AIAA 42nd Aerospace Sciences Meeting and Exhibit 5-8 January 2004, Reno, Nevada
AIAA-2004-0698
AIRFRAME NOISE MODELING APPROPRIATE FOR MULTIDISCIPLINARY DESIGN AND OPTIMIZATION
Serhat Hosder , Joseph A. Schetz , Bernard Grossman , and William H. Mason Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0203
Abstract
A Trailing Edge Noise Metric has been developed for constructing response surfaces that may be used for optimization problems involving aerodynamic noise from a clean wing. The modeling approach includes a modied version of a theoretical trailing edge noise prediction and utilizes a high delity CFD (RANS) code with a two-equation turbulence model to obtain the characteristic velocity and length scales used in the noise model. The noise metric is not the absolute value of the noise intensity, but an accurate relative noise measure as shown in the validation studies. Parametric studies were performed to investigate the eect of the wing geometry and the lift coecient on the noise metric. 2-D parametric studies were done using two subsonic (NACA0012 and NACA0009) and two supercritical (SC(2)-0710 and SC(2)-0714) airfoils. The EET Wing (a generic conventional transport wing) was used for the 3-D study. With NACA 0012 and NACA 0009 airfoils, a reduction in the trailing edge noise was obtained by decreasing the lift coecient and the thickness ratio, while increasing the chord length to keep the same lift at a constant speed. Supercritical airfoil studies showed that decreasing the thickness ratio may increase the noise at high lift coecients while a reduction may be obtained at low lift coecients. Both 2-D and 3-D studies demonstrated that the trailing edge noise remains almost constant at low lift coecients and gets larger at high lift coecients. The increase in the noise metric can be dramatic when there is signicant ow separation. Three-dimensional eects observed in the EET Wing case indicate the importance of calculating the noise metric with a characteristic velocity and length scale that vary along the span.
Graduate student, Department of Aerospace and Ocean Engineering, Student Member AIAA Fred D. Durham Endowed Chair, Department of Aerospace and Ocean Engineering, Fellow AIAA Professor, Department of Aerospace and Ocean Engineering. Currently Vice President, Education and Outreach, National Institute of Aerospace, Hampton, VA. Fellow AIAA Professor, Department of Aerospace and Ocean Engineering, Associate Fellow AIAA
Nomenclature
a b c ca cf Cd CD Cl CL D H I IN M l0 mac NM N Mupper N Mlower OASP L Remac Rec SP L Sref t/c T KE u0 V 0 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = free-stream speed of sound wing span chord mean geometric chord skin friction coecient section drag coecient overall drag coecient section lift coecient overall lift coecient directivity function distance to the ground or receiver noise intensity noise intensity indicator characteristic length scale for turbulence mean aerodynamic chord noise metric noise metric for wing upper surface noise metric for wing lower surface overall sound pressure level Reynolds number based on mac Reynolds number based on chord sound pressure level wing reference area thickness ratio turbulent kinetic energy characteristic velocity scale for turbulence free-stream velocity angle of attack trailing edge sweep angle turbulence frequency characteristic source frequency azimuthal directivity angle free-stream density polar directivity angle
Introduction
Aircraft noise has become an important performance criterion and constraint in aircraft design in recent years. Although there has been a dramatic reduction in the aircraft noise in the last three decades with the advances in airframe and engine technology, further reduction is still needed to allow civil aviation to grow and to minimize noise pollution. Aircraft
Copyright c 2004 by the authors. Published by the AIAA, Inc., with permission.
