A microperforated panel (MPP) is generally defined as a perforated plate, in which the impedance of below one millimetre perforations is dominated by viscous losses. Using MPPs in duct and silencer applications, target is to maximize transmission loss (TL) by choosing proper surface impedance parameters. Additive manufacturing (AM) has recently reduced conventional design limitations and enabled fast prototyping of complex shaped structures. MPP-based model scale silencers can be printed within reasonable time, price, and accuracy. In this paper, design and validation of AM silencers with MPPs are studied. First, the theoretical background of MPP acoustics is summarized. Second, feasible parameters for a MPP absorber for a certain tuning frequency are sought numerically using acoustic finite element method (FEM). Third, several test MPPs are prototyped and their acoustic properties are measured. Finally, MPP silencers are simulated using different approaches and the results are compared against experiments.
A microperforated panel (MPP) is generally defined as a perforated plate, in which the impedance of a hole is dominated by viscous losses [
There are two distinct MPP applications: (1), room acoustic applications, where high absorption coefficient is the target, and (2), duct and silencer applications, where surface impedance maximizing transmission loss (TL) is the target.
MPP silencers can be further divided into Cremer silencers and modal filter silencers [
In modal filter silencers, thin MPPs with predominantly resistive impedances are used and the MPPs are placed on the duct cross section to locations of high particle velocity. The modal filter concept is aimed for, and works best, in case higher order propagating modes are important. Modal filter silencers typically have moderate TL at a relatively broad frequency band at high frequencies.
In case of a Cremer silencer, the value of optimal impedance depends on frequency, duct dimensions, and the order of the propagating waveguide mode. Value of the absorption coefficient may be much smaller than one. Kabral et al. [
Typical MPP silencer constructions. Top: Cremer silencer. Bottom: modal filter silencer. Hatch patterned surfaces depict MPPs.
Resistance and reactance of the fluid volume in the hole are usually tuned using the diameter of holes, thickness of the panel, perforation ratio and depth of the backing cavity. Ideally, the air gap (backing cavity depth) behind the MPP creates a locally reacting surface [
A Cremer silencer works best in case the acoustic reaction of the MPP surface is local. In local reaction condition, sound field is uniform over the MPP-backing cavity junction surface, the particle velocity in MPP hole is in the normal direction and the sound field is uniform in the cavity. To maintain this in practice, lateral dimensions of the backing cavities should be much smaller than half wavelength at the frequency of interest. Nonlocal reaction is also called extended reaction. As an example, sound pressure distributions in case of local and extended reactions are depicted in Figure
Sound pressure distribution in Cremer silencers. Acoustic excitation on the left hand side. Top: local reaction with 6 cavities, each 15 mm long; max. TL 30 dB at 2900 Hz. Bottom: extended reaction with one cavity 90 mm long; max. TL 8.5 dB at 3550 Hz.
Sound pressure distribution in a duct at tuning frequency is depicted in Figure
Sound pressure distribution in a Cremer silencer duct (length 240 mm, diameter 34.8 mm) excited at left end using sound pressure level of 94 dB. Top: rigid duct wall. Bottom: locally reacting duct surface; tuning frequency 3500 Hz. Note that the scale is different, because the incident wave does not propagate well. It decays over 40 dB in the first 50 mm.
Cremer silencers do not always perform as expected. The main reasons for performance anomalies are (1) leaks between backing cavities, (2) cavities with too large lateral dimensions (extended reaction), and (3) unsuitable MPP impedance.
Yang et al. [
Allam and Åbom [
Additive manufacturing (AM) has recently reduced conventional design limitations and enabled fast prototyping of complex shaped structures. Model scale silencers can be printed within reasonable time and price. Concerning MPPs, holes of Ø=0.3 mm are printable with typical stereolithography (SLA) printers.
Kabral et al. [
In this paper, design and validation of additive manufactured Cremer silencers with MPPs are studied. First, the theoretical background of MPP acoustics is summarized. Second, feasible parameters for a MPP absorber for a certain tuning frequency are sought numerically using acoustic finite element method (FEM). Third, several test MPPs are prototyped and their acoustic properties are measured. Finally, MPP silencers are simulated using different approaches and the results are compared against experiments.
When a MPP is backed with a cavity (air gap) of depth
The specific acoustic impedance of a short tube (single MPP hole) is defined as
The impedance
The most well-known way to predict the impedance of circular holed MPP is the formulation by Maa [
Very large values of
The plan was to design and print a MPP-based silencer tuned to have peak TL at 3500 Hz. This particular frequency is the blade passage frequency dominating the noise of a typical turbocharger.
Three MPP options with suitable parameters were designed using the VA One software [
Diameter of the holes and area ratio were constrained. Then, suitable panel thicknesses and cavity depths were sought for the target tuning frequency of 3500 Hz. At the tuning frequency, mass-spring resonance of the air volumes in the holes (mass) and backing cavity (spring) takes place. The number of designs producing the desired tuning frequency is very large. Three MPP-gap options with reasonable panel thicknesses and cavity depths were chosen for further study. These are listed in Table
Three MPP-gap options tuned to 3500 Hz.
