Computational Aerodynamics in the Design and ...

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Computational Aerodynamics in the Design and Analysis of Ram-Air-Inflated Wings James C. Ross* NASA Ames Research Center, Moffett Field, CA 94035

A systematic application of computational aerodynamics methods is presented for the design and analysis of ram-air-inflated wings. Emphasis is placed on using the least computationally intensive method that adequately models the flows of interest. Twodimentional potential-flow computations provide guidance for minimizing the size of a ram-air inlet for the LS1-0417 airfoil. Two-dimensional Navier-Stokes computations show that a section with the smaller inlet has a significantly higher lift-to-drag ratio than a similar section with a current standard-size inlet. Wind-tunnel tests of wings employing standard- and minimum-size inlets confirm these results.

An analysis method is

presented which is based on a three-dimensional panel method and on computed twodimensional section characteristics. The method accurately computes the percentage difference in the maximum lift-to-drag ratio for the wings tested in the wind tunnel. The absolute performance predictions are higher than the measurements indicate, however. The discrepancy is most likely a result of the deformation of the trailing edge of the inflated parafoils, an effect that is not included in the computations of the section characteristics. Two-dimensional Navier-Stokes results indicate that rounding of the trailing edge significantly reduces the lifting capability of the LS1-0417 airfoil.

Nomenclature AR = aspect ratio = b2/S ANHR = anhedral ratio = Rc/b b

= wing span

c Cd

= section or wing chord length = section drag coefficient = (section drag)/(qS)

CD Cl

= wing drag coefficient = (wing drag)/(qS) = section lift coefficient = (section lift)/(qS)

CL

= wing lift coefficient = (wing lift)/(qS)

2 Cp

= static pressure coefficient = (p - ps)/q

L/D

= lift-to-drag ratio

p ps

= local static pressure = test-section or free-stream static pressure

q

= dynamic pressure = ρV2/2

Re Rc

= reynolds number based on chord = distance to confluence point

S

= wing reference area

V

= wind velocity

x

= chordwise distance measured from leading edge

z α

= vertical distance measured from leading edge = angle of attack

ρ

= air density

Introduction The development of gliding parachutes dates back to the early 1960s when a great deal of work was directed at developing a means of recovering the rocket motors and reentry capsules used in the space program. The early work concentrated on single-surface devices (parawings) which looked more like triangular parachutes than wings.1 These systems operated at relatively low lift-to-drag ratios (L/D ≤ 1.5), which limited their gliding range. The Rogallo wing was an improvement in that it had better glide performance but at the expense of additional rigid or semirigid structure to maintain the leading edge shape.2 The idea of an all-flexible, ram-air-inflated, thick wing was developed in the late 1960s.3,4 This type of wing (commonly referred to as a parafoil) can obtain reasonable gliding performance (L/D ≥ 2.0) while maintaining the nonrigid characteristic that permits it to be packaged and deployed in a manner similar to traditional parachutes. A parafoil consists of two fabric panels which form the upper and lower surfaces of the wing. Fabric ribs are sewn between these surfaces to define the aerodynamic shape. The leading edge is left open to provide the ram-air pressure needed to inflate the wing. Figure 1 is a photograph of a large parafoil in the 80- by 120-Foot Wind Tunnel at Ames Research Center.5 The structures that determine the shape of the wing are the fabric ribs and the support lines. Proper design and placement of the support lines and ribs contribute substantially to the fidelity to which the wing maintains its shape. Since the surfaces are all nonrigid pieces of fabric, there are definite limits to the achievable level of wing-form accuracy.

