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1000 Island Fluids Mechanics Meeting, 2005

1000 Island Fluids Mechanics Meeting, 2005

Introduction

The geometry of a wing tip region has long been known to be of great consequence to the aerodynamic performance of the wing. Early raked tip designs were moderately successful as drag reducing devices. The best early raked tip design reduced drag by seven percent and also improved stability[i]. In the second half of the 20th century, non-planar tip devices, most famously the winglet[ii], were tried, often with the goal of interrupting the trailing vortex formation. Many devices were successful, with the best winglets decreasing drag by up to 20 percent, however increased flow separation, increased bending moment, and adverse affects on stability sometimes result from their use. Recent raked tip designs by the Boeing Company help reduce takeoff field length, increase climb performance and have a demonstrated fuel efficiency improvement of approximately 5.5 percent[iii]. The raked tip designs have been seen as a viable alternative to the winglet, are low cost, low weight, low flutter, removable, and perform acceptably at high and low speeds.

An analysis by Eppler[iv] has suggested that adding a small dihedral angle to the tip region introduces an induced lift component which comes without a drag penalty. As such, for a given lift condition, a wing having tip dihedral and corresponding smaller projected span produces less induced drag than a planar wing having the same length, or wetted area, and greater span. He concluded that positive dihedral induces a negative lift on the wake and therefore a positive lift on the wing, whereas negative dihedral does the opposite.

Gold and Visser[v] experimentally investigated this idea with some unexpected results. Notably, a reduction of induced drag on the order of 3.5 percent was had with a negative 10° dihedral, while no significant change was observed for a positive dihedral of 10°. This is contrary to Eppler’s conclusions. Additionally, dual “wake-like” and “jet-like” characteristics were observed within the vortical wake. A secondary, unexplained inboard vortex was also observed near the tip connection to the base wing.

The focus of the present study was to computationally investigate the raked tip geometry of Gold and Visser with various dihedrals studied in an effort to verify Eppler’s conclusions. In each case, the base geometry and wetted area remains the same, and changes in projected span only occur due to adjustments of the local tip dihedral angle.

Analysis

The Tetrahedral Unstructured Software System (TetrUSS)[vi], featuring the flow solver USM3D[vii],[viii],[ix], developed by the NASA Langley Research Center, was used for Computational Fluid Dynamics (CFD) analysis of the various geometries. USM3D is a second order accurate tetrahedral cell-centered, finite volume Euler and Navier-Stokes flow solver for use with an unstructured mesh.

The surface pressure distribution across the geometry was obtained directly from the Navier-Stokes solution, and can be integrated to obtain a measure of total drag. Since the wetted areas of all geometries are the same, changes in skin friction drag are considered negligible and any reduction in total drag is due to a reduction of induced drag via induced lift. Induced drag was also obtained in this study by Trefftz[x] plane analysis, which is considered more reliable. The Trefftz plane is perpendicular to the flow far downstream of the wing and encompasses the wake region, and computation of drag in this region is based on theories put forth by Betz[xi] and Maskell[xii]. For this research, the Betz and Maskell theories were applied with the Boeing Universal Wake Data Analysis Code, written by Kusunose [xiii].

Results

For each of the geometries, a surface mesh containing nearly 75,000 triangular elements was employed, as was a 1.5mm thick boundary layer with 36 layers and nearly 8 million elements, and a volume mesh containing 1.75 million volume elements. This was the highest resolution mesh that can be solved with the computational resources available. Solution times approach 40 seconds per iteration, and solutions were converged to within tolerances reported by 20,000 iterations. Initial conditions were specified such that the inlet Mach number was 0.3, Reynolds number was 15e6, and angle of attack was 5°. Minor perturbations in the angle of attack are allowed so that for each geometry, the lift coefficient was held at a constant 0.424. This allows for a direct comparison of drag.

The results available from the present study indicate that applying small angles of dihedral to an existing tip region appears to be an effective way to reduce induced drag by inducing a lifting force on the wing. A summary of all aerodynamic loads is given in Table 1. According to the simulation results of Table 1, the largest reduction of induced drag, near 14.7 percent, was had with θ=5°, while significant reductions approaching 12 percent were observed for θ=10° and θ=-10°. Eppler had suggested an optimum angle approaching 10°, however the simulation results suggest that the optimum angle might be lower. The pressure distributions on the lifting side of the wing near the tip for the θ=0° and θ=5° geometries are given in Figure 1. It is seen that even while the total lift was held constant, there is a larger region of higher pressure associated with the dihedral case compared to the planar configuration.

