Observations on Instabilities of Cavitating Inducers

Hydraulic systems involving cavitating turbomachines are known to be susceptible to instabilities at certain critical operating conditions. Two distinct classes of cavitating inducer instabilities have been reported in the literature (Refs. 1-6). The purpose of this note is to report on some preliminary observations of these phenomena. The experiments were performed in the Dynamic Pump Test Facility (DPTF) at the California Institute of Technology (Refs. 7, 8). Results will be presented for two different inducers operating at different flow coefficients, [symbol] ([symbol]= mean axial velocity/inducer tip velocity- [equation]) and cavitation numbers, [symbol] ([symbol]=[equation]; where [equation] are the inlet and vapor pressures, and [symbol] is the liquid density). In general, the instabilities occurred just before the head breakdown. After head breakdown, the system tended to become stable again, although there were some indications of a second region of instability at very small cavitation numbers. Impeller IV is a quarter scale model of the Low Pressure Oxidizer Turbo-Pump (LPOTP) of the space shuttle main engine (Refs. 7, 8). The cavitation performance of this impeller is presented in Figure 1. Some of the mean operating states for which large, constant amplitude oscillations occurred in all the pressures and mass flow rates are indicated by stars. The cavitation in each of the blade passages oscillated in unison. This unstable behavior is termed auto-oscillation. The frequency of the auto-oscillations ranged from 28 to 35 Hz. As might be expected, there does exist a marginal region of operation for which the auto-oscillations have a time varying amplitude. These non-steady oscillations occurred as sporadic bursts of auto-oscillation. It was this feature that makes the boundaries of the auto-oscillation region difficult to define. In addition to the auto-oscillation observations on Impeller IV, two instances of "rotating cavitation" were observed and are labeled by boxes in Figure 1. The presence of rotating cavitation was determined by means of a stroboscope slaved to the rotational speed of the inducer. Rotating cavitation appeared as a non-stationary cavitation patterns which rotated with respect to the "fixed" inducer. (More recent testing has also revealed the existence of a stationary form of rotating cavitation sometime referred to as alternate blade cavitation.) The large amplitude disturbances in the upstream pressure and mass flow rates which characterized auto-oscillation were not observed during rotating cavitation. This suggests the rotating cavitation is most intimately associated with the dynamic characteristics of the cavitating inducer itself irrespective of the hydraulic system in which it resides

Trade booms, trade busts and trade costs

What has driven trade booms and trade busts in the past and present? We derive a micro-founded measure of trade frictions from leading trade theories and use it to gauge the importance of bilateral trade costs in determining international trade flows. We construct a new balanced sample of bilateral trade flows for 130 country pairs across the Americas, Asia, Europe, and Oceania for the period from 1870 to 2000 and demonstrate an overriding role for declining trade costs in the pre-World War I trade boom. In contrast, for the post-World War II trade boom we identify changes in output as the dominant force. Finally, the entirety of the interwar trade bust is explained by increases in trade costs

Small volume link orbifolds

This paper proves lower bounds on the volume of a hyperbolic 3-orbifold whose singular locus is a link. We identify the unique smallest volume orbifold whose singular locus is a knot or link in the 3-sphere, or more generally in a Z_6 homology sphere. We also prove more general lower bounds under mild homological hypotheses.Comment: 19 pages, 3 figures. Revised version, to appear in Mathematical Research Letter

The Goddess: Myths of the Great Mother

The Goddess is all around us: Her face is reflected in the burgeoning new growth of every ensuing spring; her power is evident in the miracle of conception and childbirth and in the newborn’s cry as it searches for the nurturing breast; we glimpse her in the alluring beauty of youth, in the incredible power of sexual attraction, in the affection of family gatherings, and in the gentle caring of loved ones as they leave the mortal world. The Goddess is with us in the everyday miracles of life, growth, and death which always have surrounded us and always will, and this ubiquity speaks to the enduring presence and changing masks of the universal power people have always recognized in their lives. Such power is the Goddess, at least in part, and through its workings we may occasionally catch a glimpse of the divine.https://cupola.gettysburg.edu/books/1094/thumbnail.jp

Sporadically Torqued Accretion Disks Around Black Holes

The assumption that black hole accretion disks possess an untorqued inner boundary, the so-called zero torque boundary condition, has been employed by models of black hole disks for many years. However, recent theoretical and observational work suggests that magnetic forces may appreciably torque the inner disk. This raises the question of the effect that a time-changing magnetic torque may have on the evolution of such a disk. In particular, we explore the suggestion that the ``Deep Minimum State'' of the Seyfert galaxy MCG--6-30-15 can be identified as a sporadic inner disk torquing event. This suggestion is motivated by detailed analyses of changes in the profile of the broad fluorescence iron line in XMM-Newton spectra. We find that the response of such a disk to a torquing event has two phases; an initial damming of the accretion flow together with a partial draining of the disk interior to the torque location, followed by a replenishment of the inner disk as the system achieves a new (torqued) steady-state. If the Deep Minimum State of MCG--6-30-15 is indeed due to a sporadic torquing event, we show that the fraction of the dissipated energy going into X-rays must be smaller in the torqued state. We propose one such scenario in which Compton cooling of the disk corona by ``returning radiation'' accompanying a central-torquing event suppresses the 0.5-10 keV X-ray flux coming from all but the innermost regions of the disk.Comment: 12 pages, 24 figures, ApJ accepte