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Computational Aeroacoustics Based on Hybrid
Approaches Wolfgang SchröderPhong Bui, Roland
Ewert, Elmar Gröschel Institute of
Aerodynamics, RWTH Aachen UniversityDLR,
Institute of Aerodynamics and Flow Technology,
Braunschweig
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Coming Up I

• Introduction
• General
• Classical Hybrid Approaches
• Acoustic Perturbation Equations (APE)
• Source Filtering
• APE Forms
• Stability

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Coming Up II

• Numerical Approach
• Spatial Discretization
• Boundary Conditions
• Results
• Validation
• Trailing Edge
• Combustion Noise
• Conclusions

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Introduction
1960s engine noise the dominant aircraft noise
source 1970s high bypass turbofan ? 10 db
reduction today airframe noise equally
important or even dominant over
engine noise Commercial Impact aircraft industry
(Europe) 380000 (direct), 650000
(indirect) aircraft industry (US) 680000
(direct) prediction growth 13000 new aircraft
up to 2013, i.e., 800 ? 109 European Transport
Policy for 2010 Unless ambitious new noise
standards are rapidly introduced
internationally to prevent further degradation of
the plight of local residents, there is a
risk that airports could be deprived of any
possibility of growth.
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Noise Sources During Landing
Slat Horn
Slat
Wing Tip
Flap Side Edge
Cavities
Landing Gear
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High Lift Configuration
main airframe noise sources on a high lift wing
configuration
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Experimental Methods
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JET FSEV Interaction
Comparison of various engine positions
Numerics
Experiment
TW-A
TW-A TW-B TW-C
TW- C
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DNS Resolution Requirements
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Fluid Mechanical and Acoustical Scales
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Schematic to Compute Turbulence Related Noise
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Domains of Computational Aeroacoustics
W. Zorumski, Comp. Aeroacoustics, 1993
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Computation of Acoustic Fields
Flowchart of various methods to compute
turbulence related noise (SNGR Stochastic
Noise Generation and Radiation)
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Hybrid Methods Lighthill
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Kirchhoff-Helmholtz Theorem
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Ffowcs Williams-Hawkings Method
solid boundaries
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Circular Cylinder Flow
2D CFD comp., Re 1000, Ma 0.2 3D acoustic
comp., cyl. 40D long
CFD grid 193 ? 97 cells it extends out 20D
Vorticity Field (Brentner, NASA Langley, 1997)
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Circular Cylinder Flowlocation 128D from cyl.,
90 deg from freestream

• FW-H small sensitivity to surface placement
• Kirchhoff meaningless distributions
• (Brentner, NASA Langley, 1997)

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Linearized Euler Equations (LEE)
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Wave Equation
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Error Estimate
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Computation of Far Field Noise
Extrapolation of acoustic data into the far field
from the inhomogeneous acoustic domain
surface Sa applying e.g. FW-H
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Source Filtering I
linearized Euler eqs. plus source after
Fourier/Laplace transformation
eigenvalues
eigenvectors
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Source Filtering II
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Source Filtering III
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Source Filtering IV
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Validation of Source Filtering I
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Validation of Source Filtering II
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Validation of Source Filtering III
oscillating Gaussian shape Tij distribution
T11, long. quad.
T22, long. quad.
T12, lateral quad.
numerical solution of the convolution integral
T12,y 0 line
T11, y 0 line
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Acoustic Perturbation Equation (APE) form 1
continuity and Navier-Stokes, const. coeff. on LHS
complete source S (q, f) acoustic and vorticity
modes
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APE form 1 (cntd.)
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APE form 1 (cntd.)
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APE form 1 (cntd.)
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APE form 1 (cntd.)
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APE form 1
I,II,III,V sound sources from turbulent
fluctuation and entropy
inhomogeneities IV sound from
acoustic/mean vorticity interactionII
monopolar heat sourceV entropy and
temperature fluctuations (combustion noise)I
M ltlt 1, ? ? ? 0III major
source term,
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APE form 2
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APE form 3
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APE form 4
keep the LHS of APE-1 and insert remaining terms
in the RHSobjective easy to compute source
terms in compressible flows governing equations
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Stability of APE
stability of APE is ensured by source filtering
and shifting convection terms to the left-hand
side, not by suppressing vorticity
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Stability of APE (cntd.)
linearized wave operator from Möhring
? acoustic mode
? vorticity mode
? entropy mode
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Linearized Euler Equations
(Bailly, Bogey, Juvé, AIAA Paper 2000-2047, 2000)
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Spatial Discretization I

