fundamental design optimization of an innovative

Fundamental Design Optimization of an Innovative Supersonic TransportConfiguration and Its Design Knowledge Extraction*

Naohiko BAN,1)† Wataru YAMAZAKI,1) and Kazuhiro KUSUNOSE2)

1)Department of Mechanical Engineering, Nagaoka University of Technology, Nagaoka, Niigata 940–2188, Japan2)Japan Aerospace Exploration Agency, Chofu, Tokyo 182–8522, Japan

The generation of shock waves is inevitable during supersonic cruising, which results in the generation of wave dragas well as sonic boom on the ground. Some innovative concepts, such as the supersonic biplane concept and supersonictwin-body fuselage concept, have been proposed recently to reduce the supersonic wave drag dramatically. In this study,these two concepts are adopted, and then the aerodynamic and sonic boom performance of innovative supersonic transport(SST) wing-body configurations are discussed using numerical approaches. This study is performed to obtain designknowledge for the innovative SST using an optimization method. In this research, the number of design variables is limitedto only three in order to obtain fundamental design knowledge of the innovative SST configuration. The three design var-iables are utilized to deform the wing section shape. The wing section shape of a Busemann-type-biplane/twin-body mod-el is optimized under the conditions of a design Mach number of 1.7 and angle of attack of 2 degrees. The optimized resultsshow the tradeoff relationship between lift-drag ratio and maximum overpressure of sonic boom distribution on theground. To obtain detailed knowledge of the design space, analysis of variance and visualizations of response surfacesof objective functions are also performed.

Key Words: SST, Sonic Boom, Multi-Disciplinary Optimization, Biplane Wing, Twin-Body Fuselage

1. Introduction

The Concorde supersonic transport had an advantage in itscruising speed, which overwhelmed other conventionaltransports. However, the Concorde ended operations, beingdecommissioned in 2003, mainly due to the problems of eco-nomic efficiency and environmental burden. Recently, thereare many attempts to realize a next-generation supersonictransport. One of them is to reduce strong shock waves byinterfering with them. The reduction of shock waves willcontribute to reducing wave drag and sonic boom, whichwould be beneficial for a low-boom/low-drag SST. In thisresearch, a supersonic biplane concept and a supersonictwin-body concept are adopted to reduce supersonic wavedrag.1.1. Supersonic biplane concept

In this concept, the strength of the wave drag is success-fully reduced by interfering with the shock waves betweenthe biplanes.1–4) According to Kusunose et al.,1) the wavedrag at zero lift of the biplane airfoil is reduced by nearly90% compared to an equal volume diamond-wedge airfoilin two-dimensional inviscid simulations. By simply splittingthe diamond airfoil into two elements and positioning themoppositely, the Busemann biplane airfoil is composed. Atlifted conditions, the above-mentioned concept can be ex-panded. This expanded concept is called Licher’s supersonicbiplane concept. The Licher biplane,5) whose thickness-chord ratio of the lower element is bigger than the ratio of

the upper element, provides better performance than the Bu-semann biplane at lifted conditions.1.2. Supersonic twin-body concept

A twin-body fuselage concept6) has also been proposed bythe present authors to reduce the wave drag due to the fuse-lage volume of an aircraft. The same kind of twin-fuselageconcept has been investigated previously by Wood et al.,7)

in which fundamental wind tunnel experiments were per-formed at a Mach number of 2.7. According to Jones8) andKroo,9) the supersonic wave drag due to the volume of a fu-selage body is expressed as follows:

Dwave ¼ qkV2

l4ð1Þ

where q and k are respectively the dynamic pressure and aconstant. The wave drag due to the volume is proportionalto the square of its volume V, while it is inversely propor-tional to the fourth power of the length of the aircraft l. (Note:This equation does not consider interference drag betweenbodies.) Since the wave drag of the airplane’s fuselage is pro-portional to the square of its volume when the body length isfixed, if we split a large single-body fuselage into two indi-vidual small bodies, the wave drag of each split body willbe reduced to quarter of that of the original. The total dragof the twin-body configuration, thus, becomes one-half ofthe original single-body fuselage under the constant-volumeand constant-length conditions. According to Yamazaki andKusunose,6) over 20% total drag reduction was achieved inan optimized twin-body fuselage when compared to theSears-Haack (S.H.) single-body fuselage under the constraintof fixed fuselage volume. This has been achieved by reduc-ing the interference drag between the bodies. The S.H. body

