Carlos B. da Silva

Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets

The invariants of the velocity gradient R and Q, rate-of-strain RS and QS, and rate-of-rotation QW tensors are analyzed across the turbulent/nonturbulent T/NT interface by using a direct numerical simulation DNS of a turbulent plane jet at Re120. The invariants allow a detailed characterization of the dynamics, geometry and topology of the flow during the entrainment. The invariants Q and QS are almost equal and negative outside the turbulent region close to the T/NT interface, which shows the existence of high values of strain product hence viscous dissipation of kinetic energy at that location. Right at the T/NT interface, the invariants Q W and Q S show that virtually all flow points there are characterized by irrotational dissipation, with no discernible sign of the coherent structures which are known to exist deep inside the turbulent region. Moreover, the invariants of the velocity gradient tensor Q and R show that the classical “teardrop” shape of their associated phase map is not yet formed at the T/NT interface. All the invariants rapidly change after the T/NT interface is crossed into the turbulent region. For instance, the enstrophy density, proportional to QW, is zero in the irrotational flow region and high and more or less constant inside the turbulent region, after it undergoes a sharp jump near the T/NT interface. Inside the turbulent region, at a distance of only 1.7 from the T/NT interface, where is the Kolmogorov microscale, the invariants QW and QS suggest that large scale coherent vortices already exist in the flow. Furthermore, the joint probability density function of Q and R already displays its well known teardrop shape at that location. Moreover, the geometry of the straining or deformation of the fluid elements during the turbulent entrainment process is preferentially characterized by biaxial expansion with S:S:S=2:1:x7f3,where S, S, and S are the eigenvalues of the rate-of-strain tensor arranged in descending order. Based on an analysis of the invariants, many aspects of the flow topology inside the turbulent region at a distance of only 1.7 from the T/NT interface are already similar to those observed deep inside the turbulent region.

Vortex control of bifurcating jets: A numerical study

Direct and large-eddy simulations (DNS/LES) are performed to analyze the vortex dynamics and the statistics of bifurcating jets. The Reynolds number ranges from ReD=1.5×103 to ReD=5.0×104. An active control of the inlet conditions of a spatially evolving round jet is performed with the aim of favoring the jet spreading in one particular spatial direction, thus creating a bifurcating jet. Three different types of forcing, based on the information provided by a LES of a natural (unforced) jet, are superimposed to the jet inlet in order to cause its bifurcation. The different forcing types mimic the forcing methods used in experimental bifurcating jets (Lee and Reynolds, Parekh et al., Suzuki et al.), but using excitations with relatively low amplitudes, which could be used in real industrial applications. The three-dimensional coherent structures resulting from each specific forcing are analyzed in detail and their impact on the statistical behavior of bifurcating jets is explained. In particular we focus o...

The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer

Direct numerical simulations at Reynolds numbers ranging from Reλ=30 to 160 show that the thickness δω of the turbulent/nonturbulent (T/NT) interface in planar jets is of the order of the Taylor scale δω∼λ, while in shear free, irrotational/isotropic turbulence is of the order of the Kolmogorov microscale δω∼η. It is shown that δω is equal to the radius of the large vorticity structures (LVSs) in this region, δω≈RLVS. Thus, the mean shear and the Reynolds number affect the T/NT interface thickness insofar as they define the radial dimension of the LVS near the T/NT interface.

The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet

The role of coherent vortices near the turbulent/non-turbulent (T/NT) interface in a turbulent plane jet is analysed by a direct numerical simulation (DNS). The coherent vortices near the jet edge consist of large-scale vortical structures (LSVSs) maintained by the mean shear and intense vorticity structures (IVSs) created by the background fluctuating turbulence field. The radius of the LSVS is equal to the Taylor micro-scale Rlsvs≈λ, while the radius of the IVS is of the order of the Kolmogorov micro-scale Rivs∼η. The LSVSs are responsible for the observed vorticity jump at the T/NT interface, being of the order of the Taylor micro-scale. The coherent vortices in the proximity of the T/NT interface are preferentially aligned with the tangent to the T/NT interface and are responsible for the viscous dissipation of kinetic energy near the T/NT interface and to the characteristic shape of the enstrophy viscous diffusion observed at that location.

Transition in high velocity ratio coaxial jets analysed from direct numerical simulations

Direct numerical simulations are performed to analyse the instability, transition scenario and resulting topology from high velocity ratio coaxial jets (ru u2009=u20093.3 and 23.5). The inner and outer shear layers roll up into axisymmetric vortex rings due to the Kelvin–Helmholtz instability. For ru u2009=u20093.3 the outer primary vortices evolve according to the theory considering an isolated mixing layer profile, and impose their evolution upon the inner structures which are ‘locked’ into the outer ones. For ru u2009=u200923.5 there is a big recirculation region that does not affect the development of the Kelvin–Helmholtz instabilities. The preferred mode for simple (non-coaxial) round jets is well recovered at the end of the potential core region in the case ru u2009=u20093.3 but not when ru u2009=u200923.5 due to the presence of the backflow region. The structure of the preferred mode is the same in both cases, however, and consists in a helical arrangement (mu2009=u20091). Finally, when the bubble is present one can see that the inner streamwise...

