Aerodynamic characteristics and near-field trailing vortex of a tip-mounted half-delta wing

The suppression of wingtip vortex and the reduction of lift-induced drag of aircraft wings have continuously posed a challenge to aerodynamicists and fluid dynamists. An excellent review on the airplane trailing vortices is... [ view full abstract ]

The suppression of wingtip vortex and the reduction of lift-induced drag of aircraft wings have continuously posed a challenge to aerodynamicists and fluid dynamists. An excellent review on the airplane trailing vortices is given by [1]. Various passive wingtip vortex control techniques, for example, winglets, spoilers, stub/subwing, and porous tips and leading edges have thus been attempted by researchers elsewhere to modify the strength and structure, including the trajectory, of the tip vortices. More recently, an alternative wingtip vortex control was investigated by [2] through the addition of a slender full-chord half-delta wing mounted to the tip of a static rectangular NACA 0012 wing. Reference [2] further found that the tip vortex generated behind a rectangular NACA 0012 wing was grealty diffused and enlarged by a tip-mounted 65o-sweep half-delta wing (HDW), as a result of the breakdown of the HDW vortex developed on the upper surface of the half-delta wing. The HDW tip vortex control concept was inspired by the pioneering work of [3-5] in which the HDW was attempted to improve the wing lift generating capability. References [4-5] also reported that the lift increment and also the lift-curve slope can be further enhanced by increasing the deflection the HDW, relative to the main wing chord line. Lee and Pereira further noticed that, in addition to the observed changes in the size and strength of the HDW-wing tip vortex, the lowered vorticity level also led to a much reduced lift-induced drag coefficient CDi (= Di/½*ρ∞*u∞^2*S). The HDW tip vortex control concept was inspired by the pioneering work of [3-5] in which the HDW was attempted to improve the wing lift generating capability. References [4-5] also reported that the lift increment and also the lift-curve slope can be further enhanced by increasing the deflection of the HDW, relative to the main wing chord line. Lee and Pereira further noticed that, in addition to the observed changes in the size and strength of the HDW-wing tip vortex, the lowered vorticity level also led to a much reduced lift-induced drag coefficient CDi, calculated via the Maskell method [6]. The reduced CDi also translates into a smaller CD, especially at high CL range, compared to the baseline wing at the same lift condition. Together with the HDW-induced CL increment, the zero-deflection slender full-chord HDW was therefore capable of producing the best CL/CD improvement, compared to the baseline wing, among all the deflections tested (for -10° ≤ δ ≤ +15°). This HDW tip vortex control concept is, however, shadowed by the undesired HDW-induced increase in wing weight and bending moment. A 13.4% and 41.8% increase in the total wing surface area and aspect ratio AR compared to the baseline wing, respectively, for the 65°-sweep HDW wing were produced.
The objective of this investigation was to examine the minimization of the above-mentioned undesired effects on the aerodynamics incurred by the full-chord HDW (with a root chord cr equal to the baseline-wing chord c or cr = c) through the use of small-chord HDWs with cr = 0.5c at Re = 2.45 × 10^5. Small-chord HDWs of different slenderness  ( 50o and 65o) and  were also considered. Special emphasis was placed on the impact of the small-chord HDW, of different Λ, cr and δ, on the near-filed tip vortex at x/c = 2.8 at different angles of attack α . The growth and development of the HDW vortex both along the tip and in the near field of the HDW wing, at α = 10°, was also acquired to better understand the impact of small-chord HDWs on the tip vortex.
The experiment was conducted at a subsonic wind tunnel at McGill University. The CNC-machined NACA 0012 wing model had a chord and span of 28 cm and 50.8 cm respectively. Lift and drag measurements were obtained via a two-component force balance using linear variable differential transducers (LVDTs) and spring steel flexures. The vortex flow structures both along the HDW (for x/c ≤ 1) and in the near field of the HDW wing configuration (for 1 < x/c ≤ 4) were obtained using a miniature seven-hole pressure probe of an outside diameter of 2.8 mm. The lift-induced drag (CDi) was also calculated via the Maskell method.
Figure 1a shows that the presence of full-chord HDWs, with δ = 0°, can produce an increased CL compared to the BW. A 22.4% and 13.4% increase in CL, for example, at α = 10° (a representative medium-α regime) was obtained for the 1c50HDW and 1c65HDW wings. The force-balance measurements also show that full-chord HDWs gave rise to a reduced CD, especially for CL > 0.3 regime, regardless of Λ (see Fig. 1b), and subsequently an improved CL/CD ratio compared to the BW at the same lift condition (Fig. 1c). The 1c50HDW wing, however, produced a lower CD compared to its slender counterpart.
