Stability Characteristics of Supersonic Natural Laminar Flow Wing Design Concept

Size: px

Start display at page:

Download "Stability Characteristics of Supersonic Natural Laminar Flow Wing Design Concept"

Jewel Rogers
5 years ago
Views:

1 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition January 2012, Nashville, Tennessee AIAA Stability Characteristics of Supersonic Natural Laminar Flow Wing Design Concept Yuki Ide 1 The University of Tokyo, Chiba, , Japan and Kenji Yoshida 2 and Yoshine Ueda 3 Japan Aerospace Exploration Agency, Tokyo, , Japan Japan Aerospace Exploration Agency (JAXA) developed a natural laminar flow (NLF) wing design concept to reduce supersonic friction drag for a future SST, and confirmed remarkable transition delay in the flight test conducted in After the test, stability characteristics on the NLF wing was numerically analyzed in detail, being compared with them on a typical non-nlf wing. The NLF wing has strongly rapid acceleration near leading edge (LE) and then gradual acceleration in chordwise region. Such a chordwise velocity distribution generates rapid decrease of maximum crossflow (C-F) velocity and change of its direction. According to linear stability theory with local parallel flow approximation, this feature contributes to suppress the growth of amplification rates based on the C-F instability. Nomenclature x,y,z = Cartesian coordinate C p = pressure coefficient α, β = wavenumber in the streamwise and in the spanwise ω = frequency N = N factor Ψ = propagation direction Rec = Reyonlds number based on mean aerodynamic chord (MAC) q = disturbance Subscript r = real part i = imaginary part Superscript = disturbance quantity ~ = disturbance amplitude function I. Introduction APAN Aerospace Exploration Agency (JAXA) promoted National EXperimental Supersonic Transport (NEXST) J program from 1997 to 2006, in order to develop an advanced supersonic drag reduction technology for a future international cooperative development of a next generation SST 1. In this program, JAXA had designed a natural laminar flow (NLF) wing at supersonic speed as one of the technological challenge to reduce its friction drag, and validated the effect of the NLF wing concept by a flight test in In the design process, of course, the delay of 1 Graduate student, Department of Advanced Energy, Kashiwanoha, Chiba , Japan. 2 Director, Supersonic Transport Team, Aviation Program Group, Japan Aerospace Exploration Agency (JAXA), Osawa, Mitaka, Tokyo , Japan, AIAA Member. 3 Researcher, Supersonic Transport Team, Aviation Program Group, Japan Aerospace Exploration Agency (JAXA), Osawa, Mitaka, Tokyo , Japan. 1 Copyright 2012 by the, Inc. All rights reserved.

transition was numerically and experimentally confirmed using a current e N method based on stability theory of boundary layer 1,2 and wind tunnel test with transition detection technique 1,3.

This paper shows reconsideration of principal physical mechanism on the NLF wing design concept by comparing stability characteristics on the NLF wing with those on a typical non-nlf wing, which are

2 transition was numerically and experimentally confirmed using a current e N method based on stability theory of boundary layer 1,2 and wind tunnel test with transition detection technique 1,3. To understand its physical mechanism of the transition delay, however, detailed stability characteristics have not been investigated yet. This paper shows reconsideration of principal physical mechanism on the NLF wing design concept by comparing stability characteristics on the NLF wing with those on a typical non-nlf wing, which are based on linear stability theory of the laminar boundary layer. First of all, an overview of the NEXST program is introduced at the second section. Then, the details of present stability analysis method, principal results, and considerations on stability characteristics of several physical parameters are described in the third section. II. Outline of NEXST Program In the NEXST program, JAXA designed an unmanned scaled supersonic experimental vehicle called NEXST-1 incorporating the following four aerodynamic design concepts to reduce supersonic drag; an arrow planform, a warped wing, an area-ruled body and a NLF wing 1. The first three design concepts were applied to reduce pressure drag of the NEXST-1. The last one was originally created to reduce its friction drag. To design the NLF wing, firstly, an ideal target pressure distribution on the upper surface of the wing was originally derived to delay the transition using a JAXA s e N method called LSTAB code 4. Then, a CFDbased inverse design method was also originally developed to design the wing shape of the NEXST-1 to realize the ideal pressure distribution on the upper surface of the wing 1. This design procedure is summarized in Figure 1. This design method consists of specifying the ideal target pressure distribution for delaying transition and iteration process to reduce the difference between the target and the estimated pressure distributions at each iterative step. Finally, according to those design concepts, the NEXST-1 airplane was developed and manufactured as shown in Figure 2. The flight test was conducted at the Woomera prohibited area in Australia, in And the effect of the NLF wing design concept was validated at Mach 2 flight test condition by obtaining good agreement between the measured and the target (based on CFD) pressure distributions on the wing and by confirming remarkable rearward movement of Figure 1. CFD-based inverse design method (Ref.1). Figure 2. NEXST-1 airplane (Ref.1). transition location at the design condition as shown in Figure 3 and Figure 4 5. In Figure 4, the red symbols demonstrate a turbulent state detected at each transition measurement sensor and the blue symbols show a non turbulent state, namely laminar and transitional region. 2

