Numerical Evaluation of Noise Sources and Statistics from...

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Numerical Evaluation of Noise Sources and Statistics from High-Speed Two-Phase Jet Flow Wei Wang, S. Balachandar, and S. A. E. Miller Theoretical Fluid Dynamics and Turbulence Group University of Florida Jan 2020 Wei Wang, [email protected] 1

Transcript of Numerical Evaluation of Noise Sources and Statistics from...

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Numerical Evaluation of Noise Sources and Statistics from

High-Speed Two-Phase Jet Flow

Wei Wang, S. Balachandar, and S. A. E. Miller

Theoretical Fluid Dynamics and Turbulence Group

University of Florida

Jan 2020 Wei Wang, [email protected] 1

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Acknowledgement

This research is supported by the Space Research Initiative (SRI) OR-DRPD-SRI2019: Prediction and Reduction of Noise from Rockets to Eliminate Failure and Fatigue, the University of Florida Department of Mechanical and Aerospace Engineering, and the Herbert Wertheim College of Engineering.

Jan 2020 Wei Wang, [email protected] 2

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Outline

β€’ Introduction

β€’ Computational Approach

β€’ Results and Discussions

β€’ Summary and Conclusions

β€’ Future Work

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Introduction

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Rocket Exhaust Noise

Jan 2020 Wei Wang, [email protected] 5

Objective: Understanding the physics of noise generation and propagation of two-phase particle-gas supersonic jet flow.

Delta IV rocket lifts off from Space Launch Complex 37 at Cape Canaveral Air Force

Station in Florida for an unpiloted test flight of NASA's Orion spacecraft. Image is

obtained online from nasa.gov.

Figures and data are from Jayanta Panda from NASA Ames Research Center.

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Acoustic Analogies

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β€’ Aerodynamic noise theory in which the equations of motion for a compressible fluid are rearranged in a way that separates linear acoustic propagation effects[1].

β€’ Lighthill

β€’ Curle and Ffowcs-Williams and Hawking (FW-H)

β€’ Phillip, Lilley, and Goldstein

β€’ Crighton and Ffowcs-Williams for Two-phase Flow [2]

πœ•2

πœ•π‘‘2βˆ’ π‘βˆž

2 𝛻2 𝜌 βˆ’ 𝜌∞ =πœ•π‘„

πœ•π‘‘βˆ’πœ•πΊπ‘–πœ•π‘₯𝑖

+πœ•2𝑇𝑖𝑗

πœ•π‘₯π‘–πœ•π‘₯𝑗

Monopole: 𝑄 = βˆ’πœŒπœ•

πœ•π‘‘+ 𝑣𝑗

πœ•

πœ•π‘₯𝑗ln 1 βˆ’ 𝛼

Dipole: 𝐺𝑖 = 𝐹𝑖 +πœ•

πœ•π‘‘π›ΌπœŒπ‘£π‘–

[1] Morris, P. J., and Farassat, F., β€œAcoustic analogy and alternative theories for jet noise prediction,” AIAA Journal, vol. 40, 2002, pp. 671–680.[2] Crighton, D., and Ffowcs Williams, J., β€œSound generation by turbulent two-phase flow,”Journal of Fluid Mechanics, Vol. 36,No. 3, 1969, pp. 585–603

Effect of volume fraction

Effect of drag force

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β€’ NASA Marshall

β€’ Ares I Scale Model Acoustic Test (ASMAT)[1]

β€’ Loci/CHEM code

β€’ NASA AMES

β€’ Launch, Ascent, and Vehicle Aerodynamics (LAVA) code[2]

Selected Previous Investigations

[1] Counter, D. and Houston, J., β€œAres I Scale Model Acoustic Test Above Deck Water Sound Suppression Results," 162nd Acoustical Society of America Meeting, 2011.[2] Kiris, C. C., Housman, J. A., Barad, M. F., Brehm, C., Sozer, E., and Moini-Yekta, S., β€œComputational framework for Launch, Ascent, and Vehicle Aerodynamics (LAVA),” Aerospace Science and Technology, vol. 55, 2016, pp. 189–219.

