Horizontal walls effect on the subsonic flow around airfoil by the image method
DOI:
https://doi.org/10.38152/bjtv7n4-008Keywords:
ground effect, two-wall effect, aircraft take-off, image method, cubic spline, ideal gas, pressure ratio, aerodynamics coefficientAbstract
The aim of this work consists in developing a new numerical method and a calculation program making it possible to determine the effect of one and two horizontal walls on the distribution of the pressure ratio, and the aerodynamics coefficients of a subsonic flow around airfoils. The model is considered for the perfect gas. The calculation is presented by adding the effect of one and two walls on the discretization of the airfoils boundary to obtain a closed surface. The method is called by the image method. So for the case of the existence of one wall, we will see a single image of the main airfoil, and in the case of two walls, we will have an infinity of images. The equation system is obtained by considering the effect of all images using alternating digital series, whose convergence is ensured numerically. We therefore obtain a large system of equations, the resolution of which is done by the Khaletski method to obtain the velocities and pressure. The application is made for some practical interest’s airfoils. Since the airfoils boundary is given by tabulated values, the cubic spline interpolation is used to obtain an analytical equation of the upper and the lower surfaces. The comparison is made with the case of open air flow by extending the distance between the walls and the airfoil chord towards infinity.
References
Achour D., (2017) “Séries numériques et de fonctions,” Editions universitaires européennes, Allemagne. ISBN 978-3-639-48073-3
Anderson J. D. Jr., (2001) “Fundamentals of Aerodynamics,” McGraw-Hill Inc., 3rd Edition, New York, USA
Ashley H. and Landahl M., (1985) “Aerodynamics of Wing and Bodies,” 2nd Edition, Dover Publication.
Bhargava V., Maddula S. P., Venkata N., Khan S. N., Padhy C. P. and Duttaz Y. D., (2022) “ Aerodynamic flow modelling of NACA 0010 using 2D panel and Jukouwski methods,” Aircraft Engineering and Aerospace Technology, Vol. 94 No. 6, PP. 965-980, https://doi.org/10.1108/AEAT-07-2021-0199
Bourekba F., O. Guerri O. and Nait Bouda N., (2015) “Simulation de l’écoulement autour d’un profil à l’aide d’une méthode DES,” Revue des Energies Renouvelables, Vol. 18, N°4, PP. 565-574.
Bruno C., (2019) “L’application des nombres complexes au calcul des profils d’ailes,” Comptes Rendus Mécanique, Vol. 347, PP. 544-549.
Colera M., Prez Saborid M., (2017) “An efficient finite differences method for the computation of compressible, subsonic, unsteady flows past airfoils and panels,” Journal of Computational Physics. Vol. 345, N° C., PP. 596-617
Gleason A. D., Joel I., Concessao J. Q., (2015) “Study of Aerofoil Design Parameters for Low Speed Wind Tunnel,” Journal of Mechanical Engineering and Automation, Vol. 5, N° 3B, PP. 47-54, doi:10.5923/c.jmea.201502.10
Jurkat W. B., (1982) “Best Approximations of Alternating Series,” Journal of approximation Theory, Vol. 34, PP. 391-422.
Karaca H. D., Özen G. D. and Kasnakoğlu C., (2016) “Nonlinear modelling and control of the flow over aerofoils using CFD simulations” Simulation Modelling Practice and Theory, Vol. 67, PP. 29-43
Katz J. and Plotkin A., (2015) “Low-speed Aerodynamics, From Wing Theory to Panel methods,” New York, McGraw-Hill
Roy J. F., (2018) “Fluides parfaits incompressibles,” Edition Marketing, Ellipses.
Ryhming I. L., (1988) “Dynamique des fluides,” Presse polytechniques romandes.
Suenaga K. and Sakai M., (2001) “A cubic spline approximation of an offset curve of a planar cubic spline,” International Journal of Computer Mathematics, Vol. 78, N° 03, PP. 445-450, https://doi.org/10.1080/00207160108805122
UIUC Applied Aerodynamics Group, (2013) http://www.ae.illinois.edu/m-selig/ads/coord_database.html, department of Aerospace Engineering, College of Engineering, University of Illinois at Urbana, Champaign, Il.
Vinokur M., (1983) “On one-dimensional stretching functions for finite-difference calculations,” Journal of Computational Physics, Vol. 50, N° 02, PP. 215-234, https://doi.org/10.1016/0021-9991(83)90065-7
Zebbiche T., Salhi M. and Boun-djad M., (2012) “Numerical computation of supersonic flow around a pointed airfoils,” Journal of Computational Methods in Sciences and Engineering, Vol. 12, N° 03, PP. 213-233