© 2016 The Japan Society for Aeronautical and Space Sciences+Received 19 August 2015; final revision received 16 June 2016;accepted for publication 20 July 2016.†Corresponding author, [email protected]

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is well-known as the supersonic single-body configurationthat has the lowest wave drag for specified volume andlength.10)

1.3. Objectives of this researchThe fusion of the two advanced concepts yields an innova-

tive SST configuration, which is a biplane wing/twin-bodyfuselage configuration. It has been proven that the innovativewing-body SST configuration is aerodynamically effectivefor reducing wave drag of a large-sized, twin-body (aboutfor 400 passengers) fuselage.11) However, the L=D of the400-passenger model is less than 5, while that of the Con-corde is known to be as about 7–8 (at a freestream Machnumber of 2.0). One of the major reasons is its larger fuse-lage volume than that of the Concorde.12) In this study, there-fore, the biplane wing/twin-body fuselage configuration(Fig. 1) is designed with its half-sized body, and its aerody-namic/sonic boom performance is investigated. Currently,we are considering that the total weight of the SST (includingits engines and tail wings) will be 350–400 tons, its lift co-efficient 0.15–0.20 and its center-of-gravity 0–25% meanaerodynamic chord.

We conducted biplane wing section shape optimization toobtain design knowledge for the innovative SST configura-tion. The shape optimization is performed using three geo-metric design variables. Practical optimization results are ob-tained in this relatively simple optimization problem. Inaddition, the three-dimensional design variables space is vi-sualized to obtain detailed design knowledge.

2. Computational Methodologies

In this section, the computational methodologies utilizedare concisely introduced.2.1. CFD approach

Three-dimensional supersonic inviscid flows are analyzedusing an unstructured mesh CFD solver of TAS (TohokuUniversity Aerodynamic Simulation)-code.13,14) Compressi-ble Euler equations are solved using a finite-volume cell-ver-tex scheme. The numerical flux normal to the control volumeboundary is computed using the approximate Riemann solv-er of Harten-Lax-van Leer-Einfelds-Wada (HLLEW).15) Thesecond-order spatial accuracy is achieved using the Unstruc-tured MUSCL (U-MUSCL) approach14,16) with Venkatak-rishnan’s limiter.17) The LU-SGS implicit method for un-structured meshes18) is used for time integration. Three-dimensional unstructured meshes are generated using theTAS-mesh package, which includes surface mesh generationapplying an advancing front approach19,20) and tetrahedral

volume mesh generation using the Delaunay approach.21)

The high accuracy of this unstructured mesh CFD approachhas already been confirmed in other literature.14,22)

2.2. Sonic boom analysisThe sonic booms on the ground are predicted using the

nonlinear acoustic propagation solver of Xnoise,23,24) whichwas developed by the Japan Aerospace Exploration Agency(JAXA). An augmented Burgers equation is numericallysolved using an operator splitting method that takes into ac-count the effects of nonlinearity, geometrical spreading, theinhomogeneity of the atmosphere, thermo-viscous attenua-tion and molecular vibration relaxation. In this approach, ini-tial (input) pressure distributions are extracted from CFD so-lutions on the lower side of the SST configurations(Fig. 2(a)). Then the propagation of the pressure distribution(Fig. 2(b)) to the ground (Fig. 2(c)) is solved using the aug-mented Burgers equation. We investigated the influence ofthe extracted position of the initial pressure distribution,which indicated that the extraction at two fuselage lengthsbelow was sufficient for accurate sonic boom evaluationsin this study.2.3. Skin friction drag estimation

The skin friction drags of various SST configurationsare estimated by introducing simple algebraic skin frictionmodels. Assuming that the boundary layer along the bodyis fully turbulent, the skin friction drag coefficient can beestimated as:

CDf ¼ CfSwet

Srefð2Þ

where Cf is the averaged turbulent skin friction coefficienton the wetted area of the body, and Swet and Sref are respec-tively the wetted area of the body and reference area. Theskin friction coefficient for turbulent boundary layer condi-tions can be calculated using the following Prandtl-Schlicht-ing flat-plate skin friction formula25–27):

Cf ¼ 0:455

ðlog10 ReÞ2:58ð1þ 0:144M21Þ0:65 ð3Þ

where Re andM1 are respectively the Reynolds number andfreestream Mach number. The Reynolds number is given ap-plying the cruise conditions of the Concorde (total length of

Fig. 1. Design specifications of twin-body/biplane wing supersonic trans-port model.

(a) Extraction of pressure signaturefor sonic boom analysis

(b) Pressure signature (extraction line)

(c) Pressure signature (ground)

Fig. 2. Sonic boom analysis.

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62m). Since the speed of sound (a1) and kinematic viscosity(�1) at the altitude of 18,000m are respectively 295.069m/sand 1:1686� 10�4 m2/s according to Handbook of Aero-space Engineering,27) the Reynolds number for the fuselagebody is calculated as:

Re ¼ M1a1l

�1¼� 266� 106 ð4Þ

The Reynolds number for the main wing is calculated in thesame manner with its mean chord length (i.e., Re of32:5� 106, mean chord length of 0.122 l). The skin frictiondrag coefficients of the fuselage and wing are separately es-timated with the corresponding Reynolds numbers usingEqs. (2) and (3). In Kusunose et al.,1,2) and Hu,28) predictedfriction drags based on the algebraic skin friction models arecompared with those based on viscous CFD computations. Ithas been concluded that the simple algebraic skin frictionmodels are reasonably accurate for the prediction of frictiondrag in supersonic flows.

3. Validation Study

The validity of the present computational approaches isconcisely discussed in this section. The sonic booms gener-ated from the N-wave model (NWM) and low-boom model(LBM) atM1 of 1.58–1.59 are discussed. These are test caseconditions for the D-SEND#1 project of JAXA.29,30) In itsexperiments, the sonic boom distributions were measuredat about 3,500m away from the models. In this validationstudy, the CFD analyses are performed at the same free-stream Mach number to extract the initial pressure distribu-tions as shown in Fig. 3(a). Then the sonic boom propaga-tions are solved to compare with the experimental sonicboom distributions, whose results are shown in Fig. 3(b).The fluctuations of the experimental data in the range of0.03< time <0.05 s are considered to be the effect of atmo-spheric turbulences. Qualitative agreement with the experi-mental data can be confirmed for both NWM and LBMcases, which indicates the validity of the present CFD/sonicboom analysis approaches. The validity of the present CFDanalysis method in supersonic flow was also confirmed byUmeda et al.,22) through comparing the experimental dataof NEXST-1.

4. Basic Shape Definition

In this section, the basic shape of the twin-body/biplanewing configuration is defined.4.1. Definition of wing shape

The section airfoil thickness ratios of the Busemann bi-plane are set to 5% of the chord length for both the upperand lower wings. For the Licher biplane,5) the sum of thethickness ratios of the upper and lower elements is set to10% of the chord length, so the sectional airfoil areas ofthe two biplane models are the same. The thickness ratioof the lower element is about 43.9% larger than the upper el-ement for the Licher biplane model. Unswept tapered biplane

wing configurations are designed for a three-dimensional bi-plane wing in this research. The aspect and taper ratios arerespectively set to approximately 7 and 0.25. The chordlength of the main wing at the root section is approximatelyl/6. Since the effectiveness of the wingtip plate in the Buse-mann biplane wing was demonstrated by Odaka and Kusu-nose,31) a vertical wingtip plate is arranged between thewings to increase the two-dimensionality of the flow aroundthe biplane wing (Fig. 4). The inner side of the wingtip plateis a flat-plate shape and its outer side has a thickness distri-bution based on the S.H. body radius distribution (maximumthickness ratio of 3.36%). For appropriate shock interactions,the vertical distance between the wings is shortened at theouter wing by adding a dihedral angle to the lower wing.The non-dimensional section airfoil shape is the same at allsemi-span positions.4.2. Definition of body shape

