Analysis of Unsteady Aerodynamics of Airfoils by RANS Based CFD

Abstract

In this work, the transonic unsteady aerodynamics calculations associated with simple harmonic pitching, indicial response to a step change in angle of attack, for NACA 64A010 airfoil are computed using CFD based on RANS. The parametric efiect of Spalart-Allmaras and SST-k! turbulence models on the unsteady aerodynamics of airfoils is investigated. These results are compared with the available experimental results together with the in- viscid solutions. The unsteady aerodynamics of airfoils plays a major role in flxed-wing as well as rotary-wing aircraft. For flxed-wing aircraft, these unsteady aerodynamics calculations are part of the ∞utter analysis of the aircraft. Also, they are required for dynamic response analysis of the rigid as well elastic aircraft. These dynamic responses are required for stability and control analysis as well as to determine the gust loads on the aircraft. For rotary wing aircraft, such as helicopters and tilt-rotor air- craft, the steady state ∞ight itself is unsteady. This is because the rotor blade in forward ∞ight experiences difierential lift dur- ing its azimuthal rotation. On the advancing side ( = 0 o to 180 o ), the blade experiences higher lift than on the retreating side ( = 180 o to 360 o ) as shown in flgure 1, due higher blade element velocities on the advancing side. To balance the dif- ferential lifts experienced on advancing and retreating sides, to avoid rolling problem, blades are provided with cyclic pitch. This cyclic pitch is the flrst harmonic variation of the pitch in the form £cyclic = £1c cos + £1s sin, where = ›t. This cyclic pitch reduces the blade pitch on the advancing side while increasing on the retreating side to balance the difierential dynamic pressures on the both sides. Thus, the aerodynamics of the steady state ∞ight itself becomes unsteady. In addition, the blade experiences a ∞uctuating free stream of the form VR = ›r + V cosfisin, where fi is the rotor disk plane (hub plane) angle of attack as shown in flgure 2. Also, compressibility efiects are important for outboard sections since they operate at high subsonic Mach numbers. Thus, the unsteady aerodynamics becomes very important for classical ∞ight control and stability analysis and for blade aero-elastic instabilities. In addi- tion, the retreating blade experiences dynamic stall near reverse ∞ow boundary. The reverse ∞ow boundary is given by VR = ›r + V cosfisin = 0. The circular region inside this boundary is the reverse ∞ow region where the local ∞ow takes place from the trailing edge to leading edge. The dynamic response of the blade in this region is very important because of its efiect on the blade loads, control loads, stall ∞utter, and vibrations. All these analyses require the unsteady aerodynamics. The unsteady aerodynamics calculation are usually performed employing classical potential ∞ow theories developed over several decades starting in