3 Figure 3. Measured and CFD-based pressure distributions at design condition (Ref.5). Figure 4. Summary of transition data measured with hot-film (HF), dynamic transducer (DP), Preston tube (Pr) and thermocouple (TC) techniques in flight test at design point (Ref.5). III. Stability Analysis A. Outline of numerical method In this study, we adopted a well-known linear stability theory of laminar boundary layer with local parallel flow approximation. According to this theory, flow quantities consist of mean flow and disturbed flow quantities. And three dimensional disturbance is expressed by the following relation; q ~ i,, x z t x y z t q y e, c.c. (1) Here, x and z are space coordinates in external streamwise and crossflow-wise directions, respectively and c.c denotes complex conjugate. Frequency ω was assumed real number while α and β are complex (spatial theory). Furthermore the β i was set to be zero to supplement one more condition to solve basic stability equations. This assumption was derived from a physical viewpoint that principal flow direction of disturbance is approximately streamwise. Substituting Eq. (1) into the linearized compressible Navier- Stokes equations, present basic stability equations are summarized in the following form 4 ; 8 d i aij j dy j 1 i 1,2,,8, (2) where each component of a vector φ and each element of a matrix a ij consist of quantities related to both disturbances (for velocity, density, temperature) and boundary layer profiles of mean flow. Present ordinary differential Eq. (2) can be solved with a shouting method, Runge-Kutta technique for integration and Newton method for iteration. To estimate transition location, a current e N method was applied. According to the method, N factor which is a criterion to judge transition location can be defined as the following equation; N i dx, (3) C where C is an integral path which is chosen as an external streamline. Although amplification rate -α i is generally computed at each frequency ω and each propagation direction angle Ψ=tan -1 (β r /α r ), we used socalled envelope strategy 6 to integrate those amplification rates for computing N factor. This strategy means to focus on a maximum amplification rate -α i (Ψ m ) at each ω and Re(x), where Ψ m is the 3

4 propagation direction angle where -α i has maximum value. According to this strategy, the envelope of several curves of those N factors defined as the following relation is applied to judge transition location. N x Max N : x (4) Envelope i m, B. Analysis Results at Inner Wing Region Using linear stability theory summarized in previous section, we analyzed stability characteristics of laminar boundary layer on the NLF wing and compared them with those on a typical non-nlf wing. As a typical non-nlf wing, we selected a wing geometry and pressure distributions of a kind of Concorde-like configuration. Although the detailed data of the real Concorde have never been opened, JAXA originally designed a Concorde-like configuration by using supersonic linear theory and several information described in some published reports 7,8. The main design concept is demonstrated in Figure 5. Its airfoil shape at each spanwise station was designed by using a conical camber concept and thickness distribution of the NACA 64A airfoil linearly tuned to thinner thickness-to-chord ratio, for example t/c=2.5%. JAXA also estimated flow-field around the Concorde-like configuration using a own CFD solver and pressure distributions on the upper wing of it at each spanwise station. A typical result is demonstrated in Figure 6 as a non-nlf wing. However, this Concordelike configuration has a large scale and different design condition. Therefore, in present transition analysis, we adjusted the design lift condition and the Reynolds number condition, namely assumed the same Reynolds number as that of the NEXST-1 flight test case. To clarify our consideration, we firstly focus on the stability characteristics at a representative spanwise location Y/s = 0.3 as a reference of inner wing region, where Y is spanwise coordinate and s is semi-span length. Then, we investigate them at Y/s=0.7 as a reference of outer wing region, and the corresponding results are summarized in the later section. Figure 5. Design concepts of Concorde-like Configuration. 1. Pressure distributions and Boundary layer profiles Figure 6 shows typical C p distributions on the upper surface at the front part of two special wings which were designed as the NLF wing of the NEXST-1 airplane and the non-nlf wing of the Concordelike configuration, respectively. As shown in this figure, the shape of -C p distribution of the NLF wing has strongly rapid increase near its leading edge and gradual increase after the rapid one. It was originally derived in the NEXST program 1 that such a special C p shape was very effective in suppressing crossflow (C-F) instability near its leading edge. The basic idea of the shape is based on the following fact: although the region of increase of -C p generates crossflow within laminar boundary layer, to shorten the region leads to effective suppression of growth of the crossflow and also gradual increase is effective to suppress Tollmien-Schlichting (T-S) instability. To understand the effect on such C p shape of the NLF wing, three dimensional boundary layer characteristics were firstly analyzed using the variation of C p distributions in spanwise direction as shown in Figure 7. As a reference, velocity distributions at boundary layer edge are also summarized in Appendix. Figure 8 shows a comparison of C-F velocity profiles V of the NLF and non-nlf wings, which the height and the velocity are normalized by the boundary layer thickness and the streamwise velocity U e at the edge, respectively. Although two wings have almost same maximum C-F velocities at x/c=0.01, where c is the cord length, the maximum C-F velocity of the NLF wing at x/c=0.05 rapidly decreases comparing with that of the non-nlf wing. On the other hand, the non-nlf wing keeps larger C-F velocity in the same direction even at x/c=0.2 than that of the NLF wing. Obviously, these C-F velocity profiles show that present C p shape of the NLF wing is very effective to suppress the growth of C-F velocity. 4

