Aero Char Light Ac

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machine design, Vol.6(2014) No.3, ISSN 1821-1259 pp. 71-78

*Correspondence Author’s Address: University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16,11120 Belgrade 35, Serbia, [email protected]

Original scientific paper

DETERMINATION OF AERODYNAMIC CHARACTERISTICS OF A LIGHT AIRCRAFT

USING VISCOUS CFD MODELINGZoran STEFANOVIĆ1 - Ivan KOSTIĆ1, * - Olivera KOSTIĆ1

1 University of Belgrade, Faculty of Mechanical Engineering, Belgrade, Serbia

Received (28.04.2014); Revised (16.06.2014); Accepted (19.06.2014)

Abstract: The CFD calculations with included viscous effects represent the latest analyses, aimed for the assessment ofaerodynamic characteristics of a new light airplane. During the evolution of such an aircraft, appropriate calculationmethods should be applied at the different design development stages. The general trend is application of fairly simple,but reliable analytical and semi-empirical methods at the initial stages, combined with simplified - inviscid CFDcomputational models, and complex viscous CFD analyses at its final design levels. At the present stage of light

aviation development, it is assumed that the contemporary design tools for each of those steps should be appropriateenough, so that they actually verify and additionally fine-tune each other's results. Here presented viscous CFDcalculations have been based on the application of unstructured meshes with reasonably small number of elements,

combined with robust physical model, involving RANS k- SST turbulence treatment, which has enabled analyses ataround-critical and post-stall angles of attack. These calculations have provided very useful, both quantitative andqualitative aerodynamic data, while the results for aerodynamic coefficients have shown fair agreements with thoseobtained by methods at previous design levels

Key words: light aircraft, aerodynamic design, viscous CFD calculations, unstructured mesh, RANS k- SST

1.

INTRODUCTION

This paper is primary focused on the latest stage of the

aerodynamic analyses of a new light aircraft (NLA),designed at the Innovation Centre of the Faculty of

Mechanical Engineering, University of Belgrade. This is a

two-seat, single piston-engine trainer, of metal primary

structure, with plastic composite engine cowling, wing

and tail tips, aimed for primary and advanced flight

training under VFR and IFR conditions, aerobatic

training, sport flying, etc. (see Fig. 1.).

From the historical perspective, in the initial stages of the

aerodynamic computational analyses of NLA, a fairly

simple CFD model based on 3D vortex lattice method

(VLM) was used [1, 2]. Such inviscid calculation modelinherently neglected boundary layer influence and

separation effects, so the effectiveness of the flaps and

control surfaces were overestimated at moderate and

higher deflection angles, and parasite drag components

could not be determined. Also, the lift and moment curves

could have been determined only in their linear domains,

and just induced drag polars could be calculated. In order

to overcome these problems and obtain complete final

diagrams, the authors have applied the hybrid method

approach, developed in two directions.

First, to obtain proper effectiveness of flaps and control

surfaces within the CFD calculations, the non-linear

calibration factors had been successfully derived, from

wind tunnel test data of a domestic aircraft of similar

category. They also included the additional circulation

correction parameters, which took into account the

different lifting characteristics and influences of applied

slotted flaps, instead of the plane flaps simulated by VLM

[3, 4]. Second, the parasite drag components, which can

not be obtained by the applied VLM calculations, were

determined using reliable analytical and semi-empirical

methods. These results have been superimposed with the

induced drag values, which VLM successfully calculates

for many combinations of flaps and elevator deflections,

and angles of attack [5].

On the other hand, these methods also have some

inevitable inherent shorcomings: The VLM (also called

the "inviscid CFD") omits viscous effects and can not

verify analytically determined aerodynamic predictions atarround-critical angles of attack; obtained parabolic polars

give minimum drag at zero lift, while actual minimums

are at some small positive lift coefficients, etc.

