A two-dimensional model of the aerodynamics of rotor blades in forward flight is proposed in which the motion of the blade is represented by periodical variations of the freestrearn velocity and incidence. A novel implicit methodology for the solution of the compressible Reynolds averaged Navier-Stokes equations and a twoequation model of turbulence is developed. The spatial discretisation is based upon Osher's approximate Riernann solver, while time integration is performed using a Newton-Krylov method. The method is employed to calculate the steady transonic aerodynamics of two supercritical aerofoils and the unsteady aerodynamics of pitching aerofoils. Comparison with experiment and independent calculations for these test cases is satisfactory. Further calculations are performed for the self-excited periodic flow around a biconvex aerofoil. Comparison of quasi-steady and unsteady calculations suggests that the flow instability responsible for the self-excited flow is due to the presence of a shock induced separation bubble in the corresponding steady flow. Finally the method is used to predict the aerodynamics of aerofoils performing inplane and combined inplane-pitching motions. Results show that quasi-steady aerodynamic models are unsuitable at conditions representative of high-speed forward flight. For shock free flows, the unsteady effects of freestrearn oscillations can be represented by a simple phase lag. For transonic flows the influence of unsteadiness on shock wave dynamics is shown to be complex. Calculations for indicial motion show that the unsteady behaviour of the flow is related to the finite time taken by disturbance waves to travel to the shock wave from the leading and trailing edges of the aerofoil
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