Kenneth C. Hall | Scholars@Duke

Kenneth C. Hall
Julian Francis Abele Distinguished Professor

Research Interests: Unsteady aerodynamics, structural dynamics, and aeroelasticity of turbomachinery and aerospace vehicles. Novel approaches to modelling complex physical phenomena using computational fluid dynamics. Optimization and sensitivity analysis. Optimal aerodynamics of flight vehicles and animal propulsion.

Current Research Interests

Unsteady aerodynamics, structural dynamics, and aeroelasticity of turbomachinery and aerospace vehicles. Novel approaches to modeling complex physical phenomena using computational fluid dynamics. Optimization and sensitivity analysis. Fluid dynamics of animal propulsion.

Current Appointments & Affiliations

Julian Francis Abele Distinguished Professor, Mechanical Engineering and Materials Science, Pratt School of Engineering 2004
Professor of Mechanical Engineering and Materials Science, Mechanical Engineering and Materials Science, Pratt School of Engineering 2000

Contact Information

184 Hudson Eng Ctr, Box 90300, Durham, NC 27708
184 Hudson Eng Ctr, Box 90300, Durham, NC 27708-0300
kenneth.c.hall@duke.edu (919) 660-5328
AeroElasticity Group

Background
Education, Training, & Certifications
- D.Sc., Massachusetts Institute of Technology 1987
- M.S., Massachusetts Institute of Technology 1983
- B.S., Massachusetts Institute of Technology 1981
Duke Appointment History
- Chair, Department of Mechanical Engineering and Materials Science, Mechanical Engineering and Materials Science, Pratt School of Engineering 2001 - 2007
- Associate Professor, Mechanical Engineering and Materials Science, Pratt School of Engineering 1996 - 2000
- Assistant Professor, Mechanical Engineering and Materials Science, Pratt School of Engineering 1990 - 1996
Academic Positions Outside Duke
- Visiting Associate Professor, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology. 1997 - 1998
- Research Assistant, Gas Turbine Laboratory, Massachusetts Institute of Technology. 1981 - 1987
Recognition
In the News
- FEB 11, 2020 Pratt School of Engineering
  
  Hall Elected to National Academy of Engineering
- MAY 23, 2018 Pratt School of Engineering
  
  Professor Kenneth Hall Takes His Love of Aerodynamics and Aviation to the Skies
Awards & Honors
- Fellow. American Institute of Aeronautics and Astronautics. 2011
- Fellow. American Society of Mechanical Engineers. 2000
Research
Selected Grants
- Editorial Work for American Society of Mechanical Engineers awarded by American Society of Mechanical Engineers (ASME) 2017 - 2018
- Editorial Work for American Society of Mechanical Engineers awarded by American Society of Mechanical Engineers (ASME) 2016 - 2017
- Minimum Power Requirements and Optimal Rotor Design for Conventional and Compound Helicopters Using Higher Harmonic Blade Root Control awarded by Army Research Office 2013 - 2016
- Editorial Work for American Society of Mechanical Engineers awarded by American Society of Mechanical Engineers (ASME) 2015 - 2016
- Development of rapid linear and non-linear physics based flutter/LCO analysis methods awarded by Continuum Dynamics, Inc. 2015
External Relationships
- Alphabet Inc
- Apple Inc.
Publications & Artistic Works
Selected Publications
- Books
  - Dowell, E. H., R. Clark, D. Cox, H. C. Curtiss, J. W. Edwards, K. C. Hall, D. A. Peters, et al. A modern course in aeroelasticity. Vol. 116, 2005.
- Academic Articles
  - Hall, K. C., and O. Coutier-Delgosha. “Special issue on the 17th ISROMAC conference.” Journal of Turbomachinery 141, no. 2 (February 1, 2019). https://doi.org/10.1115/1.4042566.
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  - Giovanetti, E. B., and K. C. Hall. “Optimum design of compound helicopters that use higher harmonic control.” Journal of Aircraft 52, no. 5 (January 1, 2015): 1444–53. https://doi.org/10.2514/1.C032941.
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  - Thomas, J. P., C. H. Custer, E. H. Dowell, K. C. Hall, and C. Corre. “Compact implementation strategy for a harmonic balance method within implicit flow solvers.” Aiaa Journal 51, no. 6 (June 1, 2013): 1374–81. https://doi.org/10.2514/1.J051823.
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  - Hall, K. C., K. Ekici, J. P. Thomas, and E. H. Dowell. “Harmonic balance methods applied to computational fluid dynamics problems.” International Journal of Computational Fluid Dynamics 27, no. 2 (February 1, 2013): 52–67. https://doi.org/10.1080/10618562.2012.742512.
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  - Ekici, K., R. E. Kielb, and K. C. Hall. “The effect of aerodynamic asymmetries on turbomachinery flutter.” Journal of Fluids and Structures 36 (January 1, 2013): 1–17. https://doi.org/10.1016/j.jfluidstructs.2012.08.009.
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  - Ekici, K., and K. C. Hall. “Harmonic balance analysis of limit cycle oscillations in turbomachinery.” Aiaa Journal 49, no. 7 (July 1, 2011): 1478–87. https://doi.org/10.2514/1.J050858.
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  - Hall, K. C., and S. R. Hall. “A variational method for computing the optimal aerodynamic performance of conventional and compound helicopters.” Annual Forum Proceedings Ahs International 3 (December 1, 2010): 2767–84.
  - Hall, K. C., and S. R. Hall. “A variational method for computing the optimal aerodynamic performance of conventional and compound helicopters.” Journal of the American Helicopter Society 55, no. 4 (October 1, 2010): 0420061–616. https://doi.org/10.4050/JAHS.55.042006.
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  - Ekici, K., K. C. Hall, and R. E. Kielb. “Harmonic balance analysis of blade row interactions in a transonic compressor.” Journal of Propulsion and Power 26, no. 2 (January 1, 2010): 335–43. https://doi.org/10.2514/1.43879.