3 Historically, parafoils have been used for applications in which landing at a predetermined site is critical. Sport parachutists commonly use parafoils for this reason. These wings have an aspect ratio of about 2 and a maximum L/D of about 2. The relatively low gliding performance is not a severe penalty since reliable deployment and good lateral control are the most important features sought in this application. More recently, the sport of paragliding has become popular. In paragliding, the emphasis is on maximizing glide performance while maintaining the ability to stow the wing in a small package. Paragliding is typically done in mountainous regions. The wing is inflated by the wind while the pilot stands on the ground after which the launch is simply a matter of stepping off the mountain. Deployment is therefore much less an issue with paragliders than with parachutists. This shift in emphasis has resulted in paraglider designs specifically aimed at good glide performance. The resulting wings have larger aspect ratios (3 - 4) and higher L/D than gliding parachutes. There is no published data available documenting the performance achieved by the new paragliders, but the observed gliding performance is impressive. Long flights are easily achieved while slope soaring, and thermalling is even possible in strong conditions. The current NASA interest in parafoils is in response to the need for a gliding recovery system for the propulsion and avionics systems of future launch vehicles. Recovering and refurbishing these expensive vehicle systems can significantly reduce the cost of delivering payloads into orbit.6 A successful gliding recovery system for this mission must have sufficient gliding range and wind penetration to reach the desired landing zone. It must also be able to achieve low horizontal and vertical speed for landing in order to minimize damage to the payload and/or passengers. The design of parafoils (and paragliders) has evolved, primarily through a process of trial and error, to their current state of reliable operation. There is still room for significant improvements in gliding performance, but accurate design and analysis tools are needed to achieve this goal. Chatzikonstantinou7 presented a coupled potential-flow/finite-element analysis of non-rigid wings but this level of analysis is relatively rare in the literature. Computational fluid dynamics techniques can provide important insight into the effects of parafoil geometry and into the critical flow features. This paper presents the results of two-dimensional potential-flow and NavierStokes methods as the basis of a design of a minimum-size inlet for a ram-air-inflated airfoil. A method of predicting full-configuration performance is also described. Finally, the effect of trailing-edge distortion caused by the wing inflation is discussed.

4 Minimum Inlet Size Concept The idea of minimizing the inlet opening on parafoils may not be an original one, but the aerodynamic basis of the concept and methods for designing such an inlet have, to the author's knowledge, not been presented in the literature. In order for a parafoil to assume the desired aerodynamic shape, the pressure inside the wing must be higher than the highest pressure on the entire outer surface. To a first approximation, the smallest inlet that insures complete inflation is one that encompasses only the range of stagnation point locations (on a given solid airfoil) for the expected lift conditions. Computational aerodynamics methods provide the means to define this inlet and to estimate the performance gains over more standard designs.

Two-Dimensional Potential-Flow Analysis A parafoil typically operates at lift coefficients (CL) between 0.75 and 1.0. This requires that the section work efficiently at section lift coefficients (Cl) between 0.5 and 1.5. The stagnation point range for these lift coefficients is shown in Fig. 2 for a complete LS1-0417 airfoil. The stagnation points were determined using a two-dimensional panel code, HILIFT.8 Many codes of this type are available and require only a few seconds of computation time on personal computers for a solution at a given angle of attack. The inlet need only encompass the region between the arrows in the figure. As illustrated in Fig. 3, this inlet is significantly smaller than the inlets typically used on parafoils. The minimum inlet has an opening that is 4% of the airfoil chord whereas the standard inlet spans a length of 8.4% of the airfoil chord. From the figure one can imagine that less air should “spill out” around the edges of the smaller inlet, thus making the starting conditions for the outer-surface boundary layers much more benign. More important, by retaining more of the airfoil leading-edge contour as a “solid” surface, the low pressures on the forward-facing fabric surface near the leading edge can significantly reduce the section drag.

Navier-Stokes Analysis In order to obtain an estimate of the effect that inlet size has on the drag of a parafoil section, the two-dimensional, incompressible Navier-Stokes code INS2D was used.9 The computations were performed using a C-grid to discretize the flow field. The far-field boundaries were located a minimum of 10 chord lengths from the airfoil. Since the flow must be computed both interior and exterior to the section, the grid extended from the far field through the airfoil surface into the interior of the section as shown in Fig. 4a. The trailing edge was modeled with a finite thickness to allow the grid lines inside the section to follow the wake cut downstream.

5 A no-slip condition is applied on the line of grid points coincident with the airfoil surface and on the adjacent grid line just inside the surface.

