A fast algorithm for inverse airfoil design using a transpiration model and an improved vortex panel method

Abstract

A fast algorithm for inverse airfoil design using an efficient panel method for potential flow calculation is presented. The method employs linear vortex distributions on the panels and a consistent procedure for imposing the Kutta condition, thus eliminating the spurious aerodynamic loading that usually appears at a cusped trailing edge. The algorithm searches the airfoil ordinates attending to a given surface velocity distribution with fixed abscissas. It begins with a guessed starting shape and successively modifies it by an iterative process, such that the normal velocity vanishes and the calculated velocity distribution gradually approaches the required one. Each iteration is performed in two main steps: 1) the flow calculation step; 2) the geometrical marching step, where the calculated velocity distribution is compared with the required one and a transpiration model is applied to modify the current shape towards another one more close to the target shape. The geometrical marching is conducted by varying the panel slopes as a function of the normal velocity excess induced by the difference between the required and calculated velocities. A scheme is applied in order to close the body shape. Various test cases were carried out and are presented for the efficiency and robustness validation of the proposed inverse algorithm

Computational analysis of NACA 0010 at moderate to high Reynolds number using 2D panel method

“…The method as described before evaluates the relative velocity and its components on every panel of the airfoil surface and predicts the pressure coefficient, Cp, by calculating the influence coefficients and tangential velocity vector. The present panel method has been validated using the results obtained from the inverse design method, 6 Hess and Smith method 6 and analytical results of (Petrucci, 2007) as shown in Figure 7. The vortex panel method was implemented to verify the inverse design algorithm for the incompressible flows on a conformal mapped symmetric jukouwski airfoil having 10 % thickness.…”

“…The vortex panel method was implemented to verify the inverse design algorithm for the incompressible flows on a conformal mapped symmetric jukouwski airfoil having 10 % thickness. 6 It was revealed that source panel method implementation by Petrucci et al, showed geometric convergence problems for cambered airfoils. In his study, several iterations were required for geometric convergence in case of cambered airfoils in contrast to symmetric airfoils for different flow configurations.…”

“…The application of source and vortex panel was done consistently on each panel of airfoil geometry to ensure integrity in every calculation step (Figures 4-7). In the study of Petrucci 6 the results of the pressure coefficient obtained from inverse design algorithm were also compared with analytical results of the Boundary Integral method that includes boundary layer thickness and viscous effects. The pressure peaks near the leading edge are under predicted in all inverse design methodologies.…”

“…The polynomial equations representing the geometry of NACA 4 digit airfoils are detailed in text. [6][7][8] Figure 2 is the illustration of the airfoil shape parameters with its leading edge radius representing the roundness of airfoil and also the flow stagnation point.…”

A comprehensive review of the theoretical approaches for the airfoil design of lift-type vertical axis wind turbine

“…It should be noted that the pure inverse design can be implemented by conformal mappings, streamline coordinatebased transformations, boundary integral formulations and Panel method [118]. Thus, it may be better to integrate the Panel method into the inverse airfoil design, especially for the CP prediction of the Darreius rotor [119].…”