Jacob Schichtel Project 2 Page 1 of 9 Setup The geometry was created in ANSYS Design modeler as specified in the report instructions. A plane of symmetry was used to reduce the computation time and to analyze the velocities at the midplane. Fine meshing was used with 1-layer inflation at the wall boundaries. A slow growth face sizing mesh control was imposed on the outlet to increase the accuracy of Task 2. Normal gravity was set in the downwards direction. Figure 1. Meshing of the pipe. Task 1 For Task 1, the outlet was set as a zero-gauge pressure outlet, which is the same outlet condition as the five smaller pipes. Case 1 Figure 2. Velocity contour for case 1. Figure 3. Mass flow rates for case 1.
Velocity in the Direction of Axis (m/s) Static Gauge Pressure in the Direction of Axis (Pa) Mass Flow Rate (kg/s) Jacob Schichtel Project 2 Page 2 of 9 Case 1: Mass Flow Rates.1.8.6.4.2 Outlet 1 Outlet 2 Outlet 3 Outlet 4 Outlet 5 Figure 4. Mass flow rates for case 1. Case 1: Static Gauge Pressure Along the Axis in the Direction of the Axis 15 1 5.5 1 1.5 2 2.5 3 Figure 5. Static gauge pressure along the axis in the direction of the axis for case 1. Case 1: Velocity Along the Axis in the Direction of the Axis.7.6.5.4.3.2.1.5 1 1.5 2 2.5 3 Figure 6. Velocity along the axis in the direction of the axis for case 1.
Static Gauge Pressure in the Direction of Axis (Pa) Mass Flow Rate (kg/s) Jacob Schichtel Project 2 Page 3 of 9 Case 2 Figure 7. Contour plot of velocity for case 2. Figure 8. Mass flow rates for the 5 outlet pipes in case 2. Case 2: Mass Flow Rate.14.12.1.8.6.4.2 Outlet 1 Outlet 2 Outlet 3 Outlet 4 Outlet 5 Figure 9. Mass flow rates for the 5 outlet pipes in case 2. Case 2: Static Gauge Pressure Along the Axis in the Direction of the Axis 15 1 5.5 1 1.5 2 2.5 3 Figure 1. Static gauge pressure along the axis in the direction of the axis for case 2.
Velocity in the Direction of Axis (m/s) Jacob Schichtel Project 2 Page 4 of 9 Case 2: Velocity Along the Axis in the Direction of the Axis.8.6.4.2 -.2.5 1 1.5 2 2.5 3 Figure 11. Velocity along the axis in the direction of the axis for case 2. Task 2 i) Best case for uniform mass flow rates. The best case with the smallest S index was with the outlet B completely closed and outlet diameters 1 through 5 set to 5 cm, 4.13 cm, 3.59 cm, 3.14 cm, and 2.92 cm, respectively. This obtained an S index of.57. This value is already quite small, but could have been further reduced by continuing the iterative process I will describe in part (ii). S Index for Best Case.57 Figure 12. Velocity contour for the best-case scenario. Figure 13. Mass flow rates for the best-case scenario.
Velocity in the Direction of Axis (m/s) Static Gauge Pressure in the Direction of Axis (Pa) Mass flow rate (kg/s) Jacob Schichtel Project 2 Page 5 of 9 Mass flow rates for "best case".12.1.96546993.95967621.959811.96962.9738988.8.6.4.2 Outlet 1 Outlet 2 Outlet 3 Outlet 4 Outlet 5 Figure 14. Mass flow rates for the best-case scenario. Static Gauge Pressure Along the Axis in the Direction of the Axis for "Best Case" 1 8 6 4 2.5 1 1.5 2 2.5 3 Figure 15. Plot of Static Gauge Pressure Along the Axis in the Direction of the Axis for "Best Case." Velocity Along the Axis in the Direction of the Axis for "Best Case".8.6.4.2 -.2.5 1 1.5 2 2.5 3 Figure 16. Velocity Along the Axis in the Direction of the Axis for "Best Case".
