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Table of contents
Abstract
Résumé
Acknowledgements
1 Introduction
1.1 Background
1.2 Objectives
1.3 State of the Art
1.3.1 Existing methods
1.3.2 Previous works
1.4 Scheme and Approaches
2 Experimental Approaches on PISE-1A and Corresponding Numerical Interpretation
2.1 Introduction to PISE-1A
2.2 Free-vibration experiments on PISE-1A
2.2.1 Free-vibration experiments in air
2.2.2 Free-vibration experiments in water
2.2.3 Free-vibration experiments in water-glycerol mixtures
2.3 Numerical simulations based on PISE-1A experiments
2.3.1 Introduction to the numerical methodologies
2.3.1.1 Governing equations
2.3.1.2 Boundary conditions
2.3.1.3 Algorithms
2.3.1.4 Mesh
2.3.1.5 Stability
2.3.1.6 Comments
2.3.2 Introduction to data analysis methodologies for frequency and damping coefficient
2.3.2.1 Regression method
2.3.2.2 ERA method
2.3.2.3 FFT method
2.3.3 Methodologies of signal processing
2.3.3.1 Butterworth filter
2.3.3.2 Hanning filtering
2.4 Methodologies of analysis on velocity and energy of PISE-1A
2.4.1 Velocity
2.4.2 Energy
2.5 Free-vibration experiments in air
2.5.1 Frequency and damping coefficient
2.5.2 Velocity and energy
2.5.3 Homogeneous problem
2.6 Experiments with different water heights
2.6.1 Flow behaviour
2.6.2 Frequency and damping coefficient
2.6.3 Velocity and energy
2.7 Experiments with water-glycerol mixture
2.7.1 Frequency and damping coefficient
2.7.2 Velocity and energy
2.8 Conclusions
3 Experimental and Analytical Approaches on PISE-2C
3.1 Introduction to PISE-2C
3.2 Reticulate model
3.2.1 Position of problem
3.2.1.1 General hypothesis
3.2.1.2 Dimensions
3.2.1.3 Fluid
3.2.1.4 Solid
3.2.2 Coupling
3.2.2.1 Kinematic coupling
3.2.2.2 Dynamic coupling
3.2.2.3 Phenomenological analysis
3.2.2.4 Mesh
3.2.2.5 Countings
3.2.3 Resolution
3.2.3.1 Notations
3.2.3.2 Trivial simplifications
3.2.3.3 Kinematic constraints
3.2.3.4 Symmetries
3.2.3.5 Counting
3.2.3.6 States
3.2.3.7 Equations
3.2.3.8 Integrations
3.2.3.9 Characteristics of flow
3.2.4 Energetic balance
3.2.4.1 Initial formulation
3.2.4.2 Geometrical elements
3.2.4.3 Evaluation of balance
3.2.4.4 Equations
3.2.4.5 Energy of assemblies
3.2.4.6 Kinetic energy of fluid
3.2.4.7 Dissipation of the structure
3.2.4.8 Dissipation of fluid
3.2.4.9 Flux at outlets
3.2.4.10 Phenomenological analysis
3.2.5 Conclusions
3.3 Free-vibration experiments on PISE-2C
3.4 Methodologies of analysis on global behaviour of PISE-2C
3.4.1 Displacement
3.4.2 Velocity of assembly
3.4.3 Indicators of symmetry
3.4.4 Energy of assembly
3.4.5 Volume of liquid contained in the mockup
3.4.6 Average outflow velocity
3.4.7 Surface confined by assemblies’ center of external crown
3.5 Total flowering
3.5.1 Displacements
3.5.2 Velocity
3.5.3 Energies of assembly
3.5.4 Volume contained in whole mockup
3.5.5 Average outflow velocity
3.5.6 Surface confined by centres on external crown
3.5.7 Indicators of symmetry
3.6 Partial flowering : Internal crown
3.6.1 Displacements
3.6.2 Velocity
3.6.3 Energies of assembly
3.6.4 Volume contained in whole mockup
3.6.5 Average outflow velocity
3.6.6 Surface confined by centres on external crown
3.6.7 Indicators of symmetry
3.7 Partial flowering : External crown
3.7.1 Displacements
3.7.2 Velocity
3.7.3 Energies of assembly
3.7.4 Volume contained in whole mockup
3.7.5 Average outflow velocity
