Predictive calculation of noise directivity and propagation from industrial chimneys-stacks using SILDIS^® software

General information on the predictive calculation of noise directivity and propagation from industrial chimneys-stacks using SILDIS^® software

The Module 8A of SILDIS^®[0] software (in Excel format) enables the predictive calculation of noise directivity and propagation from industrial chimneys-stacks, making it possible - at specified locations - to quantify the difference (which varies with frequency) between:

• the sound power level, a characteristic considered intrinsic^[1] of the considered facility for given operating conditions e.g. fluid composition, temperature, flow rate, load (usually expressed in dB ref. 1 pW)
• the sound pressure level, which depends on the measurement location (usually expressed in dB ref. 2 × 10⁻⁵ Pa)

The difference between these two quantities - aside from a correction factor applied when the characteristic impedance used for calculations differs from 400 Rayls (400 Nsm⁻³), the value upon which the equality of sound pressure level (as mentioned above) and sound intensity level (usually expressed in dB ref. 1 pW/m²) is based - is relating to the following: 

• the area of ​​the equidistant envelope containing the measurement points (referred to as the "equidistant area"); this can only be treated as the surface area of ​​a simple geometric shape (such as a sphere or hemisphere centered on the chimney-stack outlet plane) only if the noise source can be considered a point source (meaning the distance between the measurement point and the chimney-stack opening must be sufficiently large relative to the stack's diameter): 
  • in cases where sound levels measurements are taken close to the stack opening (often done to avoid background noise interference), this assumption rarely holds true for large industrial chimneys-stacks
• the directivity index, which expresses the variation in sound level in a specific direction (e.g. defined by the angle relative to the vertical) compared to the average level (across all directions)

This difference is namely used in the following contexts:

• determining the sound power level at chimney-stack outlet based on sound pressure level measurements
• evaluating the sound pressure level in the vicinity of a chimney-stack (e.g. in the context of a noise impact assessment)

The SILDIS^® software can be used:

• by ITS personnel responsible for programming, marketing, training, and support - in addition to performing calculations with the software in various contexts - ("internal use")
• by external users who are not necessarily interested in having access to advanced features, such as those used in Research & Development (R&D) contexts ("external use")

Accordingly, a distinction is made below between the two modes of use: "internal use" and "external use"; however, this distinction is not rigid or definitive, as an external user may opt to utilize the extended features.

Input data can be selected by the user:

• either by entering numerical values (as the software operates in Excel format, this is done in designated cells highlighted in yellow)
• or by selecting a model from a drop-down menu for various stages of the calculations 

Regarding the names of the Excel worksheets in the workbook that make up the module(s) of the SILDIS^® program (depending on the considered version), those with names beginning with:

• "in": allow for user data input
• "out": allow for the viewing of output data (e.g. calculation results)
• "in-out": allow for both data input and the viewing of output data (e.g. calculation results)

For both "internal use" and "external use," the predictive calculation of industrial chimney-stack noise directivity and propagation using SILDIS^® software involves two Excel sheets (within the same workbook).

Summary of Excel spreadsheets relating to the predictive calculation of chimney-stack noise directivity and propagation using SILDIS^® software, for "internal use" and "external use" (Table 1)

The calculations are performed in the 20 Hz - 20 kHz frequency range, using 1/3-octave frequency bands (center frequencies from 25 Hz to 20 kHz) and octave bands (center frequencies from 31.5 Hz to 16 kHz). 

Procedure for the predictive calculation of directivity and noise propagation from industrial chimneys-stacks

Procedure for determining the equidistant area for the predictive calculation of noise propagation from industrial chimneys-stacks

Determining the equidistant area for the predictive calculation of noise propagation from industrial chimneys-stacks involves the use of specific models and settings at various stages of the calculation process. Certain models are programmed into the software to enable comparisons with reference data from the literature, sometimes relying on ambiguous or approximate formulations.

Summary of models for determining the equidistant area used for the predictive calculation of noise propagation from industrial chimneys-stacks in the "in-out 10logS & teta" Excel sheet of the SILDIS^® software for "external use"

For an "external use," the recommended model(s) are those that are both underlined and displayed in bold in the table above.

Procedure for determining the sound ray angle

Determining the sound ray angle for predictive calculation of noise propagation from industrial chimneys-stacks involves considering models and settings for different calculation steps. Some models are programmed into the software to allow comparisons with reference bibliographic data, sometimes using ambiguous or approximate formulations.

Summary of models for determining the straight sound ray angle θo for predictive calculation of noise propagation from industrial chimneys-stacks in the "in-out 10logS & teta" Excel sheet of the SILDIS^® software for "external use" 

For an "external use," the recommended model(s) are those that are both underlined and displayed in bold in the table above.

For the effective angle θ (°) (upon which the directivity index calculation is based), various corrections, where appropriate applied to the straight sound ray angle θo may or may not be taken into account:

• correction for curvature Δθ (°)
• correction for temperature Δθ1 (°)
• correction for fluid velocity Δθ2 (°)
• correction for wind speed Δθ3 (°)
• correction for velocity ratio and density ratio Δθ4 (°)
• correction for velocity ratio and absolute temperature ratio Δθ5 (°)

For each of these corrections, implementation is not automated but determined by the user - via a binary activation indicator (0/1) serving as an input - based not only on the respective scope of validity (displayed by the software) but also on the desire to enable comparisons with various bibliographic datasets that vary in the precision of their contextual information and in their compatibility with such a detailed approach. 