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  - Ekici, K., R. E. Kielb, and K. C. Hall. “Aerodynamic asymmetry analysis of unsteady flows in turbomachinery.” Journal of Turbomachinery 132, no. 1 (January 1, 2010). https://doi.org/10.1115/1.3103922.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Using automatic differentiation to create a nonlinear reduced-order-model aerodynamic solver.” Aiaa Journal 48, no. 1 (January 1, 2010): 19–24. https://doi.org/10.2514/1.36414.
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  - Miyakozawa, T., R. E. Kielb, and K. C. Hall. “The Effects of aerodynamic asymmetric perturbations on forced response of bladed disks.” Journal of Turbomachinery 131, no. 4 (October 1, 2009): 1–8. https://doi.org/10.1115/1.3068319.
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  - Dowell, E. H., J. P. Thomas, K. C. Hall, and C. M. Denegri. “Theoretical predictions of F-16 fighter limit cycle oscillations for flight flutter testing.” Journal of Aircraft 46, no. 5 (January 1, 2009): 1667–72. https://doi.org/10.2514/1.42352.
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  - Schwarz, J. B., E. H. Dowell, J. P. Thomas, K. C. Hall, R. D. Rausch, and R. E. Bartels. “Improved flutter boundary prediction for an isolated two-degree-of-freedom airfoil.” Journal of Aircraft 46, no. 6 (January 1, 2009): 2069–76. https://doi.org/10.2514/1.30703.
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  - Ekici, K., and K. C. Hall. “Nonlinear frequency-domain analysis of unsteady flows in turbomachinery with multiple excitation frequencies.” Aiaa Journal 46, no. 8 (August 1, 2008): 1912–20. https://doi.org/10.2514/1.26006.
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  - Dowell, E. H., K. C. Hall, J. P. Thomas, R. E. Kielb, M. A. Spiker, and C. M. Denegri. “A new solution method for unsteady flows around oscillating bluff bodies.” Solid Mechanics and Its Applications 8 (January 1, 2008): 37–44. https://doi.org/10.1007/978-1-4020-8630-4_4.
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  - Ekici, K., K. C. Hall, and E. H. Dowell. “Computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors.” 46th Aiaa Aerospace Sciences Meeting and Exhibit, January 1, 2008. https://doi.org/10.2514/6.2008-1439.
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  - Ekici, K., and K. C. Hall. “Nonlinear analysis of unsteady flows in multistage turbomachines using harmonic balance.” Aiaa Journal 45, no. 5 (May 1, 2007): 1047–57. https://doi.org/10.2514/1.22888.
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  - Liu, L., E. H. Dowell, and K. C. Hall. “A novel harmonic balance analysis for the Van Der Pol oscillator.” International Journal of Non Linear Mechanics 42, no. 1 (January 1, 2007): 2–12. https://doi.org/10.1016/j.ijnonlinmec.2006.09.004.
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  - Ekici, K., and K. C. Hall. “Fast estimation of unsteady flows in turbomachinery at multiple interblade phase angles.” Aiaa Journal 44, no. 9 (September 1, 2006): 2136–42. https://doi.org/10.2514/1.23288.
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  - Liu, L., J. P. Thomas, E. H. Dowell, P. Attar, and K. C. Hall. “A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator.” Journal of Computational Physics 215, no. 1 (June 10, 2006): 298–320. https://doi.org/10.1016/j.jcp.2005.10.026.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Static/dynamic correction approach for reduced-order modeling of unsteady aerodynamics.” Journal of Aircraft 43, no. 4 (January 1, 2006): 865–78. https://doi.org/10.2514/1.12349.
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  - Hall, K. C., and K. Ekici. “Multistage coupling for unsteady flows in turbomachinery.” Aiaa Journal 43, no. 3 (January 1, 2005): 624–32. https://doi.org/10.2514/1.8520.
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  - Thomas, J. P., K. C. Hall, and E. H. Dowell. “Discrete adjoint approach for modeling unsteady aerodynamic design sensitivities.” Aiaa Journal 43, no. 9 (January 1, 2005): 1931–36. https://doi.org/10.2514/1.731.
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  - Dowell, E. H., J. P. Thomas, and K. C. Hall. “Transonic limit cycle oscillation analysis using reduced order aerodynamic models.” Journal of Fluids and Structures 19, no. 1 (January 1, 2004): 17–27. https://doi.org/10.1016/j.jfluidstructs.2003.07.018.
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  - Kholodar, D. B., E. H. Dowell, J. P. Thomas, and K. C. Hall. “Limit-cycle oscillations of a typical airfoil in transonic flow.” Journal of Aircraft 41, no. 5 (January 1, 2004): 1067–72. https://doi.org/10.2514/1.618.
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  - Kholodar, D. B., E. H. Dowell, J. P. Thomas, and K. C. Hall. “Improved understanding of transonic flutter: A three-parameter flutter surface.” Journal of Aircraft 41, no. 4 (January 1, 2004): 911–17. https://doi.org/10.2514/1.467.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Modeling viscous transonic limit-cycle oscillation behavior using a harmonic balance approach.” Journal of Aircraft 41, no. 6 (January 1, 2004): 1266–74. https://doi.org/10.2514/1.9839.
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  - Kholodar, D. B., J. P. Thomas, E. H. Dowell, and K. C. Hall. “Parametric study of flutter for an airfoil in inviscid transonic flow.” Journal of Aircraft 40, no. 2 (January 1, 2003): 303–13. https://doi.org/10.2514/2.3094.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Three-dimensional transonic aeroelasticity using proper orthogonal decomposition-based reduced-order models.” Journal of Aircraft 40, no. 3 (January 1, 2003): 544–51. https://doi.org/10.2514/2.3128.
