optimization of canard surface positioning of ...

33rd AIAA Fluid Dynamics Conference and Exhibit Orlando, Florida 23-26 Jun 2003

OPTIMIZATION OF CANARD SURFACE POSITIONING OF SUPERSONIC BUSINESS JET FOR LOW BOOM AND LOW DRAG DESIGN

Minoru Yoshimoto*, Naoki Uchiyama† Aerodynamics Research Section Nagoya Aerospace Systems Mitsubishi Heavy Industries, Ltd., Nagoya, Japan

1.ABSTRACT The present study focuses on the advantages of optimized canard surface positioning for supersonic transport in terms of sonic boom reduction and improvement in lift to drag ratio(L/D). The presence of the canard surface may affect the longitudinal lift load distribution of the aircraft in a favorable way which leads to sonic boom reduction while achieving higher L/D due to lower trim drag under constant lift condition. The present study first confirms these canard effects through CFD analysis for preliminary designed baseline configuration of supersonic business jet (SSBJ) aircraft. The study is then proceeded to develop design tool for optimized canard surface positioning with sonic boom intensity and L/D being the objective functions. The design tool consists of near-field CFD code, the waveform parameter method for evaluating on-ground sonic boom signature and an optimization scheme based on genetic algorithm for canard surface positioning. After the tool being developed, it was then applied for realistic flight condition. The results revealed the fact that among chosen design variables, setting angle was the most sensitive to the two objective functions; sonic boom intensity and L/D. Consequently, our target of reducing the peak pressure of sonic boom signature below 1psf was achieved within application of the presently developed tool. 2. INTRODUCTION Among concerns on environmental impacts in realizing the next generation supersonic transport concept, sonic boom remains to be one of the major issues. Such problems had limited the supersonic flight envelope of the Concord. On the other hand, SSBJ concept can focus on smaller size aircraft, thus with lower lift and lower sonic boom intensity. This leaves possibility for its transcontinental supersonic flight, which is deemed as inevitable condition for the concept. Figure 1 shows the estimated sonic boom

intensity in terms of on-ground peak pressure rise against weight of typical supersonic aircrafts concerned. Although there leave discussions on achievable goal for the reduced peak pressure, an amount below 1psf is strongly expected. The technical difficulty stems in the fact that reduction of sonic boom intensity and increase in L/D are generally conflicting issues. Intensive studies are ongoing, however, not little of the proposed concepts have difficulty to put in practice when considering aspects such as airframe structures, flight maneuverability and its economical relevancy. With realistic application in mind, we focused on the advantageous potential of optimized canard surface positioning in terms of sonic boom reduction and higher L/D, besides its original purpose of controlling pitch trim and improving maneuverability. 3. LOW BOOM AND LOW DRAG DESIGN Canard Effects Generally, each component of the airframe is responsible for enhancing sonic wave generation through its volume and lift effects. Both effects can be discussed identically in terms of equivalent area distribution within the framework of Whitham’s ‘F-function method’ 1. Modifying the volume distribution of the forebody by blunting the nose configuration is an effective way in relatively mitigating the concentration of equivalent area distribution at main-wing portion, where major source of pressure distribution responsible for sonic wave generation exists. However, blunt nose generally gives rise to form drag which results in severe trade-off study in design process. Optimal design of fuselage configuration is another issue. After the main-wing been designed, the area distribution of the fuselage can be adjusted to achieve ideal equivalent area distribution as a whole. Many of the proposed SSBJ configurations possess canard surface, presumably for pitch control purpose. In contrast to tail-wing configuration, we consider that the canard configuration has some favorable aerodynamic 3.1

__________________________________ * Research engineer, †Assistant manager 1 American Institute of Aeronautics and Astronautics

