Computational Analysis of a Prototype Martian Rotorcraft Experiment

AIAA-2002-2815

1American Institute of Aeronautics and Astronautics

COMPUTATIONAL ANALYSIS OF A PROTOTYPEMARTIAN ROTORCRAFT EXPERIMENT

Kelly J. Corfeld*

Aerospace Engineering DepartmentThe Pennsylvania State University

University Park, PA [email protected]

Roger C. Strawn†

Army/NASA Rotorcraft DivisionArmy Aeroflightdynamics Directorate (AMRDEC)

US Army Aviation and Missile CommandAmes Research Center, Moffett Field, CA

[email protected]

Lyle N. Long‡

Aerospace Engineering DepartmentThe Pennsylvania State University

University Park, PA [email protected]

AbstractThis paper presents Reynolds-averaged Navier-Stokescalculations for a prototype Martian rotorcraft. Thecomputations are intended for comparison with anongoing Mars rotor hover test at NASA Ames ResearchCenter. These computational simulations present a newand challenging problem, since rotors that operate onMars will experience a unique low Reynolds numberand high Mach number environment. Computed resultsfor the 3-D rotor differ substantially from 2-D sectionalcomputations in that the 3-D results exhibit a stall delayphenomenon caused by rotational forces along theblade span. Computational results have yet to becompared to experimental data, but computedperformance predictions match the experimental designgoals fairly well. In addition, the computed resultsprovide a high level of detail in the rotor wake andblade surface aerodynamics. These details provide animportant supplement to the expected experimentalperformance data.

IntroductionRecent NASA efforts have been devoted to the

development of a vehicle for Mars exploration. Anumber of vehicle designs, including a Mars airplaneand balloon designs, have been proposed for use in theexploration of Mars. Land vehicles, such as rovers, andspace orbiters have already been studied. Recently,efforts have been directed towards the development ofvertical lift vehicles, such as helicopters and tilt rotors,for use in Mars exploration.

Why use vertical lift vehicles for the exploration ofMars? They have the same advantages as those onEarth, and have vertical lift capabilities that are notavailable in other Mars exploration vehicles. The abilityto hover, fly at low speeds, and take-off and land atunprepared sites gives vertical lift vehicles anadvantage over other exploration methods such as theMars airplane. Vertical lift vehicles have greater rangeand speed than a land rover, and will not be hamperedby the rugged Martian terrain.

The Army/NASA Rotorcraft Division at NASAAmes Research Center has an ongoing effort to developautonomous rotorcraft for the exploration of Mars.Preliminary studies of the design challenges associatedwith such an aircraft have been detailed in severalpapers1-4. These studies have led to a NASA experimentthat will test a prototype rotor in an environmentalchamber that simulates the atmospheric conditions onMars. Measurements of rotor thrust and torque will bemade and micro-tuft surface flow visualizations on therotor blades are also planned.

* Graduate student, Member AIAA† Research Scientist, Senior Member AIAA‡ Professor, Associate Fellow AIAAThis material is declared a work of the U.S.Government and is not subject to copyrightprotection in the United States.

20th AIAA Applied Aerodynamics Conference24-26 June 2002, St. Louis, Missouri

AIAA 2002-2815

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

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In coordination with these experimental studies, thehover performance of this Mars rotor prototype hasbeen computed using an overset-grid, Navier-StokesCFD flow solver. Such simulations present new andchallenging problems since rotors that operate on Marswill experience low Reynolds numbers and high Machnumbers. These conditions differ considerably fromconventional rotor design points.

One of the objectives of this work is to examinewhether traditional 2-D sectional aerodynamicsmethods can accurately model this Mars rotor problem.These sectional aerodynamics methods have beencalibrated for conventional rotorcraft, where 2-Dassumptions and rotor wake models typically work wellprior to rotor stall. The Mars rotor has a uniquegeometry and will run in flow conditions that areoutside of the validation ranges for 2-D lifting-lineaerodynamics.

Recent 3-D hovering rotor CFD computations haveshown good agreement with experimental performanceresults for conventional rotorcraft5-7. Unlike 2-D basedaerodynamics methods, it is expected that the 3-D CFDmethod should also be able to accurately model theMars rotor.