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Vertical tail Slats Clean wing
empth
and slats are the dominant airframe noise sources for an airplane at the approach before landing. However, Trailing Edge Noise can be a signicant contributor to the airframe noise for a non-conventional conguration that does not use traditional highlift devices on approach such as a Blended-WingBody (BWB) transport aircraft, which has a large wing area and span, a conventional aircraft or a BWB with distributed propulsion6, 7 that uses the jet-wing concept for high-lift, or an airplane with a morphing wing. A Trailing Edge Noise formulation based on proper physics may also be used to predict the noise originating from the ap trailing-edges and ap-side edges at high lift conditions. Trailing Edge Noise of a clean wing at high lift can be thought as a lower bound value of the airframe noise on approach. In other words, if we can obtain the same lift required at the approach without using the traditional high-lift devices, the noise of the clean wing would be the lowest value that can be achieved for that particular aircraft as long as there is no large region of ow separation on the wing. This value can be used as a measure of merit in noise reduction studies. In this paper, we have focused on airframe noise modeling for a clean wing at approach conditions. Our objective has been to develop a noise metric for constructing response surfaces that may be used in the optimization of a clean wing for minimum noise. We investigate the eect of wing geometry (thickness ratio, t/c, of wing sections, and the chord length c) and the lift coecient on the noise metric by performing parametric studies. Two-dimensional parametric studies were done using subsonic and supercritical airfoils. A generic conventional transport wing was used for the three-dimensional studies. We expect our noise metric to be a reliable indicator of airframe noise, but not necessarily the magnitude of the absolute noise signature. It should also be relatively inexpensive to calculate. However, we still use 3-D, Reynolds-Averaged-Navier-Stokes (RANS) calculations in our approach. Our methodology for obtaining the noise metric on a clean wing includes a modied version of the theoretical trailing edge noise prediction models given in Goldstein8 and Lilley.5, 9 We use a high delity CFD (RANS) code with a twoequation turbulence model to obtain the characteristic velocity and length scales that are used in the new noise metric developed here.
nose Nose landing gear
empth
flaps
Horizontal tail
Main landing gear
Figure 1:
Airframe noise sources (from Crighton4 )
noise regulations curtails the growth of air transportation. These regulations limit the hours and the number of operations at most airports and impede aviation infrastructure improvements such as airport expansion and construction plans.1 There has been almost a 100% increase in the number of noise related restrictions in the last decade.2 The goal of 10 dB noise reduction in 10 years was set by NASA3 in 1997 to tackle the aircraft noise problem and its negative impact on the future of civil aviation. To achieve this challenging noise reduction goal, research eorts have been focused on: (1) the design of revolutionary aircraft with innovative congurations and technologies to give the minimum noise signature (2) the improvement of conventional aircraft noise performance, and (3) optimizing the ight performance parameters or operational conditions for minimum noise. All these eorts clearly require addressing noise in the aircraft conceptual design phase. Engine noise, engine/airframe interference noise, and airframe noise are the main components of aircraft noise. The noise radiating from each component covers a dierent fraction of the total noise at dierent ight regimes. At take o, the dominant noise source is the engine. However, the use of high-bypass ratio turbofan engines and other achievements in engine technology make the airframe noise level comparable to the engine noise at approach conditions. To include aircraft noise as a constraint or an objective function in a Multidisciplinary Design and Optimization (MDO) framework, each noise component should be modeled. These models are required to predict the aircraft noise originating from dierent sources in different ight regimes. Airframe noise is dened as the non-propulsive noise of an aircraft in ight.4 Airframe noise sources on a conventional transport are the landing gear, trailing edge aps, leading edge slats, the clean wing, and tail surfaces5 (Figure 1). A clean wing has all its high-lift devices and the undercarriage in stowed position. The main noise mechanism of a clean wing is the Trailing Edge (TE) Noise. The landing gear, aps
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Clean Wing Noise Modeling
The noise originating from the interaction of the turbulent ow with a sharp-edged body such as the trailing edge of a wing or a ap has been one of the main research areas of aeroacoustics for many years. Howe10 gives a review of various trailing edge noise theories and lists them in dierent categories. Most of the theories used in predicting the trailing edge noise are based on Lighthills Acoustic Analogy.11 FfowcsWilliams and Hall12 were the rst to solve the problem of noise radiated from the turbulent ow past a semi-innite plate of zero thickness at zero angle of attack using this analogy. The trailing edge noise originates from scattering of the acoustic waves generated due to the passage of the turbulent boundary layers over the trailing edge of wings or aps.5 All theories on trailing edge noise show that the noise intensity varies approximately with the 5th power of the free-stream velocity.4, 10 It is also proportional to the trailing-edge length along the span and a characteristic