Flow-Induced Vibration Handbook for Nuclear and Process Equipment

8 Chapter 8Fig. 8-1 Typical Tube Response Spectra for Increasing Mass Fluxes at Constan...Fig. 8-2 Typical Vibration Response: Comparison Between Flexible Tube Bundle...Fig. 8-3 Vibration Response: Comparison Between Flexible Tube Bundle and One...Fig. 8-4 Schematic of Air‐Water Test Section and Tube Bundle.Fig. 8-5 Photograph of Air‐Water Test Section and Part of Air‐Water Loop.Fig. 8-6 Photograph of Cantilever Tube Bundle with Normal‐Triangular Configu...Fig. 8-7 Fluidelastic Instability Results in Air‐Water Cross Flow.Fig. 8-8 Flow Regime Maps for Air‐Water Cross Flow Showing Flow Conditions a...Fig. 8-9 Effect of P/D on Fluidelastic Instability Constant in Air‐Water Cro...Fig. 8-10 Two‐Phase Flow Structure in a Rotated‐Triangular Tube Bundle: a) S...Fig. 8-11 Two‐Phase Flow Paths in a Normal‐Triangular Tube Bundle.Fig. 8-12 Hydrodynamic Coupling Coherence as a Function of Mass Flux Ratio....Fig. 8-13 Air‐Water and Steam‐Water Fluidelastic Instability Results Plotted...Fig. 8-14 Air‐Water and Steam‐Water Fluidelastic Instability Results Plotted...Fig. 8-15 Photograph of Freon Pressure Vessel Test Section Showing Instrumen...Fig. 8-16 Schematic of Freon Test Section.Fig. 8-17 Photograph of Rotated‐Triangular Tube Bundle Instrumented with Str...Fig. 8-18 Typical Vibration Response Spectra for Two‐Phase Freon Cross Flow....Fig. 8-19 Typical Vibration Response Curves for Two‐Phase Freon Cross Flow: ...Fig. 8-20 Vibration Response: Freon versus Air‐Water.Fig. 8-21 Vibration Response In Freon at 80% Void Fraction: Flexible versus ...Fig. 8-22 Fluidelastic Instability Results in Two‐Phase Cross Flow: Comparis...Fig. 8-23a Flow Regime Map for Freon and Air‐Water Two‐Phase Cross Flow Show...Fig. 8-23b Flow Regime Map for Steam‐Water, Freon and Air‐Water Two‐Phase Cr...Fig. 8-24 Freon Results Included in Two‐Phase Fluidelastic Instability Resul...Fig. 8-25a Schematic of the Air‐Water U‐Bend Test Section and Flow Loop.Fig. 8-25b Schematic of Air‐Water U‐Bend Test Section.Fig. 8-26 Lowest Vibration Modes for an Unsupported U‐Tube.Fig. 8-27 Out‐of‐Plane U‐Tube Frequency‐Response Spectrum for 90% Void Fract...Fig. 8-28 Out‐of‐Plane Vibration Response Spectra as a Function of Mass Flux...Fig. 8-29 Out‐of‐Plane Vibration Amplitudes Measured by Strain Gages, in Liq...Fig. 8-30 In‐Plane Tangential Vibration Amplitude Measured by Strain Gages, ...Fig. 8-31 Flexible Tube Assemblies a) Single Tube, b) Central Cluster, c) Si...Fig. 8-32 Configurations of Flexible Tubes Tested Within the Test Section.Fig. 8-33 Response versus Flow‐Pitch Velocity for a Single Flexible Tube for...Fig. 8-34 Response Spectra of Single Flexible Tube in Flow at 80% Void Fract...Fig. 8-35 Response in Lift Direction versus Flow Pitch Velocity for the Sing...Fig. 8-36 Response in Lift Direction versus Flow Pitch Velocity for the Sing...Fig. 8-37 Response of Tube 7 versus Flow Pitch Velocity for the Partially Fl...Fig. 8-38 Instability Map: • Axisymetrically Flexible Tube Bundle in Air‐Wat...Fig. 8-39 Selected Frequency Spectra for Fluidelastic Instability of Clamped...

9 Chapter 9Fig. 9-1 Directional Dependence (Lift versus Drag).Fig. 9-2 Effect of Tube Bundle Orientation.Fig. 9-3 Effect of Pitch‐to‐Diameter Ratio (a) Normal‐Triangular Tube Bundle...Fig. 9-4 Effect of Upstream Turbulence.Fig. 9-5 Effect of Fluid Density (Gas versus Liquid).Fig. 9-6 Proposed Guideline for Excitation Forces.Fig. 9-7 Comparison with Previous Guidelines.

