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

Viscous wing theory development. Volume 1: Analysis, method and results

Viscous transonic flows at large Reynolds numbers over 3-D wings were analyzed using a zonal viscid-inviscid interaction approach. A new numerical AFZ scheme was developed in conjunction with the finite volume formulation for the solution of the inviscid full-potential equation. A special far-field asymptotic boundary condition was developed and a second-order artificial viscosity included for an improved inviscid solution methodology. The integral method was used for the laminar/turbulent boundary layer and 3-D viscous wake calculation. The interaction calculation included the coupling conditions of the source flux due to the wing surface boundary layer, the flux jump due to the viscous wake, and the wake curvature effect. A method was also devised incorporating the 2-D trailing edge strong interaction solution for the normal pressure correction near the trailing edge region. A fully automated computer program was developed to perform the proposed method with one scalar version to be used on an IBM-3081 and two vectorized versions on Cray-1 and Cyber-205 computers

A comparative study of the nonuniqueness problem of the potential equation

The nonuniqueness problem occurring at transonic speeds with the conservative potential equation is investigated numerically. The study indicates that the problem is not an inviscid phenomenon, but results from approximate treatment of shock waves inherent in the conservative potential model. A new bound on the limit of validity of the conservative potential model is proposed

An improved viscid/inviscid interaction procedure for transonic flow over airfoils

A new interacting boundary layer approach for computing the viscous transonic flow over airfoils is described. The theory includes a complete treatment of viscous interaction effects induced by the wake and accounts for normal pressure gradient effects across the boundary layer near trailing edges. The method is based on systematic expansions of the full Reynolds equation of turbulent flow in the limit of Reynolds numbers, Reynolds infinity. Procedures are developed for incorporating the local trailing edge solution into the numerical solution of the coupled full potential and integral boundary layer equations. Although the theory is strictly applicable to airfoils with cusped or nearly cusped trailing edges and to turbulent boundary layers that remain fully attached to the airfoil surface, the method was successfully applied to more general airfoils and to flows with small separation zones. Comparisons of theoretical solutions with wind tunnel data indicate the present method can accurately predict the section characteristics of airfoils including the absolute levels of drag

Ascent of volatile-rich felsic magma in dykes:a numerical model applied to deep-sourced porphyry intrusions

Dyke propagation is a mechanism for more rapid ascent of felsic magmas through the crust than is possible via diapirs or percolative flow. As it ascends, the magma undergoes complex physical and chemical transformations induced by decompression and cooling. These processes dramatically change the magma density and viscosity, which in turn affect magma ascent rate and the depth at which the dyke arrests. We present a mathematical model of dyke propagation for silicic magmas taking into account the presence of multiple volatile species (H2O and CO2), bubble growth, heat advection and loss, crystallization and latent heat release. We consider conditions for dykes associated with porphyry ore deposits, which may represent an end-member in rapid ascent of felsic magmas from depth. In particular, we simulate the propagation of dykes launched from a deep (900 MPa), volatile-saturated magma source, testing the effects of the magma H2O/CO2 content, temperature and mass on its ascent rate and final emplacement depth. The model predicts short ascent times (hours to days), with a large increase in viscosity at shallow depth, leading to stagnation and solidification of the dyke. Higher initial water content, higher temperature and larger mass of the magma in the dyke promote faster propagation and shallower arrest. Volatile loss from ascending magma remains limited until the stagnation depth, providing a potential mechanism for transfer of deep volatiles to hypabyssal blind intrusions associated with porphyry ore deposits. Our findings are applicable to the problem of silicic magma ascent through the crust more generally

High speed video capture for mobile phone cameras

We consider an electromechanical model for the operation of a voice coil motor in a mobile phone camera, with the aim of optimizing how a lens can be moved to a desired focusing motion. Although a methodology is developed for optimizing lens shift, there is some concern about the experimentally-determined model parameters that are at our disposal. Central to the model is the value of the estimated magnetic force constant, Kf: its value determines how far it is actually possible to move lens, but it appears that, from the value given, it would not be possible to shift the lens through the displacements desired. Furthermore, earlier experiments have also estimated the value of the back EMF constant, Kg , to be roughly five times greater than Kf, even though we present two theoretical arguments that show that Kf = Kg: a conclusion supported by readily-available manufacturers’ data

Spin-orbit interaction in three-dimensionally bounded semiconductor nanostructures

The structural inversion asymmetry-induced spin-orbit interaction of conduction band electrons in zinc-blende and wurtzite semiconductor structures is analysed allowing for a three-dimensional (3D) character of the external electric field and variation of the chemical composition. The interaction, taking into account all remote bands perturbatively, is presented with two contributions: a heterointerface term and a term caused by the external electric field. They have generally comparable strength and can be written in a unified manner only for 2D systems, where they can partially cancel each other. For quantum wires and dots composed of wurtzite semiconductors new terms appear, absent in zinc-blende structures, which acquire the standard Rashba form in 2D systems.Comment: 18 pages, 1 figur

Peculiar Features of the Velocity Field of OB Associations and the Spiral Structure of the Galaxy

Some of the peculiar features of the periodic velocity-field structure for OB associations can be explained by using the model of Roberts and Hausman (1984), in which the behavior of a system of dense clouds is considered in a perturbed potential. The absence of statistically significant variations in the azimuthal velocity across the Carina arm, probably, results from its sharp increase behind the shock front, which is easily blurred by distance errors. The existence of a shock wave in the spiral arms and, at the same time, the virtually free motion of OB associations in epicycles can be reconciled in the model of particle clouds with a mean free path of 0.2-2 kpc. The velocity field of OB associations exhibits two appreciable nonrandom deviations from an ideal spiral pattern: a 0.5-kpc displacement of the Cygnus- and Carina-arm fragments from one another and a weakening of the Perseus arm in quadrant III. However, the identified fragments of the Carina, Cygnus, and Perseus arms do not belong to any of the known types of spurs.Comment: 14 pages, 3 postscript figures, to be published in Astronomy Letter