length scale for turbulence. Most of the trailing edge noise prediction methods13, 14 used today are based on semi-empirical methods. In these methods, characteristic length and velocity scales are usually determined from curve ts obtained from experiments or ight measurements. In recent years, Computational Aeroacoustics (CAA) methods15 have been used to simulate acoustic scattering from trailing edges. These methods couple time-accurate ow eld data obtained from RANS or Large Eddy Simulation solutions with acoustic equations to propagate the noise to the far-eld. They can give accurate results, however they are restricted to simple problems due to the computational expense stemming from the very ne time and space resolution requirements. For our problem, considering the geometry of interest and the number of runs to be performed for creating response surfaces, it is impractical to use Computational Aeroacoustics . However, we still perform 3-D, steady-state (non-timeaccurate), RANS simulations to calculate the characteristic velocity and length scales. Derivation of the Noise Metric Following the approach by Goldstein8 and Lilley,5, 9 one can approximate the far-eld noise intensity per unit volume of acoustic sources at the trailing edge of a wing surface as I D(, ) 0 u4 Cos3 , 0 3 a2 2 H2 (1)
V
noise source wing TE y H z x
receiver
Directivity angles used in the noise metric (note that the trailing edge sweep angle () is 0 in this gure)
8
Figure 2:
frequency, u0 is the characteristic velocity scale for turbulence, H is the distance to the ground (receiver) and is the trailing edge sweep angle. Lilley5 gives a simplied version of Equation 1 for the yover case with a polar directivity angle () of 90 which makes the directivity term D(, ) equal to unity. He also neglects the Cos3 term given by Howe10 since the contribution of this term is small for most conventional wings. However, this term also shows that the radiated noise from scattering may be reduced to a smaller value for wings with highly swept trailing edges. We write Equation 1 for any wing conguration and receiver position. We do not include the Doppler factors due to convection of acoustic sources, since we focus on low Mach numbers which are between 0.2 and 0.3 for typical aircraft at approach before landing. The directivity term is in the form given by Ffowcs-Williams and Hall:12 D(, ) = 2Sin2 ( )Sin. 2 (2)
Here, is the polar directivity angle and is the azimuthal directivity angle. (Figure 2). Using the Strouhal relation for turbulent ow,5 w0 l0 const. u0 (3)
one can re-write Equation 1 with the characteristic length scale for turbulence l0 : I D(, ) . u5 l1 Cos3 2 3 a2 0 0 H2 (4)
where is the free-stream density, a is the freestream speed of sound, 0 is the characteristic source
Since we would like to design a wing for minimum noise, we consider the spanwise variation of the characteristic velocity, characteristic length scale, the trailing edge sweep, the directivity angles, and the distance to the receiver point (i.e., u0 = u0 (y),
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l0 = l0 (y), = (y), = (y), = (y), and H = H(y)). We have seen the importance of retaining the spanwise variation of the characteristic velocity and length scale in our three-dimensional parametric study, since the change in these variables was signicant along the span at higher lift coecients. Assuming a correlation volume per unit span at the trailing edge as 2 dV = l0 dy, (5) Equation 4 can be written for the correlation volume given above and integrated over the span b to obtain IN M = 2 3 a2
b
other suggestions in the literature like the boundary layer thickness or the displacement thickness. These lengths are related to the mean ow and do not reect anything about the turbulence structure. We obtain T KE and from the solutions of the T KE- (k-) turbulence model equations used in the Navier-Stokes calculations.
CFD Simulations
The CFD code GASP16 has been used for physical modeling of all validation and parametric noise metric cases presented in this paper. GASP is a threedimensional, structured, multi-block, nite volume, Reynolds-Averaged Navier-Stokes (RANS) code. In the CFD simulations, inviscid uxes were calculated by an upwind-biased third-order spatially accurate Roe ux scheme. Asymptotic convergence to a steady state solution was obtained for each case. The iterative convergence of each solution was examined by monitoring the overall residual, which is the sum (over all the cells in the computational domain) of the L2 norm of all the governing equations solved in each cell. In addition to this overall residual information, some of the output quantities such as the lift coecient and the T KE distributions were also monitored. Each case was run at three grid levels: coarse, medium, and ne. Medium and coarse grid levels were obtained from the ne grid by reducing the number of grid points by a factor of two at each direction. At each grid level, except the coarsest one, the initial solution estimates were obtained by interpolating the primitive variable values of the previous grid solution to the new cell locations. This method, known as grid sequencing, was used to reduce the number of iterations required to converge to a steady state solution at ner mesh levels. All the results presented in this paper were obtained with the nest mesh level. Coarse, medium, and ne grid levels were used to check the grid convergence. In the CFD simulations, we solved full Navier-Stokes equations by including all the viscous terms in the physical model. All the runs were made with the assumption of fullyturbulent ow. Menters k- SST turbulence model17 was used in all the calculations. This model has been shown18 to give better overall accuracy in dierent types of ows compared to the other two-equation turbulence models.
