Publisher’s version / Version de l'éditeur:
Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la
première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.
Questions? Contact the NRC Publications Archive team at
PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.
https://publications-cnrc.canada.ca/fra/droits
L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.
2018 Atmospheric and Space Environments Conference, 2018-06-25
READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE. https://nrc-publications.canada.ca/eng/copyright
NRC Publications Archive Record / Notice des Archives des publications du CNRC :
https://nrc-publications.canada.ca/eng/view/object/?id=86dac926-64dc-46be-836a-20e6e98d803d
https://publications-cnrc.canada.ca/fra/voir/objet/?id=86dac926-64dc-46be-836a-20e6e98d803d
NRC Publications Archive
Archives des publications du CNRC
This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.
For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.
https://doi.org/10.2514/6.2018-2867
Access and use of this website and the material on it are subject to the Terms and Conditions set forth at
Flight measurement of medium category wake vortex characteristics
Wake vortex characteristics from Medium
Category Jet Transports
Anthony P Brown*
National Research Council Canada, Ottawa, Ontario, K1A 0R6
In 2017, the NRC undertook biofuel contrail flight research, using Air Canada
A320/A321 jet transport aircraft as the contrail generators. In measuring the full contrail
cross-section, the NRC CT-133 research aircraft additionally measured the wake vortex
characteristics of the aircraft types, Medium Category jet transports. The vortex cores
tended to be large, compared to the wingspan, and thus more laterally proximate.
Long-wave instability was relatively small Long-wavelength. Short-Long-wave mutual instabilities between
vortices exhibited strong excitation of axial vortex velocity components. Cross-plane
(orthogonal to the vortex axes) contour plots of vortex parameters, particularly
quasi-vorticity, elucidated vortex structural detail. EDR contours were maxima at vortex core
edges, some vortex cores were vented, core edges were warm, and core centres cool.
Surprisingly perhaps the Brunt-Vaisala frequency contours exhibited stratified, rotating
structures to the vortices, delineating Rossby-style spiral structures.
Nomenclature
b trailing vortex generating aircraft wingspan (m)
FA20 NRC Falcon 20 research jet with GE CF700-2D2 engines
Ps static pressure (kPa)
rC vortex core radius (distance from core centre to maximum induced velocity) (m)
t time (sec)
Ta air temperature (degC)
TWV trailing wake vortex domain
V true airspeed, (m/s)
eddy dissipation rate
Γ vortex circulation (m2/s)
ρ density (kg/m3); specifically, ρo is ISA sea-level atmospheric air density, 1.225 kg/m3
I.
INTRODUCTION
HROUGH the course of 2006-2012, the National Research Council Canada undertook high altitude cruising flight wake turbulence flight research projects, using Heavy and Super Category jet transports in overflying cruising flight. Emphases included the measurement of core size, induced velocity peak magnitudes and distributional shapes,, instability modal shapes, vortex lateral separation, circulation distribution, crosswind effect and vortex decay modes.
Since 2012, the NRC has undertaken emissions and contrail flight studies. These have used a technique of holistic measurement of contrail cross-sections, including the trailing wake vortex regions of aircraft wakes. Thus, wake vortex characteristics during contrail dynamic phases (to the point of vortex decay) have been measured during the course of contrail surveys. Contrail generators, surveyed by the NRC CT-133 sampling aircraft, have
*
Address for correspondence, Flight Research Laboratory, Building U-61, Research Rd, Uplands, Ottawa K1A 0R6 2010, NRC Canada. Anthony.Brown@nrc-cnrc.gc.ca Published with Permission by American Institute of Aeronautics and Astronautics.
T
Downloaded by NATIONAL RESEARCH COUNCIL CANADA on May 6, 2019 | http://arc.aiaa.org | DOI: 10.2514/6.2018-2867
2018 Atmospheric and Space Environments Conference June 25-29, 2018, Atlanta, Georgia
10.2514/6.2018-2867 AIAA AVIATION Forum
been the NRC Falcon 20 (FA20), Boeing 777, NASA DC-8, A380, and most recently Air Canada A320/A321 aircraft. Also, wake vortex from an E190 was earlier measured during an emissions flight. The FA20, E190 and A320/321 are Medium Category jet transports, of considerable size differences to each other (wingspan ratio of 2:1) and to Heavy Category aircraft (wingspan ratio 5.2:1). The resultant wake vortex measurements have provided a useful, additional data source to complement Heavy Category wake vortex characteristics. Trailing vortex-pair characteristics are presented and compared with Heavy Category jet vortex characteristics, similarly.
II.
