Asymptotic Modeling the Aerodynamic Coefficients of The NACA Airfoil

Abstract

In this study, we are interested in the asymptotic modeling of the two-dimensional stationary flow of a viscous incompressible fluid around wing airfoil. The aim of the present paper is to use the method of matched asymptotic expansions to study the laminar boundary layer behavior over a NACA (National Aeronautic and Space Administration) airfoil. At large Reynolds number and using singular perturbations methods, we distinguish the problems inside and outside the boundary layer. These problems are coupled under asymptotic constraints according to the least degeneration principle. Using the affinity hypothesis for the velocity field in the boundary layer, and assuming that the transverse velocity is of order ꓳ(Re-1/2), we establish an approached composite solution, and follows the aerodynamic coefficients (drag and lift) are determined. The results obtained show that accurate modeling is possible for laminar incompressible flow. The predicted solutions obtained compare well with the results of a NACA43013 airfoil produced by the Ansys fluent.

Optimizing Aerodynamic Efficiency in Subsonic Flows: A Parametric Analysis of Bio-Inspired Flaps using Asymptotic Methods

“…by an order of Re −1/2 , which is usually the same thickness of the boundary layer, it manifests the disturbance in the transverse velocity. The flow is characterized by inviscid, rotational disturbances.− Outer Layer: This portion epitomizes the boundary layer without the influence of the flap and aligns with the portrayal rendered the study by Hasnaoui et al[4].…”

“…Building upon the previous chapter, where the pressure coefficient Cp and the skin friction coefficient Cf were rigorously calculated, and based on the analysis from Hasnaoui et al [4], the focus of this section shifts towards the integration of these individual components into a comprehensive drag coefficient Cd.…”

“…The incorporation of the flap significantly impacts the overall flow structure and, consequently, aerodynamic performance. The pressure and friction coefficients will be formulated as a superposition of the coefficients derived in the flap-free case, as described by Hasnaoui et al [4], and additional terms accounting for the perturbations induced by the flap. This mathematical framework offers a comprehensive view of aerodynamic behavior, facilitating further computational simulations and analytical assessments.…”

“…In line with the current trends in the field, this paper aims to extend the asymptotic model of twodimensional, stationary, incompressible fluid flow around airfoils, initially developed by M. Hasnaoui et al [4]. Specifically, this research will focus on the asymptotic modeling of passive BL control by examining the influence of various parameters such as the drag coefficient (Cd), lift coefficient (Cl), pressure coefficient (Cp), and skin friction coefficient (Cf).…”

Investigation of viscous supersonic laminar flows around F-16 airfoil: experimental, numerical, and analytical approaches

“…In other words, the entire domain is geometrically modelled by many smaller domains. The interest of meshing is to obtain the simplification of the simulations of calculations, Naamane and Hasnaoui (2019), Hasnaoui et al (2019).…”