Computational Prediction of Flow Generated Sound

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Computational Prediction of Flow Generated Sound
MAE 741
M Wang, J B Freund, Sanjiva K Lele Annual Review
of Fluid Mechanics 2006, Vol 38

• Suranjan Pai

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Agenda

• Significance of flow generated sound
• Progress so far
• Challenges Posed
• Basic Theory
• Terminology
• Source Propagation
• Lighthills Theory
• Numerical Evaluation
• Computational Approaches
• Direct Numerical Solution (DNS)
• Large Eddy Solution (LES)
• Reynolds Average Numerical Solution (RANS)
• Hybrid Approach
• Flow Control recent efforts

Computational Prediction of Flow Generated Sound
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Significance of flow generated sound

• Associated Problems
• Causes human discomfort
• Affects the stealth operations of military
  vehicles submarines
• Tightening noise regulations at the airports

• Automobiles
• Mirrors
• A-pillars
• Windshield Wipers

• Other Applications
• Wind Turbine
• Fans in rotating machines
• Helicopter rotors

• Naval Vessels
• Propellers
• Hydrofoils
• Sonar Domes

• Aircrafts
• Jet Noise
• Turbo Fan
• Airframe
• Landing Gear

Computational Prediction of Flow Generated Sound
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Progress So Far

• Lighthill, James
• first pioneering study in 1952
• unsteady flows through non-linear interaction of
  velocity fluctuations, entropy fluctuations and
  viscous stresses

Computational Prediction of Flow Generated Sound
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Progress So Far

• Howe M S
• emphasized the role of vorticity as sound sources
• In free space dominant sources are inefficient
  and that solid boundaries enhance noise radiation
  by
• Creating and augmenting noisy flow features
• Imposing a boundary inhomogeneity

Computational Prediction of Flow Generated Sound
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Challenges Posed

• Noise generating is unsteady.
• Renders steady RANS methods unsuitable
• Unsteady RANS are inefficient
• Vast disparity in magnitudes between fluid
  dynamic acoustic disturbances
• Scale separation between sound and flow
• esp. Jet Engines which have a high subsonic
  Mach No flow (M 1) there is lack of clear
  scale separation

Computational Prediction of Flow Generated Sound
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Terminology
Computational Prediction of Flow Generated Sound
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Source Propagation

• Two physical processes described
• Sound generation creates acoustic energy
• Propagation alters its character
• Dissipation is also an effect of propagation.
• Although this concept appears to be clear and
  unambiguous, mathematical implementation is less
  clear and becomes complicated with the result
  that flow can alter the efficiency of the
  acoustic source.

Computational Prediction of Flow Generated Sound
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Lighthills Theory

• Mathematically we define a flow solution q such
  that
• ?(q) 0
• Lighthill formulated an acoustic analogy by
  rearranging the above equation as
• L(q) S(q)
• where L linear wave propagation operator
• S corresponding non-linear sound
  source

Computational Prediction of Flow Generated Sound
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Lighthills Theory

• The most well known form of this analogy can be
  expressed as
• In this equation, computation of the noise comes
  down to two issues
• Accurate enough inversion of L
• Representation of S

Computational Prediction of Flow Generated Sound
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Lighthills Theory

• Shortcomings of Lighthill theory
• Truncation and numerical approximation is not
  well understood.
• For complex value of L, a numerical solution of
  the adjoint Greens Fn is used to compute far
  field sound, which causes some instable
  solutions.
• Propagation effects on S increases the relative
  errors in S which are reflected on the relative
  errors in the far field sound.

Computational Prediction of Flow Generated Sound
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Numerical Evaluation

• For unsteady flow in an unconfined region, closed
  form solution to Lighthill analogy is
• In this equation, truncation of terms is
  carried out by considering
• Hydrodynamic perturbations
• Acoustic perturbations.

Computational Prediction of Flow Generated Sound
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Numerical Evaluation

• For unsteady flow in an unconfined region, closed
  form solution to Lighthill analogy is
• Limitation of Greens Fn
• Greens Fn is unavailable for complex geometries
• Computation of complete Greens Fn is expensive

Computational Prediction of Flow Generated Sound
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Computational Approaches

• Sound Computation
• Energy content of the radiated noise is very
  small compared to the unsteady flow.
• This fact gives rise to the under-listed issues
  
• Need for accurate boundary conditions.
• Spatial resolution of the numerical schemes.
• Induction of dispersion / dissipation due to
  discretization exception are spectral methods.

Computational Prediction of Flow Generated Sound
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Computational Approaches

• Direct Numerical Solution
• Usually used to avoid modeling approximations.
• Solved using compressible flow equations using
  methods that have well understood numerical
  errors.
• However, this method has a limitation on the
  Reynolds number.

Computational Prediction of Flow Generated Sound
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Computational Approaches
Sound generated by turbulent vortex ring
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Computational Approaches
Vortex ring Formation to Exit
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Computational Approaches

• Large Eddy Simulation
• It represents large turbulence scales in flow and
  also models the effects of the smaller scales.
• Turbulence modeling is more robust as small scale
  motions are used.
• However, the grid wall resolution requirement for
  LES is quite stringent.

Computational Prediction of Flow Generated Sound
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Computational Approaches

• RANS / Hybrid Methods
• For time accurate simulation methods unsteady
  RANS provides the lowest level of flow detail and
  accuracy
• Most recent active pursuit is going on in
  incorporating RANS modeling elements into LES at
  different levels.
• RANS calculations are insufficient by themselves
  for sound predictions as they lack temporal
  information

Computational Prediction of Flow Generated Sound
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Flow Control Recent Efforts
Optimal Control of 2D mixing layer noise
Computational Prediction of Flow Generated Sound
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QuestionsSuggestions
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References

• Publications
• Computational Prediction of Flow-Generated Sound
• Meng Wang, Jonathan B Freund, Sanjiva K Lele
• Annual Review of Fluid Mechanics 2006, Vol 38
• Computing aerodynamically generated noise
• Wells V L, Renaut R A
• Annual Review of Fluid Mechanics 1997, Vol 29

• Text Books
• Mathematical Methods in Chemical Engineering
• Arvind Varma
• Oxford University Press, 1997
• A First Course in Turbulence
• H. Tennekes, J L Lumley
• The MIT Press, 1972

Computational Prediction of Flow Generated Sound