Numerical Investigations of Bio-Inspired Blade Designs

to Reduce Broadband Noise in Aircraft Engines and

Wind Turbines

Bharat Raj Agrawal∗ and Anupam Sharma†

Department of Aerospace Engineering,

Iowa State University, Ames, IA, USA, 50011.

I. Introduction

The unprecedented growth in the use of unmanned aerial vehicles (UAVs), civil aviation, and windturbines gives a new dimension to the problem of noise emitted by these machines - the noise problem willno longer be limited to spatial pockets near airports or wind farms. UAVs will be flying a few hundred feetover our houses and landing in our front yards. Wind turbines similarly will be in much closer proximity toour homes with the five-fold increase in wind energy capacity envisioned by the Department of Energy.1 Theincreased number and proximity of these machines to humans is bound to exacerbate the aerodynamic noiseissue. The adverse effects on health of noise in general,2 aircraft noise,3,4 and wind turbine noise,5,6 are wellknown. With such widespread impact, noise reduction is no longer a nice-to-have, but an enabling technologyfor next-generation energy and propulsion machines. Efforts to silence these machines will undoubtedly havea significant impact on our lives.

Nature inspires great innovations. Bio-mimicry has already provided some outstanding innovations in avariety of engineering applications.7 Termite mounds have inspired temperature-regulated buildings,8 thehydrophobic lotus leaf has inspired self-cleaning paints,9 the kingfisher bird has inspired Japan’s Shinkasen(high-speed train), etc. One such biological marvel that is yet to find its due application in engineering isthe night owl with its ability to fly silently. Of all the vehicles known to man only the owl is capable ofalmost silent flight.10 One species of the night owl - the common barn owl (Tyto alba) - is particularly adeptat flying silently. Henceforth, the common barn owl shall be referred to as the owl. The owl has evolved forover 20 million years to perfect its silent flight. Ornithologists have reported11 the unusually quiet flight ofthe owl as early as in the 1930s. It is likely that the acoustic stealth capability (“hush kit”) of the owl hasbeen known for much longer.

The owl needs to have silent flight for two reasons:12 (1) to aurally locate the prey in the dark; thissupplements its brilliant vision, and (2) to avoid aural detection by the prey. The owl is completely inaudiblein its flight if it is more than 3 meters away.13 Early investigations13,14 have reported three key anatomicalfeatures (unique feather adaptations) of the owl that enable its acoustically silent flight:

1. Stiff comb-like structure at the leading edge of the wing,

2. Flexible fringe like structure at the trailing edge of the wing, and

3. Soft, thick downy coat on the wings and legs.

The comb-like structure (referred to as serrations) is formed by extensions of the barbs of the 10thprimaries of the owl. The fringe structure, present on each primary feather, is formed by extensions of thebarbs that make up the posterior part of the vane. The thick downy (velvety) coat on the feathers and legsacts as a poroelastic surface. Each of these features serves a distinct purpose in its silent flight. Figure 1 isan illustration with close-ups to show the noise reducing features of the owl.

∗Ph.D. student, 1200 Howe Hall, Ames IA, 50011. bharatr@iastate.edu. AIAA Student Member.†Assistant Professor, 2341 Howe Hall, Ames, IA, 50011. sharma@iastate.edu. AIAA senior member.

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Figure 1: Unique feather adaptations of the owl that enable its silent flight (1) serrations at the leadingedge of the wing, (2) fringe at the trailing edge, and (3) soft, thick down coat. The bottom two zoom imageson the right are from References.13,15

This paper focuses on leading edge serrations of the owl and investigates if blade designs inspired by thisunique feather adaptation can assist in reducing aerodynamic noise from next-gen propulsion and energymachines. A particular emphasis is laid on the problem of inflow turbulence noise. Chord-based Reynoldsnumber for the barn owl in gliding flight is between 50,000 – 90,000. Small-scale micro- and unmannedaerial vehicles (MAVs/UAVs) operate in a similar Reynolds number regime. Figure 2 illustrates the range ofReynolds number over which various flying machines and animals, including the owl, operate. Bio-mimeticdesigns based on the owl wing would therefore apply directly to such UAVs and MAVs where the flow overthe blades/wings is expected to be predominantly laminar. The objective of this paper is however to exploreif similar bio-inspired designs can also mitigate noise at much higher Reynolds numbers (105 − 107), wherethe flow is expected to be turbulent. Application of bio-inspired designs in this high Reynolds number regimewould facilitate development of ultra-quiet aircraft engines and wind turbines.

Figure 2: Chord based Reynolds number of various species compared with different aircraft

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II. Numerical Methodology

Two numerical approaches are used to estimate aerodynamic sound generation. In the first approach,hydrodynamics is computed by assuming the flow to be incompressible, while in the second this assumptionis relaxed and compressibility effects are accounted for. Both approaches use the large eddy simulationmethodology where only the larger-scale, energy containing eddies are resolved. The smaller-scale turbulenceis either modeled using some sort of universal, sub-filter scale model, or removed by performing low-passfiltering (‘implicit LES’). The incompressible flow solver used in the study is pimpleFoam (part of theOpenFOAM software suite), while FDL3DI16 is used as the compressible flow solver. Noise radiation iscomputed using: (a) Amiet’s extension17 of Curle’s theory18 with incompressible flow simulation data, and(b) Ffowcs Williams-Hawkings acoustic analogy19 with compressible flow data.

