Aeroacoustic Analysis of a Simplified Landing Gear

AIAA 2004–2887

Aeroacoustic Analysis of a Simplified

Landing Gear

David P. Lockard and Mehdi R. Khorrami

NASA Langley Research Center

Hampton, VA 23681

Fei Li

High Technology Corporation

Hampton, VA

10th AIAA/CEAS Aeroacoustics Conference

May 10–13, 2004

Manchester, UK

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AIAA-2004–2887

High Resolution Calculation of a Simplified Landing Gear

∗ †

David P. Lockard , Mehdi R. Khorrami

NASA Langley Research Center

Hampton, VA

and

Fei Li

High Technology Corporation

Hampton, VA

A hybrid approach is used to investigate the noise generated by a simplified landing gear without small scale parts such as hydraulic lines and fasteners. The Ffowcs Williams and Hawkings equation is used to predict the noise at far-field observer locations from flow data provided by an unsteady computational fluid dynamics calculation. A simulation with 13 million grid points has been completed, and comparisons are made between calculations with different turbulence models. Results indicate that the turbulence model has a profound effect on the levels and character of the unsteadiness. Flow data on solid surfaces and a set of permeable surfaces surrounding the gear have been collected. Noise predictions using the porous surfaces appear to be contaminated by errors caused by large wake fluctuations passing through the surfaces. However, comparisons between predictions using the solid surfaces with the near-field CFD solution are in good agreement giving confidence in the far-field results.

Nomenclature

c speed of sound f integration surface defined by f = 0 F dipole source terms i H Heaviside function √ i − 1 M local source Mach number vector, v /c i i M Mach number, | M | i ˆ n outward directed unit normal vector i p pressure Q monopole source term t time u Cartesian fluid velocity components i v Cartesian surface velocity components i x, y, z Cartesian observer coordinates Greek: δ ( f ) Dirac delta function δ Kronecker delta ij ρ fluid density ξ, η, ζ source coordinates Superscript: ′ ′ perturbation quantity (e.g. ρ = ρ − ρ ) o Subscript: freestream quantity o

Introduction

The past thirty years have seen significant reductions in jet noise through the adoption of high-bypass-ratio turbofan engines on civil aviation transports. Formerly unimportant noise sources such as the airframe have now become a major concern for noise certification and environmental considerations. Airframe noise is most important during aircraft approach and ∗ Aerospace Technologist, Senior Member, AIAA † Aerospace Technologist, Associate Fellow, AIAA This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887 landing, when engines are operating at reduced thrust with the high-lift devices and landing gear deployed. Wind tunnel 1–3 4 tests and fl y-over measurements have revealed the leading-edge slats, fl ap edges, and the landing gear to be the major contributors to airframe noise. Each of the three primary sources of airframe noise are important on different classes of airplanes, but the main landing gear is a dominant source on most modern wide-body transports. Although fl ow compu- tations of high-lift devices such as fl aps and slats received considerable attention in the last decade, the intricacies of the landing-gear fl owfi eld and its associated sound sources have remained virtually unknown due to overwhelming geometrical 5 6 complexities. Nonetheless, computational studies of landing gear are beginning to be performed. Souliez et al. used an unstructured grid technique to investigate the same baseline landing gear used in this work, but the calculations were restricted to laminar fl ow, and the geometry was further simplifi ed by removing the door. In this paper, we present an analysis of our computational aeroacoustic study of a model landing gear. Our computational approach involves a hybrid strategy. In the fi rst step we perform an unsteady computational fl uid dynamics (CFD) simulation to provide a highly resolved near-fi eld solution. Two CFD computations have been performed to investigate the infl uence of the turbulence model on the unsteady fl ow. Unsteady Reynolds averaged Navier-Stokes (URANS) and detached eddy simulations (DES) have been performed. The results indicate that the turbulence model can greatly infl uence the levels and character of the predicted noise.

Despite continued advances in computational resources and numerical algorithms, it is still prohibitively expensive and often infeasible to attempt to resolve wave propagation from near-fi eld sources to far-fi eld observers. Integral techniques that can predict the far-fi eld signal based solely on near-fi eld input are a means to overcome this diffi culty. Hence, the 8 9 Ffowcs Williams-Hawkings (FW-H) equation solver described by Lockard is used to predict the acoustic signature at various observer locations using unsteady fl ow data from the CFD calculation.

