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]