SUMMARYA framework is described and demonstrated for CFD analysis of helicopter rotors in hover and forward ight. Starting from the Navier-Stokes equations, the paper describes the periodic rotor blade motions required to trim the rotor in forward ight (blade apping, blade lead-lag and blade pitching) as well as the required mesh deformation. Throughout, the rotor blades are assumed to be rigid and the rotor to be fully articulated with separate hinges for each blade. The employed method allows for rotors with di erent numbers of blades and with various rotor hub layouts to be analysed. This method is then combined with a novel grid deformation strategy which preserves the quality of multi-block structured, body-ÿtted grids around the blades. The coupling of the CFD method with a rotor trimming approach is also described and implemented. The complete framework is validated for hovering and forward ying rotors and comparisons are made against available experimental data. Finally, suggestions for further development are put forward. For all cases, results were in good agreement with experiments and rapid convergence has been obtained. Comparisons between the present grid deformation method and transÿnite interpolation were made highlighting the advantages of the current approach.

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Numerical simulation of three-dimensional dynamic stall has been undertaken using computational fluid dynamics. The full Navier-Stokes equations, coupled with a two-equation turbulence model, where appropriate, have been solved on multiblock strucured grids in a time-accurate fashion. Results have neen obtained for wings of square planform and of NACA 0012 section. Efforts have been devoted to the accurate modeling of the flow near the wing tips, which, for this case, were sharp without tip caps. The obtained results revealed the time evolution of the dynamic stall vortex, which, for this case, takes the shape of a capital omega Ω spanning the wing. The obtained results compare well against experimental data both for the surface pressure distribution on the wing and the flow topology. Of significant importance is the interaction between the three-dimensional dynamic stall vortex and the tip vortex. The present results indicate that once the two vortices are formed both appear to originate from the same region, which is located near the leading edge of the tip. The overall configuration of the developed vortical system takes a Π-Ω form. To our knowledge, this is the first detailed numerical study of three-dimensional dynamic stall appearing in the literature.

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The computation of the aerodynamic forces arising from forced periodic motions is required for the generation of dynamic terms in models for flight simulation. The periodicity can be used to avoid using fully unsteady calculations by using the harmonic balance method. The current paper develops an implicit solver for the harmonic balance equations. The method is tested on two transonic test cases and evaluation is made against the unsteady simulation results. The first case is for the pitching NACA 0012 aerofoil. The second is for forced pitching of the F-5 wing with a wing tip launcher and missile. A reduction in computational time by one order of magnitude compared with the unsteady solver is obtained. Nomenclature A = matrix in frequency domain equation c = chord D = matrix in harmonic balance equation E = transformation matrix between frequency and time domains e = energy F, G, H = convective fluxes I = residual of semidiscrete system I = identity matrix k = reduced frequency n H = number of harmonics p = pressure R = residual vector T = period t = time u, v, w = Cartesian velocity components W = conserved variables = angle of attack t = pseudo time step t = real time step = density ! = frequency Subscripts m = mean value hb = harmonic balance 1 = freestream value 0 = amplitude Superscripts n = time level = Fourier coefficient

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