A number of refinements in the computer code were worked out and tested. Three codes have been written to date. One program is for an isolated wing and is being used to compare with data for the vortex wake (Weston). The second code is for an isolated wing with a streamwise vortex passing above it. This program is being used to validate the computational procedure for incorporating the vortex into the Euler equation calculations. The third program is the hovering rotor code which is the overall objective of the research. The optimization calculations for a hovering helicopter rotor have been completed

Miller, R.

Murman, E. M.

English

NASA Technical Reports Server

i-y*
ANALYTICAL INVESTIGATION OF ROTOR WAKE
FORMATION AND GEOMETRY
Progress Report for
NASA Grant NAG-2-275
for Period
April 15, 1985 - October 15, 1985
January 16, 1986
/7sASa-CB-177032) A N A L Y T I C A L INVESTIGATION
01 E010B W A K E FOEEA1IOS AND GEOJ3ETEY
Progress Beport, 15 Apr.:,-. 15 Oct. /19.85
(Massachusetts lust. ,of Tech.)/ 21 ;p
N86-2S768
Qnclas
CSCL 01A G3/02 ; 43233
Prof. Rene Miller - Co-Principal Investigator
Prof. Earll M. Murman - Co-Principal Investigator
DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASS. 02139
https://ntrs.nasa.gov/search.jsp?R=19860020296 2020-03-20T14:33:47+00:00Z
During: the six months from April to October, 1985, progress was made
with both the Euler code calculation task and the rotor optimization task as
briefly described below,
EULER CODE TASK
During this period a number of refinements in the computer code were
worked out and tested. Three codes have been written to date. One program
is for an isolated wing and is being used to compare with data for the vortex
wake (Weston). The second code is for an isolated wing with a streamwise
vortex passing above it. . This program is being used to validate the com-
putational procedure for incorporating the vortex into the Euler equation
calculations. The third program is the hovering rotor code which is the
overall objective of the research. In this six month period, attention has
been given mostly to the first two of these three programs, An attached
abstract submitted to the AIAA 4th Applied Aerodynamics Conference in San
Diego in June describes our progress on these programs.
We plan to turn our attention to" the third program to get it updated
during January 1986, and then to perform the final calculations of the study
during February 1986, A more detailed description of our progress is being
written and will be available during the next period.
ROTOR OPTIMIZATION TASK
The optimization calculations for a hovering helicopter rotor have
been completed and are being prepared in a thesis by Song Young Chung
which will be submitted later.
ORIGINAL PAGE 83
OF POOR QUALITY
Abstract Submrttal Form Print or type all information
I wtah to submit an abstract for (conference/meeting): AIAA 4th Applied Aerodynamics Conf.
Place:
 San Diego, CA Date: June 9-11. 19C6
Session/organizer (this information appears in the call): Marvin M ./Walters
Reminders:
1 / AIAA has first publication rights to all papers presented at
its meetings. Manuscripts accepted for the meeting will be
evaluated for publication in the appropriate AIAA publica-
tion, if the author requests it. If a Progress Series book is
planned, papers from relevant sessions will be held for the
book.
21 Authors must inform each organizer if abstract is submitted
to more than one session topic organizer.
3/ All program participants and authors will be charged a
registration fee (AIAA member rate) at the meeting.
4/ Authors of accepted papers will be expected to submit a
100-word abstract (12 weeks before a meeting) and a
photo-ready manuscript (6 weeks before a meeting).
Authors desiring journal publication should send 4 copies of
their photo-ready manuscript directly to the Editor in Chief
of the journal of their choice (see inside front cover of each
journal for correct address), along with a covering letter,
before the meeting, if they wish to accelerate the review
procedure. Government Program Monitors/Security Officers
should be alerted as soon as authors receive formal accept-
• ance of their paper.
•OSS
ppIkx-****
.^^uX^VT.
Paper title (this title will be published in the Program):
Euler Solutions for the Flow Around a Hovering Helicopter Rotor
Author/s' name and title, AIAA membership grade, company, full mailing address, telephone number:
1 Author presenting paper
Thomas W. Roberts, Member
M.I .T . 37-354
