In the following section we will present, discuss, and explain the engineering method our team used to create the testing apparatus that solves Friedrich’s technical issues with capillary tubes. We will cover our first hypothesis, calculations, design process, testing, part selection, system design and CAD work.
HYPOTHESIS
When analyzing the issue Fredrich was having with the new supplier, we evaluated how these new identical capillary tubes where greatly underperforming. This evaluation led us to believe that possibly the key factor for this difference in performance was related to how the capillary tubes were manufactured. The different manufacturing methods could lead to a difference in how the internal surface is finished. As shown in Figure 19, we know that the roughness of pipes and ducts affects the flow rates and pressure losses on fluids passing through them. The absolute roughness, ε of a material is proportional to the friction factor, ƒ which is related to the pressure drop, ∆P across the pipe or duct. Therefore, the goal new test systems we develop will be to find the pressure drop across the capillary tube or assembly which will then allow us to estimate the roughness of the pipe. We can then compare results of new suppliers with the results of from tubes that have been proven to perform to the desired level by the engineers at Fredrich. Additionally, we will compare the results to theoretical estimates to give a second reference point on performance as well as provide a base line estimate on how a pipe should perform if there are no past results to reference.
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Figure 19: Schematic absolute roughness of pipe This observation led us to formalize two hypotheses.
Hypothesis 1:
The relative surface roughness of the tube from Minallum is different than the relative surface roughness of the tube from original capillary tube manufactures, National copper. This could be causing a lower or greater pressure drop across the capillary tube which will make the AC units less effective. We will need to create a testing system that can accurately figure out the pressure drop across the capillary tube so that the relative surface roughness estimate can be made for each capillary tube tested.
Hypothesis 2:
Running the test at a higher inlet pressure to exaggerate any issue that might exist inside the tubes. The tubes run at higher pressures in the ac units, so we want to test the capillary tubes at a pressure that better resembles the operating pressure compared to the relatively low
pressures tested in the ASHRAE 28 standard system.
34
ITERATIVE DESIGN OF TESTING APARATUS
Figure 20: First Concept for New Test System
Our first idea for the new testing apparatus as shown in Figure 20, involves replacing the old pressure regulator with a new automatic regulator that is controlled by the computer. We wanted to have a third pressure that is attached after the pressure regulator that would measure the pressure drop across the capillary tube. However, we realized that we did not want to make major changes like this to the original testing fixture as it has its design is supported by the ASHRAE 28 standard. This led us to our next idea which was a system that runs in parallel to the existing system, shown in Figure 21. This would give us more flexibility to test the capillary tubes and assemblies for the specific variables needed. It important that this system is flexible regarding where the two connectors attach to either end of the assembly as the assemblies are not just linear pipes like the capillary tubes. The inputs and outputs of the assemblies vary in height, orientation, and angle.
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Figure 21: First Version For Parallel Design
Our first idea was to use a liquid such as water or R-410a to induce a flow through the capillary tube. By using a liquid this would give us a better understanding of how the capillary tubes would perform in one of the air conditioning units. The reservoir would induce a flow and would allow us to find the pressure drop across the capillary tube.From the pressure drop measured we can find the friction factor of the capillary tube and compare it to predetermined data sets to see if the capillary tube is performing correctly. However, three issues arise from this concept. The first is that the tubes will begin to oxidize if a fluid like water comes into contact with the capillary tubes. This means that any tubes that are tested on this fixture would not be able to be installed into AC units.
Another drawback we found with the first concept for a parallel system was that using a fluid would pose safety issues such as spillages that could potentially damage electrical
equipment on the table unit and then harm the operator. Finally, the fluid would drain from the reservoir. Resulting in a pressure induced by the fluid constantly decreasing, making the test harder to operate and therefore less reliable and decreasing the validity of the results.
36
From this we developed our second idea for the parallel system that could use Nitrogen instead of a liquid and have the nitrogen at a pressure greater than that used in existing test system. This is so that the test is still cheap to run, and that there is no chance of the electrical equipment in the space getting damaged.With this design we will need to implement a safety system or device at the end of the system since we would be running tests at a higher pressure than in the main system.The first idea was to have the components on right hand side of the cap tube attached to a roller system to account for varying lengths of capillary tubes. Seen in Figure 22. However, as previously mentioned, this system needs to be flexible enough to test both capillary tubes and assemblies. We would need something to provide more flexibility than a simple roller system. This led us onto our third idea seen in Figure 23, which replaces the roller system with an articulating arm. This arm would provide the freedom needed to attach both capillary tubes and the more complex assemblies.