characters also in terms of reducing sonic boom intensity and increasing L/D. Two advantages can be pointed out. 1) Lower trim drag. In contrast to tail-wing configuration where tail wing contributes for nose-up with its negative lift to trim pitch, canard configuration make use of positive lift of the canard surface to trim drag. Under constant lift condition, this means smaller lift is required for the main-wing, leading to lower trim. 2) Potential for lower sonic boom intensity. Not only that installation of the canard can mitigate concentration of equivalent area distribution at most concerned main-wing portion as well as the case of nose blunting concept, the up/down-wash due to tip-vortex of the canard surface influence the main-wing lift load distribution in a favorable way. As shown in Fig.2, the inboard portion of the main-wing experiences down-wash that decreases the lift load of its area, while the outer portion experiences up-wash that increase the lift load of the area. Since the main-wing posses highly swept angle for these aircrafts, this shift in lift load results in widening its distribution in longitudinal direction which is favorable for achieving lower sonic boom intensity. 3.2 Canard Positioning As for positioning the canard surface, we defined four design variables to be optimized. This consists of longitudinal and vertical positions, setting angle and dihedral angle as shown in Fig.3. 3.3 Design Tool Methodology The design tool developed in the present study forms a recursive loop that consists of three major functions; near-field CFD, far-field sonic boom signature estimation and optimization of canard positioning. The overall process is shown in flowchart in Fig.4. Initially, baseline configuration is given and its near-field flow is computed with efficiently fast CFD solver. This computation is performed recursively while adjusting the angle of attack to achieve target lift. After convergence of the angle of attack, far-field on-ground sonic boom signature is evaluated using a waveform extrapolation method as well as the L/D obtained by surface pressure integration. The set of peak pressure of on-ground sonic boom signature and L/D figure is considered as a plot in 2D objective function space. Until the plot converges onto optimum front curve, i.e. the so-called Pareto optimal solution, the process proceeds for re-positioning of the canard surface which defines set of next generation of optimized candidates. After achieving convergence, a Navier-Stokes computation and evaluation of on-ground sonic boom signature is confirmed for some of the chosen configuration in interest as a final process. The detail methodologies for each process are described below. Near-field CFD Solver Two different near-field CFD solvers are applied. For

the recursive optimized design process, an efficient space-marching Euler equations solver, particularly developed for the present study, is applied. The conservative variables of the flow are obtained by spatial sweep performed from upstream to downstream, solving an implicit ADI operator consisting of block tri-diagonal matrices. The numerical fluxes for circumferential and radial directions are evaluated using the 3rd order accurate Chakravarthy-Osher scheme2. Figure 5 shows the computational grid. The grid forms a conical structure with its apex angle set to the Mach angle corresponding to the supersonic flight condition. A conical hollow portion exists downstream saving extra grid points where pressure waves assumed to take no place. In order to achieve canard re-positioning in most efficient and automatic way, multi-grid strategy was taken. The grid consists of four blocks; forebody, upper and lower canard region and aftbody region. The total grid was automatically re-gridded for each canard installation. Total grid point amounts 0.89 million, and typical computational time took approximately 5 minutes per configuration on R12000 processor of Silicon Graphics Octane2. On the other hand, for accurate near-field CFD computation required for final confirmation process, time-marching Navier-Stokes equations code was applied. Implicit time-marching is applied by solving LU-ADI operators. The numerical fluxes are evaluated using Roe scheme with 3rd order MUSCL extrapolation. L/D Estimation In the recursive design process, the lift and pressure drag are evaluated from surface air load integration. The friction drag is not considered in this phase. However, this should not impact the optimization result. Since we only consider for re-positioning of the canard surface, remaining the wetted area identical and restricting its setting angle in moderate range preventing severe flow separation, the friction drag should remain almost constant for all configuration. On the otherhand, the final phase with Navier-Stokes computation confirms the total drag amount including the friction drag. Sonic Boom Signature Estimation In order to estimate far-field on-ground sonic boom signature, the present tool applies waveform parameter method of Thomas3. The method make use of near-filed pressure distribution. The CFD obtained near-field pressure distribution was applied here as an input. The method extrapolates the pressure distribution to the far-field, estimating the wave accumulation as it propagates under atmospheric gradient effect. Optimized Canard Surface Positioning The two objective functions in the optimization process are the peak pressure value of estimated sonic boom signature and L/D figure, as functions of aforementioned

2 American Institute of Aeronautics and Astronautics

four design variables that determine the canard position. The present tool applies genetic algorithm for the optimization process. Among various optimization algorithms, the genetic algorithm suits well for multi-objective problem such as present. An initial generation of population with different canard installation was set by defining group of configurations deviating randomly from prescribed baseline configuration, in terms of four design variables.