Due to that, at the final stage of aerodynamic design, with

general aircraft configuration finally "frozen" (Fig. 2.),

aerodynamic analysis required the application of the CFD

model with includes viscous effects, taking into account

both micro and macro-vorticity influences on the

flowfield around the airplane. This way, the whole range

of angles of attack could have been investigated,

including deep stall (beyond critical) angles. Consideringcontrol surfaces, in this paper only flaps deflection cases

have been considered, and all results have been compared

with those obtained by previously applied methods.



Zoran Stefanović, Ivan Kostić, Olivera Kostić: Determination of Aerodynamic Characteristics of a Light Aircraft Using Viscous CFD Modeling ;

Machine Design, Vol.6(2014) No.3, ISSN 1821-1259; pp. 71-78

72

Fig.1. The NLA development: (1) initial conceptualdesign sketch, (2) 3D CAD model, (3) loft for viscous

CFD analyses, (4) airframe used in structural tests, and(5) completely equipped full size airplane mockup

2. THE CFD CALCULATION MODEL WITH

VISCOUS EFFECTS

To generate tree airplane lofts, necessary for the CFDanalyses, the CAD model (Fig. 1. - (2)) has been used,

with flaps deflections of = 0

o

, = 20

o

and = 30

o

. Allother undeflected control surface gaps on the airplane

have been "sealed", in order to reduce the complexity ofthe analyses, without any substantial penalties considering

the overall accuracy of the results. Also, some less

relevant details have been omitted (like spaces betweenshock absorber struts and torque arms, etc.).

In cases with flaps deflected the accurate 3D geometry of

the convergent slot between the single-slotted flaps and

the wing structure had to be modeled (more detailed

information about applied flaps type can also be found in

[3] and [6]). On the NLA, flaps extend from the aileronsto the trapezoidal centerplane segments of the wing (see

Fig. 1. - (3) and Fig. 2.).

Fig.2. Loft for CFD calculations, flaps deflection = 30o

The selection of the meshing method and the applied physical model complexity was based on an optimum

compromise, dictated by the available hardware

resources.

After a certain number of test runs, the optimum choice,

which gave satisfactory outcomes, was based on the

following:

(A) Application of a mesh with reasonably small number

of elements, in this case of the order of 1.000.000

tetrahedral elements for half-model calculations (Fig. 3.),

the exact numbers vary slightly for different flaps

configurations. It should be noted that for very large and

complex configurations, the fine meshes can exceed tens

of millions of elements, but even with very powerful

hardware, the CPU time for a single run might be

measured in hundreds of hours.





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Fig.3. Mesh applied for CFD calculations, in the vicinity

of the model

(B) Application of a very sophisticated calculation

method, capable of dealing with separation effects at high

angles of attack, fully taking into account compressibility

effects (for example, as for transonic 3D flow

calculations, although compressibility influence at the

NLA's cruising Mach number of M = 0.15 is rather

small), etc. Calculation of angles of attack around and

beyond critical has become possible after the RANS

(Reynolds-Averaged Navier-Stokes) k- SST (Shear-

Stress Transport) turbulent model [7], [8], [9] has been

applied, so this model has been adopted as standard for all

calculations.

Since only symmetrical cases have been analyzed, another

reasonable simplification was the analysis of half-models,

instead of full (also see Fig. 3.), while for the visual

presentations, the images were generated using mirroring

option with respect to the plane of symmetry. The

solution convergence had been boosted by the initial

optimum reordering of the mesh domain using the

Reverse Cuthill-McKee method [10], the application of

FMG - the Full Multi-Grid solution initialization at 4

levels [9], [10], and by active solution steering, applying

the automatic optimization of Courant number for the

achieved solution convergence stage. It had been assumed

that the solution for the given angle of attack has

converged when the solution monitors for lift, drag, and

pitching moment coefficients show no change (constant

values) within the last 100 iterations.

By this approach, with the available hardware, the

required CPU time for the convergence of the solutions

per one angle of attack had been reduced to only 1 ÷ 2

hours (longer time required for higher angles of attack).