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  - Epureanu, B. I., E. H. Dowell, and K. C. Hall. “Mach number influence on reduced-order models of inviscid potential flows in turbomachinery.” Journal of Fluids Engineering, Transactions of the Asme 124, no. 4 (December 1, 2002): 977–87. https://doi.org/10.1115/1.1511165.
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  - Hall, K. C., J. P. Thomas, and W. S. Clark. “Computation of unsteady nonlinear flows in cascades using a harmonic balance technique.” Aiaa Journal 40, no. 5 (January 1, 2002): 879–86. https://doi.org/10.2514/2.1754.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations.” Aiaa Journal 40, no. 4 (January 1, 2002): 638–46. https://doi.org/10.2514/2.1720.
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  - Dowell, E. H., and K. C. Hall. “Modeling of fluid-structure interaction.” Annual Review of Fluid Mechanics 33 (January 1, 2001): 445–90. https://doi.org/10.1146/annurev.fluid.33.1.445.
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  - Epureanu, B. I., K. C. Hall, and E. H. Dowell. “Reduced-order models of unsteady viscous flows in turbomachinery using viscous-inviscid coupling.” Journal of Fluids and Structures 15, no. 2 (January 1, 2001): 255–73. https://doi.org/10.1006/jfls.2000.0334.
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  - Florea, R., and K. C. Hall. “Sensitivity analysis of unsteady inviscid flow through turbomachinery cascades.” 38th Aerospace Sciences Meeting and Exhibit, December 1, 2000.
  - Epureanu, B. I., E. H. Dowell, and K. C. Hall. “Reduced-order models of unsteady transonic viscous flows in turbomachinery.” Journal of Fluids and Structures 14, no. 8 (November 1, 2000): 1215–34. https://doi.org/10.1006/jfls.2000.0320.
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  - Clark, W. S., and K. C. Hall. “A time-linearized Navier-Stokes analysis of stall flutter.” Journal of Turbomachinery 122, no. 3 (July 1, 2000): 467–76. https://doi.org/10.1115/1.1303073.
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  - Florea, R., K. C. Hall, and E. H. Dowell. “Eigenmode analysis and reduced-order modeling of unsteady transonic potential flow around airfoils.” Journal of Aircraft 37, no. 3 (January 1, 2000): 454–62. https://doi.org/10.2514/2.2619.
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  - Hall, K. C., J. P. Thomas, and E. H. Dowell. “Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows.” Aiaa Journal 38, no. 10 (January 1, 2000): 1853–62. https://doi.org/10.2514/2.867.
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  - Tang, D., E. H. Dowell, and K. C. Hall. “Limit Cycle Oscillations of a Cantilevered Wing in Low Subsonic Flow.” Aiaa Journal 37, no. 2–3 (January 1, 1999): 364–71. https://doi.org/10.2514/2.717.
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  - Florea, R., and K. C. Hall. “Eigenmode analysis of unsteady flows about airfoils.” Journal of Computational Physics 147, no. 2 (December 10, 1998): 568–93. https://doi.org/10.1006/jcph.1998.6102.
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  - Florea, R., K. C. Hall, and P. G. A. Cizmas. “Reduced-order modeling of unsteady viscous flow in a compressor cascade.” Aiaa Journal 36, no. 6 (January 1, 1998): 1039–48. https://doi.org/10.2514/2.477.
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  - Hall, K. C., S. A. Pigott, and S. R. Hall. “Power requirements for large-amplitude flapping flight.” Journal of Aircraft 35, no. 3 (January 1, 1998): 352–61. https://doi.org/10.2514/2.2324.
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  - Silkowski, P. D., and K. C. Hall. “A coupled mode analysis of unsteady multistage flows in turbomachinery.” Journal of Turbomachinery 120, no. 3 (January 1, 1998): 410–21. https://doi.org/10.1115/1.2841732.
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  - Dowell, E. H., K. C. Hall, and M. C. Romanowski. “Eigenmode analysis in unsteady aerodynamics: Reduced order models.” Applied Mechanics Reviews 50, no. 6 (January 1, 1997): 371–86. https://doi.org/10.1115/1.3101718.
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  - Hall, K. C., and P. D. Silkowski. “The influence of neighboring blade rows on the unsteady aerodynamic response of cascades.” Journal of Turbomachinery 119, no. 1 (January 1, 1997): 85–93. https://doi.org/10.1115/1.2841014.
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  - Hall, K. C., and S. R. Hall. “Minimum induced power requirements for flapping flight.” Journal of Fluid Mechanics 323 (September 25, 1996): 285–315. https://doi.org/10.1017/S0022112096000924.
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  - Lorence, C. B., and K. C. Hall. “Sensitivity analysis of the aeroacoustic response of turbomachinery blade rows.” Aiaa Journal 34, no. 8 (January 1, 1996): 1545–54. https://doi.org/10.2514/3.13270.
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  - Cizmas, P. G. A., and K. C. Hall. “Computation of steady and unsteady viscous flows using a simultaneously coupled inviscid-viscous interaction technique.” Journal of Fluids and Structures 9, no. 6 (January 1, 1995): 639–57. https://doi.org/10.1006/jfls.1995.1035.
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  - Hall, K. C., and R. Florea. “A reduced order model of unsteady flows in turbomachinery.” Journal of Turbomachinery 117, no. 3 (January 1, 1995): 375–83. https://doi.org/10.1115/1.2835672.
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  - Lorence, C. B., and K. C. Hall. “Sensitivity analysis of unsteady aerodynamic loads in cascades.” Aiaa Journal 33, no. 9 (January 1, 1995): 1604–10. https://doi.org/10.2514/3.12798.
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  - Hall, K. C. “Eigenanalysis of unsteady flows about airfoils, cascades, and wings.” Aiaa Journal 32, no. 12 (January 1, 1994): 2426–32. https://doi.org/10.2514/3.12309.
