«by: Alexander M. Benoliel Thesis submitted to the faculty of the Virginia Polytechnic Institute & State University in partial fulfillment of the ...»
2.3 Further Considerations The formation of the leading edge vortex has been shown to be affected by Reynolds number. Furlong and McHugh42 addressed the effect of Reynolds number in their summary of the aerodynamic characteristics of swept wings. They showed that the effect of Reynolds number on the leading edge flow separation was more prominent for wings with airfoil sections having rounded leading edges than sharp leading edges (Fig. 7). The “inflection” lift coefficient used in Fig. 7 refers to the lift coefficient at which there is an increase in lift coefficient due to the formation of a leading edge vortex.
The insensitivity of vortex flow to Reynolds number effects has been shown by a variety of researchers by analysis of force data taken from tests of HSCT planforms14,16,17, 37,43. The variation of Reynolds number for these tests were on the order of about one magnitude. However, Re and Couch16 found that Reynolds number variations during the testing of a SCAT-15F model did affect the measured forces. They found that longitudinal stability decreased with increasing Reynolds number for the configuration equipped with an unswept canard. This effect was found to be a result of the sensitivity to Page 9 Reynolds number of the flow over the canard only and not the wing. Contrary to these results, Furlong and McHugh42 found that Reynolds number effects were small on straight surfaces and more prominent on swept wings. Malcolm and Nelson 44 found that Reynolds number variation affected the position and interaction of the vortex cores in their study of a cranked fighter wing configuration dominated by vortex flow. These effects cast doubt on the validity of low Reynolds number results for wings with cranks or curved leading edges.45
Figure 7. - Effects of Reynolds number on the inflection lift coefficient for wings incorporating round and sharp leading edges.
Λc/4 = 50˚; A = 2.9; λ = 0.625 (ref. 44).
Another factor of concern is the possible effect of the testing techniques used. It was shown by Johnson, Grafton, and Yip46 that obstacles behind the model, such as a strut, can significantly affect the vortex burst angle of attack and thus the measured forces. Wentz and Kohlman35 also found similar results in their investigation of vortex breakdown.
2.4 Pitch-Up Alleviation Other than deflecting the leading edge, few active intervention methods have been developed to reduce or postpone pitch-up behavior. One method is the Pylon Vortex Generator (Fig. 8) investigated by Rao and Johnson.47 The Pylon Vortex Generator creates a streamwise vortex with a rotation opposite that of the leading edge vortex, such that it creates a downwash outboard of the vortex generator. This downwash reduces the effective angle of attack on the outboard wing section to postpone flow separation. The effect of the device is to create nose-down pitching moments at high angles of attack without a large Page 10 drag penalty. Rao and Johnson tested the device on a 74˚ sweep flat plate delta wing with sharp leading edges at subsonic speeds. The effects of the device on pitching moment are shown in Fig. 9 for the vortex generator design shown in Fig. 8 (several designs were tested). Although the severity of pitch-up that this wing experienced was comparatively small (see Fig. 2), the device made a difference. The Pylon Vortex Generator was incorporated in the configuration design of the AST3I Mach 3.0 supersonic transport. 26 On the AST3I, the vortex generator was incorporated into a leading edge notch-flap and was located at the wing crank location. A model of this configuration was tested in a water tunnel to investigate the vortex patterns. Flow visualization studies showed the device created a counter-rotating vortex over the outboard wing section as found by Rao in his investigation.
Figure 9. - Pylon Vortex Generators at 25% and 50% chord (ref.
Page 11 The Pylon Vortex Generator is similar to an engine pylon and the benefits of the device to the longitudinal stability are similar to those described by Shevell for the DC-8.48 It was found that the presence of the engine pylons postponed stall on the outboard wing section of the Douglas DC-8, thus improving the pitching moment characteristics in the stall region. The aft engine DC-9 suffered from similar longitudinal instability problems as the DC-8, but did not have wing mounted engines to alleviate spanwise flow at stall conditions. Engineers experimented with the DC-9 by installing engine pylons on the wings to improve the longitudinal stability of the aircraft in much the same way as they did with the DC-8. The spanwise placement of the device was such that the trailing vortices from the pylons created an upwash on the high horizontal tail, creating a nose-down moment. The pylons were reduced in size, streamlined, and patented as vortilons (vortex generating pylons) and incorporated on all DC-9 aircraft48.
