«by: Alexander M. Benoliel Thesis submitted to the faculty of the Virginia Polytechnic Institute & State University in partial fulfillment of the ...»
6. Extensions to Multidisciplinary Design Optimization Methodology for HSCT Configurations The new estimation method was applied to the analysis of a configuration developed during a multidisciplinary design optimization (MDO) program. This program is being conducted at Virginia Tech to generate HSCT configurations that have been optimized to minimize the takeoff gross weight while meeting a variety of design constraints. The interested reader should reference Hutchison.75,76,77 The starting point of the optimization process is a baseline design shown in Fig. 39. The leading edge sweep angles of this design are 75˚/52˚. An optimized design is also shown in Fig. 39 with leading edge sweep angles of 73.5˚/12˚. A comparison of the aerodynamic characteristics of these two configurations is shown in Fig. 40. The original Aero2s method estimate is shown for the optimized configuration only, along with the estimates using Aero2s + APE, and is intended to show the difference between current linear methods and the new estimation method. The estimate of the aerodynamic characteristics of the baseline configuration were performed with the APE method. The large sweep angle of the outboard wing section on the baseline configuration resulted in an estimate of a relatively severe pitch-up along with considerably low high angle of attack lift. It should be noted that the APE method is more likely to under-predict the lift for this type of highly swept configuration.
Figure 40. - Aerodynamic characteristics of the baseline and optimized planforms.
Page 42 Unlike the baseline configuration, the optimized configuration has a very low sweep outboard wing section. During the optimization, it was theorized that this low sweep outboard wing section was due to the maximum 12˚ “tail scrape” landing angle of attack constraint. It has been shown that a reduction of the maximum landing angle of attack to 11˚ resulted in a 4.6% weight penalty.74 In an effort to reduce the dependence on this constraint and reduce the final configuration weight, trailing edge flaps were added to the configuration with the intent of increasing the low-speed lift. The flap size was chosen to have a root chord equal to 12% of the wing root chord and extend to 40% of the semi-span.
The flap was designed such that the hinge line was parallel to the y-axis (i.e. the hinge line was not swept). The flap design was chosen arbitrarily with some attention to designing a flap that was simple and could be feasibly constructed. The APE method estimates for this configuration with the trailing edge flaps is shown in Fig. 41.
1.0 0.8 Figure 41. - Effects of adding a trailing edge flap (δTE = 30˚) to the optimized planform. Analysis performed with the APE method.
As has been previously shown, the deflection of the trailing edge flap creates a negative pitching moment which must be trimmed for level flight. Therefore, a horizontal tail was added to the configuration for the purpose of trimming the aircraft at the required landing lift coefficient. The landing lift coefficient, CL, is determined from the landing weight of the aircraft, landing speed, wing area, and air density. This value will obviously be different for each configuration, therefore an average value of 0.60 was chosen. This value is close to the actual required CL for the configurations that have been generated in Page 43 the past by the MDO program. Fig. 41 indicates that the optimized configuration achieved the 0.60 lift coefficient at about α = 14˚. The APE method was shown to estimate lower lift coefficients than the aerodynamic analysis used in the MDO program which calculated a landing angle of attack equal to 12˚. The tail design was similar to those used for previously designed supersonic transports. The tail was sized for an area equal to 6.22% of the wing area with a leading edge sweep of 46.6˚. This size is typical for supersonic transport type aircraft. For example, the tail area of the McDonnell Douglas AST configuration is equal to 7.75% of the wing area.
Results of the configuration with the horizontal tail and trailing edge flaps deflected using the APE method are shown in Fig. 42. The horizontal tail was deflected -5˚ to trim the aircraft at about CL = 0.60. Included in the figure are the results for the flap deflected and flap undeflected cases without the horizontal tail for comparison. Note that the addition of the horizontal tail for trim results in a loss of lift compared to the no-tail, flap deflected condition. However, the addition of the horizontal tail and trailing edge flaps results in a significant increase in the low speed lift compared to the original configuration. This translates into a reduction of landing angle of attack by 4.6˚ or an increase in lift coefficient of 0.185 at α = 9.3˚.
Figure 42. - Aerodynamic performance of a trailing edge flap and horizontal tail combination (δTail = -5˚, δTE = 30˚) calculated with the APE method.
The original optimized configuration shown in Fig. 42 is not trimmed at the prescribed landing lift coefficient. For this to occur the trailing edge would have to be Page 44 deflected, which would also increase the lift, or the center of gravity would have to be changed, by means of fuel transfer. To trim at the prescribed center of gravity location the trailing edge would have to be deflected 18˚. The resulting increased lift, as shown in Fig.
43, would reduce the landing angle of attack by 3.5˚. The increase in lift at the trimmed angle of attack of 11˚ is 0.143. Thus the effects of trimming the original optimized tailless configuration results in an increase in landing lift not previously accounted for during the optimization process. However, for a tailless configuration the trailing edge flap would be required to deflect up and down, thus a plain flap would have to be used. For such a flap design, a 30˚ deflection angle would be considered to be a maximum effective deflection angle. Fig. 42 shows that a 30˚ deflection angle for the tailless configuration would not provide any pitch-down control above 16˚ angle of attack. For this tailless configuration to be a viable design, additional pitch-control surfaces would have to be added. Had this analysis been performed without the APE method, a different result would be attained as shown in Fig. 44. Note that the flap deflection angle to trim was determined to be only 13˚ and that pitch-down control is available beyond 20˚ angle of attack. This result shows the impact and benefits of using the APE method during the preliminary phase. This analysis has set the stage for a trade-off study between the aft tail and tailless configurations.
