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INGENIØRHOJSKØLEN I ÅRHUS June 3rd 2010 AIR FLOW STUDY IN A TWO BRANCHES MANIFOLD MECHANICAL DESIGN FINAL PROJECT PABLO ANDRÉS YAGÜE RICARD ESTEVE MONTES JAUME LLOPART VALLS SUPERVISOR: JENS BRUSGAARD VESTERGAARD AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 1 ACKNOWLEDGEMENTS We owe a great thanks to many people who helped and supported us during the development of this project. Our deepest thanks to our supervisors, Jens Brusgaard Vestergaard and Søren Gundtoft, who suggested us the project theme and have always been there to guide and help us when we have needed it. Without the help of their valuable suggestions, guidance and encouragement, this project would not have been possible. We also express our thanks to the IHA, for giving us the opportunity of coursing here the international program Mechanical Design and offering us everything we have needed: teachers, equipment and even accommodation. Our deep sense of gratitude to our home universities, especially to the coordinators, who have followed the project development in order to check if it was compatible with our home studies and have been available to answer our questions. We could not finish the acknowledgements without express our thanks to Gerner, the carpenter who prepared all the wood pieces we demanded in order to build the models; Berner, who lent us all the equipment we needed in our tests; and Aage, who sent us the CFDesign data. Sincerely yours, Spring semester 2010, Project group Omega PABLO ANDRÉS YAGÜE RICARD ESTEVE MONTES JAUME LLOPART VALLS AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 2 TABLE OF CONTENTS 1 INTRODUCTION ........................................................................................................................... 5 1.1 PROJECT DESCRIPTION ........................................................................................................ 6 2 WIDE BRANCHES MODEL ............................................................................................................ 7 2.1 TEST REPORT ....................................................................................................................... 7 2.1.1 Model Description ....................................................................................................... 7 2.1.2 Test Description........................................................................................................... 8 2.1.3 Measurements ............................................................................................................ 9 2.1.4 Analysis of results ...................................................................................................... 10 2.2 EES REPORT ....................................................................................................................... 21 2.2.1 Model Description ..................................................................................................... 21 2.2.2 System Description .................................................................................................... 21 2.2.3 Program Construction ............................................................................................... 22 2.2.4 Solution ..................................................................................................................... 23 2.2.5 Analysis of results ...................................................................................................... 25 2.3 CFD REPORT....................................................................................................................... 29 2.3.1 Model Description ..................................................................................................... 29 2.3.2 System description .................................................................................................... 29 2.3.3 Program Construction ............................................................................................... 30 2.3.4 Analysis of results ...................................................................................................... 31 2.4 WIDE BRANCHES MODEL CONCLUSIONS .......................................................................... 36 2.4.1 Pressures ................................................................................................................... 36 2.4.2 Speeds ....................................................................................................................... 40 2.4.3 Flows.......................................................................................................................... 41 3 NARROW BRANCHES MODEL .................................................................................................... 42 3.1 TEST REPORT ..................................................................................................................... 42 3.1.1 Model Description ..................................................................................................... 42 3.1.2 Test Description......................................................................................................... 43 3.1.3 Test calibration .......................................................................................................... 44 3.1.4 Measurements .......................................................................................................... 46 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 3 3.1.5 Analysis of results ...................................................................................................... 46 3.2 EES REPORT ....................................................................................................................... 50 3.2.1 Model Description ..................................................................................................... 50 3.2.2 System Description .................................................................................................... 50 3.2.3 Program Construction ............................................................................................... 51 3.2.4 Solution ..................................................................................................................... 51 3.2.5 Analysis of results ...................................................................................................... 57 3.3 CFD REPORT....................................................................................................................... 63 3.3.1 Model Description ..................................................................................................... 63 3.3.2 System description .................................................................................................... 63 3.3.3 Program Construction ............................................................................................... 64 3.3.4 Analysis of results ...................................................................................................... 64 3.4 NARROW BRANCHES MODEL CONCLUSIONS ................................................................... 73 3.4.1 Pressures ................................................................................................................... 73 3.4.2 Speeds ....................................................................................................................... 77 3.4.3 Flows.......................................................................................................................... 78 3.5 SPHERE METHOD IMPROVEMENTS .................................................................................. 80 3.5.1 Calibration process .................................................................................................... 82 3.5.2 Test results ................................................................................................................ 84 3.5.3 Velocity curves .......................................................................................................... 87 3.5.4 Flow analysis.............................................................................................................. 89 3.5.5 Test vs. EES and CFD .................................................................................................. 91 4 PRESSURE LOSS IN A TUBE SYSTEM .......................................................................................... 92 5 PROJECT CONCLUSIONS .......................................................................................................... 102 6 BIBLIOGRAPHY ......................................................................................................................... 104 7 INDEX OF ELEMENTS ............................................................................................................... 105 7.1 INDEX OF FIGURES ........................................................................................................... 105 7.2 INDEX OF GRAPHICS ........................................................................................................ 106 7.3 INDEX OF TABLES ............................................................................................................. 107 APPENDICES .................................................................................................................................... 110 A. TEST APPENDICES ................................................................................................................ 110 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 4 B. EES APPENDICES .................................................................................................................. 117 B1. EES introduction .......................................................................................................... 117 B2. Program description .................................................................................................... 117 C. SolidWorks’ Flow Simulation Studio Tutorial. Internal flows. ............................................. 135 D. DRAWINGS .......................................................................................................................... 148 E. CD ........................................................................................................................................ 152 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 5 1 INTRODUCTION This report is the result of a semester group project and it supposes for all of us our previous step to the working world, which encouraged us to do our best and focus our effort on it. When our coordinators exposed us the idea to develop a cooling system for a wind turbine generator we did not hesitate, as we regarded the subject as very interesting and a possibility to show all the knowledge acquired in the Aerodynamic course and in the Multidisciplinary project we did last semester. In this report, we tried to display what we have learned in the last four months and a half and to show our understanding of the subject matter. