Supersonic Flow around a Dihedral Airfoil: Modeling and Experimentation Investigation
Numerical modeling of fluid flows, whether compressible or incompressible, laminar or turbulent presents a considerable contribution in the scientific and industrial fields. However, the development of an approximate model of a supersonic flow requires the introduction of specific and more precise techniques and methods. For this purpose, the object of this paper is modeling a supersonic flow of inviscid fluid around a dihedral airfoil. Based on the thin airfoils theory and the non-dimensional stationary Steichen equation of a two-dimensional supersonic flow in isentropic evolution, we obtained a solution for the downstream velocity potential of the oblique shock at the second order of relative thickness that characterizes a perturbation parameter. This result has been dealt with by the asymptotic analysis and characteristics method. In order to validate our model, the results are discussed in comparison with theoretical and experimental results. Indeed, firstly, the comparison of the results of our model has shown that they are quantitatively acceptable compared to the existing theoretical results. Finally, an experimental study was conducted using the AF300 supersonic wind tunnel. In this experiment, we have considered the incident upstream Mach number over a symmetrical dihedral airfoil wing. The comparison of the different Mach number downstream results of our model with those of the existing theoretical data (relative margin between 0.07% and 4%) and with experimental results (concordance for a deflection angle between 1° and 11°) support the validation of our model with accuracy.
 S. Lele. "Direct numerical simulation of compressible free shear flows", 1989, 27th Aerospace Sciences Meeting, Aerospace Sciences Meetings, NASA, Ames Research Center, Moffett Field; Stanford University, CA, https://doi.org/10.2514/6.1989-374.
 Y. Bartosiewicz, Z. Aidoun, P. Desevaux, Y. Mercadier“Numerical and experimental investigations on supersonic ejectors”, 2005, International Journal of Heat and Fluid Flow, doi.org/10.1016/j.ijheatfluidflow.2004.07.003.
 M. Saif Ullah Khalid*, Afzaal M. Malik “Modeling & Simulation of Supersonic Flow Using McCormack’s Technique”, 2009, Proceedings of the World Congress on Engineering 2009 Vol II WCE 2009, July 1 - 3, London, U.K.
 L. Zhou, Y. Chen, F. Chen, “Chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow” 2013; Aerospace science and technology. 25(1):138-144 https://doi.org/10.1016/j.ast.2012.01.001.
 S. Chen, J. Z. Min and Y. Zhang, “Weak Shock Solution in Supersonic Flow Past a Wedge”, 2009, pp. 115- 132, Discrete and Continuous Dynamical Systems, Volume 23, Number 1 & 2, January & February 2009.
 V. Elling, T. Liu, “Supersonic Flow onto a Solid Wedge”, 2008, Communication on Pure and Applied Mathematics, Volume 61, Number 10, 2008.
 Dilmurod T. Aliakbarov; Anatoly A. Kukin; Vladimir V. Trofimov “The possibility of studying supersonic flow profile close to the screen by the method of hydraulic analog modeling” 2018, Naučnyj Vestnik MGTU GA, Vol 21, Iss 1, Pp 60-66 (2018) DOI: 10.26467/2079-0619-2018-21-1-60-66.
 Shoja-Sani. A; Roohi. E; Kahrom. M; Stefanov. S “Investigation of aerodynamic characteristics of rarefied flow around NACA 0012 airfoil using DSMC and NS solvers”, 2014, European journal of mechanics B/Fluids, Volume 48, November–December 2014, Pages 59-74.
 Zeytounian, R. Kh., “Asymptotic Modelling of Fluid Flow Phenomena”, 2002, FMIA, vol. 64. Kluwer Academic Publishers, Dordrecht.
 D. Caillerie, J. Cousteix, J. Mauss, “Méthodes asymptotiques en mécanique”. 2016, Edition Cépaduès, I. S. B. N.: 9782364935037. S.