Figure 44. - Analysis of the tailless configuration without the APE method.
For the configurations described above a center of gravity position of 175 ft aft of the nose was chosen to give the unstable characteristics. An example was shown of how to trim the tailless configuration with only the trailing edge flaps. If center of gravity control were used to trim at the landing lift coefficient, the center of gravity would have to be moved forward by 10 ft (7.65% of the mean aerodynamic chord). Obviously no change in the low-speed lift would be attained by simply moving the center of gravity. If the trailing edge flaps were deflected to 30˚ to increase the low-speed lift, a tail deflection of -27.5˚ would be required to trim. For this center of gravity position the benefits of using flaps and a horizontal tail are reduced, as shown in a comparison to the 175 ft center of gravity position in Fig. 45. The forward center of gravity position with tail and flap deflection results in a reduction in the lift coefficient equal to 0.069 compared to the case of the flaps and tail deflected and the center of gravity at 175 ft. The lift coefficient for this case was also 0.027 less than the case of the tailless configuration with flaps deflected 18˚ and center of gravity at 175 ft. However, the low speed lift coefficient for this case was superior to the original tailless configuration without flaps with an increase in lift coefficient equal to
0.116. Although the forward center of gravity position allows for stable pitching moment characteristics, the benefits of using a high lift system is reduced. Also, it is likely that the horizontal tail will not be effective at a deflection angle equal to -27.5˚ suggesting that a larger tail would be required to trim.
Figure 45. - Effects of changing the center of gravity location for a configuration (δTE = 30˚) on the trimmed lift coefficient.
Results for initial flap deflected case (δTail = -5˚) were computed with a center of gravity position equal to 175 ft aft of the nose.
The above analysis was for the purpose of exploring and demonstrating the effects of trailing edge flap devices and horizontal tail on the trimmed lift coefficient. Although, the APE method is likely to under-predict the lift in many cases, the relative change in the lift due to the deflection of these devices should be unaffected by the under-prediction of lift. It should also be noted that these configurations, to be efficient at low speeds, will likely incorporate leading edge flap devices with the intent of reducing the vortex lift and thus the associated drag. This consideration should be taken into account in the multidisciplinary design optimization program which currently assumes that landing lift will include full vortex lift. A summary of the effects of incorporating trailing edge flaps in the aerodynamic analysis of a preliminary design is shown in Table 1 for an unstable and a stable center of gravity position.
6.1 Application to Multidisciplinary Design Optimization Process The preceding analysis simply added an arbitrary flap and horizontal tail to improve the low-speed characteristics. By doing so, the low-speed aerodynamic characteristics were improved but the design of the configuration is no longer optimum. That is, the optimization was conducted such that the design met the 12˚ tail scrape angle. With the addition of flaps, the landing angle was reduced and it is possible that a more efficient Page 47 design could be obtained with the increase in lift and reduced dependence on meeting the tail scrape angle. One means of accounting for this would be to include flap and tail design routines in the MDO program, along with a thorough subsonic aerodynamic analysis which would include the calculation of the trimmed lift and drag coefficients. This approach might lead to a better design but it would be computationally costly. A simpler approach would be to examine the results above and estimate the amount of additional lift that could be achieved with the use of trailing edge flaps. An estimate of the center of gravity range would be required to make a proper estimate of the lift increment. The optimization could then be rerun with the prescribed reduction in landing lift. If it is decided that a horizontal tail is required to trim, the additional weight and drag of this surface should be included in the optimization. With this approach the APE method would be used for analysis of the final design to determine if the low-speed requirements are actually met.
To increase the complexity of the optimization, the APE method could be used in each design cycle as described above. To reduce the computational cost of this approach, it could be implemented only when the optimizer has reached a solution close to an optimum. The complexity of the design could also include optimizing flap and tail size for minimum weight and drag. Finally, a leading edge flap system should be designed to minimize the vortex lift and thus the low-speed drag. The reduction of the low-speed drag is important in meeting the takeoff and landing noise requirements.
Many current configurations developed for supersonic transport aircraft are prone to the problem of an unstable pitch-up at angles of attack well within the low speed operating regime. It is important for the configuration designer to be aware of the aerodynamic reasons for pitch-up and the geometric factors that contribute to pitch-up and affect the type of the pitch-up behavior. Several key findings were identified and presented in this
research. They are:
• The mechanism by which pitch-up occurs. Two prime causes for pitch-up were identified. These were: 1) classical flow separation on the outboard wing section, and 2) the dominating influence of an inboard leading edge vortex coupled with vortex bursting at the trailing edge.
• Geometric factors which affect the pitch-up behavior, including planform shape and control surface deflection.
• Previously investigated methods to postpone the pitch-up behavior and improve longitudinal aerodynamics of cranked arrow wings.
• The effectiveness of flaps on highly-swept, low aspect ratio configurations.
• The development of a new method to estimate pitch-up and validation of this method with experimental data.
• Application of the new method to preliminary aircraft design The new method resulted in a simple and computationally inexpensive means of estimating the onset of non-linear aerodynamic characteristics and pitch-up of cranked arrow wings, as shown through numerous comparisons with data. The method was especially effective in estimating pitch-up when the occurrence was due to classical flow separation on the outboard wing panel.