Document
AIAA-2002-2411
Unsteady Simulation of a Landing-Gear
Flow Field
F. Li
High Technology Corporation
Hampton, VA
M. R. Khorrami
NASA Langley Research Center
Hampton, VA
M. R. Malik
High Technology Corporation
Hampton, VA
8th AIAA/CEAS Aeroacoustics Conference
17-19 June 2002
Breckenridge, Colorado
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UNSTEADY SIMULATION OF A LANDING-GEAR FLOW FIELD Fei Li l High Technology Corporation Hampton, VA 23666 Mehdi R. Khorrami 2 NASA Langley Research Center Hampton, VA 23681 Mujeeb R. Malik 3 High Technology Corporation Hampton, VA23666 Abstract noise prediction tools that incorporate the attendant physics are, therefore, highly desired and needed.
This paper presents results of an unsteady Reynolds- One approach towards this end is to numerically averaged Navier-Stokes simulation of a landing-gear simulate the full complex flow field to provide the flow field. The geometry of the four-wheel landing- unsteady near-field pressure signature required by an gear assembly consists of several of the fine details acoustic solver based on the Ffowcs Williams- including the oleo-strut, two diagonal struts, a door, Hawkings formulation (Refs. 1 and 2), which then yokes/pin and a flat-plate simulating the wing surface.
yields the acoustic far-field. Although computationally The computational results, obtained by using 13.3 intensive, direct computation of the unsteady flow field million grid points, are presented with an emphasis on provides an insight into the dominant noise sources the characteristics of the unsteadiness ensuing from which, in turn, can be used for developing reduced order different parts of the landing-gear assembly, including models and in devising means for noise suppression.
vortex shedding patterns and frequencies of dominant The combination of an accurate near-field flow solution oscillations. The results show that the presence of the with that of an acoustic propagation formulation has diagonal struts and the door significantly influence the achieved considerable success in identifying noise flow field. Owing to the induced asymmetry, vortices sources associated with high-lift systems (e.g., are shed only from one of the rear wheels and not the Khorrami et al., 3-5 Singer et al.2'6). The present study other. Present computations also capture streamwise follows a similar approach and thus, as a first step vortices originating from the upstream corners of the door.
towards a comprehensive goal of predicting landing- gear noise, highly resolved time-accurate flow Introduction simulation of a complex landing-gear configuration is attempted.
During the approach and landing phase of an While flow computations of high-lift devices such as aircraft, the wing leading-edge slats and trailing edge flaps and slats received significant attention in the last flaps are fully extended and the landing gears are decade, the intricacies of a landing-gear flow field have deployed. The interaction of the airflow with such remained essentially unknown due to overwhelming protrusions in the aircraft structures gives rise to geometrical complexities. The multiple structures that unsteady flow phenomena that are responsible for sound collectively generate gear-related noise are nose landing radiation. Because the engines are operated at reduced gear, main landing gear (MLG), and wheel wells.
thrust during landing, airframe noise, especially from Between the nose landing gear and the MLG, noise the landing gear and the high-lift system, constitutes a associated with the latter is louder and it is usually major noise source. The envisioned stricter community radiated in all directions. The wheel-well cavities noise regulations are forcing aircraft manufacturers to produce high-amplitude tones. However, these tones devise ways to minimize noise radiation from the occur at very low frequencies and hence are not current and future large transport aircraft. Efficient considered important sources from the standpoint of community noise. In addition, experiments (Dobrzynski & Heller 7) indicate that the landing gear protruding Senior Scientist, Member AIAA.
from the cavity provides a spoiling effect for the cavity 2 Research Scientist, Computational Modeling and tones. In view of these observations, the MLG noise Simulation Branch, Associate Fellow AIAA.
constitutes the dominant part of the landing-gear noise.
3 Chief Scientist, Associate Fellow AIAA.
Copyright © 2002 by High Technology Corporation. Published by the American Institute of Aeronautics & Astronautics, Inc. with permission.
