Part I. The Surface Vorticity Boundary Integral Method of Fluid Flow Analysis: 1. The basis of surface singularity modelling 2. Lifting bodies, two-dimensional aerofoils and cascades 3. Mixed-flow and radial cascades 4. Bodies of revolution, ducts and annuli 5. Ducted propellers and fans 6. Three-dimensional and meridional flows in turbo-machines 7. Free vorticity shear layers and inverse methods Part II. Vortex Dynamics and Vortex Cloud Analysis: 8. Vortex dynamics in inviscid flows 9. Simulation of viscous diffusion in discrete vortex modelling 10. Vortex cloud modelling by the boundary integral method 11. Further development and applications of vortex cloud modelling to lifting bodies and cascades 12. Use of grid systems in vortex dynamics and meridional flows Appendix.

Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems: Vortex cloud modelling by the boundary integral method

Simulations of a vertical axis turbine in a channel

Two computationally fast fluid mechanical models for vertical axis turbines are the streamtube and the vortex model The streamtube model is the fastest, allowing three-dimensional modeling of the 

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Fluid Mechanics of Vertical Axis Turbines : Simulations and Model Development

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.

An unsteady, accelerated, high order panel method with vortex particle wakes

A Discrete Vortex Method has been developed at the Department of Aerospace Engineering,
University of Glasgow, to predict unsteady, incompressible, separated flows around closed
bodies. The basis of the method is the discretisation of the vorticity field, rather than the velocity field, into a series of vortex particles which are free to move in the flow. The grid free nature of the method allows analysis of a wide range of problems for both stationary and moving bodies. This paper presents a brief description of the method and presents the results of a validation programme on bluff bodies undergoing forced transverse oscillations. The results demonstrate that the method successfully predicts the vortex lock-in phenomena around the resonance point, as well as capturing the various states of the flow field expected above and below vortex lock-in. Results are presented for the fluctuating lift coefficients, surface pressure coefficients and phase angle, for a square cylinder undergoing transverse oscillations over a range of frequencies and amplitudes. The results from the vortex method show good agreement, both qualitatively and quantitatively, with results from various experimental data.

Calculation of the Flow Field around a Square Section Cylinder undergoing Forced Transverse Oscillations using a Discrete Vortex Method. G.U. Aero report 9814

A new two-dimensional panel technique has been developed to solve Laplacian flows, which eliminates the edge effect present in traditional panel methods. Such a method is very useful for applications where the velocity induced by the panels is required at arbitrary locations. Particle based flow solvers are a prime example. The method, however, requires considerably more computational effort. In this paper the method is modified to improve computational efficiency by adapting the fast multipole algorithm for the panel method. Significant improvement in computational efficiency is obtained while ensuring that the edge effects are eliminated.

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A Fast, Two-Dimensional Panel Method

Higher order panel methods are used to solve the Laplace equation in the presence of complex geometries. These methods are useful when globally accurate velocity or potential fields are desired as in the case of vortex based fluid flow solvers. This paper develops a fast multipole algorithm to compute velocity fields due to higher order, two-dimensional vortex panels. The technique is applied to panels having a cubic geometry and a linear distribution of vorticity. The results of the present method are compared with other available techniques.

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A Fast Multipole Method for Higher Order Vortex Panels in Two Dimensions

This paper details an efficient algorithm for particles undergoing random walks in the presence of complex, two-dimensional, solid boundaries. The scheme is developed for the simulation of vortex diffusion using the random vortex method. Both vortex blobs and sheets are handled. The relevant modifications for using the algorithm with the vorticity redistribution technique are also discussed. The algorithm is designed to be used in the framework of an existing fast multipole implementation. A measure for the geometric complexity of a body is introduced and the algorithm's efficiency is studied as various parameters are changed for bodies of varying complexity.

Efficient random walks in the presence of complex two-dimensional geometries

A method is developed to obtain quick engineering estimates for the normal load on slender airbreathing shapes. Estimates of the normal load can be obtained using a Trefftz plane analysis. This computation, although two-dimensional and subsonic, agrees fairly well with experimental data (from NASA and AGARD) for three-dimensional slender bodies in supersonic flows. The computational technique is simple and extremely fast.

S. C. Rajan

Papers

A Fast, Two-Dimensional Panel Method

A Fast Multipole Method for Higher Order Vortex Panels in Two Dimensions

Efficient random walks in the presence of complex two-dimensional geometries

Engineering Estimates of Normal Loads on Slender Airbreathing Bodies

Study of the unsteady pressure oscillations induced by rectangular cavities in a supersonic flow field