5 X Y Z Figure 6. Comparison of C p distributions at 30% semi-spanwise station. Figure 7. C p contour of the NLF wing of NEXST-1 airplane interpolated with measured data in the flight test at design point condition. a), NLF wing Figure 8. Crossflow velocity profiles. 2. Eigenvalue characteristics Figure 9 demonstrates several comparisons of amplification rates α i of the NLF and non-nlf wings in variation of Ψ at each frequency; 5, 10, 15, 20 and 25 khz. In these figures, first of all, disturbances on the NLF wing have lower amplification rates than those on the non-nlf wing except for the nearest disturbance to the leading edge(x/c=0.011). It means the NLF wing has better potential to suppress the growth of T-S instability as well as C-F instability than that of non-nlf wing. Next, the maximum amplification rates of the non-nlf wing at x/c=0.073 belong to the propagation direction Ψ between 75 and 85 degrees. It generally indicates that such disturbance is dominated by C-F instability. On the other hand, the maximum amplification rates of the NLF wing at the same location is appeared in around Ψ = ± 60 degrees except lower frequency, 5 khz. It approximately demonstrates that C-F instability does not dominate especially in higher frequency region, because of lower maximum C-F velocity. Here, Ψ = 60 is corresponding to so-called oblique T-S wave, which is observed in flat plate at Mach 2 flow. Furthermore, Ψ m of the NLF wing transfers from around +60 to -60 as flow goes downstream. This is supposed to be related to the change of sign of the maximum C-F velocity, namely the change of direction of C-F velocity as shown in Figure 8. 5

6 a), NLF wing Figure 9. Amplification rates at each streamwise station. 6

7 According to envelope strategy, propagation direction angle at maximum amplification rate, Ψ m and growth of each amplification rate, α i (Ψ m ) are summarized in Figure 10 and Figure 11. In the Figure 10, the Ψ m at each frequency of 5 and 10 khz on the non-nlf wing exists in the region between 75 to 85 degrees. In general, it is considered that any disturbances on the non-nlf wing are dominated by C-F instability. On the other hand, except for the case of 5 khz, each Ψ m at each frequency on the NLF wing strongly decreases from 85 degrees to around 60 degrees before x/c=0.1. It means such disturbance is not dominated by C-F instability but mainly dominated by oblique T-S instability. Furthermore, there are rapid changes of several Ψ m around x/c=0.1 for the NLF wing. The cause of such rapid change approximately originates in symmetry feature of the curves of amplification rate in the whole region of Ψ as shown in Figure 9. a), NLF wing Figure 10. Distributions of propagation direction angle at maximum amplification rates. In the Figure 11, while both amplification rates of the NLF wing and non-nlf wing near leading edge increase as frequency increases, this feature is approximately reversed after about x/c=0.05. And maximum amplification rate of the NLF wing is located near leading edge compared to the non-nlf wing which is almost appeared in the region of rapid decease of the amplification rate of the NLF wing, namely about x/c=0.06. Then, each amplification rate of the non-nlf wing at each frequency keeps larger value after x/c=0.05 than that of the NLF wing. It is approximately considered that this character is dominated by C-F instability as mentioned in Figure 10. a), NLF wing Figure 11. Maximum amplification rates at each frequency. 7