Cambridge, MA 02139
Earll M. Murman, Assoc. Fellow
M. I. T. 33-217
Cambridge, MA 02139
Abstract due date: November 19, 1985
Draft of paper included? Yes No
Similar results been presented or published elsewhere? |~1 Yes No
Concise statement of problem (its genesis and objective covered):
See attached abstract
Scope and methods of approach, with statement of contribution to the state-of-the-art or an application of
existing analytical techniques and theories to a problem:
See attached abstract
Summary of Important conclusions:
See attached abstract
Statement of data used to substantiate conclusions, and freehand sketches of major figures to be used
(no more than two typed pages):
Euler Solutions for the Flow Around a
Hovering Helicopter Rotor
Thomas W. Roberts
Earll M. Murman
1 Introduction
In recent years, computational fluid dynamics technology has been highly
developed for fixed wing aircraft configurations. The same cannot be said for
rotary wing aircraft. In the case of a helicopter rotor in hovering flight, which
may be treated as steady in the frame of reference of the rotor, an important
effect is the interaction of the tip vortex trailed from one blade with the following
blade. This interaction results in large variations in the loading at the blade
tip. Furthermore, the semi-infinite vortex wake of the rotor has a significant
influence on performance and must be included. The need to include these
effects poses quite a challenge for existing computational techniques.
The computation of aerodynamic flows using the compressible Euler equa-
tions allows the "capturing" of vortical wakes trailed from lifting surfaces. How-
ever, due to grid stretching and numerical viscosity, the wake vorticity is diffused
as it is convected downstream. For this reason, an Euler calculation around a
complete rotor configuration is impractical, as the tip vortex of each rotor blade
will be quite diffuse by the time it reaches the following blade. The steep span-
wise gradients in the aerodynamic loading near the tip due to the blade/vortex
interaction will not be correctly computed. Also, a model for that part of the
semi-infinite wake that lies outside the computational domain is required if ac-
curate values for the thrust, induced power, and the initial radial contraction
of the wake are to be obtained.
In the proposed paper, we will solve for the flow field around a hovering
helicopter rotor using an approach that contains the following features:
1. an Euler calculation of the near field of a rotor blade, including the for-
mation and roll-up of the attached vortex wake;
2. treatment of the tip vortex of the proceeding blade such that the vortex
is not destroyed by numerical diffusion; and
3. inclusion of the influence of the semi-infinite wake.
2 Technical Approach
The basic scheme for solution of the Euler equations for the flow around
the rotor blade ia a finite volume, multi-stage algorithm based on the work of
Jameson and Baker [l). An O-O mesh topology is used to get good resolution of
the tip, leading edge, and trailing edge regions of the blade (fig. 1). The semi-
infinite vortex wake is treated using by the free wake model of Miller [2,3]. The
coupling of the free wake and the near field blade calculations will be performed
in a fashion similar to the approach used by Roberts and Murman [3] for a
lifting line representation of the blade, and is outlined below.
To account for the close encounter between the rotor blade and the tip vortex
from the proceeding blade a prescribed vortex, or perturbation, approach will be
used to include this vortex without the attendant numerical diffusion problems.
This perturbation approach has been applied to the unsteady 2-D blade/vortex
interaction problem by Srinivasan and his co-workers [4]. The implementation of
the approach here consists of freezing the wake geometry, including the position
of the tip vortex of the proceeding blade, during the Euler iterations. The state
vector of the wake flow field, UQ = (p, pu, pv, pw, pE) is then computed. The
finite volume flux balance and and artificial viscosity operator are applied to this
flow field. The residuals of the flow field UQ are subtracted from the residuals
of the total flow field U at each time step of the Euler iteration. In this way, the
truncation error of the scheme is corrected for the influence of the tip vortex of
the proceeding rotor blade such that the vortex remains well defined, even near
the outer boundary of the computational domain where the resolution of the
