the real part and in the imaginary part. The conventional cavitation test 

 at this operating condition shows a very slight reduction in output, a 

 finding consistent with the low frequency limit shown in Figure 40. We see 

 under dynamic conditions a much larger change in output pressure with 

 inlet pressure than occurs in steady flow; moreover, there is a pronounced 

 phase change for the imaginary part. We must conclude that this part of 

 the cavitation performance is complex (i.e., having real and imaginary 

 parts) and is a strong function of frequency. Similar deductions flow 

 from the terms z ?1 , the compliance, and z , which has been termed by 

 Brennen as the mass-flow gain factor. The overall impression from the 

 experiments summarized in Figure 41, is that there are significant dynamic 

 effects in the pump transfer matrix and, importantly, that these effects 

 cannot be estimated from quasi-steady tests or attached cavity cascade 

 theories (see Ng and Brennen for details). 



We have already drawn attention to the bubbly nature of this particu- 

 lar flow in Figure 42. With this in mind, Brennen (1978) has formulated 

 a dynamic model of the flow through inducer pump blade channels based upon 

 a bubbly two-phase flow concept. Although this is empirical in some 

 respects, it reproduces most of the effects of frequency and cavitation 

 number, seen in Figure 41, in a remarkable way. Inevitably, again, the void 

 fraction depends upon some initial (but unknown) microbubble population. 



Transfer function representation of pump dynamics is now becoming 

 more common. We have alluded to the work of Fanelli, and Black and Santos 

 who do, in fact, use representations essentially the same as Equation (39) 

 for the governing and control of hydraulic turbines, and in analyzing 

 self-excited oscillations in pump systems, respectively. These later 

 "auto"-oscillations (distinct from the Pogo problem) may lead to damaging 

 levels of pressure fluctuations. The onset of such oscillations in a 

 dynamically characterized hydraulic test loop has been shown recently to 

 depend on the measured pump transfer function (Braisted and Brennen 1978). 

 More importantly, Brennen (1978) has argued that the transfer function 

 itself cannot be represented simply by a collection of passive elements 

 such as compliance, resistance, and inertance, i.e., the conventional 

 lumped parameters often used in analysis of mechanical linear systems. 



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