EXPERIMENTAL DETAILS AND MEASUREMENTS MADE BY THE CT-133
HE configuration and instrumentation of the NRC CT-133 is presented in Figure 1, together with the measurement rate capabilities of the measurement sensors. It is seen that the CT-133 was in contrail/emissions measurement configuration. The primary configurational difference for this role was the installation of a pair of underwing sensor pods. The primary effect of the pods, as determined by air-data calibration manoeuvres, was a change in the aircraft static position error correction (PEC) for the static pressure sensed by the CT-133 nose-boom. This measurement is used in the derivation of the CT-133 true airspeed vector, thence the derivation of trailing vortex-induced velocity, by vector-differencing between the true airspeed and inertial vectors, both in earth-reference axes.
Two contrail projects were flown through 2017-2018. The first was sponsored by the Green Aviation R&D Network (GARDN) of the Government of Quebec. The Civil Aviation Alternate Fuels Contrails & Emissions Research (CAAFCER) project used Air Canada (AC) jets in commercial service between Montreal and Toronto as the contrail generators [1]. The AC aircraft were Medium Category A320/321 jets and a B763 Heavy Category jet. Regulated flight separation standards were observed, such that the CT-133 did not obtain clearance to climb or descend to generator altitude, until five nautical miles separation behind the Air Canada jets. This distance was typically one unit of non-dimensional wake vortex time (i.e., Sarpkaya time, t*), with the vortex pair typically descended 100-120 metres (m) by this time.
The second project was the Civil Aviation Alternate Fuels Contrails & Emissions at High-blend Bio-jet (CAAFCEB). On this project the emitter/contrail generator was the NRC Falcon 20 (FA20), a Medium Category business jet configuration [2]. Minimum trailing distance behind the NRC Falcon was approximately 200 metres (approximately 9 FA20 wingspans), whilst the Falcon was at intermediate Mach Number, M, of 0.6. The majority of contrail measurements was made at 0.8M (at which, generated circulation was reduced 25% compared to the lower M), from a minimum trailing, intercept distance of one nautical mile (Nm), 1.85 kilometres (km).
A. Wake vortex characteristics derivation methodology
The contrail measurement flight profiles included numerous wake vortex core traverses. The traverses were evident by the reversal in unsteady wind component vectors. By transforming the flightpath into the vortex
cross-T
Figure 1: NRC CT-133 research jet aeroplane configuration, together with instrumentation depiction and summary.
3
plane i.e. orthogonal to the mean axial direction of the trailing vortices, the unsteady wind vector components were spatially correlated. The resultant arc length related to the vortex core size. In this manner, the vortex core radii, at the times of vortex traverses were derived.
Additionally, observations of the development of possibly-prevalent trailing-pair vortex instability modes were made, for long-wave (Crow) instability and short-wave (elliptical) instability modes. These observations were somewhat complementary to similar observations for Heavy Category jets.
Finally, the methodology of contrail and/or emissions plume depictions, developed by NRC [3]. For this, a number of traverses, typically nine, would be concatenated to form a single contrail cross-section. The flight and concatenation methodology is depicted in Figure 2.
In the end-view of concatenated flight-paths, values of a species parameter were then interpolated over [y z] from the values of relevant species (such as ice particle number density per cc) along the flight-path segments. Contour cross-sectional plots were re-constructed from the interpolated matrix of values. Matlab operators were used for this derivation. If the concatenated flightpath segments included port and starboard vortex core traverses, then vortex-related parameters could be selected for interpolation and contouring. In the A320/A321 trailing vortex study, this was conducted for vortex-induced velocities, pressure, temperature, and quasi-vorticity. Observations were drawn from the resultant crossplane contour plots.
III.
RESULTS AND DISCUSSION OF WAKE VORTEX DATA
IGURE 3 presents a sample of vortex pair sizing and separation. The data is derived from traverses of the trailing vortex pairs of the NRC Falcon 20, Air Canada A320 and an earlier A342 aircraft respectively. All cases were taken from surveys of the aircraft in high altitude cruise, at representative Mach Numbers in the range 0.76-0.82. Such vortex core sizes and separations measured for FA20 and A320/321 aircraft trailing vortices, were assembled, analysed and discussed. This assemblage included the inclusion and comparison of vortex core radii for both Medium Category,, B752 and Heavy/Super Category jet transport aircraft types. Thereafter, contour plots of vortex parameters in the cross-plane are presented and discussed. Finally observations of vortex instability modes are presented and contour plots of vortex state parameters discussed..
A. Vortex core sizes
The examples of Figure 3 reflect wide differences in combinations of vortex core size and separation. At the moments of core traverse, the A342 vortices were of small size (reflecting small radius, r, which often varied with subtly-changing atmospheric conditions, in association with particular instability modes which are stimulated by the atmospheric, and other, conditions). Lateral separation between the vortices, bV, was approximately 35 m, whilst
core scale was approximately 2 m for each of the port and starboard vortices. Thus the ratio of separation to core scale was approximately 17:1, in other words widely-separated vortices.