There is very little data on low Reynolds numberaerodynamics and virtually none where the Machnumber is high. Thus, many questions exist as to howthese blades will perform in a Mars environment. TheNavier-Stokes calculations will complement theexperimental data, providing basic information andvalidated analysis tools for future Mars rotor designs.

The Navier-Stokes solver being used for thisanalysis is OVERFLOW-D8, which was developed bythe Army/NASA Rotorcraft Division under Departmentof Defense funding. The OVERGRID package8 wasused to develop a series of overset structured grids forthe Navier-Stokes CFD analysis. A more detaileddescription of all of this work can be found inReference 9.

Experimental setupThe prototype Mars rotor is currently being tested

at NASA Ames Research Center. The test is beingconducted in a large environmental chamber, which hasthe ability to closely simulate the Mars surfaceatmospheric conditions. A comparison of Earth andMars atmospheric properties is given in Table 110. Thechamber has the ability to match the Mars mean surfaceatmospheric pressure, which allows the experiment tomatch the Mars operating Reynolds number and Machnumber.

Table 1. Comparison of Mean AtmosphericProperties

MARS EARTHDensity (kg/m3) 0.00155 1.23Pressure (Pa) 636 101,300Temperature (K) 214 288Speed of Sound (m/s) 230 340Atmospheric Gases 95% CO2

2.7% N2

78% N2

21% O2

Gamma, γ 1.3 1.4

This proof-of-concept rotor was designed to meetthe challenges of operating in the Martian environment.Rotorcraft operating on Mars will encounter a uniquecombination of low Reynolds number and compressibleflow aerodynamics. The experimental test conditionshave a tip Mach number of 0.65 and a Reynoldsnumber of 50,000, based on tip speed and blade chord.A fairly conventional low Reynolds number airfoilsection (Eppler 38711) was chosen for the experimentalrotor.

Figure 1. Eppler 387 airfoil

Figure 2 shows the Mars rotor hover test stand.Notable features include the low aspect ratio blades andthe 40% root cut out to accommodate blade folding andtelescoping in transport and deployment. Also, theexperimental and computational studies model anisolated rotor only, while the actual design will consistof two coaxial rotors. Table 212 gives the complete listof the Mars rotor specifications.

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Figure 2. Mars Rotor Hover Test

Computational MethodsOVERFLOW-D is a scalable Reynolds-averaged

Navier-Stokes solver that uses overset structured gridsto accommodate complex geometries. OVERFLOW-Dis based on OVERFLOW13, but has been enhanced toallow for moving body applications, facilitate accuracycontrol via solution adaption, and run efficiently onscalable parallel computers. Modifications were alsomade to OVERFLOW-D to facilitate the solution ofhovering rotor problems. These modifications includethe implementation of periodicity and the addition oftwo-cell grid overlaps for increased spatial accuracy5.The Mars rotor calculations for this paper werecomputed using a Lower Upper-Symmetric Gauss-Seidel (LUSGS) scheme with fourth-order central-differencing and local time stepping.

OVERFLOW-D is used in conjunction with theOVERGRID, a software package for overset grid-generation and solution analysis. The package includesthe grid generation tool called OVERGRID, which is agraphical user interface used to generate grid systems.OVERGRID performs numerous operations such aschecking and processing input geometry, generatingsurface and volume grids, analyzing grid quality usingvarious diagnostics, and creating input parameter filesfor the domain connectivity program and the flowsolver.

Table 2. Mars Rotor DescriptionNumber of Blades 4Rotor Diameter 2.438mBlade Root Cut-Out(To simulate bladetelescoping requiredfor storage/transport)

40% blade span

Disk Loading(Nominal ‘1G’)

4 N/m2

Tip Mach Number 0.65Blade Tip ReynoldsNumber

50,000

Thrust Coefficient,CT (Nominal ‘1G’)

0.0108

Mean Blade LiftCoefficient

0.4

Blade Chord 0.3048m (constant) from40% radial station outward

Rotor Solidity 0.191Blade Linear TwistRate

0 deg. out to 40% span;+2.4 to –2.4 deg. from 40 to100% span.