The ram-air inlet is incorporated in the

computation by removing the no-slip condition on the points that occupy the desired inlet opening on the section. In order to minimize changes to the analysis code, a no-slip boundary condition is also applied to the points along the wake cut which are interior to the section. This effectively forms an additional membrane inside the section. Subsequent solutions show that the flow velocity inside the section is very low (much less than 1% of free stream) except in the immediate vicinity of the inlet. The extra membrane inside the section therefore has almost no effect on the solutions. Details of the computational grid near the leading edge of the section are shown in Fig. 4b. The grid for these computations has 150 points around the airfoil surface, 45 points streamwise in the wake region, and 101 points in the outward direction. Twenty of these points in the outward direction are inside the surface of the section. The first row of grid points in the exterior boundary layer are spaced approximately 5 x 10-6 chord length (c) from the airfoil surface. The thickness of the modeled fabric surface is approximately 1 x 10-5 c as is the spacing to the first row of points inside the inner surface. In the analysis, the fabric is assumed to be impermeable. The Baldwin-Barth turbulence model is used in the computations.10 The turbulence model is active on the entire outside surface of the airfoil, while the interior flow is assumed to be laminar. The Baldwin-Barth turbulence model has proven to be accurate for airfoil flows and gives reasonable estimates of maximum lift coefficient for airfoils.10,11 At angles of attack near maximum lift, the non-time-accurate computations show a limit-cycle oscillation in both the section lift and drag coefficients. The oscillations increase in magnitude with angle of attack, and maximum lift occurs when the lift oscillations reach approximately ±20% of the mean lift value. Beyond this angle of attack, the mean lift coefficient either remains constant or decreases. In order to determine the accuracy of the Navier-Stokes solutions, comparisons were made with experimentally measured lift, drag, and surface-pressure distributions for the full LS1-0417 airfoil with no inlet.12 Figure 5a shows the computed and measured pressure distributions for an angle of attack of 4.17° and a Reynolds number of 6 x 106. These computations use the same grid as previously described with no inlet. The shape of the upper-surface pressure distribution is well represented by the computations, but the level of suction is slightly underpredicted up to a Cl of 1.5. Comparisons of measured and computed lift curves (Fig. 5b) show that the lift at a given angle of attack is slightly under predicted by the computations. computed lift is accurate enough for this study of ram-air-inflated wings.

Nevertheless, the

6 Reliable prediction of drag is also required to determine the effect of inlet geometry on airfoil performance. The computed drag polar is compared with the measured polar in Fig. 5c. At low lift coefficients, the drag is significantly underpredicted. However, for lift coefficients between 0.75 and 1.6, the predicted drag is within ±10% of the measured value at a given lift coefficient. This is again sufficient accuracy for this study. The computed performance of the standard- and minimum-inlet sections are compared with that of the basic airfoil in Figs. 6 and 7. The basic airfoil exhibits a Clmax of 1.9 (Fig. 6). Opening a minimum-size inlet in the section reduces the maximum section lift coefficient by 17%, to just over 1.5. The standard inlet reduces Clmax even further to approximately 0.9, a 53% reduction from that of the basic airfoil. The effect on drag, and consequently on L/D, is even more dramatic. Figure 7 shows the computed lift-to-drag ratio versus lift coefficient for the three airfoils. In this case, the predicted maximum L/D is actually increased by the presence of the small inlet (18%). However, the larger inlet decreases the maximum L/D by 65%. Note that the predicted changes in drag are much larger than the error in computed drag for the baseline airfoil, adding credence to the trends cited. The computed pressure distributions for the two inlet geometries are shown in Fig. 8 for an angle of attack of 4°. This is approximately the angle of attack for the maximum L/D for both sections. The differences between the distributions are most apparent near the inlets. The large inlet produces suction spikes on both the upper and lower surfaces where the flow is forced around the edges of the inlet. In contrast, the minimum inlet has almost no sharp suction spike on the upper edge of the inlet and only a small spike on the lower edge. Particle traces generated from the computational results provide useful information about the flow around the inlet. Figures 9a and 9b show particle traces for the standard and minimum inlets, respectively, for a 4° angle of attack. There is a small separation bubble at the upper edge of the inlet of the section with the standard inlet (Fig. 9a) which covers approximately 2% of the airfoil chord. In contrast, the minimum inlet has no upper-edge separation at these conditions (Fig. 9b). Both inlets have separation bubbles on their lower edges, but the bubble is much smaller on the minimum-inlet section. In looking at Fig. 9b, it appears that an even smaller inlet could be used at this lift condition. A smaller inlet might eliminate the separation at the lower edge of the inlet, but would not necessarily maintain the “stagnation point” in the inlet for angles of attack up to Clmax . The inlet is designed for a Cl between 0.5 and 1.5, so this small separation is probably unavoidable; nonetheless, it does not appear to seriously affect the airfoil performance. This analysis shows that an inlet sized to just enclose the range of stagnation

7 points on an airfoil works well and that a two-dimensional potential-flow analysis is sufficiently accurate for use in designing such an inlet.

