135,089 research outputs found
Pressure Bifurcation Phenomenon on Supersonic Blowing Trailing Edges
Turbine blades operating in transonic-supersonic regime develop a complex
shock wave system at the trailing edge, a phenomenon that leads to unfavorable
pressure perturbations downstream and can interact with other turbine stages.
Understanding the fluid behavior of the area adjacent to the trailing edge is
essential in order to determine the parameters that have influence on these
pressure fluctuations. Colder flow, bled from the high-pressure compressor, is
often purged at the trailing edge to cool the thin blade edges, affecting the
flow behavior and modulating the intensity and angle of the shock waves system.
However, this purge flow can sometimes generate non-symmetrical configurations
due to a pressure difference that is provoked by the injected flow. In this
work, a combination of RANS simulations and global stability analysis is
employed to explain the physical reasons of this flow bifurcation. Analyzing
the features that naturally appear in the flow and become dominant for some
value of the parameters involved in the problem, an anti-symmetrical global
mode, related to the sudden geometrical expansion of the trailing edge slot, is
identified as the main mechanism that forces the changes in the flow topology.Comment: Submitted to AIAA Journa
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
Stability and instability of expanding solutions to the Lorentzian constant-positive-mean-curvature flow
We study constant mean curvature Lorentzian hypersurfaces of
from the point of view of its Cauchy problem. We
completely classify the spherically symmetric solutions, which include among
them a manifold isometric to the de Sitter space of general relativity. We show
that the spherically symmetric solutions exhibit one of three (future)
asymptotic behaviours: (i) finite time collapse (ii) convergence to a time-like
cylinder isometric to some and (iii) infinite
expansion to the future converging asymptotically to a time translation of the
de Sitter solution. For class (iii) we examine the future stability properties
of the solutions under arbitrary (not necessarily spherically symmetric)
perturbations. We show that the usual notions of asymptotic stability and
modulational stability cannot apply, and connect this to the presence of
cosmological horizons in these class (iii) solutions. We can nevertheless show
the global existence and future stability for small perturbations of class
(iii) solutions under a notion of stability that naturally takes into account
the presence of cosmological horizons. The proof is based on the vector field
method, but requires additional geometric insight. In particular we introduce
two new tools: an inverse-Gauss-map gauge to deal with the problem of
cosmological horizon and a quasilinear generalisation of Brendle's Bel-Robinson
tensor to obtain natural energy quantities.Comment: Version 2: 60 pages, 1 figure. Changes mostly to fix typographical
errors, with the exception of Remark 1.2 and Section 9.1 which are new and
which explain the extrinsic geometry of the embedding in more detail in terms
of the stability result. Version 3: updated reference
Static, spherically symmetric solutions with a scalar field in Rastall gravity
Rastall's theory belongs to the class of non-conservative theories of
gravity. In vacuum, the only non-trivial static, spherically symmetric solution
is the Schwarzschild one, except in a very special case. When a canonical
scalar field is coupled to the gravity sector in this theory, new exact
solutions appear for some values of the Rastall parameter . Some of these
solutions describe the same space-time geometry as the recently found solutions
in the -essence theory with a power function for the kinetic term of the
scalar field. There is a large class of solutions (in particular, those
describing wormholes and regular black holes) whose geometry coincides with
that of solutions of GR coupled to scalar fields with nontrivial
self-interaction potentials; the form of these potentials, however, depends on
the Rastall parameter . We also note that all solutions of GR with a zero
trace of the energy-momentum tensor, including black-hole and wormhole ones,
may be re-interpreted as solutions of Rastall's theory.Comment: Latex file, 18 pages. To fit published versio
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