ME 495: Thermal-Fluid Lab - Data Reduction & Uncertainty in Thermal Engineering - Prof. Sc | Lab Reports Mechanical Engineering

Wright State University, Department of Mechanical and Materials Engineering

ME 495: THERMAL-FLUID SCIENCE LABORATORY

Data Reduction and Uncertainty Analysis

Objective: The objective of this analysis is to gain an understanding of the difficulties in dealing

with large data files obtained during experimentation, and to learn how to estimate the

uncertainty of a computed value from measured values.

Reference: Fox, McDonald and Pritchard, Introduction to Fluid Mechanics, 6th edn., Appendix F

Preparation: Read the reference material and these instructions. Download the data file, the

PAO (Brayco Micronic) property file, and the screenshot.jpg from my webpage:

http://www.cs.wright.edu/people/faculty/sthomas/me495.html

Report: Prepare a written report to include the following:

1. Cover sheet

2. Objectives of the analysis

3. List of equations used in determining the uncertainty of each computed value.

Confidence intervals in the data must be computed at a confidence level of 90%.

4. Hand calculations showing the error analysis for one value of heat transfer coefficient

and thermal resistance.

5. Create and discuss the following figures. Make sure to completely label all axes

appropriately, including units. When did steady state occur? What is the best method to

determine steady state? Is the magnitude of the uncertainty of the heat transfer coefficient

and thermal resistance reasonable? What measurement error had the most significant

impact on the uncertainties of the calculated values?

a. Temperature versus time

b. Temperature versus time when averaged over 120 and 900 second intervals

c. The instantaneous time rate of change of temperature versus time

d. Time rate of change of temperature versus time when averaged over 120 and 900

second intervals

e. Heat transfer rate extracted by the calorimeter versus time when averaged over

900 second intervals including error bars

f. Evaporative heat transfer coefficient versus time when averaged over 900 second

intervals including error bars

g. Thermal resistance versus time when averaged over 900 second intervals

including error bars

Part 1: Determination of Steady State

The experimental data was taken where the rate of sampling is approximately 0.5 Hz (one data

point every two seconds). During experimentation, the heat input at the evaporator section of the

loop heat pipe was suddenly increased from Qe = 0 to 600 W. At this point, the temperatures

across the LHP started to increase. The objective of the experiment was to obtain steady state

evaporative heat transfer coefficient and overall thermal resistance data, but determining when

steady state occurred was problematic. A data trace was displayed on the data acquisition

computer that showed approximately five minutes of temperature data. Once steady state was

approached, it was noted that the temperatures appeared to be steady over this five-minute

window, but was this a sufficient definition of steady state? An experiment was run in which a

step heat input to the evaporator was initiated, and the test ran for approximately eight hours in

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Wright State University, Department of Mechanical and Materials Engineering ME 495: THERMAL-FLUID SCIENCE LABORATORY Data Reduction and Uncertainty Analysis Objective: The objective of this analysis is to gain an understanding of the difficulties in dealing with large data files obtained during experimentation, and to learn how to estimate the uncertainty of a computed value from measured values. Reference: Fox, McDonald and Pritchard, Introduction to Fluid Mechanics, 6th^ edn., Appendix F Preparation: Read the reference material and these instructions. Download the data file, the PAO (Brayco Micronic) property file, and the screenshot.jpg from my webpage: http://www.cs.wright.edu/people/faculty/sthomas/me495.html Report: Prepare a written report to include the following:

Cover sheet
Objectives of the analysis
List of equations used in determining the uncertainty of each computed value. Confidence intervals in the data must be computed at a confidence level of 90%.
Hand calculations showing the error analysis for one value of heat transfer coefficient and thermal resistance.
Create and discuss the following figures. Make sure to completely label all axes appropriately, including units. When did steady state occur? What is the best method to determine steady state? Is the magnitude of the uncertainty of the heat transfer coefficient and thermal resistance reasonable? What measurement error had the most significant impact on the uncertainties of the calculated values? a. Temperature versus time b. Temperature versus time when averaged over 120 and 900 second intervals c. The instantaneous time rate of change of temperature versus time d. Time rate of change of temperature versus time when averaged over 120 and 900 second intervals e. Heat transfer rate extracted by the calorimeter versus time when averaged over 900 second intervals including error bars f. Evaporative heat transfer coefficient versus time when averaged over 900 second intervals including error bars g. Thermal resistance versus time when averaged over 900 second intervals including error bars Part 1: Determination of Steady State The experimental data was taken where the rate of sampling is approximately 0.5 Hz (one data point every two seconds). During experimentation, the heat input at the evaporator section of the loop heat pipe was suddenly increased from Qe = 0 to 600 W. At this point, the temperatures across the LHP started to increase. The objective of the experiment was to obtain steady state evaporative heat transfer coefficient and overall thermal resistance data, but determining when steady state occurred was problematic. A data trace was displayed on the data acquisition computer that showed approximately five minutes of temperature data. Once steady state was approached, it was noted that the temperatures appeared to be steady over this five-minute window, but was this a sufficient definition of steady state? An experiment was run in which a step heat input to the evaporator was initiated, and the test ran for approximately eight hours in

