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BY DAVID LEDNICER

INTRODUCTIONAdvances in the field of Computa-

tional Fluid Dynamics (CFD) duringthe last three decades have had a majorimpact upon the transportation indus-try. The designer's longtime dream ofbeing able to evaluate the aerodynam-ics of a vehicle without having toconstruct a prototype has become a re-ality, thanks to advances in numericalmethods and computer power. Thisability reduces the technical risk in de-veloping a new design and allowsmore refinement with less effort, andin less time, than was ever possible be-50 APRIL 1997 ———— ——•-

fore. Automobiles, commercial airlin-ers and racing yachts, as examples, allhave had their designs heavily influ-enced by CFD.

First, a little background on theseCFD programs. The primary programused to produce the results that I willpresent here is VSAERO. This programis a product of the company I work for,Analytical Methods, Inc. VSAERO is a"panel method" program, so called be-cause the surface of the body to beanalyzed is represented as a large num-ber of small flat panels. Such programsfirst appeared in the early 1960s, buttheir range of application was very lim-

ited. Succeeding generations, whichwidened the range of application, ap-peared culminating in such programsas VSAERO, which was developed inthe early 1980s. Analytical Methodsdelivered an early version of VSAEROto NASA Ames Research Center in1982; this was subsequently rewrittenand renamed PMARC. PMARC formsthe basis of the CMARC program de-scribed by Peter Garrison in an earlieredition of Sport Aviation. As onemight imagine, VSAERO has evolvedconsiderably since 1982. Currently,over 200 customers in 14 countries areusing this program.

Figure 1 — Surface mesh used tomodel the RV-6

Figure 2 — Calculated surface pres-sure distribution on the RV-6 in cruise."Cool" colors show areas of high pres-sure, while "hot" colors show areas oflow pressure.

Figure 3 — Surface pressure distribu-tion and wake roll-up calculated incruise.

Figure 4 — Boundary layer traces onthe RV-6. The area where the traces dis-appear in front of the windshield denotesa separated region.

Panel methods compute the pres-sure and velocity of flow over thesurface of an aircraft using certainsimplifying assumptions about the be-havior of moving air. Such programsdon't know about aerodynamic phe-nomena such as shock waves.Compressibility corrections can im-prove the results for high speed flight,but if any part of the flowfield goessupersonic, the results are erroneous.Luckily, this limitation will not affectany of the results of my work pre-sented here.

Besides the conditions in the flow-field, the forces on the airplane — lift,side forces, pitching moments, yawingmoments and rolling moments — canbe calculated to a high degree of accu-racy. The forces are found by addingup the surface pressures on individualpanels, while the moments are foundby multiplying the force on each panelby its distance from a reference point,normally the CG location.

Unfortunately, the total drag can'tbe calculated with the same precision.Induced drag can be obtained, but notalways accurately. A reliable estimateof drag due to skin friction is providedby the boundary layer calculations;but neither the pressure drag due toboundary layer thickness nor the dragdue to boundary layer separations andsurface excrescences can be calcu-lated. We can glean clues aboutwhether drag has increased or de-creased after a configuration change,but total drag is still best calculated bya build-up method, or measured inflight test. For a more complete dis-cussion of this problem, see BruceCarmichael's new book Personal Air-craft Drag Reduction.

To model an aircraft, the surface isbroken up into small, four-sided pan-els. On an average configuration, 2500to 5000 panels might be required toaccurately represent the surface. Asone might imagine, this is a time-con-

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Figure 5 — Surface streamlines on the cowl of the RV-6, without propeller effects.The color coding is arranged so that high velocities are shown by "hot" colors, while"cool" colors show low velocities.

Figure 6 — Skin friction distribution calculated on the RV-6. Here, "cool" colorsshow areas of high skin friction, while "hot" colors show areas of low skin friction.Regions of low skin friction near the leading edge of components are from areas oflaminar flow. Other areas of low skin friction are from turbulent boundary layers near-ing separation, or fully separated.

suming process. However, practicehelps and after having modeled over150 different configurations, I can of-ten build a computer model insomewhere between 24 and 40 work-ing hours, given a good description ofthe geometry. Quite often, I omit de-tails such as fixed landing gear becausetheir influence on the overall aircraftaerodynamics is usually minor. Theflows into and out of openings are sim-ulated, however, because they can havea significant impact.

Examples of the use of these meth-ods abound in the aerospace industry.An often quoted instance is that of theGulfstream business jet. The Grum-man Gulfstream II wing, designed in1966, was developed using primitivecomputational aerodynamic methods.This project required wind tunnel testsof 24 different wing shapes in order torealize its full performance potential.Development of the Grumman de-signed Gulfstream III wing, done in1979, made use of more advancedcomputational aerodynamic methods.Only one wind tunnel test was re-

52 APRIL 1997

quired to verify its design. The new de-sign yielded a 3.1% cruise dragreduction, with an estimated $4 millionsaving in development costs thanks tocomputational methods.

