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TRANSONIC AIRFOIL DESIGN FOR HELICOPTER ROTOR APPLICATIONS Ahmed A. Hassan and B. Jackson McDonnell Douglas Helicopter Company Mesa, Arizona ROTOR AIRFOIL DESIGN Despite the fact that the flow over a rotor blade is strongly influenced by locally three-dimensional and unsteady effects, practical experience has always demonstrated that substantial improvements in the aerodynamic performance can be gained by improving the steady two-dimensional characteristics of the airfoil(s) employed. The two phenomena known to have great impact on the overall rotor performance are: 1 ) retreating blade stall with the associated large pressure drag, and 2) compressibility effects on the advancing blade leading to shock
formation and the associated wave drag and boundary - layer separation
losses.
GENERAL DESIGN OBJECTIVES 0 MAXIMUM LIFT CAPABILITY AT LOW SPEED 0 HIGH MACH DRAG DIVERGENCE 0 NEAR ZERO PITCHING MOMENT 0 LOW PROFILE AND COMPRESSIBILITY DRAG ROTOR AIRFOIL DESIGN IS A MULTIPLE DESIGN POINT PROBLEM 1 8 2 CLASSIFICATION OF DESIGN PROBLEMS Two design problems are identified: ITERATIVE DIRECT METHODS [ 1,2]: In these methods, direct solutions are sought with an airfoil geometry that is modified in an iterative process (either by the designer or through numerical optimization utilizing a set of geometric shape functions) to minimize the differences between the computed and the prescribed target pressures.
INVERSE METHODS [3-51: Here a target pressure distribution is prescribed and the objective is to find the airfoil geometry that would yield the specified target pressure at design conditions.
The above two inviscid procedures have also been extended to allow for integral boundary -I layer viscous effects throug6 coupling with an formulation [6,7].
INVERSE DIRECT SHOCKLESS PRESSURE DISTRIBUTION I z x/C 0.0 1 .o
1 I -x/c
0.0 1 .o ADVANTAGES : ADVANTAGES: 0 FIRM CONTROL OF GEOMETRY 0 BETTER CONTROL OF AERODYNAMICS 0 RAPID CONVERGENCE RATES 0 APPLICABLE FOR SHOCKED & SHOCKLESS DESIGNS LIMITATIONS : LIMITATIONS : 0 ABILITY TO CONTROL AERODYNAMIC 0 LACKS CO”%OL OF GEOMETRIC CHARACTERISTICS IS ABSENT (TRIAL REGULARITY AND ERROR) 0 SLOWER CONVERGENCE RATES 0 LIMITED TO SHOCK-FREE DESIGNS ITERATIVE DIRECT PROCEDURE Two primary design tools were utilized at McDonnell Douglas Helicopter Company in generating an airfoil designated "-06 [8-111.
FLO-6 OPT [ 12-14]; a two-dimensional transonic full potential direct solver with a constrained function minimization routine and, the BAUER code [15]; a two-dimensional transonic full potential direct
solver with boundary - layer corrections. In the design process, the
airfoil geometry was optimized using FLO-6 OPT to meet the prescribed design objectives. The resultant profile was then evaluated the (at design and off-design conditions) and further refined using BAUER code.
I
I !
I EVALUATf FIRST I I I I
' I I 9 - 4 I 'I BAUERCODE
I I I I I Y f S I
i 1 f V A L U A T F 6 THIRD OOJEcIIVf5 1
WITH IIAUERCODE
I i
I I I
I I I 0-J i
I I I I DESIGN PROCEDURE In the design of the "-06 airfoil, the initial profile was modified through the application of different shape functions to its upper and lower surfaces. A specific aerodynamic parameter (or object function) such as the drag coefficient is minimized through adjusting the
decision variables (e.g., n, m, p, ... etc) which control the magnitude and
location of the shape functions. Constraints, either geometric or aerodynamic, may be added to the minimization process. The effect of each shape function is then assessed by perturbing its decision variable and computing the change in the object function. The resulting gradient is then traced until a local minimum is found or a constraint is reached.
