Reduced Order Modeling of Wake Deflection in Flapping Airfoils

Abstract

Autonomous Underwater Vehicles (AUVs) are deployed in ocean for defense purposes like Anti-Submarine Warfare etc. as well as for civil purposes like marine life exploration. MIT Lab in USA has been working on AUVs design under MIT sea grant. Until now, propellers are used in AUVs which causes noise due to which stealth is compromised for marine life exploration and military purposes. Proposed solution is to look for bio-inspired designs like in fishes and birds. These organisms uses flapping motion to generate thrust and lift. Flapping motion can not be used on large scale due to structural instability. However it can be used on small scale like in AUVs to make them noise proof and increase their flight performance. Unsteady mechanisms in flapping motion are required to be understood in flapping airfoils at low Re numbers to control drag, lift and thrust. When airfoil exhibits flapping motion, it undergoes vortex shedding. At low Strouhal numbers, it experiences drag mode due to von Karman vortex street. when Strouhal number gets increased slowly, airfoil undergoes neutral mode. When Strouhal number gets increased beyond 0.6, it experiences thrust mode due to reverse von Karman street. At high Strouhal numbers, deviation of wake happens in upward or downward direction. Due to this, transverse force is experienced by airfoil. Wake deflection is a complex phenomenon and need to be modeled. Experimental approach, CFD approach and analytical approach are costly, computationally expensive and too complex to be solved respectively. To address these challenges, the proposed reduced-order modeling technique seeks to provide a computationally efficient yet accurate framework for predicting wake deflection and its impact on the overall aerodynamic characteristics of flapping airfoils. The purpose of this research was to provide a computational tool to estimate the response of flapping airfoils quickly. We presented a dynamical system’s approach and proposed a reduced order model i.e. forced Duffing oscillator to model wake deflection phenomenon. Solution of this nonlinear mathematical model was derived using the method of multiple scales (MMS). Using modulation equations obtained from MMS, we plotted frequency and force response curves. We also solved the proposed model numerically using MATLAB and plotted time series, phase portrait and Fourier spectrum diagrams. These plots identifies point of symmetry-breaking bifurcation which causes the wake deflection phenomenon. vi It is concluded by comparing these plots with results from CFD simulations of flapping airfoils that the reduced order model provides frequency and force response curves to identify the exact combination of parameters which will causes wake deflection. In this way, transverse force can be increased or decreased on heaving airfoil for lift or dive purposes through control of wake deflection.