Acoustic Equations

The FW-H equation can be written in differential form as ( )( ) ( ) ( ) ( ) 2 2 2 ∂ ∂ ∂ ∂ ∂ 2 ′ − c H ( f ) ρ = T H ( f ) − F δ ( f ) + Qδ ( f ) (1) ij i o ∂t ∂x ∂x ∂x ∂x ∂x ∂t i i i j i where ( ) ∂f 2 ′ T = ρu u + P − c ρ δ , F = P + ρu ( u − v ) , and ij i j ij ij i ij i j j o ∂x j ( ) ∂f Q = ρ v + ρ ( u − v ) . (2) o i i i ∂x i The dipole term F involves an unsteady force, and Q gives rise to a monopole-type contribution that can be thought i of as an unsteady mass addition. The function f = 0 defi nes the surface outside of which the solution is desired. The normalization |∇ f | = 1 is used for f . The total density and pressure are given by ρ and p , respectively. The fl uid velocities are u , while the v represent the velocities of the surface f . The Kronecker delta, δ , is unity for i = j and i i ij zero otherwise. The ambient speed of sound is denoted by c . A prime is used to denote a perturbation quantity relative to o the free-stream conditions denoted by the subscript o . The Cartesian coordinates and time are x and t , respectively. The i usual convention, which is followed here, involves a quiescent ambient state with f prescribed as a function of time so that it always surrounds a moving source region of interest. H ( f ) is the Heaviside function which is unity for f > 0 and zero ′ for f < 0 . The derivative of the Heaviside function H ( f ) = δ ( f ) is the Dirac delta function, which is zero for f 6 = 0 , but yields a fi nite value when integrated over a region including f = 0 . The inviscid part, P = pδ , of the compressive ij ij stress tensor P is used in this work.

ij The FW-H equation is an exact rearrangement of the Navier-Stokes equations that allows one to determine the acoustic signal at distant observer locations if the details of the source region are already known. Hence, the Navier-Stokes equations still need to be solved, but only where nonlinear and viscous effects are important. All of the linear propagation can be determined by the FW-H equation. For three-dimensional fl ows, the time-domain FW-H formulations developed by Farassat are effi cient and amenable to numerical computations. Some additional effi ciency can be obtained by restricting the source to uniform, rectilinear motion. Furthermore, the equation can be solved in the frequency domain which can be useful if one is only interested in analyzing certain frequencies. The frequency domain solution of FW-H equation can be written in the form ∫ ∫ ∂G ( y ; ξ ) 2 ′ H ( f ) c ρ ( y , ω ) = − F ( ξ , ω ) ds − iωQ ( ξ , ω ) G ( y ; ξ ) ds + I (3) i n Q o ∂y i f =0 f =0 American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887 where ( ) ( ) F = pδ + ρ ( u − U )( u + U ) + ρ U U ˆ n , Q = ρ ( u + U ) − ρ U ˆ n . (4) i ij i i j j o i j j n i i o i i The volumetric quadrupole term is denoted by I and includes effects such as nonlinear propagation and refraction. In Q this work, the volumetric contribution is expected to be small and is neglected. Souliez et al. performed FW-H predictions of landing gear noise using solid and permeable integration surfaces and found the solutions to be nearly identical in the far-fi eld, although discrepancies were noted in the near fi eld. The porous surface enclosed a signifi cant region around the gear and should have included most of the fl ow interaction effects. In this work, computations with solid and porous integration surfaces are performed. Computations with the porous surfaces appear to be contaminated because of strong wakes passing through the surfaces. However, the calculations with the solid surfaces are in good agreement with CFD data in the fl ow fi eld as long as wakes are not present.

Simplified Landing Gear Model

(a) Surface grid (b) Perturbation pressure on solid surfaces Fig. 1 CFD grid and SST results for a landing gear.