3. DISCUSSION OF THE RESULTS

The CFD aerodynamic analyses have been performed for

angles of attack [o] ranging from negative, to positive

post-stall values, at Reynolds number MRe ≈ 5.3

calculated with respect to the wing chord, for all flaps

positions (to retain full compatibility of the results,

although such MRe value would be a bit too high for

operational flaps applications). The analyses have

provided very useful quantitative and qualitative results.

3.1. Quantitative Assessments

Obtained numerical results can generally be divided into

“global” and “detailed”, where the most important global

assessments imply the lift coefficient C L, drag coefficientC D and pitching moment coefficient C M about the

nominal CG (center of gravity) position, for the entire

airplane configuration, with flaps at three characteristic

positions (retracted, i.e. = 0o, and deflected to = 20

o

and = 30o).

The results are graphically shown in Fig.'s 4. and 5, and in

Tables 1. ÷ 3.

Fig.4. Diagrams of lift and moment coefficients

for three flaps positions

Presently it has been assumed that these two flaps

positions would satisfy their purpose for take-off and

landing applications, on such a light aircraft (although

with their electric actuator, any angle can be established).





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Fig.5. Polar curves for three flaps positions

Table 1. Calculated aerodynamic coefficients for = 0o

[o] C D C L C M C L / C D

-4 0.05003 -0.184 0.1212 -3.67

0 0.04429 0.192 0.0446 4.34

3 0.05214 0.477 -0.0088 9.15

6 0.07032 0.760 -0.0571 10.81

10 0.10976 1.122 -0.1184 10.22

14 0.16689 1.438 -0.1863 8.62

15 0.18233 1.468 -0.2106 8.05

16 0.20091 1.431 -0.2621 7.12

18 0.27813 1.280 -0.4380 4.60

Table 2. Calculated aerodynamic coefficients for = 20o


-5 0.06143 0.023 0.1064 0.38

-3 0.05949 0.212 0.0655 3.57

0 0.06516 0.495 0.0066 7.59

5 0.09564 0.958 -0.0823 10.01

10 0.15023 1.376 -0.1603 9.16

12 0.17666 1.496 -0.1980 8.47

13 0.19100 1.531 -0.2253 8.01

14 0.20663 1.534 -0.2540 7.43

16 0.24574 1.481 -0.3434 6.03

Presented results, obtained by CFD analyses, show

moderate increase in maximum lift coefficient with flaps

deflection. With the applied flaps design and deflections,the configuration fully satisfies the EASA CS-23regulation requirements considering minimum speeds.

The influence of flaps is more important considering theairplane's stall characteristics (Fig. 4.). Namely, without

flaps deflection, CFD calculations indicate rather abruptstall, which presents no particular problem at normal

flying altitudes. On the other hand, during the landing phase, flaps deflections change it to smooth and sustained

stall behavior, specially at = 30o. This is of primaryimportance in case of student pilots, whose judgment of

ground proximity before touch down might be poor - evenwhen at minimum speed, the airplane will smoothly glide

towards the ground.

Table 3. Calculated aerodynamic coefficients for = 30 o


-7 0.07960 -0.049 0.1299 -0.61

-4 0.07476 0.237 0.0688 3.17

0 0.08373 0.611 -0.0091 7.29

4 0.10905 0.979 -0.0816 8.98

8 0.14968 1.326 -0.1459 8.86

11 0.18903 1.556 -0.1907 8.2312 0.20273 1.616 -0.2065 7.97

13 0.21559 1.619 -0.2368 7.51

14 0.23141 1.618 -0.2636 6.99

15 0.24912 1.599 -0.3050 6.42

16 0.29063 1.383 -0.3785 4.76

The assessed maximum value of (C L / C D) max ≈ 11 is

quite realistic and satisfactory for light aircraft of metaldesign (values in the range of 10 ÷ 12 are most commonly

reported by pilots in operational use, for such airplane

category).The detailed numerical results imply that each of thecoefficients shown in Tables 1. ÷ 3. can be divided intoseparate contributions of the airplane loft members, alsocalled the zones, or "named selections". Table 4. providesan example of the detailed contributions to the drag

coefficient C D = 0.20273, obtained for = 30o and angle

of attack = 12o (see also Table 3.).

