An improved turbine disk design to increase reliability of aircraft jet engines

An analytical study was performed on a novel disk design to replace the existing high-pressure turbine, stage 1 disk on the CF6-50 turbofan engine. Preliminary studies were conducted on seven candidate disk design concepts. An integral multidisk design with bore entry of the turbine blade cooling air was selected as the improved disk design. This disk has the unique feature of being redundant such that if one portion of the disk would fail, the remaining portion would prevent the release of large disk fragments from the turbine system. Low cycle fatigue lives, initial defect propagation lives, burst speed, and the kinetic energies of probable disk fragment configurations were calculated, and comparisons were made with the existing disk, both in its current material, IN 718, and with the substitution of an advanced alloy, Rene 95. The design for redundancy approach which necessitated the addition of approximately 44.5 kg (98 lb) to the design disk substantially improved the life of the disk. The life to crack initiation was increased from 30,000 cycles to more than 100,000 cycles. The cycles to failure from initial defect propagation were increased from 380 cycles to 1564 cycles. Burst speed was increased from 126 percent overspeed to 149 percent overspeed. Additionally, the maximum fragment energies associated with a failure were decreased by an order of magnitude

Redundant disc

A rotatable disc is described that consists of parallel plates tightly joined together for rotation about a hub. Each plate is provided with several angularly projecting spaced lands. The lands of each plate are interposed in alternating relationship between the lands of the next adjacent plate. In this manner, circumferential displacement of adjacent sectors in any one plate is prevented in the event that a crack develops. Each plate is redundantly sized so that, in event of structural failure of one plate, the remaining plates support a proportionate share of the load of the failed plate. The plates are prevented from separating laterally through the inclusion of generally radially extending splines which are inserted to interlock cooperating, circumferentially adjacent lands

Radiative falloff in Einstein-Straus spacetime

The Einstein-Straus spacetime describes a nonrotating black hole immersed in a matter-dominated cosmology. It is constructed by scooping out a spherical ball of the dust and replacing it with a vacuum region containing a black hole of the same mass. The metric is smooth at the boundary, which is comoving with the rest of the universe. We study the evolution of a massless scalar field in the Einstein-Straus spacetime, with a special emphasis on its late-time behavior. This is done by numerically integrating the scalar wave equation in a double-null coordinate system that covers both portions (vacuum and dust) of the spacetime. We show that the field's evolution is governed mostly by the strong concentration of curvature near the black hole, and the discontinuity in the dust's mass density at the boundary; these give rise to a rather complex behavior at late times. Contrary to what it would do in an asymptotically-flat spacetime, the field does not decay in time according to an inverse power-law.Comment: ReVTeX, 12 pages, 14 figure

Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations

We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal.Comment: 16 page

Radiative falloff in the background of rotating black hole

We study numerically the late-time tails of linearized fields with any spin $s$ in the background of a spinning black hole. Our code is based on the ingoing Kerr coordinates, which allow us to penetrate through the event horizon. The late time tails are dominated by the mode with the least multipole moment $\ell$ which is consistent with the equatorial symmetry of the initial data and is equal to or greater than the least radiative mode with $s$ and the azimuthal number $m$.Comment: 5 pages, 4 Encapsulated PostScript figures; Accepted to Phys. Rev. D (Rapid Communication

Radiative Tail of Realistic Rotating Gravitational Collapse

An astrophysically realistic model of wave dynamics in black-hole spacetimes must involve a non-spherical background geometry with angular momentum. We consider the evolution of gravitational (and electromagnetic) perturbations in rotating Kerr spacetimes. We show that a rotating Kerr black hole becomes `bald' slower than the corresponding spherically-symmetric Schwarzschild black hole. Moreover, our results turn over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal. In particular, we show that different fields have different decaying rates. Our results are also of importance both to the study of the no-hair conjecture and the mass-inflation scenario (stability of Cauchy horizons).Comment: 11 page

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed -- the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically-symmetric spacetime: it decays in time according to an inverse power-law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX

Radiative falloff in Schwarzschild-de Sitter spacetime

We consider the time evolution of a scalar field propagating in Schwarzschild-de Sitter spacetime. At early times, the field behaves as if it were in pure Schwarzschild spacetime; the structure of spacetime far from the black hole has no influence on the evolution. In this early epoch, the field's initial outburst is followed by quasi-normal oscillations, and then by an inverse power-law decay. At intermediate times, the power-law behavior gives way to a faster, exponential decay. At late times, the field behaves as if it were in pure de Sitter spacetime; the structure of spacetime near the black hole no longer influences the evolution in a significant way. In this late epoch, the field's behavior depends on the value of the curvature-coupling constant xi. If xi is less than a critical value 3/16, the field decays exponentially, with a decay constant that increases with increasing xi. If xi > 3/16, the field oscillates with a frequency that increases with increasing xi; the amplitude of the field still decays exponentially, but the decay constant is independent of xi.Comment: 10 pages, ReVTeX, 5 figures, references updated, and new section adde

High-Order Contamination in the Tail of Gravitational Collapse

It is well known that the late-time behaviour of gravitational collapse is {\it dominated} by an inverse power-law decaying tail. We calculate {\it higher-order corrections} to this power-law behaviour in a spherically symmetric gravitational collapse. The dominant ``contamination'' is shown to die off at late times as $M^2t^{-4}\ln(t/M)$. This decay rate is much {\it slower} than has been considered so far. It implies, for instance, that an `exact' (numerical) determination of the power index to within $\sim 1$ requires extremely long integration times of order $10^4 M$. We show that the leading order fingerprint of the black-hole electric {\it charge} is of order $Q^2t^{-4}$.Comment: 12 pages, 2 figure

3D simulations of linearized scalar fields in Kerr spacetime

We investigate the behavior of a dynamical scalar field on a fixed Kerr background in Kerr-Schild coordinates using a 3+1 dimensional spectral evolution code, and we measure the power-law tail decay that occurs at late times. We compare evolutions of initial data proportional to f(r) Y_lm(theta,phi) where Y_lm is a spherical harmonic and (r,theta,phi) are Kerr-Schild coordinates, to that of initial data proportional to f(r_BL) Y_lm(theta_BL,phi), where (r_BL,theta_BL) are Boyer-Lindquist coordinates. We find that although these two cases are initially almost identical, the evolution can be quite different at intermediate times; however, at late times the power-law decay rates are equal.Comment: 12 pages, 9 figures, revtex4. Major revision: added figures, added subsection on convergence, clarified discussion. To appear in Phys Rev