u5 l0 Cos3 0
0
D(, ) dy, H2
(6)
where IN M is the noise intensity indicator which can be evaluated on the upper or the lower surface of the wing. Note that IN M is not the absolute value of noise intensity, however we expect it to be an accurate indicator as a relative noise measure. We scale IN M with the reference noise intensity of 1012 W/m2 (the minimum sound intensity level that human ear can detect) which is a common practice in acoustics. Finally, we write the Noise Metric (N M ) for the trailing edge noise (in dB) as: N M = 120 + 10log (IN M ) . (7)
To obtain the total noise metric for a wing, we calculate the noise metric values for the upper (N Mupper ) and the lower surfaces (N Mlower ), and add them as N M = 10log 10
Modeling of u0 and l0
N Mupper 10
+ 10
N Mlower 10
.
(8)
In the noise metric, the characteristic turbulent velocity at a spanwise location of the wing trailing edge can be chosen as the maximum value of the turbulent kinetic energy (T KE) prole at that particular spanwise station: u0 (y) = M ax T KE(z) . (9)
Here, z is the direction normal to the wing surface. We model the characteristic turbulence length scale for each spanwise station as: M ax l0 (y) = T KE(z) . (10)
In Equation 10, is the turbulence frequency (dissipation rate per unit kinetic energy) observed at the maximum T KE location. We view this choice of a turbulence length scale as more soundly based than
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2-D TBL-TE Noise Metric Validation
1.40 1.20 1.00 0.80 0.60 0.40 0.20
NMsi OASPLsi
A similar scaling was done for the OASPL values: OASP Lsi = 10[0.1(OASP Li OASP L1 )] (12)
Case
0.00 1 2 3 4 5 6 7
(deg) Recx10-6
0.0 1.497
0.0 0.665
2.0 0.499
1.5 0.831
0.0 1.164
2.0 1.122
1.5 1.497
Figure 3 shows the comparison of N Msi and OASP Lsi at each case. As can be seen from this gure, the agreement between the experiment and our predictions are very good at various speeds and angles of attack. This gure also demonstrates that the noise metric is capable of capturing the variations in the trailing edge noise as a relative noise measure when dierent ow conditions and parameters are changed.
Figure 3:
The comparison of scaled predicted noise metric value (N Msi ) to the scaled experimental OASPL14 (OASP Lsi ) at each NACA 0012 validation case
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Parametric Noise Metric Studies
Parametric studies to investigate the eect of the wing geometry and the lift coecient on the noise metric were performed. Two-dimensional parametric studies were done using two subsonic (NACA 0012 and NACA 0009) and two supercritical (SC(2)0710 and SC(2)-0714) airfoils. A generic conventional transport wing was used for the three-dimensional study. The inuence of the ight speed on the trailing edge noise is well-known, since the noise is proportional to the 5th power of the velocity as shown by all the aeroacoustic theories on this subject. We include this eect in our noise metric since the characteristic velocity u0 will change in proportion to the free-stream velocity in most cases. In addition to the speed, one also would like to know the eect of the other variables such as the lift coecient and the wing geometry on the trailing edge noise. The information obtained from the parametric studies will be useful in our MDO studies, since it will help to select the appropriate design parameters in the optimization process. The main results obtained from these cases are presented and discussed in the following two sections. Two-Dimensional Studies