Figure 22: Second Version For Parallel Design
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Figure 23: Third Version For Parallel Design
Figure 25 shows the fifth version of our system design which was created due to some oversights on the earlier versions of the testing system. We realized two key issues with the fourth version. The first is that we had planned to attach the beginning of the pressure drop system to the pegboard in the same direction as the mass flow system, this would mean there is not enough length on the table to test the longest capillary tubes used at Friedrich. This issue was solved by deciding to invert the direction of the system. To achieve this the nitrogen hose would need to connect around the back, allowed the system to go from right to left, therefore enabling us to use the entire length of the table for testing. The second issue was that due to the nature of the capillary tube connectors, the capillary tubes ran perpendicular to the system, meaning the articulating arm and the second part of the system would not connect to the tubes. To solve this problem, we will add a 90-degree elbow in between the pressure transducer and the capillary tube connectors which will mean the capillary tubes run parallel to the system and the rail the articulating arm is attached to it. Additionally, a coiled capillary tube can be seen at the send of the pressure drop system, this is explained in section 6.1.
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Figure 24: Fourth Version For Parallel System Design
FINAL ITERATIVE DESIGN VERSION
Figure 25 shows the last version of our iterative design process which was substantially different to the fourth version. After creating the fourth version of the new testing system we found it would be possible to save space and money by combining the mass flow system and the pressure drop system into one system. Through extensive testing we found that testing the capillary tube around 100 psig meant the system components would not get damaged as well as the being able to amplify any coherent issues withing the capillary tubes. This meant we can add the dryer, filter and pressure transducer components found at the start of the mass flow system to the start of the pressure drop system as they are all rated at over 120 psig. This meant the system could be used to both calculate the mass flow through the tube using the AHRAE 28 standard at low pressures as well as our testing process at high pressures.
39
By combining the two systems into one system that can measure both variables required for capillary tube testing at Fredrich it meant only one more pressure transducer had to be purchased (pressure transducer #1). Pressure transducer #1 does not have to be as exact as the pressure transducers #2 and #3 since its purpose is to just ensure the system inlet is getting 120 psi supplied by the nitrogen tanks. Pressure transducers #2 and #3 need to have the highest accuracy possible since they are what measure the inlet and outlet pressure of the capillary tubes, meaning these transducers determine the pressure drop across the capillary tube.
Figure 25: Final Version Of Testing System
40
SYSTEM FLOW CHART
The flow chart seen in Figure 28 shows how our new system would operate. The main process of the new system is connecting the articulating arm to the capillary tube or assembly and setting the pressure regulator to a pressure that is higher than that on the main system. Next would-be measuring test results for the pressure drop to comparing the test results to theoretical data and previously recorded data. All this data would help us to determine whether or not the results are acceptable.
The parallel system flow chart that is predefined process box called “Computer system 2”, this process is outlined in Figure 27. This flow chart is a general outline for how we will create the LabVIEW program needed to control the test procedure. The main points of focus for this computer system are to have the ability to display the theoretical pressure drop
approximations as well as test data from other identical capillary tubes or assemblies.
Additionally, it shows we will need to process the data from the two pressure regulators to calculate a pressure drop value. After processing the pressure data, we will then have the computer compare the results and see if they are within an acceptable tolerance of both the theoretical data and past test data,
Figure 27: Computer System 2 Flow Chart
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Figure 28: Parallel System Flow Chart
42
FLUID DYNAMICS CALCULATIONS
REYNOLDS NUMBER CALCULATIONS Introduction
We need to find the Reynold’s number so that we can find the friction factor, f, for the capillary tubes. Below is the Reynolds Number calculated for part 3765018 to show the steps and equations used. This was done for multiple parts and is used in our pressure drop
equations. All our equations are from the Fundamentals of Fluid Mechanics textbook [1].
Values
Part number: 3760518
Inner Diameter, ID = 0.054 𝑖𝑛ches Outer Diameter, OD = 0.106 𝑖𝑛ches Nominal Mass flow rate, 𝑚̇𝑁= 0.461 CFM
Substitute (1) and (2) into Reynolds number equation 𝑹𝒆 = 𝟒𝒎̇
43 PRESSURE DROP CALCULATIONS
Introduction
We found two pressure drop equations and two friction factor equations. The plan is to add a pressure transducer at the end of the current test system to compare the results to the differing equations. The capillary tubes that pass and work in the ac units should have an accurate pressure drop. The capillary tubes that passed but ended up failing in the system, if our hypothesis is correct will not have an accurate pressure drop because the estimated friction factor would be smaller than the actual one. When we measure the pressure drop across the capillary tube at Friedrich, we will also be able to do these calculations but find the actual friction factor.