Our currentunderstanding of the landinggear
withexperiments _5 performed ona similar, albeit much
generated noisecomes from experiments performed
simpler, configuration. From thecomputational results,
mainly in Europe (e.g.,Davy& Remy, aDobrzynski et
vortexshedding fromthevarious components of the
al.,9 and Grosche etal.l°), atleast among those available
landing gear assembly is elucidated and thefrequencies
in open literature.These experiments haveindicated
associated withdominant unsteady structures aregiven.
that,whilethenoise fromhigh-lift devices is likelyto
The results alsohighlight the profound impactthat
dominate for mid-size aircraft,landinggearnoise
diagonal struts andthedoorattached tooleohas onthe
becomes moresignificant for large aircraft.It hasalso flowfield.
been foundthatthenoise spectra associated withthe
Landing-Gear Configuration and
landing gearareratherbroad,ranging from a few
hundred Hzto several kHz. Among theresearch work
Computational Grid
carried outin theU.S., Stoker etal.1_ hasshown thatthe
presence of thelanding gearevenimpacts thenoise
The MLG geometry simulated in the present study is associated withtheflapsystem.
shown in Figure 1, where Cartesian coordinate system x, y, z is also shown. It consists of 4 wheels, 2 diagonal
The present workisaimed atunderstanding the flow
struts, an oleo-strut (the vertical pole), a side-door
field associatedwith a representative MLG
attached to the oleo, yokes/pin and other structures that
configuration. We performUnsteady Reynolds-
join the system together. A flat plate (not shown in the
Averaged Navier-Stokes (URANS) computations for a
figure) is attached to the top-end of the oleo and struts, relatively complex four-wheel landing gearassembly, which is meant to represent the aircraft wing. For the including several of thefinedetails (e.g.,yokes, pins, sake of computational efficiency however, the flat-plate
door,etc.). Themodel gear,designed to represent a
boundary-layer is not finely resolved in the present
Boeing 757MLG,was tested (acoustically) in theLow
study. Following the tested configuration in LTPT, a
Turbulence Pressure Tunnel (LTPT) atNASALangley
wheel-well cavity is also not simulated.
Research Center using a microphone arraytechnique.
Thenear-field preliminary computational results will be
The wheel diameter is used as a reference length to
presented in thispaper.Thetime-accurate flowfield
non-dimensionalize the coordinate system. Note that in
simulations will later be usedfor computation of
Fig. 1, x is in the free-stream direction and y is in the landing gear associated far-field noise.
direction of the wheel axles with the y = 0 plane cutting through the center of the oleo. The vertical coordinate
Thefirstamong theprevious computational studies
is represented by z with z = 0 plane cutting through the
of landing geai" flow field is the workreported by
wheel centers. The top-most and bottom-most points of
Strelets, 12in whichDetached EddySimulation (DES)
the wheels are situated at z - 0.5 and z = -0.5, technique was employed. Using this approach, respectively. The top flat-plate is at z = 1.78237. The
incompressible Navier-Stokes equations were solved to
computational boundary in the streamwise direction
simulate a relativelylessdetailed, symmetric, four-
extends from x = -5 to x = 13 with x = 0 situated
wheel landing gear configuration modeled bya totalof
midway between the front and rear wheels. The 2.5million gridpoints ataReynolds number of105.
streamwise gap between the two sets of wheels is 0.106 (i.e., 0.106 times the wheel diameter).
Morerecently Souliez etal._3 used anunstructured
compressible Navier-Stokes solverfor thesame MLG
The constructed grid consists of 155 blocks with a
configuration adapted here but withoutthe door
total of 13.3 million grid points. To minimize overall
attached to theoleoandtheflat-plate representing the
number of grid points, moderate patching in certain
wingsurface.No RANSor Large EddySimulation
blocks is invoked. On the solid surfaces (excluding the
(LES) model was used in theirstudy, which employed a
top wall), there are 247606 grid cells. Numerical tests
gridconsisting of 1.2 milliontetrahedral cells.Withthe
were performed to assure that all the solid surface
aid of a FfowcsWilliams-Hawkings solver,the
boundaries of the MLG and the grid-block interfaces are
computed unsteady flow fieldwasused to predict the
specified correctly. The grid distribution on the surface
noise field associated with the selected landing gear
of the landing-gear is shown in Fig. 1 where every other configuration.
