Computational Science and Information Technology. Computation of Engine Noise .... Time Domain Formulation. ⢠Mapping onto master element Ω. M. =[-1,1]3.
AIAA-2003-0542
Computation of Engine Noise Propagation and Scattering off an Aircraft J. Xu*, D. Stanescu*, M.Y. Hussaini* and F. Farassat**
*
Florida State University
** NASA
Langley Research Center Computational Science and Information Technology
Acknowledgements • D. Weir and T. Wolownik • NASA
Computational Science and Information Technology
Introduction • Noise signature of an aircraft – fan inlet and exhaust noise
• Influenced by – flow around the wing and fuselage – scattering from aircraft surface
• Reduce noise footprint by – optimizing engine and wing location – manipulating flow
• Methodology – experimental study (extremely expensive) – numerical simulation Computational Science and Information Technology
Computational Domain
Computational Science and Information Technology
Governing Equations ~ 3 ~ ∂Fd ∂Q =0 + ∂t d =1 ∂xd where, ~ Q=
v1
vd v1vd + pδ1d
~ v2 , F =
v 2 v d + pδ 2 d
v3 E
v3vd + pδ 3d ( E + p ) vd Computational Science and Information Technology
Boundary Conditions • Zero normal velocity BC on the symmetry plane, as well as on the fuselage, nacelle, and wing surfaces. • Damping layers on other sides of the domain (D.Stanescu and D.Ait-Ali-Yahia, 1999)
• Engine noise source for spinning modes (s, d) (J.M.Tyler and T.G.Sofrin, 1962)
Es (k sd r ) cos Θ
p− p − vx − vx = A
1 c2 kx r
vr − vr
k xd
v −v
s
r rr
⋅ Es (k sd r ) cos Θ ⋅ Es (k sd r ) cos Θ ⋅ Es' (k sd r ) sin Θ ⋅ Es (k sd r ) cos Θ Computational Science and Information Technology
Solution Technique • Spectral Methods • • • •
Require relatively few points per wavelength Have low dispersion and dissipation errors Have geometric flexibility Are compact, robust and inherently parallelizable
• Time Domain and Frequency Domain Formulations • Implemented in Distributed Memory Models Computational Science and Information Technology
Time Domain Formulation • Mapping onto master element ΩM=[-1,1]3 ∂Q 3 ∂Fd =0 + ∂t d =1 ∂ξ d
where, ~ Q = JQ, and Fd = J
∂ d m =1 ∂xm 3
Computational Science and Information Technology
Time Domain Formulation • Discontinuous Galerkin spectral approximation (Q t ,
ijk
dQijk dt
where, D F=
) + (∇ ⋅ F ,
)=0
ijk
[
]
=−D +D +D F
ϕijk = hi ( )h j ( )hk ( ) 1
[ F1* (1,
j,
* ] h ( 1 ) − F 1 ( −1, k i
j
,
k
]hi (−1) − d F )
i
• Low-storage Runge-Kutta scheme optimized for wave propagation (D. Stanescu and W.G. Habashi, 1998) Computational Science and Information Technology
Frequency Domain Formulation • Equation governing the acoustic perturbations ∂ρ ' + ∇ ⋅ ( ρ ∇ Φ '+ ρ ' ∇ Φ ) = 0 ∂t
ρ'= −
ρ ∂Φ ' c
2
∂t
+ ∇ Φ ⋅ ∇Φ '
• Weak formulation: multiplied by ψ ( x , y , z ) e − i ω t and integrated using a divergence theorem. ∂ρ ' ψ rdΩ − Ω ∂t Γf
Ω
∇ ψ ⋅ ( ρ ∇ φ + ρ ' ∇ φ )rdΩ +
ψ ( ρ ∇ φ + ρ ' ∇ φ ) ⋅ rds = 0 Computational Science and Information Technology
Frequency Domain Formulation • For Ψ∈ZΓf ρ Ω
2 ω φψ + i ω u (φψ x − ψφ x ) + i ω v (φψ y − ψφ y ) + i ω w (φψ z − ψφ z ) [ 2
c + (u 2 − c 2 )φ xψ x + ( v 2 − c 2 )φ yψ y + ( w 2 − c 2 )φ zψ z + u v (φ xψ y + φ yψ x ) + u w (φ xψ z + φ zψ x ) + v w (φ yψ z + φ zψ y ) − ψσ ( i ωφ + u φ x + v φ y + w φ z )]d Ω =0
• Discretized by a Chebyshev spectral element method A{φ} = {b}
• Parallel Schur complement domain decomposition method • PETSc package is used for high-level primitives (S. Balay, W.D. McInnes, etc., 2001) Computational Science and Information Technology
Grid Generation • Non-overlapping hexahedral elements • ICEMCFD • Hexahedral representation of underlying geometry with G-L point distribution
Computational Science and Information Technology
Computation (Time Domain) • • • • • •
Tone at ω=3650 Hz, M∞=0.0 Reduced frequency ωr=26.3 Spinning mode (18, 0) and (22, 0) 103,105 hexahedral elements 22,270,680 G-L points (N=6) 32 processors of an IBM Regatta-type SP4 machine for 10 days Computational Science and Information Technology
Computation (Frequency Domain) Tone at ω=3650 Hz, M∞=0.1 Fan face Mach number Mf=0.2 Spinning mode (18, 0) 103,105 hexahedral elements 6,746,736 points 192 processors of an IBM Regatta-type SP4 machine for 2.5 days • Huge memory requirements
• • • • • •
Computational Science and Information Technology
Experiment • • • • •
M∞ = 0.3 AGL = 500 ft Mf = 0.53 Mode (22, 0) likely Kulite microphones
Computational Science and Information Technology
35o
SPL normalized to 20
o
, dB
20
15
10
5 0 20
30
40
50
60
70
Angle from inlet, degrees Computational Science and Information Technology
Acoustic pressure contours on the aircraft surface. Mode(18, 0) radiated at ωr=26.3. Computational Science and Information Technology
SPL contours on the aircraft surface. Mode(18, 0) radiated at ωr=26.3.
Computational Science and Information Technology
SPL Variation on the Wing Suction Side 30
o
SPL normalized to 20 measure value
25 20 15 10 5 0
Measured, M=0.3 Computed, (22,0), M=0
-5 -10 -15 20
25
30
35
40
45
50
55
60
65
70
Angle from inlet axis, degree Computational Science and Information Technology
SPL Variation on the Wing Suction Side
o
SPL normalized to 20 measure value
20
15
10
5
0
Measured, M=0.3 Computed, (18,0), M=0
-5
-10
-15 20
25
30
35
40
45
50
55
60
65
70
Angle from inlet axis, degree Computational Science and Information Technology
SPL Variation on the Wing Suction Side
15
10
o
SPL normalized to 20 measure value
20
5
0
Measured, M=0.3
-5
Computed, (18,0), M=0.1, Mf=0.2
-10 20
25
30
35
40
45
50
55
60
65
70
Angle from inlet axis, degree Computational Science and Information Technology
Conclusion • A realistic, complete and accurate modeling of propagation of aircraft engine noise, including the effect of scattering from fuselage, pylon, and wing, is now possible with the proposed methodology implemented on large distributed memory parallel computers. • The computer code is flexible enough to accommodate even more complicated configurations. • Still need to improve efficiency of parallel matrix solution (Schur complement ) Computational Science and Information Technology
