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

Pre-unstable set of multiple transient three-dimensional perturbation waves and the associated turbulent state in a shear flow

In order to understand whether, and to what extent, spectral representation can effectively highlight the nonlinear interaction among different scales, it is necessary to consider the state that precedes the onset of instabilities and turbulence in flows. In this condition, a system is still stable, but is however subject to a swarming of arbitrary 3D small perturbations. These can arrive any instant, and then undergo a transient evolution which is ruled out by the initial-value problem associated to the Navier-Stokes linearized formulation. The set of 3D small perturbations constitutes a system of multiple spatial and temporal scales which are subject to all the processes included in the perturbative Navier-Stokes equations: linearized convective transport, linearized vortical stretching and tilting, and the molecular diffusion. Leaving aside nonlinear interaction among the different scales, these features are tantamount to the features of the turbulent state. We determine the exponent of the inertial range of arbitrary longitudinal and transversal perturbations acting on a typical shear flow, i.e. the bluff-body wake. Then, we compare the present results with the exponent of the corresponding developed turbulent state (notoriously equal to -5/3). For longitudinal perturbations, we observe a decay rate of -3 in the inertial range, typically met in two-dimensional turbulence. For purely 3D perturbations, instead, the energy decreases with a factor of -5/3. If we consider a combination of longitudinal and transversal perturbative waves, the energy spectrum seems to have a decay of -3 for larger wavenumbers ([50, 100]), while for smaller wavenumbers ([3,50]) the decay is of the order -5/3. We can conclude that the value of the exponent of the inertial range has a much higher level of universality, which is not necessarily associated to the nonlinear interaction.Comment: Proceedings of the 17th Australasian Fluid Mechanics Conference, 5-9 December 2010, Auckland, New Zealan

Self-similarity of the turbulent mixing with a constant in time macroscale gradient

In the absence of kinetic energy production, we consider that the influence of the initial conditions is characterized by the presence of an energy gradient or by the concurrency of an energy and a macroscale gradient on turbulent transport. Here, we present a similarity analysis that interprets two new results on the subject recently obtained by means of numerical experiments on shearless mixing (Tordella & Iovieno, 2005). In short, the two results are: i -- The absence of the macroscale gradient is not a sufficient condition for the setting of the asymptotic Gaussian state hypothesized by Veeravalli and Warhaft (1989), where, regardless of the existence of velocity variance distributions, turbulent transport is mainly diffusive and the intermittency is nearly zero up to moments of order four. In fact, it was observed that the intermittency increases with the energy gradient, with a scaling exponent of about 0.29; ii -- If the macroscale gradient is present, referring to the situation where the macroscale gradient is zero but the energy gradient is not, the intermittency is higher if the energy and scale gradients are concordant and is lower if they are opposite. The similarity analysis, which is in fair agreement with the previous experiments, is based on the use of the kinetic energy equation, which contains information concerning the third order moments of the velocity fluctuations. The analysis is based on two simplifying hypotheses: first, that the decays of the turbulences being mixed are almost nearly equal (as suggested by the experiments), second, that the pressure-velocity correlation is almost proportional to the convective transport associated to the fluctuations (Yoshizawa, 2002

Dimensionality influence on passive scalar transport

We numerically investigate the advection of a passive scalar through an interface placed inside a decaying shearless turbulent mixing layer. We consider the system in both two and three dimensions. The dimensionality produces a different time scaling of the diffusion, which is faster in the two-dimensional case. Two intermittent fronts are generated at the margins of the mixing layer. During the decay these fronts present a sort of propagation in both the direction of the scalar flow and the opposite direction. In two dimensions, the propagation of the fronts exhibits a significant asymmetry with respect to the initial position of the interface and is deeper for the front merged in the high energy side of the mixing. In three dimensions, the two fronts remain nearly symmetrically placed. Results concerning the scalar spectra exponents are also presente