Values
Part Number: 1389915
Inner Diameter: 0.059 𝑖𝑛 = 0.00492 𝑓𝑡 Outer Diameter: 0.112 𝑖𝑛.
Length: 20.4 𝑖𝑛 = 1.7 𝑓𝑡
Nominal Mass Flow (volumetric flow rate): 0.69 𝑐𝑓𝑚 = 0.01150𝑓𝑡3
𝑠
Nitrogen Dynamic Viscosity: 3.68𝐸 − 07 𝑙𝑏𝑚
𝑓𝑡2∗2
Nitrogen kinematic Viscosity: 1.63𝐸 − 04𝑓𝑡2
2
The physical properties referenced above as well of the rest of the engineering theories referenced in section 6.4 are obtained from Munson, Young and Okiishi's textbook called
44
Fundamentals of Fluid Mechanics. The physical properties table from the textbook is shown in Table 5.
Table 5: Approximate Physical Properties of Gases at Standard Atmospheric Pressure [Fundamentals of Fluid Mechanics Table 1.7]
Reynolds Number Calculations for PN 1389915
The Reynolds number for pipe flow is defined as 𝑅𝑒 =𝜌𝑉𝐿
𝜇 . We found velocity by rearranging the mass flow equation and inputted in the Reynolds equation. We put out units in inches and seconds.
𝑅𝑒 = 18270.46
Pressure Drop Theory Overview
∆𝑝 = 𝑓 𝐿
2𝐷 𝜌𝑉
2ΔP = pressure drop in Pascals (psig) V = velocity in meters per second (ft/sec) L = length of pipe or hose in meters (in)
ρ = density of the fluid in kilograms per cubic meter (lb/ft for hydraulic oil) D = inside diameter of pipe (in)
f = friction factor
45 Friction Factor Theory
The friction factor is a dimensionless quantity used in the Colebrook equation, for the description of friction losses in pipe flow as well as open-channel flow. Figure 29 shows a moody chart which is a non-dimensional form that relates the Colebrook friction factor fD, Reynolds number Re, and surface roughness for fully developed flow in a circular pipe. The moody chart is used to estimate the friction factor, f from the equation below as in this formula f is a function of itself.
1
√ƒ = − 2log
10( 𝜀
3.7𝐷
ℎ+ 2.51 𝑅𝑒√ƒ )
Figure 29: Moody Diagram [Fundamentals of Fluid Mechanics Fig. 8.20]
However, since the Colebrook equation is in a form where the friction factor is a function of itself its very complicated to analytically compute a value. The Haaland equation is an easier way to solve for the friction factor and provides an adequate approximation.
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The surface roughness for pipes can be found in table 6. Therefore, for the copper tubes we are dealing with we will assume they have a similar surface roughness top drawn piping would be 𝜖 = 0.000005 ft.
Table 6: Equivalent Roughness for New Pipes [Fundamentals of Fluid Mechanics Table]
Friction factor calculations for PN 1389915
𝑅𝑒 =
18270.46
the flow is turbulent which means we will used Using the Haaland Equation to calculate the friction factor.1
Next, we cross checked this value with the moody chart to ensure that the Haaland equation produced a good approximation.
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𝜖/𝐷 =
0.0000050.00492
= 0.001.
The friction factor we got from moody chart was approximately 0.029 which is
remarkably close to what the Haaland equation approximate. We crossed checked these results with other capillary tubes and the results were all good approximations of the moody chart, this allowed up to be confident in the Haaland approximation equation when calculation friction factors of other capillary tubes.
Figure 30: Moody Friction Factor Check [Fundamentals of Fluid Mechanics Fig. 8.20]
Pressure Drop Calculations for PN 1389915
Now we have the friction factor we can use equation 6.1 to estimate the pressure drop across the capillary tubes.
∆𝑝 = 𝑓
𝐿2𝐷
𝜌𝑉
248
Table_ is the from the excel document we created to calculate the Reynolds numbers, friction factors, pressure drops for the tubes at Friedrichs facility.
Conclusion
We noticed an interesting trend in our theoretic results of the tubes the Friedrich has indicated all have a pressure drop that is a lot higher than the rest of the tubes that have not been noted of having issues. We think this shows us that these tubes are overly sensitive to factors that affect the pressure drop of the tubes. If the internal surface roughness is just slightly off from what it should be then this could greatly affect the pressure drop of the capillary tubes.
