Predicted Aerodynamic Characteristics of a NACA 0015 Airfoil

168 Pages·2015·9.46 MB·English

https://ntrs.nasa.gov/search.jsp?R=19990047898 2019-03-26T17:08:18+00:00Z
NASA / CR- 1999-209328
Predicted Aerodynamic Characteristics of a
NACA 0015 Airfoil Having a 25% Integral-
Type Trailing Edge Flap
Ahmed Hassan
The Boeing Company, Mesa, Arizona
National Aeronautics and
Space Administration
Langley Research Center Prepared for Langley Research Center
under Contract NAS1-20096 Task 6
Hampton, Virginia 23681-2199
May 1999
Available from:
NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)
7121 Standard Drive 5285 Port Royal Road
Hanover, MD 21076-1320 Springfield, VA 22161-2171
[phone] [phone]
Table Of Contents
Page
1. Summary . . 1
2. Introduction 2
3. Numerical grid generation - HYGRID 4
4. Flowfield Analysis tool n ARC2D 5
5. Mathematical Expressions For Aerodynamic Coefficients 6
5.1. Airfoil aerodynamic coefficients 7
5.2. Flap aerodynamic coefficients 10
. Aerodynamics Data Tables as an aRemate option 11
7. Results and discussion 11
7.1. Generation of the aerodynamics data tables 12
7.2. Selected flowfield predictions 14
. Conclusions 16
9. References 17
10. Appendices
-Appendix 1 Sample HYGRID output
-Appendix 2 Listing of ROTATE code
-Appendix 3 Computational grids
-Appendix 4 Sample input/output ARC2D code
-Appendix 5 Listing of CREATE code, COM file
-Appendix 6 Sample LOADS.TBL file for CREATE
-Appendix 7 Sample LOADS.TBL file for CREATE
-Appendix 8 Listing of UTIL code
Notation:
: airfoil lift curve slope
a o
C : airfoil chord length
cf : flap chord length
E • ratio of flap chord length to airfoil chord length (i.e., cf/C)
Minf : free stream Mach number
(X : airfoil angle of attack (radians, unless specified otherwise)
_o : airfoil zero-lift angle (radians, unless specified otherwise)
8 : flap deflection angle (radians, unless specified otherwise)
iv
List Of Figure Captions
Flaure Caption Paae
1 Typical C-type computational grid for the NACA-
0015 airfoil (grid resolution 211x50) ]8
2 An expanded view of the computational grid near
the leading edge of the NACA-0015 airfoil 19
3 An expanded view of the computational grid near
the 25% chord integral trailing edge flap 2O
4 ARC2D-predicted sectional drag values and the
best fifth-order polynomial fit (Minf = 0.65, (z = 5
degrees, Re = 3 million) 21
5 ARC2D-predicted sectional drag values and the
best sixth-order polynomial fit (Minf = 0.40, o_= 10
degrees, Re = 3 million) 22
6 Flow chart depicting the various steps in the
generation of the C81 aerodynamics data tables 23
7 Sketch illustrating the various subsections in a
typical C81 aerodynamics data table 24
8a Predicted u-component of velocity for the flapped
NACA-0015 airfoil (Minf = 0.30, _ = 5 degrees, 6 =
+15 degrees, Re = 3 million) 25
8b Expanded view of the predicted u-component of
velocity near the trailing edge of the flapped NACA-
0015 airfoil (Minf = 0.30, _ = 5 degrees, 6 = +15
degrees, Re = 3 million) 26
8c Expanded view of the predicted velocity vectors
near the trailing edge of the flapped NACA-0015
airfoil (Minf = 0.30, (z= 5 degrees, _ = +15 degrees,
Re = 3 million) 27
8d Predicted streamlines for the flapped NACA-O015
airfoil (Minf = 0.30, o_= 5 degrees, _ = +15 degrees,
Re = 3 million) 28
List Of Figure Captions (cont'd)
Caption Paae
9a Predicted streamlines for the flapped NACA-=0015
airfoil (Minf = 0.30, _ = 12 degrees, _ = +15
29
degrees, Re = 3 million)
9b Expanded view of the predicted velocity vectors
near the trailing edge of the flapped NACA-0015
airfoil (Minf = 0.30, (x = 12 degrees, _ = +15
degrees, Re = 3 million) 3O
lOa Predicted Mach number contours for the flapped
NACA-0015 airfoil (Minf = 0.70, c¢= 9 degrees, _ =
31
-10 degrees, Re = 3 million)
lOb Predicted sonic and supersonic Mach number
contours for the flapped NACA-0015 airfoil (Minf =
0.70, (_ = 9 degrees, 8 = -10 degrees, Re = 3
32
million)
10c Predicted particle traces for the flapped NACA-
0015 airfoil (Minf = 0.70, (x = 9 degrees, 5 = -10
33
degrees, Re = 3 million)
11a Predicted Mach number contours for the flapped
NACA-0015 airfoil (Minf = 0.70, (x = 5 degrees, 6 =
+5 degrees, Re = 3 million) 34
11b Predicted sonic and supersonic Mach number
contours for the flapped NACA-0015 airfoil (Minf =
0.70, (x = 5 degrees, 6 = +5 degrees, Re = 3
million) 35
11c Predicted streamlines for the flapped NACA-0015