• wave propagation requires low dispersive and low
  dissipative errors
• dispersive phase speed f (frequency,
  cell size)
• dissipative decay of wave amplitudes
• wave propagation characteristics ? dispersion
  relations
• ? relation between frequency and wave
  numbers of the problem
• dispersion relations of the homogeneous 2D LEE

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Spatial Discretization II
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Spatial Discretization III
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Spatial Discretization IV
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Spatial Discretization V
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Spatial Discretization VI
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Spatial Discretization VII
Padé, DRP, and central difference schemes (CDS)
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Spatial Discretization VIII
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Spatial Discretization IX
6th-order Padé, 4th-order DRP, and CDS-2, CDS-4
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Boundary Conditions I
finite comp. domain ? numerical
boundariesdiscrete form of b.c. ? physical plus
spurious waves

• waves at boundaries convection
  eqn. (left), LEE (right)
• dispersion relation of the numerical scheme
  (conv. eqn.)

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Boundary Conditions II

• reflection of spurious waves ? physical waves?
  non-physical coupling of the boundaries
• LEE subsonic mean flow u in the x-direction
• acoustic waves at u c in pos.
  xacoustic waves at u - c in neg. x
• that is, spurious waves with cg lt 0 and physical
  waves with u c travel in the negative
  x-directionfurthermore, entropy and vorticity
  waves
• its a must to suppress unphysical reflections
  (Aq/A1 ltlt 1)for long time numerical simulations

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Boundary Conditions III

• categories for local boundary conditions
• pseudo differential operators (Giles,
  Engquist, Majda)
• quasi one-dimensional characteristics
  (Thompson)
• asymptotic analysis of the governing equations
  (Tam, Webb, Turkel, Bayliss)
• absorbing / buffer zone techniques (Hu)

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Non-Reflecting BC Results I
category 3, problem 1 benchmark on a
non-Cartesian mesh
analytical and computed density distribution on y
0 at T 40 (left) and T 50 (right), PML
condition
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Non-Reflecting BC Results II
density contours at T 60
PML (top left), ?m 1.5, ? 2.0 Sponge Layer
(top right), ? 1.5, ? 2.0Thompson (bottom
left) Asymptotic Radiation (bottom right)
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Non-Reflecting BC Results III
density distribution on y 0 at T 90 using
several non-reflecting boundary conditions
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Viscous/Acoustic Splitting Method
(Hardin, Pope 1994 Shen Sorensen, 1999)
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Sheared Mean Flow
u(y) ? u ? tanh (2y / ??) ? u c?/2 monopole
source for the continuity equation
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Sheared Mean Flow, Comparison LEE/APE

• sheared mean flow, monopole source ?w 50

a) LEE, t 180
b) APE, t 180
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Sheared Mean Flow, Comparison LEE/APE

• sheared mean flow, monopole source ?w 10

snapshot p ? at t180 on line y 70
RMS of p ? on line y 70
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Spinning Vortex Pair
Vortex source L (? x u) of APE via a vortex
core model (Gaussian distribution)
2r0 separation distance of vortices ? vortex
circulation
schematic of the flow configuration
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Spinning Vortex Pair

• Pressure distribution along line, x y, 141 x
  141 points

?/a?r0 0.6, Mr 0.0477
?/a?r0 1.6, Mr 0.1274
?/a?r0 1.0, Mr 0.0796
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Spinning Vortex Pair ? / a?r0 1.0, Mr 0.0795
pressure contours, Matched Asymptotic Expansion
(MAE) solution
pressure contours, APE-4 system, 141 x 141 points
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Test Problem Cylinder Flow
CFD Computation

• Mach number Ma 0.3
• Reynolds number Re 200
• CFD grid 657 ? 513 points
• Extension R/D 80
• AUSM scheme for spatial discretization
• coarsest resolution 17 points per wave length

CAA Computations

• CAA grid 257 ? 161 points
• Extension R/D 80
• coarsest resolution 5.4 points per wave length

