Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-2015 Computational Fluid Dynamics Simulations of Oscillating Wings and Comparison to Lifting-Line Theory Megan Keddington Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Aerospace Engineering Commons Recommended Citation Keddington, Megan, "Computational Fluid Dynamics Simulations of Oscillating Wings and Comparison to Lifting-Line Theory" (2015). All Graduate Theses and Dissertations. 4473. https://digitalcommons.usu.edu/etd/4473 This Thesis is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. COMPUTATIONAL FLUID DYNAMICS SIMULATIONS OF OSCILLATING WINGS AND COMPARISON TO LIFTING-LINE THEORY by Megan Keddington A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Aerospace Engineering Approved: ____________________ ____________________ Warren F. Phillips Steven L. Folkman Major Professor Committee Member ____________________ ____________________ Douglas F. Hunsaker Mark R. McLellan Committee Member Vice President for Research and Dean of the School of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2015 ii Copyright © Megan Keddington 2015 All Rights Reserved iii ABSTRACT Computational Fluid Dynamics Simulations of Oscillating Wings and Comparison to Lifting-Line Solution by Megan Keddington Utah State University, 2015 Major Professor: Dr. Warren F. Phillips Department: Mechanical and Aerospace Engineering Computational fluid dynamics (CFD) analysis was performed in order to compare the solutions of oscillating wings with Prandtl’s lifting-line theory. Quasi-steady and steady-periodic simulations were completed using the CFD software Star-CCM+. The simulations were performed for a number of frequencies in a pure plunging setup. Additional simulations were then completed using a setup of combined pitching and plunging at multiple frequencies. Results from the CFD simulations were compared to the quasi-steady lifting-line solution in the form of the axial-force, normal-force, power, and thrust coefficients, as well as the efficiency obtained for each simulation. The mean values were evaluated for each simulation and compared to the quasi-steady lifting-line solution. It was found that as the frequency of oscillation increased, the quasi-steady lifting-line solution was decreasingly accurate in predicting solutions. (350 pages) iv PUBLIC ABSTRACT Computational Fluid Dynamics Simulations of Oscillating Wings and Comparison to Lifting-Line Theory Megan Keddington Computational fluid dynamics (CFD) analysis was performed in order to compare the solutions of oscillating wings with Prandtl’s lifting-line theory. Quasi-steady and steady-periodic simulations were completed using the CFD software Star-CCM+. Quasi-steady simulations were completed for both two- dimensional and three-dimensional setups. The steady-periodic simulations were only performed using a three-dimensional setup. The simulations were performed for nine separate frequencies in a pure plunging setup. An additional four simulations were then completed using a setup of combined pitching and plunging at four separate frequencies. Results from the CFD simulations were compared to the quasi-steady lifting-line solution in the form of the axial-force, normal-force, power, and thrust coefficients, as well as the efficiency obtained for each simulation. The mean values were evaluated for each simulation and compared to the quasi-steady lifting-line solution. It was found that as the frequency of oscillation increased, the quasi-steady lifting-line solution was decreasingly accurate in predicting solutions. It was also observed that the thrust was generated only by plunging, not pitching of the wing in the simulations. v ACKNOWLEDGMENTS I would like to thank Dr. Warren Phillips for imparting to me a small portion of his vast knowledge. He expected the highest, and for that, I am grateful. I would also like to thank Dr. Douglas Hunsaker for his constant guidance, council, and assistance. I could have never completed this thesis without his support and encouragement. I am indebted to both Dr. Phillips and Dr. Hunsaker for the extensive work they have put into teaching me and helping me along in this process. I am eternally grateful to my family, and especially my parents, for teaching me that I can do anything. Lastly, I’d like to thank my husband, for always being my rock, my champion, and my sanctuary. Words cannot express how grateful I am. Megan Keddington Jensen vi LIST OF TABLES Table Page 1 Correlation coefficients for Eqs. (1.61) and (1.62) .................................................................... 14 ω → ω = α = 2 Mean values of 2D quasi-steady cycle ˆ x 0 , ˆ y .0 07492 , and ˆ y 0.0 compared with the exact solution .............................................................................................................. 60 ω → ω = α = 3 Mean values of 3D quasi-steady cycle ˆ x 0 , ˆ y .0 07492 , and ˆ y 0.0 compared with the quasi-steady lifting-line solution .................................................................................. 68 ω → ω = α = 4 Mean values of 3D quasi-steady cycle ˆ x 0 , ˆ y .0 07492 , and ˆ y 2.0 compared with the quasi-steady lifting-line solution .................................................................................. 70 ω → ω = α = − 5 Mean values of 3D quasi-steady cycle ˆ x 0 , ˆ y .0 07492 , and ˆ y 2.0 compared with the quasi-steady lifting-line solution .................................................................................. 73 ω = ω = α = 6 Mean values of oscillation cycle with ˆ x .0 13414 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line solution ..................................................................... 76 ω = ω = α = 7 Mean values of oscillation cycle with ˆ x .0 14905 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line solution ..................................................................... 78 ω = ω = α = 8 Mean values of oscillation cycle with ˆ x .0 16162 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line solution ..................................................................... 81 ω = ω = α = 9 Mean values of oscillation cycle with ˆ x .0 19163 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line solution ..................................................................... 83 ω = ω = α = 10 Mean values of oscillation cycle with ˆ x .0 20637 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line solution ..................................................................... 86 ω = ω = α = 11 Mean values of oscillation cycle with ˆ x .0 24841 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line solution ..................................................................... 88 ω = ω = α = 12 Mean values of oscillation cycle with ˆ x .0 29162 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line theory ........................................................................ 91 ω = ω = α = 13 Mean values of oscillation cycle with ˆ x .0 33536 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line solution ..................................................................... 93 ω = ω = α = 14 Mean values of oscillation cycle with ˆ x .0 38327 , ˆ y .0 07492 , and ˆ y 0.0 compared to the quasi-steady lifting-line solution ..................................................................... 96 vii ω = ω = α = 15 Mean values of oscillation cycle with ˆ x .0 25797 , ˆ y .0 09365, and ˆ y 2.0 compared to the quasi-steady lifting-line solution ..................................................................... 99 ω = ω = α = 16 Mean values of oscillation cycle with ˆ x .0 47909 , ˆ y .0 09365 , and ˆ y 2.0 compared to the quasi-steady lifting-line solution .................................................................... 101 ω = ω = α = − 17 Mean values of oscillation cycle with ˆ x .0 17198 , ˆ y .0 06243, and ˆ y 2.0 compared to the quasi-steady lifting-line solution .................................................................... 104 ω = ω = α = − 18 Mean values of oscillation cycle with ˆ x .0 31939 , ˆ y .0 06243, and ˆ y 2.0 compared to the quasi-steady lifting-line solution .................................................................... 107 viii LIST OF FIGURES Figure Page 1 Parameters used by Theodorsen [9] to describe plunging and pitching motion (from Hunsaker and Phillips [12] with permission) .............................................................................. 2 2 Example coarse grid for computational fluid dynamics calculations (from Hunsaker and Phillips [12] with permission) .............................................................................................. 8 3 Comparison between the CFD solutions and the correlation with Eq. (1.61) (from Hunsaker and Phillips [12] with permission) ............................................................................. 14 4 Comparison between the CFD solutions and the correlation with Eq. (1.62) (from Hunsaker and Phillips [12] with permission) ............................................................................