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 6 1.1 PROJECT DESCRIPTION This project consists on a cooling system for a wind turbine generator. The main concept used to cool the generator is based on a manifold, which consists in an arrangement of pipes used to redistribute the flow of a fluid or gas, typically from a single inlet to a number of outlets, or vice versa. The first idea was to design a manifold with an inlet and four outlets using an equation solver program called EES, SolidWorks Flow Simulation as an application of computational fluid dynamics (CFD) analysis and a wooden model built and tested, and try to get the total control of the system. A first step has been to carry out all the calculations for a two branch model. This has given us a general idea of how the flow works and how it is distributed between the branches, and this two branches model (instead of four) simplifies the calculations of the model at first. This model, which its main branch is 30 mm wide and the outlet branches widths are 19.5 and 21.5 mm, has been introduced to an EES program, designed in SolidWorks and built in wood to obtain the pressures, velocities and flows for the circulating fluid along the conduits. Once the results for the three methods have been obtained, these has been analyzed and compared between them to draw some conclusions about the similarities or differences of the data from the three methods. After the first analysis we have decided to build again a two branches model but with narrower conduits, of 5 mm both the main branch and the outlet branches. This second model has been designed to see if the flow behaves the same way when it circulates through narrow conduits. Here we have had to design a new method to measure the parameters inside the thin conduits. This method, which we called “Sphere method”, consists of a small lead ball which moves more or less depending on the pressure applied on its surface. Once compared to the other two computational methods, it has been tested in the wide branches model and compared to the results obtained there measuring with a Pitot tube, and has resulted to be more accurate than expected, so we have decided to enhance it by working with more lengths to calculate the velocity profile curve and improve the calibration of the threads so the results were even more precise. In other matters we have studied the pressure loss in a tubular pipe which is narrower in the middle. This study has been performed using three computer programs; the already known EES and SolidWorks Flow Simulation Studio, and CFDesign. This last comparison has been expected to show the differences between three methods based on theoretical calculations. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 7 2 WIDE BRANCHES MODEL 2.1 TEST REPORT Test Date: March 15th, 2010 Test Engineers: Pablo Andrés, Ricard Esteve, Jaume Llopart 2.1.1 Model Description The model consists of three wood blocks separated a certain distance so the air can flow between them. These three blocks are covered on the top at some distance by another piece of wood, so we get a main branch that is split in two. This assembly wants to represent a kind of simple manifold. The drawing below shows the dimensions and an entire view of the model. Figure 1. Model overview. On both sides the system is closed with two transparent holey plastic pieces which at the same time work as union between all the parts. The holes in the plastic covers are distributed so that there are six control points for the main branch and three for each of the secondary ones. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 8 Due to the geometry of the Pitot tube, the holes have to be drilled at some distance from the control point. In the following picture is shown the exact position of the control points. Figure 2. Holes situation. The air flows through the empty spaces in the model. This air comes from a homemade fan, built with a 1.5 kW three-phase electric motor which gives a rotational speed of up to 2870rpm at its shaft. The motor is held to some blades which produce, thanks to the movement, the draft needed. This fan provides the required speed and flow at its outlet, a flexible tube connected directly to the model. Before entering the model, the flow is forced to circulate through a diffuser so it becomes better even distributed. This diffuser is made by a holey plastic plate with fifty (eight millimetres diameter) holes uniformly distributed in eleven rows, six of them with five holes and the remaining five with four holes each, as shown in Figure 3. This holey plate is placed inside a closed wood box where the air flow is introduced by one side and let out to the model by the opposite side. 2.1.2 Test Description The pressure values for each of the fifteen control points are taken with a 4-millimeter diameter Pitot tube. The tube is introduced into a hole and placed completely parallel to the flow. Although the Pitot is being held with the hand during the entire test, it is important to keep it as still as possible to get the most reliable results. The Pitot tube is moved from hole to hole to take all the measurements while the other holes are being covered. In each control point where the Figure 3. Diffusion plate. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 15 Speeds [m/s] 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Average I1 11,73 12,20 12,65 13,48 13,86 13,75 13,75 13,06 A1 9,47 9,80 10,33 10,88 10,76 10,93 10,43 10,37 A2 10,33 10,64 10,74 11,45 11,91 11,94 12,18 11,31 A3 9,96 10,20 10,25 10,74 11,18 11,22 10,98 10,65 A4 10,04 10,20 10,31 10,80 11,10 10,79 9,96 10,46 A5 10,02 10,10 10,25 10,81 11,25 11,01 10,38 10,54 A6 9,91 10,04 10,10 10,69 11,06 10,79 10,41 10,43 B1 5,80 2,53 4,13 6,31 7,97 5,93 6,53 5,60 B2 6,11 5,61 2,19 6,89 6,41 6,20 5,71 5,59 B3 6,37 5,37 4,73 5,49 5,93 5,52 5,37 5,54 O1 5,52 5,37 5,37 5,87 5,93 5,22 5,06 5,48 C1 7,34 7,23 7,80 7,70 8,07 7,16 7,16 7,49 C2 8,67 7,94 7,94 8,18 6,85 8,00 8,64 8,03 C3 8,80 7,52 7,77 7,61 7,80 7,77 8,30 7,94 O2 7,80 7,38 7,38 7,27 7,16 7,16 8,10 7,46 Table 6. Speed values. Taking all the results from the calculations, some graphics were done in order to check the speed profiles in each point, being able to see if the profiles were symmetrical as the theory shows. The graphics were done following the fluid trajectory along the branches: one following the main branch, and the two others following the different branches as well as the previous trajectory through the main branch. This previous path was considered in order to see the speed drop in the bends. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 16 Graphic 3. Main branch speed profile. Graphic 4. Branch 1 speed profile. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 9,0 9,5 10,0 10,5 11,0 11,5 12,0 12,5 A1 A2 A3 A4 A5 A6 Speed [m/s] Control points Main branch 12,0-12,5 11,5-12,0 11,0-11,5 10,5-11,0 10,0-10,5 9,5-10,0 9,0-9,5 1/8 1/4 3/8 1/2 5/8 3/4 7/8 2 3 4 5 6 7 8 9 10 11 12 13 Speed [m/s] Control Points Branch 1 12-13 11-12 10-11 9-10 8-9 7-8 6-7 5-6 4-5 3-4 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 17 Graphic 5. Branch 2 speed profile. Analysing the results and the graphics, it can be seen that the speed profiles are not as symmetrical as they should be following the theory. It can also be noticed the speed drops just after the branch bend, in points B1 and C1. Besides, the flow behaviour taking the bends can explain the speed irregularities all along the branches 1 and 2. This case is especially apparent in the branch 1 graphic, where the profile takes some ups and downs across the depths. 2.1.4.3 Flows Once the speeds were calculated, the last things to analyse were the flows. The flows allow checking the amount of air running through the manifold, and enable to prove if there is any air loss along the way. The flows are calculated using the average speed in each control point and the branch section area in that point. For these calculations, the following data was used: Branch Width [m] Depth [m] Area [m2] Main 0,03 0,2 0,006 First 0,0195 0,2 0,0039 Second 0,0215 0,2 0,0043 Table 7. Area data. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 6 7 8 9 10 11 12 13 Speed [m/s] Control Points Branch 2 12-13 11-12 10-11 9-10 8-9 7-8 6-7 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 18 And in the following table there can be seen the calculated values: Flows [m3/s] A1 0,0622 A2 0,0679 A3 0,0639 A4 0,0627 A5 0,0633 A6 0,0626 B1 0,0218 B2 0,0218 B3 0,0216 C1 0,0322 C2 0,0345 C3 0,0341 Table 8. Flow values. In Table 8, flow values are the result from the multiplication of the speed in each point and the branch area in those points. For a better comprehension of how the flows behave along the manifold, the following figure and graphic were done: A1 A2 A3 A4 A5 A6 0,0622 0,0679 0,0639 0,0627 0,0633 0,0626 B1 0,0218 C1 0,0322 B2 0,0218 C2 0,0345 B3 0,0216 C3 0,0341 Table 9. Flow values. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 19 Graphic 6. Main branch flow values. Graphic 7. Flow values in the branches. From the results table it can be noticed some incongruent values, probably caused in part by measurements imprecision. First, a flow raise occurs in point A2 and then it drops in A3, staying constant then all along the main branch. Next, between points A3 and A4, where the first branch division is placed, there is no substantial flow decrease, when the first branch flow is almost one third of the main branch flow. Finally, although the value in A6 is 0,626 m3/s, the next point in the way, C1, has only 0,0322 m3/s, almost the half when there is no flow division in this point. 0,0600 0,0620 0,0640 0,0660 0,0680 0,0700 A1 A2 A3 A4 A5 A6 Flow [m3/s] Control Points Main branch 0,0100 0,0150 0,0200 0,0250 0,0300 0,0350 0,0400 B1/C1 B2/C2 B3/C3 Flow [m3/s] Control Points Branches First Branch Second Branch AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 20 It is also important to mention that the inlet flow is 0,0622 m3/s, while the both combined outlet flows are 0,0557 m3/s, which means there is 10,5% flow loss all along the manifold system. From this result it is noticed that as the outlet flow is reasonably correct compared to the inlet flow, the most incongruent values inside the manifold are from A4 to A6, where they stay equal to the inlet flow and should be lower to compensate the lost flow in the first branch. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 21 2.2 EES REPORT 2.2.1 Model Description The system studied with EES consists of a main conduct divided in two branches. The inlet is placed in the main conduct and the outlets in the branches. The dimensions of the model are the same as the device tested in the laboratory, so that the results can be compared. Furthermore, a roughness value of 0.0001 m is assumed. Figure 4. EES model dimensions. 