LOW SPEED STABILITY DERVIATIVES FOR A HYPERSONIC TEST VEHICLE

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1 LOW SPEED STABILITY DERVIATIVES FOR A HYPERSONIC TEST VEHICLE Jonathan J. Jeyaratnam and Dries Verstraete School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW, 26, Australia, jonathan.jeyaratnam@sydney.edu.au ABSTRACT The design of hypersonic aircraft often focuses on the most challenging aerodynamic, structural and thermal issues at high Mach numbers. The stability and handling qualities of these designs at low speeds are often not considered, however, for any such design to be viable as a transport aircraft these characteristics must be incorporated into the hypersonic design process. In this article the aerodynamic coefficients of an unpowered version of a Mach 8 hypersonic test vehicle are analysed. Baseline low speed stability derivatives are extracted using a full potential flow solver. The longitudinal stability is shown to be adequate as the centre of pressure appears to be quite far aft on the bottom surface. The results indicate the vehicle is laterally unstable with no angle of attack range exhibiting negative yaw damping and positive yaw stiffness simultaneously. The anhedral wing design also results in a destabilising roll response to sideslip disturbance. Key words: Aerodynamic Stability; Hypersonics. 1. INTRODUCTION The field of hypersonic research has seen an increase in activity in recent years with numerous projects underway or completed, aimed at producing test vehicles for validating numerical studies and models. The Hexafly- International project is one example where an international collaboration is aimed at producing a Mach 8 hypersonic test vehicle. As with most projects of this type, the key design goal is aerodynamic performance and controllability at the test speed. The Hexafly-International vehicle has been designed for a cruise speed of Mach 8 and wing and tail geometry have been optimised for this speed. The bulk of current research is focused on the aerodynamic, structural, propulsion and thermodynamic behaviour at hypersonic cruise speeds as these clearly present the most challenging problems. However, for most hypersonic vehicles to be viable, it is desirable for it to be capable of taking off and landing at conventional runways. Hence the performance and handling qualities over the entire flight trajectory must be satisfactory. The vehicle therefore either has to be fully stable, for civilian applications, or capable of controllable flight via flight controllers. As most hypersonic designs are designed with the performance at cruise in mind the low speed performance is usually poor. The extent to which the design must be modified to satisfy stability requirements over the whole envelope must therefore be examined to quantify the effects on the on-design performance or to identify the modifications that are needed to obtain satisfactory handling qualities. This paper focuses on the aerodynamic analysis of the proposed Hexafly-International vehicle at subsonic Mach numbers. The longitudinal and lateral stability derivatives are obtained using Tranair, a full potential flow solver. This solver has been shown to be able to capture the main aerodynamic features of hypersonic vehicles as shown by Taguchi [TKK12] when examining the flight trajectory of another hypersonic vehicle. In this paper the results from Tranair on the Hexafly-International vehicle are analysed to estimate the stability and damping characteristics of the main longitudinal and lateral modes. 2. PREVIOUS STUDIES In the past, numerical studies have mainly focused on the on-design L/D performance of hypersonic designs. However, some research efforts such as Taguchi [TKK12], Bowcutt [Bow86], Takashima [TL99] and Long [Lon9] do examine the off-design behaviour. Other studies by Takama [TKK11] and Eggers [ESNR94] looked at the performance impact of practical modifications to pure waverider designs, which tend to have poor low speed performance and volumetric efficiency. Takama [TKK11], for instance, shows that extending the wings outboard to give better landing performance did not produce high costs in aerodynamic performance at cruise conditions which is of significance to this project given the highly swept nature of the design. However, these studies all primarily focus on the L/D performance as the key design consideration.

