Scientific Bulletin of the Politehnica University of Timisoara Transactions on Mechanics Special issue Workshop on Vortex Dominated Flows – Achievements and Open Problems Timisoara, Romania, June 10 - 11, 2005 THE VORTEX-PROFILE INTERACTION CONSIDERING POROSITY EFFECTS Corneliu BERBENTE, Professor* Department of Aerospace Sciences “Elie Carafoli” POLITEHNICA University Bucharest Sorin MITRAN, Assoc. Prof. University of North Caroline, USA Sterian DANAILA, Professor Department of Aerospace Sciences “Elie Carafoli” POLITEHNICA University Bucharest Marius STOIA-DJESKA, Lecturer Department of Aerospace Sciences “Elie Carafoli” POLITEHNICA University Bucharest *Corresponding author: Polizu 1-6, 011061, Bucharest, Romania Tel.: (+40) 21 4023967, Fax: (+40) 21 2129220, Email: berbente@yahoo.com ABSTRACT The unsteady 2D flow around a helicopter blade profile, including a moving vortex generated by the foregoing blade at a sudden change of the angle of attack is studied. The flow regime is transonic in order to analyze the vortex influence on a shock wave. In addition, a porosity effect is simulated by a channel connecting regions located upstream and downstream this shock wave, on the profile upper side. The porosity proves to lead to a slower repositioning of the shock wave on the upper side. Comparative diagrams for the iso-Mach lines as well as for the pressure distribution obtained by using the large eddy simulation are presented. KEYWORDS LES, unsteady transonic flow, vortex-shock interaction. NOMENCLATURE eff lam sgs μ μ μ = + the effective viscosity eff lam sgs λ λ λ = + the effective heat conductivity Pr lam p lam lam c μ λ = the molecular heat conductivity Pr sgs p sgs sgs c μ λ = the turbulent heat conductivity p c the specific heat at constant pressure Δ the spatial filter width k the porosity coefficient in the Darcy law , nt f f the unit normal and tangential vectors L the distance between the two pressure stations c the chord of the wing section Subscripts and Superscripts lam laminar sgs sub-grid scale inf upstream infinity conditions ABBREVIATIONS Pr Prandtl number M Mach number 1. INTRODUCTION The numerical simulation of the unsteady 2D transonic flow is of great importance for the under- standing of the mechanisms leading to noise generation. In the case of helicopter rotor blades, the main part of the aerodynamic noise is due to the interaction of the shock wave occurring in the transonic regime with the traveling vortex produced by a foregoing blade. For modern helicopters and not only, the reduction of the aerodynamic noise produced in the way briefly described above is a crucial step in the development process. The accurate prediction of the acoustic pressure fluctuations due to the interaction between the moving vortex and the shocks cannot be done without taking into account the turbulence effects. Present study solves