Over the last forty or so years interest in the study of wing-tip vortices has increased, primarily due to the introduction of larger passenger aircraft and their subsequent interaction with smaller aircraft. The vortices generated by these larger aircraft present a problem in two main areas; the wake hazard problem, where other aircraft can be subjected to the large tangential velocities of the vortex, and the interaction with ground based features of vortices created during landing and take-off. The first of these is particularly dangerous close to the ground when aircraft are in a high lift configuration at take-off and landing. As the vortices effectively scale with aircraft wing span, significant encounters between large vortices and smaller aircraft have been documented over the years. An example of one such documented wake vortex interaction incident can be found in Ogawa. In this study, the system of vortices are described as classical Batchelor vortices (or linear superpositions thereof) which are then subjected to small perturbations. By discretising the domain and solving for the eigenvalues of the system it is possible to ascertain the stability characteristics of the flow as a function of the system parameters which include the axial wave-number, the spacing of the vortices, their cross-flow decay rate and their axial strength. We first consider the inviscid instability of multiple tip vortices, an approximation which is valid in the limit of large Reynolds numbers. In this limit the stability of the flow is dominated by the axial component of the basic vortex flow. The governing equations of continuity and momentum are reduced to a second order partial differential equation (PDE). This equation is solved numerically to determine which vortex configurations produce the greatest instability growth rate. These results are extended to consider the effect of compressibility on the inviscid instability. Finally we consider the effects of viscosity on the stability of the full Batchelor similarity solution which results in a second order PDE in four dependent variables. The stability equations are solved both globally (for the entire eigenspectra) and locally (for a single eigenvalue in a pre-determined region) using codes that run in both serial and parallel form. The numerical methods are based on pseudospectral discretisation (Chebyshev polynomials for Cartesian and radial directions and Fourier for azimuthal) in the global scheme, the eigenvalues being recovered either with a QZ algorithm or a shift-and-invert Arnoldi algorithm. For the local scheme, fourth order centred finite-diffences are used in conjunction with an iterative eigenvalue recovery method. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1383207 / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2010

Over the last forty or so years interest in the study of wing-tip vortices has increased, primarily due to the introduction of larger passenger aircraft and their subsequent interaction with smaller aircraft. The vortices generated by these larger aircraft present a problem in two main areas; the wake hazard problem, where other aircraft can be subjected to the large tangential velocities of the vortex, and the interaction with ground based features of vortices created during landing and take-off. The first of these is particularly dangerous close to the ground when aircraft are in a high lift configuration at take-off and landing. As the vortices effectively scale with aircraft wing span, significant encounters between large vortices and smaller aircraft have been documented over the years. An example of one such documented wake vortex interaction incident can be found in Ogawa. In this study, the system of vortices are described as classical Batchelor vortices (or linear superpositions thereof) which are then subjected to small perturbations. By discretising the domain and solving for the eigenvalues of the system it is possible to ascertain the stability characteristics of the flow as a function of the system parameters which include the axial wave-number, the spacing of the vortices, their cross-flow decay rate and their axial strength. We first consider the inviscid instability of multiple tip vortices, an approximation which is valid in the limit of large Reynolds numbers. In this limit the stability of the flow is dominated by the axial component of the basic vortex flow. The governing equations of continuity and momentum are reduced to a second order partial differential equation (PDE). This equation is solved numerically to determine which vortex configurations produce the greatest instability growth rate. These results are extended to consider the effect of compressibility on the inviscid instability. Finally we consider the effects of viscosity on the stability of the full Batchelor similarity solution which results in a second order PDE in four dependent variables. The stability equations are solved both globally (for the entire eigenspectra) and locally (for a single eigenvalue in a pre-determined region) using codes that run in both serial and parallel form. The numerical methods are based on pseudospectral discretisation (Chebyshev polynomials for Cartesian and radial directions and Fourier for azimuthal) in the global scheme, the eigenvalues being recovered either with a QZ algorithm or a shift-and-invert Arnoldi algorithm. For the local scheme, fourth order centred finite-diffences are used in conjunction with an iterative eigenvalue recovery method. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1383207 / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2010

The primary purpose of this thesis is to quantify the effects of RANS turbulence modeling on the resolution of free shear vortical flows. The simulation of aerodynamic wing-tip vortices is used as a test bed. The primary configuration is flow over an isolated finite wing with aspect ratio, , and Reynolds number, . Tip-vortex velocity profiles, vortex core and wake turbulence levels, and Reynolds stresses are compared with wind tunnel measurements. Three turbulence models for RANS closure are tested: the Lumley, Reece, and Rodi full Reynolds stress transport model and the Sparlart-Allmaras model with and without a proposed modification. The main finding is that simulations with the full Reynolds stress transport model show remarkable mean flow agreement in the vortex and wake due to the proper prediction of a laminar vortex core. Simulations with the Spalart-Allmaras model did not indicate a laminar core and predicted over-diffusion of the tip-vortex. Secondary investigations in this work include the study of wall boundary layer treatment and simulating the wake-age of an isolated rotorcraft in hover using a steady-state RANS solver. By comparing skin friction plots over the NACA 0012 airfoil, it is shown that wall functions are most effective in the trailing edge half of the airfoil, while high velocity gradient and curvature of the leading edge make them more vulnerable to discrepancies. The rotorcraft simulation uses the modified Spalart-Allmaras turbulence model and shows proper, qualitative, resolution of the interaction between the vortex sheet and the tip vortex. / Master of Science

An isolated wing-tip vortex from a square-tipped NACA 0012 wing at an angle of attack of 5 degrees was studied in a water tunnel at a chord based Reynolds number of approximately 24000. Measurements were taken using stereo particle image velocimetry at three measurement planes downstream of the wing under each of three freestream turbulence conditions. The amplitude of wandering of the vortex axis increased with increasing distance downstream of the wing and with increasing freestream turbulence intensity. The magnitude of the peak azimuthal velocity decreased with increasing distance from the wing as well as with increases in the freestream turbulence intensity. The streamwise velocity in the vortex core was less than the freestream velocity in all cases. Time resolved histories of the instantaneous waveform shape and location of the vortex axis were determined from sequences of images of fluorescent dye released from the wing.

An isolated wing-tip vortex from a square-tipped NACA 0012 wing at an angle of attack of 5 degrees was studied in a water tunnel at a chord based Reynolds number of approximately 24000. Measurements were taken using stereo particle image velocimetry at three measurement planes downstream of the wing under each of three freestream turbulence conditions. The amplitude of wandering of the vortex axis increased with increasing distance downstream of the wing and with increasing freestream turbulence intensity. The magnitude of the peak azimuthal velocity decreased with increasing distance from the wing as well as with increases in the freestream turbulence intensity. The streamwise velocity in the vortex core was less than the freestream velocity in all cases. Time resolved histories of the instantaneous waveform shape and location of the vortex axis were determined from sequences of images of fluorescent dye released from the wing.