F
Figure 2: NRC CT-133 flight path (left) isometric view of traverses back-&-forward across the contrail with an inset image of a contrail in the upstream line-of-flight direction, and (right) end-view of the flight-path, looking upstream along the contrail axis, showing the concatenation of flight-path traverses across the contrail, from which a contrail cross-section is re-constructed.
226 228 230 232 234 236 238 240 242 244 -15 -10 -5 0 5 10 15 20
dsa-sum, based upon GS/TRK + mean winds
wc w a w Z wc wa wZ 570 580 590 600 610 620 630 640 -6 -5 -4 -3 -2 -1 0 1 2 3
dsa-sum, crossplane arc distance
wc w a w Z wc wa wZ 3520 3530 3540 3550 3560 3570 3580 3590 -20 -10 0 10 20 30 X: 3533 Y: 22.61
dso-sum, based upon TAS &
wc w a w Z wc wa wZ
Figure 3: examples of trailing vortex pair core crossings, in the enroute condition (M 0.76 to 0.82 range), showing the wide range of combinations of vortex scales and vortex pair separation: examples from (top) NRC Falcon 20, (middle) A320, and (bottom) A342.
5
In a simple vortex model, the extent of mutual induction of velocities, ΔVT at inner and outer equatorial points
of the core edges, of each vortex upon the other is related by circulation, , to be inversely proportional to the separation and directly proportional to core scale, rC, such that ΔVTinner = +/2(bV-rC) and ΔVTouter = -/2(bV+rC).
This mutual induction is the stimulation of elliptical instability, associated with the circumferential cycling of induced velocity. It is likely thus, that the lower the bV/rC ratio, the greater the elliptical instability excitation. For
the FA20 and A320 examples, the vortex separations were 6 m and 33 m, respectively (wingspans 16 and 34m, respectively). Whilst these separations probably reflect some extent of long-wave instability excitation, vortex core scale sizes are seen to have been, nevertheless, <1 and 5 m, approximately. These reflect approximate bV/rC ratios of
>6:1 and 7:1, substantially less than first case discussed, that of smaller vortex core scales and large wingspan aircraft.
Whilst Figure 3 represented a snapshot of opposite effects, throughout NRC enroute wake vortex core traverse surveys, there has been a range of vortex core-size scales from any single wake survey [4]. Individual vortex core radius derivations were previously conducted for approximately 70 vortex traverses [5], from the principal viewpoint of vortex profile shape (for type classification, such as a Rankine, Lamb-Oseen, Burnham-Hallock, Fabre-Jacquin, etc). High vortex velocities occurred for a range of vortex scales, and for vortex elements of a range of vortex instability modal shapes [6]. When particular vortex instability modes were encountered inflight, the associated vortex scales / strengths, as measured / derived, have also become part of the statistical set of flight data.
The present measurements from Medium Category aircraft (FA20, E190 and A320/321) have been added to this set of Heavy Category jet data. Incidentally, derived B752 vortex core data from 2012 flights has also been added to the data-set. The wingspan, b, division between Medium and Heavy Categories was approximately 42 m. Presently, a so-assembled set of 283 rC data-points has been analysed. The data-set is plotted as rC ~ b and rC/b ~ b in Figure 4.
Fundamentally, for each wingspan, the several wake vortex core traverses made by the CT-133 may not have necessarily captured the full range of vortex element core sizes, but it probably was a reasonably statistical representation. Vortex instability modal shapes could be expected to be deterministic (i.e. discrete states), although spatiotemporally transitioning states could be expected to possess stochastic vortex element sizes, as vorticity discretizes axially in dissipating and reforming coherence. Likewise, it was probable that minima of derived vortex elements related to the minimum resolution of the CT-133 air-data system (approximately 5 cm in the cross-plane, for flow-cosine cross-flow cylinders sensing at 600 Hz).
It is seen (Figure 4) that the maxima rC for each wingspan varied non-monotonically from 5 m at b = [16 38 ] m
to 10 m at b = [44 70 ] m. For each wingspan, the spread of rC was at least one decade, e.g., from10 m to 1 m for
b=50 to 60 m, and generally two decades, e.g., 10 m to <0.1 m for b-60 m. In spite of the wide spread in b, from 16 m to 80 m, a >four-fold ratio, maxima rC varied between 5 and 10 m, only a two-fold ratio. Therefore, the plot of
rC/b ~ b (Figure 4) showed a general, non-monotonic reduction in maxima rC/b with increasing b, from 0.31 at b=16
m to 0.08 at 80 m. Maxima, minima, mean and median values are represented in Figure 5 in semi-logarithmic format, in order to appreciate the full non-dimensional scaling of rC. Mean rC values varied from approximately
10% b for b<45 m, above which the rC reduced, to have been 4% b at b=80 m. Mean and median trends matched
each other. RC minima on the other hand, were similar at high or low b, of values in the range 0.1-1.0% b.
