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Acoustics

CAA: Computer Aided Acoustics

Aero-acoustics deals with production, propagation (transmission: air-borne or solid-borne), reflection (as sound moves from one medium to another), absorption, scattering, attenuation and reception (by human ears) of sound waves. The sound is primarily generated by fluid fluctuations forced due to unsteady motion of fluids. Sound is a small perturbation of pressure over a mean (steady state) pressure, p’/p0 which propagates as a wave. It is different from generation of sound such as organ pipe and lous-speakers. The later is referred as "classical acoustics". Excerpts from COMSOL user manual: "Acoustics is the physics of sound. Sound is the sensation, as detected by the ear, of very small rapid changes in the acoustic pressure p above and below a static value. This static value is the atmospheric pressure (about 100,000 Pa). The acoustic pressure variations are typically described as pressure waves propagating in space and time."

Jargons in Acoustics

  • Threshold of Hearing: This it the lowest level of sound intensity that can be sensed (heard) my most humans at a specified frequency of 1000 [Hz]. In air it is 20 [μPa].
  • Description of waves: frequency - ν is number of vibrations per seconds, wavelength - λ is the distance after which wave pattern repeats itself, speed of sound c - the velocity of propagation of acoustic waves = ν.λ, wave number - k is the number of waves required to cover a specified distance = 2π/λ.
  • SPL - Sound Pressure Level: This refers to the intensity of sound waves. This is represented as logarithm (because sound pressures have large ranges) of a ratio of magnitude of pressure fluctuations to the reference pressure at threshold of hearing and denoted as Decibel [dB]. SPL = 20 × log(p / pREF) [dB] where pREF = 20 [μPa]. Thus, "threshold of hearing" corresponds of SPL = 0 [dB]. Bel is another measure of SPL and is equal to 10 decibels (dB). It is dimensionless since it is a ratio of two quantities.
  • Designated as Lw, Sound Power Level is the total acoustic energy output of a noise source independent of medium of propagation of the sound (the environment). While sound power level is a constant value for each noise source, SPL are dependent on factors such as the distance from the noise source, presence of any reflective surfaces present near the source. Thus, sound pressure levels will always be higher than sound power levels.
  • Band - Band refers to a continuous range of frequencies between two limiting frequencies.
  • Bandwidth - Bandwidth is defined as range of frequencies, usually of standard size in acoustics. For example octave or one-third octave bands where octave bands are groups of frequencies named by the center frequency having upper limit always twice the lower limit of the range.. The lower and upper frequencies are also known as the -3 dB or half-power points.
  • Noise - Unwanted sound.
  • Broadband Noise - This is also called wideband noise - a type of noise whose energy is distributed over a wide range of frequencies of pressure fluctuations (or audible range).
  • Tonal Noise - Tone refers to a specified frequency. Tonal noise refers to sound wave forms that occur at a particular frequency such as RPM of a rotating wheel - also known as narrowband noise. Tonal noise are discrete and occur only at certain frequencies that is the frequency of a tonal noise remains constant for a range of mass flow rates or input flow velocity scale.
  • Acoustic Impedance - Analogous to the flow of electric current, acoustic impedance of a material it the resistance of the passage of sound waves. Impedenace is a type of resistance (as we learnt for capacitors and inductors whose resistance is function of frequency of electric current following through them and complicated by the fact that current and voltage may not be in phase). Similarly, acoustic impedance is defined as ratio of acoustic pressure p to acoustic volume flow rate Q. Z = p / Q [Pa.s/m3] ≡ [kg/m4/s] or acoustic &Omega. Similar to electric impedance, the flow and pressure may not be in phase and hence like electrical systems, complex numbers method needs to be used to handle such impedances where the real part represents the in-phase component and the imaginary part the out-of-phase component.
    • For an infinitely long pipe of cross sectional area A which is filled with a medium of density ρ and at temperature T at which speed of sound c = (γ×R×T)0.5, the acoustic impedance is [ρ×c/A].
    • The acoustic impedance of a material determines fraction of sound power that will be transmitted and reflected when the wave encounters an interface created by two different materials. The larger the difference in acoustic impedance between two materials, the smaller the amount of transmitted energy will be. Similarly, the acoustic impedance of a sound attenuation device determines fraction of sound power that will be transmitted and reflected when the wave passes through it.
  • Transmission loss - It is defined as the difference between the sound power incident at the entry of the sound attenuation device such as filter or muffler and the sound power transmitted after the device. Thus: TL = 10 × log(WIN/WOUT) = 20 × log(pIN/pOUT).