2 Eggers et al. [ESNR94] examined the off-design longitudinal stability by looking at the shift in the neutral point from roughly Mach.2 to Mach 12. They showed that the neutral point moved even further back for a design with a more distinct body and wing configuration rather than the lifting body of the pure waverider it was based off. This again suggests that modifications towards more practical designs can be achieved without too great a loss in performance. Tarpley and Lewis [TL95] on the other hand produced an analytical solution for the stability derivatives of the relatively simple caret wing design. However, for more complex designs that do not benefit from the use of 2 dimensional shock equations a more detailed numerical approach is required. However, few numerical studies actually address stability as a key factor and even studies that do look at stability tend to focus on the longitudinal performance. In contrast, several wind tunnel campaigns have examined the low speed performance of hypersonic vehicles from early tests such as Bowman [BG6] to more recent studies such as Miller [MA97] and Hahne [Hah97], [HC94]. The tests conducted by Miller focused on the longitudinal performance of the osculating cones type waverider. Studies conducted by Hahne et al utilised the low speed wind tunnel facilities at the NASA Langley facility. The LoFlyte program in particular explored the lateral stability problem in detail for a Mach 5.5 design vehicle. The low speed wind tunnel tests [Hah97] looked at angles of attack from -5 to 2 degrees and sideslip angles from -1 to 1 degrees. The results were used to evaluate the effect of an extended rudder and modification of the separation between the vertical tails on lateral performance. A similar approach will be taken to examine the stability of the Hexafly-International vehicle and the current paper presents computational results for the original design of the vehicle. 3. HEXAFLY-INTERNATIONAL VEHICLE In this paper, as a starting point, an unpowered model is produced by closing the internal engine flowpath of the powered Hexafly-International vehicle. In further studies the internal flows will also be examined based on detailed results of the intake mass flow rate and exhaust flow properties of the engine model at low speeds. The vehicle shown in Fig. 1 features a highly swept wing surface that is integrated with the lower surface of the body. The wing features negative dihedral (anhedral) to contain the shock generated at hypersonic speeds. Yaw control is provided by the twin vertical tails which are designed for neutral lateral stability at high Mach numbers. The front view shown in Fig. 2 shows the sharp leading edge of the wing leading and their integration to the nose of the vehicle. To close the engine flowpath the engine intake is replaced by a flat cover plate while the back surface of the nozzle is taken as a flat plate perpendicular to the streamwise axis. The dimensions of the high speed flight demonstrator of the projects are given in Table 1. Figure 1. Isometric View of the Hexafly Vehicle Mesh Figure 2. Front View of the Hexafly Vehicle Mesh Those dimensions are also adopted for the current study on low speed handling qualities. As shown in Figs. 1 and 2, various regions of low and high density mesh exist on the lower fuselage surface and towards the front and rear of the vehicle. This is done deliberatly as the mesh will be coupled in a later stage with the NASTRAN finite element solver for a full aerothermo structural analysis loop. As such it is desirable that the all the mesh points between the various networks match at the edges rather than using abutment area in between various grids. The results presented in this article Table 1. Vehicle Test Data Length 2.88m Span 1.37m MAC 2.13m Planform Area 2.44m 2 Mach no..2

3 show that some further refinement will be needed because of this. Particular areas of concern are the front nose network towards the base and the leading edge of the main wing towards the nose. 5. RESULTS Results for both longitudinal and lateral stability derivatives are presented and discussed in this section. Longitudinal derivatives are presented first, followed by lateral derivatives. 