10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 geometric wingspan, b (m) rC ( m ) 10 20 30 40 50 60 70 80 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 geometric wingspan, b (m) r C /b ( m )
Figure 4: plot of all vortex element derived core radii rC, (left) rC and (right) rC/b ~ b, wake generator wingspan.
20 30 40 50 60 70 80 10-3 10-2 10-1 wingspan, b (m) r C /b rC/b maximum minimum mean Median
The frequency of occurrence (fn) of various rC values, in Δb bands was reflected in the histograms of Figure 6. It
is seen that some of the histograms would appear to have had statistically representative bin numbers, perhaps >10, and this occurred for small-sized vortex elements, indicating that they were more prevalently encountered. For these (<25 m and 42<b<50 m), the histograms showed non-monotonically reducing fn with increasing rC.
Other histograms presented a ‘U’ or concave-shaped seemingly, bi-modal fn distribution wherefore, peak fn
occurred at minimum and maximum rC; whilst others had convex-shaped distributions, but with low overall fn in
these Δb ranges, the distributions are not necessarily statistically representative.
Nevertheless, the histograms were cumulatively summed in rC and non-dimensionalised. Thereafter, contour
plots were derived at various non-dimensional cumulative frequency, Cf, values ranging from 0.5-1. The resultant
plots are shown in Figure 7. The contours of rC and rC/b exhibited some high gradients at particular wingspans; for
example, smaller radius at b=38 m and a larger rC at 45 and 65 m, whilst also indicating that small vortex elements
sized <1 m were prevalent at many wingspans, with Cf values of 0.5. The rC/b contour plots highlighted the
reduction in values with increasing wingspan, for Cf =1, rC reduced from 0.28 to 0.08, a similar result to Figure 5.
The association between rC and peak vortex tangential velocity, VTmax , is depicted in the cross-plots of Figure 8.
Generally, as observed, there was an inverse relationship between size and peak induced velocity, in other words, the smallest vortex elements generally had the highest VTmax. Additionally, it is seen that occasional, intermediate
radii exhibited high VTmax. It is likely this related to the vortex element instability state at the moment of
measurement,
The association between VTmax, rC and b is observed in the contour plot of Figure 9. Contour plotting usefully
averages over the plotting domain (in this case, the Matlab contour function has been used, which applied
Delauney triangulation to the contour-forming process). However, given the uncertainty whether all vortex instability modes were spatiotemporally measured in critical modal shapes (for severity of wale vortex encounter effects), the plot was not exhaustive. Nevertheless, with the inclusion of 283 vortices, the plot contained a reasonable representation of vortex size and speed magnitudes. I
Figure 5: semi-log plot of rC/b ~ b, showing the full range of all vortex element derived core radii rC, the envelope (for eight bands of b) of maxima, minima, mean and median values.
7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2 4 6 8 10 12 14 bin centre rC (m) n u m b e r o f o c c u rr e n c e s 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 bin centre rC (m) n u m b e r o f o c c u rr e n c e s 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 bin centre rC (m) n u m b e r o f o c c u rr e n c e s 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 bin centre rC (m) n u m b e r o f o c c u rr e n c e s 0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 bin centre rC (m) n u m b e r o f o c c u rr e n c e s 0 1 2 3 4 5 6 7 8 9 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 bin centre rC (m) n u m b e r o f o c c u rr e n c e s 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 bin centre rC (m) n u m b e r o f o c c u rr e n c e s 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 12 14 16 bin centre rC (m) n u m b e r o f o c c u rr e n c e s wingspan, b (m) c u m u la ti v e f re q u e n c y , n o rm a lis e d
cumulative frequency of occurrence contours
10 20 30 40 50 60 70 80 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1 2 3 4 5 6 7 8 9
Figure 6: histograms of rC (m) in Δb bands (m), (top, left-to-right) b<25 (FA20), 25<b<36 (E190,A320),
26<b<42 (B752); (middle, L-R), 42<b<50 (B763,DC-8,A310), 50<b<62 (A330,A342,B788,,A343,B772), 62<b<66 (B773,B744); (bottom, L-R), 66<b<70 (B748), 70<b<80 (A388).
