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.

Convergence of Panel Methods Using Discrete Vortices around Two-Dimensional Bodies

Abstract: The panel method in which vorticity is distributed on the surface of a body, the surface vorticity distribution method such like the vortex lattice method, is useful for determining the Euler flow past bodies and recently has been applied to complicated body shapes together with the vortex method. In the present paper we demonstrate the mathematical analysis of two panel methods for inviscid incompressible flow past two-dimensional bluff bodies, the pointwise and piecewise-linear distributions of vortices. The governing singular integral equation is derived by distributing vortices on the surface of the body and the simultaneous linear algebraic equations are derived by approximating the integral equation by the discretization of vorticity distribution. The analytic solution of the linear algebraic equations is obtained and the accuracy of the approximate solution is discussed. We show that : (1) there exists an appropriate collocation point, (2) the accuracy of the vortices on the surface of the body is of the order of 1/n where n is the panel number and (3) the eigensolution of the governing integral equation cannot be obtained using these schemes unless they are modified.

Effect of Warping due to Aerodynamic Loadings in Composite Wings

Abstract: With the advent of composites, the accurate evaluation of the response of deformable lifting bodies when subjected to steady and unsteady aerodynamic loadings becomes an even more challenging issue for the aeroelastic design of aerospace vehicles. Static response analyses of composite wings subjected to aerodynamic loadings are presented in this paper. Wing structures are modeled via refined finite elements in the framework of the 1D Carrera Unified Formulation (CUF). CUF 1D models have recently been developed for isotropic [1, 2] and composite structures [3]. CUF models exploit arbitrary order expansions of the generalized variables above the cross-section of the structure. In this paper, Taylor-like polynomial expansions are adopted and the order N of the expansion is a free-parameter of the formulation. In other words, any-order models can be obtained with no need of ad hoc formulations by exploiting a systematic procedure to build finite element matrices in a form which is independent of the accuracy of the model. 1D CUF models allow to detect highly accurate shell-like static deformations and modal shapes of thin-walled structures with a significant reduction of computational costs. 1D CUF structural models were coupled to the Vortex Lattice Method, VLM, in [4]. The formulation was extended to the static aeroelastic analysis of lifting surfaces made by metallic and composite materials [5]. The computation of linear steady aerodynamic loads refers to the Vortex Lattice Method presented by Katz and Plotkin [6]. As usually adopted in preliminary aeroelastic design, the aerodynamic computation by the VLM did not consider the airfoilshaped section. Hence, an analysis tool for airfoils, wings and planes operating at low Reynolds Numbers, XFLR5, is herein adopted in order to accurately describe the aerodynamic field over the wing affected by the airfoil pressure distribution. In this paper, non-classical effects such as airfoil in-plane deformation and warping are introduced by enriching the displacement field over the cross-section of the wing. A number E. Carrera, A. Varello, and A. Lamberti 2 of composite wing configurations (by varying aspect ratio, airfoil geometry, dihedral, sweep angle, and lamination lay-up) are analyzed to evaluate the influence of non-classical crosssection deformation on the static response of a typical lifting system. The coupling of XFLR5 and 1D CUF models reveals the capabilities of such refined models in evaluating the aeroelastic behavior of composite wings. Table 1 shows a typical result from the present formulation. A swept tapered wing exposed to a free stream velocity V∞ = 50 m/s is considered. The results obtained through a solid Nastran analysis are taken as a reference solution. Results from the present models accurately match those from Nastran shell and solid FEs with a reduced computational costs. Table 1: Effect of the expansion order N of 1D CUF models on the maximum transverse displacement for different finite element mesh REFERENCES [1] E. Carrera and M. Petrolo, “On the effectiveness of higher-order terms in refined beam theories”, Journal of Applied Mechanics, 78(2), 2011. [2] E. Carrera, G. Giunta, and M. Petrolo, Beam Structures: Classical and Advanced Theories, John Wiley & Sons Ltd, 2011. [3] E. Carrera and M. Petrolo, “Refined One-Dimensional Formulations for Laminated Structure Analysis”, AIAA Journal, DOI: 10.2514/1.J051219, (In Press). [4] A. Varello, E. Carrera, and L. Demasi, “Vortex Lattice Method Coupled with Advanced One-Dimensional Structural Models”, Journal of Aeroelasticity and Structural Dynamics, 2(2), 53-78, 2011. [5] E. Carrera, A. Varello, and L. Demasi, “A Refined Structural Model for the Static Aeroelastic Response and Divergence of Metallic and Composite Wings”, submitted. [6] J. Katz and A. Plotkin, Low-speed Aerodynamics, Cambridge University Press, 2001.

Comparison between VLM and CFD Maneuver Loads Calculation at the Example of a Flying Wing Configuration

Abstract: This work presents the results of computational fluid dynamics (CFD) based maneuver loads calculations for a flying wing configuration. Euler solutions of the DLR Tau code are compared to vortex lattice method (VLM) results for maneuver loads in the preliminary design stage. The trim parameters of the quasi-steady maneuver load case, the structural deformation and the flow solution are determined in an iterative process. The focus is on a comprehensive loads analysis including a broad selection of load cases to cover the whole flight envelope. This is necessary to ensure a thorough preliminary design. Integration of this approach in an automated, preliminary design process and application of parametric, aeroelastic modeling allows to perform structural optimization loops to evaluate the difference between VLM and CFD on the structural design in terms of structural net mass.