Three-Dimensional Effects The two-dimensional Navier-Stokes analyses presented above showed significant gains in performance from properly locating and decreasing the size of the ram-air inlet. However, the performance increase realized on an actual wing with a properly sized inlet will be less than the two-dimensional gains. A three-dimensional analysis method is therefore needed to evaluate the overall performance of particular wing designs. Three-dimensional Navier-Stokes computations could, in theory, provide some of this information. At the present time, however, this type of analysis is too time-consuming and user intensive to be a routinely used design tool. A more flexible technique is to compute the induced drag (and span loading) of the wing by using a potential flow method (panel code). The section form drag can then be included using a "striptheory" approach and the computed two-dimensional characteristics of the airfoil. The three-dimensional panel code PMARC13 is used to compute the span loadings and induced drag of representative wings. The induced drag is computed by using a Trefftz-plane analysis which has been shown to be much more accurate than surface-pressure integration in potential-flow analyses.14 The computations allow the wake to roll up into a force-free shape. This is not strictly necessary since the error in the induced drag for rectangular wings is not strongly affected by the wake shape. A three-dimensional analysis is relatively easy to perform by using a variety of existing codes; only a personal computer of modest capability is required. Figure 10 shows the paneled geometry for a wing with an aspect ratio of 3 and an anhedral ratio of 1. The anhedral ratio (ANHR) is defined as the ratio of the wing span to the radius of curvature of the wing in the spanwise direction. This assumes that the wing lies along a circular arc which is a good approximation to the shape of most parafoils. Figure 11 shows the effects of aspect ratio (AR) and anhedral ratio on the inviscid L/D for lift coefficients ranging from 0.5 to 1.0 (neglecting section drag). When the aspect ratio is increased from 3 to 4, the L/D across the entire CL range increases by 33%. This is as expected from wing theory. The effect of anhedral ratio was much less dramatic. When the anhedral ratio was decreased from 1 to 0 (flat wing) the L/D increased by only 6%. For an anhedral ratio of -1 (wing tips up or dihedral), the L/D was nearly identical to that for ANHR = +1. Neither the flat wing nor the wing with dihedral are practical parafoil shapes, since anhedral is required to

8 maintain a stable shape.

These results do show, however, that only a small increase in

performance can be gained by flattening the wing. The three-dimensional analysis was extended to include the effects of viscosity and suspension- line drag in order to estimate the performance of a complete wing. The procedure is to first compute the span loading and induced drag of the wing by using the panel code. The section lift coefficient is computed at 25 spanwise locations on one half of the wing span (symmetry is assumed in the analysis). These local lift coefficients are then used to look up a corresponding section drag coefficient from the two-dimensional computations of the airfoil performance. The section drag coefficients are integrated along the span of the wing and added to the computed induced drag. The drag of the suspension lines is also estimated and included in the total drag. For a wing with an aspect ratio of 3.0, a drag coefficient increment of 0.033 is assumed for the suspension lines (equivalent to a drag area of 8.1 ft2 for a 240 ft2 wing). A more complete estimate of the effect of aspect ratio on wing performance using this analysis is shown in Fig. 12. For these computations, the minimum inlet airfoil performance is used. As shown in Fig. 11, increasing the aspect ratio from 3 to 4 reduces the induced drag by 33%. Because of the overhead of line drag and section drag, the net increase in the maximum L/D is only 15%. In both cases the anhedral ratio was 1. Figure 13 shows the computed effect of inlet size on the L/D of a wing with an aspect ratio of 3 and anhedral ratio of 1. The section drag for the minimum inlet is between 60% and 80% less than that of the standard inlet, but when line drag and induced drag are taken into account, the net increase in the maximum L/D is only 23% for the minimum inlet design. Also apparent in the figure is the effect of the inlet on the attainable maximum lift. In this analysis, maximum lift is defined as the wing lift for which the Cl, for any section on the wing, exceeds the Clmax of the two-dimensional section determined in the Navier-Stokes computations. The effect of inlet size on parafoil performance is demonstrated in wind-tunnel data obtained on two different wings. Both wings had an aspect ratio of 3.0 and an anhedral ratio of 1. One wing had an 8.4%c (standard) inlet and measured 60 feet in span and 20 feet in chord. The other wing had a 4%c (minimum) inlet and measured 9 by 27 ft. These are deflated planform measurements which are also used to compute the reference areas for the two wings (1200 and 243 ft2 respectively). The tests were performed in the 80- by 120-Foot Wind Tunnel at NASA Ames Research Center. The larger wing was part of the Advanced Recovery System program.5 The smaller wing was tested as part of a cooperative research program between NASA Ames Research Center and the U.S. Army Natick Research and Development Center at Natick,