4. TEST PROCEDURE AND VALIDATION 5.1. Longitudinal Stability Tranair is a non-linear full potential 3D flow solver with pseudo-3d boundary layer coupling. Tranair uses a second order transpiration method to emulate control surface deflections and has an integrated automatic trimming capability. Unsteady time harmonic oscillations are imposed on top of the steady state solution to determine static and dynamic stability derivatives. For this initial study the boundary layer solver has been omitted to ensure convergence of the Euler simulations. The steady capabilities of Tranair are used to estimate the lift, sideforce and the three moment coefficients. The unsteady capabilities can provide the roll, pitch, yaw, angle of attack rate and sideslip rate derivatives for lift, sideforce and the three moment coefficients. As an initial validation of the test procedure, the Ryan Navion was analysed in Tranair and compared with data obtained from flight test data studied by Seckel and Morris [SM]. The results are shown in Table 2 alongside USAF Datcom results obtained by Seckel and Morris. These results suggest that the unsteady Tranair results can be used to give a reasonable estimate of the rate derivatives. Lift and moment coefficients for both CG locations are shown in Figs. 3 and 4 as function of angle of attack. Fig. 3 shows that the lift almost increases linearly with angle of attack over the entire range of angles considered. A slight decrease in the lift curve slope C Lα can however be observed over the range tested. The lift coefficient for the Hexafly-International vehicle is somewhat lower than that of the Mach 5.5 vehicle tested by Hahne [Hah97], which is likely due to the higher wing sweep and lower span to length ratio of the vehicle. As indicated in Fig. 4, the moment coefficient shows a stable trend for both CG locations. This suggests that the centre of pressure on the underside is quite far aft. Over the range tested no natural trim point can be identified, however, the evolution of the moment coefficient suggests that a zero moment would be obtained around -7 degrees without elevator deflection. To obtain a trimmed flight condition with a neutral elevator position, the vehicle centre of gravity would have to be located in the aft half of the body Table 2. Tranair Comparison with Flight Test Data from Seckel [SM] using Navion Tranair Flight Test Data Datcom C lˆr C l ˆp C nˆr C n ˆp C m α + C mˆq C m α C L Figure 3. C L For the current study, The steady Tranair solver was used over a range of angles of attack from -5 to degrees for sideslip angles of -5 and degrees. The centre of gravity was positioned at.25 and.5 times the length of the body. The unsteady solver was on the other hand used over a range of to degrees angle of attack with degree sideslip. For all reported conditions the Mach number was set to.2. Figs. 5 and 6 show the moment response to the pitch rate q and angle of attack rate α. Both coefficients are negative which indicates a good longitudinal stability over the entire range of angles of attack. A shift in c.g. location from 5% of the body length to 25% of the body length results in a significant increase of the values for the derivatives. This indicates that control surfaces will have to be considerably large to ensure sufficient control authority if the vehicle c.g. is located forward. However, considering the shape of the vehicle this is unlikely.

4 C m C mq Figure 4. C m Figure 6. C mˆq -.3 C mα Figure 5. C m α 5.2. Lateral-Directional Stability The analysis of the lateral-directional derivatives indicates that some further mesh refinement is needed around the leading edge. This is illustrated by the pressure distribution shown on Fig. 7. The figure shows that slight asymmetries in the pressure distribution (and thus the flow field) exist at angle of attack (AoA). These stems from the highly vortical flow around the sharp intersection between the leading edge of the wing and the nose of the body and result in a small sideforce C y at zero sideslip. Whereas the resulting sideforce is small, further mesh refinement is needed to eliminate this and its potential impact on the stability derivatives. Figs. 8 to 1 show the results obtained for the lateraldirectional stability derivatives. The figures show that, contrary to the longitudinal case, the vehicle is laterally unstable. For lateral-directional static stability, the side force due to sideslip C yβ must be negative and the yaw moment due to sideslip C nβ must be positive [Ros7], whereas the roll moment due to sideslip C lβ has to be negative. As shown in Fig. 1 C yβ is positive only for angles of attack greater than 8. However, an examination of the sideslip response C lβ (Fig. 9) indicates a lack of lateral stability above 2 angle of attack where the roll response is positive. This is likely the result of the large anhedral angle of the wing which causes the vehicle to roll towards a sideslip. Nevertheless, it could also be a result of a too high centre of gravity which reduces the effectiveness of the vertical tails (relative to the anhedral effect) especially at higher angles of attack. As a positive C lβ could indicate an unstable dutch roll mode, further investigation is needed to determine the roll response to sideslip disturbance and its sensitivity to vertical tail size, location and c.g. position. For a c.g. located at 25% of the body length, the vehicle furthermore exhibits poor yaw stiffness C nβ characteristics up until 8-9 angle of attack. Shifting the c.g. further back has a stabilising effect with positive yaw stiffness from around 7. Hahne found similar trends for C nβ for the LoFlyte model with no vertical tail, where yaw stiffness was only positive beyond 1. This suggests that the Figure 7. Coefficient of pressure distribution at 1 AoA

