Ernani Volpe

A Study of the CST Parameterization Characteristics

This paper presents a study of the recently introduced Class-Shape function Transformation (CST). The study assesses some of the main characteristics that parameterization exhibits, such as the sensitivity to parameter perturbations, the uniqueness of a geometric representation, its filtering capability and parameter inter-dependence. In a gradient-based shape optimization process, the solutions of intermediate design cycles are naturally subject to numerical inaccuracy. Under such circumstances, those characteristics of the CST may affect the path and, eventually, compromise the performance of the optimization process depending on the gradient calculation method and minimum-search algorithm. A comparison of two different gradient calculation methods is presented in the context of inverse aerodynamic design along with some validation test cases.

Maximum entropy pdfs and the moment problem under near-Gaussian conditions

This paper focuses on a class of continuous probability density functions (pdfs) that are generated by the maximum entropy method (mem), which are of potential interest in fluid dynamics. It discusses their properties and presents a method for obtaining approximate solutions to the moment problem that is associated with this class of pdfs. The method allows one to express pdf parameters in terms of constrained moments, alone. The results thus obtained hold for pdfs that represent small perturbations from a known pdf within this class. On combining these results with exact moment equations, one obtains successful approximations to the closure relations that are associated with these pdfs. The Gaussian pdf belongs in this class, and the method can be used to explore the near-Gaussian region.

Characteristics-based Boundary Conditions for the Euler Adjoint Problem: 2 D Formulation

Over the last decade the adjoint method has been consolidated as one of the most versatile and successful tools for aerodynamic design. It has become a research area on its own, spawning a large variety of applications and a prolific literature. Yet, some relevant aspects of the method remain relatively less explored in the literature. Such is the case with the adjoint boundary conditions and, more specifically, with regard to permeable boundaries. The present work discusses at length a novel approach to the continuous adjoint boundary problem, with emphasis on the full characteristic formulation of the far– field boundary conditions. The main goal of this approach is to ensure the well–posedness of the adjoint equations and consistency with the primal problem.

Numerical Study of the Flow Around a Circular Cylinder with Dual Parallel Splitter Plates

A simple way to decrease the drag and oscillating lift forces in the flow around a circular cylinder consists of positioning splitter plates in the wake of the flow. In our work, a geometry consisting of two splitter plates placed close to a circular cylinder was studied. The length of the splitter plates is equal to the cylinder diameter and they are positioned in a side by side configuration parallel to the freestream velocity, with their leading-edges aligned with the cylinder center. This flow was studied using two-dimensional direct numerical simulations, with the Spectral Element Method being employed to solve the incompressible Navier-Stokes equations for Reynolds numbers in the range between 100 and 350. The results showed a strong dependence on the Reynolds number, with the splitter plates being more beneficial at the higher values of Reynolds numbers considered.

Inverse aerodynamic design applications using the MGM hybrid formulation

The well-known modified Garabedian–Mcfadden (MGM) method is an attractive alternative for aerodynamic inverse design, for its simplicity and effectiveness (P. Garabedian and G. Mcfadden, Design of supercritical swept wings, AIAA J. 20(3) (1982), 289–291; J.B. Malone, J. Vadyak, and L.N. Sankar, Inverse aerodynamic design method for aircraft components, J. Aircraft 24(2) (1987), 8–9; Santos, A hybrid optimization method for aerodynamic design of lifting surfaces, PhD Thesis, Georgia Institute of Technology, 1993). Owing to these characteristics, the method has been the subject of several authors over the years (G.S. Dulikravich and D.P. Baker, Aerodynamic shape inverse design using a Fourier series method, in AIAA paper 99-0185, AIAA Aerospace Sciences Meeting, Reno, NV, January 1999; D.H. Silva and L.N. Sankar, An inverse method for the design of transonic wings, in 1992 Aerospace Design Conference, No. 92-1025 in proceedings, AIAA, Irvine, CA, February 1992, 1–11; W. Bartelheimer, An Improved Integral Equation Method for the Design of Transonic Airfoils and Wings, AIAA Inc., 1995). More recently, a hybrid formulation and a multi-point algorithm were developed on the basis of the original MGM. This article discusses applications of those latest developments for airfoil and wing design. The test cases focus on wing-body aerodynamic interference and shock wave removal applications. The DLR-F6 geometry is picked as the baseline for the analysis.