Applied hydraulic transients for hydropower plants and pumping stations

This book treats the problem of transient hydraulic computation, for hydroelectric plants and pumping stations, with an emphasis on numerical methods. The topics covered include: the waterhammer in hydraulic systems under pressure; experimental results concerning the waterhammer; protection of pumping stations with reference to the waterhammer; hydraulic resonance in hydroelectric power plant and pumping stations; mass oscillation in hydraulic surge systems; hydraulic stability of systems endowed with surge tanks; experimental results in the study of mass oscillations; hydroelectric power plants and pumping stations designed in complex hydraulic schemes; and computation of unsteady motions in the intermediate domain between rapid and slow motions. This book is not a standard monograph based on previously published material, but is primarily grounded on the theoretical and applied results obtained by authors during more than 20 years of practice. It considers the problems of hydraulic computation as encountered in the design of a significant number of hydroelectric power plants and pumping stations in Romania.

Preface	p. ix
Introduction	p. xi
1. The Waterhammer Phenomenon in Hydraulic Systems Under Pressure	p. 1
1.1. The physics of waterhammer and its equations	p. 1
1.2. Waterhammer computation methods	p. 6
1.3. Waterhammer computation by the method of characteristics	p. 9
1.4. The waterhammer sensitivity of pressure ducts provided with valves	p. 20
1.5. Computation examples for hydroelectric power plants and pumping stations	p. 25
1.5.1. The waterhammer computation for hydroelectric power plants	p. 25
1.5.2. The waterhammer computation for pumping stations	p. 28
References	p. 35
2. Experimental Results Concerning the Waterhammer	p. 37
2.1. Laboratory studies	p. 37
2.1.1. Experimental installations and measuring devices	p. 37
2.1.2. Experimental results	p. 42
2.1.3. Alternative experimental installation operated by computer	p. 46
2.1.4. Programs for automatic action of the experimental installation in the laboratory	p. 50
2.2. Studies conducted at some pumping stations in operation	p. 51
2.2.1. The SPR-2 Balcescu pumping station	p. 52
2.2.2. The Petrimanu pumping station within the Lotru HPP	p. 54
2.2.3. The SP Tataru pumping station	p. 55
2.2.4. Industrial pumping installation	p. 58
References	p. 58
3. The Protection of Pumping Stations Against Waterhammer	p. 61
3.1. The classification of protection devices against waterhammer at pumping stations	p. 61
3.2. The model of compressible fluid and the model of incompressible fluid	p. 61
3.3. The protection of pumping stations with air chambers or surge tanks	p. 66
3.4. An efficient protection system of pumping stations against waterhammer	p. 70
3.4.1. The effect of non-symmetrical hydraulic resistance at the entry into the air chamber or surge tank on the extreme values of pressure in the system	p. 70
3.4.2. Special device for non-symmetrical hydraulic resistance developed at the Hydraulic Engineering Research Institute (Institutul de Cercetari Hidrotehnice--I.C.H.)	p. 71
3.4.3. Theoretical, experimental and applied results	p. 74
3.4.4. Computation of the optimum hydraulic resistance for air chambers	p. 75
3.5. Some applications to Romanian pumping stations	p. 82
3.5.1. Pumping stations provided with surge tanks	p. 82
3.5.2. Pumping stations provided with air chambers	p. 88
3.5.3. Pumping stations provided with air chambers and surge tanks	p. 95
3.5.4. Pumping stations provided with I.C.H. type air chamber	p. 99
References	p. 107
4. Hydraulic Resonance in Hydroelectric Power Plants and Pumping Stations	p. 109
4.1. The computation of resonance in hydroelectric power plants for the basic hydraulic scheme	p. 111
4.2. The resonance computation for hydroelectric power plants in complex schemes	p. 119
4.2.1. Hydraulic scheme with two surge tanks in the system	p. 121
4.2.2. Hydraulic scheme A	p. 127
4.2.3. Hydraulic scheme B	p. 130
4.2.4. Hydraulic scheme C	p. 131
4.2.5. Hydraulic scheme D	p. 133
4.3. Computation of hydraulic resonance at pumping stations for the basic hydraulic scheme	p. 135
4.4. Computation of hydraulic resonance for pumping stations provided with double protection system against waterhammer	p. 145
4.5. The sensitivity to resonance of hydroelectric power plants and pumping stations	p. 149