grid is quite coarse.
With the new Euler solution, the strengths of the wake vortices are re-
computed, and the wake geometry is updated through the free wake iteration
procedure. After updating the wake geometry, the new geometry is used to re-
compute the prescribed flow field UQ, and the Euler solution is updated. This
coupled iteration procedure is continued until convergence.
3 Results
Euler solutions have been obtained for fixed wing geometries. A comparison
of solutions obtained with this code and experimental data for the ONERA M6
wing at a = 3.06°, MO, = .84 are shown in figure 2. The calculations were
performed on a grid of 96 x 20 x 20 finite volume cells, and comparisons of
surface pressure coefficient for 3 span stations are shown.
The code has also been used to compute the flow about an unswept, unta-
pered wing with a NAG A 0012 airfoil section tested at NAS A-Langley Research
Center by Weston [5J. The purpose of this calculation is to compare the vortical
wakes computed by the Euler equations with experimental data. The calcula-
tion was performed on a 128 x 32 x 32 grid at o = 8°, A/oo = .1425. Surface
pressures are shown in figure 3. In figure 4 are shown contours of constant total
pressure and vorticity at 1/2 chord behind the trailing edge. The computed
wake is qualitative similar to experimental data, indicating that the Euler equa-
tiona do capture the vortical structure of the wake. Quantitative comparisons
with experiment will be performed to ascertain the ability of the Euler equations
to capture realistic vortex wake structures.
The use of the perturbation approach for computing the interaction of a
streamwise vortex with a semispan wing is shown in figures 5 and 6. The ge-
ometry of the configuration is sketched in figure 5a; the wing has a semispan
to chord ratio of 2:1, a NAG A 0006 airfoil section, and the free stream Mach
number is .3. The vortex passes 1/2 chord above the wing and 1/2 semispan.
from the plane of symmetry. A 96 x 20 x 20 grid was used around the wing. The
spanwise distribution of lift coefficient Ci is shown in figure 5a for the perturba-
tion approach, while figure 5b shows the results for the standard Euler solver.
The steeper gradients at the 1/2 semispan section for the perturbation approach
due to the better resolution of the vortex are apparent. In figure 6, contours
of vorticity are shown in a vertical plane passing through the mid-chord of the
wing. The contour levels are identical in figures 6a and b. Note that the vortex
is well defined with the perturbation approach, while for the non-perturbation
scheme it has virtually vanished. This calculation illustrates the ability of the
perturbation scheme to overcome the problems of coarse grid resolution near
the outer boundary and the diffusion of vorticity due to artificial viscosity. This
is a preliminary calculation; further comparisons with the experimental data of
reference [6] for this configuration will be undertaken.
For the proposed paper, the current perturbation scheme will be applied to
the case of a hovering helicopter rotor. The Euler code for a hovering rotor has
been written. Preliminary results for the hover case have been presented by
the authors [7] using an earlier version of the perturbation scheme now being
developed. (In reference [7], only the smoothing operator and not the flux
operator was applied to the wake flow field UQ.) The position of the tip vortex
passing near the rotor blade will be found from a free wake calculation. The free
wake and Euler computations will be coupled such that the strengths of the free
wake vortices will be determined from the Euler calculation. In this fashion,
the correct representation of the tip vortex of the proceeding blade within the
Euler computational domain as well as the influence of the entire semi-infinite
wake will be included in the calculations.
4 Summary
A prescribed vortex or perturbation scheme for the Euler equations around
a hovering helicopter rotor is being developed. For the rotor case, this approach
will provide several advantages over existing hover performance prediction meth-
ods. First, the scheme will allow the interaction between the rotor blade and the
tip vortex of the proceeding blade to be computed. Second, the formation and
roll-up of the near trailing vortex wake attached to the blade will be captured
by the Euler solver. Finally, by fully coupling the Euler solution of the near