Blade Weight 0.35 kg per bladeFirst FundamentalElastic Modes

1.264 per rev – first flapmode;1.118 per rev – first lagmode;2.310 per rev – first torsion

Outer Blade SpanAirfoil Section

Eppler 387

Spar Section Circular tube withchordwise flat plate stiffener(30% chord)

Blade Construction Airfoil fairing is milledfoam with internal cavities;Circular graphite tube sparacross complete span ofblade;45 deg. graphite chordwiseflat plate stiffeners from 5%to 40% station;fiberglass leading edge capon outer blade sectionairfoil fairing

Rotor HubConfiguration

Rigid/cantilevered hub, withtension/torsion straps, drycontact pitch bearings, andpitch arms at 5% radialstation

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Mars Rotor Grid SystemOVERFLOW-D discretizes the problem domain

into near-body and off-body grids14. The near-bodygrids consist of curvilinear body-fitted meshes tocapture viscous effects over surfaces. The off-bodygrids consist of uniform Cartesian meshes with varyinglevels of resolution. These Cartesian grids allow forhigh accuracy near the rotor surfaces while maintainingcomputational efficiency in the far field. The flowsolver interpolates boundary data between adjacentoverset meshes.

The near-body grid for these calculations consistsof individual body-fitted curvilinear grids for the hub,spar, and rotor blade, as shown in Fig. 3. The near-bodygrids for the single rotor blade contain 1,888,282 gridpoints.

Figure 3. Near-body grid system

The off-body grid system in OVERFLOW-D usesuniform Cartesian grids that surround the near-bodygrids with varying levels of resolution. The gridsbecome coarser as the outer computational boundary isapproached. The off-body grid system for the Marsrotor is shown in Figure 4. The off-body grids contain6,376,292 points that are distributed in four levels ofspacing, where the grid spacing doubles with eachsuccessive level. Figure 4 shows the four off-body gridlevels. The “∆s” represents the grid spacing within levelone, and the corresponding grid spacing for eachsuccessive level is indicated in the figure. This schemeallows the outer grid boundaries to be located far awayfrom the rotor with an efficient distribution of gridpoints.

Periodicity has been implemented inOVERFLOW-D and this allows a four-bladed rotorsystem to be modeled with a single rotor blade. Thus,the size of the computational domain can be reduced by

a factor of four. The total calculation consists of 21total grids and 8,264,574 total grid points.

Figure 4. Off-body grid system

Computational Results

2-Dimensional CalculationsPrior to carrying out the 3-D rotor calculations, a 2-

D Navier-Stokes CFD analysis of the Eppler 387 airfoilwas completed. These 2-D calculations were done usingARC2D, a 2-D Navier-Stokes flow solver15. Thecomputational grid used for these calculations is shownin Figure 5. Fine viscous spacing was used at the wallwith the first grid point located at y+<1 for all of the 2-D and 3-D computations.

ARC2D calculations were initially run at theexperimental conditions of Mach number 0.5(corresponding to the three-quarters span location of therotor blade) and Reynolds number 50,000, for a seriesof angles of attack. Cases were run fully laminar,transitioned and fully turbulent. The transitional caseswere simulated by specifying a turbulent region for allchordwise locations beyond a fixed transition point(typically 25% of chord).

∆∆∆∆s

2∆∆∆∆s

4∆∆∆∆s

8∆∆∆∆s

Rotor

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Figure 5. (a) 2-D grid on Eppler 387 airfoil (b) closeup of grid on Eppler 387 airfoil

Unsteady separated flow was seen for all cases(laminar, transitioned and turbulent), and at all anglesof attack. Figure 6 shows the density contours for thelaminar flow case at zero degrees angle of attack. Notethat unsteady vortices are being shed off the trailingedge of the airfoil.

This unsteadiness is consistent with recentobservations by Mayda et al.16 in a wind turbine airfoilstudy. They found that unsteady calculations on theEppler 387 airfoil resulted in high frequencyunsteadiness. When time averaged, the results agreedwell with experimental data. They also found that thistrailing edge unsteadiness did not cause a large dragpenalty. The transitioned and turbulent cases exhibiteda separated region near the trailing edge of the airfoil.However, the large eddies that were seen in the laminarcase were not present.

Figure 6. Eddies shed off trailing edge of Eppler 387in laminar calculation (density contours)

In addition, ARC2D calculations were alsocompleted for comparison with low Reynolds numberexperimental data obtained for the Eppler 387 airfoil inthe NASA Langley Low-Turbulence Pressure Tunnel(LTPT)11. Figure 7 compares the calculations andexperimental data for a series of Reynolds numbers.