Y = X" (SIN (V-XP))~ n = O Y m = 10 0.8 P = .314 TYPICAL SHAPE FUNCTIONS USED IN OPTIMIZATION
0 . 4 I \
y = X"(1-X) emx
II n = 2
m = 5 Y = xn SIN n = 10 0 0.2 0.4 0.6 0.8 1 .o X : CD @ M=0.81, Alfa=-0S0 Object function 0.10 B t/c z 0.095 Geometric Constraint Aerodynamic constraints :' ICM 12 0.010 @ M=0.30, Alfa=-OSO 1 CMIZ 0.015 @ M=0.80, Alfa=-O.5: ML d 1.400 @ M=0.80, Alfa=-0.5, ML 1.400 @ M=0.40, Alfa=l2.5 RESULTS OF THE ITERATIVE DIRECT PROCEDURE In t h e late seventies, the National Aeronautics and Space Administration awarded two contracts (Boeing VERTOL, Lockheed Georgia) for the design of an advanced airfoil for rotorcraft applications [16,17]. A set of design objectives was defined which, when met, would ensure acceptable performance during hover and through high -speed flight. The VERTOL design later evolved to the successful VR-12 family of airfoils. In 1983 engineers at the McDonnell Douglas Helicopter Company embarked on the further refinement of the Lockheed design using the NASA set objectives as design goals.
COMPARISON OF "-00 TEST RESULTS WITH DESIGN OBJECTIVES OBJECTIVE "-00 t / c = .0954 t / c = .09542 First Priority: C M ~ = .0014 1) ICMoI 5 s o 1 M = . 3 2) C L ~ ~ , 2 1.5 M = .4 3 ) M D D , 2 -81 4 ) ICM,,I I ,015 M 5 .80 Second Priority: 5) C D 5 .008 C L = .6, M = . 6 6) CL,,.,,~ 2 1.5 CL,,. = 1.21 M = .5 Ct,g = -.0174 7 ) l c M l 5 -02 CL = 1.0, M = .3 8 ) CDe 5 -01 C D , = ,0137 M = MDD,, + .02 M = ,828 Third Priority: MT, = ,800 9) MTn 2 MODO 10) Gradual Stall M = .3 MIXED M = .4 MIXED 1 1 ) C D , 5 .007 C D , = .0070 M D D = M D D - . 1 M = .708 AERODYNAMIC CHARACTERISTICS OF THE "-06 AIRFOIL A comparison is made between the aerodynamic characteristics of the designed "-06 airfoil and those of other airfoils which represent state-of-the-art designs. The comparisons represent the variation in the maximum sectional lift (Clmax) at a free-stream Mach number of 0.40 versus zero-lift drag divergence Mach number. As seen, the HH- 06 characteristics compare quite well with the other recently developed families of airfoils [ 18-21].
1.80 1.60
- HH-06 TREND WITH POROSITY
\
S A 2 1 2 VERT01 x 1.40 O N E R A - A
BINCHAM -
U 1.20 OA207 1 .oo 3 0 .70 .75 .80 .85 .90 .95 MODO HYBRID DESIGN PROCEDURE It is obvious that for many practical applications, structural or aerodynamic, that the most desirable design procedure is one which combines the advantages from a direct computational method with those of an inverse method. In this respect, the shortcomings of each are overcome by the strengths of the other. Such methods, commonly referred to as "Hybrid Methods" have been successfully applied in the design of subcritical airfoil sections for fixed wing applications [22], and in the design of supercritical cascades for turbomachinery applications [23].
PRINTOUT EFFECTIVE AIRFOIL COORDINATES I I COMPARE MACH INPUT MACH NUMBER DISTRIBUTION DISTRIBUTIONS SAME?
M A FLO6
ALTER MACH NUMBER -
INVISCID DESIGN INVISCID ANALYSIS DISTRIBUTION DIRICHLET n.c:s NEUMANNB.~:~ 1 I I 1
4 4 1
I DISPLACEMENT LTBLCEQL
1 . SURFACE I
BOUNDARY LAYER ALGORITHM
-+
I * 1 I
1 EOUNDARYLAYER 1 ' 1 S E P ~ ~ ~ ~ ~ ~ o I N T
SEPARATES? COORDINATES EFFECTIVE AIRFOIL COMPUTE EFFECTIVE
(7)
AIRFOIL COORDINATES ALTER M ATANO CROSSINGS?