Figure 7: contour plots of rC (left) and rC/b (right) plotted against wingspan and normalized cumulative frequency. wingspan, b (m) c u m u la ti v e f re q u e n c y , n o rm a lis e d
cumulative frequency of occurrence contours
10 20 30 40 50 60 70 80 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.05 0.1 0.15 0.2 0.25
0 2 4 6 8 10 12 0 5 10 15 20 25 30 35 40 r C (m) VT m a x (m /s ) 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 35 40 b (m) VT m a x (m /s ) wingspan, b (m) lo g1 0 (rC ) (m )
maximum induced velocity (m/s)
10 20 30 40 50 60 70 80 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30 35
geometric mean wing chord, c (m)
lo g10 (rC ) (m )
maximum induced velocity (m/s)
2 3 4 5 6 7 8 9 10 11 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30 35
t is seen that vortex induced velocities >15 m/s for b>40 m, and >20 m/s (roughly airframe design requirement limit discrete gust magnitude – for a 1-cos shaped gust only – for b>44 m. Peak contoured VTmax values were
50<b<60 m, although the extent of severe gustiness occurred at increasing rC with increasing b.
In this discussion, generated ([120<GEN<800] m2/s) has not been yet considered for normalization.
Measurements were typically made enroute, for t*>1, wherefore instability modes were prevalent and for weights near maximum landing weight (with a smaller number of near top-of-climb cruise measurements at lower height, namely 9 km in lieu of 12-13 km). Also, jet transport cruise efficiency is governed by the Brueget range formula, for which a constant cruise lift coefficient CL is approximately maintained. Given that, crusiing W=½V2SCL, then
for any cruise weight VW/(SV). Given =W/(VbV), thence SV/bV. Generally, cruise Mach, 0.78<M<0.84.
Under the assumption Vconstant, S/bV becomes a generalized relationship. Thus, it is also worthwhile to
consider cross-plots of VTmax against S/bV (approximately S/b, or geometric mean chord, c). A contour plot of
VTmax against [rC c] is included in Figure 9. It is seen that this has broadened the region of high VTmax>20 m/s,
namely c>6 m. For enroute cruise, this relationship might be worthwhile of further investigation. Figure 8: association between peak induced
velocity VTmax and rC (left), and wingspan (right).
Figure 9: contour plot of peak induced velocity VTmax over the rC and (left) b domain, and (right) c domain; Note, rC is present in log10(rC) format to amplify the region of highest VTmax, i.e. rC<100.6=4 m.
9 B. Vortex pair lateral spacing
A subset of vortex core traverses has consisted of paired traverses (left-then-right trailing vortex, or vice versa). For this subset, the lateral separation between trailing pair vortex centres, Δysep, is shown in Figure 10, as
non-dimensionalised by wingspan. The wide spread in Δysep/b was indicative of the extent of excitation of long-wave
instability at the point of measurement. Mean Δysep was in the range of 0.8 to 0.6, varying between aircraft types
and could be expected to have been associated with wing aerodynamic design, cruising Mach Number and Reynolds Number of each wake generator aircraft type.
20 30 40 50 60 70 80 10-1 100 geometric wingspan (m) s e p a ra ti o n b e tw e e n v o rt e x c e n tr e s / b
high values indicative of long-wave instability
low values indicative of long-wave instability
With reference to the earlier discussion, at the start of Section III, A, on vortex core edge-to-edge separation as a probable stimulator of mutual instabilities, this separation has been plotted in Figure 10 also. It is seen that the mean ratio, (Δysep-2rC)/rC, was lower for b<35 m, implying greater mutual instability between vortex core inner edges.
C. Comments on observed vortex instability states
Two significant stability mode differences have been measured and observed for FA20, E190 and A320 aircraft through the course of emissions/contrail and wake turbulence flights, when compared to large wingspan aircraft. One pertained to long-wave instability, the other to short-wave, or elliptical, instability.
Concerning wave instability, for Heavy Category, large wing-span aircraft surveyed by the NRC, long-wave period was within the range 5-8bV, where bV was defined as the elliptically-loaded wing vortex-generation
lateral spacing, bV=b/4. In the case of the E190 and A320, the long-wave period was in the range of 2-3bV. This
was so-indicated in the turbulence PSD during wake vortex surveys undertaken by the NRC CT-133 shown in Figure 11. In each pair upper and lower figures, (traverses across E190 vortices) PSD’s are presented of turbulence along the track of the wake vortices during longer sequences of wake crossings (left side) and, of short duration, during a single crossing of the trailing pair of vortices (right side). The former highlighted the long-period spatial frequencies and the latter highlight short-period spatial frequencies. A visual example of long-wave period is shown in Figure 12, showing a bi-wavelength lower condensate pattern, of relatively low period, such as the PSD of Figure 11 indicated.
As regards short-wave instability, the significant difference in modal characteristics of flight data for shorter wingspan aircraft, compared to longer, is that short-wave instability for the former, involved much greater excitation of axial velocity in the vortex core edge regions.