2.2.2 System Description 11 states have been defined in the program as control points (see the figure below): - State 1: 10 cm. before the inlet. - State 2: Inlet. - State 3: Main branch, right before the first branch. - State 4: First branch, right after the division. - State 5: Main branch, right after the division. - State 6: Main branch, before the 900 bend. - State 7: Second branch, after the 900 bend. - State 8 and 9: Outlets. - State 10 and 11: 10 cm. after the outlets. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 22 Figure 5. States defined in EES. However, these states are only employed in EES. To avoid confusion, the equivalent states employed in the laboratory test are specified in the tables where the EES solutions are shown. The goal of realizing this program is to obtain the values of static, dynamic and total pressure, pressure loss, zeta coefficients and speed in all the control points, as well as the outlets flow, so that we can understand the behaviour of the air inside the device and compare these parameters with the results in CFD and the laboratory. 2.2.3 Program Construction The whole program is defined in the Equations Window (see Appendix 2) where all the equations and input data are introduced. The input data in this case have been the properties of the air (density and kinematic viscosity), the geometric values (dimensions and roughness) and the inlet flow. The eleven states have been defined by using the formulas for pressure (pressure loss, dynamic pressure and total pressure), Reynolds number and flow:  𝑄=𝑣·𝐴  𝑅𝑒=𝑢· 𝑑 𝜐  𝑃𝑡= 𝑃+ 𝑃𝑑  𝑃𝑑= 1 2· 𝜌· 𝑢2  𝑑𝑃1,2 = 𝜁1,2 · 𝑃𝑑1,2  𝑃𝑡2= 𝑃𝑡1− 𝑑𝑃1,2 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 23 The zeta coefficient to calculate the pressure loss between two control points in straight stretches are calculated with a function dependent on the Reynolds number and the roughness called “FUNCTION zeta_fric (Re,ksd)” (Friction factor for flow in tubes, including laminar and transient area). To calculate the pressure loss in the intersection of the main branch with the first branch a double interpolation has been employed. The introduced data in the interpolation are the flow ratio and the area ratio, while the output data are “zeta_through” and “zeta_branch”. There is a critic point in the configuration process, state 4. In this point the speed has to be guessed because if not, there will be more variables than equations, which makes impossible to find a desirable solution. However, with the guessed speed, the pressure in state 10 (first outlet) is incorrect since it is different from zero. The way to change this is, once the number of equations is the same as the number of variables, pressure 10 has to be set equal to zero. Afterwards, pressing F2, the solution is recalculated and the correct speed in state 4 is found. Finally, all the input data has been highlighted to facilitate the understanding of the program by someone who has not participate in its configuration. 2.2.4 Solution All the solution provided by the program in the Solution Window has been resumed in the table below. The units are shown in SI units. The whole Solution Window can be seen in Appendix B2. Solution Window State (EES) State (Test) Speed Dynamic P. Static P. Total P. Flow 1 I1 1.50 1.38 134.80 136.20 0.0622 2 A1 10.37 65.83 37.42 103.20 undefined 3 A3 10.37 65.83 35.85 101.70 " 4 B1 6.83 28.54 0.76 29.30 " 5 A4 5.93 21.53 76.52 98.05 " 6 A6 5.93 21.53 75.97 97.50 " 7 C1 8.27 41.93 1.07 43.00 " 8 C3 8.27 41.93 0 41.93 " 9 B3 6.83 28.54 0 28.54 " 10 O1 0 0 0 0 0.0266 11 O2 0 0 0 0 0.0356 Table 10. Solution Windows resume. The flow is undefined in the Equations Window from state 2 to sate 9 because it is unnecessary to calculate it in these states. The only flows which are defined in the Equations Window are: “Q_total” (state 1), “Q_1st_branch” (state 10) and “Q_2nd_branch” (state 11). AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 24 All the input and output data, as well as a sketch of the system are shown in the Diagram Window (see the figure below). Figure 6. Diagram Window. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 31 2.3.4 Analysis of results When the Simulation has been run the results are already able to work with. Some of the results are given directly by the program, but some other valuable data, which is needed to make a good comparison with the lab test data, has to be previously set to be shown. This is required to know the values in the control points, which are actually control sections if we think in a 3D model. SolidWorks’ Flow Simulation doesn’t have a tool to control an area inside the controlled volume, so it is necessary to create a point mesh, as shown in figure 11, and later make an average with all the point values obtained. There are some different ways to see results, and SolidWorks Flow Simulation Studio gives us the opportunity to do so. One of this ways is with the result plots. The cut plot shows a cut view of the flow circulating through the conduit. In figure 12 is represented the flow pressure changes in the fluid in the centre profile of the model. Figure 12. Pressure cut plot. It can be clearly seen how the pressure changes in every bend. At the inlet the fluid has a pressure higher than the atmospheric (101325 Pa) due to the speed given by the fan. After the first division the fluid in the main branch experiences a pressure increase, and in both outlet branches the pressure decreases considerably influenced by the atmospheric pressure outside the manifold. The parameter represented on the model can be easily changed, and it allows having an idea of the speed variation throughout the model. In figure 13 can be seen how the speed of the fluid is decreasing after the first division, as some fluid is deviated to the first branch and the area remains constant for the entire main branch. Still in the main, can also be appreciated the lower speed of the fluid circulating close to the walls. Figure 11. Point mesh. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 32 Figure 13. Velocity cut plot. The speed in the outlet branches is quite higher on the right walls than on the left ones because of the fluid trajectory along the curve, most of it tends to go to the outer side of the channel so a biggest part of fluid has to circulate in the same area, and therefore the speed has to increase. The results in the following table are going to be analysed and compared to the results taken with EES and the laboratory testing. SolidWorks’ Flow Simulation Studio gives some other data as a result of the calculations made for the manifold model studied, such as Temperature variation, density, shear stress in every point, mass flow rate, etc. These data comes from the point parameter averages and the surface parameters. Although the average values are not exact at all, due to the limited number of points introduced in the control areas of the model, they can be considered very reliable. Solution Window Test State CFD State Speed Dynamic P. Static P. Total P. Volume Flow [m3/s] I1 I1 -- -- -- -- 0,0622 A1 1 10,45 66,82 27,44 94,26 -- A3 2 8,46 43,85 20,60 64,45 -- A4 3 4,98 15,16 56,15 71,31 -- A6 4 4,79 14,06 49,81 63,87 -- B1 5 5,61 19,28 5,13 24,41 -- B3 6 5,41 17,93 -0,25 17,69 -- O1 O1 -- -- -- -- 0,0276 C1 7 6,88 28,99 8,99 37,98 -- C3 8 6,76 27,98 -0,11 27,87 -- O2 O2 -- -- -- -- 0,0346 Table 12. SolidWorks' Flow Simulation results. The empty boxes in the table, where the inlet and outlets pressure values should go, are not filled because these control points are out of the computational domain. Anyway it can be guessed that the static pressure would be equal to the atmospheric pressure and the dynamic pressure would be zero. As expected, the volume flow values, given by SolidWorks, AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 33 show that the flow at the outlets equals the flow at the inlet, meaning there is no pressure loss in the conduit. The following graphics represent the pressure and speed values for each of the two trajectories followed for the fluid molecules from the inlet to one of the two outlets of the model. Graphic 12. Fluid speed between the inlet and the first outlet. In graphic 12, where the first trajectory fluid speeds are represented, the speed decreases considerably when the flow leaves the main branch and reaches the outlet branch, between control points A3 and B1. This is due to the fact that, although the area is reduced a third of its size and it should mean a speed increase, the flow is also reduced around a fifty percent and makes the fluid circulate slower. Moreover, it can also be appreciated a speed decrease between A1 and A3 and between B1 and B3, due to the wall friction and the pressure losses along the branches. 0,00 2,00 4,00 6,00 8,00 10,00 12,00 A1 A3 B1 B3 Speed [m/s] States Speeds Inlet - 1st Outlet Speed 1st branch AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 34 Graphic 13. Fluid speed between the inlet and the second outlet. Graphic 13 show the speed values along the second fluid trajectory. In this case it can be seen how the speed decreases after the fluid is deviated through the first branch, between points A3 and A4, when the flow is reduced at its half and the area remains constant. Furthermore, when the flow turns at the second branch, the area is reduced and there is no flow decrease, and that is why the speed rises again between A6 and C1. Graphic 14. Fluid pressure between the inlet and the first outlet. Regarding to the pressures, graphic 14 shows the variation of the dynamic and static pressures as well as the total pressure. Between the control points A3 and B1 there is a big decrease due to the area reduction after the first deviation, which also means a speed decrease. At the outlet B3, the static pressure tends to zero, as the atmospheric pressure is. 0,00 2,00 4,00 6,00 8,00 10,00 12,00 A1 A3 A4 A6 C1 C3 Speed [m/s] States Speeds Inlet - 2nd Outlet Speed 2nd branch -20,00 0,00 20,00 40,00 60,00 80,00 100,00 A1 A3 B1 B3 Pressure [Pa] States Pressures Inlet - 1st Outlet Dynamic P. Static P. Total P. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 35 Graphic 15. Fluid pressure between the inlet and the second outlet. Finally, graphic 15 show the pressure variations from the inlet to the second outlet. After the first division but still in the main branch the dynamic pressure decreases considerably due to the flow decrease in an unchanged section area. After the second branch deviation the pressure increases while the area is reduced and the flow is maintained constant. -20,00 0,00 20,00 40,00 60,00 80,00 100,00 A1 A3 A4 A6 C1 C3 Pressure [Pa] States Pressures Inlet - 2nd Outlet Dynamic P. Static P. Total P. