Computional Fluid Dynamics Through a Pipe

Table of Contents INTRODUCTION3 Method3 secern 23 divide 33 Part 44 Part 54 RESULTS4 Part 14 Part 26 Part 36 Part 46 Part 56 DISCUSSION7 CONCLUSION7 REFERENCES7 INTRODUCTION The of import objective of this assignment is to simulate a 3-D air bunk in a shrill using Ansys CFX. The tubing was sham on a lower floor specific conditions. These conditions are air temperature to be 25? C (degrees Celsius), adept atmospheric reference mechanical press, no heat transfer and laminar flow. The results from the computer semblance of laminar flow in the pipe were compared with the theoretical ones.Also the take was slim in the simulation to see if it is possible to get more finished results using grid convergence analysis. Method The pipe used in the simulation has dimensions of a 0. 5m axial length and a radial diam of 12mm. The air entering the pipe, inlet speeding, is set to 0. 4 m/s at a temperature of 25? C and one atmospheric pressure. No slip condition was set on the pipe w alls. The outlet of pipe was set to zero gauge average static pressure. In CFX a mesh was formed on the pipe with a default mesh spacing (element size) of 2mm. go steady (1) and (2) shows the setup of the model before simulation was preformed meet 1 Mesh without Inflation fingerbreadth 1 Mesh without Inflation course 2 Mesh with Inflation Part 2 Calculating the pressure drop ? p=fLD? Ub22Equation (1) Calculating Reynolds number Re=UbD/? Equation (2) attrition Factorf=64/ReEquation (3) The results were calculated using excel, and plot in Figure (3). Part 3 Estimating the appeal pipe length Le Le/D=0. 06ReEquation (4) Having Re=UbD/? Equation (3) The imitation results of speeding vs. axial length were plotted in Figure (5).From the graph the Le (entrance pipe length) was determined by estimating the point in the x-axis where the curve is straight horizontal line. Part 4 Comparison of the radial dissemination of the axial f number in the full highly-developed region in the sim ulated model against the following analytical equation UUmax = 1-rr02 Equation (5) The results were calculated using excel, and plotted in Figure (4). Part 5 The simulation was performed three times, each time with a different grid setting. The numbers of nodes were 121156,215875 and 312647 for the 1st, 2nd and tertiary simulation.RESULTS Part 1 Figure 3 Pressure Distribution vs. Axial Length Figure 3 Pressure Distribution vs. Axial Length Figure 4 Axial amphetamine vs. Radial Diameter Figure 5 Velocity vs. Axial Distance Part 2 Having Dynamic viscosity ? = 1. 83510-5 kg/ms and Density ? = 1. 184 kg/m3 Reynolds Number Re=UbD? == 261. 58 detrition Factorf=64Re== 0. 244667 ?p=0. 965691 Pa From the simulation the pressure estimated at the inlet is ? p=0. 96562 Pa (0. 95295-0. 965691)/0. 965691*100 = 1. 080 % Part 3 Having Re=UbD? =261. 58 The entrance pipe length Le Le=0. 06Re*D = 0. 188 mFrom the graph in Figure (3) the Le is estimated to be 0. 166667 ((0. 166667-0. 188)/0. 188)*1 00 = 11. 73% Part 4 From the graph in Figure 2 the theoretical velocity at the center of the pipe is estimated to be 0. 8 m/s. From the simulation the velocity at the center of the pipe is estimated to be 0. 660406 m/s. ((0. 688179-0. 8)/0. 8)*100= 13. 98% Part 5 Table 1 Percentage faulting for to each one Simulation Number of Nodes Axial Velocity % wrongdoing (%) Pressure % faulting (%) 120000 Simulated I 13. 98 1. 31 215000 Simulated II 12. 42 2. 24 312000 Simulated III 12. 38 2. 28Figure 6 Percentage Error vs. Number of Nodes Figure 6 Percentage Error vs. Number of Nodes The character error for the axial velocity results from the 1st, 2nd and 3rd simulation were calculated and plotted in Figure (6), as soundly as the pressure result along the pipe. Table (1) shows the axial velocity and pressure helping error for each simulation. DISCUSSION After the simulation was successfully done on Ansys CFX and the simulated results were compared with theoretical results, it was sho w that the simulated results have slight deviation from theoretical ones. In PART 2, he pressure in the simulated result differed by the theoretical by a 1. 080%, for 1st simulation. In PART 3, the simulated results for entrance pipe length, Le, differed from the theoretical results by 11. 73%. In PART 4, Figure (4), the simulated velocity curve is less accurate than that of the theoretical. In PART 5, mesh refinements and inflation were done to the simulation in order to getting breach results. Figures (6) show with more nodes and inflation the accuracy of the results adds. Increasing the nodes gradually was found to be an advantage where higher or more accurate results were obtained.This is mention in grid convergence graph, Figure (6), as the number of nodes augment the pressure percentage error is converging to 2% while for velocity percentage error is converging to 12%. On the other hand, the percentage error increased with the increase of the number of nodes while the ve locity error decreased with the increase of number of nodes. In Part 2 the percentage error for pressure drop is 1. 080%, for 1st simulation. But when trying to increase the accuracy of the simulated velocity result by refining the meshing and adding nodes the pressure drop percentage error increases, as shown in estimate (6).This is due to that Darcy-Weisbach equation, equation (1), assumes constant developed flow all along the pipe where in the simulated results the flow is observed to become developed father down the pipe from the inlet. This is assumed to change the pressure distribution along the pipe. CONCLUSION More nodes used in meshing get out produce more accurate and precise results, as shown in Figure (6). Also the meshing plays a vital rule on the sensitiveness of results in terms of the accuracy of these results. REFERENCES 1Fluid Mechanics Frank M. White one-sixth edition. 2006