A Simple and Usable Wake Vortex Encounter Severity Metric

Transcription

1 A Simple and Usable Wake Vortex Encounter Severity Metric Ivan De Visscher Grégoire Winckelmans WaPT-Wake Prediction Technologies a spin-off company from Université catholique de Louvain (UCL) WakeNet-Europe Workshop st 22 nd April 2015, Amsterdam, The Netherlands

2 Wake Vortex Encounter Rolling Moment Coefficient The RMC is the vortex induced rolling moment on the follower normalized by the follower parameters RRRRRR = 1 2 ρρ VV ff 2 SS ff where MM vv is the induced rolling moment, VV ff is the flight speed, SS ff is the wing surface and is the wing span MM vv SS ff VV ff MM vv b f b l

3 Wake Vortex Encounter Induced Rolling Moment MM vv = ρρ VV ff 2 /2 2 CC ll,αα,eeeeee cc yy Δαα yy yy dddd /2 with CC ll,αα,eeeeee the effective lift slope coefficient, cc yy the chord distribution, and Δαα yy = ww vv(yy) the relative increase of the angle of attack due to the vortex induced VV ff vertical velocity distribution along the span ww vv (yy): Δαα yy = ww vv(yy) = Γ tttttt 1 Γ rr (yy yy vv ) (SS ff, cc(yy)) VV ff VV ff 2ππππ Γ tttttt rr With rr = yy yy vv 2 + zz vv 2 Γ tttttt VV ff b f yy vv zz vv Γ(r)/Γ tttttt b l Γ tttttt

4 Rolling Moment Coefficient (RMC) Γ tot zz v yy v RRRRRR = Γ tttttt CC ll,αα,eeeeee 1 VV ff 2ππ 2 cc ηη cc 1 1 Γ rr (ηη ηη vv ) Γ tttttt [ ηη ηη 2 vv +ζζ 2 ηη ddηη vv ] with ηη = yy, ζζ = zz Hence: RRRRRR = Γ tttttt CC ll,αα,eeeeee VV ff 2ππ FF cc yy cc, Γ rr Γ tttttt, yy vv, zz vv

5 Rolling Moment Coefficient (RMC) RRRRRR = Γ tttttt VV ff CC ll,αα,eeeeee 2ππ FF cc yy cc, Γ rr Γ tttttt, yy vv, zz vv Leading order term Correction function Assumption: centered wake vortex encounter Γ tot

6 Wing chord distribution Assumption: Elliptical chord distribution cc yy cc = 4 ππ 1 yy /2 2 Used for simplicity reason for RMC to be applicable to all aircraft types In RECAT-EU, the sensitivity of RMC to the detailed wing chord distribution was shown to be low

7 Rolling Moment Coefficient (RMC) RRRRRR = Γ tttttt VV ff CC ll,αα,eeeeee 2ππ FF cc yy cc, Γ rr Γ tttttt, yy vv, zz vv Need to take into account the radial distribution of the circulation within the vortex Indeed, typically 50-60% of the circulation lies within a radius of 5% of the generator wing span; the rest of the circulation lies beyond that radius, and with a long tail in the distribution (see, AGARDograph No. 204, Vortex Wakes of Conventional Aircraft, C. du P. Donaldson and A. Bilanin, 1975) Hence, any distribution of circulation has a lengthscale that is proportional to the generator wing span

8 Circulation distribution models Burnham-Hallock (B-H) model: Γ(rr) Γ tttttt = 2 rr bb ll 2 rr +aa bb 2 ll Kaden-Winckelmans (K-W) model : Γ(rr) Γ tttttt = αα rr bb0/2 1+(αα 1) 1/2 rr bb0/2 Modified Betz model : rr with 0 θθ ππ/2 bb ll = 1 8 2αααα sin 2αααα sin αααα, Γ(rr) Γ tttttt = sin θθ

9 Vortex circulation distribution B-H circulation distribution model Γ(rr) Γ tttttt = 2 rr bb ll 2 rr +aa bb 2 ll Simple and commonly used in the WV literature The parameter aa is here taken as justified by: - Literature: typical values range from 0.03 to Energy-based analysis

10 B-H vortex parameter from energy-based analysis Determination of the aa parameter by equating the kinetic energy of the near-wake cross-flow (determined from circulation distribution) to that of the resulting rolled-up two-vortex system made of B-H vortices Example: Elliptic loading EE 0 Γ 0 2 = ππ 8 aa = ss = bb 0 bb ll = ππ 4 G. Winckelmans, I. De Visscher, RMC-based severity metrics: possibilities and scalings, WakeNet-Europe Workshop 2014, Bretigny, France, May 2014

11 Parameter of B-H vortex model Clean configuration : Γ yy Γ 0 = 1 yy bb ll /2 p 1/p Circulation distribution ss aa Elliptic (p=2) π/ Hyper-elliptic (p=2.5) Hyper-elliptic (p=3) Landing configuration : Γ yy Γ 0 = β 1 β 1 yy bb ll /2 yy bb ll /2 p 1 1/p 1, if yy < αα bbll /2 p 1 1/p ββ 1 yy αα bb ll /2 p 2 1 p2, else Circulation distribution ss aa Double hyper-elliptic (p 1 =2.5, p 2 =3) Double hyper-elliptic (p 1 =2.5, p 2 =3.5) with αα = 0.75 and ββ = 0.6

12 Correction Function to be used in the RMC With the B-H vortex model the correction function can be obtained analytically (with aa = 0.035): FF bb ll = 1 2 2aa bb ll 1 + 2aa bb ll 2 2 aa bb ll