The cross-sectional area distribution of the twin-body con-figuration is set to that of a S.H. body, which is well-knownas the supersonic single-body configuration with the lowestwave drag for specified volume and length. The volume ofthe twin-body is set to half of the previous 400-passengermodel.11) The body length is set to six times that of the wingroot chord length. The cross-sectional shapes of the twinbodies are deformed from circular (conventional S.H. body)to elliptical to reduce wing-body parasite drag (Fig. 5(a)).The twin-body/biplane wing configurations defined fromFig. 4 and Fig. 5(a) are discussed as Fig. 5(b). In Fig. 6,the pressure contours around the original Busemann bi-

(a) D-SEND#1 experimental models

(b) Sonic boom signature

Fig. 3. Comparison with experimental data of D-SEND#1 project.


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plane/twin-body configuration are shown under the condi-tions ofM1 of 1.7 and angle of attack of 2 degrees. Success-ful shock interactions between the wings can be observed.The total number of mesh points of this innovative SST con-figuration is approximately 2.6 million, which has been de-termined to achieve qualitatively accurate simulations ofshock wave interactions.

5. Wing Section Shape Optimization

In this section, the wing section shape of the biplane wing/twin-body configuration is optimized to obtain designknowledge for the innovative SST configuration using an op-timization method of the Kriging response surface model.5.1. Computational conditions

The aerodynamic performance is discussed at the designfreestream Mach number of 1.7 and angle of attack of 2 de-grees using inviscid CFD computations. The skin frictiondrag is estimated utilizing standard algebraic (turbulent) skinfriction models based on the wetted area of an SST configu-ration. In the sonic boom propagation analyses, standard at-mosphere temperature/humidity profiles are utilized. The fu-selage length and the cruise altitude are respectively set to62m and 18,000m, that are given from the flight conditionsof the Concorde.5.2. Optimization method

A surrogate model-based global design optimizationmethod that makes use of a Kriging response surface modelis utilized. An ordinary Kriging surrogate model32–34) is usedto construct the surrogate models of aerodynamic functions

in the design variable space. Firstly, initial sample pointsare generated in the design variable space using a Latin hy-percube sampling (LHS) method, and then these are eval-uated using CFD computations. Using the information ofthe initial sample points, initial surrogate models are con-structed. The search of a promising location in the designvariable space is executed applying a real-coded multi-objec-tive genetic algorithm35,36) to the surrogate models. Thepromising locations are explored using the criteria of ex-pected improvement (EI).33) The EI function expresses a po-tential for improvement in design variable space consideringboth estimated function value as well as uncertainty of thesurrogate model. The CFD computations are executed forthe explored promising locations where EI is maximal, andthen new surrogate models are created by adding its informa-tion. Using the iterative process described above, the accura-cies of the surrogate models are efficiently increased aroundthe promising locations in the design variable space.5.3. Design variables

The initial geometry is the Busemann biplane/twin-bodyconfiguration. The number of design variables is three in to-tal, and these are utilized to modify the x and z coordinates ofthe mid-chord apex of the upper and lower wings, as shownin Fig. 7 and Table 1. The design variables can be varied inrelatively wider ranges than general optimization problemsto extract detailed aerodynamic design knowledge in this de-sign optimization. The z coordinate of the mid-chord apex ofthe lower wing moves in the same distance/direction as thatof the upper wing. The deformed sectional shape of the bi-plane is employed at all span positions. This definition ena-bles a constant wing volume during the optimization process.5.4. Treatment of wing-body junction region

In this study, a wing section shape optimization is per-formed. The body near the wing is deformed using anunstructured dynamic mesh method based on the spring anal-ogy system.37) It is difficult to directly deform grid points ona three-dimensional surface. Thus, the three-dimensional sur-face of the fuselage is mapped to a two-dimensional parame-ter space s–t (Fig. 8(a)). Then, the unstructured dynamicmesh method is applied in the two-dimensional space. Fi-nally, the deformed two-dimensional grid is remapped tothe three-dimensional space (Fig. 8(b)). Using this method,the wing-body junction can be deformed while preservingthe outer shape of the original fuselage. Sufficient accuracyof the present mesh deformation method was confirmed byBan and Yamazaki.38)

(a) Busemann biplane (b) Licher biplane

(c) Biplane wing (d) wing tip

Fig. 4. Wing shape definition.

