Abstract
To numerically simulate aerodynamics of rotor-airframe interaction in a
rigorous manner, we need to solve the Navier-Stokes system for a rotor-airframe
combination as a whole. This often imposes a serious computational burden since
rotating blades and a stationary body have to be simultaneously dealt with. An efficient
alternative is to adopt a momentum source method in which the action of rotor is
approximated as momentum source over a rotor disc plane in a stationary
computational domain. This makes the simulation much simpler. For unsteady
simulation, the instantaneous momentum sources are assigned only to a portion of disk
plane corresponding to blade passage. The momentum source is obtained by using
blade element theory with dynamic inflow model. Computations are carried out for the
simple rotor-airframe model (the Georgia Tech model) and the results of the
simulation are compared with those of the full Navier-Stokes simulation with moving
mesh system for rotor and with experimental data. It is shown that the present
simulation yields results as good as those of the full Navier-Stokes simulation.
Key words : Momentum Source Method, Rotor-Airframe Interaction, Unsteady
Navier-Stokes Simulation, Blade Element Theory, Moving Mesh
Introduction
The flow field around a rotor is very complex due to the unsteadiness of the complex
rotor wake and mutual aerodynamic interferences. The strength of interaction depends on
the relative position of the rotor and the body, and on flight conditions. This highly coupled
aerodynamic interaction plays an important role in determining aerodynamic characteristics
and performance of a rotorcraft.
Many computational methods have been developed to predict rotor-airframe
interaction. Rotorcraft Wake Analysis and a source/vortex fuselage panel method have been
coupled to predict the interaction between the two components [1]. This approach was one
of many earlier attempts to account for rotor-airframe interaction [2, 3]. Following these
attempts, Euler or Reynolds-Averaged Navier-Stokes (RANS) equations have been used in
the analysis of rotor-airframe interactions. The analysis of rotor-airframe interaction
requires an unsteady three-dimensional solver which can model the actual unsteady motion
of the rotor. Generally, both structured and unstructured mesh systems are used for solving
unsteady Euler or RANS equations. Some applications of structured grid for complex
geometries have been successfully made using overset or Chimera grid methodology[4, 5].
* Student Researcher
** Professor
E-mail : sopark[at]kaist.ac.kr Tel : +82-42-350-3713 Fax : +82-42-350-3710
126 Young-Hwa Kim and Seung-O Park
Unstructured grid methods are easier to adapt to complex configurations. Recently,
unstructured three-dimensional Euler solver was developed using a sliding mesh algorithm,
in which the computational domain is divided into a moving zone rotating with the blades and
a stationary zone for airframe [6].
As is well known, computational burden becomes heavy when RANS simulations is
adopted either for overset or sliding mesh scheme since rotating blades and a stationary
body must be simultaneously dealt with in a single computational domain. One approach to
mitigate this is to consider only the time-averaged behavior of the rotor, leading to the
concept of an actuator disk instead of moving mesh for rotating blades. Two different
models exist : pressure disk model and momentum source model. The pressure disk rotor
model approximates a rotor in a time-averaged manner using inflow and outflow boundary
conditions at the surface of the disk [7]. This model uses a modified actuator disk that
allows a pressure jump varying with radius and azimuth across the disk. Another is the
momentum source method in which the action of rotor is approximated as a momentum
source applied in the disk plane[8-13]. For example, this method was utilized to analyze
mutual aerodynamic interactions between multiple rotors and airframes using FLUENT
For the time-averaged momentum source method developed by Rajagopalan
the time-averaged momentum sources are applied to the entire disk plane. The momentum
sources are not known at the start of the calculation, but computed as part of the solution via
iteration. The local angle of attack and velocity at each blade element are obtained from the
computed velocity field. The magnitudes of the momentum sources are determined by the
blade element theory using this local angle of attack and velocity. Then, the momentum
sources are updated to the flow field. Updating the momentum sources and computing the
flow field are iterated until the solution is converged. Through this method, the timeaveraged
rotor-airframe interaction can be predicted. Thus, this method is not adequate to
simulate unsteady behaviors of rotor-airframe interaction. For unsteady simulation, the
momentum source needs be estimated as the rotor rotates and therefore the momentum
source is present only for the region of blade passage and changes along the azimuth. To
determine the momentum source, induced velocity field toward rotor blade should be known.
The calculation of induced velocity field, however, is somewhat complicated. For efficient
induced velocity prediction, various inflow models have been developed. Linear inflow
models such as Coleman, Drees and Payne assume that the induced velocities of a rotor disk
are linearly distributed by Fourier first harmonic variations [15]. These models are simple
and easy to apply. However, unsteady aerodynamics of rotor can hardly be solved by using
these models since these models cannot simulate time-varying dynamic inflow behavior.
Dynamic inflow models such as Pitt-Peters and Peters-He models have been developed to
resolve this situation
In the present study, we intend to apply dynamic inflow models of Pitt-Peters and
Peters-He to estimate ‘unsteady’ momentum sources for the unsteady Navier-Stokes
(NS) simulation. Airload of each blade element is calculated by using aerodynamic
coefficients of 2D airfoil look-up table made from a two dimensional NS simulation. As we
simply adopt inflow models to determine induced velocities, the influence of airframe is not
reflected. Momentum source data so obtained corresponding to each blade passage is then
fed to a stationary NS computational domain which encloses the airframe. The results of the
simulation are compared with those from the solution obtained by solving the NS system for
an entire domain with moving mesh system employed. The present NS computations are
carried out for the simplified rotor-airframe model (the Georgia Tech configuration) using
STAR-CD.

Download full report
http://ijassOn_line/admin/files/13%EB%B2%88.pdf