airfoil (Minf = 0.70, (x= 5 degrees, (3= +5 degrees,
Re = 3 million) 36
vi
Predicted Aerodynamic Characteristics Of A NACA-0015 Airfoil
Having A 25% Integral-Type Trailing Edge Flap
1. Summary
Using the two-dimensional ARC2D Navier-Stokes flow solver analyses were
conducted to predict the sectional aerodynamic characteristics of the flapped
NACA-0015 airfoil section. To facilitate the analyses and the generation of the
computational grids, the airfoil with the deflected trailing edge flap was treated
as a single element airfoil with no allowance for a gap between the flap's
leading edge and the base of the forward portion of the airfoil. Generation of
the C-type computational grids was accomplished using the HYGRID hyperbolic
grid generation program. In the analyses, a 25% integral-type trailing edge flap
was assumed. Results were obtained for a wide range of Mach numbers,
angles of attack and flap deflections. The predicted sectional lift, drag and
pitching moment values for the airfoil were then cast in tabular format (C81) to
be used in lifting-line helicopter rotor aerodynamic performance calculations.
Similar tables providing the variation of the sectional lift and hinge moment
values with Mach number, angle of attack and flap deflection angle were also
generated for the flap.
Mathematical expressions providing the variation of the sectional lift and
pitching moment coefficients for the airfoil and for the flap as a function of flap
chord length and flap deflection angle were also derived within the context of
thin airfoil theory. Similar expressions for the airfoil's sectional drag coefficient
were also derived using the ARC2D drag predictions for equivalent two-
dimensional flow conditions which are known to exist on a flapped model
helicopter rotor blade in low speed descent flight and in level cruise flight.
2. Introduction
Earlier numerical studies [1,2], supported by recent wind tunnel experiments [3],
have shown that helicopter rotor blade aerodynamics as well as dynamic and
performance characteristics can be altered/enhanced via the use of a blade-
mounted trailing edge flap. For example, in low speed descent flight, and in
particular during conditions which give rise to strong blade-vortex interactions
(BVl), careful and selective deployment of the flap on the advancing side of the
rotor disk have been known to result in lower BVI noise levels. In high speed
cruise flight, however, the deployment of the flap on the retreating side of the
rotor disk can be used as means to reduce the otherwise large local angles of
attack, and hence blade stall, by attaining higher lift levels with moderate
deflections.
Because helicopter aerodynamics is a complex discipline which often requires
an experimental approach to unravel underlying physical phenomena and
estimate aerodynamic loads, designers are usually faced with a dilemma when
new performance enhancement concepts, such as the use of a trailing edge
flap, are being evaluated. In the preliminary design stage, rotor aerodynamic
loads, and hence rotor performance, are generally estimated using simple
analyses which are based on a lifting-line formulation such as that inherent in
the NASA Langley CAMRAD.Modl code [4]. Since these analyses are based
on locally two-dimensional (2-D) strip theory, they demand that the 2-D
aerodynamic characteristics of the airfoil(s) which constitute the blade be a
priori known. Traditionally, airfoil aerodynamic characteristics are acquired
through 2-D wind tunnel testing. Once acquired, they are then furnished to the
lifting-line code in tabular format (referred to here as a C81 format).
In trade studies where new airfoil designs, or modifications of existing airfoils
are being evaluated for best rotor performance, wind tunnel testing of a large
number of airfoils becomes no longer practical and an alternate approach must
be adopted. This approach relies on using either simplified equations derived
from thin airfoil theory to express the airfoil's aerodynamic characteristics, say
as a function of flap deflection, or the use of more accurate state-of-the-art
computational fluid dynamics (CFD) analysis tools. The use of CFD analysis
tools, of course, circumvents the assumptions inherent in thin airfoil theory as
they relate to compressibility, viscous effects and the limitation to small angles
of attack, thin airfoils and small flap deflection angles.
