The solution methodology in this case was a blind calculation following the best practices for moving body simulation within STAR-CCM+. Initial runs were performed on a coarse grid, to obtain an initial solution that was used for verification of the set-up and to identify zones for mesh refinement. The solution process followed the wind tunnel tests in reverse, with a full configuration for the S-92A hub initially, followed by removing the beanie, pushrods, scissors and servos, swash plate and bifilar in consecutive runs.
Similarly, the UH-60A runs were started with a full configuration, followed by removal of bifilar and pitch-link rods in subsequent steps. In total, there were six and three configurations each for the S-92A and UH-60A hubs, respectively. Steady-state simulations were conducted on both hubs with an inlet velocity of 150 knots, a hub rotational rate of 500rpm and an advance ratio of 0.36, similar to advance ratios on a full-scale rotorcraft. The simulations were run at the same Reynolds number and Mach number as the experiments, but at half-scale values compared with flight conditions.
Steady-state runs were conducted with the moving reference frame (MRF) approach on coarse grid for the hubs, where the hubs didn’t physically rotate but the effect of rotation was included in the flux calculation. The finer mesh runs were started from the steady-state solution, using rigid body motion for the rotor hubs.
Two unsteady runs, unsteady RANS (Urans) and detached eddy simulation (Des), were performed. The Urans runs were restarted from steady-state solution and Des runs restarted from Urans solution with SST (Menter) turbulence model. The unsteady runs were performed with a time step size varying from 0.5 to 5° of hub rotation per time step.
In terms of the results, the drag from the steady-state runs with MRF was equal to the maximum drag predicted in the Des runs with a 5° hub rotation per time step. As expected, the maximum drag occurred when the blade attachments were perpendicular to the flow with large frontal area (90°), while minimum drag occurred when the blade attachments were at a 45° angle to the flow with minimum frontal area.
The time-averaged drag value differed by 4% between the 5° and 0.5° time steps, while the difference in averaged drag between Urans and Des runs was 0.6%. The Des method resolved the turbulence in the hub wake better, but the spectral content of this turbulence did not have much impact on overall hub drag. The final validation simulations for both hubs with their different configurations were performed as Des runs with a time step of 5°.
Results from the Des runs for the S-92A hub showed that the addition of components increased drag, and correlated well with the wind tunnel results. The numerical results generally overpredicted drag slightly, and the largest error between simulations and test was less than 7%. For the UH-60A hub, the numerical results underpredicted the drag, while other trends were the same as the S-92A hub.
The S-92A hub showed a tail excitation during tests in the early stages of flight development, which was attributed to the wake from the scissor and associated fittings on the rotor hub – the only structures that could induce a 2 per rotor revolution forcing function. This was resolved by raising the vertical position of the hub and by making changes to the pylon. The unsteady analysis on the S-92A hub compared the fast Fourier transformation of the unsteady rotor hub drag with and without scissor and scissor fittings. The simulations with all components included led to a large 2p drag force, while configurations without the scissors still exhibited a small 2p content coming from a small drag from the scissor fittings.
Egolf says the results of this initial study are promising. “The blind numerical simulations showed that STAR-CCM+ could predict the hub drag reasonably well, with the largest error being 7% compared with the experiments. For an initial study without grid convergence analysis, these were acceptable. The predictions will only improve with solution-based grid refinement and time step studies.”
The process was not too demanding in terms of labour and CPU work, he says. “The time taken to go from CAD to results was 14 man-hours and 30 CPU-hours for MRF studies, and 75 CPU-hours for Des studies. These numbers showed that an experienced user could conduct a hub drag analysis as part of the design study quickly with acceptable accuracy.”
The technique also has potential for other aspects of helicopter design. As well as generating grids in a timely manner for complex hub drag studies, Egolf says that STAR-CCM+ is well-poised to take on the challenge of predicting, with high fidelity, the wake structure downstream of the hub.
Drag in helicopters is a big problem, and helicopter makers search for ways to reduce it. A recent study that used computational fluid dynamics to predict the drag of production rotor hub geometries could profoundly affect the way that these manufacturers go about establishing power and propulsive force requirements at high speeds.
The total drag on a helicopter is the sum of the parasitic, frictional and lift-induced drag. In single-rotor helicopters, almost 33% of the total vehicle drag can be caused by the parasitic drag from the hub. So makers such as US-based Sikorsky Aircraft are employing advanced CFD techniques to reduce this drag.
One way to cut hub drag on conventional articulated rotors is to use a fairing, which fits over part of the rotor mechanism. But this has an impact in terms of increased maintenance and inspection work.
Instead, lower drag can be designed in from the start. “Design the components of the hub such that they generate less drag as a whole when installed,” says Alan Egolf, supervisor of aerodynamic methodology at Sikorsky.
First, the hub drag needs to be estimated. “Traditionally, hub drag estimation involved predicting the drag build-up of the components based on data from components of similar shapes and summing up their contributions,” he says. But there are drawbacks to this. “Aside from being based on historical data, this method involves estimation of interference effects and is less valuable in a production environment where optimisation of component shapes is important. The rotor hub designed based on this subjective process is tested in a wind tunnel, leading to an expensive process if design changes are to be implemented and tested again.”
So Sikorsky has been exploring an alternative method of predicting hub drag of production geometries, based on numerical simulation. This can provide a reasonable prediction, within a short period, of hub drag for different designs, allowing easier optimisation of components in a production environment. The work has been carried out primarily in CD-Adapco’s unstructured Navier Stokes solver, STAR-CCM+, to the blind prediction of hub drag on two production rotor hub geometries, the S-92A hub and the UH-60A hub.
“Aside from time savings in the design process,” says Egolf, “the real value of numerical simulation lies in the accuracy of the prediction of hub drag, particularly in blind calculations with no knowledge of experimental data.” Such blind calculations were used in Sikorsky’s study. “The two rotor hubs in this analysis, S-92A and UH-60A, were tested at a half-size scale in a wind tunnel as part of the S-92A aircraft development process. Even though data on the drag build-up of individual components was available from this test, the numerical simulations were performed as blind calculations without knowledge of the experimental results.”
The simulations were carried out, including the wind tunnel walls and test pylon/splitter plate assembly, without considering the support structure for the assembly. The swash plates in the experiments were non-functional, so the link between the plates and their servos was removed in the experimental tests and the simulations. The hub was tilted forwards by 5°, while the test pylon/splitter assembly was kept level as in the test conditions.
Mike Dombroski, a senior application engineer at CD-Adapco, takes up the story: “The hub geometry was discretised at the surface level using the ‘surface wrapper’ method in STAR-CCM+, before remeshing the surface. The surface wrapper shrink-wrapped a mesh on to the geometry and created a watertight surface, preserving the geometric fidelity of the surface, including minor details such as nuts and bolts.
“The computational domain was then discretised using trimmed hexahedral cells in the volume, with a prismatic boundary layer mesh near the surface to capture the boundary layer flow. The body-fitted boundary layer mesh had four prismatic cells, with 10 layers of cells used on the hub cover to accurately resolve the thick boundary layer on this surface. Focused volumetric refinement, based on the solution from a coarse grid, was used behind the hub to capture the hub wake,” says Dombroski.
“A sliding mesh was used around the rotational hub assembly. The final volumetric mesh for the S-92A hub consisted of 14.8 million trimmed hexahedral cells, with the prismatic boundary layer mesh accounting for 8.2 million cells. A similar process for the UH-60A hub yielded 13.1 million advanced hexahedral cells, with 7.1 million cells in the boundary layer.”