In Fig. 7, the ARC2D calculations match theexperimental data more closely as the Reynolds numberincreases. The cause of this behavior stems from thetransitional flow and separation bubbles that occur atthese low Reynolds numbers. It was not expected thatthe ARC2D calculations would be able to match thedata at transitional Reynolds numbers as this type offlow is typically very difficult to predict. Unfortunately,the Martian rotorcraft will operate at or near thesetransitional Reynolds numbers.

3-Dimensional CalculationsHovering rotor OVERFLOW-D solutions were

computed for a series of collective pitch angles. Caseswere run as fully laminar, transitioned, and fullyturbulent, at a hover tip Mach number of 0.65 and a tipReynolds number of 50,000. As in the ARC2Dcalculations, boundary layer transition was modeled byspecifying turbulent flow in the region aft of aprescribed transition point.

Results for the transition case use an 8.4 degreescollective pitch. This 8.4 degres angle is the estimatedcollective pitch required to produce a thrust coefficientgreater than 0.1 and a hover figure of merit greater than0.4. For rotors, the figure of merit represents the ratio ofideal to actual power required for hover

The 8.3M grid point computations were run on 32processors of an SGI Origin 2000 parallel computer.Overall thrust on the rotor was used as the measure ofconvergence to steady-state for the computation. Allcases, laminar, transitional and turbulent, converged toapproximately the same steady-state thrust coefficient.This steady-state behavior contrasts with theunsteadiness in the 2-dimensional analysis. Figure 8shows a sample convergence plot for a typical case. Thecalculations were run for approximately 30,000iterations, though the thrust showed very little variationafter 15,000 iterations. A single calculation for 30,000iterations required approximately 48 hours on 32 SGIOrigin processors (1536 CPU hours).

(a)

(b)

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Figure 7. Lift coefficient comparison of ARC2Dcalculations and Langley LTPT data

Figure 9 shows a comparison of the pressurecoefficients from the 3-D rotor computations and theLangley LTPT Eppler 387 airfoil (2-D) experiment.Both plots correspond to a lift coefficient of 0.28. It canbe seen that the upper surface pressure coefficients

show poor agreement. This is due to the existence of alaminar separation bubble on the airfoil, as indicated bythe flat region on the plot of the experimental pressurecoefficient. The CFD code used in the 3-D rotorcomputations is unable to predict laminar separationbubbles, so it was not expected that the 3-D calculationswould match the 2-D data. CFD codes, at present, arenot able to predict low Reynolds number aerodynamicsvery well, as we showed with the ARC2D solutions. Anexamination of the flow near the surface of the blade,however, shows that the behavior of the flow may bealtered due to rotational and 3-D effects. Thiseffectively produces a flowfield that appears to besimilar to higher Reynolds number results. Therefore,the calculations may be more accurate than one wouldexpect. In addition, one must be careful in inferring toomuch about rotor performance from 2-D airfoilcalculations or experiments at these low Reynoldsnumbers.

Figure 8. Typical thrust convergence

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1x/c

-Cp

3-D Computation (0.75R)

LTPT data (Re = 60,000, Alpha =0 degrees)

Figure 9. Comparison of pressure coefficient for 3-Dcomputation and LTPT experiment

00.20.40.60.8

11.21.41.6

-5 0 5 10 15Alpha (degrees)

CL

ExperimentalARC2D

00.20.40.60.8

11.21.41.6


CL

ExperimentalARC2D

00.20.40.60.8

11.21.41.6


CL

ExperimentalARC2D

RE = 60K

RE = 100K

RE = 460K

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Examination of the flow field near the bladereveals some interesting flowfield features. Figure 10shows the trailing edge flow details at the three-quarterspan location of the rotor blade for both the laminar andturbulent cases. Both cases exhibit a steady thin regionof separated flow, which is slightly thicker in thelaminar calculation.