Previous work by the authors?, 20, 21 documents the details of these two noise prediction approaches. Abrief summary is provided here for completion. The compressible solver used in this study (FDL3DI) isdifferent from that used in previous studies and its details are presented here.

PimpleFoam solves the time-accurate, incompressible Navier Stokes equations using the PIMPLE (mergedPISO-SIMPLE) algorithm. We use the standard Smagorinsky approach22 to model sub-grid stresses, al-though other models23–25 are also available. The PIMPLE algorithm allows the Courant Friedrichs Lewy(CFL) number to be greater than unity while still maintaining numerical stability. Time discretization isdone using a second order implicit scheme. The flowfield is initialized with same non-dimensionalized veloc-ity (u∞ = 0.2), gauge pressure to zero, and kinematic viscosity is specified as ν = 4.2 × 10−7. Freestreamboundary condition is used at the outer boundary where the velocity switches between zero gradient foroutflow and fixed (prescribed) value for inflow. Pressure boundary condition is zero gradient, which fixesthe flux across the boundary using freestream velocity. A second order implicit scheme is used for timemarching. Gaussian integration with linear central differencing interpolation is used in computing gradients,Laplacian and divergence terms, except that divergence for the convective term is computed using linearupwind differencing interpolation. For farfield noise computation with incompressible flow data, Amiet’sapproach requires time accurate pressure data on the noise-radiating surfaces. Cross-spectral density ofsurface pressure is convolved with the free-space Green’s function to obtain far-field noise. This is performedas a post-processing step. Validation of this approach is documented in Refs.?,20

FDL3DI solves the full Navier-Stokes equations on curvilinear meshes. Compact finite difference schemes,up to sixth-order accurate, are used to discretize space. Time integration can be performed either explicitlyusing the four-stage Runge-Kutta method, or implicitly using the second-order accurate Beam Warmingscheme.26,27 For numerical stability, high-order (up to 10th order) low-pass spatial filters are applied.The solver can be run in large eddy simulation (LES) mode with the sub-grid stresses (SGS) modeledexplicitly (using the constant-coefficient Smagorinsky model22 or its dynamic variant,23,28 or implicitlyhandled using spatial filtering to remove energy at the smallest scales. The code can work with multi-block overset (Chimera) meshes with high order interpolation methods that allow extending the spectral-likeaccuracy of the solver to complex geometries. Spatial decomposition with the message passing interface(MPI) library is used to achieve parallel execution. The performance of the software can be further enhancedon multi-core machines by using multiple OpenMP threads. Inter-processor boundaries are treated usingthe overset mesh capability with high order (up to 10th order) interpolation algorithms. The governingfluid flow equations (solved by FDL3DI), after performing a time-invariant curvilinear coordinate transform(x, y, z)→ (ξ, η, ζ) written in a strong conservation form are

∂

∂t

(U

J

)+∂FI

∂ξ+∂GI

∂η+∂HI

∂ζ=

1

Re

[∂Fv

∂ξ+∂Gv

∂η+∂Hv

∂ζ

], (1)

where J is the Jacobian of the coordinate transformation, U = {ρ, ρu, ρv, ρw, ρE}; the expressions for inviscid

flux terms, FI , GI , HI and viscous flux terms, Fv, Gv, Hv are provided in Ref.16 We perform ‘implicit’ LESsimulations using FDL3DI by employing sixth-order spatial accuracy and the second order implicit timeintegration scheme. No subgrid scale model is used and dissipation at viscous scales is achieved by low-passfiltering (10th order) the solution at every time step.

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III. Model Inflow Noise Problem

The problem of the wake of a cylindrical rod interacting with a downstream airfoil (extruded to forma wing of unit aspect ratio) is used as a model problem to investigate the effect of leading edge serrationson radiated noise. The cross-section of the rod is circular and the airfoil is chosen to be the NACA 0012(symmetric) airfoil. The availability of experimental data for this problem (for straight leading edge airfoil)29

is the primary reason to select this geometry.Figure 3 shows the problem schematic in non-dimensional variables, where length is non-dimensionalized

by the airfoil chord, velocity by the speed of sound, and density by the freestream density. The rod and theairfoil are placed in tandem along the x direction, the span direction is along the z axis, and the y directionis given by the right-hand rule. This arrangement is kept in a uniform, low-turbulence flow of M∞ = 0.2and airfoil chord-based Reynolds number, Rec = 4.8× 105.

