1,263 research outputs found
O-minimal cohomology: finiteness and invariance results
We prove that the cohomology groups of a definably compact set over an
o-minimal expansion of a group are finitely generated and invariant under
elementary extensions and expansions of the language. We also study the
cohomology of the intersection of a definable decreas-ing family of definably
compact sets, under the additional assumption that the o-minimal structure
expands a field.Comment: 28 pages, 7 figures and diagrams Added the hypothesis that singletons
are construcible to section 3. Corrected misprint
Efficient prediction of broadband trailing edge noise and application to porous edge treatment
Trailing edge noise generated by turbulent flow traveling past an edge of an
airfoil is one of the most essential aeroacoustic sound generation mechanisms.
It is of great interest for noise problems in various areas of industrial
application. First principle based CAA with short response time are needed in
the industrial design process for reliable prediction of spectral differences
in turbulent-boundary-layer trailing-edge noise due to design modifications. In
this paper, an aeroacoustic method is studied, resting on a hybrid CFD/CAA
procedure. In a first step RANS simulation provides a time-averaged solution,
including the mean-flow and turbulence statistics such as length-scale,
time-scale and turbulence kinetic energy. Based on these, fluctuating sound
sources are then stochastically generated by the Fast Random Particle-Mesh
Method to simulate in a second CAA step broadband aeroacoustic sound. From
experimental findings it is well known that porous trailing edges significantly
lower trailing edge noise level over a large range of frequencies reaching up
to 8dB reduction. Furthermore, sound reduction depends on the porous material
parameters, e.g. geometry, porosity, permeability and pore size. The paper
presents first results for an extended hybrid CFD/CAA method including porous
materials with prescribed parameters. To incorporate the effect of porosity, an
extended formulation of the Acoustic Perturbation Equations with source terms
is derived based on a reformulation of the volume averaged Navier-Stokes
equations into perturbation form. Proper implementation of the Darcy and
Forchheimer terms is verified for sound propagation in homogeneous and
anisotropic porous medium. Sound generation is studied for a generic symmetric
NACA0012 airfoil without lift to separate secondary effects of lift and camber
on sound from those of the basic edge noise treatments.Comment: 37 page
Beyond Boise - Marking Memories
The Cottonwood Ranger District of the Boise National Forest was my home for the month of August, 1970
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