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By Michael R. Ruith, Fluent Inc.
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Static pressure contours on the fuselage for the forward
flight configuration, and flow ribbons through the
starboard rotor twisted by streamwise vorticity
As part of the model validation, the pressure
coefficient on the airframe vs. normalized streamwise
location is computed using the thrust and moment
trimming routine, and compared with published data
[2] for four azimuthal positions.
The flow field of a rotorcraft is highly unsteady and three-dimensional.
This complexity is attributable to the unique aerodynamic features that
a rotary wing exhibits and due to the mutual aerodynamic interference
of the many components that make up a helicopter. For example, there is
mutual aerodynamic interference between the main rotor and airframe, between
the main and tail rotors, and between the tail rotor and airframe. This
highly coupled aerodynamic interaction plays a major role in determining
the aerodynamic characteristics and performance of a rotorcraft.
Computational simulation of such complicated
flows becomes increasingly important in attempts
to minimize costly wind tunnel experiments. The
chosen computational approach depends on the
objective of the simulation, ranging from determining
detailed blade characteristics (e.g. stall behavior),
to quantifying the time-averaged, cumulative
effects of the rotating blades on each other and the
airframe. For the latter, typical applications would
be the prediction of fuselage drag and tail forces
under realistic operating conditions, as well as
plume distribution and impingement for skin heating
and infrared (IR) signature prediction and
reingestion studies.
Historically, rotorcraft simulations employed rotor disk
models that were coupled with 3D Navier-Stokes or
Euler solvers. Here individual rotor blades are not
meshed, yielding substantially lower cell counts and
requiring significantly reduced mesh generation
time. Two different flavors of the model exist. The
pressure disk rotor model [1] approximates a helicopter
rotor or propeller in a time averaged manner
using inflow and outflow boundary conditions at
the disk’s cylindrical surfaces. This yields a pressure
jump across the disk varying with radius and
azimuth. Alternatively, Zori et al. [2] developed a
technique that replaces the rotor system with
momentum sources placed in an actuator disk, indirectly
yielding a pressure jump across the disk,
which varies with radius and azimuth.
Accurate aerodynamic predictions are possible only
if the rotors operate at a desired thrust and with
zero moment about the hub. In the real rotorcraft
this is attained by varying the collective (thrust) and
cyclic (moments) blade pitch angles. Despite thiswell-known fact, many
rotor disk models
lack a robust trim routine or the entire trimming
procedure altogether, due to the
inherently non-linear relationship between
blade pitch and rotor performance. Only
recently, Yang et al. [3] suggested a robust
and automatic numerical trim routine using
a Newton-Raphson iterative method.
Static pressure contours on the
fuselage during conversion to
hover with the nacelles at 48°
Velocity
magnitude of the
V-22 in hover
about five aircraft
heights over the
aircraft carrier
deck
The virtual blade model (VBM) that has
been implemented in FLUENT is based on
Zori et al. [2], using variable momentum
source terms evolving as part of the solution
to represent the rotor blades. Here, the local
momentum source term is calculated based
on the local velocity magnitude, angle of
attack, Mach number, and Reynolds number
of a “virtual” blade section as it passes
through a computational cell inside the
rotor disk. Blade properties such as chord
length, airfoil type, and twist are allowed to
vary over the span of the blade. Following
the blade element theory [4] a look-up table
is used to obtain the resulting lift and drag
forces on the blade. The look-up table
accounts for Mach and Reynolds number
effects, allowing both incompressible and
compressible flows to be treated accurately.
The lift and drag forces are time-averaged
and cell volume-weighted to yield the local,
steady state source terms. These are used to
update the flow field, and the iterative procedure
is repeated until convergence is
obtained. For more details, the interested
reader is referred to [5].
The VBM allows for up to ten different rotors to be treated simultaneously, thus allowing a comprehensive simulation of a rotorcraft with both main and tail rotor, or other configurations involving multiple rotors such as the Quad Tiltrotor concept or even an array of wind turbines [6].
Another advantage of the VBM is that it allows for an unstructured mesh in the rotor disks, allowing for easy meshing of multiple rotor geometries in close proximity. Furthermore, the VBM is compatible with FLUENT’s dynamic mesh model, for simulations of missile release or tilt-rotorcraft. It can be easily extended to multiphase flows to allow for simulations involving icing, brownout, white-out, and many other scenarios.
As noted before, accurate aerodynamic predictions are possible only if the rotors operate at a desired thrust and with zero moment about the hub. A robust and automatic trim routine in the spirit of Yang et al. [3] has been implemented to ensure that the model will correctly calculate the collective and cyclic pitch angles at a particular flight speed in order to achieve the desired thrust coefficient and eliminate moments around the hub.
The VBM has been validated against the Georgia Institute of Technology rotor-airframe interaction experiment consisting of a cylindrical, constant diameter airframe with hemispherical nose and a two-blade teetering rotor system (see [2] and the references therein). For predictions of the pressure coefficient, good agreement was obtained
between the experiments and FLUENT, especially for the rotor wake trailing edge (see graphs). The rotor wake leading edge impingement is underpredicted, due to the proximity of the blade passing over the airframe at this location and modeling assumptions inherent to any rotor disk model.