The simulated geometry is a four-wheel landing gear model that approximately represents a ten percent scale Boeing 757 main landing gear. The model geometry is fairly complex and composed of four wheels, two side struts, an oleo, a side-door, yokes, a pin, and other structures that join the system together (fi gure 1 (a)). The gear assembly is mounted on a fl at plate that represents the aircraft wing. The structured grid consists of 155 blocks possessing a total of 13.3 million grid points. In reference 12 the authors discussed the results for a CFD grid of half the resolution of the current calculation. Figure 1(a) also shows the grid distribution on the surface of the landing gear. The reference length scale is the gear wheel diameter (3.7in=0.09398 m) and the freestream Mach number is 0.2. The CFD calculation employs 13, 14 the three-dimensional, time-dependent code CFL3D, developed at NASA Langley Research Center to solve the three- dimensional, time-dependent, thin-layer Reynolds-Averaged Navier-Stokes (RANS) equations. A more detailed discussion of the CFD calculation can be found in the paper by Li et al. We have used an unsteady RANS calculation with the shear 16, 17 stress transport (SST) k − ω turbulence model of Menter which was developed for steady fl ow. Although qualitatively 18, 19 19 good results have been obtained with this approach for unsteady problems, it is well known that the turbulence model is overly dissipative. We have also run the landing gear problem as a detached-eddy simulation (DES) as proposed by 20, 21 Spalart. The DES model essentially reduces the level of eddy viscosity in regions away from solid surfaces when the grid is suffi ciently fi ne.

Contours of the instantaneous perturbation pressure fl uctuations on the gear solid surfaces are displayed in fi gure 1(b).

The surface pressure shows the footprint of the highly nonlinear and complicated interactive near-fi eld fl ow dynamics.

22, 23 Lazos investigated a simpler four wheel landing gear experimentally and also found the fl ow around the wheels to be quite complicated. Figure 2(a) compares the SST and DES time histories of the pressure on the downstream wheel opposite the door as indicated by the arrow in fi gure 1(b). The pressure is nondimensionalized by ρ c . The time histories show the o o irregular character of the signal. The corresponding spectra are shown in fi gure 2(b). The narrow band results have been American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887 normalized to 1 Hz bin widths. The DES solution has considerably higher fl uctuation levels at all frequencies. The high frequency oscillations above 20 kHz are generated by resonances in small, triangular shaped spaces between the yokes and the door. The wave pattern seen on the door in fi gure 1(b) is caused by these tones. In the SST calculation, the phenomenon results in tones around 21 and 26 KHz, but only the 26 kHz tone is observable at this location. Several tones and a broad increase above 20 kHz are evident in the DES solution. Figure 3 compares the solutions on the oleo in the contraction just below the door. The SST solution is more regular at this location, but the overall amplitude of the fl uctuations is similar.

0.729 SST k- ω DES 0.728 Pressure SPL (dB) 0.727 SST k- ω DES 0.726 0 0 20 40 60 80 5 10 15 20 25 30 Frequency (model scale kHz) Time (a) Time history (b) spectra Fig. 2 Pressure signal on the downstream wheel opposite the door.

0.706 SST k- ω SST k- ω DES DES 120 0.705 0.704 0.703 0.702 Pressure SPL (dB) 0.701 0.7 0.699 0 0 10 20 30 40 5 10 15 20 25 30 Frequency (model scale kHz) Time (a) Time history (b) Spectra Fig. 3 Pressure signal on the oleo.

Figures 4 and 5 present the mean pressure coeffi cient and RMS pressure levels on the gear surfaces from the two CFD calculations. The mean pressure is fairly similar, although the suction peak on the oleo is stronger in the DES calculation. Furthermore, the pressure distribution on downstream side of the rear tire is somewhat altered. Considerably more discrepancies can be observed in the RMS pressure contours. The regions with high fl uctuation levels in the SST calculation are also prominent in the DES results, but the levels are noticeably higher for the DES. In addition, the area over which high fl uctuation levels are present is much larger for the DES calculation. Although the RMS pressure contours give an indication of the total fl uctuation energy in the fl ow, they do not convey any information about the scales of the fl uctuations. Figure 6 presents a comparison of the vorticity magnitude in a plane just downstream of the rear wheels.

