Quasi-Steady versus Navier–Stokes Solutions of Flapping Wing Aerodynamics

Abstract

Various tools have been developed to model the aerodynamics of flapping wings. In particular, quasi-steady models, which are considerably faster and easier to solve than the Navier–Stokes equations, are often utilized in the study of flight dynamics of flapping wing flyers. However, the accuracy of the quasi-steady models has not been properly documented. The objective of this study is to assess the accuracy of a quasi-steady model by comparing the resulting aerodynamic forces against three-dimensional (3D) Navier–Stokes solutions. The same wing motion is prescribed at a fruit fly scale. The pitching amplitude, axis, and duration are varied. Comparison of the aerodynamic force coefficients suggests that the quasi-steady model shows significant discrepancies under extreme pitching motions, i.e., the pitching motion is large, quick, and occurs about the leading or trailing edge. The differences are as large as 1.7 in the cycle-averaged lift coefficient. The quasi-steady model performs well when the kinematics are mild, i.e., the pitching motion is small, long, and occurs near the mid-chord with a small difference in the lift coefficient of 0.01. Our analysis suggests that the main source for the error is the inaccuracy of the rotational lift term and the inability to model the wing-wake interaction in the quasi-steady model.

State-space aerodynamic model reveals high force control authority and predictability in flapping flight

“…The majority of these models are empirically fitted to a small set of kinematics. Such models cannot be extended to a large variety of wing kinematic trajectories; thus, they only have a small range of validity [37,38]. Notably, Nakata et al proposed a data-driven approach [37] to fit a physics informed linear regression model to computational fluid dynamics data to improve local accuracy.…”

“…Although this data-driven approach offers an excellent prediction for the region of interest, this approach has not been tested beyond the training set or wide range of wing kinematics. Additionally, the QS assumption ignores the effects of wing motion history or the internal flow states; thus, QS models can fail to capture all essential unsteady mechanisms, including wing-wake interaction [24,37,38]. Static models like QS models cannot easily capture the 'dynamical system' underlying the aerodynamic force generation processes of flapping wings.…”

Dynamic performances of a bird-like flapping wing robot under randomly uncertain disturbances

“…C. Bose et al considered the structural model of a flapping flight as a linkage system, and established the dynamic model in the form of a Duffing oscillator, and used the lumped vortex method to calculate the aerodynamic force of the robot [14]. J. Pohly et al described the dynamic model of a flapping robot with the Navier-Stokes equation, and obtained the accuracy of a quasi-steady flapping model by analyzing the aerodynamic responses of the robot [15]. In [16], the dynamic model of a flapping wing robot was presented with governing equations and boundary conditions, an energy-based barrier Lyapunov function was used to obtain the robot stability.…”

Data-driven CFD scaling of bioinspired Mars flight vehicles for hover

“…To properly account for the unsteady lift enhancing mechanisms, the generation of large scale vortices [ 24 ] and their nonlinear interaction with the wing [ 25 , 26 ] must be properly resolved by solving the NS equations. Although there has been success in developing high-fidelity quasi-steady aerodynamics models for flapping wing motion [ 27 - 29 ], these models are less accurate when more extreme kinematics and dimensionless parameters are considered [ 30 ]. Therefore, our computational framework utilizes the benefits of solving the 3D incompressible NS equations to calculate the velocity and pressure field around the flapping wing in a low Re flow regime.…”