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
Jan 2020 Wei Wang, [email protected] 3
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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
Jan 2020 Wei Wang, [email protected] 6
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]
π2
ππ‘2β πβ
2 π»2 π β πβ =ππ
ππ‘βππΊπππ₯π
+π2πππ
ππ₯πππ₯π
Monopole: π = βππ
ππ‘+ π£π
π
ππ₯πln 1 β πΌ
Dipole: πΊπ = πΉπ +π
ππ‘πΌππ£π
[1] Morris, P. J., and Farassat, F., βAcoustic analogy and alternative theories for jet noise prediction,β AIAA Journal, vol. 40, 2002, pp. 671β680.[2] Crighton, D., and Ffowcs Williams, J., βSound generation by turbulent two-phase flow,βJournal of Fluid Mechanics, Vol. 36,No. 3, 1969, pp. 585β603
Effect of volume fraction
Effect of drag force
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Jan 2020 Wei Wang, [email protected] 7
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., βAres 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., βComputational framework for Launch, Ascent, and Vehicle Aerodynamics (LAVA),β Aerospace Science and Technology, vol. 55, 2016, pp. 189β219.
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Jan 2020 Wei Wang, [email protected] 8
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., βSound and turbulence modulation by particles in high-speed shear flows,β Journal of Fluid Mechanics, Vol. 875, 2019, pp. 254β285.[2] Horne, W. C., Burnside, N. J., Panda, J., and Brodell, C., βMeasurements of unsteady pressure fluctuations in the near-field of a solid rocket motor plume,β Int. J. Aeroacoustics, vol. 15, 2016, pp. 554β569.
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Computational Method
Jan 2020 Wei Wang, [email protected] 10
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., βToward a Comprehensive Model of Jet Noise Using an Acoustic Analogy,β AIAA Journal, Vol. 52, No. 10, 2014, pp. 2143β2164. doi:10.2514/1.j052809.[2] Panda, J., and Mosher, R., βMicrophone Phased Array to Identify Liftoff Noise Sources in Model-Scale Tests,β Journal of Spacecraft and Rockets, Vol. 50, No. 5, 2013, pp. 1002β1012. 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
Jan 2020 Wei Wang, [email protected] 11
Acoustics Solver
β’ Developed in-house
β’ Ffowcs-Williams and Hawkingβs (FW-H)
β’ Far-field acoustics
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Governing Equations
Navier-Stokes Equation
π
ππ‘ΰΆ±Ξ©
(π β πΆ)πΎπΞ© +ΰΆ»πΞ©
(π β πΆ)ππππ = ΰΆ»πΞ©
(π β πΆ)ππππ + ΰΆ±Ξ©
πΈπΞ©
whereπΎ = π, ππ’, ππ£, ππ€, ππΈ π
ππ = πππ, ππ’ππ + ππ₯π, ππ£ππ + ππ¦π, ππ€ππ + ππ§π, ππ»πππ
ππ =
0ππ₯ππ₯π₯ + ππ¦ππ₯π¦ + ππ§ππ₯π§ππ₯ππ¦π₯ + ππ¦ππ¦π¦ + ππ§ππ¦π§ππ₯ππ§π₯ + ππ¦ππ§π¦ + ππ§ππ§π§ππ₯Ξπ₯ + ππ¦Ξπ¦ + ππ§Ξπ§
,
Ξπ₯ = π’ππ₯π₯ + π£ππ₯π¦ + π€ππ₯π§ + Ξ€πππ ππ₯
Ξπ¦ = π’ππ¦π₯ + π£ππ¦π¦ +π€ππ¦π§ + Ξ€πππ ππ¦
Ξπ₯ = π’ππ§π₯ + π£ππ§π¦ +π€ππ§π§ + Ξ€πππ ππ§
Jan 2020 Wei Wang, [email protected] 12
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Governing Equations
Phase-Coupling Terms
πΈ = 0, ππ,π₯, ππ,π¦ , ππ,π§, πΈππ
ππ = βππ π½ β π½π
ππ’
πΈπ =[ππ β π½π β π½
βπππΆπ,π π β ππ
ππ]
Jan 2020 Wei Wang, [email protected] 13
Point Particles
β’ Evolution Equations
π
ππ‘ππ = π½π ,
d
dtπp =
πβπp
ππ’,
π
ππ‘ππ =
πβππ
ππ
β’ Time Scales
ππ’ =ππππ
2
18πππ’ π π, ππ =
πΆπ,πππππ2
12πππ(π π)
β’ Correlations
Naumann and Schiller(1935): ππ’ π π = 1 + 0.15π π0.687
Ranz and Marshall(1952):
ππ π π = 1 + 0.3π π1
2ππ1
3
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Ffowcs-Williams Hawking Equation
Jan 2020 Wei Wang, [email protected] 14
Inhomogeneous Wave Equation Derived from Navier-Stokes Equation
β‘2 πβ²π» π =π
ππ‘π0π£ππΏ π +
π
ππ‘π(π’π β π£π)πΏ π
βπ
ππ₯πππ’π π’π β π£π πΏ π +