The vorticity levels in the SST computation are considerably lower, and the wakes emanating from different sides of components remain distinct. In the DES calculation, all the wakes have merged, and the region is fi lled with vorticity American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887 of various scales. Considerably more interaction appears to be occurring between the vortical structures and indicates increased energy transfer between scales. The higher levels in the spectra in fi gures 2(b) and 3(b) also suggest that more energy is being transferred into high frequencies without being excessively dissipated. The comparison between the DES and SST solutions indicates that the DES calculation is more consistent with the anticipated physics, but such a comparison is not able to verify that the DES calculation is correctly capturing all of the nonlinear energy transfer.

(a) Cp (b) RMS pressure (c) RMS pressure Fig. 4 SST mean and perturbation results for a landing gear. The Flow is from right to left.

(a) Cp (b) RMS pressure (c) RMS pressure Fig. 5 DES mean and perturbation results for a landing gear. The Flow is from right to left.

(a) SST (b) DES Fig. 6 Vorticity magnitude in a cross-stream plane downstream of the landing gear. The Flow is out of the page.

American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887

Impenetrable Surface Noise Calculations

The noise calculations involve 181 total subsurfaces comprising the impermeable data surface. Only the pressure is need on impenetrable surfaces. 147 subsurfaces are on the gear itself, and 34 are on the plate above the gear. The subsurfaces are a natural consequence of the block structured grid used for the CFD calculation. Each subsurface is a boundary of one of the 155 blocks comprising the grid.

Over 12,000 nondimensional time samples with l/c ∆ t = 0 . 02 have been collected from the SST calculation. Nearly o 7, 000 samples have been collected from the DES simulation. The computations are sampled at every fourth time step. A Ffowcs Williams-Hawkings solver written specifi cally for airframe noise applications is being used to perform the noise calculations. The observer is located 100 wheel diameters away from the gear. All of the results in the paper represent an average over fi ve time histories with 50% overlap. Each segment consists of 4096 samples for the SST calculations; whereas, 2048 are used for the DES cases.

Subsurface Noise Predictions Although much of the smaller scale detail is missing from this gear model, it is not apparent which components are contributing to the different portions of the spectrum. To investigate the dominant sources in each frequency range, the landing gear was divided into 10 regions as shown in fi gure 7(a). Each region is colored differently to identify each of the subdomains.

(a) Subsurfaces (b) Pressure contours Fig. 7 Landing gear subsurfaces colored by component and instantaneous pressure contours from SST calculation.

The prediction using all of the surfaces (Gear + Ceiling) is compared with the results when using the ceiling, and everything except the ceiling (No Ceiling) in fi gure 8. The presented results are from the frequency-domain solver, although calculations in the time-domain show good agreement. The results are for an observer located 100 wheel diameters directly below the gear. The results do vary with observer position, but the general trends are similar at most observer locations of interest. However, most of the noise from the ceiling is associated with extraneous noise sources in the vicinity of patched regions of the grid. Because of the extreme complexity of the geometry, extensive patching is used to prevent the propagation of fi ne resolution to unimportant regions and thus reduce the number of grid points. Unfortunately, the disparity in grid resolution across interfaces is often insuffi cient to resolve the phenomena trying to pass through the boundaries resulting in numerical oscillations.

Figure 7(b) shows the instantaneous perturbation pressure contours on the gear and ceiling looking from below. The most intense fl uctuations occur in the wake of the sidebars. Although some interaction between unsteadiness in the wakes with the ceiling is expected, the pressure fl uctuations on the ceiling have been amplifi ed by numerical instabilities in the regions around patched interfaces. Both the SST and DES noise calculations are contaminated by these numerical errors when the ceiling is included. Useful information about the radiated noise can still be ascertained by examining the noise radiated from individual components.

The predicted noise for each of the subsurfaces in fi gure 7 is shown in fi gures 9(a)-(l). Note that the horizontal axes for 9(a)-(b) are different from the rest of the fi gures so that the effect of the high frequency oscillations in the cavities between the yokes and the door can be seen. Just as the surface spectra in fi gure 2(b) showed a broad increase above 20 kHz with several tones for the DES calculation, the noise prediction shows similar trends. In general, the SST results are more tonal, American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887 Gear + Ceiling Gear + Ceiling 60 60 Ceiling Ceiling No Ceiling No Ceiling 50 50 40 40 30 30 SPL (dB) SPL (dB) 20 20 10 10 0 0 0 2 4 6 8 10 0 5 10 15 20 Frequency (model scale kHz) Frequency (model scale kHz) (a) SST (b) DES Fig. 8 Subsurface spectra for an observer 100 wheel diameters below the landing gear.

and the decay rate with frequency is much more rapid. However, the peak frequency for many of the components is similar between the two computations. Furthermore, the wheels and gear boxes appear to be responsible for most of the noise in both calculations. In addition, both computations indicate that the sidebars primary contribution is a tone near 1 kHz.

