Wake curvature and trailing edge interaction effects in viscous flow over airfoils

A theory developed for analyzing viscous flows over airfoils at high Reynolds numbers is described. The theory includes a complete treatment of viscous interaction effects induced by the curved wake behind the airfoil and accounts for normal pressure gradients across the boundary layer in the trailing edge region. A brief description of a computer code that was developed to solve the extended viscous interaction equations is given. Comparisons of the theoretical results with wind tunnel data for two rear loaded airfoils at supercritical conditions are presented

Asymptotic theory of two-dimensional trailing-edge flows

Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient

Taxing the "Family" in the Individual Income Tax

In this paper we examine international practices in the ways in which the individual income tax is applied to families, focusing upon country practices in OECD countries. We find that countries differ significantly in their taxation of the family, but that the dominant practice is the choice of the individual rather than the family as the unit of taxation. We also calculate the income tax consequences for "representative" taxpayers across these countries, and find that the differences in taxes between singles and married couples can often be quite large. We conclude that choosing the individual as the tax unit is likely to represent the most equitable approach to income taxation, especially given the increasing complexity of family units in modern societies

Shape Memory Alloy Nanostructures With Coupled Dynamic Thermo-Mechanical Effects

Employing the Ginzburg-Landau phase-field theory, a new coupled dynamic thermo-mechanical 3D model has been proposed for modeling the cubic-to-tetragonal martensitic transformations in shape memory alloy (SMA) nanostructures. The stress-induced phase transformations and thermo-mechanical behavior of nanostructured SMAs have been investigated. The mechanical and thermal hysteresis phenomena, local non-uniform phase transformations and corresponding non-uniform temperature and deformations distributions are captured successfully using the developed model. The predicted microstructure evolution qualitatively matches with the experimental observations. The developed coupled dynamic model has provided a better understanding of underlying martensitic transformation mechanisms in SMAs, as well as their effect on the thermo-mechanical behavior of nanostructures.Comment: 8 pages, 3 figure