On the Lagrangian description of unsteady boundary layer separation. Part 2: The spinning sphere

A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time

SFF-Oriented Modeling and Process Planning of Functionally Graded Materials Using a Novel Equal Distance Offset Approach

This paper deals with the modeling and process planning of solid freeform fabrication (SFF) of 3D functionally graded materials (FGMs). A novel approach of representation and process planning of FGMs, termed as equal distance offset (EDO), is developed. In EDO, a neutral arbitrary 3D CAD model is adaptively sliced into a series of 2D layers. Within each layer, 2D material gradients are designed and represented via dividing the 2D shape into several sub-regions enclosed by iso-composition contours. If needed, the material composition gradient within each of sub-regions can be further determined by applying the equal distance offset algorithm to each sub-region. Using this approach, an arbitrary-shaped 3D FGM object with linear or non-linear composition gradients can be represented and fabricated via suitable SFF machines.Mechanical Engineerin

A Theoretical Model for Optimization of SALD Parameters

This paper addresses the need to conduct theoretical work concerning an economical way of Solid Freeform Fabrication rendering by using selective Area Laser Deposition (SALD). The part in SALD rendering process is formed layer by layer that, in turn, is composed of stripes of material produced in the path of a laser. There are three situations in which such a stripe can be rendered: a) alone, b) with one neighbor on one side, and c) with neighbors on both sides. Residual thermal stresses in the part are expected to be affected by how a stripe is rendered. Furthermore, the residual thermal stress and the mechanical property of the part are also dictated by other processing variables such as laser scanning patters, laser input power, scanning speed, scanning spacing, deposition temperature, gas precursor pressure, intrinsic thermal conductivity and mechanical properties of the rendered material. A theoretical approach is proposed to address the minimization of residual thermal stresses and rendering times and the maximization of the strength of the part. It is proposed that such multiple optimizations that are dictated by many decision variables can be solved by minimizing and/or maximizing object functions dePending on the design criteria for each attribute of the rendered partMechanical Engineerin

On the Jacobi-Metric Stability Criterion

We investigate the exact relation existing between the stability equation for the solutions of a mechanical system and the geodesic deviation equation of the associated geodesic problem in the Jacobi metric constructed via the Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical approaches to the stability/instability problem are not equivalent.Comment: 14 pages, no figure

Preparation and Properties of In-Situ Devices Using the SALD and SALDVI Techniques

One of the many advantages of Selective Area Laser Deposition (SALD) and Selective Area Laser Deposition Vapor Infiltration (SALDVI) is that they can be used to embed in-situ micro-sensors within macro-components. A single-point SiC/C thermocouple sensor embedded within a SiC macro-component and electrically insulated with silicon nitride layers has been demonstrated. In many applications, multi-point sensors within a single component are needed, e.g., in monitoring the temperature gradient and distribution at different positions. In this paper, multi-point thermocouple devices are demonstrated. The macro-component is a SiC bulk shape made by infiltrating vapor deposited silicon carbide into a silicon carbide powder bed using the SALDVI technique. Multiple SiC/C thermocouples are embedded in-situ in the SiC bulk shape using the SALD technique. The transient and steady state responses ofthe embedded thermocouples are compared to reference thermocouples probing the surfaces of the bulk shape.Mechanical Engineerin