Fourier collocation methods for unsteady flows
Abstract/Contents
- Abstract
- Fully resolved CFD simulations of unsteady aerodynamics are still too expensive to be deployed during the engineering design process. Most aerodynamic-design studies, however, only require knowledge of the steady-state flow field, not the transient behavior that precedes it. Collocation methods in time, such as the time-spectral method and the harmonic-balance method, obviate the need to model transients by directly solving for the steady state --- offering significant cost savings. They do so by using Fourier and Fourier-like basis functions to represent the flow field at a handful of points in time. The harmonic-balance method assumes the underlying spectrum is tonal, i.e. dominated by a finite set of known frequencies. This dissertation presents the discovery of "inadmissible frequency sets, " which cause the harmonic-balance method to fail unconditionally. A mathematically grounded strategy for avoiding such inadmissible sets is also proffered. Selecting harmonic-balance time instances using this new approach is shown to eliminate the presence of corrupted solutions and allows the method to admit all possible frequency sets. This dissertation will also address the use of collocation methods in time to model flow fields where the oscillatory character of the steady state is unknown a priori. Specifically, a new algorithm that allows the harmonic-balance method to be used with unknown frequency content will be discussed. In addition, two new algorithms will be presented that allow the time-spectral method, which is used to model periodic flows, to be used in cases where the underlying periodicity is either unknown or naturally occurring due to stable limit-cycle oscillations.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Naik, Kedar R |
|---|---|
| Associated with | Stanford University, Department of Mechanical Engineering. |
| Primary advisor | Alonso, Juan José, 1968- |
| Primary advisor | Iaccarino, Gianluca |
| Thesis advisor | Alonso, Juan José, 1968- |
| Thesis advisor | Iaccarino, Gianluca |
| Thesis advisor | Jameson, Antony, 1934- |
| Advisor | Jameson, Antony, 1934- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Kedar R. Naik. |
|---|---|
| Note | Submitted to the Department of Mechanical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Kedar Rajiv Naik
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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