Sincethin airfoil theory is applicableonly to incompressible potential flow, then
other means mustbe usedto arrive at the mathematical expression(s) which
providethe variationofthe airfoil'ssectional dragas a function of flapdeflection
angle. In this report, these expressions are derived using drag predictions
obtained using a CFD analysiscode for two free stream conditions which are
knownto exist locally on a modelrotor [3] having a NACA-0015 airfoil section
and a 25%chordflap extendingbetween the nondimensional 0.79 - 0.97 blade
radialstations. Inlowspeeddescentflight, lifting-line simulations ofthe flapped
model rotor haveindicatedthatthe equivalenttwo-dimensional flow, as seen by
an observer located at the flap mid-span section at the 90 degree azimuth,
correspondsto a free stream Machnumber of0.65 and an angle of attackof 5
degrees. Theseconditionsexistedfor a peakflap deflection of -10degrees. At
an advance ratiowhich is typicalof forward flight, say 0.30, an estimate of the
local two-dimensional flow conditionswhich exist at the flap mid span position
at the 270 degree azimuth yields a local free stream Mach number
approximately equal to 0.40 and an angle of attack of 10 degrees. At this
azimuth,the flap deflection is equal to +5 degrees. The objective here is to
attain a local sectionalliftvalue whichis identicalto that achieved by the single
element airfoil at a higher angleofattack. It should be mentioned here that
slightdeviationsfromthese equivalent2-D free stream conditionsare expected
with any changes in the peak flap deflection and/or the radial position for
placementoftheflap.
Inthis report we present the mathematical expressions used to calculate the
characteristics of the flapped NACA-0015 airfoil as well as the computed
characteristics using a modern CFD Navier-Stokes-based analysis tool. The
equations,as well as the CFD solutions are given here as functions of the flap
deflection angle. Results of the CFD computations are cast in tabular C81
format. Unlike a single element airfoil, for a flapped airfoil section, two C81
tables are generated; the first expressing the airfoirs lift, drag and moment
characteristics and the second expressing only the flap's characteristics. The
secondtable is primarilyusedinthe lifting-line code to determine the flap loads
and, moreimportantly,the hingemoment which dictates the proper meansfor
flap actuation (i.e., mechanical, hydraulic, pneumatic, etc.). In the following
paragraphs a brief summary of the grid generation and CFD analysis tools is
given. A detailed explanation of the procedure used to generate the C81
aerodynamics data tables for the baseline and for the flapped NACA-0015is
also included.
3. Numerical Grid Generation - HYGRID
In the present study, a C-type computational grid was generated using the
NASA Ames "HYGRID" [5] hyperbolic grid generation code. The code requires
that the approximate distance to the far field boundary as well as the normalized
chordwise grid spacing near the leading and trailing edges of the airfoil be
specified by the user. Typically, the far field boundary was located at a distance
equal to six or seven airfoil chord lengths. The HYGRID code is run interactively
on an HP9000/735 workstation. The generated grid is then displayed using the
NASA Ames "PLOT3D" graphics software package [6] and examined for proper
resolution. Appendix 1 contains a sample output file which is generated upon
the completion of the interactive session. This file contains a summary of the
grid parameters entered during the interactive session. An input file containing
the coordinates of the airfoil starting from the lower surface trailing edge point,
wrapping around the airfoil's leading edge and ending at the airfoil's upper
surface trailing edge point is required. Note that the NACA-0015 airfoil
geometry has an open trailing edge. This is acceptable for C-type grids with a
topology that incorporates a wake cut which extends from the upper and lower
surface trailing edge points to the two outflow boundaries located downstream
of the airfoil.
Figure (1) depicts the physical extent of a typical computational grid for the
NACA-0015 airfoil. For the airfoil with the 25% integral flap, the resolution of the
computational grid was equal to 21 lx50 with 151 points lying on the surface of
the airfoil (75 grid points on each surface), 31 points along each of the upper
and lower surfaces of the wake cut, and 50 points in the direction approximately
normal to the surface of the airfoil. An expanded view which illustrates the
resolution of the grid near the airfoil's leading edge is shown in Fig. (2). Grid
resolution on the flap and in the vicinity of the flap hinge point is also very
important for accurate prediction of the flap sectional lift and hinge moment
coefficients. Figure (3) illustrates an expanded view of the computational grid
on the flap for a deflection of +20 degrees. Numerical results with a finer grid on
the flap (i.e., having 30 points per surface rather than the 18 points shown in
Fig. (3)) have indicated minor differences which are on the order of 2% in the
4