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Inspired by nature, oscillating foils offer viable options as alternate energy resources to harness energy from wind and water. Here, we propose a proper orthogonal decomposition (POD)-based reduced-order model (ROM) of power generation by flapping airfoils in conjunction with deep neural networks. Numerical simulations are performed for incompressible flow past a flapping NACA-0012 airfoil at a Reynolds number of 1100 using the Arbitrary Lagrangian–Eulerian approach. The snapshots of the pressure field around the flapping foil are then utilized to construct the pressure POD modes of each case, which serve as the reduced basis to span the solution space. The novelty of the current research relates to the identification, development, and employment of long-short-term neural network (LSTM) models to predict temporal coefficients of the pressure modes. These coefficients, in turn, are used to reconstruct hydrodynamic forces and moment, leading to computations of power. The proposed model takes the known temporal coefficients as inputs and predicts the future temporal coefficients followed by previously estimated temporal coefficients, very similar to traditional ROM. Through the new trained model, we can predict the temporal coefficients for a long time duration that can be far beyond the training time intervals more accurately. It may not be attained by traditional ROMs that lead to erroneous results. Consequently, the flow physics including the forces and moment exerted by fluids can be reconstructed accurately using POD modes as the basis set. [ABSTRACT FROM AUTHOR]

Using immersed boundary methods, we perform numerical simulations for flow over an elliptical airfoil oscillating at a reduced frequency of 6.283 over a range of Strouhal number with Reynolds number 500. We quantify the response of this nonlinear system through time-histories of aerodynamic lift and thrust force coefficients, their Fourier spectra, phase maps, Poincáre sections, and higher-order spectral analysis. When the oscillation amplitude increases, this nonlinear system undergoes bifurcations, thus eventually achieving chaotic solutions. The aerodynamic response moves quasi-periodically through to chaos. We also relate these behavioral changes in the response of the system to the wake transitions. We also present cross-bispectrum between the lift and thrust coefficients, and auto-trispectrum for the lift coefficient to study cubic coupling among various frequency components. We find the strongest quadratic and cubic coupling between the excitation frequency components. We also observe the cubic coupling among various frequency components responsible for generating new harmonics in the spectra of the lift force at higher Strouhal numbers. [ABSTRACT FROM AUTHOR]

Numerical simulations have been used to analyze the equivalence of pitching and plunging motions found in a flapping NACA0012 airfoil. Two-dimensional incompressible Navier–Stokes equations are solved at Reynolds number of 103 over a range of Strouhal numbers. A novel criterion based on the Strouhal number is proposed which provides equivalence of pitching and plunging motions using the length scale traversed by the trailing edge in each case. Aerodynamic coefficients are found to match well for both the kinematics in temporal as well as spectral domains. Detailed analysis provides contribution of different mechanisms, such as vortex shedding, added mass, interaction of leading and trailing edge vortices, in the overall aerodynamic forces produced by a pitching or plunging airfoil. Wake deflection is observed for a plunging airfoil at high Strouhal numbers resulting in a bias in the lift coefficient. Further investigation reveals the dominance of second harmonic of the fundamental frequency in the lift spectrum emphasizing the role of quadratic nonlinearity in the observed phenomenon. [ABSTRACT FROM AUTHOR]