NACA 0009 and NACA 0012 airfoils
Noise Metric Validation
Noise metric validation was performed with seven test cases shown in Figure 3. These cases were selected from a two-dimensional NACA 0012 experimental database. To create this database, Brooks et al.14 conducted experiments at dierent speeds, angles of attack, and chord lengths using NACA 0012 airfoils and measured the 1/3-octave Sound Pressure Level (SPL) spectra of the noise generated by the airfoils. They also used this database to develop a semiempirical airfoil self-noise prediction method. The SPL spectrum of each case was measured at a point 1.22 m away from the mid-span trailing edge. Both directivity angles and were 90 at this location. The main noise mechanism of all the cases used in the validation study is the trailing edge noise generated by the scattering of turbulent pressure uctuations over the trailing edge. These cases were chosen to cover a wide range of speeds (71.3, 55.5, 39.6, and 31.7 m/s) at dierent angles of attack. The difference between the Reynolds number of each case shown in Figure 3 is due to the change in speed. All the other ow conditions were kept constant and the chord length of the airfoil was the same (0.3048 m). CFD simulations were performed for each noise metric validation case. The noise metric of each case, N Mi , was calculated using the characteristic velocity and the length scales obtained from the CFD simulations in Equation 8 with Equations 9 and 10. For the same cases, the Overall Sound Pressure Levels (OASP Li ) were calculated from the experimental data. The noise metric for each case was scaled with the value obtained for Case 1: N Msi = 10[0.1(N Mi N M1 )] (11)
The main purpose of the study with NACA 0012 and NACA 0009 airfoils was to investigate the noise reduction by changing the lift coecient and the thickness ratio. To study this objective, the lift coefcient was reduced while increasing the chord length to have the same lift at a constant speed. Further reduction was sought by decreasing the thickness ratio. This 2-D study can be thought of as a simplied representation of increasing the wing area and reducing the overall lift coecient of an aircraft at constant
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TBL-TE Noise reduction with Cl and (t/c) change at the same lift (NACA 0012 & NACA 0009, Low Rec )
65.00 64.00
0.08
z/c
NACA 0012, c=0.3048 m, Cl=1.046, lift=1010 N
0.04 0.00
SC(2)-0714 SC(2)-0710
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1
NM (dB)
63.00 62.00 61.00 60.00 59.00 58.00
NACA 0012, c=0.3741 m, Cl=0.853, lift=1011 N
-0.04 -0.08 0.0
2
NACA 0009, c=0.3741 m, 3 Cl=0.860, lift=1018 N
0.80
2.453 dB 1.164 dB
x/c
Figure 5:
1.10
SC(2)-0710 and SC(2)-0714 airfoils
noise sources on approach. 5 If sucient lift can be obtained with an increased wing area without using 1 3: Total Noise reduction=3.617 dB history obtained with high-lift devices, a signicant reduction in noise may Figure 4: Noise metric reduction 1 2:NACA reduction by decreasing the Cfor various lift bereduction) However all these changes should be Noise 0012 and NACA 0009 airfoils l (68% of the total achieved. 2 3:coecients at constant lift Noise reduction by decreasing (t/c) (32% of the total performed in an MDO framework to for account the reduction) To keep the lift constant, chord length is increased by 23% at the lower Cl other aircraft design requirements.
