Flow Past a Fixed and Freely Vibrating Drilling Riser System with Auxiliaries in Laminar Flow

Drilling risers used in oil and gas operations are subjected to external loads such as wave and current. One of the phenomena that arise from the external loads is the Vortex-Induced Vibration (VIV), which affects the performance of the riser due to excessive vibration from the vortex shedding. A significant factor influencing the VIV is the design of the drilling riser and its auxiliary lines. Until now, the optimum geometrical size and gap between the auxiliary and the main riser are still very scarcely studied. In this paper, the main objective is to study the effects of the gap ratio (G/D) on the vortex shedding phenomenon on a fixed and freely vibrating riser. The riser system was modelled with a main drilling riser and six auxiliary lines with a constant diameter ratio (d/D) of 0.45 and gap ratio (G/D) = 0 to 2.0 in the laminar flow regime with Reynold Number, Re = 200. The simulations were conducted for Single Degree of Freedom (SDOF) using Computational Fluid Dynamics (CFD) software, Altair AcuSolve. It was found that the freely vibrating riser experienced higher lift and drag forces as compared to the fixed riser due to the synchronization (lock-in) of the shedding vibration and the natural frequencies. The lock-in phenomenon is normally observed on the drilling riser at different current directions. The forces are reduced when G/D is higher. The vortex shedding was significantly reduced for auxiliaries between 0.3 to 1.4. It is confirmed that by modifying the interaction of the vortices in the wake region with auxiliary lines, the hydrodynamic forces will be decreased. Finally, this fundamental study could potentially be used in the designing stage of an optimum drilling riser system by considering significant governing factors.

Self-Controlled Cleaving Method for Silicon DRIE Process Cross-Section Characterization

Advanced microsystems widely used in integrated optoelectronic devices, energy harvesting components, and microfluidic lab-on-chips require high-aspect silicon microstructures with a precisely controlled profile. Such microstructures can be fabricated using the Bosch process, which is a key process for the mass production of micro-electro-mechanical systems (MEMS) devices. One can measure the etching profile at a cross-section to characterize the Bosch process quality by cleaving the substrate into two pieces. However, the cleaving process of several neighboring deeply etched microstructures is a very challenging and uncontrollable task. The cleaving method affects both the cleaving efficiency and the metrology quality of the resulting etched microstructures. The standard cleaving technique using a diamond scriber does not solve this issue. Herein, we suggest a highly controllable cross-section cleaving method, which minimizes the effect on the resulting deep etching profile. We experimentally compare two cleaving methods based on various auxiliary microstructures: (1) etched transverse auxiliary lines of various widths (from 5 to 100 μm) and positions; and (2) etched dashed auxiliary lines. The interplay between the auxiliary lines and the etching process is analyzed for dense periodic and isolated trenches sized from 2 to 50 μm with an aspect ratio of more than 10. We experimentally showed that an incorrect choice of auxiliary line parameters leads to silicon “build-up” defects at target microstructures intersections, which significantly affects the cross-section profile metrology. Finally, we suggest a highly controllable defect-free cross-section cleaving method utilizing dashed auxiliary lines with the stress concentrators.

Multiple solution problems and mathematical thinking: Wasan geometry example

Wasan geometry flourished in Edo period of Japan as arty, multiple solutioned and systematic. Teachers are not open and papers are not evaluated. Multiple solutions are seen in parallel with advanced mathematics thinking. 80 middle school and 37 high school pre service math teachers were given a Wasan problem and grouped according to correct answers, different answers, and originality. 24 different answers (equality of diagonals of a square, symmetry, equality of tangent lines, auxiliary lines and auxiliary shapes, cosines’ theorem, tan (67.5), similarities, types of triangles etc.) were detected. Answers were also coded for composite answers (who include two different rules), or simple one ways, first answers, similar solution ways and 5-6 different solutions.