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β€’ University of Michigan

Sound Generated in Compressible Shear Layers[1]

β€’ NASA

Near-field noise of solid-propellant rocket[2]

Selected Previous Investigations

[1] Buchta, D. A., Shallcross, G., and Capecelatro, J., β€œSound and turbulence modulation by particles in high-speed shear flows,” Journal of Fluid Mechanics, Vol. 875, 2019, pp. 254–285.[2] Horne, W. C., Burnside, N. J., Panda, J., and Brodell, C., β€œMeasurements of unsteady pressure fluctuations in the near-field of a solid rocket motor plume,” Int. J. Aeroacoustics, vol. 15, 2016, pp. 554–569.

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Computational Approach

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Computational Method

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CFD solver

Particle solver

Time-dependent flow-field

2-way coupling

Acoustic solver (FW-H)

Source analysis

Implicit LES Aerodynamic Aeroacoustics Far-field noise

Noise source

[1] Miller, S. A. E., β€œToward a Comprehensive Model of Jet Noise Using an Acoustic Analogy,” AIAA Journal, Vol. 52, No. 10, 2014, pp. 2143–2164. doi:10.2514/1.j052809.[2] Panda, J., and Mosher, R., β€œMicrophone Phased Array to Identify Liftoff Noise Sources in Model-Scale Tests,” Journal of Spacecraft and Rockets, Vol. 50, No. 5, 2013, pp. 1002–1012. doi:10.2514/1.A32433.

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Numerical Simulation

CFD Solver

β€’ RocfluidMP CFD Solver

β€’ Unstructured

β€’ Finite Volume

β€’ Eulerian-Lagrangian

β€’ 2-Way Coupling

β€’ Implicit LES

β€’ AUSM+

β€’ 3rd order Runge-Kutta

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Acoustics Solver

β€’ Developed in-house

β€’ Ffowcs-Williams and Hawking’s (FW-H)

β€’ Far-field acoustics

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Governing Equations

Navier-Stokes Equation

πœ•

πœ•π‘‘ΰΆ±Ξ©

(𝟏 βˆ’ 𝜢)𝑾𝑑Ω +ΰΆ»πœ•Ξ©

(𝟏 βˆ’ 𝜢)𝑭𝒄𝑑𝑆 = ΰΆ»πœ•Ξ©

(𝟏 βˆ’ 𝜢)𝑭𝒗𝑑𝑆 + ΰΆ±Ξ©

𝑸𝑑Ω

where𝑾 = 𝜌, πœŒπ‘’, πœŒπ‘£, πœŒπ‘€, 𝜌𝐸 𝑇

𝑭𝒄 = πœŒπ‘‰π‘›, πœŒπ‘’π‘‰π‘› + 𝑛π‘₯𝑝, πœŒπ‘£π‘‰π‘› + 𝑛𝑦𝑝, πœŒπ‘€π‘‰π‘› + 𝑛𝑧𝑝, πœŒπ»π‘‰π‘›π‘‡

𝑭𝒗 =

0𝑛π‘₯𝜏π‘₯π‘₯ + π‘›π‘¦πœπ‘₯𝑦 + π‘›π‘§πœπ‘₯𝑧𝑛π‘₯πœπ‘¦π‘₯ + π‘›π‘¦πœπ‘¦π‘¦ + π‘›π‘§πœπ‘¦π‘§π‘›π‘₯πœπ‘§π‘₯ + π‘›π‘¦πœπ‘§π‘¦ + π‘›π‘§πœπ‘§π‘§π‘›π‘₯Θπ‘₯ + π‘›π‘¦Ξ˜π‘¦ + π‘›π‘§Ξ˜π‘§

