Convergence characteristics of a vortex-lattice method for nonlinear configuration aerodynamics
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Rusak, Z.↗
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Optimum lattice arrangement developed from a rigorous analytical basis
The spanwise vortex-lattice arrangement is mathematically established by lattice solutions of the slender wing which are shown to be analogous to the chordwise vortex-lattice thin wing solution. Solutions for any number N of panels wing theory lift and induced drag and thin wing theory lift and moment are predicted exactly. As N approaches infinity, the slender wing elliptic spanwise loading and thin wing cotangent chordwise loading are predicted, which proves there is mathematical convergence of the vortex-lattice method to the exact answer. Based on this planform spanwise lattice arrangement, an A-vortex-lattice spanwise system is developed for an arbitrary aspect ratio A. This A-lattice has the optimum characteristic of predicting lift accurately for any value of N.
Deyoung, J.↗
Fast Rotating Scalar and Multi-component Bose Gases
We show that in the limit of large angular momentum, many equilibrium and dynamical phenomena of scalar and multi-component Bose gases can be accounted for by approximating the system to reside in an effective lowest Landau level. This method explains the origin of the mysterious stripe formation in fast rotating Bose gas recently observed at JILA, and accounts for all the dynamical details observed in this experiment. To further demonstrate the usefulness of this method, we present its predictions of the interference patterns of two vortex lattices, and rich vortex lattice structures in multi-component Bose gases.
Ho, TIn-Lun Jason↗
Pinning, flow and plastic deformation of flux vortices in high T(sub c) superconductors
In high temperature superconductor (HTSC) materials the vortices are highly mobile and flexible. This is reflected in different models of melt of a vortex lattice. Another aspect of the problem is stressed: an easy nucleation and high mobility of dislocations in the vortex lattice. Some models of plastic deformation of vortex lattice are considered as a result of its interaction with a real crystal structure. Depinning is interpreted as yield of plastic flow is vortex medium. Effect of macroscopic defects in crystal structures (pores, inclusions, grain and domain boundaries) is being considered in detail. Available experimental facts on magnetization and a critical current in HTSC and conventional superconductors are discussed from the points of view of depinning to vortices vs. plastic flow of vortices vs. plastic flow of vortices medium.
Roytburd, A.↗
Flutter Analysis of the Transonic Truss-Braced Wing Aircraft Using Transonic Correction
This paper describes a flutter analysis method for the Transonic Truss-Braced Wing aircraft using a vortex lattice method coupled to an unsteady transonic correction method to account for unsteady aerodynamics in transonic flow. A steady-state vortex-lattice model of the Truss-Braced Wing aircraft is developed using vortex lattice code VSPAERO. A transonic and viscous flow correction method is implemented in the VSPAERO model to account for steady-state transonic and viscous flow effects using transonic small disturbance code TSFOIL coupled to an in-house integral boundary layer code. In addition, a wing-strut interference correction method is developed to account for the transonic interference aerodynamics in the strut juncture region using high-fidelity CFD code FUN3D. A structural dynamic finite-element model of the Truss-Braced Wing aircraft is developed using BEAM3D in-house finite-element code and is coupled to the VSPAERO. The BEAM3D model includes a geometric nonlinearity due to the tension in the strut which causes a deflection-dependent nonlinear stiffness. An unsteady transonic correction method is developed to better capture the unsteady aerodynamics in transonic flow. The unsteady transonic correction method makes use of the Theodorsen’s theory to account for the amplitude and phase shift of the unsteady lift coefficient in transonic flow. A preliminary flutter analysis of the Truss-Braced Wing aircraft is conduct to illustrate the unsteady transonic correction approach.
Nhan Nguyen↗
A Numerical Model of Unsteady, Subsonic Aeroelastic Behavior
A method for predicting unsteady, subsonic aeroelastic responses was developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Because the unsteady vortex-lattice method predicts the wake as part of the solution, the history of the motion is taken into account; hysteresis is predicted. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting. The method can be readily extended to account for structural nonlinearities and/or substitute aerodynamic load models. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion.
Strganac, Thomas W.↗
Computer program documentation for a subcritical wing design code using higher order far-field drag minimization
A subsonic, linearized aerodynamic theory, wing design program for one or two planforms was developed which uses a vortex lattice near field model and a higher order panel method in the far field. The theoretical development of the wake model and its implementation in the vortex lattice design code are summarized and sample results are given. Detailed program usage instructions, sample input and output data, and a program listing are presented in the Appendixes. The far field wake model assumes a wake vortex sheet whose strength varies piecewise linearly in the spanwise direction. From this model analytical expressions for lift coefficient, induced drag coefficient, pitching moment coefficient, and bending moment coefficient were developed. From these relationships a direct optimization scheme is used to determine the optimum wake vorticity distribution for minimum induced drag, subject to constraints on lift, and pitching or bending moment. Integration spanwise yields the bound circulation, which is interpolated in the near field vortex lattice to obtain the design camber surface(s).