field of the blade with a free wake analysis, the proper influence of the complete
semi-infinite wake will be accounted for.
5 References
1. Jameson, A., and Baker, T.J., "Solution of the Euler Equations for Com-
plex Configurations," AIAA paper 83-1929CP, Proc. AIAA Computa-
tional Fluid Dynamics Conference, 1983.
2. Miller, R.H, "Simplified Free Wake Analyses for Rotors,9, FFA (Sweden)
TN 1982-7, 1982.
3. Roberts, T.W. and Murman, E.M., "A Computational Method for Heli-
copter Vortex Wakes," AIAA paper 84-1554, 1984.
4. Srinivasan, G.R., McCroskey, W.J., and Baeder, J.D., "Aerodynamics of
Two-Dimensional Blade-Vortex Interaction," AIAA paper 85-1560, 1985.
5. West on, R., private communication.
6. Smith, W.G., and Laweroni, F.A., "Experimental and Theoretical Study
of a Rectangular Wing in a Vortical Wake at Low Speed," NASA TN
D-339, 1960.
7. Roberts, T.W., and Murman, E.M., "Solution Method for a Hovering
Helicopter Rotor Using the Euler Equations," AIAA paper 85-0436, 1985.
PARABOLIC SINGULAR LINES
TIP SURFACE
GRID
TIP
LEADING
EDGE
CHORDWISE GRID
SECTION
SPANWISE GRID
SECTION
si
o >
O -o
C 3&
Figure 1 - O-O Mesh Features
ONERA M6 — 3.06 alpha, .84 Mach, 96 x 20 x 20 grid
CHORDWISE SECTION
o
o
o
o
o
o
UJ
o
op
d
o
o
o
o EXP. 20%
CALC. 23%
F/
-0.200 O.OOOE+00 0.200 0.400 0.600
X
0.800 1.00 1.20 1.40
20-SEP-85 13:30:02
Figure 2a - Cp Comparisons for ONERA M6 Wing - 20% span
ONERA M6 — 3.06 alpha, .84 Mach, 96 x 20 x 20 grid
CHORDWISE SECTION
+
o
o
o
o
3
o
op
o
o
o
oQ EXP. 65%
CALC. 63%
-0.200 O.OOOE+00 0.200 0.400 0.600
X
0.800 1.00 1.20 1.40
20-SEP-85 13:30:02
Figure 2b - Cv Comparisons for ONERA M6 Wing - 65% span
ONERA M6 — 3.06 alpha, .84 Mach. 96 x 20 x 20 grid
CHORDWISE SECTION
o
o
o
o
3
o
o
o
o
o
o
o
o EXP. 90%
CALC. 88%
o
12
-0.200 O.OOOE+00 0.200 0.400 0.600
X
0.800 1.00 1.20 1.40
20-SEP-85 13:30:02
Figure 2c - Cp Comparisons for ONERA M6 Wing - 90% span
WESTON TEST CASE — 8 alpha, .1425 Mach, 128 x 32 x 32 grid
CHORDWISE SECTION
U.
O.OOOE+00 0.125 0.250 0.375 0.500
X
0.625 0.750 0.875
18-AUG-85 14:54:01
Figure 3a - Cp for Plain, Unswept Wing - 3% span
WESTON TEST CASE — 8 alpha. .1425 Mach, 128 x 32 x 32 grid
CHORDWISE SECTION
CM'
o
(O
Oo
00 ^
O
9UJ
o>
o
o
00
o(D
O.OOOE+00 0.125 0.250 0.375 0.500
X
0.625 0.750 0.875 1.00
18-AUG-85 14:54:01
Figure 3b - Cp for Plain, Unswept Wing - 76% span
WESTON TEST CASE
CHORDWISE SECTION
8 alpha, .1425 Mach, 128 x 32 x 32 grid +
oil
O.OOOE+00 0.125 0.250 0.375 0.500
X
0.625 0.750 0.875 1.00
18-AUG-85 14:54:01
Figure 3c - Cp for Plain, Unswept Wing - 95% span
WESTON TEST CASE — 8 alpha, .1425 Mach, 128 x 32 x 32 grid
CHORDWISE SECTION
HI +
COT
3
CMl
o
<o
O.OOOE+00 0.125 0.250 0.375 0.500
X
0.625 0.750 0.875
18-AUG-85 14:54:01
1.00
Figure 3d - Cp for Plain, Unswept Wing - 99% span
WESTON TEST CASE — 8 alpha, .1425 Mach, 128 x 32 x 32 grid
g TOTAL PRESS INC- 0.0004
o
<*>
o
o
00
o
N
O
o
cu
o
o
o
CM
J - 20
O.OOOE+00 0500 1.00 1.50 2.00
Y
2.50
.,.•. 44.'*
+
-0.0008
0.0004
0.0016
0.0028
0.0040
0.0052
0.0064
3.00 3.50 4.00
23-OCT-85 14:37:17
Figure 4a - Total Pressure Loss, | Chord Behind Wing
WESTON TEST CASE — 8 alpha, .1425 Mach. 128 x 32 x 32 grid
g VORTICITY M INC- 0.0500CO
o
o
o
o
"8
o
o
o
o
J - 20
O.OOOE+00 0500 1.00 150 2.00
Y
250 3.00 350 4.00
23-OCT-85 14:37:17
Figure 4b - Vorticity, | Chord Behind Wing
SMITH & LAZZERON1: Euler solution
o
o
CVI-,
o
o
o
Hi
00
o>
01
o
o
o
o
o
OJ
O
o
96 x 20 x 20 grid
Cl - -.1194
Cd - -.0047
Circ - .1
Yv - J5b
Zv - J5c
o
O.OOOE+00 0.200 0.400 0.600 0.800
Y
1.00 1.20
4-NOV-85
1.40
13:35:22
1.60
Figure 5 - Spanwise C\ Distribution, Wing/Vortex Interaction
a - Perturbation Scheme
SMITH & LAZZERONI: Euler solution
o
o
8
UJoo
o>c\i
o
8
8
OJ
o
o
Non-perturbation
Solution
96 x 20 x 20 grid
Cl - -.1225
Cd - -.0036
Circ - .1
Yv - .5b
Zv -
.^OOOE+OO 0.200 0.400 0.600 0.800
Y
1.00 1.20 1.40
4-NOV-85 13:30:21
b - Standard Euler Scheme
WING/VORTEX INTERACTION — 96 x 20 x 20 grid
8 VORTICITY M INC- 0.1000
N
OO
00
O
OO
O
2
8O
OO
00
0.0000
03000
0.6000
0.9000
12000
15000
1.8000
O.OOOE-i-00 0.400 0.800 1.20 1J60
Y
2.00 2.40 2.80 3.20
10-OCT-85 19:35:14
Figure 6 - Vorticity Contours, Wing/Vortex Interaction
a - Perturbation Scheme
WING/VORTEX INTERACTION
VORTICITY M INC- 0.1000
— Non perturbation
N
o
o
CO
o
oI
o
2
o
o
o
o
o
CO
X
0.0000
03000
0.6000
0.9000
1.2000
15000
1.8000
O.OOOE+00 0.400 0.800 1.20 1.60
Y
2.00 2.40 2.80 3.20
10-OCT-85 22:25:40
b - Standard Euler Scheme


Analytical investigation of rotor wake formation and geometry

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