Exhaust silencing

ALUPOR™ performs exceptionally well alongside sintered materials for exhaust noise silencing. Moreover, silencers made of porous aluminum function perfectly under cryogenic temperatures maintaining their strength properties. Exhaust noise can occur in various technological processes involving pneumatic and compressor equipment. Technological equipment that assumes gas discharge have to be equipped with silencers to protect the environment and production personnel from the harmful effects of noise. Currently, the company offers several series of commercially produced silencers.

Increased strength and durability compared to silencers made of sintered powders
Resistance to cyclic and vibration loads
Resistance to contaminants — maintains flow capacity for extended periods even in dusty air
High dirt-holding capacity due to unique structure
Fully controlled and stable structural parameters
Durability: maximum pressure differential up to 50 atm (under normal conditions)
Any sizes and configurations available
Parts combining solid and porous sections in a single product
Thread cutting possible on both solid metal and porous sections
Low weight - only plastic is a competitor
Service life exceeding 5 years
Environmentally friendly — material can be recycled as aluminum scrap

Icing (fair for any porous silencer): when designing silencers, it should be considered that the discharged medium is throttling through the porous structure. Its temperature may drop below the crystallization point of the water. Ice formation on the silencer can reduce or completely block the flow. In such conditions, heating is required.
On large silencers, noise may be generated inside the silencer itself: it is necessary to provide additional distribution elements made of coarse-porous material at the outlet of the pipe for preliminary jet breaking.

Parameter	Material type (graded by main pore size range), μm
Parameter	140-315	200-400	315-630	630-1000	1000-1600	1600-3000
Darcy permeability, m²	4,5×10^-12	5.8×10^-12	8.9×10^-12	10.8×10^-11	17.7×10^-11	26.0×10^-11
Forhheimer permeability, m	3.3×10^-5	3.5×10^-5	3.6×10^-5	3.8×10^-5	4.2×10^-5	19.0×10^-5

Parameter	Material type (graded by main pore size range), μm
Parameter	140-315	200-400	315-630	630-1000	1000-1600	1600-3000
Mean pore size, μm	245	300	490	700	1300	2300
Mean neck size, μm	67…77	73…88	100…120	135…170	175…225	245…315
Neck per one pore (coordination number)	6.5	6.5	6.5	6.5	6.5	6.5
Pores per unit area, pcs./ m²	11.6×10⁶	6.4×10⁶	2.4×10⁶	1.2×10⁶	0.34×10⁶	0.11×10⁶
Necks per unit area, pcs./ m²	36.4×10⁶	20.9×10⁶	7.9×10⁶	3.9×10⁶	1.1×10⁶	0.36×10⁶
Porosity, %	50...75
Density***, kg/m³	675...1215
Thermal expansion coefficient, 1/°C	23.0×10^-6 (identical to solid metal)
Allowed temperature range, °C	-200...+250

More details on mechanical properties of ALUPOR™ see "Properties" page.

Parameter	Material type (graded by main pore size range), μm
Parameter	140-315	200-400	315-630	630-1000	1000-1600	1600-3000
Ultimate compressive strength, MPa	105	59	58	49	37	32
Yield point at compression, MPa	39	26	24	20	21	20
Ultimate tensile strength, MPa	29	16	16.5	14	12	8
Yield point at tensile, MPa	26	14	16	13	13	7
Ultimate shear stress, MPa	36	34	30	25	26	-
Young's modulus, GPa	3.1	2	1.9	1.7	1.7	1.6
Elongation, %	0.29	0.38	0.27	0.32	0.3	0.12

More details on mechanical properties of ALUPOR™ see "Properties" page.

Noise is generated during exhaust of compressed air from pneumatic units due to flow turbulence between the exhaust pipe and the external environment. Turbulent compressed air vortices excite acoustic vibrations in the surrounding air medium. A silencer made of ALUPOR™ porous material distributes the turbulent flow from the pipe over the filtering area of the silencer and divides it into many small streams with more favorable hydraulic characteristics, thereby reducing the sound power level. The theory of aeroacoustics is quite complex. Here we will provide the most general and simplest formulations and references for deeper understanding.

Symbols definitions

Constants

R=8,314 462 618 153 24 [J/(mol×K)] - gas constant;

Physical properties

M [kg/mol] - gas molar mass;
μ [Pa×s ] - dynamic viscosity;
ρ [kg/m³] - density;

Physical values

F_filt [m²] - filtration surface;
j [kg/(m²×s)] - specific mass flux;
T [K] - absolute temperature;
t [°C] - temperature;
V [m³] - volume;
v [m/s] - velocity;
v_filt [m/s] filtration velocity;
τ [s] - time.

ALUPOR™ structure parameters

Π [dimensionless] - porosity;
S_min [dimensionless] - ratio of minimal solid cross-section and filtration area (same as minimal void cross-section of packed bed);
d_p [μm] - mean pore size;
S_sp [m²/m³] - specific surface area;
k_v [m²] - Darcy permeability;
k_i [m] - Forhheimer permeability.