10 Chapter 10Fig. 10-1 First Normalized Guideline for Power Spectral Density of Random Tu...Fig. 10-2 Early Normalized Guideline for Power Spectral Density of Random Tu...Fig. 10-3 Normalized Guideline for Power Spectral Density of Random Turbulen...Fig. 10-4 Early Dimensionless Guideline for Power Spectral Density of Random...Fig. 10-5 CENS Air-Water Power Spectral Densities for a Normal-Square Tube B...Fig. 10-6 CENS Air-Water Power Spectral Densities at 50% Void Fraction for a...Fig. 10-7 CENS Air-Water Power Spectral Densities at a Mass Flux of 750 kg/(...Fig. 10-8 Measured Peak Frequencies from Air-Water Excitation Force Drag Pow...Fig. 10-9 Variation in Characteristic Void Length with Void Fraction and Mas...Fig. 10-10 CENS Characteristic Void Length Data (Square Symbols at 1500 kg/mFig. 10-11 CENS Air-Water Power Spectral Densities at a Mass Flux of 750 kg/...Fig. 10-12 CENS Air-Water Power Spectral Densities at fdB/U P= 0.1 for a Nor...Fig. 10-13 Air-Water Flow Regime Maps Using Kanizawa and Ribatski (2016) Bou...Fig. 10-14 Steam-Water and Freon Flow Regime Maps Using Kanizawa and Ribatsk...Fig. 10-15 CRL Air-Water Power Spectral Densities at fdB/ U p= 0.1 for a 60°...Fig. 10-16 Effect of Mass Flux on Reference Equivalent Power Spectral Densit...Fig. 10-17 Comparison of Normalized Random Excitation Power Spectral Densiti...Fig. 10-18 Comparison of Air-Water and Freon-22 Drag Power Spectral Densitie...Fig. 10-19 Comparison of Air-Water, Freon-134a and Freon-22 Drag Power Spect...Fig. 10-20 Comparison of Air-Water and Freon-22 Drag Power Spectral Densitie...Fig. 10-21 CENS Air-Water Dimensionless Power Spectral Densities at a Mass F...Fig. 10-22 Original Dimensionless Guideline with Data Points from de Langre ...Fig. 10-23 CENS Data Plotted Using de Langre and Villard (1998) Scaling Fact...Fig. 10-24 CRL and Other Data Plotted Using de Langre and Villard (1998) Sca...Fig. 10-25 Bubbly Flow Power Spectral Densities Collapsed Using Eq. (10-8) a...Fig. 10-26 Churn and Annular Flow Power Spectral Densities Collapsed Using E...Fig. 10-27 Intermittent Flow Power Spectral Densities Collapsed Using Eq. (1...Fig. 10-28 Axial Spatial Correlation of Random Pressure Fluctuations in Two-...Fig. 10-29 Measured and Predicted Vibration Amplitude versus Simulated Steam...Fig. 10-30 Effect of Flow Regime on Void Fraction Dependence of S F( f ) in Ste...Fig. 10-31 Velocity Dependence of S F( f ) in Steam-Water Axial Flow (Pettigr...Fig. 10-32 Temperature Dependence of S F (f) in Steam-Water Axial Flow (Pettig...Fig. 10-33 Normalized Power Spectral Density Results from Several Researcher...

11 Chapter 11Fig. 11-1 Typical Vibration Response (Gorman, 1976).Fig. 11-2 Laminar Vortex Formation in the Wake of a Vibrating Cylinder at a ...Fig. 11-3 Envelope of Strouhal Number versus Reynolds Number for Circular Cy...Fig. 11-4 Lift Coefficients for a Single Cylinder (Gerlach and Dodge, 1970)....Fig. 11-5 Vortex Shedding Behind the Second Row in a Rotated‐Square Array wi...Fig. 11-6 Strouhal Numbers for Tube Bundles in Liquid Flow (Pettigrew and Go...Fig. 11-7 Strouhal Number Expressions for Various Tube Bundle Geometries (We...Fig. 11-8 Strouhal Numbers for Finned Tubes (Kouba, 1986): Dots are Experime...Fig. 11-9a Vibration Response to Single‐Phase Forced Excitation (a) Normal‐S...Fig. 11-9b Vibration Response to Single‐Phase Forced Excitation (b) Rotated‐...Fig. 11-9c Vibration Response to Single‐Phase Forced Excitation (c) Normal‐T...Fig. 11-10 Fluctuating Force Lift Coefficients for Tube Bundles in Single‐Ph...Fig. 11-11 Force Spectra at 80% Void Fraction: (a) and (b) Pitch Flow Veloci...Fig. 11-12 Periodic Force Frequency and Periodic Force versus Pitch Velocity...Fig. 11-13 Force Power Spectral Density (PSD) at 80% Void Fraction and 6.8 m...Fig. 11-14 Periodic Force Frequency and Periodic Force at 80% Void Fraction ...Fig. 11-15a Vibration Response to Air‐Water Forced Excitation (Solid Circle:...Fig. 11-15b Vibration Response to Air‐Water Forced Excitation (Solid Circle:...Fig. 11-15c Vibration Response to Air‐Water Forced Excitation (Solid Circle:...Fig. 11-16 Fluctuating Force Lift Coefficients for Tube Bundles in Two‐Phase...Fig. 11-17 Flow Regime Maps for the Two‐Phase Fluctuating Force Data Sources...Fig. 11-18a Schematic Diagram of the Acoustic Cavity in a Typical Moisture S...Fig. 11-18b Tube Bundle Geometry within the Moisture Separator Reheater.Fig. 11-19 Dimensionless Equivalent Speed of Sound Ce/C versus Dd/W of the A...Fig. 11-20 Acoustic Resonance in First and Second Mode Excited by Vortex She...Fig. 11-21 Acoustic Resonance in Second and Third Modes Excited by Vortex Sh...Fig. 11-22 Acoustic Resonance Criterion for a) In-Line (Square) Bundles and ...Fig. 11-23a Damping Criteria for In‐Line Arrays, G i(Ziada et al, 1989b).Fig. 11-23b Damping Criteria for Staggered Arrays, G S(Ziada et al, 1989b)....Fig. 11-24 Maximum Sound Pressure Levels as a Function of Tube Pattern and S...