Figure 10: (left) ratio of vortex pair centre-to-centre lateral separation to wingspan, Δysep/b, plotted against b; (right), (Δysep-2rC)/rC, non-dimensionalised lateral distance between inner vortex core edges of port and starboard vortices, plotted against b.
20 30 40 50 60 70 80 100 101 102 geometric wingspan (m) ra ti o , d is ta n c e b e tw e e n v o rt e x e d g e s t o v o rt e x c o re r a d iu s , y /rC
individual vortex pairs
mean, for y/r
C for ratio<25
10-1 100 10-3
10-2 10-1
(spatial frequency)^-^1/b_) or eddy scale size/b_O {initial vortex spacing, b_G * pi/4 (m), along-wake direction
wA C Z ( P S D *bO ) (m /s ) 2/( x /bG )
E190 turbulence along track
10-1 100 101 10-4 10-3 10-2 10-1 100
(spatial frequency)(-1/b), along-wake direction
wA C Z ( P S D *bO ) (m /s ) 2/( x /bG )
A320 turbulence along wake
This is illustrated in the unsteady wind component plots of Figure 13. In the case of the upper plot, a single vortex was crossed at non-dimensional (Sarpkaya) time t* of approximately 3, over the crossplane distance interval from 955 to 958 m. No velocity component was of particularly large magnitude, but the emergence of axial velocity
10-1 100
10-3 10-2 10-1
(spatial frequency)(-1/b), along-wake direction
wA C Z ( P S D *bO ) (m /s ) 2/( x /bG )
E190 WVE turb
Figure 11: TOP:- (left) spatial frequency PSD of turbulence along an E190 wake vortex domain, over700 seconds, showing long-wave periods of 2and 2.8 bV; (right) spatial frequency PSD of 8.3 second duration wake vortex core encounter, showing short-wave modal frequencies of 0.23 and 0.32bVl
BOTTOM:- ((left) spatial frequency PSD of turbulence along an A320 wake vortex domain, over21
seconds, showing long-wave periods of 1.2and 2.3 bV; (right) spatial frequency PSD of 10 second duration wake vortex core traverse, showing short-wave modal frequencies of 0.23, 0.5 and 0.68bV.
10-1 100 10-3
10-2 10-1 100
(spatial frequency)(-1/b), along-wake direction
wA C Z ( P S D *bO ) (m /s ) 2/( x /bG )
A320 WVE turbulence
Figure 12: Medium Category contrail, showing wake vortex condensate in long-wave instability.
11
components at the vortex core edges in the downstream direction (opposite to the direction of flight) was apparent The lower pane presented an A320 vortex-pair crossing at an approximate t* of 1, between crossplane distances of 348-354 m and 369-372 m. Both vortices were bounded by axial velocities at the core edges, of magnitudes greater than crossplane or vertical velocity components.
The observation that these instabilities were apparent at different t* values, was not a reflection upon aircraft type. Rather it possibly reflected atmospheric states that discretely excited particular short-wave modes. The mechanism of excitation has not been discovered, but could reflect atmospheric turbulence state in detail, more than the extent reflected by any bulk parameter, for example. Vented vortex cores, with associated funnel features, have been observed many times, from a variety of aircraft types, at t*<1.
953 954 955 956 957 958 959 960 961 -6 -4 -2 0 2 4
dsa-sum, crossplane arc distance
wc w a w Z wc wa wZ 345 350 355 360 365 370 375 -10 -5 0 5 10 15
dsa-sum, crossplane arc distance (m)
wc w a w Z ( m /s ) wc wa wZ
D. Vortex parameter state contours
The autonomous analysis technique developed by NRC [3] to analyse emission plumes and contrails has been described in Section II,A. A similar analysis technique was applied by NRC, to quasi-vorticity contour plots within large convective maritime air-mass conditions [7]. It has been applied presently to A320 and E190 vortex core traverses to pictorially describe various state parameter distributions in the vortex cross-plane. The state parameters are induced velocity magnitude, VV, induced velocity component magnitudes [VA VC VZ ], air pressure, PS, air
temperature, TS, quasi-vorticity, yz, eddy dissipation rate, , and Brunt-Vaisala frequency, Nsq.
