| About the Authors |
|
v | |
| Foreword |
|
vii | |
|
Scientific Translation Editor |
|
| Preface |
|
ix | |
| Thoughts on Diagnostics Inspired by Reading the Monograph "Vibration Acoustics Applied to VVER-1200 Reactor Plant" |
|
xi | |
|
|
|
|
|
|
| In Lieu of a Preface --- Historical Journey and a Bibliographic Guide |
|
xvii | |
| Abbreviations |
|
xxxi | |
|
Chapter 1 Equations of Motion of Dynamic System |
|
|
1 | (26) |
|
1.1 Single Degree of Freedom Dynamic Systems |
|
|
1 | (1) |
|
1.2 Simplest Analytical Model of Oscillations of Main Equipment of VVER Heat-Exchanging Loop |
|
|
2 | (12) |
|
1.3 Points of Application of External Driving Vibration Forces |
|
|
14 | (2) |
|
1.4 Numerical Estimates of the Ratio of MCP and SG Natural Oscillation Frequencies |
|
|
16 | (6) |
|
1.5 On Modal Analysis in the Simplest Case of Oscillations of Connected Masses |
|
|
22 | (5) |
|
Chapter 2 Parameters of Basic Dynamic System |
|
|
27 | (64) |
|
2.1 DS Dynamic Stiffness and Transfer Function |
|
|
27 | (3) |
|
2.2 Global Properties of the Dynamic System |
|
|
30 | (20) |
|
2.2.1 Modulus and phase of the transfer function |
|
|
30 | (12) |
|
2.2.2 Deterministic and random applied force |
|
|
42 | (2) |
|
2.2.3 DS secular equation |
|
|
44 | (6) |
|
2.3 Solutions of DS Homogeneous Equation |
|
|
50 | (14) |
|
|
|
50 | (14) |
|
2.4 Evaluating Parameters of Motion Equation Based on Spectral Measurements |
|
|
64 | (5) |
|
2.5 Practical Aspects of Measuring Parameters of DS Transfer Function |
|
|
69 | (11) |
|
2.5.1 Assessment of small damping factor |
|
|
69 | (5) |
|
2.5.2 Assessment of arbitrary damping ratios |
|
|
74 | (6) |
|
2.6 Coolant Pressure Fluctuation as an External Vibration Force Perturbation |
|
|
80 | (11) |
|
Chapter 3 Vibration Diagnostic Features |
|
|
91 | (28) |
|
3.1 Dynamic System with One Degree of Freedom as a Diagnostic Model |
|
|
91 | (4) |
|
3.2 Vibration Diagnostic Spaces |
|
|
95 | (7) |
|
3.3 Integral Parameters of Resonance in a DS with One Degree of Freedom |
|
|
102 | (1) |
|
3.4 Relative Vibration Diagnostic Thresholds |
|
|
103 | (8) |
|
3.5 Considerations on Diagnostic Feature Engineering in Local Diagnostics Systems |
|
|
111 | (4) |
|
3.6 DS Resonance Parameters as a Function of Time |
|
|
115 | (4) |
|
Chapter 4 MCC Vibrations Modeling |
|
|
119 | (10) |
|
4.1 Mathematical Model of Interaction Between Mechanical Dynamic System and MCC Pressure Pulsations Field |
|
|
119 | (3) |
|
4.2 Finite Element Modeling |
|
|
122 | (4) |
|
4.3 Uncertainties of Mathematical Modeling |
|
|
126 | (3) |
|
4.3.1 External field of generating forces and interpretation of classical concept "natural frequency of oscillations of a structural element" |
|
|
126 | (3) |
|
Chapter 5 MCC Acoustics in Lumped Parameters |
|
|
129 | (36) |
|
5.1 Analytical and Empirical Approaches Applied to Description of MCC Acoustics |
|
|
129 | (3) |
|
5.2 Acoustic Mass, Acoustic Stiffness, Acoustic Damping as Analogs of Motion Equation Parameters, Analogs from Mechanics and Electrical Engineering |
|
|
132 | (12) |
|
5.3 MCC Elements in Lumped Electrical Analogies --- Pressurizer as a Helmholtz Resonator |
|
|
144 | (16) |
|
5.4 Fresnel Equations, Nearly Optical Analogy for Point Acoustic Inhomogeneities |
|
|
160 | (5) |
|
|
|
165 | (48) |
|
6.1 Features of Wave Equation |
|
|
165 | (8) |
|
6.2 Particular Solutions of the Harmonic Oscillator Equation |
|
|
173 | (2) |
|
6.3 Types of Complex Harmonic Solutions of Wave Equations |
