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A Discontinuous Galerkin Method for Turbomachinery and Acoustics Applications

Wukie, Nathan A
http://orcid.org/0000-0002-0129-1992
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045

Abstract Details

2018, PhD, University of Cincinnati, Engineering and Applied Science: Aerospace Engineering.
Numerical methods for computational physics have been applied for many years in the fields of turbomachinery and acoustics. The computational approach to addressing problems in these fields has strongly influenced improvements in performance and advancements in understanding for the systems and physical processes that govern such applications. Particularly within the turbomachinery community, the spectrum of numerical methods being applied is dominated by second-order accurate finite-volume and finite-difference discretizations of the governing equations. These have been quite successful and their robustness has been important in their adoption within industrial engineering as tools for design and analysis. At the same time, such approaches are very dissipative and require dense computational grids to resolve sharp features and capture wave propagation. As problems become more complex and inter-related, the numerical methodologies for analysis tools that are used to address such problems and inform solutions must improve in their fidelity, accuracy, and mathematical rigor. At the same time, high-order finite-element methods have experienced significant attention in the computational fluid dynamics community for their mathematical formalism, localized approach for obtaining high-order accuracy, and amenability to adaptation of the numerical grid and accuracy of the numerical approximation. The challenges of such approaches are to achieve efficiency and stability for the numerical method. The result of many research efforts in this area has pushed the applicability of high-order finite-element methods into many fields and they are approaching the point where they might soon find routine application to industrial problems for engineering design and analysis. This dissertation details the development and application of an implicit discontinuous Galerkin method to applications in turbomachinery and acoustics. This is carried out for the purpose of advancing the applicability of the discontinuous Galerkin method to problems in these fields. A selection of the developments included in this work include a study on the efficiency of automatic differentiation for the discontinuous Galerkin method, adoption of a new approach for computing distance fields based on solving a p-Poisson equation, the development of a new adiabatic no-slip boundary condition for moving walls, and the development of implicit nonlocal nonreflecting boundary conditions along with a new stabilizing correction that significantly improves their efficiency and robustness. Mixing-plane interfaces for turbomachinery applications were also developed for the first time within a discontinuous Galerkin discretization. Finally, the numerical method that was created in the context of this work was applied to several turbomachinery problems. These problems include steady, Reynolds-Averaged Navier-Stokes (RANS) calculations for a two-dimensional stator, a three-dimensional stator, and a quasi three-dimensional 1.5 stage turbine using nonreflecting mixing-plane interfaces. These contributions and their application significantly advance the state-of-the-art for high-order finite-element methods applied to computational fluid dynamic problems in turbomachinery.
Paul Orkwis, Ph.D. (Committee Chair)
Shaaban Abdallah, Ph.D. (Committee Member)
John Benek, Ph.D. (Committee Member)
Mark Turner, Sc.D. (Committee Member)
Eric Wolf, Ph.D. (Committee Member)
282 p.
Aerospace Materials
High-order methods; Computational Fluid Dynamics; discontinuous Galerkin; Nonreflecting boundary conditions; Turbomachinery; Finite-elements

Recommended Citations

Citations

  • Wukie, N. A. (2018). A Discontinuous Galerkin Method for Turbomachinery and Acoustics Applications [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045

    APA Style (7th edition)

  • Wukie, Nathan. A Discontinuous Galerkin Method for Turbomachinery and Acoustics Applications. 2018. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045.

    MLA Style (8th edition)

  • Wukie, Nathan. "A Discontinuous Galerkin Method for Turbomachinery and Acoustics Applications." Doctoral dissertation, University of Cincinnati, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045

    Chicago Manual of Style (17th edition)

ucin1543840344167045
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© 2018, some rights reserved.Creative Commons License A Discontinuous Galerkin Method for Turbomachinery and Acoustics Applications by Nathan A Wukie is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.