,

Θπ‘₯ = π‘’πœπ‘₯π‘₯ + π‘£πœπ‘₯𝑦 + π‘€πœπ‘₯𝑧 + Ξ€π‘˜πœ•π‘‡ πœ•π‘₯

Ξ˜π‘¦ = π‘’πœπ‘¦π‘₯ + π‘£πœπ‘¦π‘¦ +π‘€πœπ‘¦π‘§ + Ξ€π‘˜πœ•π‘‡ πœ•π‘¦

Θπ‘₯ = π‘’πœπ‘§π‘₯ + π‘£πœπ‘§π‘¦ +π‘€πœπ‘§π‘§ + Ξ€π‘˜πœ•π‘‡ πœ•π‘§

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Governing Equations

Phase-Coupling Terms

𝑸 = 0, 𝑓𝑝,π‘₯, 𝑓𝑝,𝑦 , 𝑓𝑝,𝑧, 𝐸𝑝𝑇

𝒇𝒑 = βˆ’π‘šπ‘ 𝑽 βˆ’ 𝑽𝒑

πœπ‘’

𝐸𝑝 =[𝒇𝒑 βˆ™ 𝑽𝒑 βˆ’ 𝑽

βˆ’π‘šπ‘πΆπ‘,𝑝 𝑇 βˆ’ 𝑇𝑝

πœπœƒ]

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Point Particles

β€’ Evolution Equations

𝑑

𝑑𝑑𝒙𝑝 = 𝑽𝑝 ,

d

dt𝐕p =

π•βˆ’π•p

πœπ‘’,

𝑑

𝑑𝑑𝑇𝑝 =

π‘‡βˆ’π‘‡π‘

πœπœƒ

β€’ Time Scales

πœπ‘’ =πœŒπ‘π‘‘π‘

2

18πœ‡π‘“π‘’ 𝑅𝑒, πœπœƒ =

𝐢𝑝,π‘πœŒπ‘π‘‘π‘2

12π‘˜π‘“πœƒ(𝑅𝑒)

β€’ Correlations

Naumann and Schiller(1935): 𝑓𝑒 𝑅𝑒 = 1 + 0.15𝑅𝑒0.687

Ranz and Marshall(1952):

π‘“πœƒ 𝑅𝑒 = 1 + 0.3𝑅𝑒1

2π‘ƒπ‘Ÿ1

3

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Ffowcs-Williams Hawking Equation

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Inhomogeneous Wave Equation Derived from Navier-Stokes Equation

β–‘2 𝑝′𝐻 𝑓 =πœ•

πœ•π‘‘πœŒ0𝑣𝑛𝛿 𝑓 +

πœ•

πœ•π‘‘πœŒ(𝑒𝑛 βˆ’ 𝑣𝑛)𝛿 𝑓

βˆ’πœ•

πœ•π‘₯π‘–πœŒπ‘’π‘– 𝑒𝑛 βˆ’ 𝑣𝑛 𝛿 𝑓 +

πœ•

πœ•π‘₯𝑖𝐿𝑖𝛿 𝑓

+πœ•2

πœ•π‘₯π‘–πœ•π‘₯𝑗[𝑇𝑖𝑗𝐻(𝑓)]

Where

β–‘2 =1

𝑐2πœ•2

πœ•π‘‘2βˆ’

πœ•2

πœ•π‘₯𝑖2

𝐿𝑖 = βˆ’ 𝑝 βˆ’ 𝑝0 𝛿𝑖𝑗 βˆ’ πœŽπ‘–π‘— ෝ𝑛𝑗𝑇𝑖𝑗 = πœŒπ‘’π‘–π‘’π‘— βˆ’ πœŽπ‘–π‘— + 𝑝 βˆ’ 𝑝0 βˆ’ 𝑐0

2πœŒβ€² 𝛿𝑖𝑗

Loading noise

Quadrupole source

Thickness noise

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Ffowcs-Williams Hawking Equation

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Farrasat’s Formulation[1]

