for a given situation (say flow over a cylinder) and obtained the

expression “f” in Eq. (3) (i.e., obtained the appropriate “correlation”), the correlation can then be

used for any other dynamically similar flow (i.e. different fluid, different tube diameter).


In the current study, we are interested only in airflow, and we will assume that the Prandtl

number is fixed for all tests. Thus, we are specifically looking for a correlation of the form:

mDD C

k

DhNu Re (4)

Note that if we take the log of both side of the above equation, we get an equation of the form

CmNu DD logReloglog .

If one plots “log NUD” as a function of “log ReD”, one obtains a straight line with the slope being

the power component m. Before we can obtain m, however, we need to obtain Nu and Re.

Now we consider the issue of obtaining Nu and Re. In order to generate flow over an object for

the purpose of measuring heat transfer, test models are typically mounted in “wind tunnels” (for

gas flow). These are typically used because they provide a means of good control over the

volume flow rate of air (and hence gas velocity) in the vicinity of the test piece (model).

In our case, we have the tube bunk pressure drop measurements and the velocity pressure

measurements upstream of the tube bank. Through the use of Bernoulli’s equation1 applied to an

air particle decelerating from the centerline velocity to zero velocity at the Pitot probe1 tip, we

can determine the velocity of the air upstream of the tube bank, by using the velocity pressure.

You will find the references to be very helpful. (You may find the conversion 1 cmH2O = 98.1

N/m2 helpful in your conversion of pressure into velocity.) In Bernoulli’s equation, the density of

the air is needed. Since the air flow is incompressible for our experiment, you can evaluate the

density of air using the ideal gas law together with the measured ambient pressure and

temperature.

By convention, for flow through a tube bank, the Reynolds number is defined as

dVmaxRe (5)

Where the density () and dynamic viscosity () can be estimated based on the measured fluid

temperature. For our tube bank, Vmax is evaluated as the velocity of the air as it passes through

the effective flow area of a tube row. The effective flow area is the available area in a plane that

passes through the centerlines of the tubes in a tube row through which the air can flow. You will

need to calculate the exact relationship that applies in our case, but you will find that

approximately Vmax 2Vcenterline, where Vcenterline is the measured centerline velocity upstream of

the tube bank, which you will obtain from the Bernoulli relation:

gH

VPP water

centerlineairso

2

2

(6)

Where the centerline velocity pressure (H) is measured with the pitot-static tube. Then the centerline air

velocity can be determined by the following expression:

air

watercenterline gHV

2 (7)

Now consider the Nusselt number. In our case, the heat transfer coefficient, and hence Nusselt

number, is obtained using a transient test. The value of the convection heat transfer coefficient


corresponding to a given test is obtained as follows. Consider an energy balance on the

aluminum rod:

storedoutin qqq (8)

While the rod is cooling in the wind tunnel, there is no heat being added to the rod. Utilizing

Newton’s law of cooling for qout, and treating the entire rod as a lumped system, we obtain

dt

dTmcTThA rod

airrodsurface )( (9)

where Asurface, m, and c are the surface area, mass and specific heat of the rod (pure aluminum in

our case), respectively. If treating h as a constant, after separating variables in the above

equation, and integrating from time equals to zero, the following relationship is obtained:

lnln,

airinitialrod

airrod

p

surface

TT

TTt

mC

hA (10)

Using the data collected by the data acquisition system (for several different flow rates at tube

position #3), a plot of ln() versus time can be created. Once the plot has been created, a linear

curve fit can be performed, and the slope (a) of the resulting line can be found. From this

calculated slope (a), the heat transfer coefficient can be found:

surfaceA

mcah (11)

Next, using the value of the heat transfer coefficient just found, the Nusselt number can be

calculated:

k

dhNud (12)

With the thermal conductivity of the air, k, estimated based on the measured air temperature.

References:

1. Munson, B.R, Young, D.F. and T.H. Okiishi, Fundamentals of Fluid Mechanics, 3rd Ed.,

John Wiley & Sons, 1998.

2. Incropera, F.P. and D.P. DeWitt, Introduction to Heat Transfer, 3rd Ed., John Wiley &

Sons, 1996.


4. REPORT/PRESENATION REQUIREMENTS

Include the required correlation between the Reynolds and Nusselt number.

Include the required correlation between the Reynolds and Nusselt number with

respect to the location in the tube bundle (depth in the tube bundle).

Include all assumptions used in your analysis, and a benchmark to validate your

analysis.

Discuss the type of flow in the duct.

Include a general correlation good for each and any of the tubes indicated as required.

This implies evaluating “h” as a function of tube depth.

Include all original data in appendix.

Include detailed analysis and calculations in appendix.

Include an uncertainty analysis.

Include appropriate plots and charts.

Proofreading.


5. SAMPLE DATA SHEETS:

Table 2. Measured Velocity pressure distribution at 80, 60 or 40% of full open flow

(mmH2O)

Throttle Position:_________ % of full open

Vertical

Location

(mm)

Horizontal Location

1 2 3 4 5

0

10

30

50

70

90

110

Table 3. Static pressure drop across tube bundle and centerline velocity pressure upstream

of tube bundle, versus throttle position.

Throttle Position, % of Full Flow

100 80 60 40 30 20 10

Static

Pressure

Drop

(cmH2O)

Centerline

Velocity

Pressure

(mmH2O)


Table 4. Various Solved Parameters at Different Percent Flows

for Aluminum Tube Position #17

Calculated Parameters

Throttle Position (% of Full Flow)

100 80 60 40 30 20 10

Centerline Velocity (m/s)

Maximum Velocity (m/s)

Reynolds Number

Heat Transfer Coefficient (W/m2-K)

Nusselt Number

Table 5. Various Solved Parameters at Different Tube Locations and 100% Flow

#3 #8 #12 #17

Row Number 1 2 3 4

Centerline Velocity (m/s)

Reynolds Number

Heat Transfer Coefficient (W/m2-K)

Nusselt Number


Grade Sheet for TASK 1 (for both report and presentation)

Heat Transfer in Tube Bundle

Fall 2015 Name_____________

Technical Content (70 pts): Procedure, Experimental Method (did you adhere to _______(10 pts)

a reasonable method and focus)

Data (does it look reasonable) _______(10 pts)

Correlation/Curve Fit (Appropriate presentation _______(10 pts)

of the primary results)

Discussion of Uncertainty _______(10 pts)

Appropriate Reliance on Theoretical Background _______(10 pts)

Plots & Data Presentation _______(10 pts)

Discussion and Analysis of Results _______(10 pts)

Total Technical _______/70 pts

Presentation (30 pts):

Arrangement of Report/Presentation ________(10 pts)

Spelling & Grammar ________(10 pts)

Style (Length, ease of reading) ________(10 pts)

Total Presentation ________/ 30 pts

Total Grade ________/100 pts


Grade Sheet for TASK 2, open design (for both report and presentation)

Heat Transfer in Tube Bundle

Fall 2015 Name_____________

3-D solid model with appropriate 2-D cross sections of the proposed facility

_______(10 pts)

Design strategy and methodology _______(15 pts)

Analytical background (including the governing equations, assumptions, solutions)

_______(25 pts)

Implementation of the methodology and calculations Flowchart of information

_______(20 pts)

Description of the optimization procedure and its results _______(10 pts)

Conclusions and recommendations _______(10 pts)

Appropriate appendices (if necessary) to fully support your analysis and design

_______(10 pts)

Total Grade ________/100 pts

melab ht fall2015

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