Localization of unresolved regions in the selective large-eddy simulation of hypersonic jets

A method for the localization of the regions where the turbulent fluctuations are unresolved is applied to the selective large-eddy simulation (LES) of a compressible turbulent jet of Mach number equal to 5. This method is based on the introduction of a scalar probe function f which represents the magnitude of the twisting-stretching term normalized with the enstrophy [1]. The statistical analysis shows that, for a fully developed turbulent field of fluctuations, the probability that f is larger than 2 is zero, while, for an unresolved field, is finite. By computing f in each instantaneous realization of the simulation it is possible to locate the regions where the magnitude of the normalized stretching-twisting is anomalously high. This allows the identification of the regions where the subgrid model should be introduced into the governing equations (selective filtering). The results of the selective LES are compared with those of a standard LES, where the subgrid terms are used in the whole domain. The comparison is carried out by assuming as high order reference field a higher resolution Euler simulation of the compressible jet. It is shown that the selective LES modifies the dynamic properties of the flow to a lesser extent with respect to the classical LE

Small scale of subgrid scales in the Large Eddy Simulation of compressible turbulent flows

It is proposed a methodology for the automatic selective insertion-elimination of subgrid scale stresses in the numerical simulation of transitional laminar-turbulent flows in both compressible and incompressible regimes. By means of a functional of the filtered vorticity field, it is possible to approximatively locate the flow regions that are rich in small scale motions. In these regions, it can be opportune to filter the equations of motion to carry out a Large Eddy Simulation, that is, a simulation where the larger scales only are resolved, but the small scale dynamics is considered and represented through proper terms in the equations. In case of compressible regimes, a functional of the pressure local variation and divergence can be associated to the functional previously mentioned in order to determine the eventual presence of shocks. In such a way, it is possible to locate the regions where, to capture the shock, it is necessary to insert an explicit numerical dissipation and suppress the subgrid mode

Cross and magnetic helicity in the outer heliosphere from Voyager 2 observations

Plasma velocity and magnetic field measurements from the Voyager 2 mission are used to study solar wind turbulence in the slow solar wind at two different heliocentric distances, 5 and 29 astronomical units, sufficiently far apart to provide information on the radial evolution of this turbulence. The magnetic helicity and the cross-helicity, which express the correlation between the plasma velocity and the magnetic field, are used to characterize the turbulence. Wave number spectra are computed by means of the Taylor hypothesis applied to time resolved single point Voyager 2 measurements. The overall picture we get is complex and difficult to interpret. A substantial decrease of the cross-helicity at smaller scales (over 1-3 hours of observation) with increasing heliocentric distance is observed. At 5 AU the only peak in the probability density of the normalized residual energy is negative, near -0.5. At 29 AU the probability density becomes doubly peaked, with a negative peak at -0.5 and a smaller peak at a positive values of about 0.7. A decrease of the cross-helicity for increasing heliocentric distance is observed, together with a reduction of the unbalance toward the magnetic energy of the energy of the fluctuations. For the smaller scales, we found that at 29 AU the normalized polarization is small and positive on average (about 0.1), it is instead zero at 5 AU. For the larger scales, the polarization is low and positive at 5 AU (average around 0.1) while it is negative (around - 0.15) at 29 AU.Comment: 14 pages 5 figures. Accepted for publication on European Journal of Mechanics B/Fluids (5/8/2015

Turbulence in the solar wind: spectra from Voyager 2 data at 5 AU

Fluctuations in the flow velocity and magnetic fields are ubiquitous in the Solar System. These fluctuations are turbulent, in the sense that they are disordered and span a broad range of scales in both space and time. The study of solar wind turbulence is motivated by a number of factors all keys to the understanding of the Solar Wind origin and thermodynamics. The solar wind spectral properties are far from uniformity and evolve with the increasing distance from the sun. Most of the available spectra of solar wind turbulence were computed at 1 astronomical unit, while accurate spectra on wide frequency ranges at larger distances are still few. In this paper we consider solar wind spectra derived from the data recorded by the Voyager 2 mission during 1979 at about 5 AU from the sun. Voyager 2 data are an incomplete time series with a voids/signal ratio that typically increases as the spacecraft moves away from the sun (45% missing data in 1979), making the analysis challenging. In order to estimate the uncertainty of the spectral slopes, different methods are tested on synthetic turbulence signals with the same gap distribution as V2 data. Spectra of all variables show a power law scaling with exponents between -2.1 and -1.1, depending on frequency subranges. Probability density functions (PDFs) and correlations indicate that the flow has a significant intermittency.Comment: 14 pages, 7 figures. Discussion improved since the previous versio