Figure 13: induced velocity components plotted against crossplane flightpath distance, dsa_sum, showing vortex short-wave instability modal characteristics: TOP:- (left) E190, vortex core crossed between 955-958 m, highlighting core edge axial flows in the downstream direction; BOTTOM:- A320 vortex-pair core traverses, with vortex cores crossed between 348-354 m and 369-372 m – both vortex cores were dominated by annular vorticity, with the strongest component being axial flow, downstream at the oute core edges and upstream at the inner edge at 354 m, spatiotemporally.
y (m)
z
(
m
)
A320 WV induced velocity, m/s, M0.5 wake length 6 nm)
-10 -5 0 5 10 -20 -15 -10 -5 0 5 10 15 20 2 4 6 8 10 12 14 16 y (m) z ( m ) A320 P
S, kPa, M0.5 wake length 6-9 nm)
-15 -10 -5 0 5 10 -20 -15 -10 -5 0 5 10 15 20 -0.25 -0.2 -0.15 -0.1 -0.05 0 y (m) z ( m ) A320 log
10(EDR)EDR wake length 6-9 nm)
-15 -10 -5 0 5 10 -25 -20 -15 -10 -5 0 5 10 15 20 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 y (m) z ( m )
A320 quasi-vorticity, s-1, M0.5 wake length 6-9 nm)
-15 -10 -5 0 5 10 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 y (m) z ( m ) A320 T S, K, M0.5 wake length 6-9 nm) -15 -10 -5 0 5 10 15 -20 -15 -10 -5 0 5 10 15 20 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 y (m) z ( m )
A320 Nsq wake length 6-9 nm)
-15 -10 -5 0 5 10 -20 -15 -10 -5 0 5 10 15 20 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01
Figure 14: A selection of cortex cross-plane contour plots of an A320 vortex-pair traverse (differing vortex heights could reflect shear-induced tilt or long-wave instability): (top, L-R) VV, YZ; (middle, L-R), Ps, T; (bottom, L-R), log10(), Nsq.
13 y (m) z ( m )
E190 WV induced velocity, m/s, M0.72 wake length 6-9 nm)
0 10 20 30 40 -40 -30 -20 -10 0 10 20 0 2 4 6 8 10 12 14 y (m) z ( m )
E190 PS, kPa, M0.5 wake length 6-9 nm)
0 10 20 30 40 -40 -30 -20 -10 0 10 20 -0.25 -0.2 -0.15 -0.1 -0.05 0 y (m) z ( m ) E190 log
10(EDR)EDR wake length 6-9 nm)
0 10 20 30 40 -50 -40 -30 -20 -10 0 10 20 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 y (m) z ( m ) E190 quasi-vorticity, s -1, M0.72 wake length 6-9 nm) 0 10 20 30 40 -40 -30 -20 -10 0 10 -20 -15 -10 -5 0 5 10 15 20 25 y (m) z ( m )
E190 TS, K, M0.72 wake length 6-9 nm)
0 10 20 30 40 -50 -40 -30 -20 -10 0 10 -0.4 -0.2 0 0.2 0.4 0.6 y (m) z ( m )
E190 Nsq wake length 6-9 nm)
0 10 20 30 40 -50 -40 -30 -20 -10 0 10 20 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025
Figure 15: A selection of cortex cross-plane contour plots of an E190 vortex-pair traverse (differing vortex heights could reflect shear-induced tilt or long-wave instability): (top, L-R) VV, YZ; (middle, L-R), Ps, T; (bottom, L-R), log10(), Nsq.
A selection of vortex state parameters is presented for an A320 vortex-pair traverse in Figure 14. Each vortex was flown through twice in-turn, i.e. left, left, then right, right vortex traverse. It is seen that in spite of the relatively low coverage of the cross-plane domain by the flight-path segments, substantial information is presented in the contour plots. In particular, YZ is coherent, and showed largely same-sign vorticity in the starboard vortex and
mixed +/- vorticity in the port vortex [6]. This likely reflected differing vortex states between the pair. However, both structures were annular, rather than circular. Concerning PS and T, the starboard vortex was vented, had a cool
centre, warm edge (and yet maximum expansion in core edge annuli – such warm expansions have often been observed in NRC wake vortex flight data). maxima occurred in core edges. The vortices were stratified, of varying stratification in spiral shapes reminiscent of hurricane Rossby waves.
Contour plots of a similar selection of parameters are presented in Figure 15 for an E190 wake vortex survey. The interpretation of the plots is more difficult in this case, partly due to the vortex core traverses being conducted whilst the generator was climbing, for which the wake vortices are also climbing, but are being generated in continuously-changing background atmospheric conditions. The contours plots would appear to include two vortex states, one towards the bottom-left corner, the other towards the top-right corner. In the former, a reasonably quiescent state is evinced by the coherent vortex-pair delineation by YZ, PS, T, and Nsq contours, but possessed
low VV magnitudes. In the latter case, a large, energetic vortex state is evinced by the VV contours, and supported
by all other parameters. The structure is highly asymmetric but may be annular of an implied diameter of 10 m, with +/- YZ (although net YZ would appear to be positive).
IV.
