A theoretical analysis of the fast transients of turbomachineries, based on the study of unsteady and incompressible fluids mechanics equations applied to an impeller, is proposed. It leads to internal torque, internal power, and impeller head of an impeller during transient periods. The equations show that the behavior of a pump impeller is not only depending on the acceleration rate and flow rate, as it is usually admitted, but also on velocity profiles and their evolution during the transient. Some hypotheses on the flow in a radial flow pump are proposed. They are validated by comparison with the experimental results of a single stage, single volute radial flow pump during some fast acceleration periods. The model is also used to analyze the behavior of the pump during a fast startup.

The startup of rocket engine turbopumps is generally performed only in a few seconds. It implies that these pumps reach their nominal operating conditions after only a few rotations. During these first rotations of the blades, the flow evolution in the pump is governed by transient phenomena, based mainly on the flow rate and rotation speed evolution. These phenomena progressively become negligible when the steady behavior is reached. The pump transient behavior induces significant pressure fluctuations, which may result in partial flow vaporization, i.e., cavitation. An existing experimental test rig has been updated in the LML Laboratory (Lille, France) for the startups of a centrifugal pump. The study focuses on the cavitation induced during the pump startup. Instantaneous measurement of torque, flow rate, inlet and outlet unsteady pressures, and pump rotation velocity enable to characterize the pump behavior during rapid starting periods. Three different types of fast startup behaviors have been identified. According to the final operating point, the startup is characterized either by a single drop of the delivery static pressure, by several low-frequency drops, or by a water hammer phenomenon that can be observed in both the inlet and outlet of the pump. A physical analysis is proposed to explain these three different types of transient flow behavior.