Table 4. Detailed contributions to total drag coefficient,

for = 12 o and = 30 o (number of decimal digits is shown as provided by the software)

Zone Pressure Viscous Totalflap 0.061359989 0.000577269 0.061937259

wing 0.091292484 0.009768767 0.101061250

nose leg 0.001511985 5.11388e-05 0.001563124

main leg 0.005003766 0.000163604 0.005167371

fuselage 0.017627113 0.006439333 0.024066446

horiz. tail 0.005470524 0.001742480 0.007213005

vert. tail 0.000730859 0.000993846 0.001724705

Total 0.18299672 0.01973644 0.20273316

3.2. Qualitative assessments

The most relevant qualitative characteristics of theairplane design have been obtained using flow pattern

(represented by eddy viscosity) and pressure distributionvisualization tools (Fig. 6.).





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Fig.6. Examples of flow pattern (eddy viscosity - left), and

pressure (right) visualizations, = 6 o and = 0 o

In this sense, the CFD post-processing tools provide

information which are, at least, of the same relevance as

those obtained by the wind tunnel visualization

techniques. It must be kept in mind that the applied CFD

calculation method had previously been thoroughly tested

and verified by comparisons with the relevant

experimental data, used for the so called “software

parameter calibration” purposes.Figure 7. shows the flow field pattern development for

flaps-retracted configuration, and angles of attack ≥ 10o.

The eddy, or vortex generated viscosity visualization

gives the most relevant insight in the flow characteristics

around, and behind the airplane. Small red colored

domains in Fig. 7. – (3) indicate initial separation, which

occurs close to the wing roots (also see point ”3” on C L –

diagram), at the critical angle of attack of cr = 15o,

where maximum lift coefficient is achieved. One degree

more, at = 16o, the separated flow intensity obviously

drastically increases, indicating the airplane’s tendency of

rather abrupt stall with flaps retracted.

Only three degrees beyond critical angle of attack, at =

18o, the airplane is in a deep stall condition, with very

massive separation, which is clearly identified by dark-red

and yellow domains, looking like “fire” coming out of the

wings (actually, these are the zones of very intensive air

turbulence). Very important is the fact that, at this angle

of attack, the bottom side of horizontal tail is out of the

turbulent domain (see Fig. 7. – (5) right). This contributes

to the airplane’s natural tendency for stall recovery, by

pitching the nose down towards smaller, sub-critical

angles of attack, which is very important for training

airplanes. Also, up to about = 14o, the horizontal tail is

also out of the turbulent flow generated by the wing (see

Fig. 7. – (2) left). This way, flow visualization has

confirmed the appropriate positioning of the tail. Fig.7. Quite abrupt stall, occurring with flaps retracted





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Fig.8. Sustained stall with flaps deflected to = 30 o

Figure 8. shows quite different behavior of the airplane in

landing configuration, with flaps deflected to = 30o. The

maximum lift coefficient is reached at about = 12o, and

this value remains practically constant until = 15o (Fig.

8. - (2) ÷ (5)), and after that the airplane drops into a deep

stall (Fig. 8. - (6)). During such sustained stall behavior,

the flow separation, which laterally occurs at the wing-centerplane junction (flaps root section, see Fig. 8.),

longitudinally slowly moves from the trailing edge, for

some 40% chord forward, within 3o of domain. That

keeps most of the wing area still "flyable" in this

range, and as already mentioned, helps student pilots to perform smoother landings, considering their limited

flying experience during the initial flight training stages.