(a) Twin-body shape (b) Wing/body configuration

Fig. 5. Basic shape definition.

Fig. 6. Pressure contours around original Busemann biplane/twin-bodyconfiguration.


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5.5. Objective functionsThe maximization of L=D and the minimization of maxi-

mum overpressure (Pmax), which is the peak pressure valueof propagated pressure distribution on ground, are the objec-tive functions of this problem. The former corresponds toaerodynamic performance, while the latter corresponds tosonic-boom performance. The Pareto optimal solutions aresearched by solving the multi-objective optimization prob-lem.5.6. Results and discussion

The number of initial sample points is set to 25, in which24 points are generated using the LHS method. An additionalsingle point corresponds to Busemann’s biplane. This num-ber of initial sample points is considered to be sufficient forthe present three design variables space. Next, 39 additional

sample points are iteratively evaluated to observe detailedtendencies of non-dominated solutions. This number of addi-tional sample points is considered to be sufficient to makeaccurate surrogate models in the three-dimensional space.Figure 9 shows the performance of the solutions obtainedin the multi-objective low-boom/low-drag shape optimiza-tion. The tradeoff relationship between L=D and Pmax canbe observed. For the purpose of comparison, Licher biplaneperformance was also included in Fig. 9. It is interesting thatthe performances of the Busemann/Licher models are com-parable to the Pareto optimal solutions obtained. Three opti-mal designs are selected for comparison and named as Com-promise, Max_L/D and Min_Pmax. “Compromise” is acompromised solution selected from the Pareto designs.“Max_L/D” has the highest value of L=D, while “Min_Pmax” has the lowest value of Pmax. The aerodynamic/sonicboom performances of these designs atM1 of 1.7 and angleof attack of 2 degrees are summarized in Table 2.

Figures 10, 11 and 12 are respectively the non-dimensionalsection airfoil shapes of the representative designs, Cp distri-butions of the designs in the symmetrical plane, and the pres-sure visualizations of the designs in the symmetrical plane. InFig. 10, the x coordinates of the mid-chord apex of the upperand lower wings of the representative designs are movedslightly in the inflow direction. Since the gap between thetwo elements of the biplane is fixed, the movement leadsto a reduction in CDP due to better shock wave interference.It can be observed that the Max_L/D has a thicker lower wingthan the upper wing in Fig. 10. The thicker lower wing leadsto a strong shock wave at the front/upper-side of the lowerwing. Then, the strong shock wave leads to an increase in CL

at the rear/lower-side of the upper wing. In Fig. 11, higherpressure is confirmed in the Max_L/D model at the rear/

Table 1. Design variables.

Design variable Design range

dv1 Upper wing midchord apex coordinate X � 0.15cdv2 Upper and lower wing midchord apex

coordinate Z� 0.025c

dv3 Lower wing midchord apex coordinate X � 0.15c

(a) Grids of two-dimensional space

(b-2) Deformed (b-3) Original/deformed(b-1) Original

Fig. 8. Grid deformation of wing-body junction region.

Fig. 9. Pareto optimal solutions obtained.

Table 2. Aerodynamic/sonic boom performance of representative SSTconfigurations at M1 = 1.7 and angle of attack of 2 degrees.

CL CDP CDf L=DPmax

[Pa]Pmax � Pmin

[Pa]

Busemann 0.1202 0.01197 0.01200 5.02 30.5 65.9Licher 0.1514 0.01272 0.01200 6.12 34.4 70.5Compromise 0.1379 0.01221 0.01200 5.69 32.4 68.1Max_L/D 0.2115 0.01872 0.01201 6.89 42.4 83.2Min_Pmax 0.0650 0.01478 0.01200 2.43 28.1 65.2

Fig. 7. Wing shape modification.