Kuhlman, J. M.↗
Rotational transition, domain formation, dislocations, and defects in vortex systems with combined sixfold and twelvefold anisotropic interactions
We introduce a phenomenological model for a pairwise repulsive interaction potential of vortices in a type-II superconductor, consisting of superimposed sixfold and twelvefold anisotropies. Using numerical simulations we study how the vortex lattice configuration varies as the magnitudes of the two anisotropic interaction terms change. A triangular lattice appears for all values, and rotates through 30 ° as the ratio of the sixfold and twlevefold anisotropy amplitudes is varied, in agreement with experimental results. The transition causes the vortex lattice to split into domains that have rotated clockwise or counterclockwise, with grain boundaries that are “decorated” by dislocations consisting of fivefold and sevenfold coordinated vortices. We also find intradomain dislocations and defects, and characterize them in terms of their energy cost. We discuss how this model could be generalized to other particle-based systems with anisotropic interactions, such as colloids, and consider the limit of very large anisotropy where it is possible to create cluster crystal states.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Steady and unsteady incompressible free-wake analysis
The flows around highly sweptback wings and bodies of revolution at high angle of attack are described, and inviscid model approximations and mathematical formulation of the problem are given to steady and unsteady incompressible flows. A general presentation of the methods of solution is given, with emphasis on current computational techniques. Detailed descriptions of the nonlinear vortex-lattice and vortex-panel techniques are presented to show how the boundary conditions are enforced using iteration. Typical numerical results are compared with the available experimental data.
Kandil, O. A.↗
Analytical investigation of aerodynamic characteristics of highly swept wings with separated flow
Many modern aircraft designed for supersonic speeds employ highly swept-back and low-aspect-ratio wings with sharp or thin edges. Flow separation occurs near the leading and tip edges of such wings at moderate to high angles of attack. Attempts have been made over the years to develop analytical methods for predicting the aerodynamic characteristics of such aircraft. Before any method can really be useful, it must be tested against a standard set of data to determine its capabilities and limitations. The present work undertakes such an investigation. Three methods are considered: the free-vortex-sheet method (Weber et al., 1975), the vortex-lattice method with suction analogy (Lamar and Gloss, 1975), and the quasi-vortex lattice method of Mehrotra (1977). Both flat and cambered wings of different configurations, for which experimental data are available, are studied and comparisons made.
Reddy, C. S.↗
Aerodynamic Load Analysis of a Variable Camber Continuous Trailing Edge Flap System on a Flexible Wing Aircraft
This paper presents an investigative aerodynamic analysis conducted on the novel control surface known as a Variable Camber Continuous Trailing Edge Flap (VCCTEF). The VCCTEF is modeled as a control effector on the NASA Generic Transport Model (GTM) where wing flexibility is considered. Aerodynamic modeling of the aircraft is conducted using vortex-lattice method (VLM), and an aeroelastic model of the aircraft that utilizes a coupled finite-element analysis (FEA) vortex-lattice solution is employed. VLM solutions are used to determine quasi-steady aerodynamic loading over the aeroelastic wing structures with VCCTEF. The load data is used to calculate aerodynamic sensitivities to control surface deployment and is also integrated to determine overall hinge moments. This analysis is conducted for different flight conditions, where control sensitivities compare the VCCTEF effectiveness against conventional control surfaces. Hinge moment results provide insight into aeroelastic wing loads, and worst case hinge moments for the VCCTEF can be estimated. Results show that the VCCTEF offers greater control authority than conventional ailerons at cruise, and nominal flap settings are determined for a low-speed take-off condition where the VCCTEF maintains comparable control effectiveness. Worst case hinge moment values are presented, where for a possible VCCTEF configuration, the stiff wing model demonstrates up to a 5.90 percent increase in flap hinge moment relative to a rigid model, and a reduced stiffness model demonstrates up to an 11.42 percent increase.
Aeroelasticity↗
Higher order farfield drag minimization for a subcritical wing design code
A higher order Trefftz plane model of the undistorted interacting wing wakes of two symmetric subsonic planforms has been developed and integrated with an existing vortex lattice wing design code. The Trefftz plane calculation provides continuous, piecewise quadratically varying bound circulations, which are then interpolated in the nearfield vortex lattice representation of the wing. Integration of the surface slopes for a specified chord loading function provides the design wing camber surfaces. This paper outlines the theoretical development and presents comparisons between results obtained using the present theory and (1) previous exact solutions for minimum induced drag and (2) previous wing designs obtained using a discrete vortex wake moded.
Kuhlman, J. M.↗
Theoretical analysis of an augmentor wing for a VTOL fighter
A method based on potential flow theory was developed for predicting forces and moments acting on augmentor wings for prescribed ejector jet characteristics. A three dimensional nonplanar vortex lattice is laid out on the chordal planes of the augmentor wing components. Jet induced effects are included in the boundary condition from which the horseshoe vortex strengths are obtained. The jet within the diffusor is made to expand from the primary nozzles to the diffusor exit and is represented by a distribution of vorticity on the jet boundary to provide proper entrainment. The jet downstream of the diffusor exit is modeled by a vorticity distribution and blockage panels and its centerline location and spreading rate are taken from experimental data. The vortex lattice and jet models are used in an iterative manner until the predicted diffusor exit velocity matches the specified one. Some comparisons with available data show good agreement at lower power settings.
