| |
By Christoph Hiemcke, Fluent Inc.
View the pdf of this article
Propeller of the AIAA-LA replica
One of the great achievements of the Wright Brothers was their design
of the two counter-rotating propellers used on the 1903 Wright Flyer.
During the past year, FLUENT has been used to simulate the propeller under
a number of different flight conditions, and the results have contributed
to the design of one of the Flyer replicas being built. Before describing
the aerodynamics of the propellers in modern terms, it is interesting
to turn the clock back one hundred years, to the time when the Wright
Brothers were busy with the design.
Following successful glider tests at Kitty Hawk in the summer of 1902,
the Wright Brothers returned home to Dayton and focused on the design
of the propulsion system. Orville preoccupied himself mostly with the
motor, while Wilbur concentrated on the propeller. Realizing that the
design of marine propellers at the time was based primarily on empirical
methods, they set out to develop a theory for airplane propellers. They
combined the momentum theory of W.J.M. Rankine and R.E. Froude and the
blade element theories developed by Wm. Froude and S. Drzewiecki. A derivative
of their propeller theory is still used routinely today. The approach
is as follows: the blade is split into a number of spanwise slices or
elements, and then contributions to the thrust and torque from each segment
are computed using the local flow velocity and angle of attack. Corrections
are made for the losses associated with the leakage of air around the
tip, and all contributions are summed to arrive at the total thrust and
torque for the blade. The Wright Brothers used a single blade element
and chose to analyze the flow at the 5/6 (83.3%) spanwise position, a
location they referred to as the blade’s “center of pressure.”
They had measured the aerodynamic performance of a number of airfoils,
and they settled on Wright Airfoil Number 9 for their propeller analysis.
Pressure contours at the surface, tip pathlines, and velocity information
in the form of line contours and vectors illustrate the flow around the
propeller for an advance ratio of J=0.69
The brothers intuitively recognized that the
performance of a propeller during a static test
would be quite different from the performance
during forward flight, so they tested a
small (28" diameter) fan in their wind tunnel
at 1,600 rpm and at a forward speed of about
25 mph. Their first full-scale propeller underwent
static testing in February 1903, whereas
the final 1903 propellers were first tested
in November of that year, just weeks before
the first flight. Each propeller had been manufactured
by gluing together three planks of
kiln-dried spruce, and then carving the
resulting beam. The Wright Brothers measured
a static thrust of 67 pounds per propeller,
at 350 rpm. Wilbur predicted an efficiency of
66 % (efficiency is the ratio of the power available
to propel the airplane to that required
to spin the propeller). Luckily, the propellers
performed better than that, since their airplane
came in overweight by 75 pounds. Without
the additional efficiency of the propeller, the
craft would not have flown!
The Wright Brothers conducted four
flights on December 17th, 1903, but the Flyer
was severely damaged by a wind gust later
in the day. The propellers survived intact and
were reused for the testing of the 1904 Flyer;
they were eventually broken in a flight demonstration
in May 1904. After that, they were
placed into the crate that contained the broken
parts of the 1903 Flyer. They now belong
to the National Park Service.
One of the replicas being readied for the
centennial flight this year was designed and built
by the Los Angeles section of the American Institute
of Aeronautics and Astronautics (AIAA-LA). This
replica incorporates several deviations from the
historic design that were introduced to
improve the safety of the airplane. One such
design change is that the more modern engine
will spin authentic replicas of the 1903 propellers
at speeds above the historic 350 rpm. This will
help to prevent stalls by increasing the airspeed.
In the first 3D Navier-Stokes analysis of the
Wright propellers, FLUENT was used to shed
light on the aerodynamics of the propeller,
especially at higher speeds. The solid model
of the propeller was made in GAMBIT, based
on the blueprints made by Louis B. Christman
while the Flyer and its propellers were at the
Science Museum in London between 1928
and 1948. Christman’s blueprints provide the
shape of the propeller profile at five spanwise
sections, and these profiles were drawn in
GAMBIT. The overall radius of the propeller
is 51 inches (4' 3"). The GAMBIT model differs
from the original only near the hub, since
the blueprint provides no mathematical definition
of the transition from an airfoil profile
to the rounded, rectangular root. However,
this deviation should not affect the aerodynamics
much. Only one propeller blade was modeled in a 180-degree rotationally
periodic domain.The root of the propeller blade was placed at the center
of a hemispherical domain whose radius was about 20 times the blade
span. A triangular surface mesh was generated,
and TGrid was used to generate five layers
of wedges in the boundary layer, and
tetrahedral elements elsewhere for a total of
1.79 million cells.
It was assumed that the problem was steady
when viewed by an observer spinning with
the blade, so the single (rotating) reference
frame (SRF) model was used. For the Wright
Flyer, this assumption meant that the effects
of the ground, wings, and propeller drive components
were neglected, along with all aeroelastic
deformations of the blades. Because of
the anticipated widespread separation, the realizable
k-e turbulence model with enhanced
wall treatment was chosen. The flow was
assumed to be turbulent everywhere. To help
the solution converge, the rotational speed
was increased in increments. Once the flow
was converged at the final rotational speed,
a second order solution was performed.
To validate the model, it was first applied to the static condition
at 350 rpm, for which the Wright Brothers had recorded a thrust of 67
pounds per propeller. The FLUENT result was 69.5 pounds, which represents
a five percent difference, and is quite acceptable given the numerous
assumptions made. The static case is characterized by significant amounts
of flow separation, so is perhaps the most difficult case to solve. Once
it was completed, however, the FLUENT model was run over a range of operating
conditions to produce propeller performance charts. At cruise conditions,
the results showed that the flow was remarkably well attached.
Predominantly attached flow for cruise conditions J = 0.887 (30 mph, 350
RPM)
Important insight can be gained from a plot of propeller efficiency
vs. advance ratio (J), which is the ratio of the freestream speed to the
rotational speed at the tip. Simulations were run for advance ratios that
span the actual flight. With a propeller speed of 350 rpm and the Flyer
at a standstill on the launch rail, J has a value of 0. Halfway through
the takeoff run, J = 0.35, and at the end of the takeoff run, J = 0.69.
Three cruise conditions were modeled, corresponding to J = 0.89, 0.92,
and 1.1. After throttling back at full forward speed, the advance ratio
increases to J = 1.4. Finally, two cases were considered with the aircraft
descending and the engine idling: J = 1.7 and 2.1.
Surface mesh near the propeller tip
Efficiency curve, based on the CFD results
The results of these simulations indicate a
peak efficiency of just over 70%, which is one
of the impressive achievements of the Wright
Brothers. This is particularly true if one considers
that the highest efficiencies of modern
propellers are about 85%. The present result
compares well to Wilbur’s prediction of 66%,
especially if one considers that the Wright
Brothers had underpredicted the efficiency.
The Wright Brothers would surely have enjoyed seeing the flow visualized
by means of CFD. It would have allowed them to witness and grasp the separation
phenomenon for the first time, and they would have had proof that their
design was outstanding for cruise conditions.
More Information
www.wrightflyer.org
AIAA Los Angeles Chapter, Wright Flyer Project
|
|
|