Jacob Schichtel Project 2 Page 6 of 9 i) Process for finding the best case for uniform mass flow rates. To find the conditions for the lowest S index in the most efficient way, I first thought I should optimize the B outlet opening, and then with that opening, optimize the pipe diameters. If necessary I could return to optimizing the B outlet opening with these new pipe diameters and continue in that fashion. In order to change the area of opening for outlet B, I split the outlet face into two parts as shown in Figure 17. The inner face was set as an outlet with zero-gauge pressure, while the outer face was set as a wall. The mesh size was increased near this outlet to increase the accuracy of the results. All the exact results are given in the appendix. Figure 17. Meshing of the B outlet showing the refined mesh and the split face. I started with 5% flow area and compared the results with case 1 and case 2. Case 1 with 1% flow area had an S index of.24, case 2 with % flow are had an S index of.187755, and the case with 5% flow area had the lowest index of.85. One of the velocity contours for the partial opening at outlet B is shown in Figure 18. Figure 18. Velocity contour for partial opening at outlet B.
Jacob Schichtel Project 2 Page 7 of 9 I then tried 25% flow area by adjusting the diameter of the split face, but surprisingly, this had an S index that was higher than both the % and the 5%. This indicates that the S-index has a multipeak relationship with the outlet flow area. I next tried 4% and 45% flow area, but both were still higher than 5%, so I switched sides and tried 6% flow area and the S index dropped to.25. I was looking for the spread of outlet flow values. The mass flow was increasing across each outlet for % flow area, but decreasing across each outlet for 1% area, so I hoped to find a condition in the middle where the flows were higher at the beginning and end, but dropped in the middle. Then I would be able to adjust the diameter of the outlets, to further refine the mass flow at the outlets. However, I realized that the lowest S index could be achieved more easily when the mass flow was higher, because the relative error would be lower. So, I changed my strategy to what I should have done from the beginning. I set the outlet to be completely closed, which not only increases the mass flow rate through the other outlets, but also sets the mass flow rate to a constant value, eliminating a variable. With the outlet B closed, the mass flow rates tend to increase successively, so I set the first outlet 1 to the max diameter of 5 cm. I knew I could eliminate another variable by setting this diameter to a constant, and the best solution would have the 1 st diameter as the largest. From this point on I would only adjust the other four diameters based on the results. I looked at the results of each iteration and adjusted based on the mass flow results. I would generally increase the diameter of the lower mass flow rate pipes, and decrease the diameter of the pipes with mass flow ratees greater than the average, keeping in mind that increasing flow in one pipe would decrease the flow in the pipes around it. Because I closed the B outlet, I knew what the mass flow rate through each pipe should be because it is constant, so I