grid point is displayed. Special attention was paid to appropriately model all the fine details of the MLG
In the present unsteady RANS simulation, we
assembly.
employ the thin-layer Navier-Stokes code,CFL3D, _4
where a multi-block structured gridconsisting of 13.3
In order to facilitate the subsequent presentations
milliongrid pointsis utilized. The details of the
and discussions, we will refer to the four wheels of the computed flow field are presented in this paper.
landing gear system as front-left, rear-left, front-right
Computed wheel surface pressure variation iscompared
and rear-right wheels, respectively, in the coordinate
system of anobserver traveling withthelanding gear
complex as it is in the wake of the front-right wheel. A and facing theincoming flow.
low-pressure region appears near the downstream side of the wheel, indicating high velocity in that region.
Computational Results Figures 3 through 6 show the pressure coefficients The flow solver used is CFL3D, developed at NASA (Cp -2(p-p_)/p_UZ ) along the mid-wheel circum- Langley Research Center (Thomas et a1.16). The two- ference for 13 selected instances over a duration of equation k-co turbulence model of Menter 17 is employed approximately 20 non-dimensional time units. During in this study. The parallel version of the code is used this time period, a particle moving with the free-stream for the present computations, which are performed on speed travels a distance of 4 wheel diameters. Note that the SGI-cluster at the National Aerodynamic Simulation the azimuthal angle of each wheel is measured from its (NAS) facility utilizing a total of 55 processors. To front-most point. We refer to the upper side (see Fig. 1) match the conditions of the NASA Langley LTPT of a wheel as the wing-side and the lower-side as the experiment referred to above, present computations are ground-side. Therefore, 90-degrees on the wing-side conducted at a free-stream Mach number of 0.2 and a refers to the top-most point of a wheel, and 90-degrees Reynolds number based on the wheel-diameter of on the ground side refers to the bottom-most point.
1.23x 106. The free-stream static temperature is 3_ 02.9°K Here, an angle of 180-degrees refers to the rear-most and the wheel diameter is .094m.
point.
We first carried out steady-state computations on a Due to asymmetry of the flow (caused by the struts coarser grid (i.e., half the resolution in each direction and the door) the stagnation points on the two front- resulting in about 1.7 million total grid points) for wheels do not lie at the front-most points. Therefore, 14,000 iterations using a CFL number of 0.5. This the pressure coefficients there are slightly smaller than helped reduce the residual by at least two orders of 1. The distributions of pressure coefficients on the four magnitude. Subsequently, the time-accurate wheels are different from each other, exhibiting computations were started with a non-dimensional time- different degrees of unsteadiness. We, therefore, step of 0.01 (At = At* co/d , where d is the wheel discuss these results separately.
diameter, co is the speed of sound, and t* is the time in In Figure 3, the pressure on the front-left wheel seconds) on the same grid. With this time step, a drops as expected for a circular-shaped body. Minimum particle in the free stream would travel a distance of one pressure is reached at an azimuthal angle of landing gear wheel-diameter in 500 time steps. We approximately 90 and 85 degrees for the wing-side and monitored the convergence of the inner iterations as the ground-side, respectively. The pressure rises until well as data from computational probes in the flow field approximately 140 and 130 degrees, respectively, on the to ensure that a stable numerical solution was obtained.
wing-side and the ground-side. Then, the pressure Once this was assured, the computation was switched coefficients computed at different instances start to drop (at t = 44.6) to the fine grid (13.3 million grid points) and begin to have slight differences. This is an with a time step of 0.005. Calculations were then indication that flow is separated from these locations.
carried out up to a nondimensional time of 84.3.