Subscripts

#_f value related to fluid ;
#_s value related to solid (metal matrix);
#_p value related to pore volume(example: velocity in pores);
#_n value related to necks between pores (example: velocity in necks);
#_Me value related to solid metal;
#_AP value related to ALUPOR™;
#_eff effective property of composite (example:"ALUPOR™-air" system);

Estimation of silencer's noise level

We can apply known aeroacoustics relations to single mini-jet generated by a single pore neck. For that end we want to define some usual flow parameters for the unit neck.

Reynolds number
Concerning specifics of ALUPOR™ structure we are implementing two variants of Reynolds number:

Reynolds number at pores: $R e_{p} = \frac{ρ_{f} v_{p} d_{p}}{μ_{f}}$
Reynolds number at necks: $R e_{n} = \frac{ρ_{f} v_{n} d_{n}}{μ_{f}}$

Characteristic frequency of vortex formation

Turbulent air discharge produces broadband noise with a peak at a specific frequency. This characteristic frequency can be estimated using the Strouhal number. It is a dimensionless frequency of vortex formation: $S h_{n} = \frac{f \cdot d_{n}}{v_{n}}$ In order to determine the Sh number based on the medium velocity in the neck, one can use the criterion relationship obtained for cylinder flow (see graph).

Sound power of jet from a single neck
Looking forward to estimate sound power of silencer, we can consider well known Lighthill equations. Applying some assumptions one can derive following formulas for sound power of sub-sonic and sonic jets:

P_{n} = k \frac{ρ_{c}^{2} {v_{n}}^{6} {d_{n}}^{2}}{ρ c^{3}} M a < 0.5, k \approx 10^{- 5}

P_{n} = k \frac{ρ_{c}^{2} {v_{n}}^{8} {d_{n}}^{2}}{ρ c^{5}} 0.5 \leq M a < 2, k \approx 3 \cdot 10^{- 5}

where
k [dimensionless] — empirical coefficient;
ρ_c [kg/m³] — jet density at nozzle exit;
ρ [kg/m³] — density of surrounding gas medium;
c [m/s] — speed of sound in surrounding medium;
here Ma [dimensionless] — Mach number Ma=v/c;
From the formula above, it is evident that sound power can be reduced by decreasing the linear air discharge velocity, as well as jet density and nozzle size. The silencer length must ensure pressure reduction in the exhaust chamber to required values within the operating cycle time.
The jet density ρ_c can be calculated based on gas pressure at a distance of one pore d_p from the silencer surface, assuming linear pressure distribution in pores in the filtration direction:

ρ_{c} = \frac{M [p_{i n} - (p_{i n} - p_{o u t}) (1 - d_{p} / l)]}{R T}

Here M [kg/mol] — this is the molar mass of the gas.
WARNING
(1) The formulas provided above require experimental calibration before application.
(2) Calculating ρ_c using linear distribution may be incorrect.

Sound power level
Sound power level is calculated as:

L_{W} = 10 \log_{10} (\frac{N_{n} P_{n}}{P_{0}}) dB

где
P₀=10^-12 W - reference sound power;
N_n - quantity of necks on the silencer surface .

Sound pressure level
Since sound power level of silencer is known we now can estimate sound pressure level at R [m] distance form silencer as follows:

L_{P} = L_{W} - 10 \log_{10} (\frac{2 π R^{2}}{A_{0}}) dB

where
A₀=1 m² reference area.
Finally we can apply standard A or B correction and obtain desired L_PA or L_PВ which have to be compared with ISO specified limits.

ISO 1999:2013 Acoustics — Estimation of noise-induced hearing loss

ISO 14163:1998 Acoustics — Guidelines for noise control by silencers

ISO 11820:1996 Acoustics — Measurements on silencers in situ

ISO 20145:2019 (Expected to be replaced by ISO/DIS 20145) Pneumatic fluid power — Test methods for measuring acoustic emission pressure levels of exhaust silencers

ISO 4871:1996 Acoustics — Declaration and verification of noise emission values of machinery and equipment

ISO 9053:1991 Acoustics - Materials for acoustical applications - Determination of airflow resistance

ISO 3740:2019 Acoustics — Determination of sound power levels of noise sources — Guidelines for the use of basic standards

ISO 9612:2009 Acoustics — Determination of occupational noise exposure — Engineering method

ISО 7235 Acoustics - Measurement procedures for dueled silencers-Insertion loss, flow noise and total pressure loss

ISO 6358-1:2013 Pneumatic fluid power — Determination of flow-rate characteristics of components using compressible fluids. Part 1: General rules and test methods for steady-state flow

ISO 6358-2:2019 Pneumatic fluid power — Determination of flow-rate characteristics of components using compressible fluids. Part 2: Alternative test methods

ISO 6358-3:2014 Pneumatic fluid power — Determination of flow-rate characteristics of components using compressible fluids. Part 3: Method for calculating steady-state flow-rate characteristics of systems

Advantages

Limitations

SPECIFICATIONS

MANUFACTURE ABILITIES

Theory reference

EU legislation reference

Noise and silencing standards