NEAR TRAILING EDGE RESULTS OF HYBRID PROCEDURE The inverse design procedure is based on a conformal transformation of the semi-infinite, two-sheeted Riemann hodograph free-surface representation of the airfoil into the unit circle. The input to the procedure includes a prescription of a target subsonic-sonic pressure distribution (or Mach number) and the free-stream conditions. The analysis of the airfoil configuration which results from the inviscid inverse procedure at design and off-design conditions is carried out using Jameson's [24] full potential solver FL06. To account for viscous
effects, the basic approach is to calculate a boundary - layer
displacement thickness and use it to correct the location of the displacement surface. That is, vector subtraction of the displacement thickness from the inviscid displacement surface yields the effective airfoil configuration.
0.00 0.21 0.W 0.75 1 Q ANGUIAR POSITION l w m ) Y K 4 XIC
-0.12 , t
I I I
0.00 0.31 ' o h 0.75 1.00
INPUT MACH NUMBER AND RESULTING AIRFOIL M CL CD CM ALFA 0.75 0.055 0.0093 -0.065 1 . 3 0 DESIGN : -0.083 8.24 O F F - D E S I G N 0.40 1 . 1 7 5 0.0124 A PROPOSED EFFICIENT HYBRID DESIGN PROCEDURE It is apparent that the existing structure of the hybrid design procedure could be further enhanced if a more "GENERAL" flow solver assumes the roles of both the existing direct (FL06) and inverse (IDA) solvers. This in turn, eliminates the required interpolation of the computational results between the two different grid systems.
START
c r '
INPUT M A C H NUMBER GUESS INITIAL GEOMETRV I I I I SOLVER I (ISES) I I I I I I I I I I I DESIGNCONSTRAINTS I ~ --.--.---
I l l , +
2-0 NAVIER
I I '1 GEOMETRIC + 1
STOKES SOLVER
1 A;Hl;s;s, AERODVNAMIC
AERODYNAMIC GEOMETRIC PRINTOUT AIRFOIL COORDINATES CONCLUSIONS OPTIMIZATION ROUTINES ARE A POWERFUL TOOL FOR FINDING SOLUTIONS TO MULTIPLE DESIGN POINT PROBLEMS THE OPTIMIZATION PROCESS MUST BE GUIDED BY THE JUDICIOUS CHOICE OF GEOMETRIC AND AERODYNAMIC CONSTRAINTS 0 OPTIMIZATION ROUTINES SHOULD BE APPROPRIATELY COUPLED TO VISCOUS, NOT INVISCID, TRANSONIC FLOW SOLVERS HYBRID DESIGN PROCEDURES I N CONJUNCTION WITH OPTIMIZATION ROUTINES REPRESENT THE MOST EFFICIENT APPROACH FOR ROTOR AIRFOIL DESIGN 0 UNSTEADY EFFECTS RESULTING IN THE DELAY OF LIFT AND MOMENT STALL SHOULD BE MODELED USING SIMPLE EMPIRICAL RELATIONS 0 INFLIGHT OPTIMIZATION OF AERODYNAMIC LOADS (e.g.,
use of variable rate blowing, flaps, etc ........) C A N
SATISFY ANY NUMBER OF REQUIREMENTS A T DESIGN AND OFF-DESIGN CONDITIONS REFERENCES 1. Volpe, G. and Melnik, R. E. "The Role of Constraints in the Inverse Design Problem for Transonic Airfoils," AIAA Paper 8 1 - 1233, June 1981.
2. Hicks, R. M. and Vanderplaats, G. N. "Application of Numerical Optimization to the Design of Supercritical Airfoils Without Drag Creep," SAE Paper 770440, March 1977.
3. Hassan, A. A,, Sobieczky, H. and Seebass, A. R. "Subsonic Airfoils ~ With a Given Pressure Distribution," AIAA J,, Vol, 22, No. 9, pp. 1185- I 1 191, September 1984.