3.7.6 Surface confined by centres on external crown
3.7.7 Indicators of symmetry
3.8 Conclusions
4 Conclusions
A Analytical Analysis Based on Added Mass and Damping
A.1 Position of the problem
A.1.1 Geometry
A.1.2 Solid
A.1.3 Fluid
A.1.4 Equations and boundary conditions
A.2 General properties
A.2.1 Dynamic approaches
A.2.1.1 Imposed movement
A.2.1.2 Free movement
A.2.1.3 Fluid force
A.2.2 Energy approach
A.2.2.1 Imposed movement
A.2.2.2 Free movement
A.3 Linearisation
A.3.1 Fluid flow
A.3.1.1 Scaling
A.3.1.2 Equations
A.3.1.3 Boundary conditions
A.3.2 Interaction force
A.3.3 Kinetic energy
A.3.4 Viscous dissipation
A.4 Resolution
A.4.1 Perfect fluid
A.4.2 Real fluid
A.4.2.1 Imposed movement
A.4.2.2 Free movement
A.5 Conclusion
B Oscillations of two cylinders coupled by fluid
B.1 Introduction
B.2 Position of problem
B.2.1 Geometry
B.2.2 Fluid
B.2.3 Solid
B.2.4 Boundary conditions
B.2.4.1 Non-penetration condition
B.2.4.2 No-slip condition
B.3 Scaling
B.3.1 Geometry
B.3.2 Fluid
B.3.2.1 Equations
B.3.2.2 Stress tensor
B.3.2.3 Pressure force
B.3.3 Solid
B.3.4 Boundary conditions
B.3.4.1 Non-penetration condition
B.3.4.2 No-slip condition
B.4 Phenomenological analysis
B.4.1 Hypothesis
B.4.2 Dynamics of the assemblies
B.4.3 Boundary conditions
B.5 Resolution
B.5.1 Integration
B.6 External fixed cylinder
B.7 Spectra
B.8 Conclusion
C System of DOF at 2
C.1 Position of the problem
C.2 Initial equilibrium
C.3 Transient equations
C.3.1 Time domain
C.3.2 Frequency domain
C.4 Energies
C.4.1 Kinetic energy
C.4.2 Potential energy
C.4.3 Total energy
C.4.4 Energy balance
C.5 Resolution
C.6 Conclusion
D 3D Effects: Recirculation Flow
D.1 Geometry and kinematics
D.1.1 Geometry
D.1.1.1 Boundary condition
D.2 Fluid and flow
D.2.1 Equations
D.2.2 Boundary conditions
D.2.3 Scaling
D.2.3.1 Independent variables
D.2.4 Velocity and pressure
D.2.5 Non-dimensionalised formulation
D.2.5.1 Mass conservation
D.2.5.2 Momentum conservation
D.2.5.3 Boundary conditions
D.2.5.4 Geometrical developments
D.3 Perfect fluid
D.3.1 Statement of problem
D.3.1.1 Equations
D.3.1.2 Slipping condition
D.3.1.3 Scaling of pressure
D.3.2 External scaling, first approximation
D.3.2.1 Small amplitude, 1
D.3.3 Internal scaling
D.3.3.1 First approximation
D.4 Conclusions
E Analytical and Numerical Analysis on Two-dimensional Fluid Channel Model with Oscillating Wall and Continuous Injection
E.1 Phenomenological analysis
E.1.1 Two-dimensional geometry and basic conditions
E.1.2 Dimensioned equations
E.1.3 Decomposition
E.1.4 Scaling
E.1.5 Non-dimensioned equations
E.1.6 Thin-layer approximation
E.1.7 Reference solution
E.1.7.1 Mass conservation
E.1.7.2 Momentum conservation
E.1.7.3 Boundary conditions
E.1.8 Perturbation
E.1.8.1 Mass conservation
E.1.8.2 Momentum conservation
E.1.8.3 Boundary conditions
E.1.8.4 First approximation
E.1.9 Kinetic energy theorem
E.1.9.1 Stationary solution
E.1.9.2 Perturbation
E.1.10 Conclusions
E.2 Numerical analysis
E.2.1 Conditions of the Simulations
E.2.1.1 Simulation conditions
E.2.1.2 Governing equations solved by Cast3M
E.2.1.3 Non-dimensional parameters and scalings
E.2.2 Data analysis
E.2.2.1 Velocity and pressure profiles
E.2.2.2 Time evolutions
E.2.2.3 Average pressure on the oscillating plate
E.2.2.4 Average inlet pressure
E.2.2.5 Dissipation and pressure work
E.2.3 Conclusions
E.3 Conclusions
Bibliography