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  - Hall, K. C., W. S. Clark, and C. B. Lorence. “A linearized euler analysis of unsteady transonic flows in turbomachinery.” Journal of Turbomachinery 116, no. 3 (January 1, 1994): 477–88. https://doi.org/10.1115/1.2929437.
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  - Hall, S. R., K. Y. Yang, and K. C. Hall. “Helicopter rotor lift distributions for minimum-induced power loss.” Journal of Aircraft 31, no. 4 (January 1, 1994): 837–45. https://doi.org/10.2514/3.46569.
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  - Hall, Kenneth C., and William S. Clark. “Errata: Linearized Euler Predictions of Unsteady Aerodynamic Loads in Cascades.” Aiaa Journal 31, no. 5 (May 1993): 970–970. https://doi.org/10.2514/3.49039.
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  - Hall, K. C. “Deforming grid variational principle for unsteady small disturbance flows in cascades.” Aiaa Journal 31, no. 5 (January 1, 1993): 891–900. https://doi.org/10.2514/3.11701.
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  - Hall, K. C., and C. B. Lorence. “Calculation of three-dimensional unsteady flows in turbomachinery using the linearized harmonic euler equations.” Journal of Turbomachinery 115, no. 4 (January 1, 1993): 800–809. https://doi.org/10.1115/1.2929318.
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  - Hall, K. C., and W. S. Clark. “Linearized euler predictions of unsteady aerodynamic loads in cascades.” Aiaa Journal 31, no. 3 (January 1, 1993): 540–50. https://doi.org/10.2514/3.11363.
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  - Hall, K. C., and J. M. Verdon. “Gust response analysis for cascades operating in nonuniform mean flows.” Aiaa Journal 29, no. 9 (January 1, 1991): 1463–71. https://doi.org/10.2514/3.10761.
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  - Hall, K. C., and E. F. Crawley. “Calculation of unsteady flows in turbomachinery using the linearizedEuler equations.” Aiaa Journal 27, no. 6 (January 1, 1989): 777–87. https://doi.org/10.2514/3.10178.
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  - Crawley, E. F., and K. C. Hall. “Optimization and mechanisms of mistuning in cascades.” Journal of Engineering for Gas Turbines and Power 107, no. 2 (January 1, 1985): 418–26. https://doi.org/10.1115/1.3239742.
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- Reports
  - Verdon, Joseph M., Mark Barnett, Kenneth C. Hall, and Timothy C. Ayer. “Development of unsteady aerodynamic analyses for turbomachinery aeroelastic and aeroacoustic applications,” 1991.
- Conference Papers
  - Giovanetti, E. B., and K. C. Hall. “Minimum loss load, twist, and chord distributions for coaxial helicopters in hover.” In Journal of the American Helicopter Society, Vol. 62, 2017. https://doi.org/10.4050/JAHS.62.012001.
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  - Giovanetti, E. B., and K. C. Hall. “Axisymmetric potential flow model of single or coaxial actuator disks.” In Annual Forum Proceedings Ahs International, 1:747–57, 2016.
  - Giovanetti, E. B., and K. C. Hall. “A variational approach to multipoint aerodynamic optimization of conventional and coaxial helicopter rotors.” In Annual Forum Proceedings Ahs International, 2:752–64, 2015.
  - Giovanetti, E. B., and K. C. Hall. “Minimum loss load, twist and chord distributions for coaxial helicopters in Hover.” In Annual Forum Proceedings Ahs International, 1:648–57, 2015.
  - Marpu, R. P., C. H. Custer, V. Subramanian, J. M. Weiss, and K. C. Hall. “Comparison of numerical methods for the prediction of timeaveraged flow quantities in a cooled multistage turbine.” In Proceedings of the Asme Turbo Expo, Vol. 2C, 2015. https://doi.org/10.1115/GT2015-43717.
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  - Giovanetti, E. B., and K. C. Hall. “Optimum design of compound helicopters using higher harmonic control.” In Annual Forum Proceedings Ahs International, 4:2607–18, 2014.
  - Clark, S. T., R. E. Kielb, and K. C. Hall. “A van der pol based reduced-order model for non-synchronous vibration (NSV) in turbomachinery.” In Proceedings of the Asme Turbo Expo, Vol. 7 B, 2013. https://doi.org/10.1115/GT2013-95741.
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  - Subramanian, V., C. H. Custer, J. M. Weiss, and K. C. Hall. “Unsteady simulation of a two-stage cooled high pressure turbine using an efficient non-linear harmonic balance method.” In Proceedings of the Asme Turbo Expo, Vol. 6 C, 2013. https://doi.org/10.1115/GT2013-94574.
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  - Hall, K. C., and E. B. Giovanetti. “Minimum power requirements and optimal rotor design for conventional and compound helicopters using higher harmonic control.” In Annual Forum Proceedings Ahs International, 3:1867–83, 2013.
  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Discrete adjoint method for nonlinear aeroelastic sensitivities for compressible and viscous flows.” In 54th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics, and Materials Conference, 2013. https://doi.org/10.2514/6.2013-1860.
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  - Ekici, K., K. C. Hall, H. Huang, and J. P. Thomas. “Stabilization of explicit flow solvers using a proper-orthogonal- decomposition technique.” In Aiaa Journal, 51:1095–1104, 2013. https://doi.org/10.2514/1.J051945.
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  - Lipp, G. M., K. C. Hall, and B. P. Mann. “Effect of rider position on bicycle stability.” In Asme International Mechanical Engineering Congress and Exposition, Proceedings (Imece), Vol. 4 A, 2013. https://doi.org/10.1115/IMECE2013-63809.
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  - Clark, S. T., R. E. Kielb, and K. C. Hall. “Developing a reduced-order model to understand nonsynchronous vibration (NSV) in turbomachinery.” In Proceedings of the Asme Turbo Expo, 7:1373–82, 2012. https://doi.org/10.1115/GT2012-68145.