3.4 Baseline Configuration The baseline configuration provides the starting point for the optimized design. It is to be noticed that baseline configuration grossly defines the overall aerodynamic. In defining the general figure of the aircraft, the present study referred the SSBJ configuration proposed by Dassault4 and Sukoi/Gulfstream5. Figure 6 shows planform of the defined baseline configuration. Also shown are the comparison of canard surface and main-wing planforms between present baseline configuration and those of referred configurations. Table1 shows the general figure designed. Vertical tail-wing and engine nacelle were not considered in the present study. The design condition was also defined as below by referring the typical range of SSBJ aircrafts.

distribution of the configuration without the canard surface from that of with the canard surface. The pressure difference distribution on both the upper and lower surface clearly indicates the pressure shift on inboard portion of the main-wing that decreases the main-wing lift as a whole, due to down-wash of the canard. Also clear is the lift load created on forebody where the canard surface being installed. Figure 9 shows the pressure distribution on symmetric plane for both configurations. While the canard surface contributes to increase the pressure level around its installed area, the pressure gradient around the main-wing area relatively weakens, especially on the lower surface. This effect is quantitatively addressed in Fig.10 where near-field pressure distribution was taken one body length below the airframe. The figure clearly shows the fact that the maximum peak pressure has been reduced due to canard installation. To conclude, the results are summarized in Fig.11. Three sets of results are plotted against 2D plane of L/D versus peak pressure of estimated on-ground sonic boom signature. Either for high(CL=0.201) and low(CL=0.161) lift cases, as well as for the case of constant angle of attack (AOA=5.55deg.), configuration with canard surface showed lower peak pressure and higher L/D compared to that of without the canard surface. 4.3

Cruise Altitude: 60,000[ft] Cruise Mach Number: 1.8 Maximum take-off weight: 40,000[kg]

4. RESULTS AND DISCUSSIONS CFD Validation Firstly, in order to validate the aerodynamic estimation ability of the developed tool, near-field of Concord-like configuration was computed and the results were used to estimate the on-ground sonic boom signature by means of waveform parameter method. The flight altitude was considered to be 50,000[ft] and flight Mach number of Mach=2.0. Figure7 shows the near-field pressure distributions and the obtained on-ground sonic boom signature compared with corresponding flight data6. The excellent agreement between the two sonic boom signatures insists validity of both the present CFD solver and the waveform parameter method applied.

4.1

4.2

Canard Effect Next, in order to confirm our views on canard effects upon reducing sonic boom intensity and improving L/D, we performed design condition computations for baseline configuration with and without the canard surface. Figure 8 shows the obtained surface pressure distributions for both configurations. The angle of attack was set to 5.55deg. for these cases. In order to focus on the difference, also shown are the pressure difference distribution obtained by subtracting the surface pressure

Optimized Configuration After confirming the advantageous effect of the canard surface installation, our succeeding objective was to derive an optimized canard position by means of optimized design. The first condition tested was for the case at cruise with total lift CL=0.161, which corresponds to maximum take-off weight of 40tons. Flight altitude and cruise Mach number are as aforementioned in section 3.4. For the genetic algorithm applied in the optimization process, population of 8 configurations per generation was set. The constraints given to the range of design variables were set as shown in table 2. Figure 12 shows the set of solution in 2D objective function space, obtained after number of 5 generation loops. The results show population of the optimized configuration all superior to baseline configuration either in terms of lower sonic boom intensity or higher L/ Dp (Dp: pressure drag only). As can be seen in Fig.13 and Fig.14, setting angle and dihedral angle were found sensitive to both the peak pressure and the L/Dp, while longitudinal and vertical displacements showed little correlation. The second condition tested was for the lift case CL=0.141, corresponding to typical cruise condition with weight of 35tons. Figure 15 shows the converged solution obtained after number of 5 generation loops for population of 16 configurations. For this case, however, the solution tended to mal-distribute over low boom and low L/Dp region. An adoption of sharing process of individual fitness in the objective function space may