Dillenius, M. F. E.↗
An Analytical Investigation of Wing-Jet Interaction
The aerodynamic interaction between the wing and an inviscid jet with Mach number nonuniformity is formulated by using a two-vortex-sheet model for the jet. One of the vortex sheets accounts for the induced jet flow and the other the induced outer flow. No additional source distribution is needed for the jet at an angle of attack. The above problem is solved by satisfying the jet and wing tangency and the jet pressure-continuity conditions and using a quasi vortex lattice method for computing the induced flow field. The latter method is derived through theoretical consideration by properly accounting for singularities present in the equations and possesses the same simplicity and generality as the conventional vortex lattice method but has a better rate of numerical convergence. The resulting system of algebraic equations is solved by Purcell's vector method. The numerical formulation is first applied to the wing-slipstream interaction problem. Results for one centered-jet configuration are compared with those predicted by some existing theories.
Lan, E. C.↗
Prediction of forces and moments for flight vehicle control effectors. Part 2: An analysis of delta wing aerodynamic control effectiveness in ground effect
Many types of hypersonic aircraft configurations are currently being studied for feasibility of future development. Since the control of the hypersonic configurations throughout the speed range has a major impact on acceptable designs, it must be considered in the conceptual design stage. Here, an investigation of the aerodynamic control effectiveness of highly swept delta planforms operating in ground effect is presented. A vortex-lattice computer program incorporating a free wake is developed as a tool to calculate aerodynamic stability and control derivatives. Data generated using this program are compared to experimental data and to data from other vortex-lattice programs. Results show that an elevon deflection produces greater increments in C sub L and C sub M in ground effect than the same deflection produces out of ground effect and that the free wake is indeed necessary for good predictions near the ground.
Maughmer, Mark D.↗
Unsteady forces on counter-rotating propeller blades
Unsteady forces experienced by counter-rotating propeller blades are examined in this paper. A fully coupled vortex lattice model of counter-rotation is used to obtain a quasi-steady solution to the propeller loadings, and an unsteady Sears (1941) analysis provides an estimate of the unsteady loads from the quasi-steady results. The vortex lattice method predicts the overall performance of counter-rotation well, based on comparisons of measured and predicted results. The effects of propeller spacing and blade number on the unsteady loadings are investigated. The peak-to-peak variation about the mean of the unsteady loads on the rear propeller varied from 9 percent for a 2 x 2 counter-rotation system to 2 percent for an 8 x 8 system.
Lesieutre, D. J.↗
General Approach to Solving Spin Moiré Superstructures
Recently, a host of exciting magnetic textures such as topologically protected skyrmion lattices has been discovered in several bulk metallic lanthanide compounds. In addition to hosting skyrmion phases, a hallmark of this class of materials is the appearance of numerous spin textures characterized by superposition of multiple magnetic modulations: spin moiré superlattices. In order to understand the multitude of complex phases often present in these materials, we require a general-purpose experimental and theoretical framework. Here, we demonstrate such an approach in EuAg4Sb2 by comprehensively characterizing and modeling its three complex zero-field magnetic textures. Systematic symmetry-breaking experiments using uniaxial strain determine that the ground-state incommensurate magnetic phase (ICM1) is single 𝑞, meaning the magnetic moments modulate along one magnetic propagation vector. In contrast, ICM2 and ICM3 are both double 𝑞, meaning they are formed from the superposition of two sinusoidal spin modulations, i.e., spin moiré superlattices. Further, through application of polarized small-angle neutron scattering and spherical neutron polarimetry, we demonstrate that ICM1 is a single-𝑞 cycloid and ICM2 and ICM3 are double-𝑞 vortex lattices. Despite the quasi-two-dimensional nature of EuAg4Sb2, the modulations propagate out of the ab plane, leading to a shift of the spin texture between triangular lattice planes. Further, the ICM3 to ICM2 transition includes an unusual 45° rotation of the magnetic vortex lattice. Motivated by the coexistence of such drastically different phases in this compound, we conclude by developing a phenomenological model that sheds light on the energetic origins of these varied phases. Our experimental probes and theoretical modeling definitively characterize three different and tunable phases in one material and provide insight for the design of topological spin-texture materials.
Neves, Paul [Massachusetts Institute of Technology↗
Modeling of the aerodynamic response to arbitrary aircraft maneuvres - A numerical validation
The regime of validity of an aerodynamic mathematical model, applicable to describe the nonlinear aerodynamic reactions to a delta wing maneuvering at high angles of attack is investigated. An unsteady vortex-lattice method is used to compute the unsteady flowfields, and thus to evaluate the aerodynamic data required by the model, in terms of specified characteristic motions. Time-histories of the aerodynamic responses to complex motions are generated by means of the model and the evaluated aerodynamic data, and are compared with baseline aerodynamic responses obtained from direct vortex-lattice computations. The validity of the mathematical modeling approach for the maneuvering delta wing is demonstrated by the close agreement of the force and moment responses obtained from the two approaches.
Katz, J.↗