Optimization of Reinforcement Methods for Non-round Pressure Vessels

1. Optimization of Reinforcement Methods for Non-round Pressure Vessels By Shawn McMahon A Presentationof a Thesis In Partial Fulfillment of the Requirements for the Degree of Masters of Science Major Subject: Mechanical Engineering

2. Abstract For a number of reasons the exhaust of a modern gas turbine engine is moving away from the conventional round pipe, and being replaced by one with an elliptical cross section. However, designing a low weight, non-round pressure vessel is more challenging than a typical round pressure vessel. The problem posed is how to create the lightest weight round to elliptical pressure vessel. In order to accomplish this, analytical models were created and optimized based on a number of parameters. Two different optimization approaches were investigated. The results showed that the first optimization method was simpler to build and optimize, but provided less than optimal weights. The second optimization method was much more complicated to build, was more sensitive to the controls of the optimization, but provided the lightest results.

3. Optimization Methods • ANSYS was used as the finite element solver. • The first optimization method used was shape optimization, also called topological optimization. • Simple ANSYS commands • Pseudo-density manipulation • Limited element selection and optimization controls • Simulated topological optimization. • Design optimization of shell thickness • Simulated manufacturability constraints • The second method used was design optimization. • Requires parametric model to be built with APDL • More difficult but more functionality • Yields better results

4. Table of Ellipse Parameters Pressure Vessel Description • Dimensions: • 40” diameter • 50” long • 12” spool piece Edge fixed in all DOF 12” spool piece Material: Ti-6Al-V4 Constraints: Edge of spool fixed in all DOF Load: 80 psi

5. P Quick Test of Topological Opt. • Dimensions: • 10 inch long • 1 inch high • Elements: • Plane82 • Goal: • 75 percent reduction in volume Results:

6. Topological Optimization • Dimensions: • Ellipse ratio 1.5 • 6 inches thick • Elements: • Solid95 • Goal: • 50 percent reduction in volume

7. Axial Segments Spool piece Equal length segments Angular Segments Equal angle segments Equal arc length segments Simulated Topological Opt. • Optimization: • Vary segment thickness • Simulated manufacturing constraints • Model Types: • Axial segments • Angular segments

8. Results Table Sample Results Screen Shot Shell Thickness per Axial Segment Simulated Topo. Opt. Results • Results: • Aft most segment always thickest • Segment 7 and/or 8 thicker in highly elliptical models

9. Results Table Sample Results Screen Shot Shell Thickness per Axial Segment Simulated Topo. Opt. Results • Results: • Segment 10 always the thickest • Segment 7 always the thinnest • Segment 7 is actually the middle segment

10. Model Type A Mesh Elements Shell181 Beam188 Model Type B Design Optimization • Model Types: • Axially spaced ribs • Addition of four circumferentially spaced ribs • Optimization Parameters: • Number of ribs • Distribution of ribs • Position of first ribs • Rib height • Shell thickness

11. Design Optimization Optimization Flowchart:

12. Total Volume vs. Model Number Rib Number vs. Model Number Model A Results Table Rib Height vs. Model Number Model B Results Table Design Optimization Results • Results: • Higher total volume of model with circumferentially spaced ribs • Short rib height of model with circumferentially spaced ribs • Increase in rib number with increase ellipse ratio

13. Beam Nomenclature Shell Nomenclature K Coefficient per Ellipse Ratio Hand Calculations • Info: • Quick check of the results of the analysis • Beam bending equations from Roark’s and Timoshenko • ANSYS results and hand calc results match pretty well. Hand calcs predict slightly lower deflections than ANSYS.

14. Q & A