Applications of the unsteady vortex-lattice method in aircraft aeroelasticity and flight dynamics

Unsteady aerofoil flows are often characterized by leading-edge vortex (LEV) shedding. While experiments and high-order computations have contributed to our understanding of these flows, fast low-order methods are needed for engineering tasks. Classical unsteady aerofoil theories are limited to small amplitudes and attached leading-edge flows. Discrete-vortex methods that model vortex shedding from leading edges assume continuous shedding, valid only for sharp leading edges, or shedding governed by ad-hoc criteria such as a critical angle of attack, valid only for a restricted set of kinematics. We present a criterion for intermittent vortex shedding from rounded leading edges that is governed by a maximum allowable leading-edge suction. We show that, when using unsteady thin aerofoil theory, this leading-edge suction parameter (LESP) is related to the term in the Fourier series representing the chordwise variation of bound vorticity. Furthermore, for any aerofoil and Reynolds number, there is a critical value of the LESP, which is independent of the motion kinematics. When the instantaneous LESP value exceeds the critical value, vortex shedding occurs at the leading edge. We have augmented a discrete-time, arbitrary-motion, unsteady thin aerofoil theory with discrete-vortex shedding from the leading edge governed by the instantaneous LESP. Thus, the use of a single empirical parameter, the critical-LESP value, allows us to determine the onset, growth, and termination of LEVs. We show, by comparison with experimental and computational results for several aerofoils, motions and Reynolds numbers, that this computationally inexpensive method is successful in predicting the complex flows and forces resulting from intermittent LEV shedding, thus validating the LESP concept.

Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding

Nonlinear aeroelastic analysis is essential for high-altitude long-endurance (HALE) aircraft. In the current paper, we have presented a computational aeroelastic tool for nonlinear-aerodynamics/nonlinear-structure interaction. Specifically, a consistent nonlinear time-domain aeroelastic methodology has been integrated via tightly coupling a geometrically exact nonlinear intrinsic beam model and the generalized unsteady vortex-lattice aerodynamic model with vortex roll-up and free wake. The effects of discrete gust as well as flow separation at various angles of attack from attached flow to the stall and poststall ranges are also included in the nonlinear aerodynamic model. A HALE-wing model is analyzed as a numerical example. The trim angle of attack is first found for the wing, and the results show that aeroelastic instability could occur at higher angles of attack. The HALE-wing model under the trim condition is then analyzed for various gust profiles to which it is subject. It is found that for certain gust levels, the elastic deformations of the HALE wing tend to become unstable: notably, the in-plane deflections become very significant. It is noted for the unstable solution of the HALE wing that the flow may be well beyond the stall range. An engineering approach with the use of the nonlinear sectional lift is attempted to consider such stall effects.

Nonlinear-Aerodynamics/Nonlinear-Structure Interaction Methodology for a High-Altitude Long-Endurance Wing

Continuous photocatalytic, electrocatalytic and photo-electrocatalytic degradation of a reactive textile dye for wastewater-treatment processes: Batch, microreactor and scaled-up operation

This work investigates the effect of aerodynamic interference in the coupled nonlinear aeroelasticity and flight mechanics of flexible lightweight aircraft at low speeds. For that purpose, a geometrically exact composite-beam formulation is used to model the vehicle flexible-body dynamics by means of an intuitive and easily linearizable representation based on the displacement and Cartesian rotation vectors. The aerodynamics are modeled using the unsteady vortex-lattice method, which captures the instantaneous shape of the lifting surfaces and the free inviscid wake, including large deformations and interference effects. This results in a framework for simulation of high aspect ratio planes that provides a medium-fidelity representation of flexible-aircraft dynamics with a modest computational cost. Previous independent studies on the structural-dynamics and aerodynamics modules are complemented here with the integrated simulation methodology, including vehicle trim, and linear and nonlinear time-domain solutions. A numerical investigation is next presented on a simple wing-fuselage-tail configuration, assessing the interference effects between wing wake and horizontal tail, and the downwash due to the proximity of the wake is shown to play a significant role in the longitudinal dynamics of the vehicle. Finally, a brief discussion of direct wake-tail encounters is included to show the limitations of the approach.