0.70
Cl
0.90
1.00
For chord=0.3048 m, Rec=1.497x106 & for chord=0.3741 m, Rec=1.837x106 lift and speed. As part of this study, three conguSC(2)-0710 and SC(2)-0714 airfoils
rations were considered: (1) NACA 0012 airfoil with 1 a chord length of 0.3048 m, (2) NACA 0012 airfoil with a chord length of 0.3741 m, and (3) NACA 0009 airfoil with a chord length of 0.3741 m. All cases were run with a free-stream velocity (V ) of 71.3 m/s and a Mach number of 0.2. The Reynolds number based on the chord (Rec ) was 1.497 106 for Case 1 and 1.837 106 for the other two cases. CFD simulations were performed for each case. Computational grids had C-topologies, each having 388 cell centers in the streamwise direction and 64 points in the normal direction to the airfoil surface. The noise metric was calculated at a distance (H) 1.22 m away from the trailing edge with the directivity angles = 90 and = 90 (the same values used in the validation studies). Note that these values are arbitrary since we are interested in the relative change of the noise metric and we assume that the receiver is at the same location for all the cases. Figure 4 shows the noise reduction history of this study. We started from Case 1 with the NACA 0012 airfoil at a lift coecient (Cl ) of 1.046. Cl was reduced to 0.853 at Case 2 while increasing the chord length by 23% to keep the lift at a constant value of approximately 1010 Newtons. A noise reduction of 2.45 dB was achieved between Case 1 and Case 2. When the thickness of the airfoil was decreased by 25% (NACA 0009) while keeping the same chord length and the lift, we got an additional reduction of 1.16 dB in the noise metric. Total noise reduction was 3.61 dB . Decreasing the lift coecient contributed 68% of the total noise reduction. This simple example showed that it is possible to reduce the trailing-edge noise by increasing the chord length (wing area) and decreasing the lift coecient and the thickness ratio. Another benet from this approach can come from eliminating the need to use high-lift devices which are the dominant airframe
In addition to the NACA four digit airfoil cases, two-dimensional parametric studies were performed with supercritical airfoils at realistic ight conditions to study the eect of the lift coecient and the thickness ratio on the noise metric. We used two supercritical airfoils, SC(2)-0710 and SC(2)-0714 (Figure 5). These airfoils belong to the same family, but have different thickness ratios19 (t/c = 10% for SC(2)-0710 and t/c = 14% for SC(2)-0714). CFD simulations were performed at Rec = 44 106 with V = 68 m/s and M ach = 0.2. These values approximately correspond to the conditions of a typical transport aircraft having a mean aerodynamic chord (mac) of 9.54 m at an altitude of 120 m before landing. At this location, the aircraft is approximately above the point where the noise certication measurements at approach (2000 m away from touchdown point on the runway) are taken.5 Airfoil grids used in the CFD calculations had 388 64 cells. The noise metric values were calculated for H = 120 m, = 90 , and = 90 . Figure 6 shows the section lift coe2.4 2.0 1.6
SC(2)-0714 SC(2)-0710
Cl
1.2 0.8 0.4 0.0 0.0 2.0 4.0 6.0 8.0
10.0
12.0
14.0
16.0
18.0
Figure 6:
Section lift coecient (Cl ) vs. angle of attack () for SC(2)-0710 and SC(2)-0714 airfoils
cients obtained at dierent angles of attack for the two airfoils. For each airfoil, the angle of attack was
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2.4 2.0 1.6
50.0
SC(2)-0714
40.0
(TKE)max
TKE (J/kg)
Cl
1.2 0.8 0.4 0.0 0.00 0.01 0.02
SC(2)-0710
30.0 20.0 10.0 0.0
(TKE)max
Cl=1.853
Cl=0.550
zz
0.03
Cd
0.04
0.05
0.06
0.0
0.1
0.2
0.3
0.4
0.5
zn (m)
TBL-TE Noise Metric at different Cl (SC(2)-0710 Figure 7: Drag Polars for SC(2)-0710 and SC(2)-0714 Figure 9: Turbulent Kinetic Energy (T KE) proles at airfoils & SC(2)-0714 airfoils, high Rec ) the upper surface trailing edge of SC(2)-0714 airfoil
50.0 45.0
for Cl = 0.550 and Cl = 1.853. zn is the normal distance from the airfoil surface
zz
4.0E-02
6
NM (dB)
40.0 35.0
SC(2)-0710
4
3.5E-02 3.0E-02
l0 (m)
2.5E-02 2.0E-02 1.5E-02 1.0E-02
30.0 25.0 20.0 0.3 0.5 0.7 0.9 1.1 1.3 1.5
SC(2)-0714
l0 at (TKE)max Cl=0.550 l0 at (TKE)max
0.0 0.1 0.2
Cl=1.853
zz
1.7
1.9
2.1
2.3
5.0E-03 0.0E+00
Cl
