In recent years, there has been a growing interest in low-Reynolds-number, unsteady flight applications, leading to renewed scrutiny of the Kutta condition. As an alternative, various methods have been proposed, including the combination of potential flow with the triple-deck boundary layer theory to introduce a viscous correction for Theodorsen's unsteady lift. In this research article, we present a dynamical system approach for the total circulatory unsteady lift generation of a pitching airfoil. The system's input is the pitching angle, and the output is the total circulatory lift. By employing the triple-deck boundary layer theory instead of the Kutta condition, a new nonlinearity in the system emerges, necessitating further investigation to understand its impact on the unsteady lift model. To achieve this, we utilize the describing function method to represent the frequency response of the total circulatory lift. Our analysis focuses on a pitching flat plate about the mid-chord point. The results demonstrate that there is an additional phase lag due to viscous effects, which increase as the reduced frequency increases, the Reynolds number decreases, and/or the pitching amplitude increases.
State Space Modeling of Viscous Unsteady Aerodynamic Loads
In this paper, we started by summarizing our recently developed viscous unsteady theory
based on coupling potential flow with the triple deck boundary layer theory. This approach
provides a viscous extension of potential flow unsteady aerodynamics. As such, a Reynolds-
number-dependence could be determined. We then developed a finite-state approximation of
such a theory, presenting it in a state space model. This novel nonlinear state space model of
the viscous unsteady aerodynamic loads is expected to serve aerodynamicists better than the
classical Theodorsen’s model, as it captures viscous effects (i.e., Reynolds number dependence)
as well as nonlinearity and additional lag in the lift dynamics; and allows simulation of arbitrary
time-varying airfoil motions (not necessarily harmonic). Moreover, being in a state space form
makes it quite convenient for simulation and coupling with structural dynamics to perform
aeroelasticity, flight dynamics analysis, and control design. We then proceeded to develop a
linearization of such a model, which enables analytical results. So, we derived an analytical
representation of the viscous lift frequency response function, which is an explicit function
of, not only frequency, but also Reynolds number. We also developed a state space model
of the linearized response. We finally simulated the nonlinear and linear models to a non-
harmonic, small-amplitude pitching maneuver at 100 , 000 Reynolds number and compared the
resulting lift and pitching moment with potential flow, in reference to relatively higher fidelity
computations of the Unsteady Reynolds-Averaged Navier-Stokes equations.
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- Award ID(s):
- 2005541
- PAR ID:
- 10226551
- Date Published:
- Journal Name:
- AIAA SciTech
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.2514/6.2021-1830
