Fiber Bundle Topology Optimization for Surface Flows

This paper presents a topology optimization approach for the surface flows on variable design domains.Via this approach,the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized,where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold.The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle.The material distribution method is used to achieve the evolution of the pattern of the surface flow.The evolution of the implicit 2-manifold is realized via a homeomorphous map.The design variable of the pattern of the surface flow and that of the implicit 2-manifold are regularized by two sequentially implemented surface-PDE filters.The two surface-PDE filters are coupled,because they are defined on the implicit 2-manifold and base manifold,respectively.The surface Navier-Stokes equations,defined on the implicit 2-manifold,are used to describe the surface flow.The fiber bundle topology optimization problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space.Several numerical examples have been provided to demonstrate this approach,where the combination of the viscous dissipation and pressure drop is used as the design objective.

Vertical vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock

An axisymmetrical analytical solution is developed to investigate the vertical time-harmonic vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock. The soil is described by porous medium model established by Boer, while the pile is described by a beam vibration theory. By using separation theory of differential operator and variables to solve the dynamic governing equations for the soil, the fundamental solutions for the soil reactions on side and bottom of the pile are obtained. The dynamic impedance of the pile head is then derived by solving the vibration equation for the pile according to the compatibility condition between the pile and the soil. The proposed model is validated by comparing special cases of our model with the existing results. Numerical examples are presented to analyze the vibration characteristics of the pile.

Effects of Geometry on Leakage Flow Characteristics of Brush Seal

In order to better application of brush seal in rotating machinery,the leakage flow characteristics of the brush seal considering geometry effects are numerically analyzed using Reynolds-Averaged Navier-Stokes( RANS) model coupling with a non-Darcian porous medium model. The reliability of the present numerical method is proved,which is in agreement with the experimental and numerical results from literatures. Three different bristle pack thicknesses,fence heights and initial clearances under different pressure ratios,rotational velocities and other operating conditions are utilized to investigate the effects of geometry modification on the brush seal leakage flow behaviors. It discusses the effectiveness of various geometry configurations outlining important flow features. The results indicate that the increase of fence height and clearance would lead to the increase of leakage rate. But the leakage is not linearly with respect to the bristle pack thickness,and the effect of rotational velocity is not obvious. Moreover,the detailed leakage flow fields and pressure distributions along the rotor surface,free bristle height,and fence height of the brush seals are also presented. The static pressure drop amplitude through the bristle pack and the pressure rise amplitude through the cavity would increase while the pressure differential increases. And the axial pressure is the main reason of bristle blow down. The results provide theoretical support for the brush seal structure optimal design.