Assessment of Wake-Tail Interference Effects on the Dynamics of Flexible Aircraft

A numerical iterative vortex lattice method is developed to study flow past wing(s) at high angles of attack where the separated flow is modelled using NY nascent vortex filaments. The wing itself is modelled using NX × NY bound vortex rings, where NX and NY are the number of sections along the chord and span of the wing respectively. The strength and position of the nascent vortex along the chord corresponding to the local effective angle of attack are evaluated from the residuals in viscous and potential flow, i.e. (Cl ) visc − (Cl ) pot and (Cm ) visc − (Cm ) pot . Hence, the 2D airfoil viscous Cl − α and Cm − α is required as input (from experiment, numerical analysis or CFD). Aerodynamic characteristics and section distribution along span are predicted for 3D wings at a high angle of attack. Effect of initial conditions and existence of multiple solutions in the post-stall region is studied. Results are validated with experiment.

https://iopscience.iop.org/article/10.1088/1742-6596/822/1/012005/pdf

High-Alfa Aerodynamics with Separated Flow Modeled as a Single Nascent Vortex

A discrete vortex model coupled with a vortex dissipation and vortex core criteria is used to study the unsteady flow past two airfoils in configuration. The unsteady wakes of the airfoils are modeled by discrete vortices and time-stepping is used to predict the individual wake shapes. The coupled flow is solved using a combined zeronormal flow boundary condition and Kelvin condition which result in (2N + 2)X(2N + 2) equations. Results are presented showing the effect of airfoil-airfoil and airfoil-wake interaction on the aerodynamic characteristics of the configuration. The effect of relative velocity, rate of pitching and phase-lag are studied on airfoil performance and wake shape is predicted.

https://jafmonline.net/JournalArchive/download?file_ID=41413&issue_ID=237

Vortex Interaction and Roll-Up in Unsteady Flow past Tandem Airfoils

Blunt nose cones used in launch vehicles can excite buffet due to shock oscillations over the payload fairing on the leeward side at transonic Mach numbers and small angles of attack. Wind-tunnel t...

Passive Control of Transonic Flow over a Blunt Body Using Aerospikes

A potential flow model is used to study the unsteady flow past a set of two airfoils, each of which have been set into motion by a sudden acceleration. In the current work, results are presented and validated with the analytical results of Wagner. Using the two-airfoil configuration, results are obtained for the variation of ( ) t Cl , ( ) t Cd , ( ) t Cm and wake shape of both airfoils due to (i) variation of X-location of the trailing airfoil with respect to the leading airfoil (ii) variation of Y-location of the trailing airfoil with respect to the leading airfoil and (iii) variation of angle of attack of the leading airfoil. Selected results of the study carried out are presented here.

Unsteady aerodynamics of suddenly accelerated multiple airfoils

A potential flow model is used to study the unsteady flow past two airfoils in configuration, each of which is suddenly set into motion. The airfoil bound vortices are modeled using lumped vortex elements and the wake behind the airfoil is modeled by discrete vortices. This consists of solving a steady state flow problem at each time-step where unsteadiness is incorporated through the “zero normal flow on a solid surface” boundary condition at every time instant. Additionally, along with the “zero normal flow on a solid surface” boundary condition Kelvin’s condition is used to compute the strength of the latest wake vortex shed from the trailing edge of the airfoil. Location of the wake vortices is updated at each time-step to get the wake shape at each time instant. Results are presented to show the effect of airfoil-airfoil interaction and airfoil-wake interaction on the aerodynamic characteristics of each airfoil.

Rinku Mukherjee

Papers

High-Alfa Aerodynamics with Separated Flow Modeled as a Single Nascent Vortex

Vortex Interaction and Roll-Up in Unsteady Flow past Tandem Airfoils

Passive Control of Transonic Flow over a Blunt Body Using Aerospikes

Unsteady aerodynamics of suddenly accelerated multiple airfoils

Unsteady Aerodynamics of Multiple Airfoils in Configuration