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lower-side of the upper wing (0:5 < x=c < 0:8), which alsopropagates toward the ground, increasing Pmax. Thus,L=D issignificantly affected by the thickness difference between theupper and lower wings. The Max_L/D and Compromisemodels have larger CDP than the Busemann model. Thereason is that they have thicker lower wings and that leads

to increasing both drag and lift. Since the higher pressureat the rear/lower-side of the upper wing leads to increasingPmax, the Max_L/D and Compromise models have largerL=D and Pmax than the Busemann model. In Fig. 10, itcan be observed that Min_Pmax has a thicker upper wingand the x coordinate of the mid-chord apex of the lower wingis moved in the inflow direction more than that of the upperwing. For the former, the thicker upper wing, in other words,thinner lower wing, leads to lower pressure at the front/upper-side of the lower wing. As a result, the shock wavereflected at the rear/lower-side of the upper wing and propa-gated to ground is reduced. For the latter, two reasons can beconsidered. Firstly, the thicker upper wing generates strongshock waves at the front/lower-side of the upper wing,which leads to a larger shock-wave angle. To achieve betterinterference of the shock waves, the x coordinate of themid-chord apex is moved in the inflow direction. Secondly,it can be observed that Min_Pmax has larger expansion forthe lower wing at 0:35 < x=c < 0:4 (Fig. 11). The expan-sion wave is impacted at the rear/lower-side of the upperwing and propagates to the ground. Then, it is confirmed thatMin_Pmax has the weakest compression wave propagatingtoward the ground (although losing the model’s lift signifi-cantly). As a result, Min_Pmax has lower pressure at0:73 < x=l < 0:83, which can be seen in Fig. 13. InFig. 14, the pressure waveforms at two body lengths belowthe representative designs are compared. We can see thelargest peak at the middle of the distribution for the

Fig. 10. Sectional airfoil shapes of representative designs, upper: upperairfoil, lower: lower airfoil.

Fig. 11. Cp distributions around wings at the symmetrical plane, upper:upper airfoil, lower: lower airfoil.

(a) Compromise (b) Max_L/D

(c) Min_Pmax

(e) Licher

(d) Busemann

Fig. 12. Visualization of pressure variation in symmetrical plane.


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Max_L/D model (x ¼� 35). This is due to the effect of largerpressure variation propagating in the lower direction, whichcan be seen in Fig. 12(b). In Fig. 15, the pressure waveformsat the ground are compared, indicating a reduction in Pmax inthe Min_Pmax configuration.5.7. Visualizations of design variables space

An analysis of variance (ANOVA)33) is performed to ana-lyze the significances of design variables, as shown inFig. 16. This can be performed on the response surface mod-els that were constructed in the optimization process. Theareas of dv1, dv2 and dv3 correspond to the effects of the sin-gle design variables. Other areas correspond to the interac-tions of multiple design variables. It is confirmed that theL=D is sensitive to the z coordinate of the mid-chord apex(dv2), but is almost insensitive to the x coordinates of themid-chord apex of the upper wing (dv1) and of the lowerwing (dv3). In other words, the L=D deeply depends onthe thickness difference between the upper and lower wings.It is confirmed that Pmax is sensitive to the x coordinate of themid-chord apex of the upper wing (dv1) and the z coordinateof the mid-chord apex (dv2), but is almost insensitive to the xcoordinate of the mid-chord apex of the lower wing (dv3). Itis also confirmed that L=D and Pmax are significantly af-fected by the thickness difference between the upper andlower wings. Since the rear/lower-side of the upper wing

is important for sonic boom performance, dv1 is also impor-tant for Pmax.

Since we used only three design variables in this optimiza-tion, the distributions of objective functions can be visual-ized in the three-dimensional design variables space. The re-sponse surfaces of L=D and Pmax are visualized in Fig. 17.The differences between the left- and right-hand-side figuresare only the viewing locations, for better understanding ofthe three-dimensional space. The x, y and z coordinatesare normalized by the ranges of the design variables. Thesmaller-size spheres indicate the positions of the Pareto opti-mal solutions. The medium-size spheres indicate the posi-tions of the Busemann/Licher models (almost at the centerof the space). The larger-size spheres indicate the positionsof the three representative designs. Roughly speaking, thePareto optimal solutions with larger L=D stand along dv2,

Fig. 13. Cp distributions under the wing.

