Effects of Cavitation on Rotordynamic Force Matrices

When designing a turbomachine, particularly one which is to operate at high speed, it is important to be able to predict the fluid-induced forces, both steady and unsteady, acting on the various components of the machine. This paper concentrates on the fluid-induced rotordynamic forces acting upon the impeller and therefore on the bearings. Self-excited whirl, where the rotor moves away from and whirls along a trajectory eccentric to its undeflected position, can result from these fluid-induced forces. The purpose of the present work is to study the full range of these forces so that they can be included in any rotordynamic analysis at the design stage. To study the fluid-induced rotordynamic force on an impeller vibrating around its machine axis of rotation, an experiment in forced vibration was conducted. The prescribed whirl trajectory of the rotor is a circular orbit of a fixed radius. A rotating dynamometer mounted behind the rotor measures the force on the impeller. The force measured is a combination of a steady radial force due to volute asymmetries and an unsteady force due to the eccentric motion of the rotor. These measurements have been conducted over a full range of whirl/impeller speed ratios at different flow coefficients for various turbomachines including both centrifugal impellers aand axial inducers. A destabilizing force was observed over a region of positive whirl ratio. The range of flow conditions includes an examination of the effects of cavitation on the observed rotordynamic forces

Unsteady Diffuser Vane Pressure and Impeller Wake Measurements in a Centrifugal Pump

Unsteady surface pressure measurements on a vaned diffuser of a centrifugal pump, and wake measurement of the flow exiting a centrifugal impeller into a vaneless diffuser are presented. Frequency spectra and ensemble averages are given for the unsteady measurements. Two different impellers were used, the pump impeller of the HPOTP (High Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Engine) and a two-dimensional impeller. The magnitude of the unsteady total pressure measured in the stationary frame at the impeller exit was found to be of the same order of magnitude as the total pressure rise across the pump. The magnitude of the unsteady diffuser vane pressures was observed to be significantly different on suction and pressure side of the vane, attaining its largest value on the suction side near the leading edge while decreasing along the vane

Yang-Lee Theory for a Nonequilibrium Phase Transition

To analyze phase transitions in a nonequilibrium system we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can identified with two different phases. In a region of the parameter space both of these phases coexist. The condensation point can be computed with high accuracy.Comment: 4 pages, accepted for publication in Phys.Rev.Let

Rotordynamic Forces on Centrifugal Pump Impellers

The asymmetric flow around an impeller in a volute exerts a force upon the impeller. To study the rotordynamic force on an impeller which is vibrating around its machine axis of rotation, the impeller, mounted on a dynamometer, is made to whirl in a circular orbit within the volute. The measured force is expressed as the sum of a steady radial force and an unsteady force due to the eccentric motion of the impeller. These forces were measured in separate tests on a centrifugal pump with radically increased shroud clearance, a two-dimensional impeller, and an impeller with an inducer, the impeller of the HPOTP (High Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Enginer). In each case, a destabilizing force was observed over a region of positive whirl

Coherent bubble-sum approximation for coupled-channel resonance scattering

For coupled-channel resonance scattering we derive a model with a closed form solution for the $T$-matrix that satisfies unitarity and analyticity. The two-channel case is handled explicitly for an arbitrary number of resonances. The method focuses on the expansion of the transition matrix elements, $\Gamma(s)$, in known analytical functions. The appropriate hadronic form factors and the related energy shifts can be determined from the scattering data. The differences between this method and the $K$-matrix and the Breit-Wigner approximation are illustrated in the case of the $S_{11}$ resonances $S_{11}(1535)$ and $S_{11}(1650)$.Comment: 8 pages, 1 figure, code available from http://www.phyast.pitt.edu/~norbertl/bubblegum2

Electronic Structure and Lattice dynamics of NaFeAs

The similarity of the electronic structures of NaFeAs and other Fe pnictides has been demonstrated on the basis of first-principle calculations. The global double-degeneracy of electronic bands along X-M and R-A direction indicates the instability of Fe pnictides and is explained on the basis of a tight-binding model. The de Haas-van Alphen parameters for the Fermi surface (FS) of NaFeAs have been calculated. A $\mathbf{Q}_{M}=(1/2,1/2,0)$ spin density wave (SDW) instead of a charge density wave (CDW) ground state is predicted based on the calculated generalized susceptibility $\chi(\mathbf{q})$ and a criterion derived from a restricted Hatree-Fock model. The strongest electron-phonon (e-p) coupling has been found to involve only As, Na z-direction vibration with linear-response calculations. A possible enhancement mechanism for e-p coupling due to correlation is suggested

Breakdown of chiral expansion for parton distributions

In the framework of the chiral perturbation theory we computed two- and three-loop corrections to the pion parton distributions which posses $\delta$-function singularities at x->0. This calculation explicitly demonstrates that in the region of small x ~ mpi^2/(4 pi F)^2 standard ChPT breaks down and one needs resummation of all orders. We give an example of such resummation.Comment: 10 pages, 7 figure

Geodynamic and metabolic cycles in the Hadean

International audienceHigh-degree melting of hot dry Hadean mantle at ocean ridges and plumes resulted in a crust about 30km thick, overlain in places by extensive and thick mafic volcanic plateaus. Continental crust, by contrast, was relatively thin and mostly submarine. At constructive and destructive plate boundaries, and above the many mantle plumes, acidic hydrothermal springs at ~400°C contributed Fe and other transition elements as well as P and H2 to the deep ocean made acidulous by dissolved CO2 and minor HCl derived from volcanoes. Away from ocean ridges, submarine hydrothermal fluids were cool (=100°C), alkaline (pH ~10), highly reduced and also H2-rich. Reaction of solvents in this fluid with those in ocean water was catalyzed in a hydrothermal mound, a natural self-restoring flow reactor and fractionation column made up of carbonates and freshly precipitated Fe-Ni sulfide and greenrust pores and bubbles, developed above the alkaline spring. Acetate and the amino acetate glycine were the main products, much of which was eluted to the ocean. Other organic byproducts were retained, concentrated and reacted within the compartments. These compartments comprising the natural hydrothermal reactor consisted partly of greigite (Fe5NiS8). It was from reactions between organic modules confined within these inorganic compartments that the first prokaryotic organism evolved. These acetogenic precursors to the Bacteria diversified and migrated down the mound and into the ocean floor to inaugurate the "deep biosphere". Once there the Bacteria, and the recently differentiated Archaea, were protected from cataclysmic heating events caused by large bolide impacts. Geodynamic forces led to the eventual obduction of the deep biosphere into the photic zone where, initially protected by a thin veneer of sediment, the use of solar energy was mastered and photosynthesis emerged. The further evolution to oxygenic photosynthesis was effected as catalytic [CaMn4+] bearing molecules that otherwise would have been interred in the mineral ranciéite in the shallow marine manganiferous sediments, were sequestered and invaginated within the cyanobacterial precursor where, energized by light, they could oxidize water with greater efficiency. Thus, chemical sediments were required both for the emergence of chemosynthesis and of oxygenic photosynthesis, the two innovations that did most to change the nature of our planet

The energies and residues of the nucleon resonances N(1535) and N(1650)

We extract pole positions for the N(1535) and N(1650) resonances using two different models. The positions are determined from fits to different subsets of the existing $\pi N\to\pi N$, $\pi N\to\eta N$ and $\gamma p\to\eta p$ data and found to be 1515(10)--i85(15)MeV and 1660(10)--i65(10)MeV, when the data is described in terms of two poles. Sensitivity to the choice of fitted data is explored. The corresponding $\pi \pi$ and $\eta \eta$ residues of these poles are also extracted.Comment: 9 page