could also gauge my adjustments based on how off they were from that value. My adjustments became more refined as the number of iterations increased. I stopped once the S-index fell below.1, but I could have further refined the diameter sizes indefinitely to reach lower values. These trials were very easy to iterate because all I needed to do was change the diameters, and update the project. I set gravity in the downwards direction, which slightly affected the results of my project. I compared my results with Jack Miller s.
Jacob Schichtel Project 2 Page 8 of 9 Appendix: S Indices and Plots of Mass Flow Rates Across Outlets 1-5 for Task 2 CASE 2 % Area Outlet 1.7561.96568.463 Outlet 2.81849.96568.217 Outlet 3.92159.96568 1.94E-5 Outlet 4.19154.96568.158 Outlet 5.124615.96568.787.482838 S index:.187755.15.1.5 2 4 6 6% Area Flow DO=.387, 3D =.5 Outlet 1.51184.64497.177 Outlet 2.5567.64497.194 Outlet 3.63164.64497 1.78E-6 Outlet 4.6955.64497 2.51E-5 Outlet 5.8866.64497.555 S index:.214124.1.5 2 4 6 25% Area Flow D=.25 Outlet 1.63722.78431.216 Outlet 2.64486.78431.194 Outlet 3.73647.78431 2.29E-5 Outlet 4.87497.78431 8.22E-5 Outlet 5.1283.78431.594.392155 S index:.189961 4% Area Flow D=.3162 Outlet 1.6353.733 4.59E-5 Outlet 2.62778.733 5.66E-5 Outlet 3.67498.733 7.87E-6 Outlet 4.74768.733 1.99E-5 Outlet 5.82941.733.16.351516 S index:.18334 45% Area Flow D=.335 Outlet 1.6281.6782 1.82E-5 Outlet 2.699.6782 3.81E-5 Outlet 3.64537.6782 6.47E-6 Outlet 4.7166.6782 9.52E-6 Outlet 5.76986.6782 9.81E-5.33548 S index:.8735 5% Area Flow D=.35355 Outlet 1.6313.62695 5.67E-6 Outlet 2.5681.62695 3.46E-5 Outlet 3.59292.62695 1.16E-5 Outlet 4.6519.62695 5.83E-6 Outlet 5.7195.62695 8.57E-5.313473 S index:.85412 6% Area Flow D=.387 Outlet 1.5999.58666 1.75E-6 Outlet 2.5639.58666 5.18E-6 Outlet 3.57718.58666 8.99E-7 Outlet 4.58946.58666 7.82E-8 Outlet 5.6288.58666 2.63E-6 S index:.24745 CASE 1 1% Area r=.25 Outlet 1.54151.4198.15 Outlet 2.49453.4198 5.69E-5 Outlet 3.43829.4198 3.69E-6 Outlet 4.36764.4198 2.65E-5 Outlet 5.25345.4198.274.29541 S index:.241296.15.1.5 2 4 6.1.5 2 4 6.1.5 2 4 6.1.5 2 4 6.1.5 2 4 6.1.5 2 4 6 95% Area Flow DO=.387, 3D =.5 Outlet 1.5324242.5291 1.1E-7 Outlet 2.5798882.5291 4.46E-6 Outlet 3.5425144.5291 1.8E-6 Outlet 4.55298992.5291 5.71E-6 Outlet 5.595851.5291 3.81E-6 S index:.33685 Outlet Area 1%, D1=.5, D2=.45, D3=.4, D2=.35, D5=.3 Outlet 1.82511157.96568.198 Outlet 2.93945965.96568 6.87E-6 Outlet 3.129659.96568 3.6E-5 Outlet 4.1717162.96568.112 Outlet 5.97114176.96568 2.98E-7 S index:.86363 Outlet Area 1%, D1=.5, D2=.4, D3=.3, D2=.25, D5=.2 Outlet 1.1114.96557.22 Outlet 2.122778.96557.688 Outlet 3.147.96557 6.63E-5 Outlet 4.8559.96557.12 Outlet 5.58316.96557.1462 S index:.234197 Outlet Area 1%, D1=.5, D2=.35, D3=.35, D2=.3, D5=.25 Outlet 1.11691344.96557.414 Outlet 2.8948.96557 5.1E-5 Outlet 3.1587414.96557 8.68E-5 Outlet 4.9763547.96557 1.16E-6 Outlet 5.72883487.96557.56 S index:.15459 Outlet Area 1%, D1=.5, D2=.38, D3=.37, D2=.36, D5=.35 Outlet 1.1153287.96566 2.47E-5 Outlet 2.8223411.96566.26 Outlet 3.858146.96566.116 Outlet 4.9892941.96566 5.46E-6 Outlet 5.11435517.96566.316 S index:.119675 Outlet Area 1%, D1=.5, D2=.4, D3=.38, D2=.36, D5=.33 Outlet 1.926.96565 1.57E-5 Outlet 2.8525.96565.258 Outlet 3.86871944.96565 9.4E-5 Outlet 4.165.96565 1.67E-5 Outlet 5.1222.96565.657 S index:.149462 Outlet Area 1%, D1=.5, D2=.42, D3=.4, D2=.36, D5=.33 Outlet 1.85329.9656.126 Outlet 2.82697.9656.192 Outlet 3.9686.9656 2.25E-7 Outlet 4.1589.9656 8.7E-5 Outlet 5.1128.9656.264 S index:.119822.1.5 2 4 6.15.1.5 2 4 6.15.1.5 2 4 6.15.1.5 2 4 6.15.1.5 2 4 6.15.1.5 2 4 6.15.1.5 2 4 6
