488 research outputs found
A Kinematically Consistent Two-Point Correlation Function
A simple kinematically consistent expression for the longitudinal two-point correlation function related to both the integral length scale and the Taylor microscale is obtained. On the inner scale, in a region of width inversely proportional to the turbulent Reynolds number, the function has the appropriate curvature at the origin. The expression for two-point correlation is related to the nonlinear cascade rate, or dissipation epsilon, a quantity that is carried as part of a typical single-point turbulence closure simulation. Constructing an expression for the two-point correlation whose curvature at the origin is the Taylor microscale incorporates one of the fundamental quantities characterizing turbulence, epsilon, into a model for the two-point correlation function. The integral of the function also gives, as is required, an outer integral length scale of the turbulence independent of viscosity. The proposed expression is obtained by kinematic arguments; the intention is to produce a practically applicable expression in terms of simple elementary functions that allow an analytical evaluation, by asymptotic methods, of diverse functionals relevant to single-point turbulence closures. Using the expression devised an example of the asymptotic method by which functionals of the two-point correlation can be evaluated is given
A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence
The turbulent mass flux, or equivalently the fluctuating Favre velocity mean, appears in the first and second moment equations of compressible kappa-epsilon and Reynolds stress closures. Mathematically it is the difference between the unweighted and density-weighted averages of the velocity field and is therefore a measure of the effects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the effects of the mean density gradients, in the same way the anisotropy tensor characterizes the effects of the mean velocity gradients. An evolution equation for the turbulent mass flux is derived. A truncation of this equation produces an algebraic expression for the mass flux. The mass flux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results
The Favre-Reynolds Average Distinction and a Consistent Gradient Transport Expression for the Dissipation
Two equation and higher order closures for compressible turbulence fail to capture the compressible wall layers' log scaling. Accounting for the distinction between Favre and Reynolds averaged variables in the compressible moment equations indicate that turbulent transport expressions obtained using the 'variable density approximation' are in error. The error is related to the enstrophy, a Reynolds averaged variable appearing in the equation for the Favre averaged k; recognizing this fact an expression for the transport of dissipation consistent with simple mixing length arguments is obtained. Within the (limited) context of a gradient transport hypothesis a rational form for the turbulent transport of the dissipation is found. Modestly better agreement with the well established compressible Van Driest log scaling is found in k - epsilon calculation
Decay of scalar variance in isotropic turbulence in a bounded domain
The decay of scalar variance in isotropic turbulence in a bounded domain is
investigated. Extending the study of Touil, Bertoglio and Shao (2002; Journal
of Turbulence, 03, 49) to the case of a passive scalar, the effect of the
finite size of the domain on the lengthscales of turbulent eddies and scalar
structures is studied by truncating the infrared range of the wavenumber
spectra. Analytical arguments based on a simple model for the spectral
distributions show that the decay exponent for the variance of scalar
fluctuations is proportional to the ratio of the Kolmogorov constant to the
Corrsin-Obukhov constant. This result is verified by closure calculations in
which the Corrsin-Obukhov constant is artificially varied. Large-eddy
simulations provide support to the results and give an estimation of the value
of the decay exponent and of the scalar to velocity time scale ratio
Exploring the beta distribution in variable-density turbulent mixing
In assumed probability density function (pdf) methods of turbulent
combustion, the shape of the scalar pdf is assumed a priori and the pdf is
parametrized by its moments for which model equations are solved. In
non-premixed flows the beta distribution has been a convenient choice to
represent the mixture fraction in binary mixtures or a progress variable in
combustion. Here the beta-pdf approach is extended to variable-density mixing:
mixing between materials that have very large density differences and thus the
scalar fields are active. As a consequence, new mixing phenomena arise due to
