Session W03: Aerodynamics: Theory (10:00am - 10:45am CST)

Abstract Withdrawn

We illustrate how the diffusion of vorticity from the boundary layer into the bulk flow can be modelled using a single point vortex. Existing studies that use impulse theory to calculate the fluid forces on a body do not account for the viscous diffusion of vorticity because it is unnecessary for their specific flow conditions or research aims. However, this means that existing models are only valid where advection of vorticity dominates, making them unsuitable for use during the initial period in which the body starts to move or at low Reynolds numbers. In this work, we show how models based on impulse theory can also account for the viscous diffusion of vorticity by encapsulating it in a single point vortex, the speed of which can be analytically calculated. Consequently, we show how impulse theory, already successfully used at high Reynolds numbers, can also be applied at low Reynolds numbers and smaller timescales, where the viscous diffusion of vorticity is significant.   

The effect of Viscous Boundary Condition On Kelvin's Conservation of Circulation: Modified Theodorsen Function

One of the essential tools that have been ubiquitously used in theoretical modeling of unsteady aerodynamics is Kelvin's law of zero total circulation. It implies that, for inviscid fluids, the total circulation in the fluid domain is conserved yielding a relation between the bound and wake circulation. In this study, we show that, by virtue of the viscous boundary condition (no slip), the vorticity generated on the fluid-solid interface (which is proportional to the angular velocity of the body) disturbs such a conservation law. Taking this viscous contribution into account, we developed an extension of Theodorsen's inviscid lift frequency response in the case of a pitching airfoil. The results show more phase lag and lift deficiency compared to Thodorsen's function, which have been reported by many scholars in the literature, and also validated against URANS simulations in this study.   

Investigation of Lift Distribution and Its Effect on Aerodynamic Performance

This effort evaluates the use of bell-shape lift distributions, as opposed to elliptical, to improve aerodynamic performance of flying-wing aircraft configurations. Such a distribution was originally proposed by Prandtl in 1923 to minimize bending moment along the wing and thus reduce structural wing weight. Using unique, geometric wing twist to change the lift distribution, the landscape of regions of upwash and downwash change with potential ramifications for drag reduction. Through a computational fluid dynamics (CFD) investigation, we evaluate how these changes impact aerodynamic efficiency. In particular, the efficacy of a coordinated turn is examined by observing how the inboard regions of upwash create induced thrust at the aileron-deflected wingtips. This induced thrust creates a favorable differential longitudinal force in roll, otherwise known as proverse yaw. CFD results indicate that the use of a bell-shaped lift distribution may improve aerodynamic performance for certain aircraft configurations.   

Geometry-agnostic Methods for Determining Bound Circulation in Potential Flows

A core detriment of potential flow theory, inherent in its kinematic nature, is that it is agnostic of the local work required to produce its divergence-free flowfield. The auxiliary Kutta-Joukowski condition has long served in prescribing circulation for airfoils at low angles of attack, but leads to unsatisfactory predictions for unsteady, separated flows, and its lack of a mathematical basis has made its extensions to these nonlinear regimes ad hoc and geometry dependent. This research posits existence of an upper bound on acceleration within the flowfield, and moreover, that such a limit is a function of streamtube diameter, Reynolds number, and Mach number, representing the constraints, ratio of inertial and viscous forces, and the ratio of local flow velocity to the speed of sound, respectively. Novel, geometry-agnostic methods, using the variational concepts of least constraint, and minimization of maximum accelerations, are presented for determination of bound circulation; both of which require no a priori assumptions for circulation or separation points. The result serves as a physical basis for obviating the Kutta-Joukowski condition, in a form which is amenable to aerodynamic analysis of arbitrary geometry in nonlinear and unsteady regimes.