Jacob Schichtel Project 2 Page 9 of 9 Outlet Area 1%, D1=.5, D2=.42, D3=.4, D2=.35, D5=.31 Outlet 1.84463567.96565.146 Outlet 2.83921.96565.16 Outlet 3.1146.96565 2.4E-5 Outlet 4.189295.96565.153 Outlet 5.145129.96565 5.6E-5 S index:.1754.15.1.5 2 4 6 Outlet Area 1%, D1=.5, D2=.42, D3=.35, D2=.31, D5=.29 Outlet 1.95.96559 2.43E-6 Outlet 2.13.96559 1.4E-5 Outlet 3.95338.96559 1.49E-6 Outlet 4.9496.96559 2.56E-6 Outlet 5.97198.96559 4.8E-7 S index:.21164.15.1.5 2 4 6 Outlet Area 1%, D1=.5, D2=.42, D3=.39, D2=.33, D5=.3 Outlet 1.858614.96562.115 Outlet 2.8868.96562 6.21E-5 Outlet 3.1287.96562 3.98E-5 Outlet 4.124.96562 3.41E-5 Outlet 5.13.96562 4.14E-5 S index:.79134.15.1.5 2 4 6 Outlet Area 1%, D1=.5, D2=.4, D3=.35, D2=.31, D5=.29 Outlet 1.19583.96568 1.93E-5 Outlet 2.9356939.96568 8.99E-6 Outlet 3.9581734.96568 5.73E-7 Outlet 4.9516.96568 1.98E-6 Outlet 5.9734271.96568 5.97E-7 S index:.25958.15.1.5 2 4 6 Outlet Area 1%, D1=.5, D2=.42, D3=.38, D2=.32, D5=.29 Outlet 1.878378.96565 7.62E-5 Outlet 2.9279669.96565 2.1E-5 Outlet 3.13165.96565 4.36E-5 Outlet 4.113.96565 2.24E-5 Outlet 5.984436.96565 3.53E-6 S index:.59631.15.1.5 2 4 6 Outlet Area 1%, D1=.5, D2=.41, D3=.35, D2=.31, D5=.29 Outlet 1.99268.96567 7.3E-6 Outlet 2.96423.96567 2.7E-8 Outlet 3.95227.96567 1.8E-6 Outlet 4.95277.96567 1.66E-6 Outlet 5.9664.96567 5.33E-9 S index:.1526.15.1.5 2 4 6 Outlet Area 1%, D1=.5, D2=.42, D3=.37, D2=.31, D5=.28 Outlet 1.9554.96562 3.61E-5 Outlet 2.9364.96562 8.54E-6 Outlet 3.1385.96562 5.31E-5 Outlet 4.9965.96562 6.27E-6 Outlet 5.957.96562 7.43E-7 S index:.4743 Outlet Area 1%, D1=.5, D2=.42, D3=.35, D2=.3, D5=.28 Outlet 1.975.96534 9.33E-7 Outlet 2.123.96534 3.32E-5 Outlet 3.985.96534 3.87E-6 Outlet 4.9257.96534 1.57E-5 Outlet 5.918.96534 2.24E-5 S index:.4432 Outlet Area 1%, D1=.5, D2=.42, D3=.35, D2=.3, D5=.28 Outlet 1.975.96534 9.33E-7 Outlet 2.123.96534 3.32E-5 Outlet 3.985.96534 3.87E-6 Outlet 4.9257.96534 1.57E-5 Outlet 5.918.96534 2.24E-5 S index:.4432.15.1.5 2 4 6.15.1.5 2 4 6.15.1.5 2 4 6 Outlet Area 1%, D1=.5, D2=.412, D3=.352, D2=.312, D5=.292 Outlet 1.9794.96564 1.89E-6.15 Outlet 2.9669.96564 1.58E-8.1 Outlet 3.949.96564 2.77E-6 Outlet 4.95558.96564 1.1E-6.5 Outlet 5.977338.96564 1.37E-6 S index:.1234 2 4 6 Outlet Area 1%, D1=.5, D2=.413, D3=.354, D2=.313, D5=.292 Outlet 1.974469.96539 8.25E-7.15 Outlet 2.97994.96539 2.12E-6.1 Outlet 3.94561.96539 3.91E-6 Outlet 4.9597226.96539 3.99E-7.5 Outlet 5.96784756.96539 6.5E-8 S index:.12528 2 4 6 Outlet Area 1%, D1=.5, D2=.413, D3=.36, D2=.313, D5=.292 Outlet 1.96576959.96568 8.75E-11.15 Outlet 2.96113488.96568 2.6E-7.1 Outlet 3.98611.96568 2.23E-6 Outlet 4.94979987.96568 2.52E-6.5 Outlet 5.9716569.96568 2.9E-7 S index:.169 2 4 6 Outlet Area 1%, D1=.5, D2=.413, D3=.359, D2=.314, D5=.292 Outlet 1.96546993.96568 4.3E-1.15 Outlet 2.95967621.96568 3.6E-7.1 Outlet 3.959811.96568 3.44E-7 Outlet 4.96962.96568 1.55E-7.5 Outlet 5.9738988.96568 6.61E-7 S index:.5712 2 4 6