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Vortex lattice method
About: Vortex lattice method is a research topic. Over the lifetime, 779 publications have been published within this topic receiving 9242 citations.
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01 Dec 1977
TL;DR: In this paper, the concept of the generalized principal part of an integral yields a residual term to the vorticity-induced velocity field, and the proper incorporation of this term into the velocity field generated by the discrete vortex lines renders the present vortex lattice method valid for supersonic flow.
Abstract: If the discrete vortex lattice is considered as an approximation to the surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vorticity-induced velocity field. The proper incorporation of this term to the velocity field generated by the discrete vortex lines renders the present vortex lattice method valid for supersonic flow. Special techniques for simulating nonzero thickness lifting surfaces and fusiform bodies with vortex lattice elements are included. Thickness effects of wing-like components are simulated by a double (biplanar) vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentrical cylindrical surfaces. The analysis of sideslip effects by the subject method is described. Numerical considerations peculiar to the application of these techniques are also discussed. The method has been implemented in a digital computer code. A users manual is included along with a complete FORTRAN compilation, an executed case, and conversion programs for transforming input for the NASA wave drag program.
167 citations
TL;DR: In this paper, the design optimization of a flapping wing in forward flight with active shape morphing, aimed at maximizing propulsive efficiency under lift and thrust constraints, was performed with an inviscid three-dimensional unsteady vortex lattice method, whose lack of fidelity is offset by a relatively inexpensive computational cost.
Abstract: This work considers the design optimization of a flapping wing in forward flight with active shape morphing, aimed at maximizing propulsive efficiency under lift and thrust constraints. This is done with an inviscid three-dimensional unsteady vortex lattice method, whose lack of fidelity is offset by a relatively inexpensive computational cost. The design is performed with a gradient-based optimization, where gradients are computed with an analytical sensitivity analysis. Wake terms provide the only connection between the forces generated at disparate time steps, and must be included to compute the derivative of the aerodynamic state at a time step with respect to the wing shape at all previous steps. The cyclic wing morphing, superimposed upon the flapping motions, is defined by a series of spatial and temporal approximations. The generalized coordinates of a finite number of twisting and bending modes are approximated by cubic splines. The amplitudes at the control points provide design variables; increasing the number of variables (providing the wing morphing with a greater degree of spatial and temporal freedom) is seen to provide increasingly superior designs, with little increase in computational cost. I. Introduction HE design and optimization of artificial flapping wing flyers presents considerable difficulties in terms of computational cost: the complex physical phenomena associated with the flight (unsteady low Reynolds number vortical flows in conjunction with a nonlinear elastic wing surface undergoing large prescribed rotations and translations) may require a high-fidelity computational tool. Furthermore, the search optimization process typically requires many function evaluations to converge to a relevant optimum. Lower fidelity numerical tools may help alleviate the burden, either used during the search process in conjunction with a higher-fidelity model 1
136 citations
TL;DR: In this paper, a parametric geometry definition of induced, friction, wave, and interference drag is presented and validated for subsonic and transonic aircraft configurations, and the model is compared with a wing/body configuration used previously in drag prediction workshops.
Abstract: Accurate drag estimation is critical in making computational design studies. Drag may be estimated thousands of times during a multidisciplinary design optimization, and computational fluid dynamics is not yet possible in these studies. The current model has been developed as part of an air-vehicle conceptual-design multidisciplinary design optimization framework. Its use for subsonic and transonic aircraft configurations is presented and validated. We present our parametric geometry definition, followed by the drag model description. The drag model includes induced, friction, wave, and interference drag. The model is compared with subsonic and transonic isolated wings, and a wing/body configuration used previously in drag prediction workshops. The agreement between the predictions of the drag model and test data is good, but lessens at high lift coefficients and high transonic Mach numbers. In some cases the accuracy of this drag estimation method exceeds much more elaborate analyses.
125 citations
TL;DR: In this article, an analytic expression describing the aerodynamic roll moment has been obtained from the numerical simulation of wing rock, which is used in the equation governing the rolling motion of a delta wing around its midspan axis.
Abstract: An analytic expression describing the aerodynamic roll moment has been obtained from the numerical simulation of wing rock. This expression is used in the equation governing the rolling motion of a delta wing around its midspan axis. The result is used to construct phase planes, which reveal the general global nature of wing rock—stable limit cycles, unstable foci, saddle points, and domains of initial conditions leading to oscillatory motion and divergence. An asymptotic approximation to the solution of the governing equation is obtained; this result provides expressions for the amplitudes and frequencies of limit cycles. The present analysis provides a penetrating global view of the wing-rock phenomenon.
123 citations
TL;DR: In this article, the unsteady vortex lattice method is used to model the oscillating plunging, pitching, twisting, and flapping motions of a finite-aspect-ratio wing.
Abstract: The unsteady vortex lattice method is used to model the oscillating plunging, pitching, twisting, and flapping motions of a finite-aspect-ratio wing. Its potential applications include design and analysis of small unmanned air vehicles and in the study of the high-frequency flapping flight of birds and other small flyers. The results are verified by theory and, in the plunging and pitching cases, by experimental data. The model includes free-wake relaxation, vortex stretching, and vortex dissipation effects and is implemented using object-oriented computing techniques
122 citations