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Table of contents
1 A review on the cross flow induced vibrations and theoretical models of the fluidelastic instability in tube arrays
1.1 Introduction
1.2 Vibration Mechanisms
1.2.1 Vortex shedding / Strouhal periodicity
1.2.2 Turbulent buffeting
1.2.3 Acoustic resonance
1.2.4 Fluidelastic excitations
1.3 The fluidelastic instability models
1.3.1 Jet switch model
1.3.2 Quasi-static, quasi-steady models
1.3.3 Semi-analytical models
1.3.4 Unsteady models
1.4 The parameter space and definitions
1.4.1 Array orientation
1.4.2 Natural frequency
1.4.3 Mass of the tube
1.4.4 Damping
1.4.5 The critical flow velocity
1.5 Conclusion
2 Numerical simulation of the flow in tube arrays by using the Unsteady Reynolds Averaged Navier-Stokes turbulence modeling
2.1 Introduction
2.2 Surface pressure profiles in triangular arrays
2.2.1 Experimental and numerical configurations
2.2.2 Results and discussion
2.3 Dynamic simulation of the fluidelastic instability in a single cylinder of an in-line tube array
2.3.1 Experimental and numerical configurations
2.3.2 Results comparison and discussion
2.4 Conclusion
3 Analysis of the fluidelastic instability by using the Large Eddy Simulations
3.1 Introduction
3.2 Configuration
3.2.1 Experiments
3.2.2 Large Eddy Simulations (LES)
3.2.3 Fluid-structure coupling
3.3 Results comparison
3.4 Flow analysis
3.5 The onset of fluidelastic instability
3.5.1 Comparison between the static and dynamic case simulations
3.5.2 Dynamics of the fluid forces acting on the cylinder
3.6 Conclusion
4 A theoretical model of the fluidelastic instability in square inline tube arrays
4.1 Introduction
4.2 Theory
4.2.1 Mathematical Model
4.2.2 Estimation of the critical flow velocity
4.3 Model predictions of experimental results
4.4 Conclusion
5 Introduction to Reduced-Order Modeling
5.1 Introduction
5.2 Preliminary definitions
5.2.1 Dynamical systems
5.2.2 Transfer functions
5.2.3 Controllability and Observability Gramians
5.2.4 Stability and Passivity
5.2.5 Subspace projections
5.2.6 Hankel singular values
5.3 Model order reduction techniques
5.3.1 Truncated Balanced Realization
5.3.2 Krylov subspaces
5.3.3 Proper Orthogonal Decomposition
5.4 Conclusion
6 A Galerkin-free model reduction approach for the Navier-Stokes equations
6.1 Introduction
6.2 Mathematical formulation
6.2.1 Method of snapshots POD
6.2.2 Periodicity of POD temporal modes
6.2.3 Linear interpolation
6.2.4 A posteriori error estimate
6.2.5 Stability of the interpolation ROM
6.3 Flow past a cylinder at low Reynolds number – a case study
6.3.1 Governing flow equations and numerical methods
6.3.2 Results and discussion
6.4 Conclusion
7 Model reduction of fluid-structure interactions by using the Galerkin-free POD approach
7.1 Introduction
7.2 Mathematical formulation
7.2.1 The Snapshots POD
7.2.2 The POD time modes (Chronos)
7.2.3 Linear interpolation
7.2.4 Error estimate
7.3 Vortex induced vibration of a cylinder at Re = 100 for various mass ratios
7.3.1 The flow equations
7.3.2 Fluid-structure coupling
7.3.3 POD analysis
7.3.4 ROM solution states
7.4 Conclusion
8 Conclusions and outlook
8.1 Conclusions
8.2 Outlook
Appendix A Turbulence modeling
A.1 Unsteady Reynolds Averaged Navier-Stokes (URANS)
A.1.1 Linear eddy viscosity models
A.1.2 Non-linear eddy viscosity models
A.2 Large Eddy Simulations (LES)
A.2.1 Smagorinsky-Lilly Model
Appendix B Modal analysis 163
B.1 Half-Power Bandwidth Method (HBM)
B.2 Time Domain Modal Analysis (TMA)
B.2.1 The characteristic functions
B.2.2 The number of modes and parameters of the characteristics functions
B.2.3 Statistical estimation of the modal parameters
References
