Conclusion

System analysis of rotodynamic machines

Figure 1 - Black box&#34; diagram of a machine coupled to a system

Figure 2 - General appearance of a &#34;system&#34; characteristic in the first quadrant of pump or fan operation and operating point at the intersection with the machine characteristic

Figure 3 - Possible pump characteristic curves

Figure 4 - Example of the potential existence of several points of intersection between a machine characteristic and a system characteristic

Figure 5 - Diagram of a fan or compressor circuit

Figure 6 - Demonstration of operating instabilities during transition from initial to final flow rate

Figure 7 - Fluid circulation diagrams in pump or turbine mode

Figure 8 - Diagram of the system characteristic curve for turbine direction flow

Figure 9 - Characteristic curves of a hydraulic turbine

Figure 10 - Determining the turbine operating point by intersection of the &#34;machine&#34; and &#34;system&#34; curves

Figure 11 - Characteristic curve of a reversible Francis turbine-pump operating in the turbine direction for a given guideway opening.

Figure 12 - Four-quadrant pump-turbine behavior

Figure 13 - Dimensioned flow versus dimensioned time

Figure 14 - Evolution of the resistive and inertial parts of the scaled drop in height as a function of scaled time

Figure 15 - Complete characteristic curves for a constant speed centrifugal pump

Figure 16 - Two-slope closure law for a hydraulic turbine (doc. Jean-Louis Kueny, Grenoble)

Figure 17 - Diagram of the experimental installation

Figure 18 - Time trends in pump speed and dimensionless flow during the start-up transient

Figure 19 - Time evolution of pump delivery head and pump head term derived from system resistance

Figure 20 - Temporal evolution of available height at wheel entry

Figure 21 - Experimental comparison of pressure changes at the inlet (suction) and outlet (discharge) of a pump [18].

Figure 22 - Pressure evolution during cavitation start-up [18]

Figure 23 - Schematic diagram of a test bench for measuring the source terms and transfer matrix of a rotodynamic machine.