Wake Vortex Dynamics Study in Temperature Inversion Conditions · viscous interaction with the...
Transcript of Wake Vortex Dynamics Study in Temperature Inversion Conditions · viscous interaction with the...
Wake Vortex Dynamics Study in Temperature Inversion Conditions
Baranov N.A.
Dorodnicyn Computing Centre, Federal Research Center “Computer Science and
Control” of Russian Academy of Sciences
Abstract
The presented results have been obtained following numerical modeling of aircraft
wake vortex dynamics in the conditions of surface temperature inversion of the
atmosphere. Modeling was based on data from surface temperature profile
monitoring, which took place in winter and spring at Sochi airport using MTP-5
meteorological temperature profiler. A comparative analysis of the wake vortex
dynamics in the absence and presence of a side wind of varying intensity was
carried out for a number of temperature inversion cases, such as surface inversion,
elevated inversion with different layer altitude inversion, elevated inversion with
surface isothermy.
The work was supported by the Russian Foundation for Basic Research under
Project 16-07-01072.
Introduction
One of the factors which determine flight safety is the problem of wake vortex
safety provision. Different countries conduct researches on the analysis of the
wake vortex evolution generated after the aircraft specifics in different
meteorological conditions, assessment of the persistence level depending on
atmospheric conditions and the level of hazard to aircraft of different weight
categories [1]. It is important to mention WakeNet-Russia, WakeNet-USA,
WakeNet3-Europe, FP7 Project "UFO - UltraFast wind sensOrs for wake-vortex
hazards mitigation", and a number of projects under European SESAE project/
The wake vortex dynamics is determined not only by the existence of wind and
level of atmospheric turbulence, but also depends on atmospheric stratification [2,
3]. The impact on the wake vortex behavior of the stratification type of the surface
atmosphere layer is analyzed via mathematical modeling in this paper
Assumptions and input data
A numerical algorithm based on the method of discrete vortices was used. It
takes into account the changes in the wake vortices lowering speed and their
additional decay due to the temperature stratification of the atmosphere [4, 5].
Wake vortex was calculated on the basis of the hypothesis quasi-plane-parallel
flow.
As the example was taken low-altitude flight of the B-747-800 aircraft.
Flight altitude was chosen so that the wake vortex dynamics was determined by
viscous interaction with the boundary layer of earth. It was assumed that the flight
is conducted in the landing configuration with maximum landing weight. Time of
the calculation was 100 sec.
The data from the surface monitoring of temperature profiles in the-winter-
spring period at the Sochi airport gathered with the meteorological temperature
profiler MTP-5 (rpoattex.com) was used for modeling. The spatial resolution of the
temperature profile height was 25m to a height of 100m and 50m - more than
100m, accuracy of the estimation (RMSD) – 0.2°C to 0.5°C in first 500 m
(temperature accuracy decreases with altitude and depends upon the temperature
profile shape). Four types of profiles were used for the analysis (Figure 1.):
profile 1 – elevated inversion at 200m,
profile 2 – surface inversion,
profile 3 - elevated inversion with surface isothermal,
profile 4 – elevated inversion at 100m.
During the analysis the impact of the weak side wind on the dynamics of the
wake vortex at different conditions of temperature inversion has been also
considered
Figure 1 – Considered temperature profiles
A brief description of the model
During the modeling of the wake vortex dynamics was used a two-phase
model of the vortex intensity decay, whereby it was assumed that at the first stage
the slow decay of the wake vortex intensity took place, and from a certain point in
time, the vortex trail enters a phase of rapid decay. [3]
The influence of temperature profile on wake vortex decay is taken into
account by modifying the time of the vortex life which determines decay
circulation rate: instead of the function of dimensionless time of vortex life
Tdemise(η) a function is considered
demisedemisedemise 185,0exp, TTT NN ,
where η is turbulence kinetic energy speed dissipation, N - Brent-Vaisal
dimensionless frequency:
20 with max ,0 max ,0
p
g dT g g dt N N
T dz c dz
N .
T(z) – temperature profile, cp – heat capacity at constant pressure, and g – gravity
acceleration.
8 10 12 14 16 T0
200
400
600
800
1000 h
Profile 1Profile 2Profile 3Profile 4
Besides the change of wake vortex circulation decay rate the model takes
into account the wake lowering, due to stratification influence according to the
following equation
strat2
22
strstrstrat
dt
zdv
dt
d , strat
2
2
02
strstr 21
dt
zdb
dt
d ,
0
22
2( )
z
zstrat
d zN z dz
dt
,
where αstr , βstr are given model coefficients, z and z0 respectively are the current
and initial height of vortices [1].
Viscous interaction of wake vortices with the surface was taken into account
by secondary vortices simulation which shows separation of the boundary layer of
the earth.
Results
The figure 2 shows the influence of the various types of temperature
stratification on the wake vortex dynamics in the absence of a crosswind. A change
in his attitude in terms of the adiabatic temperature profile is shown as the wake
vortex sample trajectory
It is possible to see, that in the adiabatic conditions at first the wake vortex
rises. It is explained by the interaction with the separated boundary layer. Then the
speed of rising is decreased and it almost stops moving at a certain height.
