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Appendix B: Computational Fluid Dynamics:
The method of Computational Fluid Dynamics (CFD) used in the analysis of flow characteristics of the original plenum and the final intake system was Finite Element Analysis (FEA). Algor Software was used to perform the FEA. Although the turbulent air flow behavior in the intake system necessitated the use of 3 dimensional (3D) FEA, the demands of 3D FEA could not be met by university hardware. Flow patterns were analyzed from several angles and it was determined that a two dimensional FEA could approximate the intake system. Both velocity and pressure distributions of the original system and the final design were produced. The 2D distributions of pressure were verified with a simple pipe analyzed by Algor and calculated by hand.
Justification of Using 2D Analysis
| Although 3D FEA was desirable, it was not possible to run a 3D analysis at the university, this will be expanded on in a later section. In lieu of using 3D analysis, 2D analysis was shown to approximate air flow in the original plenum and the horizontal symmetry of the final design allowed for 2D analysis.
Analysis of original system to assess use of 2D FEA
To analyze the flow in the original plenum a longitudinal cross section was taken and flow and pressure analyses were performed. Since the intake to the plenum is from the air box (the filter housing), the air box was modeled with the plenum. The flow through the plenum is seen to be very symmetric horizontally and the pressure gradient was almost perfectly horizontal. The same analysis was performed on the final design with similar results.
The horizontal symmetry of velocity and pressure of the original and final design verified FEA would be a useful tool to compare the final design and the original system. |
2D Finite Element Analysis
To perform 2D FEA on the original plenum, measurements were taken of the plenum during the experiment. The top view was outlined with a CAD package and used in Algor. A 2D FEA was performed on the horizontal centerline of the final design. The FEA’s performed on the original and final design were kept as identical as possible to allow for precise comparison. The following lists relevant FEA parameters:
· Algor 2D Unsteady State Fluid Analysis was chosen for FEA due
to the possible turbulent flow. |
· Algor cannot analyze compressible flow. However, the maximum
mach number of air in the original and final design was about 0.01.
It is generally accepted that compressible fluids behave as
incompressible if their mach number is below 0.3. |
· After importing the CAD outlines to Algor, the Supergen Mesh
Engine was used to create a quadrilateral mesh. The mesh was
created with an average element edge length of 0.25”. |
· A velocity of 100 in/s was defined exiting the carburetor side of
each design. 100 in/s is the average velocity of the air through a
1.5 in pipe during the maximum flowrate the 550cc engine creates
at 7000 rpm. |
· The flow was modeled as planar flow. |
· The density of air was calculated in slugs/in3 and the dynamic
viscosity was chosen to be 1/Re, as suggested by Algor. |
· Five load curves were applied to the flow to simulate the sinusoidal
intake of the motor cylinder. Each curve was 100 steps, the final
loading was 100%. |
· All convergence criteria were set to 1e-6. |
· After analysis the last 50 steps of the load curves were viewed to
determine if any extremely turbulent behavior existed. There flow
was not turbulent, so the last step of 100% loading of each design
was used for comparison. |
Verification of Results
Since Algor FEA was not well known by any team members, it was prudent to perform FEA on a simple geometric shape and check the results against hand calculations. A pipe of 12 in. length with one 90° bend was used to verify the results of the design analysis. The FEA pressure distribution was compared to hand calculated exit pressure.
The pipe was analyzed with the setup described above, but with an exit velocity of 86.6 in/s. The mesh used and the FEA pressure distribution can be seen below.
The average pressure of the nodes at the exit was –0.00685684 psig for the FEA
Pipe used for verification of FEA.
For hand calculations the air was modeled in a smooth pipe and the following was used:
Gage Pressure = Velocity Head Loss + Bend Head Loss
The air was assumed to be drawn from a large reservoir. The hand calculations produced an exit pressure of -0.00666149 psig.
The 3% difference between hand calculations and FEA results confirmed the FEA was being conducted correctly.
Problems Encountered with 3D FEA
Three-dimensional FEA was attempted and successfully completed on a simple pipe. The pipe used was 1.5 in diameter with a 5 in straight section and one 90° bend. The Algor velocity pressure and velocity distributions can be seen below.
The major problem encountered with 3D analysis was the required hard disk space. With 24 MB of RAM allocated to Algor, the simple case used 250 MB of hard disk space during analysis. When attempting to analyze the original plenum Algor created a single file of 2 GB before exhausting the computer’s hard drive and aborting analysis.
The hard disk space is directly related to the number of elements used in the analysis. Unfortunately, Algor does not provide adequate control over the element size generated by Hexagen, Algor’s 3D element engine. The simple pipe was divided into 5000 elements, the original plenum was divided into 15,000 elements.
Simple pipe analyzed with 3D Algor FEA.
Several methods were attempted to complete 3D analysis. These included, along with the results of the attempts:
· Exploring all possible options within Hexagen. Both the graphical
user interface options and DOS command line options were
reviewed. No options were found to control mesh density. |
· Using simpler elements for FEA produced improbable results.
(Algor insisted on using all eight-node bricks for fluid FEA. When
simpler elements were used obvious incorrect flow patterns were
observed. For example, on the simple pipe shown above, when
other than all 8-node bricks were used, velocity tapered to 0
before rounding the bend. That velocity distribution resembled the
pressure distribution shown above.) |
· Generating the design entirely with Algor software did not change
the number of elements generated. |
· Scaling the design by ½. This had no effect on the number of
elements generated. |
· Manually building a cubic mesh of the original plenum. Due to the
many circular geometries of the plenum, a very small mesh had to
be generated to model the plenum. The number of elements used
by the mesh was over 12,000 and had similar hard disk
requirements as the Hexagen mesh. |
· Using an approximate plenum design, with no circular
regions. Hexagen created over 10,000 elements. Manually cubic
meshing of the non-circular approximate design produced
unreliable results. The design could be analyzed, however, flow
tended to follow the straight line node paths. |
Exhausting the possibility of modeling the system with 3D FEA, 2D FEA proved a viable alternative.
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