Figure 6a. Flow past a helicopter: boundaries of the computational domain.
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Figure 6b. Flow past a helicopter: surfaces of the shear-slip mesh layer.
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Figure 6c. Flow past a helicopter: pressure on the fuselage and the rotor.
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The DSD/SST formulation and the SSMUM approach have been used to simulate a flow around a helicopter with a spinning main rotor. The computational domain, shown in Figure 6a, has dimensions 30.00 m x 20.00 m x 20.00 m. The fuselage of the helicopter is modeled after Boeing Sikorsky Comanche prototype, although an exact reproduction of a particular type of helicopter was not among our top priorities. The length of the fuselage (without the rotor) is 13.22 m. The main rotor, with five blades, has a diameter of 11.90 m. The shear-slip layer is an axisymmetric shell with interior radii of 6.00 m and 0.25 m, and a mostly uniform thickness of 0.10 m. The shell is closed, except for the opening at the base of the rotor. To accommodate the close spacing between the top of the fuselage and the rotor blades, the thickness of the layer in that area is reduced to 0.04 m.

The mesh consists of 361,434 space-time nodes and 1,096,225 tetrahedral elements. The regular shear-slip layer, which is one element thick, has 80 segments in the circumferential direction and 100 segments in the radial direction. This layer goes through shear deformation during each time step, and at the end of the time step re-connects to the new nodes belonging to the rotating interior disk. The unstructured meshes in both the inner (rotating) and the outer (stationary) rigid regions of the domain were generated using an automatic mesh generator.

The structured mesh which fills the shear-slip region was generated manually. The helicopter is assumed to be in a forward horizontal flight, and a free-stream velocity of (10.0, 0.0, 0.0) m/s is imposed at the upstream boundary. The Reynolds number based on the upstream velocity and the main rotor diameter is approximately 8x10⁶. In the Smagorinsky turbulence model we use C=0.15. Zero normal velocity and zero shear stress conditions are specified at all transverse boundaries, and a traction-free condition is imposed at the outflow. The steady-state solution at Reynolds number 8 serves as the initial condition. The unsteady flow is computed for 480 time steps with a time step size of 0.00234 s. The rotor is rotating in counter-clockwise direction when viewed from the top, with a tip velocity of 200 m/s. Figure 6b shows the outer (stationary, blue) and inner (rotating, red) surfaces of the slip layer. Figure 6c illustrates the evolution of the pressure field on the fuselage of the helicopter.

This computation has been carried out on the CRAY T3E-1200. At every time step the coupled, nonlinear equations are solved with 4 Newton-Raphson iterations. The coupled, linear equations that need to be solved at each Newton-Raphson step are solved also iteratively, with the GMRES update techniques with a Krylov space size of 40. More information on the SSMUM approach and on this simulation can be found in Behr and Tezduyar (1999a) and (1999b).