1 Optimization of Reinforcement Methods for Non-round Pressure Vessels By Shawn McMahon A Presentation of 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 Pressure Vessel Description Dimensions: 40” diameter 50” long 12” spool piece Edge fixed in all DOF Material: Ti-6Al-V4 Constraints: Edge of spool fixed in all DOF Load: 80 psi Table of Ellipse Parameters

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

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

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

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

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

10 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 Model Type A Model Type B Mesh Elements Shell181 Beam188

11 Design Optimization Optimization Flowchart:

12 Design Optimization Results Model A Results Table Model B Results Table Total Volume vs. Model Number Rib Number vs. Model Number Rib Height vs. Model Number 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 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. K Coefficient per Ellipse Ratio Beam Nomenclature Shell Nomenclature

14 Q & A