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 36 2.4 WIDE BRANCHES MODEL CONCLUSIONS In the following graphics it is shown a comparison between the results of the three different study methods employed. It is assumed that the test values representation might defer from the other two computational methods, as they both are more accurate in the internal flow analysis. Furthermore, the represented test values are averages from a few measurements taken in the laboratory, and it can lead to some inaccuracies. 2.4.1 Pressures The high dynamic pressure value in the inlet control point A1 is due to the introduction of an amount of air (0.0622 m3/s) into a small section area (60 cm2). At A3 the Test and EES results show that the dynamic pressure keeps almost constant, while CFD shows an unexpected decrease. This fact could be the result of placing the control area too close to the first deviation branch, and then the values would be influenced by the lower flow speed after the branch. The first control point values in the branch (B1) show the dynamic pressure drop as a result of the flow division. At this point the three results are fairly similar. At the first branch outlet the pressure remains almost constant as the flow and area are invariant. Graphic 16. Dynamic pressure from the inlet to the first outlet. In graphic 17 the A1 and A3 control points are the same described in graphic 16. At point A4 the dynamic pressure experiences a big decrease due to the flow reduction although the area stays invariant. However, the test values do not show this fact because the flow after the first division seems to remain constant. Probably the values taken during the test for the 0 10 20 30 40 50 60 70 80 A1 A3 B1 B3 Dyn. pressure [Pa] Control Points DYNAMIC P. INLET - 1st OUTLET TEST EES CFD AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 37 A4, A5 and A6 control points were mistaken and this makes the averages go wrong. After the second bend, the dynamic pressure rises again (at least in the EES and the CFD lines) while the area has been reduced. Graphic 17. Dynamic pressure from the inlet to the second outlet. In graphic 18 it can be seen how the tendency lines are quite similar, although the test line is not as low as the other two are. The static pressure at the main branch is higher due to the injection of air into a certain volume. When the air reaches the first outlet branch the static pressure becomes influenced by the atmospheric pressure and it decreases until zero. The test value at B1 shows a negative static pressure; it can be explained as a lack of data taken in that control point, as the flow trajectory through the outlet branch makes that at the interior wall the static pressure takes negative values. If the values taken in B1 are nearer to the interior wall than to the exterior, the average value is distorted. 0 10 20 30 40 50 60 70 80 A1 A3 A4 A6 C1 C3 Dyn. pressure [Pa] Control Points DYNAMIC P. INLET - 2nd OUTLET TEST EES CFD AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 38 Graphic 18. Static pressure from the inlet to the first outlet. Points A1 and A3 are the same than the ones in graphic 18. At point A4, still in the main branch and after a flow decrease, the static pressure is raised as Bernoulli’s equation1 says when the velocity drops the pressure has to increase. After the bend, the static pressure is affected by the atmospheric pressure at the outlet and it tends to zero again. Graphic 19. Static pressure from the inlet to the second outlet. 1 Bernoulli’s equiation: -30 -20 -10 0 10 20 30 40 50 A1 A3 B1 B3 Static pressure [Pa] Control Points STATIC P. INLET - 1st OUTLET TEST EES CFD -10 0 10 20 30 40 50 60 70 80 A1 A3 A4 A6 C1 C3 Static pressure [Pa] Control Points STATIC P. INLET - 2nd OUTLET TEST EES CFD AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 39 The following graphics, showing the total pressures for the two trajectories in the manifold, are a sum of the dynamic and static pressures for each of the three methods. Graphic 20. Total pressure from the inlet to the first outlet. Graphic 21. Total pressure from the inlet to the second outlet. 0 20 40 60 80 100 120 A1 A3 B1 B3 Total pressure [Pa] Control Points TOTAL P. INLET - 1st OUTLET TEST EES CFD 0 20 40 60 80 100 120 A1 A3 A4 A6 C1 C3 Total pressure [Pa] Control Points TOTAL P. INLET - 2nd OUTLET TEST EES CFD AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 40 2.4.2 Speeds As in the graphic 16, where the dynamic pressure is shown, graphic 22 shows that the CFD value for the point A3 is influenced by the speed in the first outlet branch. Nevertheless, the values for the three methods are very alike in all the other control points and the tendencies are very close. The speed at the inlet is the one given by the fan and it does not decrease along the main branch. Once the flow reaches the outlet branch the speed is decreased due to the flow reduction despite the area has been decreased. Graphic 22. Flow speed from the inlet to the first outlet. The next graphic shows how the speed is reduced when almost the half of the flow is deviated through the first outlet branch. At the second branch, the speed rises again due to the area reduction. As the speed values are calculated from the dynamic pressure values, the tendency line for the test does not decrease between A4 and A6. Graphic 23. Flow speed from the inlet to the second outlet. 0 2 4 6 8 10 12 A1 A3 B1 B3 Speed [m/s] Control Points SPEED INLET - 1st OUTLET TEST EES CFD 0 2 4 6 8 10 12 A1 A3 A4 A6 C1 C3 Speed [m/s] Control Points SPEED INLET - 2nd OUTLET TEST EES CFD AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 47 Inlet Speed Control Point mm Dynamic P. [Pa] Static P. [Pa] Total P. [Pa] 15 m/s A1 66 176,98 29,42 206,40 A2 33 57,58 34,32 91,90 B1 25 38,08 0,98 39,06 C1 25 38,08 7,85 45,93 Table 18. Pressure values 15 m/s. Inlet Speed Control Point mm Dynamic P. [Pa] Static P. [Pa] Total P. [Pa] 20 m/s A1 90 303,24 47,07 350,31 A2 52 118,66 54,92 173,58 B1 42 83,92 0,00 83,92 C1 43 87,14 12,75 99,88 Table 19. Pressure values 20 m/s. As there could be only four control points in the model, there are no control points enough to make an accurate pressure loss analysis along a single branch. However, it can be noticed that from A1 to A2 there is a dynamic pressure loss of 185 Pa due to the division in the middle of the two points. Also, in the last bench between points A2 and C1 there is a dynamic pressure loss of approximately 30 Pa. Regarding the static pressure, values in points B1 and C1 are zero or close to zero. 3.1.5.2 Speeds Speeds are very useful to imagine and analyse how the fluid is behaving as it is running in the branches. In order to calculate the speeds in our system, the formula below was used: 𝑐= 𝜌𝑤·2·𝑔·∆ℎ 𝜌𝑎𝑖𝑟 ·1000 Where: c = speed, in [m/s] ρw = density of water, being 1000 kg/m3 g = gravity, being 9,80665 m/s2 Δh = dynamic pressure in each point, in [mm.w.c.] ρair = density of air, being 1,225 kg/m3 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 48 The formula was applied to every dynamic pressure value taken from the tests. In the following table there can be seen all the results: Inlet Speed Control Point mm Dynamic P. [Pa] Speed [m/s] 10 m/s A1 39 74,62 11,04 A2 15 18,90 5,55 B1 14 17,29 5,31 C1 13 15,75 5,07 Table 20. Speed values 10 m/s. Inlet Speed Control Point mm Dynamic P. [Pa] Speed [m/s] 15 m/s A1 66 176,98 17,00 A2 33 57,58 9,70 B1 25 38,08 7,89 C1 25 38,08 7,89 Table 21. Speed values 15 m/s. Inlet Speed Control Point mm Dynamic P. [Pa] Speed [m/s] 20 m/s A1 90 303,24 22,25 A2 52 118,66 13,92 B1 42 83,92 11,71 C1 43 87,14 11,93 Table 22. Speed values 20 m/s. From the speed values in the tables it can be seen that the sum of the values in A2 and B1 is almost the value in A1. It can also be seen that the speed value in A2 remains almost the same in C1 just after the last bench. 3.1.5.3 Flows Once the speeds were calculated, the last things to analyse were the flows. The flows allow checking the amount of air running through the manifold, and enable to prove if there is any air loss along the way. The flows are calculated using the speed value in each control point and the branch section area in that point. For these calculations, the following data was used: Branch Width [m] Depth [m] Area [m2] Main 0,005 0,2 0,001 First 0,005 0,2 0,001 Second 0,005 0,2 0,001 Table 23. Geometry data. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 49 And in the following table there can be seen the calculated values: Inlet Speed Control Point mm Flow [m3/s] 10 m/s A1 39 0,01104 A2 15 0,00555 B1 14 0,00531 C1 13 0,00507 Table 24. Flow values 10 m/s. Inlet Speed Control Point mm Flow [m3/s] 15 m/s A1 66 0,01700 A2 33 0,00970 B1 25 0,00789 C1 25 0,00789 Table 25. Flow values 15 m/s. Inlet Speed Control Point mm Flow [m3/s] 20 m/s A1 90 0,02225 A2 52 0,01392 B1 42 0,01171 C1 43 0,01193 Table 26. Flow values 20 m/s. Analysing the flow values in the tables, it can be read that the flows keep constant all along the model, as the sum of the flows in B1 and C1 (outlets) is almost the value in A1 (inlet) in all three inlet speeds. As well as the outlets, the sum of the values in A2 and B1 (first division) is also almost the value in A1 considering the error. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 50 3.2 EES REPORT 3.2.1 Model Description The system introduced in EES in order to be analyzed is very similar to the model previously studied, with the only differences that in this case all the branches are narrower (5mm. instead of 20 and 30mm.) and the main branch has the same width as the secondary branches. Figure 19. Model geometry 3.2.2 System Description The 11 states defined in this case are the same as in the previous study (see Figure 4). However, as it happened before, these states are only employed in EES, so it has been necessary to show the equivalent states employed in the laboratory test. In this study, as the number of points tested in the laboratory is very small (only four control points), the lab points do not coincide with the EES points, so the test points are placed between two EES points. TEST Point EES Point A1 Between point 2 and point 3 A2 Between 5 and 6 B1 Between 4 and 9 C1 Between 7 and 8 Table 27. EES points equivalent to the TEST points AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 51 3.2.3 Program Construction The Equations Window is almost the same shown in the Appendix B2 with one difference in the input data: the inlet flow. In this model three different cases have been studied depending on the inlet flow values, calculated by multiplying the inlet speed obtained in the lab by the branch area (0.001m3). All the results shown in the next sections are related to the theoretical inlet speed. Theoretical Inlet Speed (m/s) Inlet Speed from the TEST (m/s) Inlet Flow (m3/s) 20 22.25 0.0223 15 17.00 0.0170 10 11.04 0.0110 Table 28. Inlet flows 3.2.4 Solution All the solutions provided by the program in the Solution Window have been resumed in the tables below. The units are shown in SI units. The three whole Solution Window can be seen in Appendix B2.  