4.6. An arithmetic property in the analysis of the behaviour to resonance of a hydraulic system equipped with a surge tank with strangulation	p. 154
References	p. 157
5. Mass Oscillation in Hydraulic Surge Systems	p. 159
5.1. Computational models for mass oscillations	p. 163
5.1.1. Differential equation of oscillations	p. 163
5.1.2. Non-dimensional form of the oscillation equation	p. 164
5.1.3. Integral variational formulation	p. 165
5.1.4. Finite difference formulation	p. 166
5.2. Computation of mass oscillation by analytical methods	p. 167
5.2.1. Computation of hydroelectric power plants shutdown	p. 167
5.2.2. Computation of hydroelectric power plants start-up	p. 171
5.2.3. Surge tanks currently used in practice	p. 172
5.3. Computation of mass oscillation by numerical methods	p. 175
5.3.1. Systems with a single surge tank or air chamber	p. 175
5.3.2. Hydraulic systems with several surge tanks	p. 177
5.4. Computation examples for hydroelectric power plants and pumping stations	p. 181
5.4.1. The hydroelectric system on Bistrita river	p. 181
5.4.2. Pumping station with air chamber	p. 183
5.4.3. I.C.H. Laboratory set-up	p. 184
5.4.4. Hydroelectric power plant with two surge tanks	p. 185
References	p. 186
6. Hydraulic Stability of Systems Endowed with Surge Tanks	p. 189
6.1. Small and large oscillations of the water level in surge tanks. Generalities	p. 190
6.1.1. The case of small oscillations	p. 190
6.1.2. The case of large oscillations	p. 195
6.2. Methods for analysis of hydraulic stability of surge tanks	p. 198
6.2.1. The case of a single surge tank	p. 198
6.2.2. The case of two surge tanks in the system	p. 209
6.3. Numerical methods for analysis of hydraulic stability of hydroelectric power plants protected by surge tanks	p. 217
6.3.1. Systems with a single surge tank	p. 218
6.3.2. Systems with several surge tanks	p. 220
6.4. Applications to hydroelectric power plants	p. 223
6.4.1. The Somes--Mariselu hydraulic power plant	p. 223
6.4.2. Hydroelectric power plant with two surge tanks	p. 225
References	p. 229
7. Experimental Results in the Study of Mass Oscillations	p. 231
7.1. Laboratory studies	p. 231
7.1.1. Experimental results on the I.C.H. installation	p. 231
7.1.2. Experimental results obtained on a different installation	p. 237
7.2. Studies conducted on hydroelectric power plants in operation	p. 242
7.2.1. The Moroieni hydroelectric power plant	p. 242
7.2.2. The Bicaz hydroelectric power plant	p. 243
References	p. 245
8. Hydroelectric Power Plants and Pumping Stations Designed with Complex Hydraulic Schemes	p. 247
8.1. Hydraulic computation of transient regimes for hydroelectric power plants designed with complex schemes	p. 247
8.1.1. Numerical methods	p. 247
8.1.2. Analytical methods	p. 254
8.2. Hydroelectric power plants and pumping systems with combined water conveyance structures	p. 264
8.2.1. Equations of motion	p. 266
8.2.2. Numerical method	p. 268
8.2.3. On the use of numerical models for unsteady regimes in open channels	p. 271
8.3. Hydraulic computation of transient regimes for pumped-storage hydroelectric power plants	p. 277
8.3.1. Hydraulic computation methods	p. 280
8.3.2. Computation examples and comparisons	p. 282
8.4. Applications to several hydroelectric power plants and stations in Romania	p. 285
8.4.1. The Tismana hydroelectric power plant	p. 285
8.4.2. The Lotru hydroelectric power plant	p. 288
8.4.3. The SRP-2 pumping station of the Rasova-Vederoasa irrigation system	p. 294
8.4.4. The Riul Mare-Retezat hydroelectric power plant	p. 299
References	p. 300
9. Computation of Unsteady Motions in the Intermediate Domain between Rapidly and Slowly Varying Water Motions	p. 303
9.1. Experimental results	p. 304
9.2. Computation method	p. 305
References	p. 315
Appendix 1. Validity of the Model of Incompressible Fluid in the Study of Hydraulic Stability of Surge Tanks	p. 317
A1.1. Introduction	p. 317
A1.2. The mathematical model for the compressible fluid	p. 317
A1.3. The non-dimensional form of the mathematical model	p. 319
A1.4. Approximation by the model of the incompressible fluid	p. 319
References	p. 321
Appendix 2. The Method of Liapunov's Function in the Stability Theory	p. 323
A2.1. Definitions	p. 323
A2.2. The stability theorem by the first approximation	p. 324
A2.3. A general theorem	p. 325
References	p. 326
Author Index	p. 327

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