3-D Printed Pressure Vessel Design to Maximize Volume to Weight Brandon Straight, Steven Artis, Krishan Magan

Outline Title Outline Approach Results Conclusions Summary Background Requirements Design Information Theory Statement of Objective Approach Results Mass Results FEA Results Conclusions Summary

Background Information Design idealized for an upper-stage rocket nearing the mass requirement without structures Hybrid rocket requirement- solid fuel and cryogenic nitrous oxide in a vortex configuration 24 pounds of liquid nitrous oxide at a pressure of 700 psi A minimum ∆𝑉 requirement along with a total mass requirement were given to constrain the project Spherical pressure vessels commonly used on rockets (maximum volume to surface area)

Background Information A pressure vessel made from 3-D printing requires a laser sintering printer to ensure that the vessel is built with a high enough quality there is no leakage between the pores created when building the part. Laser sinter printing is much like welding but is a process applied to very thin printed plastics to seal them allowing them to be pressurized.

Theory The thickness required for a spherical pressure vessel can be found from: 𝑡= 𝑝∗𝑟 2𝜎 . The mass of any pressure vessel can be found by: 𝑚=𝑆𝐴∗𝑡∗𝜌 The volume of a hollow cylinder is: 𝑉 𝐻𝑜𝑙𝑙𝑜𝑤 𝐶𝑦𝑙𝑖𝑛𝑑𝑒𝑟 =𝜋ℎ 𝑅 2 − 𝑟 2 The hoop stress (given an internal pressure P) of a cylinder can be found from: 𝜎 𝜃 = 𝑃𝑟 2𝑡 The tensile strength of the material must be larger than the hoop stress to ensure the integrity of the structure.

Objective Create a design to optimize the mass of the oxidizer tank and motor case while still being structurally sound and able to contain given volume. Design needs to meet the thermal requirements of the cryogenic oxidizer and heat from the motor.

Approach First Design: A spherical pressure vessel and a cylindrical motor case. This design was found to be too massive. Second Design: A k-bottle pressure vessel and a cylindrical motor case. This design was also found to be too massive. Discovered motor case was pushing mass over the requirement so a design was sought after that could act as both the oxidizer tank and the motor case.

Final Design Annular tank with two half-toroids at the top and bottom chosen to be researched. Design can be seen in the photo below. Design chosen due to the center being cylindrical with pressure vessel around it to save mass and space. Design to be 3-D printed using Windform XT 2.0 due to the very high tensile strength (12,160 psi) and melting point (354.74F) for plastic that has a very low density (1.097 g/cc).

Final Design The stresses incurred by the design were found by using equations from “Optimum Shape of Constant Stress Toroidal Shells” by Truong Vu. Two types of stresses, circumferential stresses and meridional stresses. Wall thickness was needed and stress based on tensile strength and SF Wall thickness of toroidal parts able to change to optimize the mass and maintain a constant stress. Assumption was made that the center point referenced by Vu is at the interaction points between the cylinder and toroids.

Final Design The following equation was found to give the optimum thickness of the tank based on the pressure and tensile strength of the material. (Appendix contains excel data output) 𝑡 𝜑 = 𝑃𝑟 2∗ 𝜎 𝑣 ∗(𝑅+𝑟𝑠𝑖𝑛 𝜑 ) ∗ 3 𝑅 2 +3𝑅𝑟𝑠𝑖𝑛 𝜑 + 𝑟 2 sin(𝜑) 2

Results Using a varying wall thickness of Windform XT 2.0, the design was found to weigh 7.67 pounds. A spherical design was found to weigh 10.38 pounds (only the oxidizer tank) due to the increased wall thickness. These correlated to a mass savings of 26% without a motor case added to the spherical design.

Results: Masses To verify the calculated results, both of the designs were created in Solid Works and FEA was performed on them. Annular design used a median wall thickness for the toroidal part of the design for drawing simplicity. Due to a lack of technical material data on the Windform, FEA could not calculate results, but masses of the designs were returned that verified our results.

Results: FEA - Al 7068 Since the FEA could not be performed for Windform, Aluminum 7068 was used to check the validity of the results and see the pressure points. Assumed constraints on internal and external cylindrical portions Assumed motor case thickness of 0.25 inches 4340 steel for safety and melting concerns Results, shown on next slides, validated our previous results by showing that a spherical design and a motor case would weigh 21.7 pounds while the annular design would only weigh 11.4 pounds.

4340 Steel 0.25 in Wall Thickness @ 1200 psi = 16.9 lbm Aluminum 7068 Min. Thickness for SF of 3 = 4.8 lbm

Aluminum 7068 at min. wall thickness for SF of 3 @ 700 psi = 11.4 lbm

Conclusions A spherical design may not always be the best pressure vessel design for mass requirements. Annular design was much more effective for this rocket design, and actually self-cooled walls due to cryogenic material contained. Results have indicated a mass savings of 25-35% is possible due to using this design over a sphere.

Summary Annular oxidizer tank/motor case with two-half toroids at each end of cylindrical portion Wall thickness varies around toroid for a set internal pressure and SF. Trade studies must be done but design would be effective mass saving solution for similar systems that require a hybrid motor for safety or throttling capabilities Reduces length of rocket required while lowering mass over spherical designs Eliminates motor case Aft end vortex injection design allowed for wall cooling inside and out for this to be possible Further testing is needed before this design can be implemented but financial constraints did not allow for this

References Truong Vu, Vu. "Optimum Shape of Constant Stress Toroidal Shells." Journal of Pressure Vessel Technology 135 (2013): 2-6. ASME Digital Collection. Web. Mar.-Apr. 2015. "Windform XT 2.0. Polyamide Based Material Carbon Filled." Windform XT 2.0. Polyamide Based Material Carbon Filled. CRP Technology SRL, Web. 20 Apr. 2015. <http://www.windform.com/windform-xt-2-0.html>.

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