Since the differences in pressure among the data MLG Surface Pressure computed at the 13 instances are small, the separations appear to be relatively steady.
The unsteady pressure field on the landing gear In Figure 4, the same can be said about the pressure surface (or on an imaginary surface around the landing distribution on the wing-side of the front-right wheel, gear assembly) is an input for the acoustic solver.
where little difference can be noticed among the 13 Therefore, we first present computed surface pressure.
instances. However, the pressure on the ground-side is Figure 2 shows a perspective plot of instantaneous quite another story. The pressure coefficients for the 13 (at t = 84.3) pressure contours over the landing-gear instances begin to show a significant difference around surface viewed at an angle. The flow is from right to 70 or 80 degrees. For any fixed angle between left. We notice that the red contours (high pressure) in approximately 70 and 100 degrees, the pressure the front of the two front wheels representing the neigh- decreases monotonically in time. (i.e. the pressure borhood of the stagnation points do not lie on the coefficient curve at an earlier instance appears above respective centerlines of the wheels, but are shifted that at a later instance). This either indicates that the toward each other. Red contours also appear in the computed flow in the region is gradually converging to front of the oleo and the front of the front strut. The some steady state or that it is oscillating with a very low contour patterns on the rear-right wheel are much more frequency. Further computations are required to determine whatexactlyis happening in this region.
sound) at the fine grid level over a nondimensional time Beyond110degrees the monotonic natureis lost, span of approximately 40. During this time span, a
indicatingthat the flow is undergoing unsteady
particle traveling with the freestream speed covers a oscillations.
distance of 8 wheel diameters.
Thedifferent flow behavior around the twofront
We can observe that the initial high-frequency
wheels is aconsequence oftheasymmetric layout ofthe
transients rapidly decay as time progresses. Yet, as the
landing-gear system (i.e.thepresence of thestruts and
end of the time-record is approached, it is not obvious thedoor), as noted above.
that the computed flow field has reached a quasi-steady state. Thus, it appears that the present unsteady flow
Figure 5 shows thepressure coefficients oftherear-
field is still not suitable for providing the near-field
left wheel. Since it is in the wakeof the front-left
pressure signature required by an acoustic solver.
wheel, itsfront-most pointis nowhere near a stagnation
However, some interesting features of the flow are
point. Unsteadiness sets in at approximately 130and
beginning to take shape.
110degrees, respectively, for thewingsideandthe
ground side.
The two probes behind the oleo begin to show some very high frequency, growing oscillations shortly after
Figure 6 shows thepressure coefficients of therear-
the fine-grid computation starts. While the high-
rightwheel.Theground sidehaslarge oscillations in
frequency pressure oscillations recorded by the probe
pressure between approximately l0 and90 degree
behind the lower oleo grow slowly, the probe behind the
locations. This is most likely caused by the
mid-oleo detects oscillations that grow relatively
impingement of theunsteady wake fromthefront-right
rapidly. Figure 9 shows the pressure fluctuations after
wheel ontothe rear-right wheel. Both thewingside and
the data from the probe behind the mid-oleo is
the groundside begin to experience significant
processed by a high-pass filter. The initial growth unsteadiness fromapproximately 130 degrees on.
appears to be exponential. Eventually, the pressure oscillations saturate at approximately 0.03% of the
Lazos _5carriedout an experiment with a much
freestream pressure. The saturated amplitude of the
simpler landing-gear assembly thatconsists onlyof an
corresponding velocity fluctuations (not shown) is
oleo andfourwheels joined together bytwoaxles and a
approximately 0.15% of the freestream speed or
cylindrical rod. Inthiscase, theflowis symmetric with
approximately 3% of the local flow speed. A shorter
respect tothe y = 0 plane. Furthermore, the sides of the
time record of the pressure oscillations is shown in wheels are flat and do not have the fine details of the Figure 10, from which the oscillation frequency is wheels used in the present computation. Reynolds determined to be approximately 24 kHz. Note that each number in the experiment is 6z105 as compared to the period of oscillation in Fig. 10 is resolved by about 30 present value of 1.23x106. Figure 7 shows the time steps.