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  - Custer, C. H., J. M. Weiss, V. Subramanian, W. S. Clark, and K. C. Hall. “Unsteady simulation of a 1.5 stage turbine using an implicitly coupled nonlinear harmonic balance method.” In Proceedings of the Asme Turbo Expo, 8:2303–17, 2012. https://doi.org/10.1115/GT2012-69690.
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  - Ekici, K., K. C. Hall, and H. Huang. “Stabilization of explicit flow solvers using a proper orthogonal decomposition technique.” In 50th Aiaa Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2012. https://doi.org/10.2514/6.2012-1096.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “An automatic differentiation based nonlinear reduced order modeling technique for unsteady separated flows.” In 50th Aiaa Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2012. https://doi.org/10.2514/6.2012-1098.
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  - Weiss, J. M., V. Subramanian, and K. C. Hall. “Simulation of unsteady turbomachinery flows using an implicitly coupled nonlinear harmonic balance method.” In Proceedings of the Asme Turbo Expo, 7:1405–12, 2011. https://doi.org/10.1115/GT2011-46367.
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  - Thomas, J. P., C. H. Custer, E. H. Dowell, and K. C. Hall. “F-16 fighter aeroelastic computations using a harmonic balance implementation of the OVERFLOW 2 flow solver.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 2010.
  - Ekici, K., and K. C. Hall. “Harmonic balance analysis of limit cycle oscillations in turbomachinery.” In 46th Aiaa/Asme/Sae/Asee Joint Propulsion Conference and Exhibit, 2010.
  - Hall, K. C., and S. R. Hall. “A variational method for computing the optimal aerodynamic performance of conventional and compound helicopters.” In Annual Forum Proceedings Ahs International, 1:577–94, 2010.
  - Ekici, K., R. E. Kielb, and K. C. Hall. “Forced response analysis of aerodynamically asymmetric cascades.” In 46th Aiaa/Asme/Sae/Asee Joint Propulsion Conference and Exhibit, 2010. https://doi.org/10.2514/6.2010-6535.
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  - Hall, K. C., and S. R. Hall. “A variational method for computing the optimal aerodynamic performance of conventional and compound helicopters.” In Annual Forum Proceedings Ahs International, 3:2767–84, 2010.
  - Ekici, K., K. C. Hall, and R. E. Kielb. “Harmonic balance analysis of forced response in a transonic compressor.” In 47th Aiaa Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2009. https://doi.org/10.2514/6.2009-1240.
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  - Ekici, K., R. E. Kielb, and K. C. Hall. “The effect of aerodynamic asymmetries on turbomachinery flutter.” In 47th Aiaa Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2009. https://doi.org/10.2514/6.2009-893.
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  - Spiker, M. A., R. E. Kielb, J. P. Thomas, and K. C. Hall. “Application of enforced motion to study 2-D cascade lock-in effect.” In 47th Aiaa Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2009. https://doi.org/10.2514/6.2009-892.
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  - Thomas, J. P., C. H. Custer, E. H. Dowell, and K. C. Hall. “Unsteady flow computation using a harmonic balance approach implemented about the OVERFLOW 2 flow solver.” In 19th Aiaa Computational Fluid Dynamics Conference, 2009. https://doi.org/10.2514/6.2009-4270.
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  - Dowell, E. H., K. C. Hall, J. P. Thomas, R. E. Kielb, M. A. Spiker, A. Li, and C. M. Denegri. “Reduced order models in unsteady aerodynamic models, aeroelasticity and molecular dynamics.” In Icas Secretariat 26th Congress of International Council of the Aeronautical Sciences 2008, Icas 2008, 1:4002–14, 2008.
  - Ekici, K., R. E. Kielb, and K. C. Hall. “Aerodynamic asymmetry analysis of unsteady flows in turbomachinery.” In Proceedings of the Asme Turbo Expo, 5:821–34, 2008. https://doi.org/10.1115/GT2008-51176.
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  - Miyakozawa, T., R. E. Kielb, and K. C. Hall. “The effects of aerodynamic asymmetric perturbations on forced response of bladed disks.” In Proceedings of the Asme Turbo Expo, 5:779–90, 2008. https://doi.org/10.1115/GT2008-50719.
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  - Spiker, M. A., R. E. Kielb, K. C. Hall, and J. P. Thomas. “Efficient design method for non-synchronous vibrations using enforced motion.” In Proceedings of the Asme Turbo Expo, 5:735–47, 2008. https://doi.org/10.1115/GT2008-50599.
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  - Ekici, K., K. C. Hall, and E. H. Dowell. “Computationally fast harmonic balance methods for unsteady aerodynamic predictions of helicopter rotors.” In Journal of Computational Physics, 227:6206–25, 2008. https://doi.org/10.1016/j.jcp.2008.02.028.
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  - Thomas, J. P., E. H. Dowels, K. C. Hall, and C. M. Denegri. “Virtual aeroelastic flight testing for the F-16 fighter with stores.” In Collection of Technical Papers U.S. Air Force T and E Days, 2007(Test and Evaluation, 339–46, 2007.
  - Kielb, R. E., K. C. Hall, and T. Miyakozawa. “The effect of unsteady aerodynamic asymmetric perturbations on flutter.” In Proceedings of the Asme Turbo Expo, 5:649–54, 2007. https://doi.org/10.1115/GT2007-27503.
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  - Gopinath, A. K., E. Van Der Weide, J. J. Alonso, A. Jameson, K. Ekici, and K. C. Hall. “Three-dimensional unsteady multi-stage turbomachinery simulations using the harmonic balance technique.” In Collection of Technical Papers 45th Aiaa Aerospace Sciences Meeting, 16:10753–72, 2007. https://doi.org/10.2514/6.2007-892.
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  - Thomas, J. P., E. H. Dowell, K. C. Hall, and C. M. Denegri. “An investigation of the sensitivity of F-16 fighter flutter onset and limit cycle oscillations to uncertainties.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 5:3137–44, 2006.
  - Hall, K. C. “Message from the conference chair.” In Proceedings of the Asme Turbo Expo, Vol. 1, 2006.