|
|
175 | (2) |
|
6.4 Fundamental Properties of Complex Harmonic Wave Representation |
|
|
177 | (6) |
|
6.5 Connection of Helmholtz Equation and d'Alembert Equation with Lagrange Ordinary Differential Equation of Motion --- Standing Waves in the Solution of a Homogeneous Wave Equation |
|
|
183 | (2) |
|
6.6 Standing Wave in the Solution of Homogeneous Wave Equation with a Single Initial Equation, d'Alembert Method |
|
|
185 | (5) |
|
6.7 Energy Properties of a Standing Wave |
|
|
190 | (1) |
|
6.8 Non-homogeneous Wave Equation |
|
|
191 | (8) |
|
6.8.1 Zero initial conditions |
|
|
191 | (3) |
|
|
|
194 | (5) |
|
6.9 Standing Waves in the Solution of a Wave Equation with Boundary Conditions --- Fourier Method |
|
|
199 | (9) |
|
6.10 Features of Solutions to Wave Equation |
|
|
208 | (5) |
|
Chapter 7 Equations of Fluid and Gas Dynamics |
|
|
213 | (14) |
|
7.1 Standing Waves in Solution of Fluid and Gas Dynamics Equations |
|
|
213 | (3) |
|
|
|
216 | (7) |
|
7.3 Power Characteristics of Acoustic Waves |
|
|
223 | (4) |
|
Chapter 8 Long Lines as an Analogy to the Acoustic Medium |
|
|
227 | (44) |
|
8.1 Standing Wave in Solution of the Telegraph Equation System |
|
|
227 | (9) |
|
8.2 Long Lines with Losses |
|
|
236 | (8) |
|
8.3 Properties of Complex Resistance and Propagation Coefficient of the Long Line |
|
|
244 | (5) |
|
8.4 Absorption of Electrical Energy in Long Line and Acoustic Energy in the Pipeline Fluid |
|
|
249 | (7) |
|
8.5 Methods for Reducing the Standing Wave Amplitude |
|
|
256 | (3) |
|
|
|
256 | (1) |
|
8.5.2 Absorption at reflection |
|
|
256 | (1) |
|
|
|
257 | (2) |
|
8.6 Wave Equation with Linear Parameters |
|
|
259 | (2) |
|
8.7 Complex Resistance Equivalent to Long Line with Point Element |
|
|
261 | (3) |
|
8.8 Four Pole (Two-Port) Circuit as Electrical Analogy of the Acoustic Path Element |
|
|
264 | (7) |
|
Chapter 9 Long Lines with Lumped Complex Resistance |
|
|
271 | (36) |
|
9.1 Inhomogeneities Generating a "Pure" Standing Wave |
|
|
271 | (7) |
|
9.2 Inhomogeneities Causing Mixed Acoustic Field |
|
|
278 | (6) |
|
9.3 ASW Volumetric Acoustic Inhomogeneities and Q-Factors of Their Resonances |
|
|
284 | (5) |
|
|
|
289 | (14) |
|
9.5 A Set of Long Lines as Equivalent to VVER Circulation Loop in Electrical Analogies |
|
|
303 | (4) |
|
Chapter 10 Elastic Dissipative Medium. Attenuation of Acoustic Waves |
|
|
307 | (58) |
|
10.1 Wave Equation with Complex Characteristic Parameter |
|
|
307 | (5) |
|
10.2 Dispersion Relation --- Complex Function of Frequency |
|
|
312 | (2) |
|
10.3 Natural Oscillations of Elastic Dissipative Medium |
|
|
314 | (8) |
|
10.4 Forced Oscillations of Dissipative Media |
|
|
322 | (4) |
|
10.5 Examples of Constraint Forces |
|
|
326 | (2) |
|
10.6 Resonance Excitation in Case of Coincidence of MCP Set Rotational Frequency with ASW Frequency |
|
|
328 | (3) |
|
10.7 Wave Amplitude Attenuation Coefficient. Kirchhoff--Stokes Formula |
|
|
331 | (4) |
|
10.8 Derivation of Kirchhoff--Stokes Formula |
|
|
335 | (3) |
|
10.9 Damping and Viscosity |
|
|
338 | (2) |
|
10.10 Description of Viscous Medium via Diffusion Equation |
|
|
340 | (2) |
|
10.11 Viscosity as the Reason of Pressure Drop in Transversal Direction |
|
|
342 | (2) |
|
10.12 Coolant Pressure Perturbation in MCC |
|
|
344 | (5) |
|
10.13 Stokes' Waves --- Dispersion Properties of the Coolant in Steam Generator Heat Exchange Tubes |
|
|
349 | (1) |
|