improve the situation by avoiding the concentration of the solution to particular individual. For this case, dihedral angle showed little correlation to both the objective functions, which differed to the previous higher lift case. From the group of solution obtained, the configuration with the lowest peak pressure was referred as low boom configuration and was compared against the baseline configuration. Figure 16 shows the resulting installation of the canard surface. Positive setting angle and negative dihedral angle were obtained for this case. Table 3 shows the derived design variables and the evaluated on-ground peak pressure and L/D for the low boom configuration. Figure 17 shows comparison of surface pressure distribution of low boom and baseline configurations. The low boom configuration shows pressure distribution which insists higher lift generation on the canard surface than the baseline configuration. Figure18 shows the near-field pressure distribution evaluated one body length below. As prescribed, although the local pressure rise below the canard surface is higher for the low boom configuration, the maximum pressure peak occurring below the main-wing portion is lower, conversely, due to optimized canard effect. Figure 19 shows the on-ground sonic boom signature. The peak pressure intensity is yet slightly over our target 1psf. Since the setting angle obtained for this low boom configuration was near its range maximum 3.0deg., an additional test with setting angle up to 6.0deg. was performed. Here we refer this as final configuration. Table 4 shows the selected design variables and the evaluated on-ground peak pressure and L/D for this configuration. Figure 20 shows the corresponding near-field pressure distribution. The effect of canard surface has been strengthen. The magnified on-ground sonic boom signature is shown in Fig.21. For this configuration, the peak pressure finally achieved its value below 1psf.

5. CONCLUSIONS In the present study, 1) the advantageous effect of canard installation in terms of sonic boom reduction and L/D increase was confirmed for SSBJ configuration. 2) Furthermore, by applying our presently developed design tool, we demonstrated the fact that optimizing the canard surface position can make the most of this advantage. Among the case tested, the obtained set of optimized configuration showed superior characteristic either in sonic boom intensity or L/D to preliminary designed baseline configuration. 3) It was also confirmed that setting angle of the canard surface has strong correlation to sonic boom intensity. It was understood that the lift generated at the canard and its down-wash affects the overall air load distribution in a favorable way which relatively weakens the concentration of pressure rise near the main-wing portion, effective for sonic boom reduction. 4) Finally, within the application of the present

optimization tool, we were able to present a low boom configuration that estimates sonic boom intensity below our target, 1psf.

6. ACKNOWLEDGEMENTS This work was supported by the SJAC(Society of Japanese Aerospace Companies) as a part of the research and survey on various fields concerning technology development for advanced aircraft7,8. Also the authors would like to express their appreciation to the advanced technology aircraft project center of National Aerospace Laboratory, Japan for providing us the data of Concord-like configuration.

REFERENCES 1. Whitham,G.B.,”The Flow Pattern of a Supersonic Projectiles”, Communications in Pure and Applied Mathematics, Vol. V, pp.301-348, 1952. 2. Chakravarthy S.R., Osher S., “A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws”, AIAA Paper 85-0363, 1985. 3. Thomas, C.L., “Extrapolation of Wind-Tunnel Sonic Boom Signatures by the Waveform Parameter Method, “ NASA TN D-6832, 1972. 4. Burgner, N., “In der Kurze liegt die Wurze”, Flug Revue, Aug. pp.32-35, 1998. 5. Horinouchi, M.,”Super Sonic Biz-Jet”, Air World, Nov. pp.72-75, 1990. (in Japanese) 6. SJAC, “Japan Supersonic Research Program”, Results report, additional volume. pp.62, March, 1991. (in Japanese) 7. SJAC, “Research on optimized configuration for low sonic boom and low drag”, Report on research of advanced aeronautical technology development”, No.1204, 2001. (in Japanese) 8. SJAC, “Research on optimized configuration for low sonic boom and low drag”, Report on research of advanced aeronautical technology development”, No.1302, 2002. (in Japanese)


Table1

General figures of baseline SSBJ configuration.

Total figures Total length[m] Total width[m] Fuselage Body length[m] Maximum diameter[m] Area[m2] Aspect ratio taper ratio(Ctip/Croot) MAC[m] Main-wing 50%MAC location[m]

Canard

ratio to total length L.E. swept angle(deg.) strake inborad outboard T.E. swept angle(deg.) inboard outboard Area[m2] ratio to main-wing area Aspect ratio Taper ratio 50%MAC location[m] ratio to total length L.E. swept angle(deg.) T.E. swept angle(deg.)

Table2

36.0 18.56 36.0 2.3 150 2.3 0.075 11.52 23.4 65% 75 (η