Clustering of inertial spheres in a statistically unsteady flow field is believed to be different from particle clustering observed in statistically steady flows. The continuously evolving threedimensional Taylor-Green vortex (TGV) flow exhibits time-varying length-and time-scales, which are likely to alter the resonance of a given particle with the evolving flow structures. The tendency of homogeneously introduced spherical point-particles to cluster preferentially in the TGV flow is observed to depend on the particle inertia, parameterized in terms of the particle response time τ p . The degree of the inhomogeneity of the particle distribution is measured by the variance σ 2 of Voronoï volumes. The time evolution of the particle-laden TGV-flow is characterized by a viscous dissipation time scale τ d and the effective Stokes number St ef f = τ p /τ d . Particles with low/little inertia do not cluster in the early stage when the TGV-flow only consists of large-scale and almost inviscid structures and St ef f < 1. Later, when the large structures have been broken down to smaller vortices, the least inertial particles exhibit a stronger preferential concentration than the more inertial spheres. At this stage, when the viscous energy dissipation has reached its maximum level, the effective Stokes number of these particles have reached the order of one. Particles are generally seen to cluster preferentially at strain-rate dominated locations, i.e. where the second invariant Q of the velocity gradient tensor is negative. However, a memory effect can be observed in the course of the flow evolution where high σ 2 -values do not always correlate with Q < 0.
In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 8, 1063(1965], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with external force applied at k = k f in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes for k < k f , where the fluxes exhibit significant fluctuations. We show that these fluctuations arise due to the unsteady nature of the flow at small wavenumbers. For the k < k f , the shellto-shell energy transfers computed using numerical data show forward energy transfers among the neighbouring shells, but backward energy transfers for other shells.
In this paper, we investigate the intra-laminar size effect of discontinuous fiber composites (DFCs) with three different unidirectional prepreg platelet sizes (75×12, 50×8, and 25×4 mm). Experimentally, we test five different sizes of single edge notched specimens, geometrically scaled (1:2/3:1/3:1/6:1/20), with the constant thickness. We observe notch insensitivity meaning that the crack initiate away from the notch, when the structure sizes are small (from the ratio 1/20 to 1/6). However, the crack always initiate for the ratio of 2/3 and 1. Bazants size effect law is used to analyze such unconventional fracturing behaviors. The experimental results are fitted using the linear regression analysis follow by the size effect law. The transition behavior of the DFCs from the strength based criteria to the energy based criteria is clearly observed. Also, as the platelet size increases, the fracture behaviors shift away from the energy based criteria, which implies a decrease in brittleness. To obtain the intra-laminar fracture energy, G f , we have developed a finite element model based on the stochastic laminate analogy. The platelet size of 75×12 mm shows 96.8% increase in the fracture energy compared to the platelet size of 25×4 mm while behaves less brittle way. In conclusion, this study examines the effect of the platelet sizes of the DFCs in the presence of the notch. In this process, capturing the quasi-brittleness of the material using the nonlinear fracture mechanics is essential and we accomplish this using the simple size effect law. This work expands on an earlier SAMPE conference proceeding [1], and thus, there is a significant overlap in texts and figures between this and the SAMPE conference proceedings.
Preferential orientations of inertialess non-spherical particles are examined through three qualitatively different stages of a time-evolving Taylor-Green vortex flow. Despite an unexpected decorrelation between the vorticity vector and the direction of Lagrangian stretching, experienced by material fluid elements over a substantial time interval, prolate spheroids aligned with the Lagrangian stretching direction, whereas oblate spheroids aligned with the Lagrangian compression direction. We therefore infer that spheroidal tracers orient themselves relative to the Lagrangian history of the velocity gradients, defined by the left Cauchy-Green deformation tensor, rather than with the fluid vorticity vector. This preferential alignment persists all throughout the statistically unsteady flow field, and even in the inviscid and non-turbulent early stage of the time-dependent vortex flow. This explains the observed preferential spinning of rods and tumbling of disks, similarly as in homogeneous isotropic turbulence, even at the early stage when the flow is anisotropic and laminar. These preferred modes of particle rotation prevail all through the evolving flow, despite a surprisingly long time interval, during which the fluid vorticity decorrelates from the direction of Lagrangian stretching.
Rod- and disk-like particles preferentially align parallel and perpendicular, respectively, to the fluid vorticity, both at the early as well as later stages of the unsteady Taylor–Green vortex (TGV) flow. The early stage of the flow is laminar and comprises anisotropic large-scale Taylor–Green structures, while the later stages resemble homogeneous isotropic turbulence with Kolmogorov-type small-scale structures. The reason for the orientational behavior of inertialess spheroids in the early stage of the TGV-flow has been sought by examining the alignments of spheroidal particles, not only with vorticity but also with Lagrangian stretching and compression directions of the fluid elements in our earlier paper [Jayaram et al., “Alignment and rotation of spheroids in unsteady vortex flow,” Phys. Fluids. 33, 033310 (2021)]. This article is a sequel to the above paper in which the spheroids' alignments are studied locally, in contrast to the volume-averaged statistics studied previously, to observe the influence of the local flow field on the spheroidal alignment. It has been observed through our studies that the alignments vary periodically in space and these variations can be associated with the large-scale periodicity of the flow field originating from the initial conditions of the TGV flow. Additionally, the intense vortex stretching in the early stages of the flow evolution is seen to be largely influencing the orientation of the spheroids.
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