Figure 10. Velocity vectors near the trailing edge for(a) laminar and (b) turbulent calculations

Compared to the 2-D calculations, the 3-Dboundary layer is thinner and steadier. Figure 11 showsthe flow on the surface of the blade for both the laminarand turbulent cases. In both cases, rotational and 3-Deffects cause a radial outflow near the blade surface inthe separated regions. This radial outflow extends fromthe blade root to the blade tip, where it is absorbed bythe tip vortex.

The thinning of the boundary layer and radialoutflow are consistent with the stall delay phenomenonthat is often seen in propellers and rotors. Harris18

observed this phenomenon in the 1960’s in a generalstudy of radial flow effects on rotating blades. Sincethen, this phenomenon has been seen, bothexperimentally and computationally, in studiesinvolving tilt-rotor blades18, wind turbine blades19, andhighly twisted rotors20. However, due to the lowReynolds number, the phenomenon seen for the Marsrotor is more pronounced and more extensive than thatseen for the rotors used in these past studies.

In each study where this discrepancy between 2-Dand 3-D predictions occurs, there are two mainobservations: (1) rotational effects allow the flow on thesurface of the blade to remain attached longer and (2)

radial flow due to rotation thins the separated boundarylayer.

The first observation is referred to as stall delay,and this phenomenon is modeled in manycomprehensive rotor analysis codes. In these models,the stall is delayed even when the 2-D airfoil dataindicate stall.

The second observation describes more of a stallmodification than stall delay, and this is the dominantphenomenon for the 3-D Mars rotor calculations. Therotational and 3-D effects on the rotor cause a thinningof the separated boundary layer, which stabilizes theoverall flowfield and accounts for the differencesbetween the unsteady 2-D and steady 3-D computedresults.

Figure 11. Velocity vectors on the blade surface for(a) laminar and (b) turbulent calculations

Figure 12 shows performance predictions for theMars rotor in hover for a series of collective pitchangles. All of the cases, fully laminar, transitioned andfully turbulent, produced approximately the sameperformance results. Note that, while a series of laminarand turbulent cases were completed, only onetransitioned case was run. It seemed unnecessary to runthe transitioned case for the various collective pitchangles due to the similarity in the performance resultsfor the fully laminar and fully turbulent cases.

The design points shown in Figure 12 werecomputed using blade element momentum methods.Note that the computed thrust coefficients and figuresof merit are slightly higher than the design point.

(b)

(a)

(a)

(b)

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Thrust Coefficient

0

0.005

0.01

0.015

0.02

0.025

0 5 10 15Collective Pitch (degrees)

CT

LaminarTurbulentTransitionedDesign

Figure 12. Performance predictions for Mars rotor in hover (Mtip = 0.65,Retip = 50,000). (a) Thrust Coefficient (b) Figure of Merit

Figure of Merit

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15Collective Pitch (degrees)

FM Laminar

TurbulentTransitionedDesign

Figure 13 shows a section of the computed vortexwake system for the Mars rotor. This picture shows thatthe computations have captured a number of individualtip vortices, as well as their corresponding vortexsheets. Also, this vortex wake system exhibits uniquecharacteristics that are not typically seen in rotor wakesystems. Due to the 40% root cut out, a strong rootvortex is present. Also, there is minimal wakecontraction, which probably results from the low discloading and the presence of the root vortices.

Figure 13. Computed vorticity magnitude contourson a cutting plane located 60°°°° behind the rotor blade

Summary and Conclusions

This paper presents Reynolds-averaged Navier-Stokes calculations for a prototype Martian rotorcraft.The first step in this analysis was the creation of anoverset grid system. This grid was used in the presentstudy, and may be used again for future computationalstudies of this rotor system.

Solutions for hovering rotor performance at Marsexperimental flow conditions were produced for aseries of collective pitch angles. These simulationspresent results for a unique operating environment forrotorcraft. Rotors that operate on Mars will experiencelow Reynolds number and high Mach numberaerodynamics, a combination not typically seen inrotorcraft. This is an area that has not yet beeninvestigated until recently, and the CFD results provideinsight into the physics of these flows. In addition, theCFD results have already proven useful as an aid to theexperimentalists in their pre-test planning.

Computational results for the Mars rotor showsignificant three-dimensional effects. Most likely, these3-D effects can’t be modeled in a predictive way with2-D sectional aerodynamics methods. Examples ofthese 3-D effects are the stall modifications due torotation, and the presence of strong root vortices at theblade cutout. These root vortices contributesignificantly to the inflow from the rotor wake and tendto diminish the wake contraction.

