SRJSTI - The NAL method for the design andanalysis of natural laminar flow (NLP) airfoils

K.R. Srilatha, G.S. Dwarakanath, and P.Ramamoorthy

Computational and Theoretical Fluid Dynamics DivisionNational Aerospace Laboratories, Bangalore 560 017, INDIA

Abstract: A software package (called SRJSTI) for the design and analysis of NLFairfoik is described. As an illustration, an NLF airfoil for NAL's Light Transport Air-craft has been designed using this package. Its aerodynamic characteristics have beenextensively compared with GAW-2 airfoil and also with wind tunnel experiments.

1. Introduction

There is a constant endeavour to seek energy efficient technologies for general aviation,and the design of Natural Laminar Flow (NLF) airfoils provides one. In this technologythe flow is controlled to laminar on its own so as to reduce the profile drag. The availabil-ity of advanced materials for fabricating clean control surfaces without the usual surfaceroughness and the availabilty of good computational methods to custom-design any aero-dynamic shape have-paced this technology. NLF airfoils find applications in RemotelyPiloted Vehicles (RPV), gliders, wind turbines, sports aircraft and other general aviationaircraft.

2. A brief survey of NLF airfoil design and development

Even before NLF airfoils were realised in practice in the 1990's, there were continuousand concerted efforts in the development of low drag airfoils at established aeronauticalinstitutes in Europe and the U.S.A. Until 1920, airfoil development was mostly empiricalin nature. By 1940 both NACA and Gottingen in Germany had developed airfoils usingwind tunnel testing and potential flow theories. Even though some success was achievedin getting good stalling characteristics, premature transition to turbulence plagued thedesigners. In the 1950's NASA was able to achieve extensive laminar flow on airfoils andthereby cut down the drag by about 50%. The design of these airfoils (denoted by 6 digits)included the viscous effects through boundary layer theory unlike the earlier 4- and 5-digitseries. In the 1960Js there was a surge of interest in developing supercritical airfoils attransonic speeds and some interesting airfoils were developed by Whitcomb (1974) andothers. In the 1970's, when the oil crisis hit the scene there were renewed efforts to obtainlow speed versions of these supercritical airfoils; GAW-1 and GAW-2 airfoils were theoutcome of these efforts. Since the 1980's there have been systematic efforts to designand develop tailormade NLF airfoils using advanced techniques of Computational FluidDynamics (CFD). NAL has also made contributions in this direction.

191

192 K.R. Srilatha, G.S. Dwaiakzn&th, P.

3. The design methodology - basic issues

In the last six decades the task of designing an airfoil to meet given specifications mremained a difficult nut to crack even for the best brains. The first attempt was to etan airfoil for a given upper surface surface distribution without addressing oneself to »design issues which demanded such pressure distributions. Some of the work at R Ecarried out by Germain (1945), Goldstein (1948), Lighthill (1945), Thwaites (1945i >)and others was of this nature. Goldstein even succeeded in obtaining exact solutions »the airfoil contour for a class of upper surface pressure distributions.

The major flaw in this approach was the neglect of the issues related to the bound jlayer, such as transition and separation. These play a dominant role in the design rfsuch airfoils- It is only in the last two decades that Wortmann (1973), Liebeck (107 IMcMasters et al. (1979) and Miley (1974) started designing laminar airfoils with i cprimary emphasis on boundary-layer management. While these approaches are steps ithe right direction, obtaining a suitable airfoil for supporting real viscous flows still rema tan art rather than a science and no universal foolproof method seems to exist. Hence tb eis a need for such a method. The NAL method aims to meet these requirements by a t 5pronged approach of inviscid and viscous analysis: firstly we obtain an airfoil contc rfor supporting a nonviscous velocity distribution appropriate to a low drag airfoil, a Isecondly, test this airfoil for realistic performance using a viscous code. Figure 1 brir §out the intricate connections between the airfoil shape, the inviscid pressures and t 5boundary-layer interaction.

For the inviscid design we use the classical solution of Goldstein (1948) to obtain isymmetrical airfoil that supports a prescribed velocity distribution appropriate to low dr jairfoils. The velocity distribution is conceived as a three-tier distribution (Fig. 2) and \characterised by a few parameters. These parameters are: the initial acceleration (s), ti >magnitude and position of the maximum velocity (6, a?i), the extent of the transition ran i(c,Z2) and the concave recovery (7,^) in the turbulent boundary layer region. The tparameters can be tuned to obtain realistic symmetrical airfoils. Next, an appropria iNASA camber line giving the desired lift arid pitching moment and maintaining a coasteload from the leading edge to the trailing edge is superposed on this symmetrical airfbFinally the viscous performance of this airfoil is obtained. For this, an excellent, robuviscous code issued. This design procedure is repeated if the target performance is machieved. Figure 3 gives the flow chart of the design process. The robustness of the NCScode (Ramamoorthy et al. 1987) is illustrated in Fig. 4 where the theoretical predictio!are compared with experimental values for the NACA 643 — 418 airfoil. What in the effathe NAL method (Srilatha et al 1990, Srilatha and Ramamoorthy 1990) does is thzit provides a mathematical model of the airfoil that is supposed to provide a low draperformance. It then tests this model in a numerical wind tunnel in the form of the NCS1

code. It repeats this procedure till the target performance is obtained.

