Circular Duct analysis in ANSYS workbench
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Circular Duct analysis in ANSYS workbench
Objective
1. Calculate the natural frequencies of a 3D duct with rigid walls with various end conditions.
2. Sound pressure distribution along the duct for a harmonic volume velocity excitation at one end of a duct with finite length.
3. Pressure distribution along an infinitely long duct.
4. Pressure distribution along a duct with a finite length that has a frequency varying impedance at one end of the duct radiating into free space.
𝑢1𝑢2
z
x
y
L
a
Element types available for Acoustic Analyses in ANSYS based on pressure formulation
Name 2D/3D Nodes Description
FLUID29 2D 4 Planar element
FLUID129 2D 2 Line element for simulating an infinite boundary
FLUID30 3D 8 Brick element
FLUID130 3D 4,8 Planer element for simulating an infinite boundary
FLUID220 3D 20 Brick element
FLUID221 3D 10 Tetrahedral element
Natural frequencies
Description parameter Value
Diameter 2a 0.1m
Length L 3m
Speed of sound 𝑐0 343m/s
Density ρ0 1.21 kg/m3
Velocity of piston 𝑢2 0.0
Velocity at rigid end 𝑢1 0.0
configuration schematic Mode index n= Natural frequencies Mode shape
Rigid-rigid 0,1,2 n𝑐0/2L Cos(nπx/L)
Open-rigid 1,3,5 n𝑐0/4L Cos(nπx/2L)
Open-open 1,2,3 n𝑐0/2L sin(nπx/L)
• FLUID 30 acoustic element is used
Element per wavelength
Element sizeEsize=λ/epw =𝑐0/f/epw
Rigid-rigid boundary condition
Natural frequency of open-rigid
Natural frequency of open-open Duct
Pressure and velocity distribution along the duct
Description parameter Value
Diameter 2a 0.1m
Length L 3m
Speed of sound 𝑐0 343m/s
Density ρ0 1.21 kg/m3
Velocity of piston 𝑢2 1.0 m/s
Velocity at rigid end 𝑢1 0.0
Excitation frequency f 200Hz
Parameters used in the analysis of a circular duct with forced excitation at one end
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Particle velocity along a Piston-Rigid Duct
1 2 3
100
110
120
130
140
150
-500
-400
-300
-200
-100
0
100
200
300
400
500
Mic Position along Duct [m]
Mic Position along Duct [m]
Mic Position along Duct [m]
Sound p
ress
ure
lev
el [
dB
]P
arti
cle
Vel
oci
ty [
m/s
]
Imag
inar
y P
ress
ure
[P
a]
Semi-infinite duct
• Applied an absorbing boundary to the outlet of the duct to simulate a semi-infinite duct
• The upstream inlet end provides an acoustic excitation as a surface velocity of 1 m/s.
• Outlet end has a radiation boundary applied which is one method of specifying an absorbing boundary.
SPL of semi-infinite duct= 20log10ρ0∗𝑐0∗𝑢
20𝑒−6∗ 2=143.3 dB
Radiation from an Open-ended DuctPiston velocity
Free-field
FLUID 130 element
Transition region for the acoustic finite elements
Applied force magnitude of1e-3
Commands which will couple all the nodes associated with inlet axis
which will create a rigid piston face and motion in the other direction
will be zero
Imaginary part of mechanical impedance of piston attached to a Duct
Frequency [Hz]
Imag
inar
y im
pe
dan
ce[N
s/m
]
Mechanical power of piston Attached to the Duct
Frequency [Hz]
Pow
er[W
atts
]
Real part of mechanical impedance of piston attached to a Duct
Frequency [Hz]
Rea
l im
pe
dan
ce [
Ns/
m]
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