In all cases, the DES noise predictions have much higher levels, and the difference becomes greater as the frequency increases. Although experimental measurements of the noise from the simplifi ed gear is currently unavailable, comparisons with measurements from a 6 wheeled, 26%, Boeing 777 landing-gear model revealed that the DES results are much closer to the measurements, although the fall off with frequency is still slightly too rapid. The similarity between the shapes of the spectra from different components in the DES calculation indicates that at least a portion of the noise is caused by the interactions between the global, turbulent fl ow with the solid components. The level of turbulence in the fl ow is more accurately represented in the DES calculation, although there is still some extra diffusion in the computation that causes the decay with frequency to be too rapid. The lack of small-scale parts in the model also contributes to discrepancies at high frequencies.

FW-H Source Strengths Another method for identifying source locations involves plotting the integrand in equation 3 over the entire integration surface to visually show where the noise is being generated. For the frequency domain approach, this can be done for each frequency of interest. The amplitude of the complex integrand gives an indication of potential noise sources. One can be deceived by the results because the phase information is lost when only the amplitude of the complex integrand is interrogated. By examining the real and imaginary components, one can get an idea of whether the signals will combine constructively or destructively.

Figures 10 and 11 present the source strengths at three frequencies for the SST and DES calculations. The observer is located 100 wheel diameters directly below the gear. The primary view is at a slight angle from under the gear, and the superimposed image is a view from the side. The amplitudes are dimensionless, and should only be used to make relative comparisons. In general, the levels are considerably higher and more of the gear sees signifi cant source levels for the DES case. Although the ceiling appears to be an important source, it is impossible to discern how strong the real sources are because of the errors in the CFD around patched interfaces on the ceiling.

In general, the gear boxes appear to be the most important source, especially at the higher frequencies. However, fi gures 9(c) and (d) show that the contribution from the wheels is slightly higher than for the gear boxes, even out to high frequencies. Part of the reason for this is the greater surface area of the wheels, but the phase of the complex source strength is actually a more important factor. The real and imaginary parts of the FW-H integrand switch signs repeatedly over the gear boxes which results in cancellation when integrated over the area. The real and imaginary parts do not oscillate as signifi cantly on the wheels. Hence, there appears to be greater coherence on the wheels. Whether this would be true for real wheels with grooves is unclear.

Directivity The directivities from the gear components excluding the ceiling are presented in fi gure 12. Beyond the disparity in levels between the results from the two calculations, the DES predictions show much greater variation. The primary noise radiation is behind the gear in the DES results. However, somewhat higher levels are also observed to the sides of the gear, American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887 60 60 SST k- ω SST k- ω k- ω DES DES DES 50 50 40 40 30 30 SPL (dB) SPL (dB) SPL (dB) 20 20 10 10 0 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 Frequency (model scale kHz) Frequency (model scale kHz) Frequency (model scale kHz) (a) All components (including ceiling) (b) All components (excluding ceiling) (c) Wheels 60 60 60 SST k- ω SST k- ω SST k- ω DES DES DES 50 50 50 40 40 40 30 30 30 SPL (dB) SPL (dB) SPL (dB) 20 20 20 10 10 10 0 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Frequency (model scale kHz) Frequency (model scale kHz) Frequency (model scale kHz) (d) Gear boxes (e) Gear box connectors (f) Sidebars 60 60 60 SST k- ω SST k- ω SST k- ω DES DES DES 50 50 50 40 40 40 30 30 30 SPL (dB) SPL (dB) SPL (dB) 20 20 20 10 10 10 0 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Frequency (model scale kHz) Frequency (model scale kHz) Frequency (model scale kHz) (g) Axles (h) Yokes (i) Oleo 60 60 60 SST k- ω SST k- ω DES SST k- ω DES DES 50 50 50 40 40 40 30 30 30 SPL (dB) SPL (dB) SPL (dB) 20 20 20 10 10 10 0 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Frequency (model scale kHz) Frequency (model scale kHz) Frequency (model scale kHz) (j) Door (k) Pin (l) Hub caps Fig. 9 FW-H results for an observer 100 wheel diameters directly below the landing gear.