9 Massachusetts. A general description of the mounting system used in both tests is given in Ref. 4. Figure 14 shows the variation in the L/D with lift coefficient for the two wings. The smaller inlet produced a 25% increase in the maximum L/D compared with the standard inlet wing. Maximum lift was also considerably higher (nearly 40%).

No difference in the inflation

characteristics of the two wings was noted during the wind-tunnel tests. The difference in performance between the two wings is not a Reynolds-number effect. Earlier tests of wings with similar geometries but different scales did not show a clear scale effect.15 The percent increase in maximum L/D and Clmax owing to the reduced inlet size from the measurements are very close to what was predicted in the analysis. However, the measured performance of both wings was considerably lower than the predictions indicated. Deformation of the inflated wings, which was not accounted for in the analysis, is the most likely cause of the discrepancy.

Trailing-Edge Deformation Parafoils deform in several ways when they are inflated, the most obvious of which is the puffing out of the upper- and lower-surface fabric between the ribs. This makes the effective airfoil thickness vary in a periodic manner across the span of the wing (see Fig. 1). The spanwise waviness could increase the drag, but the cross flow on these wings is relatively small and should not severely affect the maximum lift. The inlet can also puff out, becoming larger at the mid-point of each cell than it was intended to be. A mesh stitched to the inlet in one of the experiments, to limit the inlet deformation had very little effect on the wing performance. The most likely deformation to have a strong effect on the performance is the rounding of the trailing edge which occurs everywhere except at the rib locations (Fig. 15). Jones and Ames presented data indicating a significant increase in the minimum drag of a NACA 4412 airfoil (ΔCdo ≈ 0.02) when its trailing edge was rounded.16 A preliminary study of the effect of rounding the trailing edge of the LS1-0417 airfoil also showed a strong effect on the lifting capability of the section. In the analysis, the radius of the trailing edge was varied from 0.25% to 2% of the chord. Figure 16 shows the four trailing-edge geometries studied: 0.25% (baseline airfoil), 0.5%, 1%, and 2% chord radius trailing edges. Observations during several wind-tunnel tests (see Fig. 15) indicate that the trailing edge of a parafoil has a trailing-edge radius that varies from near zero at the rib location to approximately 2% of the airfoil chord between the ribs. An O-grid topology is used for these computations. The computations do not include a ram-air inlet, hence the interior of the section contains no grid