One recent application of the VBM is the V-22 Osprey tilt-rotor aircraft during final approach toward an aircraft carrier. This unique aircraft is able to take off and land like a helicopter, but, once airborne, its engine nacelles can be rotated to convert it to a turboprop airplane capable of high-speed, high-altitude flight. This transition constitutes a critical maneuver and the capability to simulate this event is highly desirable.
A transient run with an inherently steady-state rotor disk model can be considered a first step, assuming that the time scales of the nacelle rotation and the climb/descent rate are at least one order of magnitude larger than the rotation period of the rotor blades. For this test case, the entire nacelle rotation takes 12.5 seconds, while the three-bladed rotors spin at 333 rpm. Thus, the rotors complete about 70 revolutions during conversion of the plane. Since the dominant unsteady effects can be expected to be in phase with the blade passage frequency (16.65 Hz), the relevant time scales are disparate by two orders of magnitude. A similar argument can be made for the 7.5 second final descent onto the carrier deck.
The simulation makes use of the VBM along with FLUENT’s dynamic mesh capability. A combined sliding-interface/layering approach is used (see figure above). The rotor disk is split so that the larger, outboard portion is encapsulated inside a cylinder-shaped, outboard part (shown in gold) that is rotated using a sliding mesh technique that allows the nacelle to rotate as well. The smaller fragment of the rotor disk (shown in magenta) is encapsulated within a smaller, inboard volume (shown in pink), and is treated by a dynamic layering approach. The reason for this split is that if one were to elongate the golden zone, it would run into the bottom of the fuselage.
The split rotor disk and sliding mesh part of the V-22 in helicopter mode;
the sliding mesh model is used for the annular region outlined in yellow,
including the green section of disk, while the dynamic mesh model is used
for the pink (inboard) region, including the magenta segment of the rotor
The static pressure distribution on the fuselage in forward flight exhibits pronounced suction peaks on the upper wing surface, as expected for a lifting wing. Pathlines through the starboard rotor, twisted by streamwise vorticity, reveal the swirl in the slipstream of the rotor. During conversion to hover mode, the suction peaks on the upper wing surfaces disappear as a result of the increasing influence of the rotor downwash on the structure. Instead, a low pressure region appears on the nacelle bulges that are oriented increasingly cross-stream and over which the flow gets accelerated. The pathlines during conversion clearly show the deflection of the oncoming freestream through the rotor disk, as well as an increase in pressure as the air passes through the rotor.
Examination of the Osprey during hover at the beginning of its vertical decent also reveals interesting flow features. The velocity magnitude on a plane cutting through the rotor centers for a vertical clearance of about five aircraft heights shows dominant rotor downwash below the outboard section of the rotor disks. The flow through the inboard section of each rotor stagnates as it encounters the wing suction side and splits into an outboard and inboard-directed stream. While the outboard-directed flow gets entrained into the wake beneath the wing, the inboard-directed flow gets accelerated towards the root of the wing and subsequently separates from the wing leading and trailing edges together with the high velocity downwash of the rotor at this location, giving rise to strongly unsteady vortex shedding, captured only in a time-averaged sense by the current steady-state simulation. The pronounced wake region in close proximity to the wing is followed by local velocity maxima further downstream. These maxima correspond to the inboard downwash of high momentum fluid, convected around the massively separated region beneath the wing. It is interesting to note that even high above the carrier deck, the wake exhibits some asymmetry. This asymmetry becomes much more pronounced as the aircraft approaches the deck.
Acknowledgments
The author wishes to express his gratitude to C. Berezin of Sikorsky
Aircraft, and to several of his colleagues at Fluent: L. Zori, S. Wirogo,
and
S. Shashidhar for several helpful discussions, and T. Vishak, R. Kumar,
and
C. Hiemcke for their help with meshing the geometry, setting up and running
the model, and postprocessing.
References
- Chaffin, M.S. A Guide to the Use of the Pressure Disk Rotor Model as
Implemented in INS3D-UP; NASA CR-4692; NASA: Washington, DC,
September 1995.
- Zori, L.A.J.; Rajagopalan, R.G. Navier-Stokes Calculation of Rotor-
Airframe Interaction in Forward Flight. J. Amer. Helicopter Soc. 1995,
40.
- Yang, Z.; Sankar, L.N.; Smith, M.; Bauchau, O. Recent Improvements
to a Hybrid Method for Rotors in Forward Flight, AIAA-2000-260; AIAA:
Reston, VA, 2000.
- Leishman, J.G. Principles of Helicopter Aerodynamics, Cambridge
Aerospace Series; Cambridge University Press: Cambridge, UK, 2000.
- Ruith, M.R. Unstructured, Multiplex Rotor Source Model with Thrust
and Moment Trimming – Fluent’s VBM Model, AIAA-2005-5217; AIAA:
Reston, VA, 2005.
- Ruith, M.R.; Shashidhar, S.; Vishak, T.; Kumar R.A Powerful Wind of
Change. Fluent News, 2004, 13, S4-S5.
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