experimental results together with the present computational data. The measured pressure distribution Given the small amplitude of the oscillations, the around the front wheel shows the same general behavior probability that these oscillations originate from the as those of the present computation. However, it is seen vortex shedding off the oleo is small. In fact, that the pressure coefficient continues to decrease up to preliminary analysis of the flow field data indicates that larger azimuthal angles for the experimental results as the source of the oscillations is, perhaps, the flow compared to the computations. We stress here that this resonance in the gap between the door and the oleo.
comparison is not intended for quantitative validation of The eventual saturation of the oscillation amplitudes is computational results, since the landing-gear assembly likely due to two reasons: (1) as time progresses, the used in the computations and the experiment are not the flow field reaches such a state that these oscillations same.
become neutrally stable and (2) the amplitude of the oscillations becomes large enough for nonlinearity to Probe Data play a part in bringing the exponential growth to a halt.
The latter is plausible because of the high oscillation In order to investigate unsteadiness in the flow, we frequency and the relatively large amplitude with positioned a total of 4 probes at distinct locations to respect to local flow speed.
record the density, velocities and pressure. One probe is placed behind the axle of the rear-left wheel, a second Flow Field probe is placed between the struts, a third probe is placed behind the mid-portion of the oleo and the last Now we discuss some of the notable features of the one is placed behind the lower portion of the oleo.
landing gear flow field, which include vortex shedding Figure 8 shows the variation of pressure with time t from various parts of the landing-gear system and (which is scaled with wheel diameter and speed of
asymmetry of the passingflow as well as its
contours in this plane at t - 84.3. The vortex shedding
consequences. Ideally, theunsteady flowfieldcanbe
appear to be alternating from either side of the
analyzed by saving computational data atintervals of a
downstream strut. The shedding frequency is estimated
fewtime-steps forsome extended duration sothatthe
to be approximately 600 Hz. No vortices seem to be
flow historyat everypointin theflow fieldcanbe
shed from the oleo/door assembly.
obtained if necessary. This,of course, requires an
As mentioned earlier, the flow past the landing gear
enormous amount of hard-disk space sincethe file
system is asymmetric with respect to the plane y = 0
containing density, velocitycomponents andinternal
(i.e. the plane bisecting the wheel axles). Therefore, the
energy of the flow fieldfor oneinstance in timeis
flow patterns on the left and on the right are different.
approximately 253MB in size. Assuming thatthe
This asymmetry is already apparent at some distance
computational dataon everyothertime-step for a
upstream of the landing gear. Figure 15 shows contours
nondimensional timeperiod of 20(i.e.,timetaken bya
of streamwise velocity at a distance of approximately
particle traveling withthefreestream speed tocovera
half a wheel diameter upstream of the front ends of the
distance of 4 wheel-diameters) isrequired, then, witha
wheels. The presence of the components of the landing
timestepof 0.005, thediskspace needed will be506
gear system is already sensed by the flow.
GB. Since currently theflow fieldhasnotreached a
quasi-steady state, wechoose nottotake thispath atthis
Figure 16 shows the contours of streamwise velocity
time. Instead, wesave the computational dataat 13
in the x-plane close to the rear of the rear wheels.
discrete instances (not quiteevenly spaced) starting
Regions of reverse flow exist behind the door/oleo and from t = 73.6 and ending at t = 84.3.
the struts, and between the wheels. There is also a high velocity region on the right side of the rear-right wheel.
We first consider the flow in the horizontal plane z = This high velocity region is possibly responsible for the 0 that cuts through the centers of all four wheels.
shear-layer type of vortex shedding discussed earlier.