Fig. 14. Near-field signature (2.0l below).

Fig. 15. Sonic boom signature at ground level.

Fig. 16. Significances of design variables analyzed using ANOVA.


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and the Pareto optimal solutions with smaller Pmax stand in adifferent region with lower dv3. As indicated in the results ofthe ANOVA, dv2 has a significant influence on the tradeoffrelationship between L=D and Pmax. It can be observed thatL=D increases with larger dv2, while lower Pmax is realizedwith lower dv2. An additional increase in L=D can beachieved with larger dv2 outside of the design space,although it results in a very-thin upper wing configuration.

6. Concluding Remarks

In this research, twin-body fuselage/biplane wing 200-passenger SST models have been discussed. Aerodynamicperformance was evaluated using inviscid CFD computa-tions. The skin friction drag was also considered utilizingstandard algebraic (turbulent) skin friction models based onthe wetted areas of SST configurations. Furthermore, thesonic boom performance of the innovative SST configura-tions was discussed. Low-boom/low-drag design optimiza-tion for the wing section shape of a Busemann biplane wing/twin-body configuration was carried out under the conditionsof M1 of 1.7 and angle of attack of 2 degrees using an opti-mization method of the Kriging response surface model.Busemann/Licher biplanes were also investigated for com-parison purposes. By the low-boom/low-drag design optimi-zation, the tradeoff relationship between L=D and Pmax

could be observed. It was confirmed that the performancesof Busemann/Licher models are comparable to those ofthe Pareto optimal solutions obtained. The z coordinates ofthe mid-chord apex of the wings have a significant effecton the tradeoff relationship between L=D and Pmax. Simply

saying, the model which has a thicker lower wing leads tolarger L=D, while the model which has a thicker upper wingleads to smaller Pmax. As the optimization result, the opti-mized SST configuration “Max_L/D” achieved a 37.3% in-crease in L=D and “Min_Pmax” achieved a 7.9% reductionin maximum overpressure compared to the Busemann bi-plane wing/twin-body configuration with the same wing vol-ume. Furthermore, significances of design variables were an-alyzed using ANOVA, and the visualization of responsesurfaces of objective functions was performed to extractsome important engineering design knowledge. It was clari-fied in these analyses that the difference in thickness betweenthe upper and lower wings strongly affects aerodynamic andsonic boom performance. The major achievement of this pa-per was to extract important design knowledge for innovativeSST configurations in a fundamental three design variablespace, which can be utilized in future, in more detailed de-sign optimizations.

Our final target performance is 8.0 in L=D and 24 Pa inPmax with the present fuselage volume. These target perfor-mance values are specified to satisfy twice the passenger ca-pacity of the Concorde, to have better aerodynamic perfor-mance than the Concorde, and to have a Pmax one-quarterthat of the Concorde. It is said that the Concorde’s perform-ance was 7 inL=D and 2psf (96Pa) in Pmax :

39) The optimizedmodel has not yet achieved the target performance (i.e., theCompromise model has 5.69 of L=D and 32.4 Pa of Pmax).Although the present optimization achieved a large improve-ment in L=D, the three design variables were not yet suffi-cient to perform detailed shape optimization. Since we haveobtained fundamental design knowledge of innovative SSTconfigurations in this study, an investigation of the appropri-ate definition for the design variables will be performed.Then, the target performances can be realized by reducingbody-body interference drag and wing-body interferencedrag of innovative SST configurations. In addition, optimiza-tions under constant CL and with better sonic boom metrics,such as A-weighted sound exposure level, will be performedfor more realistic aerodynamic/sonic boom evaluations inour future works. Furthermore, we will also discuss the struc-tural design, flight stability, off-design performance and soon to demonstrate inclusive availability.

Acknowledgments

The authors are very grateful to the numerical simulation researchgroup of JAXA for providing us the use of their nonlinear acousticpropagation solver, Xnoise, as well as for their helpful advice.

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Fig. 17. Visualizations of response surfaces of objective functions.


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J. ChoAssociate Editor


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