MPP parameters | Cavity/Gap | ||||
---|---|---|---|---|---|
Option | Perforation ratio | MPP thickness t | Hole diameter d | Perforate constant in air at 3500 Hz | Backing cavity depth D |
A | 5.0 | 1.0 | 0.3 | 5.8 | 8.0 |
B | 7.0 | 1.5 | 0.4 | 7.7 | 8.0 |
C | 10 | 1.5 | 1.0 | 19 | 9.7 |
Note that option C is, strictly speaking, not MPP because hole diameter is 1 mm.
Since the holes in options A and B are relatively small, it was decided first to manufacture suitable samples for subsequent hole analysis and impedance measurement. The samples were printed with a 3D Systems ProJet 6000 HD using 0.05 mm layer thickness and are shown in Figure
MPP samples for impedance measurements. Top: CAD figures. Bottom left: printed samples; bottom right: a sample installed in the impedance tube.
As the additively manufactured test pieces are not perfect, microscopic photographs of the samples were taken and the holes were analysed statistically using the images. For the MPPs, open area ratio has significant effect on the acoustic properties. Area of the holes was determined using image analysis and histograms of equivalent diameters were plotted (Figure
Image analysis of MPP impedance samples. Top to bottom: A (0.3 mm), B (0.4 mm), and C (1.0 mm holes). Diameter histograms on the right.
The results show that 1.0 mm holes of the option C were very accurate, whereas 0.3 and 0.4 mm holes of options A and B were, on the average, smaller than target. Accuracy of the 0.4 mm holes (B) is still relatively good, but diameters of 0.3 mm holes (A) are quite widely distributed around 0.24 and 0.3 mm. There are also quite many very small (i.e., practically closed) holes in option A.
ACUPRO Tube [
The measured impedance quantity is the ratio of sound pressure and particle velocity at the surface of interest. The rigorous name of the quantity is “normal specific acoustic impedance”. The phrase “normal” refers to the direction of the incoming wave and “specific” tells that particle velocity is used (instead of volume velocity). Normalized impedance means impedance divided by the characteristic impedance of the air,
The measured results for samples at frequency range 2000 to 5000 Hz are displayed in Figure
Measured real and imaginary parts of impedances of MPP samples A, B, and C.
In the option A sample, the frequency is approximately 3000 Hz. There is local peak in the real part at 2500 Hz (A) or 3500 Hz (B and C). This comes, presumably, from the elastic resonances in the sample.
The overall structure of the MPP silencer is shown in Figure
Silencer structure, long version.
Two versions were printed, as seen in Figure
Long and short silencer versions. Bottom figure shows grooves for assembling the parts tightly together.
Only the option C MPP was used in silencers. Options A and B were omitted at this point, because of apparent difficulties to print the holes accurately. Another reason was that equation (
Measured impedances of the three MPP-gap options at 3500 Hz compared to optimal value.
Measured | VA One prediction using theory in [ | |||
---|---|---|---|---|
Option | Real Part | Imaginary part | Real Part | Imaginary part |
A | 1.03 | 0.73 | 0.46 | 0.08 |
| ||||
B | 0.87 | 0.048 | 0.33 | 0.09 |
| ||||
C | 0.43 | 0.18 | 0.10 | 0.028 |
| ||||
Optimum according to equation ( | ||||
Real Part | Imaginary part | |||
0.31 | -0.13 |
Material of the long silencer is the same as the impedance samples. The short version of the silencer was printed with a Formlabs Form 2 SLA printer using the Formlabs black photoresistive resin and layer thickness of 0.025 mm. Young’s modulus is 1600 MPa after printing and 2800 MPa postcured but can vary depending on layer thickness.
As 3D-printing is not limited to circular hole shapes, two other hole types were printed and investigated for short silencer versions. These are the following: Eye-shaped holes, same hole area and area ratio as option C. Hole dimensions are approx. length 1.66 mm and width 0.67 mm. Triangular holes, same hole area and area ratio as option C. Hole side length is ca. 1.35 mm.
These hole types are shown in Figure
Top: option C circular holes; middle: eye-shaped holes; bottom: triangular holes. Perforation ratio is 10% and the material thickness is 1.5 mm for all variants.
An ACUPRO Tube [
Long silencer version in measurements. Bottom figure shows the sealed junction between the outer and inner parts.
TL of the silencers was simulated with acoustic FEM within VA One software [
Setting of a VA One model for TL calculation and FE Area Junction types in models with explicit cavities.
Two different types of models were created for both the short and long silencer versions. In the first type, the MPP surface and backing cavity were modelled using the impedance measured from sample C. The impedance was inserted into the model as numeric data for a 1x1 FE Area Junction (boundary condition), located on the MPP surface of the silencer passage.