  - Kielb, R. E., K. C. Hall, E. Hong, and S. S. Pai. “Probabilistic flutter analysis of a mistuned bladed disk.” In Proceedings of the Asme Turbo Expo, 5 PART B:1145–50, 2006.
  - Dowell, Earl H., Kenneth C. Hall, Jeffrey P. Thomas, Robert E. Kielb, Meredith A. Spiker, and Charles M. Denegri. “Reduced Order Models in Unsteady Aerodynamic Models, Aeroelasticity and Molecular Dynamics,” 247–67. Springer Netherlands, 2006. https://doi.org/10.1007/978-1-4020-4979-8_14.
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  - Ekici, K., and K. C. Hall. “Nonlinear analysis of unsteady flows in multistage turbomachines using the harmonic balance technique.” In Collection of Technical Papers 44th Aiaa Aerospace Sciences Meeting, 7:4920–33, 2006. https://doi.org/10.2514/6.2006-422.
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  - Ekici, K., and K. C. Hall. “Nonlinear frequency-domain analysis of unsteady flows in turbomachinery with multiple excitation frequencies.” In Collection of Technical Papers Aiaa Applied Aerodynamics Conference, 1:623–36, 2006. https://doi.org/10.2514/6.2006-2995.
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  - Spiker, M. A., J. P. Thomas, K. C. Hall, R. E. Kielb, and E. H. Dowell. “Modeling cylinder flow vortex shedding with enforced motion using a harmonic balance approach.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 7:4549–58, 2006. https://doi.org/10.2514/6.2006-1965.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Using automatic differentiation to create a nonlinear reduced order model of a computational fluid dynamic solver.” In Collection of Technical Papers 11th Aiaa/Issmo Multidisciplinary Analysis and Optimization Conference, 4:2437–49, 2006. https://doi.org/10.2514/6.2006-7115.
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  - Thomas, J. P., E. H. Dowell, K. C. Hall, and C. M. Denegri. “Further investigation of modeling limit cycle oscillation behavior of the F-16 fighter using a harmonic balance approach.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 3:1457–66, 2005.
  - Dowell, E. H., K. C. Hall, J. P. Thomas, R. E. Kielb, M. A. Spiker, and C. M. Denegri. “Reduced order unsteady aerodynamic models and aeroelasticity.” In 12th International Congress on Sound and Vibration 2005, Icsv 2005, 1:47–64, 2005.
  - Carlson, H. A., J. Q. Feng, J. P. Thomas, R. E. Kielb, K. C. Hall, and E. H. Dowell. “Computational models for nonlinear aeroelasticity.” In 43rd Aiaa Aerospace Sciences Meeting and Exhibit Meeting Papers, 4143–52, 2005. https://doi.org/10.2514/6.2005-1085.
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  - Ekici, K., D. M. Voytovycht, and K. C. Hall. “Time-linearized Navier-Stokes analysis of flutter in multistage turbomachines.” In 43rd Aiaa Aerospace Sciences Meeting and Exhibit Meeting Papers, 14259–77, 2005. https://doi.org/10.2514/6.2005-836.
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  - Hall, K. C., R. E. Kielb, K. Ekici, J. P. Thomas, and W. S. Clark. “Recent advancements in turbomachinery aeroelastic design analysis.” In 43rd Aiaa Aerospace Sciences Meeting and Exhibit Meeting Papers, 11253–74, 2005. https://doi.org/10.2514/6.2005-14.
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  - Thomas, J. P., E. H. Dowell, K. C. Hall, and C. M. Denegri. “Modeling limit cycle oscillation behavior of the F-16 fighter using a harmonic balance approach.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 3:2044–50, 2004.
  - Hall, K. C., J. P. Thomas, K. Ekici, and D. M. Voytovych. “Frequency domain techniques for complex and nonlinear flows in turbomachinery.” In 33rd Aiaa Fluid Dynamics Conference and Exhibit, 2003.
  - Kielb, R. E., J. P. Thomas, J. W. Barter, and K. C. Hall. “Blade excitation by aerodynamic instabilities - A compressor blade study.” In American Society of Mechanical Engineers, International Gas Turbine Institute, Turbo Expo (Publication) Igti, 4:399–406, 2003. https://doi.org/10.1115/GT2003-38634.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Modeling limit cycle oscillations for an NLR 7301 airfoil aeroelastic configuration including correlation with experiment.” In 44th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics, and Materials Conference, 2003.
  - Thomas, J. P., K. C. Hall, and E. H. Dowell. “A discrete adjoint approach for modeling unsteady aerodynamic design sensitivities.” In 41st Aerospace Sciences Meeting and Exhibit, 2003.
  - Thomas, J. P., K. C. Hall, and E. H. Dowell. “A harmonic balance approach for modeling nonlinear aeroelastic behavior of wings in transonic viscous flow.” In 44th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics, and Materials Conference, 2003.
  - Thomas, J. P., K. C. Hall, and E. H. Dowell. “A harmonic balance approach for modeling nonlinear aeroelastic behavior of wings in transonic viscous flow.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 7:4779–84, 2003.
  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Modeling limit cycle oscillations for an NLR 7301 airfoil aeroelastic configuration including correlation with experiment.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 1:289–97, 2003. https://doi.org/10.2514/6.2003-1429.
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  - Thomas, J. P., K. C. Hall, and E. H. Dowell. “A discrete adjoint approach for modeling unsteady aerodynamic design sensitivities.” In 41st Aerospace Sciences Meeting and Exhibit, 2003. https://doi.org/10.2514/6.2003-41.
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  - Thomas, J. P., K. C. Hall, and E. H. Dowell. “A harmonic balance approach for modeling nonlinear aeroelastic behavior of wings in transonic viscous flow.” In 44th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics, and Materials Conference, 2003. https://doi.org/10.2514/6.2003-1924.