Steps in Acoustic Calculations

Excerpts from "Surface integral methods in computational aeroacoustics — from the (CFD) near-field to the (Acoustic) far-field" by Anastasios S. Lyrintzis, School of Aeronautics and Astronautics, Purdue University:
 "Aerodynamically generated sound is governed by a nonlinear process. One class of problems is turbulence generated noise (e.g. jet noise). An accurate turbulence model is usually needed in this case. A second class of problems involves impulsive noise due to moving surfaces (e.g. helicopter rotor noise, propeller noise, fan noise etc.). In these cases an Euler/Navier-Stokes model or even a full potential model is adequate, because turbulence is not important. Furthermore, because the acoustic fluctuations are usually quite small (about three orders of magnitude less than the flow fluctuations), the use of nonlinear equations (whether Navier-Stokes or Euler) could result in errors. One usually has no choice but to separate the computation into two domains, one describing the nonlinear generation of sound, the other describing the propagation of sound."
  • Hybrid approach: This is called so because noise predictions are a two-step approach due to the large difference in requirements on the flow field and acoustic propagation. Ffowcs Williams-Hawkings formulation and Lighthill's analogy are examples of hybrid approach.
  • Step - 1 : Calculate the source of noise - this is typically achieved by a 3D simulation in a CFD program, either using RANS or LES approach. The Acoustic Analogy approach introduced by James Lighthill is used to divide computational domain into a non–linear source region and a wave propagation region. The turbulent unsteady flow is considered in the source region and used as a excitation to the acoustic propagation. CFD simulation can be either of the followings:
    • Incompressible, steady state
    • Imcompressible, transient
    • Compressible, transient
  • Step - 2 : Extract the noise sources using Lighthill's analogy for low Mach number flows and Mohring analogy for high Mach number flows.
  • Step - 3 : Use CAA tool such as SYSNOISE, ACTRAN, NUMECA to solve for noise propagation and SPL results.

Ways of Attenuation of Sound Levels

  • Helmholtz Resonator
  • Concentric Resonator
  • Flow expansion chambers: contraction and expansion
  • Acoustics Filters

Sound Attenuation Devices

There are two ways to attenuate the level of sound: reflective systems - here the incident sound is scattered and canceled by destructive interference and dissipative system - here the incident sound energy is absorbed and hence has to be converted into the heat. Expansion-contraction chambers, resonators and Herschel-Quincke tube fall under the category of refective systems.

Expansion Chamber Silencer

Expansion Chamber Silencer Velocity Profile

Automotive exhaust mufflers use perforated tubes. The STEP file and FreeCAD file of this geometry can be downloaded for mesh generation and simulation.
Expansion Chamber Silencer Velocity Profile

There are two basic types of mufflers or silencers:
  • Reflective or reactive mufflers - the operating principle is to reflect acoustic waves by abrupt area expansions or changes of impedance. Such mufflers are recommended for the low frequency range where only plane waves can propagate in the system.
  • Dissipative mufflers - these type of mufflers dissipate acoustic energy into heat through viscous losses either in fibrous materials and/or flow-related hydraulic losses such perforated pipes shown above. This type of muffler is recommended to higher frequency ranges.
  • Most of the systems have noise components varying from low to high frequency range and hence no single type of muffler serves the purpose. Hence, dissipative mufflers can be made of hybrid type where flow losses can be used to work also at low frequencies. For example, automotive exhaust mufflers are of hybrid type using a combination of reflective and dissipative muffler elements where reflective part removes low-frequency engine noise generated by combustion and valve motion while the dissipative part is designed to take care of higher-frequency noise.

Application of Aero-Acoustics - CAA

  • Automotive Exhaust Silencer (UK English) or Mufflers (US English): intake and exhaust noise can be due to pipe resonance, shell vibration and turbulent fluctuations.
  • Cabin Noise from HVAC module: tonal component due to blowers, broadband component due to turbulent flows and shell vibrations
  • Instrument panel vibration, ORVM (Outside Rear View Mirror) and A-Pillar noise
  • Rotating devices: Compressor and Fan noise, high frequency noise in turbo-chargers, whistling due to structure-borne noise.
  • Vacuum cleaners
  • Building Air-conditioning Systems

Numerical Tools for CAA

  1. SYSNOISE
  2. ACTRAN: MBD (ADMAS) &rtarrow; NASTRAN &rtarrow; ACTRAN for structure-borne noise
  3. ANSYS FLUENT: Primarily acoustic field generation using broadband noise.
  4. NUMECA
  5. ANSYS WORKBENCH ACT
  6. COMSOL

Special Boundary Conditions for CAA

  • Non-reflecting Boundary
  • Unechoic Chamber
  • Radiation Boundary

TMM (Transfer Matrix Method)

  • Step-1: Condense a complex systems into simpler sub-systems arranged into series
  • Step-2: Calculate transmission loss of each sub-system
  • Step-3: Overall TL of the system is product of TL of each sub-system in series

Noise Level Regulations

  • Pass-by Noise: ISO 7216:1992
  • Noise for agriculture and forestry wheeled tractors in motion fitted with elastic tyres or rubber tracks: governed by standard ISO 7216:2015. Test method specified by this standard require an acoustical environment which can only be obtained in an wide open space. Noise limits:
    • Tractor with no load condition < 1.5 ton: 85 dB
    • Tractor with no load condition ≥ 1.5 ton: 89 dB
  • Construction equipments
    • Noise level at operator's position at stationary condition is governed by ISO 6394:2008. For exterior locations, ISO 6393:2008 applieds.
    • Noise level at operator's position under dynamic condition is governed by ISO 6396:2008. For exterior locations, ISO 6395:2008 applies.
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