1) cubic non-linearities in the Navier-Stokes equation, 2) additional
non-linearities in the molecular diffusion terms and 3) the appearance of the
specific volume as a dynamical variable. The assumed beta-pdf approach is
extended to transported pdf methods by giving the associated stochastic
differential equation (SDE). The beta distribution is shown to be a realizable,
consistent and sufficiently general representation of the marginal pdf of the
fluid density, an active scalar, in non-premixed variable-density turbulent
mixing. The moment equations derived from mass conservation are compared to the
moment equations derived from the governing SDE. This yields a series of
relations between the non-stationary coefficients of the SDE and the mixing
physics. Our treatment of this problem is general: the mixing is mathematically
represented by the divergence of the velocity field which can only be specified
once the problem is defined. In this paper we seek to describe a theoretical
framework to subsequent applications. We report and document several rigorous
mathematical results, necessary for forthcoming work that deals with the
applications of the current results to model specification, computation and
validation of binary mixing of inert fluids.Comment: Added two paragraphs to Introduction + minor changes, Accepted in
Journal of Turbulence, July 19, 201
Planck pre-launch status: HFI beam expectations from the optical optimisation of the focal plane
Planck is a European Space Agency (ESA) satellite, launched in May 2009, which will map the cosmic microwave background anisotropies in intensity and polarisation with unprecedented detail and sensitivity. It will also provide full-sky maps of astrophysical foregrounds. An accurate knowledge of the telescope beam patterns is an essential element for a correct analysis of the acquired astrophysical data. We present a detailed description of the optical design of the High Frequency Instrument (HFI) together with some of the optical performances measured during the calibration campaigns. We report on the evolution of the knowledge of the pre-launch HFI beam patterns when coupled to ideal telescope elements, and on their significance for the HFI data analysis procedure
The complete submillimetre spectrum of NGC 891
Submillimetre maps of NGC 891 have been obtained with the PRONAOS
balloon-borne telescope and with the ISOPHOT instrument on board the ISO
satellite. In this article, we also gather data from IRAS and SCUBA to present
the complete submillimetre spectrum of this nearby edge-on spiral galaxy. We
derive submillimetre emission profiles along the major axis. The modified
blackbody fits, assuming a single dust component, lead to temperatures of 19-24
K toward the centre and 18-20 K toward the edges, with possible variations of
the dust spectral index from 1.4 to 2. The two-component fits lead to a warm
component temperature of 29 K all along the galaxy with a cold component at 16
K. The interstellar medium masses derived by these two methods are quite
different: 4.6 x 10^9 Mo in the case of the one-component model and 12 x 10^9
Mo in the case of the two-component one. This two-component fit indicates that
the cold dust to warm dust ratio is 20 to 40, the highest values being in the
wings of this galaxy. Comparing to dust mass estimates, both estimations of the
ISM mass are consistent with a gas to dust mass ratio of 240, which is close to
the Milky Way value. Our results illustrate the importance of accurate
submillimetre spectra to derive masses of the interstellar medium in galaxies.Comment: 5 pages, 2 figures, accepted May 2003 in the MNRA
Submillimeter mapping and analysis of cold dust condensations in the Orion M42 star forming complex
We present here the continuum submillimeter maps of the molecular cloud
around the M42 Nebula in the Orion region. These have been obtained in four
wavelength bands (200, 260, 360 and 580 microns) with the ProNaOS two meter
balloon-borne telescope. The area covered is 7 parsecs wide (50 arcmin at a
distance of 470 pc) with a spatial resolution of about 0.4 parsec. Thanks to
the high sensitivity to faint surface brightness gradients, we have found
several cold condensations with temperatures ranging from 12 to 17 K, within 3
parsecs of the dense ridge. The statistical analysis of the temperature and
spectral index spatial distribution shows an evidence of an inverse correlation
between these two parameters. Being invisible in the IRAS 100 micron survey,
some cold clouds are likely to be the seeds for future star formation activity
going on in the complex. We estimate their masses and we show that two of them
have masses higher than their Jeans masses, and may be gravitationally
unstable.Comment: 4 figures, The Astrophysical Journal, Main Journal, in pres
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