5 C yβ C nβ Figure 8. C yβ Figure 1. C nβ C lβ -.65 C lp Figure 9. C lβ Figure 11. C l ˆp Hexafly-International vertical tail could be ineffective at low speeds. These results, where the 3 criteria are never simultaneously met, imply that the sizing of the vertical tails would require further investigations to improve the yaw response. Larger vertical tails could improve the yaw characteristics. However, the impact on lateral stability of the vortical flows encountered around similar slender bodies such as the vehicle examined by Hahne [Hah97], indicates that all aspects of the vertical tail geometry would have to be examined. This means that spacing of the fins, fin dihedral angle as lengthwise location of the fin have to be considered in addition to the fin size. Whereas the vehicle is statically unstable for lateraldirectional motions, the dynamic derivatives suggest that good damping characteristics are nonetheless obtained. The roll damping C l ˆp shown in Fig. 11, for instance, indicates good damping behaviour with negative roll damping over the whole angle of attack range. The roll damping does decrease rapidly at higher angles of attack, which suggests a reduced vertical tail effectiveness under those conditions. After all at high angles, the tails are blanketed by the body wake. Nevertheless, roll damping remains good. For the conventional wing and tube aircraft configuration, the yaw response to roll rate tends to turn the aircraft nose into the roll which initiates the dutch roll [Ros7]. This requires positive values for C n ˆp. Fig. 12 indicates that C n ˆp is negative up to 1-11 for the Hexafly-int vehicle. Similarly, as shown in Fig. 13, the sideforce response to roll rate C y ˆp is positive up till 9. This is also opposite to normal behaviour and is most likely caused by the anhedral effect of the wings which overpowers the effect of the vertical tails. For most aircraft the roll moment due to yaw rate C lˆr is positive due to the increased lift on the wing that experiences a greater velocity due to the yaw rate. However, Fig. indicates that C lˆr for the Hexafly-International model is negative. Again, this would produce opposite dutch roll behaviour compared to a normal aircraft. Nonetheless the yaw damping coefficient, C nˆr is negative, as shown on Fig., which is desirable to damp roll and yaw rate motion. The final dutch roll behaviour will thus have to be investigated closeley once the moments of inertia of the vehicle are known and the final size of the control surfaces is determined.

6 C np -.5 C lr Figure 12. C n ˆp Figure. C lˆr. C yp C nr Figure 13. C y ˆp Figure. C nˆr Fig. 16 shows that a positive sideforce is obtained when a yaw rate is imposed. This suggests that the strange roll behaviour is more likely due to the position of the c.g., which reduces the effectiveness of the sideforce from the vertical tail, rather than the vertical tail not producing sufficient sideforce. For most aircraft the lateral coefficients, C lβ and C nˆr are negative, whereas C nβ and C lˆr are positive. The balance of their magnitudes determines if a positive steady bank angle will require positive or negative aileron deflection to achieve trim [Ros7]. For the Hexafly-International vehicle, C lβ is positive, whereas C nˆr, and both C nβ and C lˆr are negative in the range of angles of attack from 1 up to 5-1. This suggests that the vehicle will tend to bank further when given a steady bank angle. In summary, the vehicle overall exhibits good longitudinal stability characteristics; however the lateral stability characteristics are unusual to say the least. Further analysis would be required to determine what modes of motion would be present as for several lateral rate responses the behaviour is opposite to that of a conventional aircraft. 