4. The NAL method - an illustrative example

The NAL method is best illustrated for the design of an NLF airfoil of 13% thkkaesfor the design condition M = 0.6 RN = 106 and CL = 0.4. Firstly a surfacedistribution characterised by

is chosen. As s

a b C d J Xi X2 ymax

0.115 0.172 0.167 -0.194 -1.21 0.544 0.698

een from Fig. 2 the velocity distribution is given by

0.068

-VQ

SRJSTI - The NAL method for the design and analysis ofNLF airfoils 193

whereGO-MJCOS0 0 < 0 < 0 !

gs(0) = < 60 + MOS 0 0i < 0 < 02

CQ+ CiCOS 6 + C2COS 20 02 < 0 < fl"

The continuity of &,(0) at 0i,02 results in

(& — a cos $2)

(I)

, _ (c cos #1 — 6 cos #2)— COS

2c(l + 4 cos ̂ 2) + cos ) - cos

c2 =

4(1+cos 02 )2

(7 + 8 cos 02) — 8c cos 02 — 7 cos 2024(l4.Cos02)

2

(7 — 2d) + 7 cos 02 + 2c4(1 +cos 02)

2

(2)

Now by Glauert's theory, the surface slope, y'3(0) and the perturbation velocity, g3(0)are related by the following expressions:

1 r* y'(a)Smada*L (cos a- cos 0)

G(0)dao (cos 0- cos a)

(3a)

(36)

where/"*(7(0) = / ^,(or)sina

^o

and P denotes the Cauchy's principal value of the integral. Substituting Eq. (1) intoEq. (3b) and integrating, one gets the surface coordinates as

.(*) = Xi log < T-sm sm

sin 30

Xi = ~{3(a1-61)(cos20-cos20r)-6(2a0-260)(cos0-cos0i)}A ti

194 K.R. SrHatha, G.S. Dwarakanath, P. Raman**

X2 =

Xs =

X4 =

Xs =

— L {2c2(cos 30 - cos 302 ) + 3(&!LJU

-f 6(2&i - 2co + c2)(cos 0 - cos

g {3(2co - c2)7r + 6(<z0 - b0)0

•f 3(5! - GI) sin (9 - c2 sin 2^2}

IB - cos 202)

+ c2)02

- 4c2 sin 02]

Now the velocity at any lift coefficient CL is given by Goldstein's second approximat aas

COS0

QQ

where

sm

Figure 5 shows the pressure distribution on this symmetrical airfoil as obtained fGoldstein's theory. On this symmetrical airfoil a NASA camberline of lift c^ = 0.27 a Iconstant load from leading to trailing edge was superimposed. In this case the airf Icoordinates are given by

yu = yc + ys cos am = yc- ys cos axn — x -ys sin axi — x-f yss'ma

where

•«• / \2 1 i i / \2- *> log ia - z| ~ (a ~ x)

— (1 — x)2log|l — a: I -f- -(1 — x)2 — xlogx + g — hx\& j j

and

i

~

Again, the velocity distribution by Goldstein's third approximation is given by

— w AF sin(0 ± e qp 0) ± ± e

whereCl}L B=C± c = CLe<*

SRJSTI - The NAL method for the design and analysis of NLF airfoils 195

/; 4-aco- = *

27T

Figure 6 Illustrates the pressure distribution on this airfoil. This pressure distributionclearly shows that there is a good accelerated flow on both the upper and lower surfacesat the design CL. This airfoil designated as NAL-NLF-136 was tested by the NCSU codefor performance and compared with that of GAW-2. Figure 1 gives the comparison ofpressure distribution for these two airfoils at the design CL = 0.4. Figures 8-10 illustratethe Eft, drag and pitching moment coefficients for NAL-NLF-136 and GAW-2 airfoils. Onecan see the oetter performance of NAL airfoil in terms of larger L/D in the operating CLrange.

