The Problem:
The aerodynamic loading on a rotor blade, in both the hover and forward flight regimes, is highly dependent on the vortical wake shed by the previous blade passages. In hover a complex helical wake forms below the blades, while in forward flight the wake is swept downstream, rather than form below the blades, but each blade experiences completely time-dependent loads, with large variations around the azimuth as the tip vortices from previous blades vary in both strength and position.
The Challenge:
The accurate capture of the rotor wake is vital during any rotor simulation if the time-dependent blade loads are to be predicted correctly. The rotor blades must be trimmed according to the aerodynamics but, also, the noise and vibration levels and frequencies are determined by the wake characteristics. Hence, large grid densities are required, for a conventional compressible F-V code, to resolve the wake to sufficient distance to obtain the correct blade influence, as well as long numerical integration times for the wake to develop. Forward flight also requires very small time-steps to accurately resolve blade-vortex interactions (BVI), and so parallelisation is essential.
Use of HPCx:
HPCx time allocated to the UKAA Consortium allowed simulation of hover and forward flight cases using meshes of up to 32 million cells, to allow grid dependence of blade loading to be quantified. Four-bladed hover and
forward flight cases were run. The forward flight case, with intermediate
advance ratio (0.214), was run fully unsteady using the Bristol ROTORMBMGP
code, on 256 CPUs. Four cycles of revolution required six days of wall clock time.
Outcomes:
In forward flight, the grid density was shown to be critical when considering BVI. Shown below is sectional blade loading for 70% and 92% tip radius for four million cells (limit of scalar code), and 32 million, compared with experiment, and the spikes due to BVI are clearly absent in the coarser mesh.
Vorticity shading for the two meshes is shown below, again clearly demonstrating
the grid dependence.
Hover cases run on finer meshes were shown to be unsteady. All previous hover
cases simulated with compressible CFD codes were run as steady cases. However,
stability analysis shows the wake is unstable to any perturbation, and the
simulations here were the first to show this. A full unsteady simulation of
hover was then performed on 32 million cells to analyse time history. Shown
below is vorticity in the periodic plane behind one blade, and unsteadiness
in the vorticity field (green is steady), at one timestep. Fourier analysis
of the vorticity field showed the expected peaks at one, four, and eight
times rotor frequency, also shown below.
Future:
During UKAAC2, the method will be extended to include the helicopter fuselage, and aeroelastic deformation of the blades.
References:
- Allen, C.B., Parallel Simulation of Unsteady Hovering Rotor Wakes, International Journal for Numerical Methods in Engineering, Vol. 68, 2006, pp632-649.
- Allen, C.B., Parallel Universal Approach to Mesh Motion and Application to Rotors in Forward Flight, International Journal for Numerical Methods in Engineering, Vol. 69(10), 2007, pp2126-2149.
- Allen, C.B., Sunderland, A.G., Johnstone, R., Application of a Parallel Rotor CFD Code on HPCx, Aeronautical Journal - Special Supercomputing in Aerodynamics Edition, Vol. 111, No. 1117, 2007, pp145-152.
- Allen, C.B., Parallel Solution of Lifting Rotors in Hover and Forward Flight, International Journal for Numerical Methods in Fluids, Vol. 55. No. 1, 2007, pp15-27.
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