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

Delay or control of flow separation for enhanced aerodynamic performance using an effective morphed surface

An Unsteady Vortex Lattice Method is developed and validated. It is coupled with a decambering methodology to account for viscous effects on the aerodynamic coefficients. Two additional methodologies to select a unique solution when multiple solutions arise have been proposed. The transient nature of the aerodynamic loads of a suddenly moving wing at different angles of attack is examined. Sudden jumps are observed in the $$C_L(t)$$
 at post-stall angles of attack. The jumps are followed by the presence of asymmetric solutions, which then decline with time and a change in the solution state. Higher angles of attack see an increasing number of jumps.

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A study of the unsteady aerodynamics of a wing at high angles of attack using decambering to model separated flow

Low Reynolds number flows are important especially for MAV applications due to the presence of the LSB, which affects airfoil performance. The transition model of Fluent12 is used to extract the local velocity profiles and their second derivatives for flow past NACA0012 airfoil at Re=0.34X10. These form the input to a numerical linear stability code developed to understand the T-S wave characteristics in the LSB. The code solves the OrrSommerfeld equation locally for NACA0012 mean profiles at α=9 with parallel flow approach. The OSE is solved as a spatial stability problem where the temporal frequency is a real number and the eigen values are the spatial wave numbers. A complex NewtonRaphson technique is used for the Eigen value search and e method is used to predict transition. The growth of the most unstable wave is such that the amplification ratio reaches a predefined number e. Based on e method the T-S wave frequency and phase speed are predicted. The LSB is observed using the Cp and velocity vector plots from Fluent12.

Linear Stability Analysis of Laminar Separation Bubble over NACA0012 airfoil at Low Reynolds Numbers

This work is based on the vortex lattice method using a “decambering” approach, which accounts for flow separation and makes the separated flow to follow viscous flow condition at high angles of attack over the airfoil and 3D wings. This method used to study the aerodynamic hysteresis of two wings configuration at near stall and post-stall flow conditions. The hysteresis of different data and their effect have been studied. The effect of shifting stall due to presence of hysteresis for forward and backward flow regimes also has been reported.

Analysis of Aerodynamic Hysteresis in Echelon formation

Flow over airfoil is extensively studied to identify point of flow separation, transition, re-attachment (formation of laminar separation bubble), and to understand relation between aerodynamic forces generated by airfoil with change in angles of attack Extension of flow separation concept to finite wing is not straight forward as flow has an additional degree of freedom to move when it detaches from surface of wing A preliminary investigation of location of flow separation lines over finite wings is carried out using numerical simulations in ANSYS (FLUENT)

Rinku Mukherjee

Papers

Delay or control of flow separation for enhanced aerodynamic performance using an effective morphed surface

A study of the unsteady aerodynamics of a wing at high angles of attack using decambering to model separated flow

Linear Stability Analysis of Laminar Separation Bubble over NACA0012 airfoil at Low Reynolds Numbers

Analysis of Aerodynamic Hysteresis in Echelon formation

Investigation of Flow Separation Lines Over a Finite Wing