Voyager 2 solar plasma and magnetic field spectral analysis for intermediate data sparsity

The Voyager probes are the furthest, still active, spacecraft ever launched from Earth. During their 38-year trip, they have collected data regarding solar wind properties (such as the plasma velocity and magnetic field intensity). Unfortunately, a complete time evolution of the measured physical quantities is not available. The time series contains many gaps which increase in frequency and duration at larger distances. The aim of this work is to perform a spectral and statistical analysis of the solar wind plasma velocity and magnetic field using Voyager 2 data measured in 1979, when the gaps/signal ratio is of order of unity. This analysis is achieved using four different data reconstruction techniques: averages on linearly interpolated subsets, correlation of linearly interpolated data, compressed sensing spectral estimation, and maximum likelihood data reconstruction. With five frequency decades, the spectra we obtained have the largest frequency range ever computed at 5 astronomical units from the Sun; spectral exponents have been determined for all the components of the velocity and magnetic field fluctuations. Void analysis is also useful in recovering other spectral properties such as integral scales (see for instance Table 4) and, if the confidence level of the measurements is sufficiently high, the decay variation in the small scale range due, for instance, to dissipative effects.Comment: 11 pages, 7 figure

Large-eddy simulation of hypersonic flows. Selective procedure to activate the sub-grid model wherever small scale turbulence is present

A new method for the localization of the regions where small scale turbulent fluctuations are present in hypersonic flows is applied to the large-eddy simulation (LES) of a compressible turbulent jet with an initial Mach number equal to 5. The localization method used is called selective LES and is based on the exploitation of a scalar probe function! which represents the magnitude of the stretching tilting term of the vorticity equation normalized with the enstrophy (Tordella et al., 2007) [3]. For a fully developed turbulent field of fluctuations, statistical analysis shows that the probability that f is larger than 2 is almost zero, and, for any given threshold, it is larger if the flow is under-resolved. By computing the spatial field off in each instantaneous realization of the simulation it is possible to locate the regions where the magnitude of the normalized vortical stretching tilting is anomalously high. The sub-grid model is then introduced into the governing equations in such regions only. The results of the selective LES simulation are compared with those of a standard LES, where the sub-grid terms are used in the whole domain, and with those of a standard Euler simulation with the same resolution. The comparison is carried out by assuming as reference field a higher resolution Euler simulation of the same jet. It is shown that the selective LES modifies the dynamic properties of the flow to a lesser extent with respect to the classical LES. In particular, the prediction of the enstrophy, mean velocity and density distributions and of the energy and density spectra are substantially improved

Determination of density and concentration from fluorescent images of a gas flow

A fluorescent image analysis procedure to determine the distribution of species concentration and density in a gas flow is proposed. The fluorescent emission is due to the excitation of atoms/molecules of a gas that is intercepted by an electron blade. The intensity of the fluorescent light is proportional to the local number density of the gas. When the gas flow is a mixture of different species, this proportionality can be exploited to extract the contribution associated to the species from the spectral superposition acquired by a digital camera. This yields a method that simultaneously reveals species concentrations and mass density of the mixture. The procedure is applied to two under-expanded sonic jets discharged into a different gas ambient - Helium into Argon and Argon into Helium - to measure the concentration and density distribution along the jet axis and across it. A comparison with experimental and numerical results obtained by other authors when observing under-expanded jets at different Mach numbers is made with the density distribution along the axis of the jet. This density distribution appears to be self-similar.Comment: New figures in portable .eps forma

Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space

This study provides sufficient conditions for the temporal monotonic decay of enstrophy for two-dimensional perturbations traveling in the incompressible, viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's procedure (1938) to the initial-value problem allowed us to find the region of the wavenumber-Reynolds number map where the enstrophy of any initial disturbance cannot grow. This region is wider than the kinetic energy's one. We also show that the parameters space is split in two regions with clearly distinct propagation and dispersion properties