The contribution in drag reduction due to sweep is unclear. Tip sweep studies that include a range of dihedral parameters are necessary to verify Eppler’s finding that increased sweep can enhance the induced lift effect. Additionally, it is also unclear whether positive or negative dihedral has a greater impact. Gold and Visser observed that negative dihedral is far more effective than positive, which is in contrast to Eppler’s conclusions. The current study supports that either positive or negative dihedral is effective. Examination of a wider variety of dihedral angles can offer greater insight, and can lend itself to a more refined optimization study. Such studies are in progress.

Some of the experimental flow features observed by Gold and Visser were not replicated in the current study. The vortex for instance, as can be seen in Figure 2, contained only low velocity features approaching 95 percent of the freestream near the core.

a)  θ = 0°

b)  θ = 5°

Figure 1: Pressure distribution near tip

Figure 2: Tip vortex formation, θ = 10°

There are at least two possible explanations for the discrepancy: either the Gold and Visser instrumentation was sensitive to a moving vortex and interpolated high velocity features that do not exist in reality, or the numerical simulation is not refined sufficiently in either its calculation method or field calculation density to reproduce tiny fluctuations in th steady state flow that could cause high and low velocity features to appear. drag. Also absent is the inboard vortex near the tip connection to the wing. While the Gold and Visser experimental model was manufactured within small tolerances to assure smoothness, it still featured a removable tip with fastening device which could have perturbed the flow and generated rotation. The numerical model, by contrast, is perfectly smooth at the wing-tip juncture. It is unclear whether the inboard vortex from the experimental results is a fundamental effect or artificially generated.

References

[i] Norton, F.H. “An Investigation on the Effect of Raked Wing Tips.” Technical Notes: National Advisory Committee for Aeronautics. No. 69. November, 1921.

[ii] Whitcomb, R. T. “A Design Approach and Selected Wind-Tunnel Results at High Subsonic Speeds for Wing-Tip Mounted Winglets.” NASA TN D-8260, 1976.

[iii] “Aero: Boeing.” Aero, January 2002, No. 17.

[iv] Eppler, R. “Induced Drag and Winglets.” Aerospace Science and Technology, 1997, no.1, 3-15.

[v] Gold, N, and Visser, K. “Aerodynamic Effects of Local Dihedral on a Raked Wingtip.” AIAA-2002-0831, 40th Aerospace Sciences Meeting and Exhibit, 14-17 January, 2002, Reno, NV.

[vi] Frink, N.T., Pirzadeh, S.Z., Parikh, P., Pandya, M.J., and Khat, M.K. “The NASA Tetrahedral Unstructured Software System (TetrUSS).” The Aeronautical Journal, Vol 104, No 1040. Oct. 2000.

[vii] Frink, N.T. “Upwind Scheme for Solving the Euler Equations on Unstructured Tetrahedral Meshes.” AIAA Journal, Vol 30, No.1. Jan. 1992.

[viii] Frink, N.T. “Tetrahedral Unstructured Navier-Stokes Method for Turbulent Flows.” AIAA Journal, Vol 36, No 11. Nov. 1998.

[ix] Pandya, M.J., and Frink, N.T. “Agglomeration Multigrid for an Unstructured-Grid Flow Solver.” AIAA 2004-0759, 42nd

AIAA Aerospace Sciences Meeting & Exhibit, 5-8 January 2004, Reno, NV.

[x] Trefftz, E. “Prandtlsche Tragflachun-und Propeller Theorein.” Z. Agnew Math. Mech. Vol. 1, 1921.

[xi] Betz, A. “A Method for Direct Determination of Profile Drag.” ZFM Vol 16, 1925 (in German).

[xii] Maskell, E. C. “Progress Towards a Method for the Measurement of the Components of the Drag of a Wing of Finite Span.” RAE Technical Report 72232, 1972.

[xiii] Kusunose, K. “Development of a Universal Wake Survey Data Analysis.” AIAA 97-2294, 15th Applied Aerodynamics Conference, Atlanta, GA, June 23-25, 1997.