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  - Hall, K. C., and S. R. Hall. “A rational engineering analysis of the efficiency of flapping flight.” In Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, edited by T. J. Mueller, 195:249–74. AMER INST AERONAUTICS & ASTRONAUTICS, 2002.
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  - Kholodar, D. B., J. P. Thomas, E. H. Dowell, and K. C. Hall. “A parameter study of transonic airfoil flutter and limit cycle oscillation behavior.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 1:64–79, 2002.
  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “A harmonic balance approach for modeling three-dimensional nonlinear unsteady aerodynamics and aeroelasticity.” In Asme International Mechanical Engineering Congress and Exposition, Proceedings, 1323–34, 2002. https://doi.org/10.1115/IMECE2002-32532.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Modeling viscous transonic limit cycle oscillation behavior using a harmonic balance approach.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 3:1658–66, 2002. https://doi.org/10.2514/6.2002-1414.
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  - Dowell, E. H., J. P. Thomas, and K. C. Hall. “Transonic limit cycle oscillation analysis using reduced order aerodynamic models.” In 19th Aiaa Applied Aerodynamics Conference, 2001.
  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Three-Dimensional transonic Aeroelasticity using proper orthogonal decomposition based reduced order models.” In 19th Aiaa Applied Aerodynamics Conference, 2001.
  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Nonlinear inviscid aerodynamic effects on transonic divergence, flutter and limit cycle oscillations.” In 19th Aiaa Applied Aerodynamics Conference, 2001.
  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “A static/dynamic correction approach for reduced-order modeling of unsteady aerodynamics.” In 39th Aerospace Sciences Meeting and Exhibit, 2001.
  - Dowell, E. H., J. P. Thomas, and K. C. Hall. “Transonic limit cycle oscillation analysis using reduced order aerodynamic models.” In 19th Aiaa Applied Aerodynamics Conference, 2001. https://doi.org/10.2514/6.2001-1212.
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  - Dowell, E. H., J. P. Thomas, and K. C. Hall. “Transonic limit cycle oscillation analysis using reduced order aerodynamic models.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 1:255–63, 2001.
  - Epureanu, B. I., E. H. Dowell, and K. C. Hall. “A parametric analysis of reduced order models of potential flows in turbomachinery using proper orthogonal decomposition.” In Proceedings of the Asme Turbo Expo, Vol. 1, 2001. https://doi.org/10.1115/2001-GT-0434.
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  - Florea, R., and K. C. Hall. “Sensitivity analysis of unsteady inviscid flow through turbomachinery cascades.” In Aiaa Journal, 39:1047–56, 2001. https://doi.org/10.2514/2.1445.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Three-Dimensional transonic Aeroelasticity using proper orthogonal decomposition based reduced order models.” In 19th Aiaa Applied Aerodynamics Conference, 2001. https://doi.org/10.2514/6.2001-1526.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Nonlinear inviscid aerodynamic effects on transonic divergence, flutter and limit cycle oscillations.” In 19th Aiaa Applied Aerodynamics Conference, 2001. https://doi.org/10.2514/6.2001-1209.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “A static/dynamic correction approach for reduced-order modeling of unsteady aerodynamics.” In 39th Aerospace Sciences Meeting and Exhibit, 2001. https://doi.org/10.2514/6.2001-855.
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  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Three-dimensional transonic aeroelasticity using proper orthogonal decomposition based reduced order models.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 4:2555–64, 2001.
  - Thomas, J. P., E. H. Dowell, and K. C. Hall. “Nonlinear inviscid aerodynamic effects on transonic divergence, flutter and limit cycle oscillations.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 1:230–41, 2001.
  - Florea, R., and K. C. Hall. “Sensitivity analysis of unsteady inviscid flow through turbomachinery cascades.” In 38th Aerospace Sciences Meeting and Exhibit, 2000. https://doi.org/10.2514/6.2000-130.
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  - Epureanu, B. I., E. H. Dowell, and K. C. Hall. “Reduced order models of viscous flows in turbomachinery using proper orthogonal decomposition.” In American Society of Mechanical Engineers, Fluids Engineering Division (Publication) Fed, 250:205–15, 1999.
  - Clark, W. S., and K. C. Hall. “A time-linearized Navier-Stokes analysis of stall flutter.” In Proceedings of the Asme Turbo Expo, Vol. 4, 1999. https://doi.org/10.1115/99-GT-383.
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  - Dowell, E. H., K. C. Hall, J. P. Thomas, R. Florea, B. I. Epureanu, and J. Heeg. “Reduced order models in unsteady aerodynamics.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 1:622–37, 1999.
  - Hall, K. C., J. P. Thomas, and E. H. Dowell. “Reduced-order modelling of unsteady small-disturbance flows using a frequency-domain proper orthogonal decomposition technique.” In 37th Aerospace Sciences Meeting and Exhibit, 1999.
  - Hall, K. C., J. P. Thomas, and E. H. Dowell. “Reduced-order modelling of unsteady small-disturbance flows using a frequency-domain proper orthogonal decomposition technique.” In 37th Aerospace Sciences Meeting and Exhibit, 1999. https://doi.org/10.2514/6.1999-655.
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  - Florea, R., K. C. Hall, and P. G. A. Cizmas. “Eigenmode analysis of unsteady viscous flows in turbomachinery cascades.” In Unsteady Aerodynamics and Aeroelasticity of Turbomachines, edited by T. H. Fransson, 767–82. SPRINGER, 1998.
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  - Dowell, E. H., K. C. Hall, and M. C. Romanowski. “Reduced order aerodynamic modeling of how to make CFD useful to an aeroelastician.” In American Society of Mechanical Engineers, Aerospace Division (Publication) Ad, 53–3:149–63, 1997.
  - Silkowski, P. D., and K. C. Hall. “Coupled mode analysis of unsteady multistage flows in turbomachinery.” In American Society of Mechanical Engineers (Paper), 1997.