Tabulated Results of Pressure Drop Calculations
The physical dimensions for our pressure drop and surface roughness calculations come from Table 1.7 in the Fundamentals of Fluid Mechanics and can be seen on the dimension's sections of Table 7. The nominal flow rates and velocity are shown in the middle column. In the far-right column, our calculation for pressure drop is shown. We got all our equations from the Fundamentals of Fluid Mechanics textbook. The part numbers in red are the parts that were failing in the AC units. 28 different capillary tubes, as seen in the table below, that Friedrich currently has in the San Antonio facility were used for these calculations.
49 Tabulated Results
Table 7: Excel Data Sheet for Pressure Drop
ID (in.) ID (ft) Length
(ft/s)
𝜖
Reynold number f Pressure drop (PSI)1389902 0.075 6.25E-03 32.00 2.67 0.395 6.58E-03 214.58 5E-06 8.23E+03 3.35E-02 5.17 1389903 0.054 4.50E-03 33.75 2.81 0.427 7.12E-03 447.47 5E-06 1.24E+04 3.08E-02 30.23 1389975 0.064 5.33E-03 21.00 1.75 0.5155 8.59E-03 384.58 5E-06 1.26E+04 3.04E-02 11.57 1389985 0.064 5.33E-03 27.50 2.29 0.44 7.33E-03 328.26 5E-06 1.07E+04 3.15E-02 11.46 1390000 0.064 5.33E-03 37.50 3.13 0.381 6.35E-03 284.24 5E-06 9.30E+03 3.27E-02 12.14 1390005 0.064 5.33E-03 23.50 1.96 0.483 8.05E-03 360.34 5E-06 1.18E+04 3.09E-02 11.54 1390212 0.059 4.92E-03 37.00 3.08 0.507 8.45E-03 445.07 5E-06 1.34E+04 3.01E-02 29.31 1390223 0.075 6.25E-03 12.63 1.05 0.615 1.03E-02 334.10 5E-06 1.28E+04 3.01E-02 4.43 3760383 0.075 6.25E-03 26.63 2.22 0.4315 7.19E-03 234.41 5E-06 8.99E+03 3.28E-02 5.02 3760394 0.064 5.33E-03 17.50 1.46 0.546 9.10E-03 407.34 5E-06 1.33E+04 3.00E-02 10.68 3760395 0.075 6.25E-03 22.00 1.83 0.478 7.97E-03 259.67 5E-06 9.96E+03 3.19E-02 4.96 3760432 0.08 6.67E-03 15.00 1.25 0.697 1.16E-02 332.79 5E-06 1.36E+04 2.96E-02 4.82 3760452 0.049 4.08E-03 35.00 2.92 0.323 5.38E-03 411.09 5E-06 1.03E+04 3.23E-02 30.56 3760470 0.075 6.25E-03 16.25 1.35 0.54 9.00E-03 293.35 5E-06 1.12E+04 3.10E-02 4.54 3760473 0.059 4.92E-03 28.50 2.38 0.585 9.75E-03 513.54 5E-06 1.55E+04 2.91E-02 29.14 3760479 0.049 4.08E-03 44.25 3.69 0.286 4.77E-03 363.99 5E-06 9.12E+03 3.32E-02 31.18 3760482 0.049 4.08E-03 25.00 2.08 0.382 6.37E-03 486.17 5E-06 1.22E+04 3.11E-02 29.39 3760501 0.064 5.33E-03 30.25 2.52 0.432 7.20E-03 322.29 5E-06 1.05E+04 3.17E-02 12.20 3760502 0.04 3.33E-03 20.00 1.67 0.298 4.97E-03 569.14 5E-06 1.16E+04 3.18E-02 40.38 3760504 0.09 7.50E-03 24.00 2.00 1.148 1.91E-02 433.09 5E-06 1.99E+04 2.70E-02 10.60 3760507 0.064 5.33E-03 13.75 1.15 0.61 1.02E-02 455.08 5E-06 1.49E+04 2.93E-02 10.22 3760508 0.08 6.67E-03 18.00 1.50 0.612 1.02E-02 292.21 5E-06 1.20E+04 3.05E-02 4.59 3760510 0.09 7.50E-03 30.00 2.50 1.061 1.77E-02 400.27 5E-06 1.84E+04 2.75E-02 11.51 3760511 0.059 4.92E-03 23.25 1.94 0.6345 1.06E-02 556.99 5E-06 1.68E+04 2.87E-02 27.49 3760518 0.054 4.50E-03 29.00 2.42 0.461 7.68E-03 483.10 5E-06 1.33E+04 2.86E-02 28.11 3760526 0.054 4.50E-03 27.00 2.25 0.476 7.93E-03 498.82 5E-06 1.38E+04 2.83E-02 27.67 3760451 0.049 4.08E-03 19.50 1.63 0.43 7.17E-03 547.26 5E-06 1.37E+04 3.03E-02 28.30 1389915 0.059 4.92E-03 20.40 1.70 0.69 1.15E-02 605.71 5E-06 1.83E+04 2.82E-02 28.03
Pressure Drop Part Number
Dimensions Flow rates
50
STRENGTHS CALCULATIONS
PRESSURE VESSEL CALCULATIONS Introduction
The strength of the capillary tubes was calculated to predict if the copper tubing could withstand a higher pressure. The tube functions with higher pressures inside the AC unit so we wanted to test the at more realistic pressures to ensure the tube will not have issues
or exaggerate any issues. We were also able to compare these strength calculations to the data we collected from conducting an experiment at 120 PSI. We used part number 3760518 to show the strength calculations that we used. Figure 31 shows the stresses on a diagram of the copper tube which is considered a thick-walled vessel.