For the cr = 0.5c nonslender HDW (i.e., 0.5c50HDW) wing, the CL increment was consistently lower than its full-chord counterpart while the CD reduction remained comparable. More importantly, the 0.5c50HDW wing was found to produce the best CL/CD performance among all HDWs tested (Fig. 1c). The cause for the observed CD reduction can be examined via the lift-induced drag coefficient CDi computation based on the vw-velocity measurements. Figure 1d shows that the CDi of the 0.5c50HDW wing always had a lower-than-BW value, especially, for the high α or lift regime. The full-chord HDWs, however, produced a further reduction in CDi compared to the cr = 0.5c HDW wing. The 1c65HDW was found to generate the smallest CDi or CDi/CD ratio (Fig. 1e). Figure 5e further indicates that at higher α the total CD is dominated by CDi.
The effect of the size or root chord of the HDW on the aerodynamic characteristics was further investigated by the use of the 0.3c50HDW wing. A 10% increase in CL and 23% decrease in CDi at α = 10° compared to the BW were obtained. The CL/CD, however, remained somewhat inferior to the BW value at the same lift condition. The 0.3c50HDW was also able to produce a reduced CDi similar to that of the 0.5c50HDW wing (see Fig. 1d) and also a CDi/CD ratio comparable to the 1c65HDW wing (see Fig. 1e).
The observed CL increment and CDi reduction achieved by the employment of the 0.3c50HDW, which rendered a 2.1% and 26.6% increase in the total surface area Stotal and aspect ratio AR compared to the BW, deserves some articulations. Generally, AR is illustrative of the efficiency of a wing and also the mitigation of the 3-D effects on wing performance. This is particularly true for rectangular or swept planform wings, where a large AR necessarily means a proportionally large span, thus resulting in a minimized tip vortex effect on the total wing. This minimization comes not directly from the attenuation of the 3-D effects but by instead reducing the proportion of impacted wing area. When dealing with the present 0.3c50HDW wing configuration, the AR should become less representative due to the HDW’s triangular planform. The 2.1% increase in Stotal thus leads to a 26.6% increase in AR. The observed performance increases compared to the BW therefore should not be solely attributed to the AR, since the area impacted by the 3-D effects is virtually unchanged. Instead, the improvement can be, to a larger extent, attributed to a modification of the tip effects. Nevertheless, to reinforce the observed changes in CL, CD, CL/CD and CDi, the tip vortex generated by the small-chord HDW wings with cr ≤ 0.5c are discussed.
Figures 2a-d shows a three dimensional representation of the flowfield of: (a) BW at α = 10°, (b) 1c65HDW wing at α = 10°, (c) 0.5c50HDW at α = 10°, and (d) 0.3c50HDW at α = 10°. The HDW wing configurations are also illustrated in the insets at the upper left corner of the subfigures. Figure 2a shows that the BW tip vortex always remained concentrated and had the highest normalized peak vorticity ζp compared to all the HDW wings tested in the present study. Figure 2b shows that the addition of the full-chord HDWs, however, led to an enlarged and diffused tip vortex with a lower ζp compared to the BW counterpart. The lowered vorticity level can be attributed to the HDW vortex breakdown on the slender half-delta wing surface. Figure 2b further show that at α = 10° the HDW vortex breakdown was observed between x/c = 0.85 and 0.9 (denoted by the large drop in the peak vorticity of the HDW vortex) on the 1c65HDW wing, resulting in a diffused tip vortex.
Figures 2c-d show that the tip vortex generated by HDW wings with cr ≤ 0.5c is characterized by a double-vortex pattern (i.e., the coexistence of a BW vortex, originating from the free tip portion of the rectangular NACA 0012 wing, and a HDW vortex). The BW vortex was also found to be located below the HDW vortex. Meanwhile, the HDW vortex moved toward and engulfed the BW vortex, causing a greatly enlarged and circulation-flow-like tip vortex as α was increased.
In summary, the tip vortex developed behind a rectangular NACA 0012 wing with tip-mounted HDWs, of different Λ, cr and δ, was investigated in a subsonic wind tuunel. The results show that, regardless of Λ, cr and δ, the addition of HDWs always led to an enlarged and diffused tip vortex and increased CL compared to the baseline wing. The near-field vortex flow behind the small-chord HDW, however, exhibited a double-vortex pattern, which interacted and merged with each other as it progressed downstream, forming a circulation-like flow. The smaller the cr of the nonslender HDW the lower the lift-induced drag. The zero-deflection cr = 0.5c nonslender HDW wing produced the largest lift-to-drag ratio among all the HDWs tested.

References
[1] Spalart, P.R., 1998, ”Airplane trailing vortices,” Ann Rev Fluid Mech., 30, pp.107-138.

[2] Lee, T., and Pereira, J., 2013, “Modification of static-wing tip vortex via a slender half-delta wing,” J. Fluids & Struc., 43, pp.1-14.

[3] Staufenbiel, R., and Vitting, T., 1991, “On aircraft wake properties and some methods for stimulating decay and breakdown of tip vortices,” In AGARD Conference Proceedings 494, Vortex Flow Aerodynamics, Advisory Group for Aerospace Research and Development, Neuilly Sur Seine, France.

[4] Nikolic, V.R., 2005, “Movable tip strakes and wing aerodynamics,” J. Aircraft, 42(6), pp.1418-1426.

[5] Nikolic, V.R., 2011, “Optimal Movable Wing Tip Strake,” J. Aircraft, 48(1), pp.335-341.

[6] Maskell, E., 1973, “Progress towards a method for the measurement of the components of the drag of a wing of finite span,” RAE Technical Report 72232.