  - Hall, K. C., S. A. Pigott, and S. R. Hall. “Power requirements for large-amplitude flapping flight.” In 35th Aerospace Sciences Meeting and Exhibit, 1–11, 1997.
  - Hall, K. C., S. A. Pigott, and S. R. Hall. “Power requirements for large-amplitude flapping flight.” In 35th Aerospace Sciences Meeting and Exhibit, 1–11, 1997.
  - Silkowski, P. D., and K. C. Hall. “A coupled mode analysis of unsteady multistage flows in turbomachinery.” In Proceedings of the Asme Turbo Expo, Vol. 4, 1997. https://doi.org/10.1115/97-GT-186.
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  - Florea, R., K. C. Hall, and P. G. A. Cizmas. “Reduced order modelling of unsteady viscous flow in a compressor cascade.” In 32nd Joint Propulsion Conference and Exhibit, 1996.
  - Florea, R., K. C. Hall, and P. G. A. Cizmas. “Reduced order modelling of unsteady viscous flow in a compressor cascade.” In 32nd Joint Propulsion Conference and Exhibit, 1996. https://doi.org/10.2514/6.1996-2572.
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  - Cizmas, P. G. A., and K. C. Hall. “A viscous-inviscid model of unsteady small-disturbance flows in cascades.” In 31st Joint Propulsion Conference and Exhibit, 1995.
  - Clark, W. S., and K. C. Hall. “A numerical model of the onset of stall flutter in cascades.” In Proceedings of the Asme Turbo Expo, Vol. 5, 1995. https://doi.org/10.1115/95-GT-377.
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  - Clark, W. S., and K. C. Hall. “Numerical model of the onset of stall flutter in cascades.” In American Society of Mechanical Engineers (Paper), 1995.
  - Hall, K. C., and P. D. Silkowski. “The influence of neighboring blade rows on the unsteady aerodynamic response of cascades.” In Proceedings of the Asme Turbo Expo, Vol. 1, 1995. https://doi.org/10.1115/95-GT-035.
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  - Hall, K. C., and P. D. Silkowski. “Influence of neighboring blade rows on the unsteady aerodynamic response of cascades.” In American Society of Mechanical Engineers (Paper), 1995.
  - Lorence, C. B., and K. C. Hall. “Sensitivity analysis of the aeroacoustic response of turbomachinery blade rows.” In 33rd Aerospace Sciences Meeting and Exhibit, 1995. https://doi.org/10.2514/6.1995-166.
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  - Florea, R., and K. C. Hall. “Reduced order modeling of unsteady flows about airfoils.” In American Society of Mechanical Engineers, Aerospace Division (Publication) Ad, 44:49–68, 1994.
  - Hall, K. C. “Eigenanalysis of unsteady flows about airfoils, cascades, and wings.” In Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics and Materials Conference, 2:967–76, 1994.
  - Hall, K. C., R. Florea, and P. J. Lanzkron. “Reduced order model of unsteady flows in turbomachinery.” In American Society of Mechanical Engineers (Paper), 1–11, 1994.
  - Hall, K. C., R. Florea, and P. J. Lanzkron. “A reduced order model of unsteady flows in turbomachinery.” In Proceedings of the Asme Turbo Expo, Vol. 5, 1994. https://doi.org/10.1115/94-GT-291.
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  - Hall, K. C., W. S. Clark, and C. B. Lorence. “Linearized Euler analysis of unsteady transonic flows in turbomachinery.” In American Society of Mechanical Engineers (Paper), 1993.
  - Hall, K. C., W. S. Clark, and C. B. Lorence. “A linearized euler analysis of unsteady transonic flows in turbomachinery.” In Asme 1993 International Gas Turbine and Aeroengine Congress and Exposition, Gt 1993, Vol. 1, 1993. https://doi.org/10.1115/93GT094.
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  - Hall, K. C., and C. B. Lorence. “Calculation of three-dimensional unsteady flows in turbomachinery using the linearized harmonic Euler equations.” In Asme 1992 International Gas Turbine and Aeroengine Congress and Exposition, Gt 1992, Vol. 5, 1992. https://doi.org/10.1115/92GT136.
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  - Crawley, E. F., and K. C. Hall. “OPTIMIZATION AND MECHANISMS OF MISTUNING IN CASCADES.” In American Society of Mechanical Engineers (Paper), 1984.
  - Crawley, E. F., and K. C. Hall. “OPTIMIZATION AND MECHANISMS OF MISTUNING IN CASCADES.” In American Society of Mechanical Engineers (Paper), 1984.
  - Hall, K. C., and W. M. Johnson. “Accurate centroid tracking.” In Proceedings of Spie the International Society for Optical Engineering, 363:106–13, 1983. https://doi.org/10.1117/12.934167.
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  - Hall, Kenneth C., Kivanc Ekici, and Dmytro M. Voytovych. “MULTISTAGE COUPLING FOR UNSTEADY FLOWSIN TURBOMACHINERY,” 217–29. Kluwer Academic Publishers, n.d. https://doi.org/10.1007/1-4020-4605-7_17.
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Teaching & Mentoring
Recent Courses
- ME 472: Aircraft Performance 2020
- ME 672: Unsteady Aerodynamics 2020
- ME 472: Aircraft Performance 2019
- ME 555: Advanced Topics in Mechanical Engineering 2019
- ME 672: Unsteady Aerodynamics 2019
- ME 472: Aircraft Performance 2018
- ME 555: Advanced Topics in Mechanical Engineering 2018
- ME 672: Unsteady Aerodynamics 2018
- ME 759: Special Readings in Mechanical Engineering 2018
Scholarly, Clinical, & Service Activities
Service to the Profession
- Editor. Journal of Turbomachinery. ASME. July 1, 2015 - June 30, 2020 2015 - 2020
- Member. Board of Directors. International Gas Turbine Institute (IGTI). 2003 - 2009 2003 - 2009

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