13 Sensitivity to the circulation distribution model Case of an elliptical wing Model Parameter ΓΓ(rr = 0.05 bb) ΓΓ tttttt B-H aa = K-W αα = Betz αα = Obtained correction function FF bb ll Model b l /b f =0.5 b l /b f =1.0 b l /b f =1.5 b l /b f =2.0 B-H K-W Betz

14 Sensitivity to the circulation distribution model Case of double hyper-elliptic with p 1 =2.5, p 2 =3 Model Parameter ΓΓ(rr = 0.05 bb) ΓΓ tttttt B-H aa = K-W αα = Betz αα = Obtained correction function FF bb ll Model b l /b f =0.5 b l /b f =1.0 b l /b f =1.5 b l /b f =2.0 B-H K-W Betz

15 Rolling Moment Coefficient (RMC) RRRRRR = Γ tttttt VV ff CC ll,αα,eeeeee 2ππ FF bb ll Need to take into account the effective lift slope coefficient in case of wake vortex encounter

16 Effective lift slope in wake encounter: CC ll,αα,eeeeee Case of an elliptical wing in level flight Uniform effective lift slope along the span (Prandtl correction) AAAA CC ll,αα,eeeeee = CC ll,αα AAAA + 2 UU αα αα dd VV dd Note: the angles are not to scale as εε dd αα. αα ee = αα αα dd AAAA AR + 2 αα

17 Effective lift slope in wake encounter: CC ll,αα,eeeeee Case of a wing in a wake encounter «( ) for the rolling-moment coefficient, the functions ( ) should be based on half of the span of the following wing. It is reasoned that the entire wing is in either an upwash or downwash for maximum lift, but when the maximum rolling moment occurs, only half of the wing is in an upwash and half is in a downwash.» V. J. Rossow (1999), Lift-generated vortex wakes of subsonic transport aircraft, Progress in Aerospace Sciences 35, pp Applying Prandtl correction with half wing aspect ratio : AARR haaaaaaaaaaaaaa = 1 2 b f cc = 1 2 AR CC ll,αα,eeeeee = CC ll,αα AARR haaaaaaaaaaaaaa AARR haaaaaaaaaaaaaa + 2 = CC ll,αα 1 2 AARR = CC 1 ll,αα 2 AAAA + 2 AAAA AAAA + 4

18 Effective lift slope in wake encounter: CC ll,αα,eeeeee Solving Prandtl integral equation Case of an elliptical wing with AAAA from 5 to 20, encountering a B-H vortex with aa b l b f from 2% to 8% and CC ll,αα = 2ππ αα VV ff Γ tttttt Example with AR=10 and aa b l b f = 4% Capart, R., & Winckelmans, G. (2004). Wake vortex induced rolling moment on a follower aircraft, AW-UCL D3. AWIATOR Technical Note, UCL.

19 Effective lift slope A posteriori and global fit of the obtained induced RMC (with CC ll,αα = 2 ππ ) RRRRRR = Γ tttttt VV ff AAAA (AAAA + CC) CC ll,αα 2ππ FF bb ll CC ll,αα,eeeeee 2 ππ For the elliptical wing chord distribution, CC = was consistently obtained. No sensitivity observed to the vortex parameters nor to the wing aspect ratio This value is hence taken for the RMC metric

20 Sensitivity of the CC ll,αα,eeeeee to the wing chord distribution When varying the wing chord distribution and for AAAA varying from 5 to 20, and for aa b l b f = 4% one obtains 4.0 C 4.37

21 Sensitivity of the CC ll,αα,eeeeee to the vortex location When moving the vortex to yy vv b f = 5%, for the various wing chord distributions, for AAAA varying from 5 to 20, and for aa b l b f = 4%, one obtains 3.99 C 4.38

22 Assessment of the metric: RRRRRR = Γ tttttt VV ff AAAA (AAAA+4) FF bb ll Reference data: Airbus flight encounter tests (2011) Leaders: A380 and A346 in landing configuration Followers: A343 and A320 Database contains measurements of Flight speed VV ff Air density ρρ Roll acceleration and corresponding rolling moment MM vv Estimated wake vortex circulation Γ tttttt Estimated minimum distance to vortices Manual quality screening of the data by an independent expert panel (A380 ICAO pilot working group led by EASA) Data selection for metric assessment High quality rated by expert panel «Almost centered» encounters (distance to vortex core < 0.25 b f ) Reasonable estimated circulation (compared to aircraft type)

23 Assessment of the metric: Rolling Moment calculated from RMC vs measurements Best linear fit coefficient: 0.98 MM vv = RRRRRR 1 2 ρρ VV ff 2 SS ff with RRRRRR = Γ tttttt AAAA VV ff AAAA + 4 FF bb ll

24 Assessment of the metric: Rolling Moment calculated from leading order term of RMC vs measurements Best linear fit coefficient: 1.71 MM vv = Γ tttttt VV ff 1 2 ρρ VV ff 2 SS ff Correction function significantly improves the correlation with measured M v

25 Assessment of the metric: Rolling Moment Coefficient from metric vs from measurements Mean deviation: RMS deviation: RRRRRR = Γ tttttt AAAA VV ff AAAA + 4 FF bb ll

26 Assessment of the metric: Rolling Moment Coefficient from leading order term of metric vs from measurements Mean deviation: RMS deviation: RRRRRR = Γ tttttt AAAA VV ff AAAA + 4 FF bb ll When using only the leading order term, differences between aircraft pairs, that are not observed in the experiments, are created

27 Acknowledgment Part of this work was funded by EUROCONTROL in the framework of SESAR P6.8.1 The authors thank AIRBUS for providing access to the experimental flight test data results