Computional Fluid Dynamics Through a Pipe

Table of Contents INTRODUCTION 3 Method: 3 Part 2 3 Part 3 3 Part 4 4 Part 5 4 RESULTS 4 Part 1 4 Part 2 6 Part 3 6 Part 4 6 Part 5: 6 DISCUSSION 7 CONCLUSION 7 REFERENCES 7

INTRODUCTION
The main objective of this assignment is to simulate a 3-D air flow in a pipe using Ansys CFX. The pipe was simulated under specific conditions. These conditions are air temperature to be 25⁰C (degrees Celsius), one atmospheric reference pressure, no heat transfer and laminar flow. The results from the simulation of laminar flow in the pipe were compared with the theoretical ones. Also the mesh was refined in the simulation to see if it is possible to get more accurate results using grid convergence analysis.
Method:
The pipe used in the simulation has dimensions of a 0.5m axial length and a radial diameter of 12mm. The air entering the pipe, inlet velocity, is set to 0.4 m/s at a temperature of 25⁰C and one atmospheric pressure. No slip condition was set on the pipe walls. 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. Figure (1) and (2) shows the setup of the model before simulation was preformed
Figure 1: Mesh without Inflation
Figure 1: Mesh without Inflation

Figure 2: Mesh with Inflation

Part 2
Calculating the pressure drop Δp=fLDρ Ub22 Equation (1)
Calculating Reynolds number Re=UbD/μ Equation (2)
Friction Factor f=64/Re Equation (3)
The results were calculated using excel, and plotted in Figure (3).
Part 3
Estimating the entrance pipe length Le: Le/D=0.06Re Equation (4)
Having Re=UbD/μ Equation (3)
The simulated results of velocity 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 distribution of the axial velocity in the fully developed region in the simulated 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 3rd simulation.
RESULTS
Part 1
Figure 3: Pressure Distribution vs. Axial Length
Figure 3: Pressure Distribution vs. Axial Length

Figure 4: Axial Velocity vs. Radial Diameter

Figure 5: Velocity vs. Axial Distance
Part 2 Having: Dynamic viscosity μ = 1.835x10-5 kg/ms and Density ρ = 1.184 kg/m3 Reynolds Number Re=UbDμ== 261.58 Friction Factor f=64Re== 0.244667 Δp=0.965691 Pa From the simulation the pressure estimated at the inlet is Δp=0.96562 Pa (0.95295-0.965691)/0.965691*100 = 1.080 %
Part 3
Having Re=UbDμ=261.58
The entrance pipe length Le: Le=0.06Re*D = 0.188 m
From the graph in Figure (3) the Le is estimated to be ~ 0.166667
((0.166667-0.188)/0.188)*100 = 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 Error for Each Simulation Number of Nodes | Axial Velocity % error (%) | Pressure % error (%) | 120000
Simulated I | 13.98 | 1.31 | 215000
Simulated II | 12.42 | 2.24 | 312000
Simulated III | 12.38 | 2.28 |

Figure 6: Percentage Error vs. Number of Nodes
Figure 6: Percentage Error vs. Number of Nodes

The percentage error for the axial velocity results from the 1st, 2nd and 3rd simulation were calculated and plotted in Figure (6), as well as the pressure result along the pipe. Table (1) shows the axial velocity and pressure percentage 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 found that the simulated results have slight deviation from theoretical ones.
In PART 2, the 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, meshing refinements and inflation were done to the simulation in order to getting better results. Figures (6) show with more nodes and inflation the accuracy of the results increases. Increasing the nodes gradually was found to be an advantage where higher or more accurate results were obtained. This is noted in grid convergence graph, Figure (6), as the number of nodes increase 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 velocity 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 figure (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 will produce more accurate and precise results, as shown in Figure (6). Also the meshing plays a vital rule on the sensitivity of results in terms of the accuracy of these results.
REFERENCES
[1] Fluid Mechanics Frank M. White Sixth edition. 2006

References: [1] Fluid Mechanics Frank M. White Sixth edition. 2006