π
ππ₯ππΏππΏ π
+π2
ππ₯πππ₯π[ππππ»(π)]
Where
β‘2 =1
π2π2
ππ‘2β
π2
ππ₯π2
πΏπ = β π β π0 πΏππ β πππ ΰ·πππππ = ππ’ππ’π β πππ + π β π0 β π0
2πβ² πΏππ
Loading noise
Quadrupole source
Thickness noise
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Ffowcs-Williams Hawking Equation
Jan 2020 Wei Wang, [email protected] 15
Farrasatβs Formulation[1]
4ππβ² π, π‘ =
ΰΆ±
ΰ΅©
π0 αΆπ£ππ 1 βππ
2+π0π£π π αΆππ + π ππ βπ2
π2 1 β ππ3
+αΆππ
ππ 1 β ππ2+ππ β ππ β ππ
π 1 βππ2+
ππ π αΆππ + π ππ βπ2
ππ2 1 βππ3 +
αΆπ π’π β π£π + π αΆπ’π β αΆπ£ππ 1 β ππ
2 1 +β³π +
π π’π β π£ππ 1 β ππ
2αΆβ³π +
π π’π β π£π π’π β π’πππ
π2 1 βππ2 +
π π’π β π£π 1 +β³π
π2 1 βππ3 π αΆππ + π ππ βπ2
πππ‘
ππ
π = |π β π|
Subscripts:
n = surface normal direction
r = radiation direction
[1] Brentner, K. S., and Farassat, F., βAnalytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces,β AIAA Journal, Vol. 36, No. 8, 1998, pp. 1379β1386. doi:10.2514/2.558, URL https://doi.org/10.2514/2.558.
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Geometry and Computational Grid
Jan 2020 Wei Wang, [email protected] 17
β’ SMC016 Nozzle (SHJAR)[1]
β’ π· = 0.0508 π ,ππ = 1.5
β’ Smooth Nozzle Wall
β’ 50π· Γ 30π·
β’ 2.1M hexahedra cells
β’ O-H Structured-like Grid
β’ Minimum cell ~10β4 π ~1%D
[1] Brown, C., and Bridges, J., βSmall Hot Jet Acoustic Rig Validation,β 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, ππ
ParticleMass Flux (ππ/π2π )
ParticleDiameter
(ππ)
1 3.67 1 1.5 0 N/A
2 3.67 1 1.5 30 10
Gas: π0, π0
Particle: αΆπ, ππ
Nozzle
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Mean Streamwise Velocity
Jan 2020 Wei Wang, [email protected] 19
[1] Bridges, J., and Brown, C., βValidation of the small hot jet acoustic rig for aeroacoustic research,β 11th AIAA/CEAS aeroacoustics conference, 2005, p. 2846.[2] Lau, J. C., Morris, P. J., and Fisher, M. J., βMeasurements in Subsonic and Supersonic Free Jets Using a Laser Velocimeter,β Journal of Fluid Mechanics, Vol. 93, No. 1, 1979,p. 1β27. doi:10.1017/S0022112079001750.
π) 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
Jan 2020 Wei Wang, [email protected] 20
π) 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 = 160Β°,π
π·= 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 π11 of Lighthillβs Stress Tensor on the Nozzle Lipline
Jan 2020 Wei Wang, [email protected] 22
π) Variance
b) Skewness c) Kurtosis
Sound sources are greatly altered in the particle-laden jet
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Two-Point Cross-Correlation of π11 of Lighthillβs 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 = π·, π = Ξ€π· 2 ,π = 0.
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Convection of π11 of Lighthillβs Stress Tensor
Jan 2020 Wei Wang, [email protected] 24
π) 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 π11 of LighthillβsStress Tensor
π) Gas jet
b) Particle-laden jet
β’ Nozzle lipline
β’ Frequency-wavenumber space
β’ Phase-velocity π/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 FfowcsWilliamsβ acoustic analogy[1]
β’ Monopole:
π = βππ
ππ‘+ π£π
π
ππ₯πln 1 β πΌ
β’ Dipole:
πΊπ = πΉπ +π
ππ‘πΌππ£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., βSound generation by turbulent two-phase flow,βJournalof Fluid Mechanics, Vol. 36,No. 3, 1969, pp. 585β603
π) Centerline
b) Lipline
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π) 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 = 10π·, π = 0, π = 0.
Reference point location: X = 10π·, π = Ξ€π· 2 , π = 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 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 Lighthillβstensor 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