10 points. To avoid any effect of the wake-cut boundary condition at the important trailing-edge location, the wake cut in the computational domain is located at approximately the 75% chord position on the lower surface of the airfoil. An example of the grid topology is shown in Fig. 17. The computed effect of increasing trailing-edge radius on the lift of the LS1-0417 airfoil is shown in Fig. 18 for a Reynolds number of 4 x 106. The lift coefficients are based on the actual section chord for each geometry. There is a significant decrease in the lift coefficient at a given angle of attack with increasing trailing-edge radius. Increasing the trailing-edge radius also reduces the maximum lift coefficient. The 2% radius trailing edge reduces the maximum lift by 22% from the baseline value. The computed effect of trailing-edge radius on drag has not been determined as yet, but it is likely to increase the drag significantly over that of the baseline airfoil. This may account for much of the difference between the predicted and measured wing performance (Figs. 13, 14). Figure 19 illustrates the effect of rounding the trailing edge on the chordwise pressure distribution. These results are for α = 4° and Re = 4 x 106. The principal effects are to reduce the trailing-edge loading and the overall lift of the section as the trailing-edge radius is increased. The trailing edge actually makes a negative contribution to the lift when it has a radius of 2% of chord. The biggest problem caused by a rounded trailing edge is that a proper Kutta condition is not imposed. One very effective device used to modify the effective Kutta condition on wings is the Gurney flap.17 A Gurney flap is a flat plate, or tab, of the order of 1% of the airfoil chord, attached perpendicular to the lower surface of an airfoil near the trailing edge. It forces the flow to separate from the lower surface with more downward velocity than would be the case without the tab. The tab must carry a drag load so making one out of fabric for a parafoil would be relatively ineffective. Since these tabs are so small, however, it is possible to use the trailingedge seam as a tab by placing it on the lower surface of the parafoil (Fig. 20). Navier-Stokes computations of the flow over airfoils employing Gurney flaps are reliable18,19 so the effect of such a device on a rounded trailing edge should also be predictable. The computed effects of tabs of various heights on the lift of the LS1-0417 airfoil with at 2% radius trailing edge are shown in Fig. 21. Nearly all of the lift lost owing to the rounded trailing edge can be recovered by a tab with a height of only 0.36% of the airfoil chord. Even more lift can be had by increasing the tab height further, but probably at the expense of additional drag.17-19 These are preliminary computational results and a more complete analysis of this concept on parafoil sections with inlets is necessary; however, the potential benefits are significant.

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Concluding Remarks The design of parafoils and paragliders has evolved through trial and error to a relatively refined state. Further improvements in performance can be made, but accurate design and analysis tools will be required. The capabilities of several computational aerodynamics methods have been demonstrated using real-life design issues for parafoils. Two-dimensional, potential-flow computations provide the necessary guidance to design a minimum-size inlet for the LS1-0417 airfoil. The performance benefits that this type of inlet provides over a typical parafoil inlet are illustrated by two-dimensional Navier-Stokes computations. The computed maximum lift of the minimum-inlet section is 75% greater than that for the more standard inlet design. The computed maximum lift-to-drag ratio for the minimum-inlet section is also more than twice that computed for the standard inlet section. A three-dimensional panel code provided a straightforward way to assess the effect of various geometric parameters on wing performance. By computing the induced drag, the effects of aspect ratio and anhedral ratio are easily computed. A strip analysis is used to include the computed drag characteristics of the airfoil and the suspension-line drag. The three-dimensional analysis shows that a 33% decrease in a wing's induced drag only increases the maximum L/D by 15% because of the overhead of section and suspension-line drag. The increase in maximum wing L/D resulting from the use of a minimum versus standard inlet section is only 23% compared with a 75% increase in section L/D because of the overhead of induced and suspension-line drag. Comparisons with experimental data showed that although the threedimensional analysis predicted the relative increase in parafoil performance owing to the minimum inlet, it did not accurately predict the absolute L/D values. The relatively strong effect of trailing-edge deformation appears to be the reason for the inaccurate performance predictions. Observations during the wind-tunnel tests indicate that the trailing edge took on a circular shape with a radius of approximately 2% of the airfoil chord. Two-dimensional Navier-Stokes computations showed that this kind of deformation has a significant effect on the lift generated by the LS1-0417 airfoil. The computations also showed that placing a tab (or fabric seam) with a height of approximately 0.36% of the airfoil chord on the lower surface just forward of the radius at the trailing edge can increase the lift performance to that for a sharp trailing edge. Acknowledgments

12 The author would like to acknowledge the contributions of several co-workers: Paul Askins of NASA Ames Research Center and Fred Elliott of NASA Marshall Space Flight Center for making the wind-tunnel tests a success; Robert Geiger, Bill Wailes, and Robert Golden of Pioneer Aerospace for building and testing a large wing with the LS1-0417 airfoil as part of the Advanced Recovery System program; and James Sadeck of the U.S. Army Natick Research and development center for agreeing to build and test the minimum inlet wing. References 1

Falarski, M. D. and Mort, K. W., "Wind-Tunnel Investigation of Several Large-Scale AllFlexible Parawings," NASA TN D-5708, 1970.