NAL has utilised this design method to design two other NLF airfoils designated asNAL-NLF-208 and NAL-NLF-120 for NALLA and for an RPV respectively (Srilatha etal. 1990, Srilatha and Ramamoorthy 1990). Figure 11 gives the contours of these airfoils/

5. Wind tunnel and flight testing of the NAL-NLF-136 airfoil

Wind tunnel tests were conducted at the NAL V x I' tunnel to study the off-designperformance of the NAL-NLF-136 airfoil whose design procedure was explained above. Amild steel model of chord 6" was tested at M = 0.52 and RN = 2.6 x 106. Figure 12shows the comparison between theory and experiment. One can see that for the off-designcondition the theory and the experiments show an excellent correlation. Efforts are alsounder way for testing the NALLA NAL-NLF-208 airfoil using gliders. This airfoil wasoriginally designed for the NAL Light Aircraft (NALLA).

8. Concluding remarks and future directions

Using the computational and wind tunnel resources at NAL it has been possible to designand develop NLF airfoils for general aviation applications. Efforts for testing these airfoilsin a low turbulence tunnel are under consideration. Design of finite wings (with NLF wingsections) using a full-potential code and 3-D boundary layer calculations are under activeexploration.

Germain, P. (1945), "The computaion of certain functions occuring in profile theory,"ARC Rep. No. 8692.

Goldstein, S. (1948), "Low drag and suction airfoils," J. Aero. Sci., 15(4).Liebedc, R.H. (1973), "A class of airfoils designed for high lift in incompressible flow," J.Aircraft, 10(10).

LighthiU, M.J. (1945), "A new method of two dimensional aerodynamics design," R andM No. 2112, ARC.

McMasters, J.ELand Henderson, M.L. (1979), "Low speed single element airfoil analysis-PartI,»NASA.CP-2085.M2ey, S.J. (1974), "On the design of airfoils for low Reynolds numbers," Proc. 2nd Int.Gonf. on Tech. and Sci. of Low Speed and Motorless Flight, MIT, Cambridge, Mass.

Ramamoorthy, P. and Dhanalakshmi, K. (1987), "NCSU Code: Validation and extensionon NAL's UNIVAC 1100/60 system, NAL PD FM-8760.

196 K.R. SriJatha, G.S. Dwarakanath, P. Rajnaroo thy

Srilatha, K.R., Dwarakanath, G.S., and Ramamoorthy, P. (1990), "Design of a nat nllaminar flow airfoil for a light aircraft," J. Aircraft, 27(11).

Srilatha, K.R. and Ramamoorthy, P. (1990), "Design of a natural laminar flow airfoi 'oran unmanned aircraft," NAL PD CF-90Q4.

Thwaites, B. (1945a), "A method of airfoil design - Part I," R and M No. 2166, ARCThwaites, B. (1945b), "A method of airfoil design - Part II," R and M No. 2167, ARi

Whitcomb, R.T. (1974),"A review of NASA supercritical airfoils," ICAS Paper 74-10.Wortmann, F.X. (1973), "A critical review of the physical aspects of airfoil design at «Mach numbers," NASA CR-2315.

NON VISCOUSANALYSIS

!L G MFuTARGET

PRESSURE

INVERSE

DESIGN

INVERSE BOUNDARYLAYER CODE

NCSU

CODE

Figure L Connection between the boundary-layer development,pressure distribution and section geometry.

ASSUMED

vmax / vo(1 * b)

0.2 0,4 0.6 0,8 1.0X

Fig.2 A PLAUSIBLE MODEL FOR NATURAL LAMINAR FLOW AIRFOIL DESIGN

SrO0.

to-rtQ.

Q.

B

a,

e.ii5T

CO

198 K.R. Srilatha, G.S. Dwarakanath, P.

CHANGE

PARAMETERS

NO

START

PARAMETERS CHARACTERISING

VELOCITY DISTRIBUTION

ON A SYMMETRICAL AIRFOIL

GOLDSTEIN'S

INVERSE METHOD

1VISCOUS ANALYSIS

( NCSU )

ADD APPROPRIATE

CAMBER

DISTRIBUTION

1

TARGET

r

AIRFOIL

STOP

PRINT RESULTS

NO

ANY FURTHER

CHANGES ?

Figure 3. Flow chart for NLF Airfoil design

NACA 6 4 3 - 4 1 8

1.6

1.2

0.8*

0.4

0.0

-0.8

-i.a JL / .. I-24 -16 -8

M «0.|7• •CAt.(NAL)<~*EXPT. (NASA)

0 8tC'

16 24

.030 r-

.016

,012CD

.008

.004

0.0

-O.Im.