Another means of controlling the pitch-up is spanwise blowing on the outboard wing section. Bradley, Wray and Smith49 tested the effects of blowing on 30˚ and 45˚ sweep delta wings to augment the leading edge vortex. This technique was incorporated by Rao in the test of a 70˚/50˚ sweep uncambered, untwisted wing36. The model tested incorporated a chordwise blowing slot which exhausted over the outboard section of the wing (Fig. 10).
The intent of having a jet of air blown over the outboard wing section was to maintain a stable vortex core, thus producing lift and preventing vortex breakdown from occurring.
Results of the test by Rao are shown in Fig. 11. The investigation of this technique revealed marked improvements in postponing the pitch-up behavior and allowed for increased aileron effectiveness for roll control at high angles of attack for a range of cµ = 0.01 to
0.02. However, this test was performed at a relatively low Reynolds number (Re =
0.8x106). Further testing is required to validate the concept.
3.1 Leading Edge Flap Effects The effect of leading edge flap deflection is to postpone the formation of the leading edge vortex and classical flow separation. This effect is accomplished by deflecting the control surface to an angle such that the local leading edge incidence to the oncoming flow is zero.8 As shown in Fig. 12, the effect of deflecting the leading edge flap for an uncambered, untwisted wing with a uniform flap deflection of 30˚ is to postpone the pitchup behavior while reducing the lift. Coe, et al11 showed that the effects for a cambered and twisted wing with the same leading edge-flap deflection were to change the zero angle of attack lift and pitching moment and had only a small effect on the pitch-up behavior. This was due to the fact that the pitch-up for this configuration was dominated by the influence of the strong inboard vortex.
Figure 12. - Effect of leading edge flap deflection for a 74˚/70.
5˚/60˚ sweep untwisted, uncambered cranked arrow wing similar in planform to the AST-200. (ref. 11).
Several studies have investigated the optimization of flap deflections with the use of multi-segmented flaps to allow for the flow incidence relative to the leading edge to be approximately zero along the entire span. Coe, Huffman, and Fenbert10 found that using a continuously variable leading edge deflection had a favorable effect on the lift/drag ratio compared to an uniformly deflected flap. This effect was only realized if the leading edge Page 13 flap was smoothly faired aerodynamically, which would be difficult mechanically. No significant improvement in the pitch-up characteristics was found for segmented flap compared to the uniformly deflected flap. Fairing the flap had little effect on the lift and pitching moment. Furthermore, the unfaired segmented flap had higher drag values than the faired flap and the uniformly deflected flap, most likely due to the discontinuity between each flap segment.10 The effects of the faired multi-segmented flap are shown in Fig. 13 for a cambered and twisted model. Yip and Parlett19 also tested the effects of deflecting a multi-segmented leading edge flap and presented results for a variety of combinations of flap deflections. They found that deflecting the leading edge did not change the angle of attack at which pitch-up occurred, but it did reduce the magnitude of the pitch-up.
Figure 13. - Effects of a multi-segmented flap for a 74˚/70.
5˚/60˚ sweep cambered and twisted cranked arrow wing planform (ref. 10).
3.2 Trailing Edge Flap Effects Trailing edge flaps are used to produce both an increment in lift and pitching moment. If leading edge flaps are used for low-speed, high angle of attack flight, it is desirable to deflect the trailing edge flaps to recover the lost vortex lift. Due to large root chords on HSCT planforms, trailing edge flaps are often of small chord lengths compared to the local chord, thus limiting their performance. Prediction of trailing edge flap performance becomes critical when designing for adequate control power. Wolowicz and Yancey50 showed that available elevator control power during landing was an issue of concern during flight tests of the North American Rockwell XB-70 aircraft. They found that the actual required deflection angles to trim at landing were approximately 4˚ higher than the predicted values. During one landing the elevator had to be deflected to the maximum down position to trim.