Figures 11 and 12 show, respectively, the instantaneous The presence of the struts forces the flow to go around density and spanwise velocity contours at t = 84.3.
the struts and causes the flow over the rear-right wheel Vortices are being shed from the rear-right wheel but to be faster than that over the rear-left wheel.
not from the rear-left wheel. This must be due to the fact that the flow is asymmetric with respect to the Figure 17 shows the contours of streamwise velocity centerline dividing the two rows of wheels. At all other at a distance of approximately half a wheel-diameter 12 instances the shedding patterns are similar. The downstream of the back ends of the wheels. The shedding frequency is estimated to be approximately features seen in Fig. 16 are further amplified here.
800 Hz.
However, there is no backflow at this x location. In both Figs. 16-17, a vortex can be seen near the oleo/flat- We note that the shedding pattern is different from plate junction. The origin of this vortex will be that of a typical blunt body in that, instead of two rows discussed later.
of vortices coming off the wheel alternately from either side, only one row of vortices is seen. The density Figure 18 shows the streamwise velocity contours in contours in Fig. 11 resemble those of a plane shear the y = -0.463 plane that cuts through the left wheels.
layer. The shear-layer instability mechanism is likely The wake behind the left wheels does not appear to have responsible for this shedding pattern. The speed of flow an identifiable wave structure. Near the top wall is a past rear-right wheel on the right hand side is higher slow-flow region that starts just after the x-location of than that on the left hand side because of the blockage the oleo. This is, in fact, inside the vortex earlier seen effects of the solid blocks, the oleo and the wheel-axles, in Figs. 16-17.
creating a strong enough local shear layer so that Kelvin-Holmholtz type of instability sets in. As the Figure 19 shows the results in the plane (y = 0.463) horizontal plane is moved up or down (i.e. out of or into containing the right wheels. The wake behind the right the paper), the shedding pattern seems to diminish and wheels exhibits strong waviness, consistent with what is eventually disappear. The flow in the plane is highly discussed earlier (Fig. 11). This plane also cuts through three-dimensional with the vertical (z) velocity the two struts (note the two thin, rectangular slits above amplitude being of the same order as that of the the wheels). The wake from the struts tends to spanwise (y) velocity.
accelerate the flow around the rear-right wheel. This is made more clear in Fig. 20, which gives a close-up view We now investigate vortex shedding behind the of the velocity contours shown in Fig. 19. The reverse struts. A horizontal plane at z = 1.3 is chosen so that it flow regions behind the wheels and the struts, and the cuts through the mid-portion of the struts. Note that z = fast flow region between the strut-wake and the rear- 0.5 signifies the top-most points of the wheels. Figures right wheel are clearly seen. Note that the range of 13 and 14 show the density and spanwise velocity
velocity contours (-0.1to0.25)in Fig.20wasselected
Computational results show that vortex shedding
to showthe overalldetails of the flow field in the
with a frequency of approximately 800 Hz occurs off
selected plane. However, the maximum (0.311) and
the rear-right wheel, i.e., the one on the side of the
minimum (-0.1605) streamwise velocities occur outside
diagonal struts. Vortex shedding at a frequency of thisrange.Themaximum velocity occurs in thesmall about 600 Hz also occurs off the downstream strut.
hollowregionon top of the rearwheel,whilethe
Pressure fluctuations with a frequency of about 24 kHz
minimum velocity occurs in thehollowregion near the
are found behind the mid-portion of the oleo. The lower rightpart ofthefrontwheel.
results also indicate that the flow separates at the leading edge of the door and never reattaches. While
An interesting feature of theflowis thattheflow
the flow around the rear-right wheel undergoes strong
coming towards thedooris incident atanangle tothe
oscillations, there is no evidence of such oscillations
planecontaining the doorand,therefore, the flow
from the left wheel. This flow asymmetry is caused by
separates at theleading edgeof the doorandnever
the geometric asymmetry induced by the presence of the
reattaches to it. Figure21 shows the streamwise
diagonal struts and the door attached to the oleo.
velocity contours attheplane z = 1.3 in the vicinity of
Computations also show the existence of streamwise the door. Reverse flow is clearly seen. Figure 22 shows vortices that originate from the top and bottom upstream streamwise velocity profiles in the vertical plane x = corners of the door.