Figure 8: Noise metric values Flyover conditions for a typical transport obtained with SC(2)0710 and SC(2)-0714 airfoils at dierent section lift Chord=9.54 m, Rec=44x106, Mach=0.2 Figure 10: Characteristic length scale (l0 ) proles at coecients NM value scaled with the suction side NM obtained at Cl=0.507 with SC(2)-0710 surface trailing edge of SC(2)-0714 airfoil the upper for C Large increase in noise metric at high lift coefficients where flow is close to l = 0.550 and Cl = 1.853 separation increased noise the highest lift coecient before stall. For Cl>1.35, theto getmetric for SC(2)-0710 larger than SC(2)-0714 2 As can be seen from this gure, SC(2)-0710, the airfoil with the smaller thickness ratio has a lower maximum Cl value compared to the SC(2)-0714 airfoil. The drag polars for each airfoil are shown in Figure 7. For lift coecients greater than 0.8, the drag of the SC(2)-0710 airfoil is larger at the same lift. Looking at the noise metric values (Figure 8), we see that the noise of each airfoil stays approximately constant up to a certain lift coecient value. At this range of lower Cl , the thicker airfoil has higher noise metric values. The dierence is approximately 2 dB at Cl = 0.7. A dramatic increase in the noise metric value can be observed for each airfoil at higher lift coecients. The large increase in the noise metric at high lift coecients originates from the increase of both the maximum T KE and the characteristic length scale l0 . Figure 9 shows the T KE proles at the upper surface trailing edge of the SC(2)-0714 airfoil at two Cl values. The signicant dierence between the maximum T KE values can be seen. A similar observation can be made for the length scale (Figure 10). At high lift coecients, the adverse pressure gradient close to the upper surface trailing edge increases the thickness of the turbulent boundary layer and the magnitude of the turbulent uctu-
zn (m)
0.3
0.4
0.5
ations. These values become larger as the ow gets 7 closer to separation. Figure 8 shows another important eect of the thickness ratio on the noise metric. The noise from the SC(2)-0710 airfoil is larger than the noise of the thicker airfoil at Cl > 1.35. This implies that reducing the thickness ratio may in fact increase the noise at higher lift coecients. Three-Dimensional Study The objective of the three-dimensional study was to examine the eect of the overall lift coecient CL on the clean wing airframe noise by using a realistic wing geometry at realistic conditions. This study also permitted investigation of the spanwise variation of the characteristic velocity and length scale as the lift coecient was changed. The geometry used in this study is the EnergyEcient Transport (EET) Wing.20 This is a generic conventional transport aircraft wing (Figure 11) used in many experimental studies at NASA. For our study, we scaled the original dimensions of the experimental model so that the mean aerodynamic chord is 9.54 m. The scaled wing has a reference area (Sref )
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1.20 1.05 0.90 0.75
343 300
0.60 0.45 0.30 0.15 0.00 0.0 2.0 4.0 6.0
86 43 0
8.0 10.0 12.0 14.0 16.0
Z X
Y
Figure 13:
Overall lift coecient (CL ) and Wing Loading (W/S) vs. angle of attack () for the EET Wing
1.20 1.05 0.90
Z
Figure 11:
A view of the EET Wing and the C grid around the root section
0.75
CL
X Y
0.60 0.45 0.30 0.15 0.00 0.00 0.02 0.04 0.06
9
CD
0.08
0.10
0.12
0.14
Figure 14:
Drag Polar for the EET Wing
Figure 12:
A view of the EET Wing tip region
of 511 m2 (based on the wing planform including the leading-edge and trailing-edge extensions of the inboard section) and a span of 64.4 m. It has an aspect ratio of 8.16, a dihedral angle of 5 , and a sweep angle of 30 at the quarter chord. The outboard section of the wing starts at 2y/b = 0.375. Wing sections are supercritical airfoils with t/c = 14% at the root, t/c = 12% at the break point, and t/c = 10% at the tip. The computational grid used in the CFD simulations has a C-O topology consisting of four blocks with a total number of 884,736 cells (Figures 11 and 12). For the CFD simulations and the noise metric calculations, the same ow parameters given in the previous section were used. These correspond to the approach conditions of a typical transport aircraft (Remac = 44 106 , V = 68 m/s, and M ach = 0.2). We evaluate the noise metric at an altitude of 120 m, for an observer at the ground level directly below the aircraft which corresponds to = 90 at y = 0 plane (see Figure 2). The azimuthal angle is calculated at each spanwise station, however the eect of the change in along the span is negligible.