-1.5 -1 -0.5 0 0.5 1 1.5

y

x0.1

Figure 3: A schematic showing the non-dimensional size and relative positions of the rod and the airfoil

A. Meshing

The meshing strategy for incompressible simulations using pimpleFoam is similar to that described in Agrawaland Sharma.? The structured volume mesh is generated using the Pointwise software (www.pointwise.com/pw) in a four step process: (1) create surface meshes for the rod and the wing, (2) using normal extrusion,create volume meshes around both geometries suitable for capturing boundary layers, (3) create a mid-sectionblock connecting the volume mesh blocks around the rod and the wing, and (4) create a volume mesh aroundthese three blocks all the way to the farfield boundary. Each of these steps require careful assessment ofquality parameters in order to obtain a good final mesh which can be used with pimpleFoam. The firststep for straight leading-edge wing is straightforward. Wings with serrated leading edges however requiremultiple iterations of the entire meshing process to ensure that the surface quadrilateral elements are of goodquality. In particular, ensuring near-orthogonal meshes is very challenging to achieve. The total number ofcells in the grid is approximately 19 million for the straight-edge and serrated leading edge geometries. Also,the first cell height is also kept the same at 4× 10−5 in nondimensional sense to give approximately y+ = 1.

The overlapping grid (Chimera) capability is exploited in developing the meshes for use with FDL3DI.Eight simple individual meshes comprise the full mesh for the rod-airfoil problem. The rod and the airfoilare discretized using O-meshes, where normal extrusion from the surface is used to refine the grid nearthe walls. Each O-mesh (for the rod and the airfoil) is split into two meshes with overlapping boundariesto convert them into regular H-meshes in the computational space. Three background H-meshes are usedto mesh the space between the rod and the airfoil, and the space upstream and downstream of the rod-airfoil system. The boundaries of the overall mesh and the individual meshes as well as the overlappingregion between individual meshes are shown in Fig. 4. A minimum of 5 point overlap is required by theFDL3DI solver to ensure high-order accurate interpolation between individual meshes. Similar interpolationis performed between blocks when domain decomposition is used to split individual meshes into multipleblocks for parallel execution. NASA’s PEGASUS software is used to perform hole cutting and identifyingoverlapping (fringe) points. The BELLERO software by the Air Force Research Laboratory (AFRL) is usedto compute high-order accurate interpolation weights. The overall mesh size is similar to that used withpimpleFoam.

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(a) Mesh boundaries (b) Overlapping grids (c) Zoom view of overlapping grids

Figure 4: Overset (Chimera) grid used with FDL3DI for the rod-airfoil problem: (a) boundaries of individualmeshes, (b) overview of overlapping grids, and (c) zoom view of the overlap region between the airfoil O-meshand the H-mesh.

B. Serrated Leading Edge Airfoil

Figure 5 compares the sound power spectral density (PSD) between the baseline (straight-edge) and aserrated leading edge wing design. The PSDs are computed at a point in the far field. This particular resultis obtained using the incompressible + Amiet’s theory approach. Reduction of the order of approximately 5dB is observed in the mid-to-high frequency range for this particular design.

30

40

50

60

70

80

f1 f2 f3 f40.1 1

Spp(ω

)dB/H

z(w

ref4×10

−10Pa2)

St = fd/U∞

BaselineSerrated LE

(a) PSD

−2

0

2

4

6

8

10

f1 f2 f3 f40.1 1

∆Spp(ω

)dB/H

z

St = fd/U∞

(b) Delta PSD

Figure 5: Comparison of predicted power spectral densities (PSDs) of acoustic pressure 18.5 chords awayfrom the leading edge of the wing for baseline and a serrated leading edge wing. The figure on the rightshows the reduction in PSD (+ive value implies reduction) due to serrations.

C. Parametric Studies

Results from a reduced set of parametric studies varying the serration frequency and the height (amplitude)of the serrations will be presented in the final paper. Figure 6 shows the wing designs that will be evaluatedfor the rod-airfoil interaction problem. Comparisons with the baseline wing will be drawn for surface pressureas well as far field sound power spectral densities.

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(a) Low (b) Medium (c) High

(d) Low (e) Medium (f) High

Figure 6: Various leading edge serration designs to be investigated. Top row - variation of serration frequency;bottom row - variation of serration amplitude.

IV. Conclusions

Preliminary numerical results (see Fig. 5) show unambiguous reduction in broadband noise due to lead-ing edge serrations for the model problem of rod-airfoil interaction. The tonal noise at the fundamentalfrequency remains unaffected. The final manuscript will include detailed comparisons between the straight-edge and serrated leading edge geometries. The physics behind noise reduction, e.g. whether it is the phasedecorrelation along the span or reduced unsteady lift on the airfoil due to the serrations will be presented.

Acknowledgments

Funding for this research was provided by the Iowa Space Grants Consortium (Grant #475-20-5), theNational Science Foundation National Science Foundation (Grant #NSF/CBET-1438099), and the IowaEnergy Center (Grant #14-008-OG). Computational resources used for this research were provided by NSFXSEDE (Grant #TG-CTS130004). Technical support for the FDL3DI software provided by Dr. DanielGarmann of Air Force Research Laboratory and Dr. Umesh Paliath of the General Electric company is alsoacknowledged.

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