CONCLUSIONS
EDIUM Category wake turbulence jet transport wake vortex characteristics, gathered in-flight, in enroute cruise and enroute climb conditions, from the NRC Falcon 20 aircraft and Air Canada A320 and E190 aircraft, has been amalgamated with Heavy/Super Category wake vortex data, relating to vortex core size, peak induced velocities and vortex separations.
For the amalgamated data-set of 283 treverses, vortex core radius rC, did not demonstrate a dependency upon
wing-span, b. Rather, the rC/b envelope varied between approximately 0.25 at b=16.3 m and 0.08 at b=80 m. For
any aircraft type, there was a wide range of rC. The smallest rC values were similar between all types, indicate of
energetic, small vortex elements. These were measured in vortex core edges. The largest rC varied between 5 m for
the smallest b (16.3 m), 10 m for 50<b<60 m, and 8 for b=80 m.
A vortex peak-velocity contour plots presented mild values for the Medium Category aircraft. The contour-plateau of peak values >20 m/s emanated widely for b>45 m, but did not exhibit a dependency upon b, other than occurring at progressively larger rC, with increasing b. Cruise parameterisation suggested that wing mean chord c
might be a useful aircraft size parameter for correlation of enroute vortex induced velocity, perhaps more than b. VTmax>20 m/s occurred for c>6 m.
Vortex edge lateral separations were lower for the Medium Category jet aircraft. Consequently, greater propensity for mutual interactions between vortices could be expected. This may have been an explanation for A320-sized Medium Category jets having shorter long-wave period, 2-3bV, compared to that measured by the NRC
for larger wing-span Heavy/Super Category, namely 5-8bV. Short-wave, or elliptical, instability, for the shorter
wingspan (Medium Category) aircraft exhibited strong excitation of axial velocity at vortex core edges, moreso than upon larger wingspan (Heavy Category) aircraft.
Acknowledgements
Wake turbulence data was gathered under the sponsorship of the NRC and the FAA. Additionally, Medium Category wake vortex data was gathered under projects CAAFCER, CAAFCEB and AEEM.
Project CAAFCER was an award from the Green Aviation R&D Network (GARDN) of the Government of Quebec, under the executive direction of Stefan Covsky, made to a consortium of the Waterfall Group, Air Canada, the NRC, University of Alberta, SkyNRG and Boeing. The contributions and consultancy of the following in the analysis of CAAFCER data are acknowledged: Mena Salib and Francesco Femia, Air Canada, Fred Ghatala, The Waterfall Group, Jason Olfert, University of Alberta, Renco Beunis and Misha Valk, SkyNRG, Nathalie Gaudet, QETE, DND, and Steven Baughcum, The Boeing Company.
Project CAAFCEB, the flight research of contrails high-blend bio-jet fuels, acknowledges gratefully the sponsorship of Environment & Climate Change Canada Low-carbonisation Program, Transport Canada, International Aviation Office, NRC and Lanza Tech.
Project AEEM was a 2009 award under the PERD program of the Office of Energy R&D of Natural Resources Canada.
M
15
References
1. Brown, A.P., M Bastian, F Femia, M Salib, F Ghatala, J Olfert, R Beunis, M Valk and N Gaudet, “Civil Aviation Alternate Fuels Contrails and Emissions Research – Operations and Contrail Observations,” LR-FRL-2018-0013, 2017.
2. Brown, A.P., Bastian, M., Canteenwalla, P., “Civil Aviation Alternate Fuels Contrails and Emissions from high-Blend Biofuels – Contrails Analysis,” LTR-FRL-2018-0029, March 2018. 3. Brown, A.P., Bastian, M., Alavi, S., Wasey, M., “FLIGHT RESEARCH REPORT:- PROJECTS
AEAFFR, CAAFER AND NASA ACCESS II JET TRANSPORT EMISSIONS MEASUREMENTS,’ NRC LTR-FRL-2015-0054, March 2015.
4. Brown, A.P., M Bastian,, “Wake Vortex Core Flowfield Dynamics and Encounter Loads In-situ Flight Measurements,” AIAA-2008-468, 46th AIAA Aerospace Sciences Meeting and Exhibit7 - 10 January 2008, Reno, Nevada
5. Brown, A.P., “Wake Vortex Core Profiles and Stability from Enroute Flight Data,” AIAA Atmospheric & Space Environment Conference, AIAA-2011-2032, June 2011.
6. Brown, A.P., “Flight data of axial flows in wake vortex instability,” AVIATION 2016, AIAA-2016-3435, June 2016.
7. Brown, A.P., Wolde, M. & Korolev, A., “In-situ Wind-fields Measured in Ice Crystal Cloud-mass by the NRC Convair during HIWC 2015,” AIAA AVIATION 2016, 8th
ASE Conference, Washington, B.C.,13th-17th June 2016