In the second type of models, the cavities were modelled explicitly. Then the MPP was modelled as a 2x2 transfer impedance of the area junctions between the duct and cavities. The transfer impedance is based on the Bauer perforate model [
The models are depicted in Figure
Selected model data. Typical element size in the models is 1-2 mm.
Model | Number of nodes | Number of elements | Number of eigenmodes below 16 kHz |
---|---|---|---|
Short, Local reaction | 7577 | 31892 | 174 |
Short, Explicit cavities | 45977 | 211728 | 299 |
Long, Local reaction | 27141 | 123529 | 261 |
Long, Explicit cavities | 102110 | 457621 | 624 |
Acoustic FE models. Models using the given impedance boundary condition are on the top left and in the middle. Models with explicit cavities are on the top right and on the bottom.
Comparison of measured and simulated values of TL is in Figure
TL results for circular holes.
In short version, maximum value of simulated TL is considerably higher than maximum value of measured TL. In long version, maximum values of simulated and measured TLs agree better. In both versions, bandwidth of simulated TL is considerable higher than bandwidth of measured TL. The nominal tuning frequency 3500 Hz is quite well in the middle of TL band.
Reasons for these differences include leaks between backing cavities, uncertainties in impedance and structure-borne sound. TLs above 60 dB seen in simulation results are speculative, because of the limited dynamic range of the apparatus. The coherence around tuning frequency was very low in case of the long version.
TL of short silencers with different hole versions is in Figure
TL results for circular, cateye, and triangular holes, short silencer version.
MPP-based silencers tuned to have peak TL at 3500 Hz were successfully realised using 3D-printing (additive manufacturing).
Three different circular hole options (A, B, and C) of MPP, combined with a suitable backing cavities tuned to 3500 Hz, were designed. These options had target hole diameters of 0.3, 0.4, and 1.0 mm and perforation ratios of 5, 7, and 10 %, respectively. Acoustic impedance measurements showed that quite accurate tuning was achieved with all options (imaginary part changed sign at 3000-3500 Hz range).
The image analysis of the MPP samples showed that the holes of options A and B were, on the average, approx. 0.275 and 0.375 mm compared to targeted 0.3 and 0.4 mm. The shapes of the holes deviated from the round shape. The 1.0 mm holes of the option C sample were far more accurate.
A long and a short version of a MPP silencer with option C holes were printed. The TL measured for the long version was 50…60 dB in the targeted frequency range. In fact, the maximum of TL could not be measured accurately due to poor signal to noise ratio downstream of the silencer. The short version showed TL of approx. 30…35 dB at the tuning frequency.
Two other short versions with the same hole area and area ratio than option C were printed. These were versions with eye-shaped holes and with triangular holes. The performance of these was similar with the performance of the option C. This is because in relatively large holes, reactance is the dominating component of the impedance. Then the different shapes of holes having the same area have no effect.
Two different types of acoustic FE models were created for both the short and long silencer versions. In first type, the MPP surface and backing cavity were modelled using the measured impedance of option C sample. The impedance was inserted into the model as numeric data for a 1x1 FE Area Junction (boundary condition), located on the MPP surface of the silencer passage. In the second type of model, the cavities were modelled explicitly. Then the MPP was modelled as a 2x2 transfer impedance of the area junctions between the duct and cavities.
In the short version, maximum value of simulated TL was considerably higher than maximum value of measured TL. In long version, maximum values of simulated and measured TLs agree better. In both versions, bandwidth of simulated TL is considerable higher than bandwidth of measured TL. The nominal tuning frequency 3500 Hz is quite well in the middle of simulated TL band. Reasons for these differences include leaks between backing cavities, and structure-borne sound. TLs above 60 dB seen in simulation results are speculative, because of the limited dynamic range of the apparatus.
There is no clear superiority between the two types of acoustic FE models. Both types gave useful results, but the accuracy was only approximate. The limitations in both were the exclusion of structural propagation and leaking between cavities. The limitation of the first type of model is the assumption of pure local reaction given as predefined boundary condition. The limitation of the second type of models is probably the accuracy of the perforation theory used.
3D-printing has many advantages in concept development of small scale ducted silencers. These include the following: (1) printing is very fast compared to any other manufacturing method, (2) there are no limitations to shape, and (3) the overall accuracy is good. The main limiting factor noticed in the special context of MPP-based silencers is the printing of very small holes (i.e., below 0.5 mm, say).
There are several possibilities for the next steps, including, but not limited to, (a) effect of simplifying the backing cavity structure (less ribs, axially longer cavities), (b) printing of larger silencers for the TL-tube, (d) development of modular structure for silencer with annular passage, and (e) issues in FE-modelling: plane wave, diffuse and other types of excitation on prediction results.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work has been supported by Wärtsilä Finland Ltd Energy Solutions and VTT Technical Research Centre of Finland Ltd.