A Closure for the Virtual Origin of Turbulent Plumes

An isolated source of surface buoyancy, be it a campfire or burning city, gives rise to a turbulent plume. Well above the surface, the plume properties asymptote to the well-known solutions of Morton, Taylor, and Turner (MTT), but a closure is still lacking for the virtual origin. A closure for the virtual origin is sought here in the case of a turbulent plume sustained by a circular source of surface buoyancy in an unstratified and unsheared fluid. In the high Reynolds number limit, it is argued that all such plumes asymptote to a single solution. Direct numerical simulation (DNS) of this solution exhibits a virtual origin located a distance below the surface equal to 1.1 times the radius of the buoyancy source. This solution is compared to the previously used assumption that the MTT plume is fully spun-up at the surface, and that assumption is found to give buoyancies that are off by an order of magnitude. With regards to the citywide firestorm triggered by the nuclear attack on Hiroshima, it is found that the spun-up-at-surface MTT solution would have trapped radioactive soot within about a hundred meters of the surface, whereas the DNS solution presented here corroborates observations of the plume reaching well into the troposphere.

Treadmill-to-Overground Mapping of Marker Trajectory for Treadmill-Based Continuous Gait Analysis

A treadmill was used to perform continuous walking tests in a limited space that can be covered by marker-based optical motion capture systems. Most treadmill-based gait data are analyzed based on gait cycle percentage. However, achieving continuous walking motion trajectories over time without time normalization is often required, even if tests are performed under treadmill walking conditions. This study presents a treadmill-to-overground mapping method of optical marker trajectories for treadmill-based continuous gait analysis, by adopting a simple concept of virtual origin. The position vector from the backward moving virtual origin to a targeted marker within a limited walking volume is the same as the position vector from the fixed origin to the forward moving marker over the ground. With the proposed method, it is possible (i) to observe the change in physical quantity visually during the treadmill walking, and (ii) to obtain overground-mapped gait data for evaluating the accuracy of the inertial-measurement-unit-based trajectory estimation. The accuracy of the proposed method was verified from various treadmill walking tests, which showed that the total travel displacement error rate was 0.32% on average.

Research on an automatic leveling method with a feedback mode for a parallel 3D printer

Purpose The purpose of this study is to propose an automatic leveling method for a printing platform based on a three-point coordinate feedback. The proposed method is used in fused deposition modeling additive manufacturing systems. The coordinate error of the leveled plane is constrained to within  ± 0.2 mm, which is less than the printed layer thickness. Design/methodology/approach First, the model of the forward and inverse solutions of the parallel arm is obtained based on the principles of vector algebra. Second, the automatic leveling mechanism for collecting the z-coordinate is designed. The best position of the virtual origin plane is obtained by comparing the z-coordinates of the test points. Finally, after making multiple adjustments through a closed-loop z-coordinate feedback, the parallelism of the printing plane and the virtual origin plane is limited to an effective range. Findings The experimental results show that after three leveling attempts, the z-coordinate of the test points can be constrained to within  ± 0.2 mm, which shows that this method can effectively achieve automatic leveling in a delta three-dimensional (3D) printer. Originality/value This study presents a novel and distinctive delta 3D printer leveling system by designing a leveling mechanism and a leveling algorithm. The method uses a closed-loop feedback mode to make the leveling process simple, convenient and efficient without requiring major changes to the printer. The error after leveling is less than the printed layer thickness, which fully guarantees the accuracy of the leveling process.

The effect of slip and surface texture on turbulence over superhydrophobic surfaces

Superhydrophobic surfaces are able to entrap gas pockets in between surface roughness elements when submerged in water. These entrapped gas pockets give these surfaces the potential to reduce drag due to the overlying flow being able to locally slip over the gas pockets, resulting in a mean slip at the surface. In this work we assess the separate effects that surface slip and surface texture have on turbulence over superhydrophobic surfaces. We show that the direct effect of surface slip does not modify the dynamics of the overlying turbulence, which remains canonical or smooth-wall like. The surface drag is governed by the difference between two virtual origins, the virtual origin of the mean flow and the virtual origin experienced by the overlying turbulence, in an extension of the theory from Luchini, Manzo & Pozzi (J. Fluid Mech., vol. 228, 1991, pp. 87–109) for riblets. Streamwise slip deepens the virtual origin of the mean flow, while spanwise slip deepens the virtual origin perceived by the overlying turbulence. Drag reduction is then proportional to the difference between the two virtual origins. We decompose the near-wall flow into background-turbulence and texture-coherent components, and show that the background-turbulence component experiences the surface as homogeneous slip lengths. The validity of the slip-length model can then be extended to larger texture size $L^{+}$ than thought in previous studies. For $L^{+}\gtrsim 25$, however, we observe that a nonlinear interaction with the texture-coherent flow develops that alters the dynamics of the background turbulence, exhibiting a modified distribution of turbulent energy across length scales. This has the effect of reducing the velocity increment $\unicode[STIX]{x0394}U^{+}$ compared to that predicted using homogeneous slip lengths and sets the upper limit of applicability of slip-length models.