The present work is addressed to the Computational Analysis of a Passive Wake Alleviation Scheme, based on a basic and simple approach for a limited objective using desktop computer for educational purposes. To this end Biot-Savart Law and Vortex Lattice Method (VLM) are employed to calculate velocity field and visualization, which has been successfully carried out by Chao Liu’s [1] Wake Vortex Analysis and computational scheme Using Vortex-Lattice Method and with Different Wake Vortex Models. The work attempt to use the basics principles to study the flow situation in the near wake and far wake, by using Biot-Savart and different vortex models, and to visualize and compare the results with more sophisticated numerical and experimental results. McCauley et al’s [2] passive alleviation scheme will be utilized as the study model.

For this purpose, the wing set up used by McCauley will also be investigated. Outboard triangular flaps for passively inciting Crow-like instabilities in the trailing vortices will be considered. The computational studies thus carried will be limited to qualitative analyzes of the general wake features.

To assess the plausibility of the work and to assess the quantitative gap between experimental and computational results, comparison will be made to McCauleys spectral Navier-Stokes simulation used to analyze the evolution of the vortical structures in the wake for the calculation of the forces and rolling moments induced on a trailing wing. Further assessment will be made for the significant reductions in both downwash and rolling moment that will be clearly present in the numerical work, and on the magnitude and time scale of their correlation with recent experimental studies.

Four (4) different vortex profiles will be compared throughout their properties. The maximum induced rolling moment depends on the vortex model, the core radius and the vortex spacing. A short distance behind the wing of an aircraft the cross-flow kinetic energy of the vortex pair is directly related to the induced drag of the wing and this provides a condition for the initial vortex core size.

The decay of the vortex core radius can be calculated with an effective viscosity turbulence model; the decay of the wake vortex circulation and decay of induced rolling moment can be obtained. For different vortex models, all the different decays are compared numerically.

The flow induced by a vortex filament can be expressed using Biot-Savart law as the increment of the velocity dV at a point p due to a segment of a vortex filament dl at point q is.

A special form of vortex which is used in the vortex lattice method is the horseshoe vortex. The horseshoe is actually a simplified case of the vortex ring. It consists of four vortex filaments. The two trailing vortex segments AB and CD are placed parallel to the x axis and start in infinity. Two finite vortex segments BC and AD. Normally the effects of AD can be neglected because of the infinite distance, in practice the horseshoe vortex contains three parts. The straight bound vortex segment BC models the lifting properties and the two semi-infinite trailing vortex lines model the wake.

The velocity field calculation is carried out using in-house MATLAB® program. Earlier in-house developed program has successfully produced wake geometry results.

The four vortex models considered are the Rankine, Lamb-Oseen, Winckelmans and Jacquin vortex models [2]. The Rankine vortex is the result of a discontinuous combination of two solutions of the 2D anti-symmetrical vorticity equation with circular streamlines. It is combined of the pure rotational region and a pure circulation region. The inner part of the vortex is in solid rotation, then its modulus is proportional to r, while the outer part is inversely proportional to the radial distance r.

The maximum intensity of the flow is reached at the characteristic distance of the vortex, where there is the change between the inner linear behavior and the external hyperbolic one. The Lamb-Oseen vortex model is a solution to the one-dimensional laminar Navier-Stokes equations, i.e. an antisymmetric solution for the swirl velocity with the assumption that the axial (streamwise) and radial velocities are zero. It is the result of normalizing a Gaussian vortex in such a way that the peak velocity occurs at the core radius. Winckelmans vortex model is a high order algebraic model proposed by Winckelmans.

The Jacquin VM2 model is a modification of the original Jacquin VM1 model which uses two length scales. According to Jacquin the inner length scale a1 is related to the ”inner” vortex core and a2 is related to the ”outer” vorticity region.

Some basic results will be compared with similar one, like the one from McCauley. Attention is also given in the choice of turbulence model in the CFD simulation. An appropriate model out of a host of available turbulence models developed to date has to be chosen. Judging from its generic clarity and user-friendliness, the k ˗ ε turbulence model is adopted, without disregarding other models that may be suitable for the purpose of the present work. Although turbulence model, especially its implementation for the near-wall treatment, has been considered by some authors still to incorporate a mystery, its numerical implementation has a decisive inﬂuence on the quality of simulation results. In particular, a positivity-preserving discretization of the troublesome convective terms is an important prerequisite for the robustness of the numerical algorithm [5]. Of particular concern in validating the CFD numerical simulation, the wall functions can be used to inspect the plausibility in CFD modelling. The wall functions will be chosen such that the computational domain is assumed to start at a distance y from the wall.

References:

1. Gregory J. McCauley, Philip S. Marcus, Omer Savas, Computational Analysis of a Passive Wake Alleviation Scheme, AIAA 2006-2820, 24th Applied Aerodynamics Conference 5 - 8 June 2006, San Francisco, California

2. Chao Liu, Wake Vortex Encounter Analysis with Different Wake Vortex Models Using Vortex-Lattice Method A numerical study, MSc, TU Delft, November 2007

3. Harijono Djojodihardjo, Combined Scalar And Vector Velocity Potential in Acousto-Aeroelastic Problem, ICAS2010-687, Nice, 2010

4. Harijono Djojodihardjo, Unsteady Aerodynamics of Lifting Body Using Combined Boundary Element Method and Vortex Particle Approach, IFASD2011, Paris, 2011

5. Harijono Djojodihardjo, Mohd Faisal Abdul Hamid and Surjatin Wiriadidjaja, Two-Dimensional CFD Visualization Studies Of Coandă Jet For Aerodynamic Performance Improvements, Proceedings, ASV12, Tainan, 2012

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