0.15 cutting through the door slightly ahead of the rear wheels. A vortex on the door-top can be clearly seen. Acknowledgements The origin of this vortex is the upstream top-corner of the door. The signatures of this streamwise vortex were This research work was made possible by the earlier seen in Figs. 16-18. We note that another vortex financial support provided to High Technology is present near the lower part of the door which Corporation under NASA Contract NAS 1-00088 originates from the upstream lower-corner of the door.
through a Lockheed Martin subcontract.
While this vortex seems to merge with the rest of the References flow field, its signature can be seen in Fig. 16 near the top of the left wheel. In between the top and bottom tip- vortices, there exists a region of reverse flow. 1. Ffowcs Williams, J. E. and Hawkings, D. L., "Sound Generation by Turbulence and Surfaces in The small spaces between the yoke and the door also Arbitrary Motion," Philosophical Transactions of produce high-frequency oscillations. Figure 23 shows the Royal Society of London A, Vol. 342, 1969, pp.
pressure contours on the surface of the door downstream 264-321.
of the oleo. Islands in the vicinity of junctions of door, 2. Singer, B. A., Brentner, K. S., Lockard, D. P., and yoke, etc. are signatures of the high frequency waves.
Lilley, G. M., "Simulation of Acoustic Scattering Several probes will need to be placed in these locations from a Trailing Edge," J. of Sound and Vibration, to determine the frequencies accurately. In order to Vol. 230, No.3, 2000, pp. 541-560.
provide the unsteady pressure field for his acoustic solver, Lockard _8 continued our coarse grid (1.7 million 3. Khorrami, M. R., Berkman, M., and Choudhari, nodes) simulation for a much longer time period. In M., "Unsteady Flow Computations of a Slat with a that case, a probe behind the lower portion of the oleo Blunt Trailing Edge," AIAA J., Vol. 38, No.l l, picked up high frequency oscillations (see Figure 24) November 2000, pp. 2050-2058.
including a frequency of 25.4 kHz, which is close to the 4. Khorrami, M. R., Singer, B. A., and Berkman, M.
value of 24 kHz referred to above.
E., "Time-Accurate Simulations and Acoustic Conclusions Analysis of Slat Free Shear Layer," AIAA Paper 2001-2155,2001.
RANS simulations of unsteady flow past a landing- 5. Khorrami, M. R., Singer, B. A., and Radeztsky, gear assembly, which consists of four wheels, axles, Jr., R. H., "Reynolds Averaged Navier-Stokes connecting blocks, a door, an oleo and two struts, are Computations on a Flap Side-Edge Flow Field," carried out. The oleo and the diagonal struts are AIAA Paper 98-0768, 1998.
attached to a flat-plate to simulate the wing surface.
The grid consists of 155 block with a total of 13.3 6. Singer, B. A., Lockard, D. P., and Brentner, K. S., million grid point. Computations are performed on the "Computational Aeroacoustic Analysis of Slat SGI-cluster at the NAS facility utilizing a total of 55 Trailing-Edge Flow," AIAA J., Vol. 38, No.9, processors. The flow has a Mach number of 0.2 and a September 2000, pp. 1556-1564.
Reynolds number of 1.23x106.
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Thomas, J., Krist, S., and Anderson, W., "Navier- 10.
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"::'::z_J?_lli% .... _!_._ %N Figure 1. Grid distribution over landing gear surface.
Every other grid point is shown. The oleo and the two diagonal struts attach to a flat-plate (not shown).
Figure 2. Perspective plot of instantaneous pressure contours. Flow from right to left.
.... i .... i .... i .... i ....
.... i .... i .... i .... I ....
1.0 ing side 0.5 Wing side 0.0 Gro " -0.5 -0.5 -1.0 -1.0 , , , , I , , , h I , r , , I , , , , I r , , , ' ' ' , I _ , , , I J , , , I , , , , I , , , , -50 0 50 100 150 200 -50 0 50 100 150 200 Azimuthal Angle Azimuthal Angle Figure 3. Variation of pressure coefficient around the Figure 6. Same as in Fig. 3 except for the rear-right (mid-wheel) circumference of the front-left wheel at 13 wheel.
selected time instances.
