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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. It is different from generation of sound such as organ pipe and lous-speakers. The later is referred as "classical acoustics".

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].
  • 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 magnitudue 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 paricular 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

  • 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. 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 cancelled by destructive interference and dissipative system - here the incident sound energy is absorved and hence has to be converted into the heat. Expansion-contraction chambers, resonators and Herschel-Quincke tube fall under the category of reective systems.

Expansion Chamber Silencer

Expansion Chamber Silencer Velocity Profile


Application of Aero-Acoustics - CAA

  • Automotive Exhaust Silencer (UK English) or Mufflers (US English)
  • Cabin Noise frm HVAC ducts
  • ORVM (Outside Rear View Mirror) and A-Pillar noise
  • Rotating devices: Compressor and Fan noise, high frequecy noise in turbo-chargers
  • Vacuum cleaners
  • Building Air-conditioning Systems

Numerical Tools for CAA

  1. SYSNOISE
  2. ACTRAN
  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
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