Page 14 Quinto and Paulson51 studied the effects of leading and trailing edge deflection of flaps on the aerodynamics of a 70˚/48.8˚ sweep uncambered, untwisted wing. As shown in Fig. 14, the effects of the trailing edge flap deflection are to shift the lift curve in a positive direction and the pitching moment curve in a negative direction. It can be seen in Fig. 15 that the effect of flap deflection is not linear and the effectiveness decreases with an increase in the angle of attack for the lift. The flap effectiveness for the pitching moment was fairly linear throughout the angle of attack range tested.
The effectiveness of the trailing edge flaps are also dependent on the leading edge contour. Coe and Weston8 found that trailing edge flap effectiveness increased when the leading edge flap was properly deflected such that flow conditions at the leading edge were improved and the flow was attached at the trailing edge. McLemore and Parlett43 found that the effectiveness of the outboard trailing edge flaps was small due to the flow separation on the outboard wing panel. This will impact the roll control concept of the aircraft.
Figure 14. - Trailing edge flap effectiveness for a 70˚/48.
8˚ sweep uncambered, untwisted cranked arrow wing planform with δLE = 20˚ (ref. 51).
Figure 15. - Increments in lift and pitching moment for various trailing edge flap deflections for a 70˚/48.
8˚ sweep flat cranked arrow wing (ref. 51).
Estimation methods used to date that are of relatively low computational time and cost are linear aerodynamic methods. These methods work quite well in the linear aerodynamic range but, as expected, do not accurately predict the aerodynamic forces and moments in relatively high angle of attack regimes where non-linear aerodynamics (i.e.
vortex interaction, vortex burst, and basic flow separation) plays an important role. As shown above, high-sweep, low-aspect ratio configurations can experience non-linear aerodynamic effects at rather low angles of attack, thus reducing the accuracy of basic codes even further.
To increase the prediction accuracy, these codes can be modified to incorporate some type of vortex effect.29,52 A common method used for predicting the effects of leading edge vortices is through the use of variations on the Polhamus suction analogy. 34,53, 54 The premise behind these methods is that for separated flow around the leading edge of a swept wing, the additional normal force due to the suction pressure under the vortex is related to the leading edge thrust for attached flow. The calculated axial leading edge suction force is rotated such that it is normal to the surface. This suction can then be integrated along the span to determine the overall contribution of the leading edge vortex to the lift and drag. Empirical correlation can also be used to locate the position of the vortex core and distribute the contribution chordwise, rather than applying it at just one chordwise point on each spanwise station, to improve the accuracy in the calculation of the moments. 53 The contribution of the side edge vortex can be calculated in a manner similar to the leading edge force determination.55 The side edge force can become an important factor for highly swept wings with large tip chords.
Harry Carlson56,57 has improved the accuracy of prediction methods by using datatheory correlation to estimate the actual attainable thrust of the leading edge taking into account local viscous effects. The method, developed for drag prediction with partially separated flow, calculates the attainable thrust and then applies the remaining thrust as vortex lift through the suction analogy. This method has been employed for wings with leading and trailing edge flaps, and in combination with canard and tail configurations.
With the current linear theory methods available, the contribution of vortex lift can be calculated with relatively good accuracy for many configurations. However, the vortex lift imparted on some planforms, such as cranked arrow planforms, is due to a complex system of multiple vortices which are difficult to model accurately. Current methods do not
where Cl is the 3-D sectional lift coefficient at a particular span station and Λref is the reference sweep angle at that span station. For this method, the reference sweep is chosen to be the mid-chord sweep angle. The vortex lattice code used calculates the normal and axial forces at each spanwise station by integrating the pressures. The sectional lift
coefficient can then be calculated by:
Cl = Cn cosα − Ca sinα (2) where Cn and Ca are, respectively, the 3-D sectional normal and axial force coefficients.
The vortex lift and leading edge thrust effects were unchanged.