6. FUTURE WORK The results presented in this article are part of an initial study to examine the general trends in the stability derivatives. Therefore a thorough analysis of the sensitivity of the values to the size of the computational grid was not undertaken. The results for some of the lateral stability derivatives, most notably C yβ, indicate that further mesh refinement is warranted and a mesh sensitivity study will be undertaken.. Besides a mesh sensitivity study, the effect of the placement of the c.g. will also be studied further. Some of the undesirable lateral behaviour could have been the result of a too high c.g. location. A lower c.g. location could drastically improve the roll characteristics of the vehicle by increasing the effectiveness of the vertical tails. Tranair offers the capability to apply boundary layers around the vehicle surfaces to give a good indication of drag. As strong vortical effects are present around any highly swept slender wing aircraft at low speeds and high angles of attack, adding the boundary layer effects could

7 C yr ACKNOWLEDGMENTS This work was performed within the High Speed Experimental Fly Vehicles - International project fostering International Cooperation on Civil High-Speed Air Transport Research. HEXAFLY-INT, coordinated by ESA-ESTEC, is supported by the EU within the 7th Framework Programme Theme 7 Transport, Contract no.: ACP3-GA Further info on HEXAFLY-INT can be found on int..5 improve the results. Figure 16. C yˆr The pressure distributions shown on Fig. 7 indicates that abrupt flow changes occur around the sharp leading edge. A further investigation into the effect of radius curvature on both the low speed handling qualities as well as the high speed aerodynamic performance of the vehicle is thus warranted. Finally a range of parametric studies will be conducted. Control surfaces will be modelled to determine whether the vehicle can be trimmed and how much control authority will be available to the flight controller. Sufficient control authority will definitely be required to deal with the unstable lateral modes. Variation in the sizing, positioning and dihedral of the vertical tails will also be studied to determine if their positioning can improve the lateral stability without compromising performance at hypersonic speed. An extension of the outboard portion of the wings at the location of the tail will be investigated as this can potentially improve the stability characteristics of the vehicle at low speed without a significant penalty in overall performance. 7. CONCLUSIONS An initial study of an unpowered version of the Hexafly- International vehicle has been presented. The results from the study show that significant deficiencies in the lateral-directional stability characteristics might occur and that this is most likely due to vertical positioning of the c.g. and the significant wing anhedral. However, the vehicle shows a very high longitudinal stability due to the aft positioning of the centre of pressure. The effect of the location of the control surfaces, their size, and the size and positioning of the vertical tails will thus need to be examined in detail to determine how controllable the Hexafly vehicle is. REFERENCES [BG6] J. Bowman and W. Grantham. Low-speed aerodynamic characteristics of a model of a hypersonic research airplance at angles of attack up to 9 for a range of reynolds numbers. Technical report, NASA Technical Note D- 43, 196. [Bow86] K. Bowcutt. Optimization of Hypersonic Waveriders Derived from Cone Flows Including Viscous Effects. PhD thesis, University of Maryland, [ESNR94] T. Eggers, D. Strohmeyer, H. Nickel, and R. Radespiel. Aerodynamic off-design behaviour of integrated waveriders from takeoff up to hypersonic flight. Proceeds of the Second European Symposium on Aerothermodynamics for Space Vehicles, [Hah97] D. Hahne. Evaluation of the low-speed stability and control characteristics of a mach 5.5 waverider concept. Technical report, NASA Technical Memorandum 4756, [HC94] D. Hahne and P. Coe. The low-speed stability and control of three airbreathing transatmospheric vehicles. 32nd Aerospace Sciences Meeting and Exhibit January, [Lon9] L. Long. Off-design performance of hypersonic waveriders. Journal of Aircraft, 27(7): , 199. [MA97] R. Miller and B. Argrow. Subsonic aerodynamics of an osculating cones waverider. AIAA, 35th Aerospace Sciences Meeting and Exhibit, [Ros7] J. Roskam. Airplane Fligth Dynamics and Automatic Flight Controls. Design, Analysis and Research Corporation, 27. [SM] E. Seckel and J. Morris. Technical Report Rep. No. FAA-RD-71-6, Department of Transportation. [TKK11] H. Taguchi, H. Kobayashi, and T. Kojima. Practical waverider with outer wings for the improvement of low-speed aerodynamic performance. 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 211.

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