In the near future, the computational results will becompared to the experimental data, and thesecomparisons will provide an assessment and validationof these CFD tools for use in future Mars rotor designs.

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The rotor that was designed for the hover test wassimply a proof-of-concept design. Future computationalefforts will test possible design changes in order toimprove performance. In addition, the CFD calculationswill also be useful to help extrapolate the experimentaldata to the true Martian atmosphere.

References

1. Young, L.A., Aiken, E.W., Gulick, V., Manicinelli,R., and Briggs, G.A., “Rotorcraft as Mars Scouts,”2002 IEEE Aerospace Conference, Big Sky, MT,March 2002.

2. Young, L.A. and Aiken, E.W., “Vertical LiftPlanetary Aerial Vehicles: Three Planetary Bodiesand Four Conceptual Design Cases,” EuropeanRotorcraft Forum, September, 2001.

3. Young, L.A., “Vertical Lift – Not Just forTerrestrial Flight,” AHS/AIAA/RaeS/SAEInternational Powered Lift Conference, Arlington,VA, October 2000.

4. Young, L.A., Chen, L.A., Aiken, E.W., and Briggs,G.A., “Design Opportunities and Challenges in theDevelopment of Vertical Lift Planetary AerialVehicles,” American Helicopter Society VerticalLift Aircraft Design Conference, San Francisco,CA, January 2000.

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AIAA Aerospace Sciences Meeting, Reno, NV,Jan. 11-14, 2002.

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9. Corfeld, K.J., “Computational Analysis of aPrototype Martian Rotorcraft Experiment,” M.S.

Thesis, Pennsylvania State University, Departmentof Aerospace Engineering, May 2002.

10. Lodders, K. and Fegley, Jr., B., The PlanetaryScientist’s Companion, Oxford University Press,1998.

11. McGhee, R.J., et al, “Experimental Results for theEppler 387 Airfoil at Low Reynolds Number in theLangley Low-Turbulence Pressure Tunnel,” NASATM-4062, 1988.

12. Young, L.A., Aiken, E.W., Derby, M.R.,Demblewski, R., and Navarette, J., “ExperimentalInvestigation and Demonstration of Rotary-WingTechnologies for Flight in the Atmosphere ofMars,” American Helicopter Society 58th AnnualForum, Montreal, Canada, June 2002.

13. Buning, P.G., Jespersen, D.C., Pulliam, T.H.,Chan, W.M., Slotnick, J.P., Krist, S.E., and Renze,K.J., “OVERFLOW User’s Manual, Version1.8g,” NASA Langley Research Center, March1999.

14. Meakin, R., “Automatic Off-Body Grid Generationfor Domains of Arbitrary Size,” AIAA 2001-2536,15th AIAA CFD Conference, Anaheim, CA, June2001.

15. Pulliam, T., ARC2D V3.00, NASA AmesResearch Center, Copyright 1992.

16. Mayda, E.A. et al, “Bubble Induced Unsteadinesson Wind Turbine Airfoils,” AIAA Wind EnergyConference, Reno, NV, 2002.

17. Harris, F.D., “Preliminary Study of Radial FlowEffects on Rotating Blades,” Journal of theAmerican Helicopter Society, Volume 11, No. 3,1966.

18. Narramore, J.C. and Vermeland, R., “Use ofNavier-Stokes Code to Predict Flow PhenomenaNear Stall as Measured on a 0.658-Scale V-22Tiltrotor Blade,” AIAA 20th Fluid Dynamics,Plasma Dynamics and Lasers Conference, Buffalo,NY, June 1989.

19. Snel, H. and van Holten, Th., “Review of RecentAerodynamics Research on Wind Turbines withRelevance to Rotorcraft,” AGARD FDPSymposium on Aerodynamics and Aeroacousticsof Rotorcraft, Berlin, Germany, 1994.

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20. Yamauchi, G.K. and Johnson, W.R., “Navier-Stokes Calculations for a Highly-Twisted RotorNear Stall,” American Helicopter SocietyAeromechanics Specialists Conference, SanFrancisco, CA, January 1994.

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Computational Analysis of a Prototype Martian Rotorcraft Experiment