Session: 01-08-01: Flow-Induced Noise and Vibration

Paper Number: 112402

112402 - Singularity Based Method for Small Perturbation Unsteady Aerodynamics Using Higher Fidelity Steady State Pressure Profiles 

Singularity methods are Lagrangian or mesh-free and relatively low-cost methods for computational fluid mechanics. These methods were developed in the 1930’s by Rosenhead (1931) and 1940’s by Falkner (1943) to study high Reynolds number, potential flows, but gained momentum in the 1970’s and 1980’s with the rise of computers because of their relative simplicity and remarkable accuracy (Magason &Lamar, 1971). Much research was conducted on numerical issues inherent to singularity methods including convergence and accuracy (for instance James (1972), Hunt (1973), wake roll-up (Krasny, 1987), and the use of a free-wake model instead of a prescribed wake model, wake contraction / alignment (for example, Rusak, et al., 1985), viscous effects (Ahmad, et al., 2014 and Epps, et al., 2019), boundary layer in coupled Computational Fluid Dynamics (CFD)/ Vortex Method approaches (Drela, , 1989). Although, historically, Vortex Methods were first applied to rigid fixed-wing aircraft, because of their ability to include camber, thickness, and sweep, they also have been extended to High Altitude Long Endurance aircraft (Murua, et al., 2012), but also for multi-wing configurations such as rotorcraft. In the latter case, wake interactions become crucial. However, the use of singularities inherently leads to instabilities when two of them become too close to each other as the wakes are convected away, leading to irrationally large velocities. Several solutions were investigated to overcome this difficulty, the most well-known being the vortex blob method, which consists of replacing the singularity with a smooth function (Ref: Chorin (1973), Bael et Medja (1985), and Bramesfeld and Maughmer (2008) for another type of solution). Wake interactions also become relevant in multi-element airfoil configurations such as Slotted Natural Laminar Flow (SNLF) airfoils. In the design configuration, when the flow remains fully attached and laminar, the wakes of the fore and aft element remain distinct until several chord-lengths downstream.  In the case of relative motion of the airfoils, there is a risk of wake interactions, and wake impingement on the aft element. This phenomenon can in turn affect the instantaneous aerodynamic loads on both elements and sustain, damp, or exacerbate the motion. Vortex methods model the wake of airfoil and wings with either vortex sheets (prescribed wake) or discrete vortex particles (free wake model), thereby allowing to track the trajectory of the vortices during the motion of the aerodynamic surface. 

The tool presented in this paper is a low-cost, singularity-based method, developed for the study of multi-element airfoil vibrations: small perturbations in heaving and pitching are superposed on an equilibrium position. One key element of such an approach is to capture accurately this reference position, particularly the mean wake on which the vortices are being shed. The method consists of distributing singularities and solving for their strengths, to reproduce the mean pressure distribution along the surface thereby generating the proper lift and moment coefficients, obtained, for instance, from a higher resolution CFD solver or experiments. The non-penetration requirement is enforced on the actual airfoil surface and the Kutta condition is met by forcing the singularity strength to match the desired pressure profile. The method is applied to a symmetric, cambered,  SNLF airfoil. With the mean flow defined at various airfoil configurations, the wake location and its mean velocity are retained. Time dependent calculations are then commenced for small airfoil vibrations where a new pressure distribution is found that solves the non-penetration condition. The net change in circulation is then shed into the wake and allowed to convect for influence at later time steps. The solution is allowed to reach steady state oscillations where unsteady aerodynamic coefficients are obtained for flutter analysis.

Presenting Author: Michael Jonson PSU

Presenting Author Biography: Dr. Michael L. Jonson is an Associate Research Professor and Division Scientist at the Applied Research Laboratory and member of the graduate faculty in Aerospace Engineering at The Pennsylvania State University. Dr. Jonson has conducted research in fluid dynamics, flow acoustics and structural acoustics regarding underwater vehicles for the US Navy applications for 38 years. Dr. Jonson has authored numerous conference and journal papers, serves as a paper reviewer for several national/international technical journals, and advises several graduate students at Penn State. Dr. Jonson’s teaching experience includes undergraduate courses in advanced engineering mathematics and machine dynamics. He has also taught the graduate course in aeroelasticity for several years. Dr. Jonson has been very active in the American Society of Mechanical Engineers where he has been a member of the Noise Control and Acoustics Division (NCAD) for 28 years. Within NCAD Dr. Jonson has been the technical chair for the flow acoustics for several years. He also served on NCAD’s Executive Committee where he organized the NCAD conference at the International Mechanical Engineering Conference and Exposition in Seattle, WA in 2007. Dr. Jonson holds a BS in Aeronautical Engineering from the California State Polytechnic State University, San Luis Obispo, and MS and Ph.D. in Mechanical Engineering from The Pennsylvania State University.

Authors:

Auriane Bottai Penn State University
Michael Jonson PSU
Robert Campbell Penn State University