2

Rogallo F. M., "NASA Research on Flexible Wings," presented at International Congress of Subsonic Aeronautics, New York, New York, April 1967.

3

Niccolaides, J. D., "Parafoil Wind-Tunnel Tests," AFFDL-TR-70-146, Air Force Flight Dynamics Laboratory, June 1971.

4

Ware, G. M. and Hassell, J. L. Jr., "Wind-Tunnel Investigation of Ram-Air Inflated AllFlexible Wings of Aspect Ratios 1.0 to 3.0," NASA TM SX-1923, 1969.

5

Geiger, R. H. and Wailes, W. A., "Advanced Recovery System Wind Tunnel Test Report," NASA CR 177563, 1990.

6

Wailes, W., "Advance Recovery Systems for Advance Launch Vehicles (ARS) Phase 1Study Results," AIAA Paper 89-0881, April 1989

7

Chatzikonstantinou, T, "Numerical Analysis of Three-Dimensional Non-rigid Wings," AIAA Paper 89-0907, Apr. 1989.

8

Olson, L. E., James, W. D., and McGowan, P. R., "Theoretical and Experimental Study of the Drag of Single- and Multi-Element Airfoils," Journal of Aircraft, Vol. 16, No. 7, July 1979, pp. 462-469.

9

Rogers, S. E. and Kwak, D., "An Upwind Differencing Scheme for the Time-Accurate Incompressible Navier-Stokes Equations," AIAA Paper 88-2583, June 1988.

10

Baldwin, B., and Barth, T., "A One-Equation Turbulence Transpot Model for High Reynolds Number Wall-Bounded Flows," AIAA paper 91-0610, January 1991, Reno, Nev.

11

Rogers, S. E., Wiltberger, N. L, and Kwak, D., "Efficient Simulation of Incompressible Viscous Flow Over Single- and Multi-Element Airfoils," AIAA Paper 92-0405, January 1992, Reno, Nev.

13 12

McGhee, R. J., and Beasley, W. D., "Low-Speed Aerodynamic Characteristics of a 17Percent Thick Airfoil Section Designed for General Aviation Applications," NASA TN D7428, 1973.

13

Ashby, D. L., Dudley, M. R., Iguchi, S. K., Brown, L. E., and Katz, J., "Potential Flow Theory and Operation Guide for the Panel Code PMARC," NASA TM-102851, 1990.

14

Smith S. C., and Kroo, I. M., "A Closer Look at the Induced Drag of Crescent-Shaped Wings," AIAA Paper 90-3063, Aug. 1990, Portland, Oreg.

15

Ross, J. C., and Olson, M. E., "Experience with Scale Effects in Non-Airplane Wind-Tunnel Testing," AIAA Paper 90-1822, Feb. 1990, Los Angeles, Calif.

16

Jones, R. T. and Ames, M. B. Jr., "Wind-Tunnel Investigation of Control-Surface Characteristics V - The Use of a Beveled Trailing Edge to Reduce the Hinge Moment of a Control Surface," NACA ARR L-464, Mar. 1942.

17

Liebeck, R. H., "Design of Subsonic Airfoils for High Lift," Journal of Aircraft, Vol. 15, No. 9, Sept. 1978, pp. 547-561.

18

Jang, C. S., Ross, J. C., and Cummings, R. M., "Computational Evaluation af an Airfoil with a Gurney Flap," AIAA Paper 92-2708, June 1992, Palo Alto, Calif.

19

Storms, B. L., and Jang, C. S., "Lift Enhancement of an Airfoil Using a Gurney Flap and Vortex Generators," AIAA Paper 93-0647, Jan. 1993, Reno, Nev.

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Figure 1. Photograph of large parafoil flying in the 80- by 120Foot Wind Tunnel at Ames Research Center.

Figure 2. Range of stagnation point on LS1-0417 airfoil for Cl ranging from 0.5 to 1.0 computed using 2-D panel code.

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Figure 3. Sketch of the LS1-0417 airfoil section with "standard" and minimum size inlets.

16

4a. Topology of C-grid for inlet computations.

4b. Details of computational grid near leading edge of airfoil (only every other grid point is shown for clarity) Figure 4. Computational grid used for analysis of 2-D parafoil sections.