Figure 31: Stress Diagram of Thick-Walled Vessel Values
Part number: 3760518 Inner radius, ri = 𝐼𝐷
2 =0.054 𝑖𝑛
2 = 0.027 𝑖𝑛 Outer radius, ro = 𝑂𝐷
2 =0.106 𝑖𝑛
2 = 0.053 𝑖𝑛 Thickness, t = ro – ri = 0.052 in
Internal pressure, Pi = 120 psi (max pressure system components can handle) External pressure, Po = 0 psi
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Therefore, this capillary tube can be considered as a thick-walled vessel.
RADIAL STRESS:
Figure 32: 3D stress states
52 Example Calculations for PN 3760518
RADIAL STRESS:
53
Tabulated Results of Stress at Both the Inner and Outer Radius
The tables below are the results of assuming a 120 PSI pressure. The goal of this
experiment was to test our hypothesis that a higher pressure is more realistic and could amplify any issues with the capillary tube. Table 8 is the stress at the inner radius and Table 9 is the stress at the outer radius. The data helps to show that the copper tubing will not fail even at a higher pressure such as 120 psi. The red part numbers show the parts that had existing issues when placed in the AC units. The maximum stress happens on part number 3760551 due to its thin walls.
1389902 120 0.0375 0.0625 0.0375 -120.00 255.00 67.50 324.8
1389903 120 0.027 0.053 0.027 -120.00 204.12 42.06 280.7
1389975 120 0.032 0.0625 0.032 -120.00 205.27 42.63 281.7
1389985 120 0.032 0.0625 0.032 -120.00 205.27 42.63 281.7
1390000 120 0.032 0.0625 0.032 -120.00 205.27 42.63 281.7
1390005 120 0.032 0.0625 0.032 -120.00 205.27 42.63 281.7
1390212 120 0.0295 0.056 0.0295 -120.00 212.18 46.09 287.7
1390223 120 0.0375 0.0625 0.0375 -120.00 255.00 67.50 324.8
3760383 120 0.0375 0.0625 0.0375 -120.00 255.00 67.50 324.8
3760394 120 0.032 0.0625 0.032 -120.00 205.27 42.63 281.7
3760501 120 0.032 0.0435 0.032 -120.00 403.05 141.53 453.0
3760511 120 0.0295 0.056 0.0295 -120.00 212.18 46.09 287.7
3760518 120 0.027 0.053 0.027 -120.00 204.12 42.06 280.7
3760526 120 0.027 0.053 0.027 -120.00 204.12 42.06 280.7
1389915 120 0.0295 0.056 0.0295 -120.00 212.18 46.09 287.7
3760451 120 0.0245 0.0495 0.0245 -120.00 197.87 38.94 275.3
Table 8: Stresses on select capillary tubes inner diameter.
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Table 9: Stresses on select capillary tubes out diameter.
Conclusion
After checking all the different capillary tubes at Friedrichs facility we can see that the copper tubing will not fail if tested at a pressure of 120 psi as the yield stress of the copper used in to construct the capillary tube is over 10 times greater than the maximum stress induced on the capillary tube.
𝜎
𝑦= 4830 𝑃𝑆𝐼 ≫ 𝜎
𝑣,𝑚𝑎𝑥= 453 𝑃𝑆𝐼
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CAPILLARY TUBE FINITE ELEMENT ANALYSIS
The goal of this analysis was to prove that under the maximum pressure load the capillary tubes will experience of 120 psi, there is no risk of them failing. As the analysis suggests, the greatest stress that will be experienced by the capillary tube we selected will be 3502.4 psi.
However, these values are located at the end of the tube we were required to plug the capillary tube to perform the analysis. However, these plugs will not present in the test fixture as the
However, these values are located at the end of the tube we were required to plug the capillary tube to perform the analysis. However, these plugs will not present in the test fixture as the