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Direct numerical simulations of transitional flow in a rectangular duct of cross-sectional aspect ratio
being the duct half-span and half-height, respectively) have been performed in the Reynolds number range
being the bulk velocity and the kinematic viscosity, respectively) in order to investigate the dependence on the aspect ratio of spatially localized turbulence structures. It was observed that the lowest Reynolds number
, estimated in a specific way, for localized (transiently sustaining) turbulence decreases monotonically from
(square duct) with increasing aspect ratio, and for
it nearly attains a minimal value
that is consistent with the onset Reynolds number of turbulent spots in a plane channel (
). Turbulent states consist of localized structures that undergo a fundamental change around
is streamwise-localized similar to turbulent puffs in pipe flow, while for
–9 turbulence at
is also localized in the spanwise direction, similar to turbulent spots in plane channel flow. This structural change in turbulent states at
is attributed to the exclusion of turbulence from the vicinity of the duct sidewalls in the case of a wide duct with
: here the friction length on the sidewalls is so long that the size (around 100 times the friction length) of a self-sustaining minimal flow unit of streamwise vortices and streaks is larger than the duct height and, therefore, it cannot be accommodated.
We here studied photosensitized radical reaction of poly(L-lactic acid) (PLA) using spectrophotometry, electron spin resonance (ESR), gel permeation chromatography (GPC) measurements, and semiempirical molecular orbital calculation. PLA doped with N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD) was irradiated at 77 K using UV light. After the irradiation, we observed a new broad absorption band that is assigned to TMPD radical cation produced by two-photon ionization. ESR spectrum of the irradiated sample also indicated presence of main chain scission radical of PLA as well as the TMPD radical cation. By increasing the irradiation time, the ESR spectrum changed by another radical species which is produced by dehydrogenation of PLA main chain. Spectral simulation for the obtained ESR spectra revealed changes of relative amounts. The GPC measurements clearly indicated decrease in molecular weight of PLA after the irradiation. The semiempirical molecular orbital calculation was used to confirm the reaction scheme of radical anion decomposition.
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