Vortex Sheet Strength in the Sears, Küssner, Theodorsen, and Wagner Aerodynamics Problems

Variation of leading-edge suction during stall for unsteady aerofoil motions

“…In the current formulation, is set equal to the forward velocity, which is the component of the aerofoil's velocity in the negative direction. Although recent research efforts (Xia & Mohseni 2017; Epps & Greeley 2018; Epps & Roesler 2018; Taha & Rezaei 2019) have provided updates to the Kutta condition at the trailing edge, the current formulation, which is based on the approach of Katz and Plotkin (Katz & Plotkin 2000), assumes zero vortex-sheet strength at the trailing edge, and implicitly enforces the Kutta condition by imposing a zero vortex strength at each time step at the trailing edge. The Fourier coefficients are determined using the instantaneous local downwash on the aerofoil due to all bound and shed vorticity by enforcing the boundary condition that the flow must remain tangential to the aerofoil surface: …”

On Aerodynamic Models for Flutter Analysis: A Systematic Overview and Comparative Assessment

“…Although inherently limited in applicability [9,10], explicit airload expressions and theoretical solutions grant a clear overview of the underlying phenomena and offer rigor-ous validation as well as fundamental insights for both educational and practical scopes in both academic and industrial activities, with a convenient trade-off between reliability and affordability [11][12][13]. Focusing on two-dimensional, incompressible, potential flow without loss of generality for the fundamental purpose of this conceptual work, the unsteady aerodynamic model is first reviewed by adopting a vorticity-based approach [14,15], showing its formal equivalence with Thodorsen's and Wagner's models [16,17]. All previously mentioned approximations for the aerofoil's airload are hence systematically derived by successive simplifications of physical effects and mathematical terms within a unified approach, ranging from the more complex unsteady aerodynamics to the more straightforward steady aerodynamics.…”

On the leading-edge suction and stagnation-point location in unsteady flows past thin aerofoils

“…Expressing these vorticity components from Epps & Roesler (2018) in terms of the chord-wise transformation variable θ, we have γ n = 2 sin θ W 3qc cos θ −α c 4 (cos θ + cos 2θ) (3.13)…”

“…The first two wake coefficients may be evaluated analytically (Epps & Roesler 2018) as 3.19) while the remaining terms must be calculated numerically. In the equations above, K n (ik) is the modified Bessel function of the second kind of order n.…”

“…The wake is assumed to be planar and extending to infinity, on the basis of which closed-form expressions are derived for the velocities induced by the wake on the aerofoil. The vorticity distribution on the aerofoil in Theodorsen's theory is derived in Epps & Roesler (2018). The vorticity is partitioned into a non-circulatory part γ n , a circulatory part associated with the motion γ c0 (the quasi-steady part), and a circulatory part associated with the wake γ w .…”