4. Bauer, F., Garabedian, P. and Korn, D. "Supercritical Wing Sections 111," Lecture Notes in Economics and Mathematical Systems, Springer Verlag, New York, 1977.
5. Hassan, A. A., Sobieczky, H. and Seebass, A. R. "Shock-Free Transonic Airfoils with a Given Pressure Distribution," Computer Methods in Applied Mechanics and Engineering, Vol. 58, pp. 285-304, 1986.
6. Hassan, A. A. "The Design of Shock-Free Supercritical Airfoils Including Viscous Effects," Communications In Applied Numerical Methods, Vol. 2, pp. 37-45, 1986.
7. Melnik, R. E., Mead, H. R. and Jameson, A. A Multi-Grid Method for the Computation of Viscid/Inviscid Interactions on Airfoils," AIAA Paper 83-0234, January 1983.
8. Jackson, B. "Wind Tunnel Report for the Development of Airfoils for MDHC," McDonnell Douglas Helicopter Company Technical Report ATN 86-018, February 1986.
9. Wegryn, S. J. "BSWT 602 A Supersonic Wind Tunnel Test of Nine Two-Dimensional Airfoils," Boeing Report Number D6-52979, October 1985.
10, Brown, B. "Two-Dimensional Wind Tunnel Tests of Hughes Helicopter Inc. Airfoils "-01, "-02, and CR-2961 (Data Release)," Lockheed Report LR-3053 1 (S-434), September 1983.
~ 11. Prouty, R. "Wind Tunnel Report of Potential HARP Airfoils," Hughes Helicopters Report 150-A-1015.
12. Vanderplaats, G. N. "CONMIN - A FORTRAN Program for Constrained Function Minimization," NASA TM-X-62282, 1973.
13. Hicks, R. and Vanderplaats, G. N. "Application of Numerical Optimization to the Design of Low Speed Airfoils," NASA TM-X-3213, March 1975.
14. Hicks, R. and Vanderplaats, G. N. "Airfoil Section Drag Reduction the at Transonic Speeds by Numerical Optimization," Presented at Society of Automotive Engineers, Business Aircraft Meeting, April 1976.
15. Bauer, F., Garabedian, P., and Korn, D. "Supercritical w i n g Sections 11," Lecture Notes in Economics and Mathematical Systems, Volume 108, Springer Verlag, 1975.
16. Blackwell, J. and Hinson, B. "The Aerodynamic Design of an Advanced Rotor Airfoil," NASA CR-2961, May 1977.
17. Dadone, L. "Design and Analytical Study of a Rotor Airfoil," NASA Report CR-2988, 1978.
18. Thibert, J. and Gallot, J. "Advanced Research on Helicopter Blade Airfoils," Vertica, Vol. 5, No. 3, 1981.
19. McVeigh, M. and MuHugh, F. "Recent Advances in Rotor Technology at Boeing VERTOL," Presented at the American Helicopter Society Forum, May 1982.
20. Bingham, G. and Noonan, K. "Two-Dimensional Aerodynamic Characteristics of Three Rotorcraft Airfoils at Mach Numbers from 0.35 to 0.90," NASA TP-2000, March 1982.
21. Wortmann, F. X. and Drees, J. M. "Design of Airfoils for Rotors," Presented at CAL/AVLABS Symposium on Aerodynamics of Rotary Wing and VTOL Aircraft, 1969.
22. Hassan, A. A. "A Viscous-Inviscid Coupling Method for the Design of Low Reynolds Number Aerofoil Sections," Communications In Applied Numerical Methods, Vol. 2, pp. 419-427, 1986.
23. Ives, D. C. "Inverse and Hybrid Cascade Design Methods," Proc. Int.
Conf. on Inverse Design Concepts in Engineering Sciences (ICIDES), Austin, Texas, pp. 555-572, 1984.
24. Jameson, A. "Iterative Solution of Transonic Flows Over Aerofoils Math., Vol.
and Wings, Including Flows at Mach 1," Comm. Pure Appl.
27, pp. 283-309, 1974.