8 3. N factor Figure 12 shows each curve of N factor defined in Eq.(3). As easily understood in Figure 11, it is shown in Figure 12 that each N factor on the non-nlf wing is larger than that on the NLF wing. In general, both N factors on the NLF and non-nlf wings are dominated at higher frequency from leading edge to about x/c=0.05. After the location, the growth of each N factor on the NLF wing is reduced by comparing with that on the non-nlf wing, because of lower amplification rates of the NLF wing shown in Figure 11. The envelope of each N factor at each frequency on the NLF wing shows more impressive feature than that on the non-nlf wing which is usually characterized by strong growth due to C-F instability near its front part. This shape of envelope on the NLF wing certainly demonstrates to suppress C-F instability. And it originates in decrease of maximum C-F velocity and change of the direction, because this feature generates lower amplification rates. Furthermore, gradual growth of each N factor after the front part, namely at mid-chord region, is reflected by well-controlled oblique T-S instability due to gradual increase of present C p distribution, that is, gradual acceleration specified in the ideal pressure distribution. In the design process of the NEXST-1 airplane, N=14 was assumed as a threshold due to natural transition in flight condition, namely little freestream disturbance, based on Ref. 9. According to the N=14, transition location of the non-nlf wing is estimated to be about x/c=0.04. On the other hand, estimated transition location of the NLF wing is largely delayed at least beyond x/c=0.3. Consequently, shorter strong acceleration region near the leading edge as shown in Figure 6 generates rapid decrease of the maximum C-F velocity as shown in Figure 8 a), then it reduces the growth of amplification rates as shown in Figure 11 a), and suppresses the increase of N factor after rapid growth near the leading edge as shown in Figure 12 a),. This is an aerodynamic explanation from the viewpoint of stability theory for the NLF wing design concept. Figure 12. N factors. a), NLF wing C. Analysis Results at Outer Wing Region In this section, we describe analysis results at Y/s=0.7 including some considerations similar to the section B. Figure 13 shows the pressure distributions on the upper surface at the front part of the NLF and non- NLF wings at Y/s=0.7 spanwise station. In general, local lift coefficient at outer wing region is larger than that at inner wing region. Therefore, it requires larger acceleration near the leading edge. The NLF wing has a similar type of C p shape with that at inner wing region. On the other hand, the non-nlf wing has a large accelerated region as shown in Figure 13. Figure 14 shows the comparison of C-F velocity profiles and almost the same situation is demonstrated. And we confirmed the same feature on the growth of amplification rates of both the NLF and the non-nlf wings in variation of propagation direction angle Ψ at each frequency as shown in Figure 15. 8

9 According to those characteristics of amplification rates, corresponding N factors are summarized in Figure 16. This figure easily demonstrates more delayed transition of the NLF wing than that of the non- NLF wing as similar to the transition feature at inner wing region. Figure 13. Comparison of C p distributions at 70% semi-spanwise station. a), NLF wing Figure 14. Comparison of crossflowvelocity profiles. a), NLF wing Figure 15. Maximum amplification rates at each frequency. 9

a), NLF wing Figure 16. N factors. Finally, according to present stability analysis, we can estimate the N contour maps for both NLF and non-nlf wings as shown in Figure 17.

10 a), NLF wing Figure 16. N factors. Finally, according to present stability analysis, we can estimate the N contour maps for both NLF and non-nlf wings as shown in Figure 17. This figure also includes several external streamlines indicated by red dotted lines. At the NLF wing, the larger region between the leading edge and streamwise location corresponding to each N value is found more easily than them of the non-nlf wing. By comparing present envelope curve of N factors with measured transition location (boundary between red and blue symbols in Figure 17 a),) in the flight test of the NEXST-1 airplane summarized in Figure 4, so-called transition N value, N Tr is estimated to be about 12~13 at inner wing region. Therefore, we confirmed large laminar region under the judgment due to this N Tr. Consequently, it is clearly confirmed that present NLF wing design concept leads to large gain for delaying the transition location at the NEXST-1 flight test condition, namely flight test Reynolds number. a), NLF wing Figure 17. Estimated N contours. IV. Conclusion Stability characteristics on the NLF wing of the NEXST-1 airplane was analyzed and reconsidered at Mach 2 flight test condition, comparing with them on a typical non-nlf wing which was designed as a Concorde-like configuration. The NLF wing has strongly rapid acceleration near leading edge and then gradual acceleration in chordwise velocity distribution. Such chordwise distribution generates rapid decrease of maximum crossflow velocity and change of its sign, namely direction. According to linear stability analysis, this feature contributes to suppress the growth of amplification rates due to C-F instability and also those due to oblique T-S instability as shown in each amplification rate at each frequency in variation of propagation direction angle. As a result, the maximum amplification rate on the NLF wing is rapidly increased near leading edge, but the growth of each N factor which is defined as 10