1st case. Inlet speed = 20m/s. Solution Window State (EES) Speed Dynamic P. Static P. Total P. Flow 1 1.50 1.38 489.80 491.20 0.0223 2 22.25 303.20 36.36 339.60 undefined 3 22.25 303.20 27.82 331.00 “ 4 7.58 35.22 1.11 36.33 “ 5 14.67 131.80 179.00 310.7 “ 6 14.67 131.80 175.10 306.90 “ 7 14.67 131.80 3.85 135.60 “ 8 14.67 131.80 0 131.80 “ 9 7.58 35.22 0 35.22 “ 10 0 0 0 0 0.0076 11 0 0 0 0 0.0147 Table 29. Solution Window resume for 20m/s in EES states AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 52 Solution Window State (Test) Speed Dynamic P. Static P. Total P. Flow A1 22.25 303.20 32.09 335.29 0.0223 A2 14.67 131.80 177.05 308.85 undefined B1 7.58 35.22 0.56 35.78 0.0076 C1 14.67 131.80 1.93 133.73 0.0147 Table 30. Solution Window resume for 20m/s in TEST states  2nd case. Inlet speed = 15m/s. Solution Window State (EES) Speed Dynamic P. Static P. Total P. Flow 1 1.50 1.38 282.60 284.00 0.0170 2 17.00 177.00 18.50 195.50 undefined 3 17.00 177.00 13.40 190.40 “ 4 5.65 19.55 0.65 20.20 “ 5 11.35 78.91 99.42 178.3 “ 6 11.35 78.91 97.05 176.00 “ 7 11.35 78.91 2.37 81.27 “ 8 11.35 78.91 0 78.91 “ 9 5.65 19.55 0 19.55 “ 10 0 0 0 0 0.0057 11 0 0 0 0 0.0114 Table 31. Solution Window resume for 15m/s in EES points Solution Window State (Test) Speed Dynamic P. Static P. Total P. Flow A1 17.00 177.00 15.95 192.95 0.0170 A2 11.35 78.91 98.24 177.145 undefined B1 5.65 19.55 0.33 19.88 0.0057 C1 11.35 78.91 1.18 80.09 0.0114 Table 32. Solution Window resume for 15m/s in TEST points AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 53  3rd case. Inlet speed = 10m/s. Solution Window State (EES) Speed Dynamic P. Static P. Total P. Flow 1 1.50 1.38 118.60 119.90 0.0110 2 11.04 74.65 7.96 82.61 undefined 3 11.04 74.65 5.71 80.36 “ 4 3.67 8.26 0.29 8.55 “ 5 7.37 33.25 42.01 75.27 “ 6 7.37 33.25 40.96 74.21 “ 7 7.37 33.25 1.05 34.31 “ 8 7.37 33.25 0 33.25 “ 9 3.67 8.26 0 8.257 “ 10 0 0 0 0 0.0037 11 0 0 0 0 0.0074 Table 33. Solution Window resume for 10m/s in EES points Solution Window State (Test) Speed Dynamic P. Static P. Total P. Flow A1 11.04 74.65 6.84 81.49 0.0110 A2 7.37 33.25 41.49 74.74 undefined B1 3.67 8.26 0.15 8.41 0.0037 C1 7.37 33.25 0.53 33.78 0.0074 Table 34. Solution Window resume for 10m/s in TEST points AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 54 All the input and output data concerning to the three studies, as well as a sketch of the system are shown in the Diagram Window (see the figures below). Figure 20. Diagram Window for 20m/s AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 55 Figure 21. Diagram Window for 15m/s AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 56 Figure 22. Diagram Window for 10m/s AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 63 3.3 CFD REPORT 3.3.1 Model Description In this second test, the model is almost the same than the one used for the first test. The differences between them are the conduit dimensions. It is still a main conduit deviated in two outlet branches, but in this case the area remains invariant throughout the hole model. If in the previous model the conduits were 30, 19.5 and 21.5 mm thick, now the three of them are only 5 mm. The conduits are considerably narrower this time, to check if the flow behaves the same way after de division. The main branch is still 200 mm wide and the first division is at 250 mm from the inlet, but in this case the whole branch is a bit shorter, it is reduced to 510 mm. The outlet branches are both 150 mm long and 250 mm wide as in the first model. Figure 23. Model overview. 3.3.2 System description The control points used for this second test will be the same used in the first one, from one to eight. But in this case the test control points (A1, A2, B1 and C1) are displaced in the middle of the branches as figure 24 shows. The values taken from the CFD program will be operated and an average value will be taken to determine the value in the middle of each branch. Figure 24. Control points. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 64 The lids will be placed again at the inlet and the two outlets to set the inlet flow up and to get the flow rates in each one of the outlets. 3.3.3 Program Construction The program is made the same way than the first time. Starting with the assembly and setting up the Flow Simulation Studio and following with the wizard. This test will be done working with air again, and with a wall roughness of 0.0001 micrometer. In this case, the inlet flows will depend on the inlet speed we are working with. For a flow speed of 10 m/s the flow rate will be 0.0110 m3/s. When the speed is increased to 15 m/s the flow will be 0.0170 m3/s. And finally with a 20 m/s speed at the inlet, the flow will increase to 0.0223 m3/s. The air temperature for this test is set to 293.15 K (20 ºC). The outlets are again under the effect of the atmospheric pressure. 3.3.4 Analysis of results As in the first test, once the simulation is run we can get the first results. However, it is needed to place several point meshes to get the control point values and later compare them to the test results. The following tables show the results from the SolidWorks’ CFD program for the three different speeds tested. As it can be seen the flow is not even distributed through the branches, but more flow is going to the second branch even the thickness is the same in both outlet branches. Solution Window CFD State Speed [m/s] Dynamic P. [Pa] Static P. [Pa] Total P. [Pa] Volume Flow [m3/s] I1 -- -- -- -- 0,0110 1 8,96 49,13 25,78 74,91 -- 2 8,74 46,80 -7,17 39,63 -- 3 5,50 18,49 37,62 56,11 -- 4 5,39 17,77 23,76 41,54 -- 5 4,06 10,09 1,36 11,45 -- 6 4,06 10,09 -0,72 9,37 -- O1 -- -- -- -- 0,0042 7 5,12 16,07 9,42 25,49 -- 8 5,14 16,16 0,78 16,94 -- O2 -- -- -- -- 0,0069 Table 37. SolidWorks' Flow Simulation results for 10 m/s. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 65 Solution Window CFD State Speed [m/s] Dynamic P. [Pa] Static P. [Pa] Total P. [Pa] Volume Flow [m3/s] I1 -- -- -- -- 0,0170 1 13,87 117,83 43,03 160,86 -- 2 13,57 112,68 -18,98 93,70 -- 3 8,89 48,43 81,18 129,61 -- 4 8,74 46,78 53,52 100,30 -- 5 5,83 20,83 1,91 22,73 -- 6 5,83 20,83 -1,76 19,07 -- O1 -- -- -- -- 0,0060 7 8,28 41,93 17,88 59,81 -- 8 8,34 42,62 1,55 44,17 -- O2 -- -- -- -- 0,0110 Table 38. SolidWorks' Flow Simulation results for 15 m/s. Solution Window CFD State Speed [m/s] Dynamic P. [Pa] Static P. [Pa] Total P. [Pa] Volume Flow [m3/s] I1 -- -- -- -- 0,0223 1 18,21 203,12 91,23 294,35 -- 2 17,97 197,66 -24,20 173,46 -- 3 11,83 85,70 129,51 215,22 -- 4 11,65 83,12 88,86 171,98 -- 5 7,43 33,82 3,22 37,04 -- 6 7,44 33,85 -2,09 31,76 -- O1 -- -- -- -- 0,0077 7 10,98 73,87 24,61 98,48 -- 8 11,12 75,69 2,10 77,80 -- O2 -- -- -- -- 0,0147 Table 39. SolidWorks' Flow Simulation results for 20 m/s. Figures 25, 26 and 27 show the pressure variations for a 10, 15 or 20 meters per second flow. The differences between them are the highness of the values, but the behaviour is the same in the three cases. The pressure in the inlet is reduced while the flow is moving through the conduit, but increases again in the main branch after the division. And in the two branches the pressure decreases again influenced by the atmospheric pressure in the outlets. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 66 Figure 25. Pressure changes along the conduit at 10 m/s. Figure 26. Pressure changes along the conduit at 15 m/s. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 67 Figure 27. Pressure changes along the conduit at 20 m/s. In figures 28, 29 and 30 is represented the speed along the branches. Again it can be seen how the tendency in the three cases is maintained; only being changed the magnitude of the values. The speed in the inlet is maintained until the division; there, the fluid going to the first branch decreases more the speed than the fluid going through the main branch. This is due to the fact that there is more fluid going through the second branch than through the first and the areas remain constant. Figure 28.Velocity changes along the conduit at 10 m/s. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 68 Figure 29.Velocity changes along the conduit at 15 m/s. Figure 30.Velocity changes along the conduit at 20 m/s. Graphics 34 and 35 show the speed variances from the inlet to each one of the outlets for the three speeds. It can be appreciated how the speed from 1 to 2 is lightly reduced; this is due to the friction between the walls and the flow. The same is happening from 3 to 4, when the flow remaining in the main branch reduces its speed a very few points, and from 7 to 8. From 2 to 5 the speed gap is considerably bigger than before, as the flow is reduced to its half and the area remains constant. The same happens from 2 to 3, when the flow is reduced in the same way than from 2 to 5 and the area does not change. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 69 Graphic 34. CFD fluid speed from inlet to first outlet for the three different inlet speeds. Graphic 35. CFD fluid speed from inlet to second outlet for the three different inlet speeds. In the following six graphics are represented the dynamic, static and total pressures from the inlet to each of the outlets. As it can be appreciated the flow pressure behaviour with the three speeds is very similar. 0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00 18,00 20,00 1 2 5 6 Speed Inlet - 1st Outlet 10 m/s 15 m/s 20 m/s 0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00 18,00 20,00 1 2 3 4 7 8 Speed Inlet - 2nd Outlet 10 m/s 15 m/s 20 m/s AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 70 Graphic 36. CFD fluid pressure between inlet and first outlet for a 10 m/s inlet speed. Graphic 37. CFD fluid pressure between inlet and second outlet for a 10 m/s inlet speed. -20,00 -10,00 0,00 10,00 20,00 30,00 40,00 50,00 60,00 70,00 80,00 1 2 5 6 Pressures Inlet - 1st Outlet 10 m/s Dynamic P. Static P. Total P. -20,00 -10,00 0,00 10,00 20,00 30,00 40,00 50,00 60,00 70,00 80,00 1 2 3 4 7 8 Pressures Inlet - 2nd Outlet 10 m/s Dynamic P. Static P. Total P. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 71 Graphic 38. CFD fluid pressure between inlet and first outlet for a 15 m/s inlet speed. Graphic 39. CFD fluid pressure between inlet and second outlet for a 15 m/s inlet speed. -40,00 -20,00 0,00 20,00 40,00 60,00 80,00 100,00 120,00 140,00 160,00 180,00 1 2 5 6 Pressures Inlet - 1st Outlet 15 m/s Dynamic P. Static P. Total P. -40,00 -20,00 0,00 20,00 40,00 60,00 80,00 100,00 120,00 140,00 160,00 180,00 1 2 3 4 7 8 Pressures Inlet - 2nd Outlet 15 m/s Dynamic P. Static P. Total P. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 72 Graphic 40. CFD fluid pressure between inlet and first outlet for a 20 m/s inlet speed. Graphic 41. CFD fluid pressure between inlet and second outlet for a 20 m/s inlet speed. -50,00 0,00 50,00 100,00 150,00 200,00 250,00 300,00 350,00 1 2 5 6 Pressures Inlet - 1st Outlet 20 m/s Dynamic P. Static P. Total P. -50,00 0,00 50,00 100,00 150,00 200,00 250,00 300,00 350,00 1 2 3 4 7 8 Pressures Inlet - 2nd Outlet 20 m/s Dynamic P. Static P. Total P. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 79 Outlet B Outlet C Speed (m/s) mm.w.c Average Speed Flow mm.w.c Average Speed Flow 20 3,4 3,533 7,523 0,00752 3,9 4 8,004 0,00800 3,8 4,2 3,4 3,9 15 1,8 1,800 5,369 0,00537 1,7 1,83 5,419 0,00542 1,8 1,9 1,8 1,9 10 0,8 0,767 3,504 0,00350 0,8 0,8 3,580 0,00358 0,8 0,8 0,7 0,8 Table 40. Pitot tube values in outlets. Considering all the data taken in the three different methods and taking a general overview of the comparisons, we can say that the values obtained in the test are pretty acceptable, and even more if we consider that the sphere method was thought as an orientative tool. The differences in the results from the EES and the CFD programmes may be due to the sometimes too much theoretical method of the EES and the imprecision of the control area in the CFD. Anyway, these differences between two trustable programmes make more insignificant the distance from the test results to the computational methods. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 80 3.5 SPHERE METHOD IMPROVEMENTS After studying the results of the tests, it has been necessary to study some improvements to the sphere method. After discussing how this method could be improved so that the results were more accurate four decisions were made.  In the first test, the inlet dynamic pressure used to calculate the velocity and the flow was measured with the Pitot tube. We realized that it was blocking a 42% of the inlet area and the results obtained could be wrong. So, in the next test the inlet flow should be calculated in a different way. The best option is to calculate the millimeters of water column to be introduced in the scale2 depending on the inlet speed needed and then check the flow in the manufacturer graphic according to the inlet (A, B or C) employed.  As the test had been decided to be repeated, a new and more accurate calibration was regarded as very appropriate. The calibration took place in the wind tunnel where the thread with the sphere was hanged from a nail. The nail was hammered into a piece of wood, so that it was placed in the beginning of a scale (see figure 32). When the wind tunnel is turned on, the sphere moves and it can be seen in the scale how big the displacement is in function of the dynamic pressure. Afterwards, the process is the same as in the first test, it is necessary to create a tendency line in Excel. Figure 31. Wind tunnel calibration. 2 ∆h = c2·ρair ·1000 ρH2O ·2·g AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 81 Figure 32. Wind tunnel calibration II.  There was another point to be revised: the thread length. The first test was made using only a 13cm. thread. So, taking advantage of repeating the test, it was made with three different threads of 6, 13 and 18cm. in order to calculate a tendency line for each one of them and, therefore, a more complete data is obtained.  Finally, the outlets were modified. Previously, the branches went directly to the atmosphere and, owing to the geometry (a rectangle 5 x 200mm.) it is rather inaccurate to measure the outlet flow. An adaptor made of paper was made to change the rectangular shape into a circular one (d = 4.15 cm, area = 13.52 cm2). With this adaptor the air flow is more concentrated and the dynamic pressure is easier to be measured. Figure 33. Paper adaptor. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 82 3.5.1 Calibration process The results of the wind tunnel calibration are resumed in the table below. The dynamic pressure is measured with the Pitot tube installed in the wind tunnel. Dynamic Pressure [Pa] cm thread 78.45 117.68 156.91 215.75 274.59 6 17 28 36 43 48 13 74 92 102 113 122 18 106 125 139 154 162 Ball Displacement [mm] Table 41. Sphere method new calibration. In the table below it can be seen the speed calculated in function of the measured dynamic pressure. Dynamic P. Wind Speed 78.45 11.32 117.68 13.86 156.91 16.01 215.75 18.77 274.59 21.17 Table 42. Speed values. The table 41 was entered in an Excel sheet and was used to make a graphic with a tendency line for each one of the thread lengths. Graphic 51. Sphere calibration tendency lines. y = 38,731e0,0401x y = 10,794e0,0264x y = 7,5837e0,0219x 0 100 200 300 400 500 600 700 800 900 1000 050 100 150 200 250 300 Dynamic Pressure [Pa] Ball displacement 6 cm 13 cm 18 cm AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 83 Three exponential tendency lines were obtained: y = 38.071·e0.0401x in the case of the 6 cm. thread, y = 10.794·e0.0264x for 13 cm. and finally, y = 7.58370.0219x when the 18 cm. thread is calibrated; being x the ball displacement and y the dynamic pressure. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 84 3.5.2 Test results After making the sphere test again, three tables are obtained for the every inlet speed (one table for each thread). The dynamic pressure in the modified outlets was checked with the Pitot tube.  Inlet Speed = 10 m/s Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 6 10 A1 19 82.97 11.64 0.0116 A2 7 51.28 9.15 0.0092 B1 4 45.47 8.62 0.0086 C1 6 49.27 8.97 0.0090 Table 43. Sphere test. Inlet speed = 10 m/s. 6 cm thread. Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 13 10 A1 69 66.73 10.44 0.0104 A2 29 23.21 6.16 0.0062 B1 25 20.88 5.84 0.0058 C1 27 22.02 5.99 0.0060 Table 44. Sphere test. Inlet speed = 10 m/s. 13 cm thread. Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 18 10 A1 105 75.60 11.11 0.0111 A2 46 20.77 5.82 0.0058 B1 42 19.03 5.57 0.0056 C1 48 21.70 5.95 0.0060 Table 45. Sphere test. Inlet speed = 10 m/s. 18 cm thread. Outlet Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] PITOT B 9.81 4.00 0.0054 C 12.75 4.56 0.0062 Table 46. Sphere test. Inlet speed = 10 m/s. Outlet measurements. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 85  Inlet Speed = 15 m/s Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 6 15 A1 30 128.98 14.51 0.0145 A2 11 60.20 9.91 0.0099 B1 10 57.84 9.72 0.0097 C1 11 60.20 9.91 0.0099 Table 47. Sphere test. Inlet speed = 15 m/s. 6 cm thread. Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 13 15 A1 89 113.14 13.59 0.0136 A2 43 33.59 7.41 0.0074 B1 37 28.67 6.84 0.0068 C1 43 33.59 7.41 0.0074 Table 48. Sphere test. Inlet speed = 15 m/s. 13 cm thread. Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 18 15 A1 133 139.59 15.10 0.0151 A2 72 36.70 7.74 0.0077 B1 63 30.14 7.01 0.0070 C1 70 35.13 7.57 0.0076 Table 49. Sphere test. Inlet speed = 15 m/s. 18 cm thread. Outlet Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] PITOT B 17.65 5.37 0.0073 C 23.54 6.20 0.0084 Table 50. Sphere test. Inlet speed = 15 m/s. Outlet measurements. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 86  Inlet Speed = 20 m/s Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 6 20 A1 36 164.06 16.37 0.0164 A2 18 79.71 11.41 0.0114 B1 13 65.23 10.32 0.0103 C1 18 79.71 11.41 0.0114 Table 51. Sphere test. Inlet speed = 20 m/s. 6 cm thread. Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 13 20 A1 105 172.60 16.7869 0.0168 A2 66 61.64 10.0322 0.0100 B1 57 48.61 8.9084 0.0089 C1 64 58.47 9.7708 0.0098 Table 52. Sphere test. Inlet speed = 20 m/s. 13 cm thread. Thread [cm] Inlet Speed [m/s] Control Point Ball displ. [mm] Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] 18 20 A1 151 207.034 18.39 0.0184 A2 100 67.76 10.52 0.0105 B1 91 55.64 9.53 0.0095 C1 99 66.29 10.40 0.0104 Table 53. Sphere test. Inlet speed = 20 m/s. 18 cm thread. Outlet Dynamic P. [Pa] Speed [m/s] Flow [m^3/s] PITOT B 29.42 6.93 0.0094 C 39.23 8.00 0.0108 Table 54. Sphere test. Inlet speed = 20 m/s. Outlet measurements. All the data concerning to the air flows calculations and measurements shown in the previous tables is resumed in the table 55. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 87 3.5.3 Velocity curves As a in the new test three different threads were used, the possibility of studying the shape of the velocity curve appeared. According to the theory this curve has to be a parabola with velocity equal to zero in the walls and maximum velocity in the center of the conduit (see the figure below). Figure 34. Velocity profile. To do the study the inlet and outlets speed values were studied with the three thread lengths (see figure 35): Figure 35. Sphere method velocity profiles. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 88 Having a look at the figure 35, it can be concluded that the sphere method cannot be employed to draw the speed parabola. However, a tendency can be observed. In the three cases the speed is higher in A1 than in C1 and C1 is higher than B1, as well. In the outlets (B1 and C1) the lines are very similar, with a higher speed for the 6 cm. thread. The 13 and 18 cm. threads give a very similar result for low velocities. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 95 Figure 37. CFDesign Static pressure plot. Figure 38. CFDesign narrowing Static pressure plot. Figure 39. CFDesign widening Static pressure plot. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 96 Figure 40. CFDesignn Velocity plot AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 97 Figure 41. SolidWorks FS Static pressure plot. Figure 42. SolidWorks FS narrowing Static pressure plot. Figure 43. SolidWorks FS widening Static pressure plot. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 98 Figure 44. SolidWorks FS Velocity plot Figure 45. SolidWorks FS Centre part Velocity plot AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 99 Graphic 52. EES Static and Total pressure values Graphic 53. EES Velocity values. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 100 Graphic 54. Static pressure comparison. Graphic 55. Total pressure comparison. -400 -200 0 200 400 600 800 1000 1 2 3 4 5 6 Pressure [Pa] State Static Pressure EES SolidWorks FS CFDesign -200 0 200 400 600 800 1000 1 2 3 4 5 6 Pressure [Pa] State Total Pressure EES SolidWorks FS CFDesign AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 101 In the previous graphics the static pressure values are very similar in the three cases, with the only difference on state 5 when it is read in EES. The total pressure graphics are not as coincident because the speed changes are not studied in the same way: in EES the speed changes almost immediately when the area varies; in CFDesign the changes are slower than in SolidWorks Flow Simulation when the velocity decreases, but they are faster when the velocity increases. To conclude, we can say that even working with two CFD programs which are supposed to use the same principles when simulating a flow study, the results obtained are similar, but not the same (for example, the pressure loss difference is around 12.5%). This variation between two similar programs could be explained as a consequence of the mesh accuracy employed. The difference with EES is due to the fact that EES is just a mathematical program which does not take into account points such as the fluid inertia and the speed curve shape. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 102 5 PROJECT CONCLUSIONS Once the project is over, is time to make an overview, analyse and take some conclusions about what we have been doing for the last half year. After studying two different two-branched models and analyzing the values in the outlets, we can say that the results are not the expected before doing the project, as we thought that the air flow would be the same in both outlets when their geometry is the same. However, once studied the first model results, we realized that the flow inertia along the main branch takes part on the flow distribution, so the second outlet flow rate is higher than the first one. If we had studied a bigger model with higher number of branches, we could have understood a little better this interesting behaviour of the air flow in the “T” divisions. It must also be commented that the models assembly exceeded all the expectations. As we used materials such as wood pieces, plastic plates, screws and washers, the isolating methods were pretty homemade using bicycle tires trimmings for the first model, and the assembly was made by nonprofessional people, we thought there would be a lot of flow loss between the joints along the conduits comparing the inlet and the two outlets. However, there was a little flow loss in both models, which probably took place in the diffusion box. Another point to be explained is the result differences depending on the tool employed in the study: EES, CFD or test. In our opinion, the different results are due to the fact that both programs use a lot of theoretical equations to obtain the results, especially EES, which actually is just an equations solver. SolidWorks Flow Simulation goes one step further and shows a more real analysis than EES, but is still closer to the theory than to the reality. We could not conclude the project conclusions without expressing our satisfaction with the results obtained by employing the sphere method. At the beginning we were not sure at all that it would work. Although we were very confident on the method, we were not sure to be able to make it accurate enough to get some satisfactory results. After analysing the first test results, we noticed that with some improvements this method would be accurate enough and we were encouraged by the supervisors to do so. When we were told to make this project, the initial goal was to design a cooling system for a generator. After the semester has past we have realized the complexity and the time you have to spend to make a project of this importance. So far, we have understood how the air behaves when it is divided and now should be time to start evaluating the cooling power of the flow. This could take, for us, another entire project. Perhaps we would have liked to get to know how this kind of projects are faced and developed on a company, and work in close cooperation with them. But anyway, the IHA environment proved to be very professional, serious and we have had everything we needed to make our project succeed. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 103 To conclude, the last five months we have learnt to work with two different programmes, new for us, and analyse the results and compare it to a real test. This has shown us the importance of complementing the theoretical analysis with practical tests. Moreover, because of the magnitude of the project, we have learnt to divide and assign tasks to the components of the group, and to work in an international environment. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 104 6 BIBLIOGRAPHY - Donald S. Miller, Internal Flow Systems BHRA Fluid Engineering 1978 - D.J. Tritton, Physical Fluid Dynamics Van Nostrand Reinhold Company Ltd 1977 - Joseph P. DeCarlo, Fundamentals of flow measurement Instrument Society of America 1984 - Richard W. Miller, Flow measurement engineering handbook McGraw-Hill Publishing Company 1983 - Solid Works Flow Simulation 2009 Online Tutorial - P. Charbonneau, B. Knapp, Engineering Equation Solver for Microsoft Windows Operating Systems Online Tutorial. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 111 3/8 Testing values [mmH2O] 1st/upper wall Middle 2nd/lower wall Dyn Stat Total Dyn Stat Total Dyn Stat Total Control Points Fan -- -- -- 6,5 6,5 -- -- -- I1 -- -- -- 10 7,8 17,8 -- -- -- A1 3,4 1 4,4 10 1 11 6,6 0,7 7,3 A2 7,2 1,2 8,4 7,8 1,3 9,1 6,6 1 7,6 A3 6,8 5,2 12 7,8 4,5 12,3 5,1 4,1 9,2 A4 7,8 4,4 12,2 7,4 4,5 11,9 4,7 4,4 9,1 A5 7,1 4,6 11,7 7,1 4,6 11,7 5,5 4,6 10,1 A6 6,7 4,4 11,1 6,9 4,6 11,5 5,5 4,8 10,3 B1 -3,9 -2,1 -6 -2 -2,5 -4,5 9,1 -2 7,1 B2 -0,2 0,2 0 0,9 0 0,9 0,2 5,3 5,5 B3 1,4 0 1,4 1,4 0 1,4 1,4 0 1,4 O1 -- -- -- 1,8 0 1,8 -- -- -- C1 -3,2 -0,5 -3,7 7,2 -1 6,2 7,4 -0,6 6,8 C2 1,8 0,4 2,2 3,6 0,3 3,9 6,4 0,4 6,8 C3 2,7 -0,1 2,6 3,5 0 3,5 5,1 0 5,1 O2 -- -- -- 3,4 0 3,4 -- -- -- 1/2 (I) Testing values [mmH2O] 1st/upper wall Middle 2nd/lower wall Dyn Stat Total Dyn Stat Total Dyn Stat Total Control Points Fan -- -- -- 6,5 6,5 -- -- -- I1 -- -- -- 10,5 7,4 17,9 -- -- -- A1 2,6 1 3,6 10,4 1 11,4 5,4 0,8 6,2 A2 6,9 1,2 8,1 7,8 1,3 9,1 6,6 1,1 7,7 A3 6,4 5,1 11,5 7,8 4,7 12,5 5 4 9 A4 7,8 4,4 12,2 7,4 4,4 11,8 4,8 4,3 9,1 A5 6,9 4,6 11,5 7,2 4,6 11,8 5,6 4,6 10,2 A6 6,8 4,3 11,1 6,8 4,7 11,5 5,7 5 10,7 B1 -3,8 -2,1 -5,9 -3 -1,9 -4,9 9,2 -1,8 7,4 B2 0,1 0,2 0,3 3,3 0 3,3 6,4 0.3. 6,4 B3 1,6 0 1,6 1,6 0 1,6 1,6 0 1,6 O1 -- -- -- 2,3 0 2,3 -- -- -- C1 -2,6 -0,4 -3 7,2 -1 6,2 7,8 -0,4 7,4 C2 1,7 0,5 2,2 3,2 0,4 3,6 7 0,6 7,6 C3 2,2 0,1 2,3 3,4 0 3,4 5,3 0 5,3 O2 -- -- -- 3,4 0 3,4 -- -- -- AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 112 1/2 (II) Testing values [mmH2O] 1st/upper wall Middle 2nd/lower wall Dyn Stat Total Dyn Stat Total Dyn Stat Total Control Points Fan -- -- -- 6,5 6,5 -- -- -- I1 -- -- -- 12,2 7,5 19,7 -- -- -- A1 6,2 1,7 7,9 11,6 1,5 13,1 8,2 1,5 9,7 A2 8,6 1,8 10,4 10,4 1,8 12,2 8,8 2 10,8 A3 7,8 7 14,8 8,8 5,5 14,3 7,4 4,5 11,9 A4 9 5,2 14,2 8,8 5,1 13,9 5,9 5,1 11 A5 8,8 5,5 14,3 8,4 5,5 13,9 6,9 5,6 12,5 A6 8 5 13 8,5 5,2 13,7 7 5,8 12,8 B1 -4 -1,3 -5,3 7,9 -2,7 5,2 8,6 -1,7 6,9 B2 -0,2 0,4 0,2 2,4 0 2,4 5,8 0,2 6 B3 1,2 0 1,2 2,3 0 2,3 3 -0,1 2,9 O1 -- -- -- 2 0 2 -- -- -- C1 -3,2 -0,2 -3,4 5,2 -0,4 4,8 7,8 -0,4 7,4 C2 1,5 0,7 2,2 4,8 0,4 5,2 6,9 0,7 7,6 C3 2,4 0 2,4 3,3 0 3,3 5,1 0 5,1 O2 -- -- -- 3,2 0 3,2 -- -- -- 5/8 Testing values [mmH2O] 1st/upper wall Middle 2nd/lower wall Dyn Stat Total Dyn Stat Total Dyn Stat Total Control Points Fan -- -- -- 6,5 6,5 -- -- -- I1 -- -- -- 12 7 19 -- -- -- A1 1,5 1,5 3 11,4 1 12,4 8,8 1,1 9,9 A2 8,8 1,7 10,5 9,5 1,6 11,1 8,3 1,7 10 A3 7,7 6,8 14,5 8,7 5 13,7 7 4,3 11,3 A4 9 5,3 14,3 8,4 5 13,4 5,7 5,1 10,8 A5 8,3 5,4 13,7 8,4 5,5 13,9 7 5,6 12,6 A6 7,9 5 12,9 8,2 5,1 13,3 6,8 6 12,8 B1 -4,2 -1,4 -5,6 7 -2,1 4,9 9,1 -2,1 7 B2 0,1 0,4 0,5 2,4 0,3 2,7 5,2 0,3 5,5 B3 1,4 0 1,4 2,2 0 2,2 3 0 3 O1 -- -- -- 2,2 0 2,2 -- -- -- C1 -3,4 -0,3 -3,7 7,8 -0,6 7,2 7,8 -0,4 7,4 C2 1,4 0,6 2 3,6 0,4 4 3,8 0,6 4,4 C3 2,6 0 2,6 3,5 0 3,5 5,3 0 5,3 O2 -- -- -- 3,2 0 3,2 -- -- -- AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 113 3/4 Testing values [mmH2O] 1st/upper wall Middle 2nd/lower wall Dyn Stat Total Dyn Stat Total Dyn Stat Total Control Points Fan -- -- -- 6,5 6,5 -- -- -- I1 -- -- -- 11,8 8 19,8 -- -- -- A1 3 1 4 11,2 0,6 11,8 8,2 1 9,2 A2 9 1,7 10,7 9,2 1,7 10,9 8,5 1,7 10,2 A3 8,4 6 14,4 8,6 4,7 13,3 6,6 4,3 10,9 A4 8,6 5 13,6 8 5 13 5,2 5 10,2 A5 8,3 5,5 13,8 8 5,5 13,5 6,4 5,5 11,9 A6 7,6 4,9 12,5 7,7 5,1 12,8 6,5 5,5 12 B1 -4,3 -1,8 -6,1 2,5 -1,7 0,8 8,4 -2 6,4 B2 0 0,2 0,2 2,4 0 2,4 4,8 0 4,8 B3 1,4 0 1,4 1,7 0 1,7 2,6 0 2,6 O1 -- -- -- 1,7 0 1,7 -- -- -- C1 -3,8 -0,1 -3,9 5,8 -0,6 5,2 7,6 -0,4 7,2 C2 2 0,6 2,6 3,6 0,6 4,2 6,4 0,4 6,8 C3 2,7 0,1 2,8 3,4 0 3,4 5,2 0 5,2 O2 -- -- -- 3,2 0 3,2 -- -- -- 7/8 Testing values [mmH2O] 1st/upper wall Middle 2nd/lower wall Dyn Stat Total Dyn Stat Total Dyn Stat Total Control Points Fan -- -- -- 6,5 6,5 -- -- -- I1 -- -- -- 11,8 8 19,8 -- -- -- A1 3,8 0,8 4,6 11,2 0,7 11,9 5,4 0,4 5,8 A2 10 1,6 11,6 9,6 1,6 11,2 8,2 1,7 9,9 A3 8,4 5,2 13,6 8,4 4,6 13 5,8 4 9,8 A4 8,2 5 13,2 6,8 4,8 11,6 3,6 5 8,6 A5 7,3 5,4 12,7 7,1 5,5 12,6 5,8 5,4 11,2 A6 7,1 4,7 11,8 6,9 5,1 12 6,3 5,5 11,8 B1 -4,4 -2 -6,4 4 -2 2 8,4 -2 6,4 B2 0 0 0 1,3 -0,1 1,2 4,8 -0,1 4,7 B3 1,2 0 1,2 1,6 0 1,6 2,6 -0,1 2,5 O1 -- -- -- 1,6 0 1,6 -- -- -- C1 -3,6 0,3 -3,3 6,4 -0,3 6,1 6,8 -0,3 6,5 C2 3 0,3 3,3 5 0,4 5,4 6 0,3 6,3 C3 3,2 0 3,2 4,3 0 4,3 5,4 0 5,4 O2 -- -- -- 4,1 0 4,1 -- -- -- AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 114 For the speed analysis, there were made speed profiles in each control point. With these profile graphics it could be done a better visual comprehension of how the flow speed behaves inside the manifold. All these speed profiles are below. 11 12 13 14 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth Inlet 9 10 11 12 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth A1 10 11 12 13 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth A2 9 10 11 12 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth A3 9 10 11 12 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth A4 9 10 11 12 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth A5 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 115 9 10 11 12 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth A6 0 1 2 3 4 5 6 7 8 9 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth B1 0 1 2 3 4 5 6 7 8 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth B2 2 3 4 5 6 7 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth B3 4 5 6 7 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth Outlet B 6 7 8 9 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth C1 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 116 6 7 8 9 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth C2 6 7 8 9 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth C3 6 7 8 9 1/8 1/4 3/8 1/2 5/8 3/4 7/8 Speed [m/s] Depth Outlet C AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 117 B. EES APPENDICES B1. EES introduction One of the tools employed in this project has been the software EES (Engineering Equation Solver). The main function provided by this program is the solution of a set of algebraic equations. However, it can also solve differential equations, equations with complex variables, do optimization, provide linear and non-linear regression, generate publication-quality plots, simplify uncertainty analyses and provide animations. There are two major differences between EES and the existing numerical equationsolving programs. On the one hand, EES automatically identifies and groups equations that must be solved simultaneously. This feature simplifies the process for the user and ensures that the solver will always operate at optimum efficiency. On the other hand, EES provides many built-in mathematical and thermophysical property functions useful for engineering calculations. The first exercise solved by using EES was a tube as shown in the picture below where four states were defined: - State 1: 0.1 m. before the inlet. - State 2: Right after the inlet. - State 3: Before the outlet. - State 4: 0.1 m. after the outlet. Figure 46. Tube model: 4 states To be able to find a solution the following assumptions were used: - P1 = 0 bar. - Q = 0.015 m3/s. - L = 1 m. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 118 - Ϛinlet = 0.5 - Ϛoutlet = 1 The mathematical expressions employed were:  𝑄=𝑣·𝐴  𝑅𝑒=𝑢· 𝑑 𝜐  𝑃𝑡= 𝑃+ 𝑃𝑑  𝑃𝑑= 1 2· 𝜌· 𝑢2  𝑑𝑃1,2 = 𝜁1,2 · 𝑃𝑑1,2  𝑃𝑡2= 𝑃𝑡1− 𝑑𝑃1,2 Equations Window The Equations Window operates like a Word processor with commands such as Cut, Copy and Paste. The equations that EES is to solve are entered in this window. In the case of the tube model, , it was necessary to include a little function, apart from the previously mentioned equations, which makes possible to calculate the pressure loss between two points taking into account the roughness and diameter of the tube and the Reynolds number. Figure 47. Friction function AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 119 Figure 48. Equations Window Solution Window The Solution Window will automatically appear in front of all other windows after the calculations, initiated with the Solve icon or by pressing F2 on the keyboard, are completed. The values and units of all variables appearing in the Equations window will be shown in alphabetical order. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 120 Figure 49. Tube model: Solution Window Arrays Window and Plot Window EES allows the use of array variables. EES array variables have the array index in square brackets in the Equations Window. In most ways, array variables are just like ordinary variables. The values of all variables including array variables are normally displayed in the Solution Window after calculations are completed. However, array variables may optionally be displayed in a separate Arrays Window, rather than in the Solution Window. If this is the case, an Arrays Window will automatically be produced. The values in the Arrays Window may be plotted using the New Plot Window command in the Plot menu. Table 58. Tube model: Arrays table AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 127 "State-9" u_9 = u_4 Re_9 = u_9 * d_1st_branch/nu zeta_4_9 = zeta_fric(Re_9,ks/d_1st_branch) pd_9 = pd_4 dp_4_9 = zeta_4_9 * pd_9 pt_9 = pt_4 - dp_4_9 p_9 = pt_9 - pd_9 "State-10" u_10 = 0 zeta_9_10 = 1 "ZETA IN THE OUTLET" dp_9_10 = zeta_9_10 * 1/2*rho*u_9^2 pd_10 = 1/2 * rho * u_10^2 pt_10 = pt_9 - dp_9_10 p_10 = pt_10 - pd_10 p_10 = 0 "State-11" u_11 = 0 zeta_8_11 = 1 "ZETA IN THE OUTLET" dp_8_11= zeta_8_11 * 1/2 * rho * u_8^2 pd_11 = 1/2 * rho * u_11^2 pt_11 = pt_8 - dp_8_11 p_11 = pt_11 - pd_11 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 128 p_11 = 0 The following equations are the definition of the Arrays Window calculated in order to plot the results obtained in the Solution Window by using the Plot menu. "Chart - Main branch" p[1] = p_1 p[2] = p_2 p[3] = p_3 p[5] = p_5 p[6] = p_6 p_t[1] = pt_1 p_t[2] = pt_2 p_t[3] = pt_3 p_t[5] = pt_5 p_t[6] = pt_6 p_d[1] = pd_1 p_d[2] = pd_2 p_d[3] = pd_3 p_d[5] = pd_5 p_d[6] = pd_6 L[1] = 0 L[2] = L[1] + dL L[3] = L[2] + L L[5] = L[3] + h_1st L[6] = L[5] + L "Chart - 1st branch" p[4] = p_4 p[9] = p_9 p[10] = p_10 p_t[4] = pt_4 p_t[9] = pt_9 p_t[10] = pt_10 Graphic 57. Plot Window: Main branch Graphic 58. Plot Window: 1st Branch AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 129 p_d[4] = pd_4 p_d[9] = pd_9 p_d[10] = pd_10 L[4] = 0 L[9] = L[4] + L_branch L[10] = L[9] + dL "Chart - 2nd branch" p[7] = p_7 p[8] = p_8 p[11] = p_11 p_t[7] = pt_7 p_t[8] = pt_8 p_t[11] = pt_11 p_d[7] = pd_7 p_d[8] = pd_8 p_d[11] = pd_11 L[7] = 0 L[8] = L[7] + L_branch L[11] = L[8] + dL Graphic 59. Plot Window: 2nd branch AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 130 Table 59. Wide branches model: Arrays table AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 131 The solution table shown in both the “Wide Branches Model”and “Narrow Branches Model” reports is a resume of the Solution Window calculated by the program (see the figures below). Figure 51. Wide branches model: Solution Window AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 132 Figure 52. Narrow branches model: Solution Window (Inlet speed = 10m/s) AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 133 Figure 53. Narrow branches model: Solution Window (Inlet speed = 15m/s) AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 134 Figure 54. Narrow branches model: Solution Window (Inlet speed = 20m/s) AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 135 C. SolidWorks’ Flow Simulation Studio Tutorial. Internal flows.  Model preparation.  Create and set up a new flow simulation project.  Set up boundary conditions and goals.  Results visualization. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 136 Model preparation To start the SolidWorks’ Flow Simulation Study it is needed to have a SolidWorks’ part or assembly to work with. To make an internal flow studio it is needed a part or assembly with an empty cavity, while for an external flow studio it is only needed a part or assembly with any wanted shape. In this tutorial we are going to work with a tubular pipe as an example of how the Flow Simulation works. To start with the internal flow analisys open the part which you are going to work with and click New and Make Assembly from Part/Assembly as shown in the figure to the right . Then it is necessary to create a lid as a new part to enclose the flow field. Open the assembly and the lid part and tile them so you can drag the lids into the assembly. Then make the lids concentric and coincident with the ends of the pipe by adding mates between them. Create and set up a new flow simulation project Click on Flow Simulation in the CommandManager and then click Wizard to start configuring a new project. The Flow Simulation Wizard dialog box appears, as shown in the next figure: AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 143 When you clock on the run button you will see the software monitoring window. After the measuring progress is completed you can graph the goals to monitor the progress. Click on the graph icon and select the three goal items specified earlier. Now you can close the monitor window. Notice that the results tree has filled with colour indicating that the results are loaded. Results visualization. First of all, hide the computational domain by right clicking on the icon and then click Hide. Now make the pipe transparent, so we can see the flow. Right click on the pipe and click Change Transparency . On the Results tree you can see many different ways to see the results. We are going to use some of them to see what the SolidWorks’ Flow Simulation can offer. Right click on Cut Plots and insert a new cut plot. Now you can select on which plane you want to see the cut and which way you want to display the results; contours , isolines , vectors or mesh . Select the Top Plane and dislplay Contours and then click OK . You can click on Pressure under the legend to change it to many other parameters you can show. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 144 You can also double-click on the legend to open the cut plot Settings box and modify the legend, the magnitudes you want to see and some other options. Now let’s make a velocity flow trajectory starting from the inlet. First hide the Cut Plot, right click on and the select Hide. Select the inlet boundary condition and right click on the item to choose Insert. Leave the number of trajectories at 20 and draw the trajectories as pipes. Click OK . AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 145 This is how it should look like. It is possible to animate the flow trajectories. To do so is better to change the way the trajectories are drawn from pipes to spheres. Right click on and select Edit Definition. Change to Spheres and select the number of trajectories you want (i.e. 50). You can see an example in Appendix X.x.x (CD). It is possible to determine the parameters in a concrete point inside the bounding box, and consequently the parameters on a determined area inside the computational domain. Right click on and the click on Insert. On the Point Parameters box, like the one below, you can choose to pick the points one by one or you can select a plane or a face and let the Flow Simulator make a point grid on it. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 146 Select Grid in the Point picking menu and go to the FeatureManager design tree and select the Right Plane. Set the Number of points to 50 and the Plane position to -0.139. This point is placed 5 mm before the pipe narrowing. Now click on Add to add the point grid and then click on Evaluate. If you change to the Table tab you will see all the parameters detailed as it follows. By clicking on Excel, Flow Simulator gives a Microsoft Excel™ sheet with all de data calculated from the points in the grid. Now let’s check the outlet parameters. Select the outlet lid and right click on Surface Parameters and click on Insert. Now you can see AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 147 the local and integral values at the outlet. Click on Evaluate and the on the Local tab. You can appreciate that the velocity on the lid gets 4.26 m/s and we configured 4 m/s at the outlet. This is due to the fact that the velocity is a vector, and the X-component of it is the one we configured to be 4 m/s, and it is 3.99 m/s, so the value is the expected. Clicking on the Integral tab will show the integrated values for the outlet lid. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 148 D. DRAWINGS In the following pages there are some drawings of the models we have been working with, as well as the diffusion box. AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 149 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 150 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 151 AIR FLOW STUDY IN A INGENIØRHØJSKOLEN I ÅRHUS TWO BRANCHES MANIFOLD 152 E. CD In the attached CD-Room it can be found, in digital format, some extra data and information about the project. Included, there are:  Whole report in PDF format  Complete EES model  Pictures of the project realization  Videos of the project realization