A change in powerplants, from theRolls-Royce Spey to the Rolls-RoyceTay, brought about development of theGulfstream IV in 1983. The new en-gines, with 50% greater volume, poseda significant aerodynamic challengebecause of their potential interferencewith wing flow. Computational meth-ods were used once again to redesignthe wing, and wind tunnel test con-firmed that the new design yielded afurther decrease in drag.

The use of these computational toolshas been primarily restricted to the "in-dustrial" sector of the aerospaceindustry. My daily job involves con-sulting work in this area. But I havealways been curious about the aerody-namics of general aviation, homebuiltand historic aircraft, and I feel thatthere is quite a bit to be learned fromstudying them. 1 have prepared manycomputer models of these types of air-craft (on my own t ime) and haveanalyzed them. This article, and I hopesubsequent ones, will present the re-sults of some of these analyses. I hopethe information I present will be usefulto designers, builders and modifiers ofhomebuilt airplanes.

RV-6 ANALYSISThe aircraft we shall look at here is

the Van's Aircraft, Inc. RV-6. Beforean analysis can be done, all of the exte-rior surfaces of the airplane must firstbe modeled on the computer. Thismodeling might sound simple, but try-ing to generate all of these 3-D pointscan be rather d i f f icul t . Luck i ly , Iworked with Steve Barnard on thisproject, and he lent me his RV-6 plans.With this information, it only took meseven or eight evenings to generate amodel on my home PC.

The computer model resembles amesh lying on the surface of the aircraft,as you can see in the accompanying pic-ture (Figurel). The layout of this mesh isnot arbitrary; VSAERO likes somemeshing techniques better than others,and experience plays a major part in thelayout of the grid.

I first did a series of three runs inVSAERO: at zero angle of attack andno elevator deflection; at one degreeangle of attack and no elevator deflec-

Cf

0.00600

Cp Z/C

-1.00 0.4

Body Geometry——Cp UPPER SURFACE""Cp LOWER SURFACE""U UPPER SURF ACE""C'fLOWKR SURFACE

BUTTUNK CUT Y= 60 00

Figure 7 — Two-dimensional cut through the calculated pressure and skin fric-tion distribution on the wing, near midspan.

tion; and at zero angle of attack andwith one degree of elevator deflection.From these I extracted the longitudinal

stability derivatives, which are the re-lationships among angle of attack,elevator deflect ion, l i f t , and nose-

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up/nose-down moments. These deriva-tives allow one to determine the angleof attack and elevator deflection re-quired to trim for a given gross weightand CG location.

The derivatives can also be used tocalculate the stick-fixed neutral point.This is the CG location at which achange in angle of attack produces nochange in nose-up or nose-down mo-ment; it other words, it the point atwhich the airplane's longitudinal sta-bility is zero.

I modeled the RV-6 as a glider,omitting propeller effects. The pro-peller affects longitudinal stability in54 APRIL 1997

two ways. First, the forces produced bythe propeller produce moments aboutthe airplane CG; for a tractor propeller,these are destabilizing. Secondly, theslipstream produced by the propellerinteracts with downstream surfaces toreduce the aircraft's longitudinal sta-b i l i t y . In the case of the RV-6, theneutral point with power on is three to

. four percent of chord forward of theneutral point with power off.

What the pilot senses when flyingthe airplane, however, are the controlforce gradients, which are indicative ofthe aircraft's stick free longitudinalstability. The stick-free neutral point is

Figure 8 — Surface pressure isobarsfor the stock RV-6.

Figure 9 — Surface pressure isobarsfor the modified RV-6.

usually somewhat ahead of the stick-fixed neutral point. To achieveacceptable handling qualities (such asspeed stability), a positive change instick force with increasing load factoris desired; and so the CG needs to bestill farther forward. Experience hasshown that the aft limit on the CG en-velope should be around six to tenpercent of chord forward of the power-off stick-fixed neutral point.