.... i .... i .... i .... i ....
.... r .... i .... i .... i ....
Wingside (computalion) ..... Groundside (compulation) ing side O Wingside (experiment) 0.5 0.5 [] Groundside (experiment) Cp Cp 0.0 / 0.0 Ground side ___ -0.5 •. / 0 -1.0 -1.0 , , , , I , , , , I I I I / [ r , , , I , , , , -50 0 50 100 150 200 -50 0 50 100 150 Azimuthal Angle Azimuthal Angle Figure 4. Same as in Fig. 3 except for the front-right Figure 7. Pressure coefficient around the circumference wheel, of the front-left wheel. Comparison with experiment.
MLG geometries used in the experiment and the computation are not the same.
.... I .... I .... I .... I ....
0.715 , , _ .... _ .... i .... a ' ' Wing side 0.710 0.5 (1) Cp ft.
0.0 0.705 -0.5 0.700 -1.0 Behind lower oleo ' ' , r I / , , , L I , , , , I , , , , 0.695 I -50 0 50 100 150 200 50 60 70 80 Azimuthal Angle Time Figure 5. Same as in Fig. 3 except for the rear-left Figure 8. Pressure data from four probes.
wheel.
0.0004 0.0002 D.
0.0000 -0.0002 -0,0004 50 60 70 80 Time Figure 9.
High-pass filtered pressure data from probe behind mid-oleo.
/ i
0.0004 Figure 12. Spanwise velocity contours in the z = 0 plane at t = 84.3 (blue: -0.12 and red: 0.12).
0.0002
i
ft.
0.0000 , / /'''-. \ ,,
'-.. ',,,,//F--..\ /
-0.0002
•
-0.0004 I , , , , I , , _ , 81.0 81.5 82.0 82.5 83.0 Time Figure 10. A shorter time record of high-pass filtered pressure data of Fig. 9. The frequency of oscillation is ...... ......... .,// L...l 24 KHz.
Figure 13. Density contours in the z = 1.3 plane at t = 84.3 (blue: 0.97 and red: 1.02).
Figure 11. Density contours in the z = 0 plane at t = 84.3 (blue: 0.97 and red: 1.02).
Figure 14. Spanwise velocity contours in the z = 1.3 Figure 16. Streamwise velocity contours in the x = 0.95 plane at t = 84.3 (blue: -0.12 and red: 0.12).
plane at t = 84.3, as viewed from downstream (blue: -0.1 and red: 0.35).
it lml i !iiiiiit!tl 1
\ \ \'_\,'.., iiiili ._ i:ii: Figure 15. Streamwise velocity contours in the x = -1.5 Figure 17. Streamwise velocity contours in the x = 1.5 plane at t = 84.3, viewed from upstream (blue: 0.17 and plane at t = 84.3, as viewed from downstream (blue" 0.0 red: 0.2).
and red: 0.2).
Figure 18. Streamwise velocity contours in a plane Figure 20. An enlarged view of results in Fig. 19.
cutting through the left wheels at y - -0.463 (blue -0.1 and red: 0.25).
Figure 19. Streamwise velocity contours in a plane Figure 21. Streamwise velocity contours in the plane cutting through the right wheels at y - 0.463 (blue: -0.1 z - 1.3. Reverse flow is seen near the surface of the and red: 0.25).
door indicating flow separation (blue: -0.1 and red: 0.25).
0.7020 0.7000 0.6980 ,,,-% c_ 0.6960 0.6940 0.6920 0.6900 0 100 200 300 400 Time Figure 24. High frequency oscillations behind lower oleo. From Lockard. _8 Figure 23. Pressure contours on the surface of the door.
Islands in the vicinity of junctions of door, yoke and oleo are signatures of high-frequency waves (blue: 0.70 and red: 0.71).