The three-dimensional conservation equations relating energy and momentum transfer in a vibrated three-dimensional granular bed have been solved numerically by the finite element method. Two closures based on granular kinetic theory were used: one, the standard Fourier law relating heat flux to temperature gradient and the other, including an additional concentration gradient term. Each prediction of the two-dimensional axisymmetric granular temperature and packing fraction fields was compared against a one-dimensional model and three-dimensional experimental results, acquired using the technique of positron emission particle tracking. Both closures resulted in solutions that were in reasonable agreement with the experimental results, but it was found that differences between the predictions of each of the closures were relatively small in comparison to the anisotropy of the experimentally determined temperature distribution.

An experimental investigation of an idealized rapidly sheared granular flow was performed to test the predictions of a model based on the kinetic theory of dry granular media. Glass ballotini beads were placed in an annular shear cell and the lower boundary rotated to induce a shearing motion in the bed. A single particle was tracked using the positron emission particle tracking (PEPT) technique, a method that determines the location of a particle through the triangulation of gamma photons emitted by a radioactive tracer particle. The packing fraction and velocity fields within the three-dimensional flow were measured and compared to the predictions of a model developed using the conservation and balance equations applicable to dissipative systems, and solved incorporating constitutive relations derived from kinetic theory. The comparison showed that kinetic theory is able to capture the general features of a rapid shear flow reasonably well over a wide range of shear rates and confining pressures.

This study investigates the aerodynamic noise generated and radiated from a standard squareback body with various inclined side-view mirrors using a hybrid computational aeroacoustics method based on a stress-blended eddy simulation coupled with the Ffowcs-Williams and Hawkings acoustic analogy. The results indicate that in the absence of the side-view mirror, the idealized A-pillar is identified as the subsequent major contributor to the overall noise radiated from the vehicle body, and the coefficient of drag decreases by approximately 13.3% despite a minimal change in the projected frontal area. However, the behavior of the drag coefficient becomes nonlinear and highly dependent on the complex flow features, including the vortex shedding patterns and the interaction between the flow and side surface of the body, with increasing mirror inclination angle. In contrast, the radiated noise exhibits a constant decrease as the mirror inclination angle (θ) increases to 32°. Additionally, when the side-view mirror is considered as the sole source, the noise radiated is minimal for an inclination angle of 16°, and a further increase in inclination angle has no significant reduction on the noise radiated but alters the overall drag coefficient of the vehicle. These findings have practical implications for the design of side-view mirrors to reduce aerodynamic noise in automotive applications and highlight the complex tradeoffs between noise reduction and changes in the drag coefficient that must be considered in such designs.

We present numerical simulations of dripping to jetting transitions that occur during the flow of a Newtonian liquid. An axis-symmetric, Volume of Fluid (VOF) model along with Continuum Surface Force (CSF) representation is developed to capture various regimes of drop formation. By numerically studying different nozzle diameters subjected to various flow rates, we examine the critical conditions under which the dripping to jetting transition takes place. At every stage of dripping and jetting, we assess the accuracy of the present simulations through a number of comparisons with previously published experimental data and empirical correlation and find reasonable agreements. Our numerical simulations show different responses that characterize the dripping and the dripping faucet regimes leading to chaotic dripping patterns. Within the chaotic regime, we identify four unique modes of satellite formation and their merging patterns which have not been reported earlier. Finally, we observe that as soon as the flow rate approaches a threshold the jetting regime begins where, subsequent disintegration of drops and coalescence patterns are observed downstream. Detailed flow patterns, pressure distributions and drop shapes are provided for various dimensionless numbers alongside the spatial-temporal resolutions of both jetting and coalescence of primary drops. Of the many complex dynamics that influence the primary droplet coalescence, we find that the oscillatory motion of drops during their travel downstream, which is dampened normally due to viscous effects, can be influential and can aid both coalescence and breakup of droplets.

We study convective motion in vertically vibrated three-dimensional granular beds by comparing the predictions of a model based on a hydrodynamic description to Navier–Stokes order with experimental results obtained using positron emission particle tracking (PEPT). The three-dimensional conservation equations relating mass, momentum and energy are solved using the finite element (FE) method for a viscous vibrofluidized bed by using only observable system parameters such as particle number, size, mass and coefficients of restitution. The mean velocity profiles from the viscous model show reasonable agreement with the experimental results at relatively low altitudes for the range of experimental values studied, though the velocity fields at higher altitudes were systematically underestimated by the model. We confirm that the convection rolls are influenced by the sidewall coefficient of restitution and demonstrate the scaling relationships that operate, where increasing amplitude of vibration leads to a reduction in the angular velocity of the rolls.