The turbulent rollup of a vortex generated by a rectangular wing has been investigated. Extensive mean and turbulence measurements of the flowfield on a wingtip and in the near field have been completed. Velocity fluctuation measurements show that the near-field core is not laminar. A large axial velocity excess was found to exist in the core of the vortex. A momentum balance in the near-field of the wingtip showed that the magnitude of the core Reynolds-stress gradient terms are the same order as the largest terms in the governing equations. Navier-Stokes computations of the identical configuration, including wind tunnel walls and using measured inflow and outflow boundary conditions, reproduced many of the features of the experiment. Inherent limitations of the Baldwin-Barth turbulence model combined with limited grid resolution caused the computed vortex core to be more diffuse than desired. The momentum balance also demonstrated that the level of numerically generated false diffusion in the vortex core is relatively high.
The near-field behavior of a wingtip vortex flow has been studied computationally and experimentally in an interactive fashion. The computational approach involved using the method of artificial compressibility to solve the three-dimensional, incompressible, Navier-Stokes equations with experimentally determined boundary conditions and a modified Baldwin-Barth turbulence model. Inaccuracies caused by the finite difference technique, grid resolution, and turbulence modeling have been explored. The complete geometry case was computed using 1.5 million grid points and compared with mean velocity measurements on the suction side of the wing and in the near wake. Good agreement between the computed and measured flowfields has been obtained. The velocity distribution in the vortex core compares to within 3% of the experiment.
The equations are represented in a simplified format with only a few leading terms needed in the expansion. The set of equations are then solved numerically using vector finite element method. To validate the algorithm, they analyzed a two-dimensional rectangular waveguide consisting of a linear core and nonlinear identical cladding. The exact nonlinear solutions for three different modes of propagations, TE0, TE1, and TE2 modes are generated and compared with the computed solutions. Next, they investigate the effect of a more intense monochromatic field on the propagation of a 'weak' optical field in a fully three-dimensional cylindrical waveguide.
This paper presents an overview and summary of the many different research work related to tip vortex flows and wake/trailing vortices as applied to practical engineering problems. As a literature survey paper, it outlines relevant analytical, theoretical, experimental and computational study found in literature. It also discusses in brief some of the fundamental aspects of the physics and its complexities. An appendix is also included. The topics included in this paper are: 1) Analytical Vortices; 2) Experimental Studies; 3) Computational Studies; 4) Wake Vortex Control and Management; 5) Wake Modeling; 6) High-Lift Systems; 7) Issues in Numerical Studies; 8) Instabilities; 9) Related Topics; 10) Visualization Tools for Vertical Flows; 11) Further Work Needed; 12) Acknowledgements; 13) References; and 14) Appendix.
The most widely accepted theories for the formation of the Solar system claim that small solid particles continue to settle into a thin layer at the midplane of the Solar nebula until it becomes gravitationally unstable and collapses directly into km-sized planetesimals. This scenario has been challenged on at least two grounds: (1) due to turbulence, the particles may not settle into a thin layer, and (2) a thin layer may not be unstable. The Solar nebula contains at least three sources of turbulence: radial shear, vertical shear, and thermal convection. The first of these is small and probably negligible, while the last is poorly understood. However, the second contribution is likely to be substantial. The particle-rich layer rotates at nearly the Keplerian speed, but the surrounding gaseous nebula rotates slower because it is partly supported by pressure. The resulting shear generates a turbulent boundary layer which stirs the particles away from the midplane, and forestalls gravitational instability. Our previous work used a 'zero-equation' (Prandtl) model to predict the intensity of shear-generated turbulence, and enabled us to demonstrate numerically that settling of particles to the midplane is self-limiting. However, we neglected the possibility that mass loading by particles might damp the turbulence. To explore this, we have developed a more sophisticated 'one-equation' model which incorporates local generation, transport, and dissipation of turbulence, as well as explicit damping of turbulence by particles. We also include a background level of global turbulence to represent other sources. Our results indicate that damping flattens the distribution of particles somewhat, but that background turbulence thickens the particle layer.
The accuracy of tip vortex flow prediction in the near-field region is investigated numerically by attempting to quantify the shortcomings of the turbulence models and the flow solver. In particular, some turbulence models can produce a 'numerical diffusion' that artificially smears the vortex core. Low-order finite differencing techniques of the convective and pressure terms of the Navier–Stokes equations and inadequate grid density and distribution can also produce the same adverse effect. The flow over a wing and the near-wake with the wind tunnel walls included was simulated using 2.5 million grid points. Two subset problems, one using a steady, three-dimensional analytical vortex, and the other, a vortex obtained from experiment and propagated downstream, were also devised in order to make the study of vortex preservation more tractable. The method of artificial compressibility is used to solve the steady, three-dimensional, incompressible Navier–Stokes equations. Two one-equation turbulence models (Baldwin–Barth and Spalart–Allmaras turbulence models), have been used with the production term modified to account for the stabilizing effect of the nearly solid body rotation in the vortex core. Finally, a comparison between the computed results and experiment is presented. Published in 1999 by John Wiley & Sons, Ltd.
The accuracy of tip vortex flow prediction in the near-field region is investigated numerically by attempting to quantify the shortcomings of the turbulence models and the flow solver. In particular, some turbulence models can produce a 'numerical diffusion' that artificially smears the vortex core. Low-order finite differencing techniques of the convective and pressure terms of the Navier–Stokes equations and inadequate grid density and distribution can also produce the same adverse effect. The flow over a wing and the near-wake with the wind tunnel walls included was simulated using 2.5 million grid points. Two subset problems, one using a steady, three-dimensional analytical vortex, and the other, a vortex obtained from experiment and propagated downstream, were also devised in order to make the study of vortex preservation more tractable. The method of artificial compressibility is used to solve the steady, three-dimensional, incompressible Navier–Stokes equations. Two one-equation turbulence models (Baldwin–Barth and Spalart–Allmaras turbulence models), have been used with the production term modified to account for the stabilizing effect of the nearly solid body rotation in the vortex core. Finally, a comparison between the computed results and experiment is presented. Published in 1999 by John Wiley & Sons, Ltd.
We study the effects of macroscopic bends and twists in an optical waveguide and how they influence the transmission capabilities of a waveguide. These mechanical stresses and strains distort the optical indicatrix of the medium, producing optical anistropy. The spatially varying refractive indices are incorporated into the full-wave Maxwell's equations. The governing equations are discretized by using a vector finite-element method cast in a high-order finite element approximation. This approach allows us to study the complexities of the mechanical deformation within a framework of a high-order formulation that can, in turn, reduce the computational requirement without degrading its performance. The optical activities generated, total energy produced, and power loss due to the mechanical stresses and strains are reported and discussed.
The usual theory of planetesimal formation is untenable because turbulence inhibits gravitational instability. However, turbulence can actually concentrate chondrule-sized particles by factors up to a million near stagnation points. The implications for accretion may be profound.