order to determine when steady state occurred. Even with this complete data set, it was not clear when steady state was reached. An alternative method was devised: The time rates of change of the temperatures were tracked. This method proved to be much more sensitive and reliable in terms of tracking when steady state was reached. Part 2: Uncertainty Analysis In any experiment, it is of the utmost importance for the experimentalist to attempt to quantify the uncertainties associated with measured values and computed values obtained by using an equation. Errors in measurements arise from several sources, which will be outlined here. In addition, the uncertainty involved in a calculated value based on measurements will be addressed. Sources of Error In any measurement, the value obtained by using a device such as a thermocouple is inherently incorrect. It is the experimentalist’s job to estimate the magnitude of that error. This must start with the calibration procedure, where the thermocouple reading is compared to the reading from a NIST-traceable instrument http://www.nist.gov/, such as a platinum resistance temperature detector (RTD). To calibrate a thermocouple, the thermocouple and RTD are immersed in a recirculating chiller bath, which holds the temperature of the liquid in the bath at a very nearly constant value. Once steady state has been reached, the temperatures read by the thermocouple and the RTD are recorded. In general, an average and standard deviation of each will be obtained by recording several hundred readings from the thermocouple and the RTD. In this way, a confidence interval can be obtained at a specified confidence level. The temperature of the bath is then increased, steady state is reached, and the temperatures are again recorded. The average thermocouple readings can be compared to the average RTD readings over the range of temperature expected during experimentation, and a best-fit curve can be obtained using a statistical package. In order to determine the uncertainty in the calibrated thermocouple, the following sources of error must be accounted for:

Typically, the RTD is provided with a NIST-traceability statement from the manufacturer listing the error associated with the RTD, which may be a function of temperature.
The error associated with the best-fit curve, i.e., the disagreement between the actual data and the prediction provided by the curve.
The confidence interval error in the thermocouple data. These sources of error must be added together to obtain a total uncertainty in the measured reading. Confidence Interval If a population of data can be described by a normal distribution, the mean of the population μ can be determined by finding the mean of a random sample ¯ x^ of n measurements. However,

¯ x^ is only an estimate of μ , so the error in ¯ x^ must be provided: μ =¯ x ± ε^. The confidence

interval is the range of the estimate for μ :

¯ x − ε^ ≤ μ ≤¯ x^ +^ ε

The question surrounded the volumetric flow rate through the different tubes for both air and water. Merely looking at the average values, one would think that the flow rate of air increases in the gray tubing compared to the clear tubing, but this is not the case when the uncertainties are factored in. The uncertainty literally tells us that the actual value of the flow rate for air in clear tubing lies somewhere between 689 and 869, and the flow rate ranges from 760 to 940 for the gray tubing. Since the ranges overlap, we can not make any conclusions with regard to the trend in the data. For water, however, it can be seen that the flow rate decreased slightly from the clear tubing to the gray tubing, which was probably due to the increase in the head loss in the smaller diameter tube, as expected. Equations for Evaporative Heat Transfer Coefficient and Thermal Resistance Newton’s Law of Cooling:

Q ˙= hA

e (^ ¯ T^ e − T^ sat )^ , W Heat Transfer Rate from the Calorimeter:

Q ˙= m ˙ C

p ( T^ out − Tin )^ , W Overall Thermal Resistance: Rth =( T ¯ (^) e − T ¯ (^) c ) / Q ˙ , K/W Evaporator Area:

Ae = π DL

, cm^2 Evaporator Inner Diameter: D = 2.500 ± 0.025 cm

Evaporator Length: L = 25.00 ± 0.025 cm Average Evaporator Temperature:

T ¯ e =( TA 4 + TA 5 + TA 6 )/ 3

, ºC

Saturation Temperature:

T sat = TA 8

, ºC

Calorimeter Mass Flow Rate: m ˙^ , kg/sec

Specific Heat of PAO: Evaluate Cp at the average of the outlet and inlet temperatures of the calorimeter. See Brayco Micronic 889 Spec Sheet for the temperature dependence and units. Calorimeter Outlet Temperature:

T out = TA 1

, ºC

Calorimeter Inlet Temperature:

Tin = TA 0

, ºC

Average Condenser Temperature:

T ¯ c =( TA 9 + TA 10 + TA 11 + TA 12 ) / 4

, ºC

For all measured temperatures, the uncertainty was ±0.11ºC. The uncertainty of the mass flow rate measurement was ±7.0%. Assume that the uncertainty of the specific heat is ±2.0%.

ME 495: Thermal-Fluid Lab - Data Reduction & Uncertainty in Thermal Engineering - Prof. Sc, Lab Reports of Mechanical Engineering

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Partial preview of the text

Download ME 495: Thermal-Fluid Lab - Data Reduction & Uncertainty in Thermal Engineering - Prof. Sc and more Lab Reports Mechanical Engineering in PDF only on Docsity!

¯ x^ is only an estimate of μ , so the error in ¯ x^ must be provided: μ =¯ x ± ε^. The confidence

¯ x − ε^ ≤ μ ≤¯ x^ +^ ε

Q ˙= hA

Q ˙= m ˙ C

Ae = π DL

T ¯ e =( TA 4 + TA 5 + TA 6 )/ 3

, ºC

T sat = TA 8

, ºC

Calorimeter Mass Flow Rate: m ˙^ , kg/sec

T out = TA 1

, ºC

Tin = TA 0

, ºC

T ¯ c =( TA 9 + TA 10 + TA 11 + TA 12 ) / 4

, ºC