American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887 (a) 353 Hz (b) 4637 Hz (c) 10,000 Hz Fig. 10 FW-H source strengths from SST calculation. The Flow is from right to left.

(a) 353 Hz (b) 4637 Hz (c) 10,000 Hz Fig. 11 FW-H source strengths from DES calculation. The Flow is from right to left.

with the region opposite the door being most prominent. The minimum is nearly directly below the gear. For the SST computation, the primary noise radiation is to the sides of the gear, especially opposite the door. In complete contrast to the DES calculation, the minimum occurs behind the gear. Clearly, the differences in the directivities involve more than just changes in fl uctuation levels.

Porous Surface Predictions

Unsteady fl ow data has been collected on the permeable surfaces surrounding the landing gear as shown in fi gure 13(a).

These surfaces were placed relatively close to the gear so they would be within regions of fi ne resolution. Unfortunately, some of the surfaces are subjected to strong wakes. Figure 13(b) shows RMS streamwise velocity contours normalized by the freestream velocity. The perturbation fl uctuation levels exceed 25% of the mean around the wheels and behind the oleo. Signifi cant velocity fl uctuations are also present around the sidebars. Although the FW-H equation has been 9, 25 used successfully for cylinder shedding problems when wakes encounter porous surfaces, errors are generated as the vortices pass through because the volumetric contribution, which is neglected, should cancel some of the surface terms that are included. When the strength of the vortices is suffi ciently large, errors can be generated that are of the same order of the radiated noise.

FW-H predictions of the noise using the permeable surfaces produces levels that are signifi cantly higher than those when using the solid surfaces. Because the errors caused by vortices passing through the surfaces were suspected as the cause, calculations were made for an observer just off of the upstream panel in front of the wheels in fi gure 13(a). The calculated signals are compared with the density from the CFD computation in fi gure 14. Clearly, the calculation using the solid surfaces is in much better agreement with the CFD. The dominant frequencies in the porous solution computation actually correspond to the frequencies of the shedding around the wheels and sidebars. Attempts to exclude portions of porous surfaces with the largest wake fl uctuations have not yielded reasonable results. Although our porous surface data is useful to query the state of the fl owfi eld, it is not appropriate for making noise predictions with the FW-H solver.

Conclusions

The current calculations show that numerical simulations of the noise from landing-gear are possible, but they are far too computationally intensive to be used as a design tool. Using a cluster of forty 2.53 GHz Intel P4 computers with a American Institute of Aeronautics and Astronautics Paper AIAA-2004–2887 (a) SST (b) DES Fig. 12 Directivity contours for an observer located on a hemisphere of radius 100 wheel diameters from the landing gear. The fl ow is from left to right.

(a) Surfaces (b) RMS u/U % ∞ Fig. 13 Penetrable surfaces used for data collection and RMS streamwise velocity from the SST computation. The Flow is from right to left.

high-speed Myrinet network, nearly 6 months would be required just to accumulate a data record of the size used in this work. Nonetheless, the data is extremely useful to guide the development of simple models. However, the differences between the SST and DES results suggests that further validation is needed. Experimental measurements are planned to verify some of the current results. We are also pursuing advances in numerical algorithms, grid generation, and turbulence modeling that should improve our simulation capability.

In the DES calculation, most of the gear is engulfed in regions of high turbulence that tends to minimize regular vortex shedding. Geometric irregularities also seem to prevent regular shedding. The peaks in the spectra still correspond reasonably well with those that would be predicted based on Strouhal shedding, but the spectral shapes are very broad rather than exhibiting distinct tones. The sidebars are an exception, perhaps because of their rectangular shape, orientation, and distance from most of the other gear components. Despite the complexity of the problem, a picture is emerging of the characteristic fl owfi eld around a landing gear that will be used to guide future modeling efforts.

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American Institute of Aeronautics and Astronautics Paper