-0.2

-0.3 U

NACA 643-118

RH - 6x10°M = 0 . 1 7• =CAL.(NAL)— e EXPT. (NASA)

•1.6 -1.2 -0.8 -0,4 0.0 0.4 0.8 1.2 1.6

g

fcrOa.

ta-rt

£3

a

I

§'

a,•*ie.>-isf!t5"

AERODYNAMIC PERFORMANCE OF NACA 04 - 41 fl AIRFOIL3

CDCO

-Cp1.0

0.5 -

0.0 -

-0.5-

-1.0

1.00 -,

0.50 -

0.00 -

-0.50 -

0.6—I1.00.0 0.2 0.4 0.6 0.8

FIG.S Cp OF SYMMETRICAL NLF AIRFOIL

0.00 0.20 0.40 0.60 0.80 1.00 X/C

— NAL-NLF-136 .004 -.068- - GA W(2)

1/4

,ooe -,11 a

o.o

-0.5

-1.00.00 0.20 0,40 0.60 0.80 1.00 X/C

FIG.6 Cp OF DESIGNED NLF AIRFOIL Fig.7 Cp OF NAL-NLF-136 & GAW(2) AIRFOILSAT C^—.4 Rf,— 10E6 M=.6

NAL-NLF-tSeGAW(t)

0.0

Fig.8 CL CURVES OF NAL-NLF-136 * GAW(Z)

AIRFOILS AT RN=10E6 M=.6

C D E 21.5 -i

1.0 -

0.5 -

*• NAL-NLF-136A CAW(Z)

0.5

-0.20.0

1.5

Fig.9 CDAND CM CURVES OF NAL-NLF-136

A GAW(2) AIFOILS AT R

L/D100.00 n

80.00 -

60.00 -

40.00 -

20.00

0.00

NAL-NLF-i3eCA*(2)

0 60 0^OO

Fig. 10 L/D CURVES FOR NAL-NLF-136 *

GAW(Z) AIRFOILS AT R^tOEB M-.6

toO

-Cp1.0

0.5 -

0.0 -

-0.5-

-1.0

-Cp1.00

0.50 -

0.00 -

-0.50 -

0.0 0.2 0.4—P_0.6 0.8

—l -r/r -1.001.0 X'C 0.00

-S

0.20 0.40 0.60 0.80

FIG.5 Cp OF SYMMETRICAL NLF AIRFOIL1.00 x/c

NAL-NLF-136 ,004 -.068GAW(Z) ,006 -.118

0.0

-0.5

-1.00.60 0.20 0.40 0.60 0.80 1.00 X/C

FIG.6 Cp OF DESIGNED NLF AIRFOIL Fig.7 Cp OF NAL-NLF-136 & GAW(Z) AIRFOILSAT CL=.4 RN=10E6 M=.6

«.Sr

tl

II-£3to£r

NAL-NLF-136

°'°-"^—o^o—3^ 55 S» ALFA

Fig.8 CL CURVES OF NAL-NLF-136 * GAW(Z)

AIRFOILS AT RN=10E6 M=.6

C D E Z1.5 -[

1.0 -

0.5 -

*• NAL-NLF-136A GA1T(2)

0.0 0.5

-0.2 15" TS"

1.5

T?5O.'O 0.5 i.O 1.5 "L

Fty.S CDAND CM CURVES OF NAL-NLF-136

* GUFTf*; AIFOILS AT R(f=10E6 Af=.6

I/JO100.00 -]

80.00 -

60.00 -

40.00 -

20.00

0.00

NAL-NLF-136CAW (2)

0 00 CK^O Too TsO CLFig./O L/D CURVES FOR NAL-NLF-136 A

GAW(Z) AIRFOILS AT R^=10E6 M=.6

toO

202 K.R. Srilatha, G.S. Dwarakanath, P. Ramamoot

Y/C

0.2 -i

0.0 -

-0.20.0

Y/C0.2 -

0.0 -

-0.20.0

Y/C0.2 -i

o.o H

•0.2

UNMANNED AIRCRAFTM—.2

NAL-NLF-120

0.2 0.4 0.6 0.8 1.0

LIGHT TRANSPORT AIRCRAFTM—.6

x/c

0.2 0.4 0.6 0.8 1.0

TWO SEAT TRAINERC =.3 R=4.6E6 M=.16

X/C

0.0 0.2 0.4 Q.6 0.8 1.0 X/C

Fig, 11 NAL'S NATURAL LAMINAR FLOW AIRFOILS

SRISTI - The NAL method for the design and analysis of NLF airfoils 203

-Cp1.0 -i

0.5 -

0.0 -

-0.5

-1.0

* * *£-*-**

C = .355L -THEORY (NCSU 5%TRIP)

* EXPT (NAL)

0.0 0.2 0.4 0.6 0.8 1.0

Fig, 12 PERFORMANCE OF NAL-NLF-136AIRFOIL AT R =2.6E6 M=.52

N

' X/C