4πœ‹π‘β€² 𝒙, 𝑑 =

ΰΆ±

ΰ΅©

𝜌0 αˆΆπ‘£π‘›π‘Ÿ 1 βˆ’π‘€π‘Ÿ

2+𝜌0𝑣𝑛 π‘Ÿ αˆΆπ‘€π‘Ÿ + 𝑐 π‘€π‘Ÿ βˆ’π‘€2

π‘Ÿ2 1 βˆ’ π‘€π‘Ÿ3

+αˆΆπ‘™π‘Ÿ

π‘π‘Ÿ 1 βˆ’ π‘€π‘Ÿ2+π‘™π‘Ÿ βˆ’ 𝑙𝑖 βˆ™ 𝑀𝑖

π‘Ÿ 1 βˆ’π‘€π‘Ÿ2+

π‘™π‘Ÿ π‘Ÿ αˆΆπ‘€π‘Ÿ + 𝑐 π‘€π‘Ÿ βˆ’π‘€2

π‘π‘Ÿ2 1 βˆ’π‘€π‘Ÿ3 +

ሢ𝜌 𝑒𝑛 βˆ’ 𝑣𝑛 + 𝜌 αˆΆπ‘’π‘› βˆ’ αˆΆπ‘£π‘›π‘Ÿ 1 βˆ’ π‘€π‘Ÿ

2 1 +β„³π‘Ÿ +

𝜌 𝑒𝑛 βˆ’ π‘£π‘›π‘Ÿ 1 βˆ’ π‘€π‘Ÿ

2αˆΆβ„³π‘Ÿ +

𝜌 𝑒𝑛 βˆ’ 𝑣𝑛 π‘’π‘Ÿ βˆ’ 𝑒𝑖𝑀𝑖

π‘Ÿ2 1 βˆ’π‘€π‘Ÿ2 +

𝜌 𝑒𝑛 βˆ’ 𝑣𝑛 1 +β„³π‘Ÿ

π‘Ÿ2 1 βˆ’π‘€π‘Ÿ3 π‘Ÿ αˆΆπ‘€π‘Ÿ + 𝑐 π‘€π‘Ÿ βˆ’π‘€2

π‘Ÿπ‘’π‘‘

𝑑𝑆

π‘Ÿ = |𝒙 βˆ’ π’š|

Subscripts:

n = surface normal direction

r = radiation direction

[1] Brentner, K. S., and Farassat, F., β€œAnalytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces,” AIAA Journal, Vol. 36, No. 8, 1998, pp. 1379–1386. doi:10.2514/2.558, URL https://doi.org/10.2514/2.558.

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Results and Discussions

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Geometry and Computational Grid

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β€’ SMC016 Nozzle (SHJAR)[1]

β€’ 𝐷 = 0.0508 π‘š ,𝑀𝑗 = 1.5

β€’ Smooth Nozzle Wall

β€’ 50𝐷 Γ— 30𝐷

β€’ 2.1M hexahedra cells

β€’ O-H Structured-like Grid

β€’ Minimum cell ~10βˆ’4 π‘š ~1%D

[1] Brown, C., and Bridges, J., β€œSmall Hot Jet Acoustic Rig Validation,” Tech. Rep. NASA TM-2006-214234, April 2006.

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Flow Conditions

β€’ Reproduction of SHJAR dataset

β€’ On-design

β€’ Cold jet

β€’ Particle mass flow rate ~ 10% gas mass flow rate

Jan 2020 Wei Wang, [email protected] 18

Case NPR TTR

Fullyexpanded

Mach number, 𝑀𝑗

ParticleMass Flux (π‘˜π‘”/π‘š2𝑠)

ParticleDiameter

(πœ‡π‘š)

1 3.67 1 1.5 0 N/A

2 3.67 1 1.5 30 10

Gas: 𝑝0, 𝑇0

Particle: αˆΆπ‘š, 𝑑𝑝

Nozzle

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Mean Streamwise Velocity

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[1] Bridges, J., and Brown, C., β€œValidation of the small hot jet acoustic rig for aeroacoustic research,” 11th AIAA/CEAS aeroacoustics conference, 2005, p. 2846.[2] Lau, J. C., Morris, P. J., and Fisher, M. J., β€œMeasurements in Subsonic and Supersonic Free Jets Using a Laser Velocimeter,” Journal of Fluid Mechanics, Vol. 93, No. 1, 1979,p. 1–27. doi:10.1017/S0022112079001750.

