Shengxiang Lin

Lattice structures have excellent mechanical properties and can be designed by changing the cellular structure. However, the computing scale is extremely large to directly analyze a large-size structure containing a huge number of lattice cells. Evaluating the equivalent mechanical properties instead of the complex geometry of such lattice cells is a feasible way to deal with this problem. This paper aims to propose a series of formulas, including critical structural and material parameters, to fast evaluate the equivalent mechanical properties of lattice structures. A reduced-order model based on the finite element method and beam theory was developed and verified by comparing it with the corresponding full model. This model was then applied to evaluate the equivalent mechanical properties of 25 types of lattice cells. The effects of the material Young’s modulus and Poisson’s ratio, strut diameter, cell size, and cell number on those equivalent mechanical properties were investigated and discussed, and the linear relationship with the material parameters and the non-linear relationship with the structural parameters were found. Finally, a series of analytical-fitting formulas involving the structural and material parameters were obtained, which allows us to fast predict the equivalent mechanical properties of the lattice cells.

The impact of fluid shear on the bubble distribution in channel flows with periodically oscillating pressure gradient is examined by direct numerical simulations. Equal-sized and nearly circular bubbles are placed randomly in the channel at the initial time. In the absence of shear, the bubbles form columns spanning the width of the channel, but a strong enough shear breaks up the columns, leading to a more random bubble distribution. The effect of the nondimensional shear rate on the flow can be divided into low shear rate, moderate shear rate, and high shear rate regimes. The flow dynamics is also influenced by the Reynolds and the Euler number, and when these numbers decrease, the low shear rate regime, with stable tilted columns of bubbles, becomes smaller. Comparison of results for two- and three-dimensional flows shows that the dynamics observed in two-dimensional flows is also found in three dimensions.

Direct numerical simulations of two-way oscillating bubbly flows in a domain bounded by solid walls are presented. Ignoring gravity, the two- and three-dimensional flows of equal-sized bubbles are driven by periodically oscillating pressure gradients in the X and Z directions with the same amplitude and frequency but different phases. The results show that the oscillations will drive the bubbles together, promoting coalescence. The results depend on the amplitude and frequency, resulting in “crawling” flow, “revolving” flow, and “oscillating” flow. As the amplitude increases, the critical frequency separating these three flow regions increases. For each amplitude, there is an optimum frequency near the transition region between the crawling flow and the revolving flow that yields the fastest coalescence. A qualitative comparison between two- and three-dimensional flows shows that the dynamics observed for the two-dimensional flows is also found in three-dimensions.