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Cylinder Flow Perturbation Pressure
Acoustic / Viscous Splitting (Problem A, P? from
compr. CFD)
DNS solution
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Cylinder Flow
Pressure Time Signal Ac. Visc. Splitting (Problem
A, P? from compr. CFD)
Pert. Vorticity Level DNS solution
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Cylinder Flow
Pert. Vorticity Level DNS solution
Pert. Vorticity Level Lin. Euler Eqs.
Pert. Pressure on x 0 (Problem F unstable)
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Cylinder Flow Perturbation Pressure
DNS solution
APE-2 (Problem D)
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Cylinder Flow Perturbation Pressure
APE-4 - ?? ? u? (Problem H)
p? as a fct. of y on x 0
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Trailing Edge Flow
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Schematic and Boundary Conditions
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Rescaling Method
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Compressible Rescaling Method
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Skin Friction and Stress Tensor
Les of a turbulent boundary layer Re? 1400 and
Ma 0.4.
LES of a turbulent boundary layer at Re?0 1400
and Ma 0.4.
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Trailing Edge Flow, Re? 5.33 ? 105, Ma 0.15
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Trailing Edge Flow
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LES and Acoustic Grids
LES grid, every 2nd grid point shown, l/?0
52.288, ?z 0.64?0, 17 grid points in the
spanwise direction (2.22 . 106 points)
acoustic grid, every 4th grid point shown, 2 .
105 points, 17585 points in the LES domain
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Vortex Source (? x u)
(A)
(B)
P ? and vector plot of a suddenly started source
(? x u) (0, ?(x - u?t))T
(B) pressure and uo . u ? along x 0
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Suppression of Spurious Sound at Boundaries
spurious sound p (contour) and velocity field
induced at an inflow boundary at x 0 by
passively convecting vorticity
no compensation, sudden jump over ?x 0.1
compensation
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Suppression of Spurious Sound at Boundaries
Modulus of damping function ?F(?)?over wave
number ?, scaled with damping zone of width d
p ? along y 35 for passively convecting
vorticity inflow boundary at x 0, effect of
onset zone width d and analytical compensation on
spurious sound
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Trailing Edge Noise

• plate l 0.2m, M 0.15, Re 5 105
• 503 vortex source (? ? v) data levels from LES
  for CAA, every 160th LES time level used (!)
• sufficient temporal resolution up to ? 42 kHz
  (10 PPW)
• experimental measurements up to 10 kHz
• full LES resolution yields even higher
  resolution - subgrid scale contribution a
  problem ? - unsteady RANS sufficient ?

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APE Source Terms

• L? (? ? u) ? (L?x, L?y)T
• L?x (left) and L?y (right) and CAA grid

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APE-4 source term ? ? v, y-component
Y-component
APE-4, p? at t5.0
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Grid Dependence
APE-4 solution t3.0, 1.5² higher grid density
APE-4 solution t3.0
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Trailing Edge Directivity
computed directivity APE-4 simulation
approximate non-compact edge noise Greens
function according to Howe
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Trailing Edge Directivity
comparison of the trailing edge noise directivity
for r1.5 and APE-4 (p ?) vs. Howe/Möhrings
acoustic analogy (B ?)
directivity for r0.4, APE-4
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Details of the LES Mesh
Subsonic airfoil flow Ma 0.088, Re 8 105,
ci 0.6
Enlargement of the leading (left) and trailing
edge region (right). Total of Points 7.3 106
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High frequency test with harmonic source

• CAA mean flow from time averaged LES solution

Directivities obtained for M0, 0.088 applying
LEE and APE
Sound field generated by a harmonic source
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Y-component and Trailing Edge Sound

• source from 350 temporal LES points via linear
  interpolation

Y-component
Pressure distribution
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Combustion Noise

• - Different computational domains (LES / CAA)
  used in this hybrid approach
• Hybrid Method vs. Compressible CFD

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APE-RF Sources I

• Source terms (RHS) of the APE-RF system

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APE-RF Sources II

• Source terms (RHS) (qe only)

Pressure-density relation of the APE-RF system.
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APE-RF System

• Neglecting all mean flow effects andeffects of
  acceleration of density inhomogeneities
• Combustion at constant pressure

Energy equation for reacting flows
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H3 flame flow data
F. Flemming, A. Sadiki, and J. Janicka,
Institute for Energy and Powerplant Technology,
Darmstadt University of Technology

• open non-premixed turbulent flame
• fuel 50/50 vol H2/N2
• nozzle diameter 0.008 m
• bulk velocity 34.8 m/s
• coflow velocity 0.2 m/s
• stoichiometric mixture f 0.31

Mixture fraction
density
u-velocity
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H3 source term
- The major contribution to combustion noise in
low Mach number flows is encoded in the total
time derivative of the density.
Contours of the source term in the z/D 0 plane
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H3-flame intensity data

• Perturbation pressure field,2D-Slice (z/D0),
  T300
• Comparison of the radial intensity with
  experimental data

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Conclusions

• why hybrid methods was discussed
• a family of acoustic perturbation equations
  (APE) was derived
• unlike LEE APE is stable at arbitrary mean flow
• silent formulation on the fluid acoustic
  interface
• sheared mean -, spinning vortex -, cylinder -,
  trailing edge -, and combustion problems
  showed the hybrid approach to be successful