VSAERO placed the RV-6's stick-fixed neutral point at 39.21% of theaircraft 's mean aerodynamic chord(MAC). Factoring in the aforemen-tioned influences, the aft limit on theCG range should be somewhere near29-33% MAC. The published CGrange for the RV-6 is from 1 5% to29% MAC. CAFE flight test resultspublished in Sport Aviation (Septem-ber 1993) reveal that the aircraftexperiences weak positive stick-freelongitudinal stability with the CG lo-cated 26.9% MAC and s l ight lystronger stick free stability at a CG lo-cation of 22% MAC. This weakstability is evidenced by the shallowpositive slope of the elevator stickforce vs. airspeed plot, especially at themore aft location. This is in strongcontrast to the Cessna 152, also shownon the plot, which exhibits strong lon-gitudinal stability, as evidenced by avery positive slope. An extrapolationof the CAFE data given in the articleshows that the point of neutral stick-free stability of the RV-6 is relativelyclose to the aft end of the CG range,indicat ing that destabi l iz ing effectsconsume a little less than 10% MAC.

By adding up the area of all of thesurface panels, a very accurate wettedarea for the entire aircraft (Swet) can befound. 1 have a list of wetted areas, cal-culated by VSAERO, for approximately100 different aircraft. Currently, themanned aircraft on the list with the low-est wetted area is the Rutan/QACQuickie, with only 190.5 square feet;and the largest is the Boeing 747-200,with 30,745 square feet, excluding theengine pylons, which were not mod-eled. The RV-6 was found to have 427.2square feet of wetted area. As the CAFEflight test results show the RV-6 tohave an equivalent flat plate drag area(f) of 2.32 square feet, the CDswet

(f/Swet) of the RV-6 is .0054. Theterm CDswet is regarded as a measureof the aerodynamic "cleanness" of anaircraft . A value of.0054 places theRV-6 in a league with such aircraft asthe NAA P-51 Mustang (.0053),Beechcraft V35 Bonanza (.0054), andRutan Long-EZ (.0055).

Once the angle of attack and eleva-tor deflection required to trim werecalculated for a high gross weight andmid-range CG location, the model wasrun in VSAERO with these values.The resulting surface pressure distribu-tion is shown in the accompanyingpictures (Figures 2-3). The colors arearranged so that the highest pressures(and lowest velocities) have "cool"colors, with the highest or "stagnation"pressure being dark blue. Similarly, thelowest pressures (and highest veloci-ties) are shown by the "hot" colors,with magenta indicating the lowestpressure on the aircraft. As one mightexpect, the lowest pressure occurs pri-mari ly on the upper surface of thewing. The lift that holds the airplaneup is the difference between the lowpressure on the top of the wing and theslightly higher pressure on the bottomof the wing.

VSAERO also generated stream-lines on the surface and calculated theproperties of the boundary layer alongthese streamlines. Several iterationswere run where the boundary layerthickness calculated on each panel wasused to correct the initial flow solutionon that panel. The color coding in thepictures (Figure 4) indicates the skinfriction distribution along the path ofeach streamline. All the boundary lay-ers start off with the very low skinfriction of a laminar boundary layerand quickly transition to the high skinfriction of a turbulent boundary layer.Depending on the pressure gradientsthey are exposed to, most of the bound-ary layers then start to get thicker andtheir surface skin friction decreases asthey near separation.

Several things are immediately ap-parent to the experienced eye. Theboundary layer solution stops in front ofthe windshield. This indicates local flowseparation caused by the steepness of thewindshield, a common occurrence inboth airplanes and cars. Other than this,the surface flowfield appears to be freefrom separations at this flight condition.

The streamlines on the cowl show astrong downwards orientation of the

flow over the carb box (Figure 5 — thecolor coding here is that of velocityalong the streamline). This flow patternwill probably lead to a vortex as theflow leaves the back end of the box.Any vortex formation produces to drag,so this is undesirable.

The RV-6 wing airfoil is a NACA23013.5. The 23000-series airfoils havetheir maximum thickness fairly far for-ward, with the peak suction at roughlythe same spot as the maximum thick-ness. As the laminar boundary layer canbe estimated to transition to turbulent atthis location, one can guess that the RV-6 wing wil l not have much laminarflow. Laminar early transition fromlaminar to turbulent flow can be seen

both in the two-dimensional cut throughthe wing pressure and skin friction dis-tributions, and in the 3D map ofcalculated skin friction (Figure 6). Inthese pictures, "cool" colors (blue) rep-resent high friction and "hot" ones(magenta) indicate low friction. Thecalculated boundary layers start outwith the low drag indicative of a lami-nar boundary layer. They quicklychange to the cool colors of the highfriction turbulent boundary layer. As theturbulent boundary layer progresses aft,the skin friction decreases again, be-cause the turbulent boundary layer isflowing into a region of rising pressure,where it is slowing down and starting toapproach separation. By the time the

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Figure 10 — Distribution of surfacepressure on the modified RV-6.

Figure 11 — Streamlines on the uppersurface of the modified RV-6.

Figure 12 — Streamlines on the lowersurface of the modified RV-6.