10.14 Acoustic Impedance for Small-Diameter Pipelines |
|
|
350 | (2) |
|
10.15 Pressure Pulsation Sensor Signal Modulation Parameters |
|
|
352 | (6) |
|
10.16 Typical Errors in Application of Analytical Models of Elastic Media |
|
|
358 | (7) |
|
Chapter 11 ASW Globality-Locality |
|
|
365 | (40) |
|
11.1 ASWs in Loop and its Harmonics |
|
|
365 | (6) |
|
11.2 A Priori Qualitative Comparison of Vibration-Acoustic Properties of VVER-1200 and VVER-1000 |
|
|
371 | (5) |
|
11.3 Basic ASW Types of VVER-1000 and WER-1200 |
|
|
376 | (6) |
|
11.4 Experimental Loop Components of Coolant Pressure Pulsations in the VVER Main Coolant Loop |
|
|
382 | (9) |
|
11.5 Globality of Low ASW Types |
|
|
391 | (14) |
|
Chapter 12 ASW Phenomenology |
|
|
405 | (32) |
|
12.1 Identification of Resonance Spectral Features of Vibration Sensors and PPSs During Unit Heating Up and Archiving Full Power Operation |
|
|
405 | (5) |
|
12.2 Linear Approximations of Temperature Dependences of ASW Parameters in VVER-1200 |
|
|
410 | (6) |
|
12.3 Common Signal Sources of Pressure Pulsation Sensors and Accelerometers |
|
|
416 | (6) |
|
12.4 Forced Oscillations of Reactor Vessel and MCP at ASW Frequencies |
|
|
422 | (8) |
|
12.5 Change of the Global Field of the First Loop ASW with the Change of the Number of MCP in Operation |
|
|
430 | (7) |
|
Chapter 13 MCP Vibrations |
|
|
437 | (38) |
|
13.1 Classes of Vibration Diagnostic Features of MCP |
|
|
437 | (5) |
|
13.2 Vibration Amplitude and Power |
|
|
442 | (3) |
|
13.3 Pressure Pulsations of Coolant in MCC and MCP Vibrations in a Wide Frequency Range |
|
|
445 | (14) |
|
13.4 Motion Trajectory of AEM and MCP Shaft |
|
|
459 | (3) |
|
13.5 Vibrations of Operating MCP and Vibrations of Turned off MCP affected by Coolant Counterflow --- The Single Operating MCP as a Source of Coherent Traveling Pressure Waves |
|
|
462 | (2) |
|
13.6 Amplitude Modulation of Oscillations of the Switched-off MCP |
|
|
464 | (4) |
|
13.7 Detection of Cavitation Effects according to PPS Signals |
|
|
468 | (7) |
|
Chapter 14 Experimental Results on VVER-1200 Vibration Acoustics |
|
|
475 | (50) |
|
14.1 Vibration Acoustics Tasks during Commissioning Measurements |
|
|
475 | (3) |
|
14.2 Diagnostic Information, Obtained During Joint Measurements of Commissioning System Signals and Standard Diagnostic System Signals |
|
|
478 | (5) |
|
14.3 Example of Identifying the Primary Source of Joint Oscillations |
|
|
483 | (4) |
|
14.4 Vibration Characteristics during lifting the Reactor Plant Power from MCC to 100% ASW Resonance Frequency as a Diagnostic Feature of Coolant State |
|
|
487 | (8) |
|
14.5 Vibration Measurements During Power up stages of Novovoronezh NPP-2 Unit 1-2 |
|
|
495 | (5) |
|
14.5.1 Reactor vessel oscillations |
|
|
495 | (5) |
|
14.6 Control of CPS Control Rods in Power Ascension Mode of Reactor Plant according to VNDS Vibration Channels |
|
|
500 | (25) |
|
14.6.1 Vibration by neutron measurements of central ASW frequencies |
|
|
504 | (21) |
|
Chapter 15 Mutual Oscillations of Reactor Vessel and Reactor Core Barrel |
|
|
525 | (24) |
|
15.1 Structural Features of Reactor Vessel and RCB Attachment Points |
|
|
525 | (4) |
|
15.2 Oscillations of Reactor Vessel and RCB at Different Numbers of MCP Sets in Operation |
|
|
529 | (13) |
|
15.3 Neutron-Vibration Measurements at 100% Power, Novo Voronezh NPP Unit 6 |
|
|
542 | (7) |
| References |
|
549 | (30) |
| Index |
|
579 | |
Lisainfo e-raamatute kohta