Kinetic energy budgets near the turbulent/nonturbulent interface in jets

The dynamics of the kinetic energy near the turbulent/nonturbulent (T/NT) interface separating the turbulent from the irrotational flow regions is analysed using three direct numerical simulations of turbulent planar jets, with Reynolds numbers based on the Taylor micro-scale across the jet shear layer in the range Reλ ≈ 120–160. Important levels of kinetic energy are already present in the irrotational region near the T/NT interface. The mean pressure and kinetic energy are well described by the Bernoulli equation in this region and agree with recent results obtained from rapid distortion theory in the turbulent region [M. A. C. Teixeira and C. B. da Silva, “Turbulence dynamics near a turbulent/non-turbulent interface,” J. Fluid Mech. 695, 257–287 (2012)]10.1017/jfm.2012.17 while the normal Reynolds stresses agree with the theoretical predictions from Phillips [“The irrotational motion outside a free turbulent boundary,” Proc. Cambridge Philos. Soc. 51, 220 (1955)]10.1017/S0305004100030073. The use of co...

The effect of subgrid-scale models on the vortices computed from large-eddy simulations

Direct numerical and large-eddy simulations (DNS/LES) of temporal plane jets are carried out in order to analyze the effect of the subgrid-scale (SGS) models on the vortices obtained from LES. The dynamics of the filtered vorticity norm (or filtered enstrophy) is analyzed through the application of a box filter to temporal DNS of turbulent plane jets (Reλ≈100), using a methodology similar to da Silva and Metais [J. Fluid Mech. 473, 103 (2002)]. Special emphasis is placed on the enstrophy SGS dissipation term, which represents the effect of the SGS models on the vortices computed from LES. When the filter is placed in the inertial range region the evolution of the vorticity norm is governed by the enstrophy production and enstrophy SGS dissipation, which represents, in the mean, a sink of resolved enstrophy. Thus the coherent vortices obtained from LES are subjected to an additional (nonviscous) dissipation mechanism. Locally, however, the enstrophy SGS dissipation can be either a sink or a source of resol...

Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets

Direct numerical simulations of a planar jet and of shear free turbulence at Reλ = 115–140 using very fine resolutions allow the first direct identification and characterisation of the viscous superlayer (VSL) that exists at the edges of mixing layers, wakes, jets, and boundary layers, adjacent to the turbulent/non-turbulent interface. For both flows the VSL is continuous with higher local thicknesses forming near the larger intense vorticity structures. The mean thickness of the VSL is of the order of the Kolmogorov micro-scale and agrees well with an estimate based on the Burgers vortex model.

Analysis of the gradient-diffusion hypothesis in large-eddy simulations based on transport equations

The gradient-diffusion hypothesis is frequently used in numerical simulations of turbulent flows involving transport equations. In the context of large-eddy simulations(LES) of turbulent flows, one modeling trend involves the use of transport equations for the subgrid-scale (SGS) kinetic energy and SGS scalar variance. In virtually all models using these equations, the diffusion terms are lumped together, and their joint effect is modeled using a “gradient-diffusion” model. In this work, direct numerical simulations of homogeneous isotropic turbulence are used to analyze the local dynamics of these terms and to assess the performance of the “gradient-diffusion” hypothesis used in their modeling. For this purpose a priori tests are used to assess the influence of the Reynolds and Schmidt numbers and the size of the implicit grid filter in this modeling assumption. The analysis uses correlations, variances, skewnesses, flatnesses, probability density functions, and joint probability density functions. The correlations and joint probability density functions show that provided the filter width is within or close to the dissipative range the diffusion terms pertaining to the SGS kinetic energy and SGS scalar variance transport equations are well represented by a gradient-diffusion model. However, this situation changes dramatically for both equations when considering inertial range filter sizes and high Reynolds numbers. The reason for this lies in part in a loss of local balance between the SGS turbulent diffusion and diffusion caused by grid/subgrid-scale (GS/SGS) interactions, which arises at inertial range filter sizes. Moreover, due to the deficient modeling of the diffusion by SGS pressure-velocity interactions, the diffusion terms in the SGS kinetic energy equation are particularly difficult to reconcile with the gradient-diffusion assumption. In order to improve this situation, a new model, inspired by Clark’s SGS model, is developed for this term. The new model shows very good agreement with the exact SGS pressure-velocity term in a priori tests and better results than the classical model in a posteriori(LES) tests.

The behavior of subgrid-scale models near the turbulent/nonturbulent interface in jets

The behavior of subgrid-scale models near the turbulent/nonturbulent interface in jets is analyzed by using direct numerical simulation and large-eddy simulation (LES). The subgrid scales of motion near this region are far from equilibrium and contain an important fraction of the total kinetic energy. The Smagorinsky constant CS needs to be corrected near the jet edge and the method used to obtain the dynamic Smagorinsky constant CD is not able to cope with the intermittent nature of this region. A priori tests and LES show that near the jet edge the Smagorinsky model is superior both to the dynamic Smagorinsky and to the gradient models.