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Using high-resolution 3-D vortex simulations, this study seeks a mechanistic understanding of vorticity dynamics in transverse jets at a finite Reynolds number. A full no-slip boundary condition, rigorously formulated in terms of vorticity generation along the channel wall, captures unsteady interactions between the wall boundary layer and the jet – in particular, the separation of the wall boundary layer and its transport into the interior. For comparison, we also implement a reduced boundary condition that suppresses the separation of the wall boundary layer away from the jet nozzle. By contrasting results obtained with these two boundary conditions, we characterize near-field vortical structures formed as the wall boundary layer separates on the backside of the jet. Using various Eulerian and Lagrangian diagnostics, it is demonstrated that several near-wall vortical structures are formed as the wall boundary layer separates. The counter-rotating vortex pair, manifested by the presence of vortices aligned with the jet trajectory, is initiated closer to the jet exit. Moreover tornado-like wall-normal vortices originate from the separation of spanwise vorticity in the wall boundary layer at the side of the jet and from the entrainment of streamwise wall vortices in the recirculation zone on the lee side. These tornado-like vortices are absent in the case where separation is suppressed. Tornado-like vortices merge with counter-rotating vorticity originating in the jet shear layer, significantly increasing wall-normal circulation and causing deeper jet penetration into the crossflow stream., United States. Dept. of Energy. Office of Science (MICS) (Grant Number DE-FG02-98ER25355)

We study the convergence characteristics of two algebraic kernels used in vortex calculations: the Rosenhead–Moore kernel, which is a low-order kernel, and the Winckelmans–Leonard kernel, which is a high-order kernel. To facilitate the study, a method of evaluating particle-cluster interactions is introduced for the Winckelmans–Leonard kernel. The method is based on Taylor series expansion in Cartesian coordinates, as initially proposed by Lindsay and Krasny [J. Comput. Phys., 172 (2001), pp. 879–907] for the Rosenhead–Moore kernel. A recurrence relation for the Taylor coefficients of the Winckelmans–Leonard kernel is derived by separating the kernel into two parts, and an error estimate is obtained to ensure adaptive error control. The recurrence relation is incorporated into a tree-code to evaluate vorticity-induced velocity. Next, comparison of convergence is made while utilizing the tree-code. Both algebraic kernels lead to convergence, but the Winckelmans–Leonard kernel exhibits a superior convergence rate. The combined desingularization and discretization error from the Winckelmans–Leonard kernel is an order of magnitude smaller than that from the Rosenhead–Moore kernel at a typical resolution. Simulations of vortex rings are performed using the two algebraic kernels in order to compare their performance in a practical setting. In particular, numerical simulations of the side-by-side collision of two identical vortex rings suggest that the three-dimensional evolution of vorticity at finite resolution can be greatly affected by the choice of the kernel. We find that the Winckelmans–Leonard kernel is able to perform the same task with a much smaller number of vortex elements than the Rosenhead–Moore kernel, greatly reducing the overall computational cost., U.S. Department of Energy, Mathematical, Information, and Computational Sciences (MICS) program (DE-FG02-98ER25355)

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, June 2007., Includes bibliographical references (p. 89-91)., This thesis describes progress in several areas related to three dimensional vortex methods and their application to multiphysics problems. The first is the solution of a generic scalar transport equation by advecting and diffusing the scalar gradient along a particle trajectory and onto a mesh, respectively, and recovering the scalar values using a Biot-Savart-like summation. The second is the accurate, high-resolution calculation of the velocity gradient using a fast treecode, which avoids using kinematic relations between the evolution of the gradients and the distortion of the flow map. The same tree structure is used to compute all the variables of interest and those required during the integration of the governing equations. Next, we apply our modified interpolation kernel algorithm for treating diffusion and remeshing to maintain long time accuracy. The coupling between the vorticity transport and that of a dynamic scalar, in this case the temperature or density in a gravitational field, is manifested by the generation of vorticity. We demonstrate the performance of the multiphysics algorithm by solving a number of buoyant and reacting flow problems., by Fabrice Schlegel., S.M.