EET Wing calculations were performed at eight dierent angles of attack ranging from 0 to 14 with increments of 2 . Figure 13 10 shows the lift coecients and corresponding wing loading (W/S) values obtained at each angle of attack. The CL vs. curve is linear up to 12 where CL = 1.084. At the last angle of attack, one can see the break of the linear pattern which indicates stall. This can also be seen from the drag polar given in Figure 14. The sharp increase in drag at the last angle of attack, where CL = 1.106, is due to a large ow separation on the wing. With this wing conguration, the highest wing loading value that could be achieved was 315.7 kg/m2 (64.8 lb/f t2 ). On the other hand, for a B-777 like transport aircraft, we nd that W/S is approximately 432 kg/m2 (88.8 lb/f t2 ) when using the maximum design landing weight of such an aircraft and Sref of our wing. Although one can reach relatively high lift coecients with a clean wing by increasing the angle of attack without having substantial separation, it is clear that it would be almost impossible to achieve the lift required to sustain a conventional aircraft at the approach without using high-lift devices. This again shows the importance of having a large wing area to reduce the wing loading at a constant speed, if one wants to design a clean wing at approach conditions that will y with a low
8
American Institute of Aeronautics and Astronautics
W/S (kg/m2)
257 214 171 128
CL
1.6 1.4 1.2 1.0
Inboard
1.106 1.084 0.970 0.836 0.689 0.534 0.375 CL= 0.219
Outboard
CL=1.106
=14
Cl
0.8 0.6 0.4 0.2 0.0 0.0 0.2
0.4
2y/b
0.6
0.8
1.0
CL=0.970
=10
Figure 15:
EET Wing
2.0 1.8 1.6
Section lift coecient distributions for the
Inboard
1.106 1.084 0.970 0.836 0.689 0.534
Outboard
12
CL=0.689
Cl c/ca
1.4 1.2 1.0 0.8 0.6
=6
0.375 0.4 0.2 CL= 0.219 0.0 0.0 0.2
Cf 0.0094 0.0086 Cf 0.0078 0.0094 0.0070 0.0086 0.0062 0.0078 0.0070 0.0054 0.0062 0.0046 0.0054 0.0038 0.0046 0.0030 0.0038 0.0030 0.0023 0.0023 0.0015 0.0015 0.0007 0.0007 -0.0001 -0.0001 -0.0009 -0.0009 -0.0017 -0.0017
0.4 2y/b
0.6
0.8
1.0
CL=0.375
Figure 16:
Spanload distributions for the EET Wing
=2
lift coecient to give the minimum noise signature. The section lift coecient (Cl ) and the spanload 13 distributions are given in Figures 15 and 16. The spanload and the Cl exhibit smooth variations along the half-span for all CL except the highest value. At this lift coecient, a large loss in lift on the outboard section of the wing starting from 2y/b 0.6 can be seen. The large separation on the outboard section of the wing at CL = 1.106 is visible in Figure 17 which shows the skin-friction (cf ) contours of wing upper surface at four lift coecients. For CL = 0.375 and 0.689, the skin-friction lines show a smooth pattern along the span except the small kink at the break point. At CL = 0.970 which corresponds to = 10 , a large separation is not observed, but small separated ow regions close to the trailing edge along the span, which can increase the T KE and length scale l0 , can be seen. In fact, looking at the maximum TKE (Figure 18) and the l0 (Figure 19) distributions along the span, we see this increase starting at CL = 0.836 especially on the outboard section of the wing where the section lift coecients are higher. At the highest lift coecient, a large increase in the maximum T KE and l0 at the trailing edge of the outboard section where there is massive separation is observed. The change in T KE and l0 is small along the span at
0
0.20
0.40
2 y/b
0.60
0.80
1.00
Figure 17:
Skin friction contours of the EET Wing upper surface at dierent CL values
lower lift coecients (CL < 0.836), except for the tip region where we see the eect of the tip vortex and an increase in T KE (Figure 20). The tip vortex region is small at moderate angles of attack and does not have a signicant eect on the overall noise metric. At higher lift coecient values (CL > 0.836), the maximum T KE and l0 are not uniform along the span, and they get larger at outboard sections due to three-dimensional eects. This shows the importance of calculating the noise metric, especially at high lift coecients, with a characteristic velocity and length scale that vary along the span. The noise metric results for the EET Wing are given in Figure 21. At lower lift coec...