/ >"''turbulent boundary layer reaches thetrailing edge of the wing, its skin fric-tion is very low, indicating that it isready to separate. At higher angles ofattack it will separate, increasingly asthe airplane approaches the stall.

A two-dimensional cut through thispressure and skin friction informationon the wing yields more information(Figure 7). Here can be seen the pres-sure (in coefficient form) on the upperand lower surface. In this case, thepressure coefficient is plotted with they axis going backwards — negativepressure coefficient (suction) is up.This is how this information is tradi-tionally presented by acrodynamicists.The difference between the upper andlower surface suction is the lift. Theother two lines are the skin friction onthe two surfaces. Examining thetraces, it can be seen that the skin fric-tion starts high and then drops quitelow in the laminar boundary layer.When the transition to a turbulentboundary layer takes place, the skinfriction suddenly jumps in value. Onlynear the trai l ing edge does the skinfriction start decreasing, as the turbu-lent boundary layer nears separation.

When the pressure distribution onthe upper surface of the wing wasviewed as isobars (lines of constantpressure, like on a weather map) (Fig-ure 8), it was immediately obviousthat the wing suffers from large threedimensional effects. All of the isobarsbehind the peak suction sweep for-ward as one moves out towards thetip. Ideally, the isobars would all beparallel, with no sweep, resulting inthe wing airfoil operating at all span-wise locations as it was designed to intwo dimensions. Such flow distortionsuggests the need for a wing/bodyfair ing. Correctly done, this wil lstraighten out the inboard isobars.

To improve the wing pressure distri-bution, I first designed a new wingtip.My aim straighten out the isobars nearthe tip of the wing, with the constraintsthat the wing span could not be in-creased and that all changes to the tiphad to occur aft of the faired-in naviga-tion light. After three design iterations,the wingtip isobars were now well-

56 APRIL 1997

shaped and the calculated induced drag had decreased.Next, I designed a wing root fairing. I felt that a large

convex obstruction was needed at the wing root to force theisobars forward. After several iterations, I found such ashape, and the calculated induced drag again diminished(Figures 9-10). By contrast, a conventional concave fairingwas found to have little effect on the wing pressure distribu-tion and to produce no improvement in induced drag. Thetraditional concave wing root fairings are not always theway to reduce drag!

Once I had designed the new wing tip and wing root fair-ing, I translated the coordinates into a .DXF file andtransmitted them to Steve Barnard. He used them to cutfoam masters of the shapes and to build new parts for instal-lation on his RV-6. Steve's flight testing snowed that thenew wing tips produced a cruise speed increase of 2 kt,while the wing root fairings produced no change. Perhapsthe increased wetted area of the root fairings is offsetting aninduced drag reduction.

Since the time this work was done, a second after-marketwingtip has appeared for the RV-4 and -6. This tip, whichon inspection appears to be a planar, "plain vanilla" tip, iscredited in side-by-side fly-offs with increasing the topspeed of the RV-6 also by 2 kt. Model ing th is tip inVSAERO confirms that the induced drag is also reduced. Acomparison of the stock tip with this newer tip also shows,however, that the wing span has been increased approxi-mately 10 inches, raising the aircraft's wing aspect ratiofrom 4.81 to 5.17. As induced drag, by a commonly-usedapproximation, varies inversely with the square ofwingspan, it is not surprising that increasing the aircraft'swingspan will have such an effect. Development work onwinglets has shown that it is very hard to match the drag re-duction due to a span increase with a winglet that doesn'tincrease the wingspan.

We have seen here how CFD can be used to analyze theaerodynamics of a sport aircraft. Once problem areas wereidentified, the CFD model was used to determine modifica-tions to improve the aerodynamics. Lastly, flight test wasused to measure the effects of these modifications. In futurearticles, we will look at the aerodynamics of pusher aircraft,canards and historic aircraft.

About the Author 'A little about myself- I'm an aeronautical engineer, spe-

cializing in applied computational fluid dynamics. I got myBSE and MSB at the University of Michigan, where I was astudent of Ed Lesher is. Right out of school, I joined Siko-rsky Aircraft and ended up working there for a bit over fiveyears. I then joined on with John Roncz at his companyGemini Technologies, Inc., working with him to provideaero support to Scaled Composites and Beech Aircraft. Af-ter three years with John, I came out to the Seattle area in1989 to work at Analytical Methods, Inc. I got my VSAEROtraining back in 1984, and have used the program exten-sively in each of my three jobs. Being a Total AviationPerson, I've got my flying license (though I haven't flownin quite a while) and I've helped out in the construction ofseveral homebuilts. Of late, I've been more of an armchairTAP, spending most of my free time modeling aircraft inVSAERO, though this has to share time with my passion forsea kayaking and cross-country skiing. ^

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