17

Figure 5. Comparison of computed and measured pressure distributions on the LS1-0417 airfoil at 4.17° angle of attack and Re = 6x106.

Figure 6. Comparison of computed and measured lift curves for the LS1-0417 airfoil at Re = 6x106.

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Figure 7. Comparison of computed and measured drag versus lift characteristics of the LS1-0417 airfoil for Re = 6x106.

Figure 8. Effect of inlet size on the lift of the LS1-417 airfoil. Computational results, Re = 4x106.

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Figure 9. Effect of inlet size on the lift-to-drag ratio of the LS1-417 airfoil. Computational results, Re = 4x106. -3.0

-2.5 4% inlet

-2.0 -1.5 Cp

8.4% inlet -1.0 -0.50 0.0 0.50 1.0 0

0.2

0.4

0.6 0.8 1 x/c Figure 10. Effect of inlet size on the exterior surface pressure distribution for a ram-air inflated wing section. LS1-0417 section, Re = 4x106, α = 4°.

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Separation bubble

Upper surface Lower surface

Separation bubble 11a. 8.4% inlet, Cl = 0.75.

Upper surface Lower surface

Separation bubble 11b. 4% inlet, Cl = 0.9. Figure 11. Computed particle traces near leading edge of LS1-0417 section with different ram-air inlets operating near maximum L/D condition for Re = 4 x 106.

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Figure 12. Paneled representation of a parafoil without ram-air inlet: AR = 3.0, ANHR = 1.0. 25 AR = 3, ANHR = 1 AR = 3, ANHR = 0 AR = 3, ANHR = -1 AR = 4, ANHR = 1

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L/D 15

10

5 0.5

0.6

0.7

0.8 0.9 1 CL Figure 13. Effects of aspect ratio and anhedral ratio from 3-D potential-flow analysis.

22 10 AR = 4.0 9 8 7 AR = 3.0

L/D 6 5 4 3 2 0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

CL Figure 14. Computed effect of aspect ratio on lift-to-drag ratio including section drag characteristics and line drag ratio. Rectangular planform with minimum-inlet 4% inlet, Re = 4x106.

23

9 4% inlet 8 7

L/D

6 5 8.4% inlet 4 3 2 0

0.2

0.8 1.0 1.2 1.4 CL Figure 15. Computed effect of inlet size on lift-to-drag ratio of a 3-D parafoil: AR = 3, ANHR = 1, Re = 4x106. 5.2 5.0

0.4

0.6

4% inlet

4.8

L/D

4.6 4.4 8.4% inlet

4.2 4.0 3.8 0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

CL Figure 16. Measured effect of inlet size on lift-to-drag ratio of a parafoil: AR = 3.0m, Re = 4x106 and 6x106 for 4%- and 8%-inlet wings, respectively.

24 Figure 17. Rear-quarter view of parafoil flying in 80- by 120Foot Wind Tunnel at NASA Ames Research Center.

2%c radius 1%c radius

0.5%c radius 0.25% radius (baseline)

Figure 18. Detail of trailing-edge radiuses used in analysis.

Figure 19. Computational grid used for analysis of trailinge-edge raduis effects. Only every other computational point shown for clarity.

25

2 Baseline 0.5%c radius

1.5

Cl

1 1%c radius 0.5

2%c radius

0 -5

0

0

0.2

5

10 15 20 25 !, deg. Figure 20. Computed effect of trailing-edge radius on lift curve of LS1-0417 airfoil; Re = 4x106. -1.5 Sharp t.e. 0.5% radius 1% radius -1 2% radius -0.5 Cp 0

0.5

1 0.4

0.6

0.8

1

x/c Figure 21. Effect of trailing-edge radius on chordwise pressure distribution. LS1-0417 airfoil, no ram-air inlet, α = 4°, Re = 4x106.

26

~4% c

Thick seam acting as lift-enhancing tab Figure 22. Seam at trailing edge to serve as a lift-enhancing tab. 2 with 0.74% tab Baseline 1.5

Cl

with 0.36% tab 1

with 0.17% tab 2% radius trailing edge

0.5

0 -5

0

5

10 15 20 25 !, deg. Figure 23. Computed effect of trailing-edge tabs on the lift of an LS1-0417 airfoil with a 2%c trailing-edge radius; Re = 4x106.