Book contents
- Frontmatter
- Brief Contents
- Contents
- Preface
- 1 The Finite Element Method: Introductory Remarks
- 2 Some Methods for Solving Continuum Problems
- 3 Variational Approach
- 4 Requirements for the Interpolation Functions
- 5 Heat Transfer Applications
- 6 One-Dimensional Steady-State Problems
- 7 The Two-Dimensional Heat-Conduction Problem
- 8 Three-Dimensional Heat-Conduction Applications with Convection and Internal Heat Absorption
- 9 One-Dimensional Transient Problems
- 10 Fluid Mechanics Finite Element Applications
- 11 Use of Nodeless Degrees of Freedom
- 12 Finite Element Analysis in Curvilinear Coordinate
- 13 Finite Element Modeling of Flow in Annular Axisymmetric Passages
- 14 Extracting the Finite Element Domain from a Larger Flow System
- 15 Finite Element Application to Unsteady Flow Problems
- 16 Finite Element-Based Perturbation Approach to Unsteady Flow Problems
- Appendix A Natural Coordinates for Three-Dimensional Surface Elements
- Appendix B Classification and Finite Element Formulation of Viscous Flow Problems
- Appendix C Numerical Integration
- Appendix D Finite Element-Based Perturbation Analysis: Formulation of the Zeroth-Order Flow Field
- Appendix E Displaced-Rotor Operation: Perturbation Analysis
- Appendix F Rigorous Adaptation to Compressible-Flow Problems
- Index
16 - Finite Element-Based Perturbation Approach to Unsteady Flow Problems
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Brief Contents
- Contents
- Preface
- 1 The Finite Element Method: Introductory Remarks
- 2 Some Methods for Solving Continuum Problems
- 3 Variational Approach
- 4 Requirements for the Interpolation Functions
- 5 Heat Transfer Applications
- 6 One-Dimensional Steady-State Problems
- 7 The Two-Dimensional Heat-Conduction Problem
- 8 Three-Dimensional Heat-Conduction Applications with Convection and Internal Heat Absorption
- 9 One-Dimensional Transient Problems
- 10 Fluid Mechanics Finite Element Applications
- 11 Use of Nodeless Degrees of Freedom
- 12 Finite Element Analysis in Curvilinear Coordinate
- 13 Finite Element Modeling of Flow in Annular Axisymmetric Passages
- 14 Extracting the Finite Element Domain from a Larger Flow System
- 15 Finite Element Application to Unsteady Flow Problems
- 16 Finite Element-Based Perturbation Approach to Unsteady Flow Problems
- Appendix A Natural Coordinates for Three-Dimensional Surface Elements
- Appendix B Classification and Finite Element Formulation of Viscous Flow Problems
- Appendix C Numerical Integration
- Appendix D Finite Element-Based Perturbation Analysis: Formulation of the Zeroth-Order Flow Field
- Appendix E Displaced-Rotor Operation: Perturbation Analysis
- Appendix F Rigorous Adaptation to Compressible-Flow Problems
- Index
Summary
Overview
Since its inception, the finite element method has followed the tracks of other well established computational techniques, particularly the finite-difference method. The fluid mechanics applications remained limited to mostly steady-state flow applications in two-or three-dimensional domains, with one or more complicating real-flow effects (e.g., compressibility, turbulence, etc.) being part of the computational model. Differing in complexity and accuracy, the finite-elements themselves have been taken as fixed-geometry subdomains, and this is the critical point where the following analysis categorically differs.
In many real-life applications, the flow domain itself undergoes small timedependent changes (or distortions) that, in most cases, are periodic. The problem of wing flutter is an example of such a situation in the external aerodynamics discipline. The problem under focus here involves the vibration of a fluid-encompassed rotor in a confined-flow type of arrangement (Figure 16.1) and is known to have a major impact on the system's rotordynamic integrity.
Originally handled via finite-difference techniques, the solution strategy was to repeatedly solve the entire physical problemby marching in time while slightly altering the flow-domain geometry at each time level. Tedious as it was, this approach is hardly economical, nor is it based on prior knowledge of what controls the time increment and, often, what fluid/structure features are to be monitored. Prohibiting solid advances in addressing the problem, many believe, is that it was historically handled in either a fluid-dynamics or a mechanical-vibrations type of approach but not a combination of the two mentalities.
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- Publisher: Cambridge University PressPrint publication year: 2013