π‘Ž) Mean streamwise velocity b) Radial profile of mean velocity

c) Pressure contour

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Comparison of the Mean Streamwise Velocity of Gas and Particles

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π‘Ž) Mean streamwise velocities of gas and particles on the centerline

b) Mean velocity profiles of gas and

particles in the radial direction

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Comparison of Far-field SPL Spectra

β€’ Far-field SPL spectra at downstream direction

β€’ πœƒ = 160Β°,𝑅

𝐷= 100

β€’ Large-scale mixing noise

β€’ Mach wave radiation

β€’ Attenuation at St below 1

Jan 2020 Wei Wang, [email protected]

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Statistics of 𝑇11 of Lighthill’s Stress Tensor on the Nozzle Lipline

Jan 2020 Wei Wang, [email protected] 22

π‘Ž) Variance

b) Skewness c) Kurtosis

Sound sources are greatly altered in the particle-laden jet

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Two-Point Cross-Correlation of 𝑇11 of Lighthill’s Stress Tensor on the Nozzle Lipline

β€’ Highly correlated in small region

β€’ Semi-periodic in single-phase jet

β€’ De-correlated in two-phase jet

β€’ Length scale difference

β€’ Different source compactness

Jan 2020 Wei Wang, [email protected] 23

Zero time-lagged two-point cross-correlation. Reference point location: X = 𝐷, π‘Œ = ΀𝐷 2 ,𝑍 = 0.

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Convection of 𝑇11 of Lighthill’s Stress Tensor

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π‘Ž) Gas jet b) Particle-laden jet

β€’ Convective velocity is reduced in the particle-laden jet

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Jan 2020 Wei Wang, [email protected] 25

Phase Velocity of 𝑇11 of Lighthill’sStress Tensor

π‘Ž) Gas jet

b) Particle-laden jet

β€’ Nozzle lipline

β€’ Frequency-wavenumber space

β€’ Phase-velocity πœ”/π‘˜ is lower than convective velocity

β€’ Reduced convective velocity in the downstream direction

β€’ Reduced phase-velocity in the particle-laden jet

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Monopole and Dipole Sound Source

Crighton and FfowcsWilliams’ acoustic analogy[1]

β€’ Monopole:

𝑄 = βˆ’πœŒπœ•

πœ•π‘‘+ 𝑣𝑗

πœ•

πœ•π‘₯𝑗ln 1 βˆ’ 𝛼

β€’ Dipole:

𝐺𝑖 = 𝐹𝑖 +πœ•

πœ•π‘‘π›ΌπœŒπ‘£π‘–

β€’ Monopole source is not zero due to slip effect of the particles

Jan 2020 Wei Wang, [email protected] 26

[1] Crighton, D., and Ffowcs Williams, J., β€œSound generation by turbulent two-phase flow,”Journalof Fluid Mechanics, Vol. 36,No. 3, 1969, pp. 585–603

π‘Ž) Centerline

b) Lipline

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π‘Ž) Monopole source on the centerline

b) Dipole source on

the centerline

c) Monopole source on

the liplined) Dipole source on

the lipline

Reference point location: X = 10𝐷, π‘Œ = 0, 𝑍 = 0.

Reference point location: X = 10𝐷, π‘Œ = ΀𝐷 2 , 𝑍 = 0.

Time-lagged Two-point Correlation of Monopole and Dipole Sound Source

Jan 2020 Wei Wang, [email protected] 27

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Summary and Conclusion

Jan 2020 Wei Wang, [email protected] 28

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Summary and Conclusionβ€’ Summary

β€’ FWH method based on implicit LES two-phase gas-particle simulation

β€’ Comparison of far-field sound spectra of gas and particle-laden jets

β€’ Source statistics based on the C-FW acoustic analogy

β€’ Important findingsβ€’ Sound spectrum is greatly altered in particle-laden jet

β€’ The location, convection and phase velocity of Lighthill’stensor are altered.

β€’ Monopole and dipole sources arise in two-phase flows.

β€’ The strength of monopole and dipole sources are significantly smaller than the quadrupole source.

Jan 2020 Wei Wang, [email protected] 29

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Future Work

β€’ Develop a volumetric integration method for each sources in particle-laden jet

β€’ Evaluate the spectral component of sound generated by the monopole and dipole sources.

β€’ Study the effects of particle size and mass loading

Jan 2020 Wei Wang, [email protected] 30

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Thank You

Jan 2020 Wei Wang, [email protected] 31