Fig.9. Pressure distribution, flaps at = 30 o , = 12 o





77

This phenomenon can directly be attributed to the appliedslotted flaps type. Through the convergent gap, generated bytheir deflection (again see Fig. 2.), a certain amount of air isaccelerated towards the upper flaps surfaces, where the initialstall begins. This air energizes the flow in the domains whereit tends to separate, suppresses the abrupt stall tendency, and prolongs the generation of maximum lift.

A benefit of the presented visualization procedure, whichshould be additionally emphasized, is the detection oflateral spanwise position of initial flow separation. It isobvious that in both cases, without and with flapsdeflected, it occurs close to the wing root, at the junctionof the outer rectangular wing and the trapezoidalcenterplane sections. Another requirement for primaryflight training airplanes is that the initial stall shouldappear as close to the wing root as possible. In case ofasymmetric stalling conditions, where flow over one sideof the wing separates before the other (in sideslip, withsideways wind gusts, etc.), such an airplane will showlittle tendency to roll-over and fall into a spin, after stall.

Figure 9. shows the pressure distribution over the loftwith flaps fully deflected, calculated with respect to theambient atmospheric pressure at the cruising altitude,taken as zero reference. By this approach, the under- pressure is quantified by negative, and over-pressure by positive values. The under-pressure, seen as bright yellowdomain over the upper wing surface overflows thefuselage in the domain of the canopy, by which this partof the fuselage additionally contributes to a certain extentto the overall lift. It is known that in the presence of wing,the fuselage generates more lift than the same fuselageshape as an isolated body. In the domain of profiled wingtips, which could be treated as very small winglets, the

same low pressure extends all the way to the trailing edge,also improving lift in that part of the wing, etc.

3.3. Comparisons with previous results

The results calculated by here presented CFD model arecompared in Fig.'s 10. and 11. with those obtained bymethods applied in previous design steps [3, 4, 5].Keeping in mind the fact that several principally differentcalculation methods have been applied during threeconsecutive design development stages, the obtainedresults for the NLA’s aerodynamic characteristics showquite fair agreements.Lift coefficient curves give very close values for lift curveslopes for all three configurations. Viscous CFDcalculations provide more optimistic assessments ofmaximum lift coefficient values (higher in all three casesthan obtained by Datcom). The only principal differenceis in stall characteristics – unlike Datcom, the viscousCFD has predicted abrupt stall with flaps retracted, andslow and sustained stall with full flaps extended.Considering pitching moment characteristics, the VLMand viscous CFD results coincide well for all threeconfigurations, where slopes of moment curves define themeasure of airplane’s longitudinal static stability (pitchingmoment had not been analyzed by Datcom).Finally, certain differences in polar curves are readilyexpected. Namely, in hybrid method calculations, polarsare obtained in simplified parabolic forms of the typeC D = A + B CL

2, suitable for performance calculations,

which give minimum drag at zero lift coefficient. Inreality, minimum drag is achieved at certain small positive lift coefficients, as predicted by viscous CFD

calculations. On the other hand, the order of drag valuesat lift coefficients used in standard operational flyingconditions has been mutually confirmed by all methods.

Fig.10. Comparisons of lift and moment curves





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Fig.11. Comparisons of drag polars

4. CONCLUSION

Aerodynamic analyses presented in this paper have been performed using a CFD method which takes into accountviscous, but also compressibility effects (no matter howsmall in case of light aircraft). The calculation model uses

mesh with a reasonably small number of elements, and avery sophisticated physical model, based on the RANS k-

SST equations for turbulence. By this, and applying thehalf-model analysis, the CPU time for calculations ofdifferent angles of attack had been substantially reduced,

while the range of angles of attack had been extended tothe post-stall values, compared with methods applied at

previous design steps. Calculations have provided a vastscope of very useful quantitative and qualitative data.Results obtained by all methods during the aerodynamicdevelopment of NLA, including the latest CFDcalculations, have shown fair agreements for practicalengineering purposes. This way, the requirement postedin contemporary airplane design, that the calculation toolsand methods applied at all different design levels should

generally confirm, supplement and fine-tune each-other,has been satisfied.

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