Simultaneously the wake vortices are shifted to the axis of the wake vortex pair
symmetry.
Figure 2 – Wake vortex vertical position change at different temperature profiles in
the absence of wind
In terms of surface inversion wake vortex dynamics changes radically: there is no
stabilization height wake vortex lift. In the conditions of the elevated inversion,
including surface isotherm, the height of the stabilization occurs earlier than under
adiabatic conditions, wherein the vortex lifting height depends on the surface
gradient and the height of the inversion layer. It should be noted that despite the
fact that under adiabatic conditions the vortex height stabilization occurs at an
altitude of less than 100m the vortex dynamics is influenced by the presence of the
inversion layer at an altitude of 200m, due to a change in the temperature gradient
in the height range 50 ... 100m: even weak variations of the temperature gradient (
0.5 ... 1С for 100m altitude) affect both lifting height and change in the lateral
position of the wake vortex.
The figure 3 shows the results of the wake vortex modeling in the conditions of
weak side wind
0 30 60 90 z0
25
50
75
100
125 yProfile 1Profile 2Profile 3Profile 4Adiabatic
T(z) Wind 1m/s Wind 2m/s
1
2
3
4
Figure 3 – Wake vortex vertical position change at different temperature profiles in
the conditions of weak side wind
-100 0 100 200 z0
15
30
45
60 y
left vortexright vortex
-100 0 100 200 300 z0
15
30
45
60 y
left vortexright vortex
-100 0 100 200 z0
30
60
90
120
150 y
left vortexright vortex
-100 0 100 200 300 z0
30
60
90
120
150 y
left vortexright vortex
-100 0 100 200 z0
20
40
60
80 yleft vortexright vortex
-120 0 120 240 z0
20
40
60
80 yleft vortexright vortex
-100 0 100 200 z0
20
40
60
80 yleft vortexright vortex
-100 0 100 200 300 z0
20
40
60
80 yleft vortexright vortex
The shown data shows that the side wind presence depending on the stratification
type can lead to nearly hanging of one of the vortices in the vicinity of the aircraft
trajectory. This phenomenon is an unfavorable factor for the aircraft to land, as the
flight of the aircraft takes place on the same trajectory and the presence of a wake
vortex increases the risk of an accident. The most unfavorable conditions are
isothermal surface and slightly lifted inversion in low crosswind.
For comparison figures 4 and 5 show the disturbance rolling moment distribution
in the wake vortex of a B-747-800 aircraft which encounters the wake vortex of B-
767 type aircraft 60sec and 100sec after generator passing. The results obtained by
modeling the case of the wake vortex dynamics in the surface isothermal
conditions (temperature profile number 3) with weak side wind 1m /sec. The
Figure 6 shows the disturbance rolling moment distribution for the case with
100sec parameter and elevated inversion (profile number 4) with weak side
wind 1m/s.
The results reflect the high sensitivity of the dynamics of the wake vortex to the
parameters of temperature stratification.
Figure 4 – Rolling moment distribution after 60 sec from the case of elevated
inversion with surface isotherms
-50 0 50 100 150 200 2500
20
40
60
80
100
120
140
160
180
200
z
y
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
Figure 5 – Disturbance rolling moment distribution after 100 sec for the case of
elevated inversion with surface isotherms
Figure 6 – Disturbance rolling moment distribution after 100 sec for the case of
surface inversion (profile number 4)
Conclusion
The conducted research, based on numerical simulations show that the
change in the spatial position of wake vortex essentially depends on the type of the
temperature stratification of the atmosphere. In this regard, the wake vortex
-50 0 50 100 150 200 2500
20
40
60
80
100
120
140
160
180
200
z
y
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-50 0 50 100 150 200 2500
20
40
60
80
100
120
140
160
180
200
z
y
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
attitude prediction models in different meteorological conditions is necessary to
assimilate the data on the temperature profile in the surface layer. These results
show that even small variations in the temperature profile can significantly change
the attitude of the vortex disturbance zone. Preliminary estimation based on
mathematical modeling data show that the measurement accuracy of the
temperature profile should not be below 0.5 with spatial resolution of height 25-
50m.
Reference list
1. Holzäpfel F. et al. Aircraft Wake Vortex - State-of-the-Art & Research
Needs. 2015, DOI 10.17874/BFAEB7154B0
2. Sarpkaya T., Day J.J. Effect of ambient turbulence on trailing vortices.
J.Aircraft, 1987, 24, № 6, 399-404.
3. Sarpkaya T. New model for vortex decay in the atmosphere. . J.Aircraft,
2000, 37, № 1, 53-61.
4. Baranov N.A., Turchak L.I. Investigation of aircraft vortex wake structure.
AIP Conference Proceedings, 2014, Volume 1629, Issue 1, p.44-55. DOI:
10.1063/1.4902258.
5. Turchak L. I., Baranov N.A. Modeling of Aircraft Vortex Wake Structure.
Fifth International Conference on Application of Mathematics in Technical
and Natural Sciences, 24-29 June 2013, Albena, Bulgaria. Book of
Abstracts, p. 69 – 73.