11 integration of amplification rate at each frequency, is suppressed at the front part to mid-chord region. Such feature was also observed at other spanwise station, for example, Y/s=0.7. Finally, from present study, principal physical mechanism to maintain natural laminar flow on the wing surface at supersonic speed is summarized as follows: it is based on both rapid decrease of C-F velocity near leading edge and change of its direction at the front part smoothly. Appendix As a reference, the pressure coefficient (Cp) distributions and velocity distributions at boundary layer edge of the NLF wing at both representative spanwise stations (y/s=0.3 and 0.7) are summarized in table 1 and Fig. A1.Here X, Y, Z, Ue, Ve, We are demonstrated in Fig. A2. Figure A1. Velocity distributions of the NLF wing at flight test condition. Figure A2. Definition of vatriables in table 1. 11

12 Table 1. Pressure coefficient and velocity distributions of the NLF wing (1/4) y/s=0.30 Y[m]= S/C X[m] Z[m] Ue[m/s] Ve[m/s] We[m/s] Cp

13 Table 1. Pressure coefficient and velocity distributions of the NLF wing (2/4) y/s=0.30 Y[m]= S/C X[m] Z[m] Ue[m/s] Ve[m/s] We[m/s] Cp

14 Table 1. Pressure coefficient and velocity distributions of the NLF wing (3/4) y/s=0.70 Y[m]= S/C X[m] Z[m] Ue[m/s] Ve[m/s] We[m/s] Cp

15 Table 1. Pressure coefficient and velocity distributions of the NLF wing (4/4) y/s=0.70 Y[m]= S/C X[m] Z[m] Ue[m/s] Ve[m/s] We[m/s] Cp

16 Acknowledgments The authors thank Mr.Hiroaki Ishikawa of the SST team in JAXA/APG for CFD computations. References 1 Yoshida, K., Supersonic Drag Reduction Technology in the Scaled Supersonic Experimental Airplane Project by JAXA, Progress in Aerospace Sciences, Vol.45, 2009, pp Yoshida, K., Sugiura, H., Ueda, Y., Ishikawa, H., Tokugawa, N., Atobe, T., Takagi, S., Arnal, D., Archambaud, J, P., and Seraudie, A., Experimental and Numerical Research on Boundary Layer Transition Analysis at Supersonic Speed: JAXA-ONERA cooperative research project, JAXA-RR E, Sugiura, H., Yoshida, K., Tokugawa, N., Takagi, S., and Nishizawa, A., Transition Measurements on the Natural Laminar Flow Wing at Mach 2, Journal of Aircraft, Vol. 39, No. 6, 2002, pp Yoshida, K., Ishida, Y., Noguchi, M., Ogoshi, H., and Inagaki, K., Experimental and Numerical Analysis of Laminar Flow Control at Mach 1.4, AIAA , Yoshida, K., Kwak, D, Y., Tokugawa, N., and Ishikawa, H., Concluding Report of Flight Test Data Analysis on the Supersonic Experimental Airplane of NEXST Program by JAXA, ICAS , Arnal, D., Boundary Layer Transition Prediction Based on Linear Theory, AGARD Report 793, Rech, J., and Leyman, C., A Case Study By Aerospatiale And Britisch Aerospace On The Concorde, AIAA Professional Study Series, Orlebar, C., The Concorde Story, British Airways, Osprey Publishing, Westminster MD, 2007, pp Joslin, R. D., Aircraft laminar flow control, Annual Review of Fluid Mechanics, Vol.30, 1998, pp

ADVERSE REYNOLDS NUMBER EFFECT ON MAXIMUM LIFT OF TWO DIMENSIONAL AIRFOILS

ICAS 2 CONGRESS ADVERSE REYNOLDS NUMBER EFFECT ON MAXIMUM LIFT OF TWO DIMENSIONAL AIRFOILS Kenji YOSHIDA, Masayoshi NOGUCHI Advanced Technology Aircraft Project Center NATIONAL AEROSPACE LABORATORY 6-