Procedure for determining the directivity index per one-third-octave frequency band 

Determining the directivity index per one-third octave band for the predictive calculation of noise propagation from industrial chimneys-stacks involves the use of specific models and settings at various stages of the calculations.  

Summary of models for determining the directivity index per one-third octave band for the predictive calculation of noise propagation from industrial chimneys-stacks in the "in-out CODIR" Excel sheet of the SILDIS^® software for "external use"

For an "external use," the recommended model(s) are those that are both underlined and displayed in bold in the table above.

Summary of sub-models for determining the directivity index per one-third octave band for the predictive calculation of noise propagation from industrial chimneys-stacks in the "in-out CODIR" Excel sheet of the SILDIS^® software for "external use"

For an "external use," the recommended model(s) are those that are both underlined and displayed in bold in the table above.

Summary of conversion models for determining the directivity index per one-third octave band for the predictive calculation of noise propagation from industrial chimneys-stacks in the "in-out CODIR" Excel sheet of the SILDIS^® software for "external use" 

For an "external use," the recommended model(s) are those that are both underlined and displayed in bold in the table above.

Procedure for determining the directivity index per octave frequency band  

Determining the octave-band directivity index for the predictive calculation of noise propagation from industrial chimneys-stacks involves the use of specific models and settings at various stages of the calculations.  

Summary of conversion models for determining the directivity index per one-third octave band for the predictive calculation of noise propagation from industrial chimneys-stacks in the "in-out CODIR" Excel sheet of the SILDIS^® software for "external use" 

For an "external use," the recommended model(s) are those that are both underlined and displayed in bold in the table above.

Input data for the predictive calculation of noise directivity and propagation from industrial chimneys-stacks using SILDIS^® software

The input data for the predictive calculation of noise directivity and propagation from industrial stacks using SILDIS^® software must be entered into two separate Excel sheets (see Table 1):

• in the "in-out 10logS & teta" Excel sheet:
  • chimney-stack dimensions (radius, wall thickness, height), where the center of the (horizontal) exit plane constitutes the (sound waves) emission point
  • the position of the (sound waves) reception point - depending on the context: either where sound pressure level measurements are taken to determine the sound power level of the chimney-stack outlet, or where the sound pressure level is to be predicted (e.g. in case of an impact study) given a known sound power level for the chimney-stack outlet
  • binary indicators (0 or 1) determining whether or not to apply corrections to the staright sound ray angle θo when calculating the effective sound angle θ
• in the "in-out CODIR" Excel sheet:
  • thermodynamic characteristics of the fluid transported (by the chimney-stack) and of the ambient air (atmosphere)
  • for determining the directivity index per 1/3-octave frequency band:
    • a general model, and if the INT model is selected a sub-model
    • a conversion model
  • for determining the directivity index per octave frequency band:
    • a conversion model
  • for calculating sound power level from sound pressure level:
    • the latter specified per 1/3-octave or octave band
  • for calculating sound pressure level from sound power level:
    • the latter specified per 1/3-octave or octave band

Results of the predictive calculation of directivity and noise propagation for industrial chimneys-stacks using SILDIS^® software

Results of the determination of the equidistant area for the predictive calculation of noise propagation from industrial chimneys-stacks

The result of the predictive calculation of the equidistant area is displayed: 

• in the "in-out 10logS & teta" Excel sheet: as an absolute value (expressed in m²) and as ten times its base-10 logarithm - used to calculate the difference between the sound pressure level and the sound power level, regardless of which of these two physical quantities is the input and which is the unknown - 

Results of the determination of the directivity index for industrial chimneys-stacks

The result of the predictive calculation of the industrial stack directivity index is displayed:

• in the "in-out CODIR" Excel sheet: 
  • curves and tables: per 1/3-octave and 1/1-octave frequency band 

Results of the calculation of sound power level from sound pressure level in specified locations

The result of the predictive calculation of the industrial stack directivity index is displayed:

• in the "in-out CODIR" Excel sheet: 
  • tables: per 1/3-octave and 1/1-octave frequency band 

Results of the calculation of sound pressure level in specified locations from sound power level

The result of the predictive calculation of the industrial stack directivity index is displayed:

• in the "in-out CODIR" Excel sheet: 
  • tables: per 1/3-octave and 1/1-octave frequency band 

^[0] Sound Impact Limitation - Design for Industrialized Solutions 

^[1] "intrinsic" is not entirely suitable for the context, as it should not be understood to mean "independent of any external factor or convention." Namely: 

• when assessing the in-situ sound power level based on sonometer readings, using a limited number of measurement points (e.g. one above the stack outlet plane and one below) and a simplified calculation formula - as cited in certain reference documents - can yield results that are approximate or of limited applicability
• when the sound power level derived from stack outlet measurements is used to characterize an upstream noise source (e.g. at the exhaust flange of a combustion turbine), the resulting assessment may well differ significantly from reality (even if the stack has no silencer); unfortunately, in such cases, in-duct noise measurements present other challenges regarding the accuracy of the sound power level assessment 

^[2] the (sound waves) reception point being close to the stack outlet; the calculation does not account for phenomena that must be considered at greater distances e.g. the atmospheric sound absorption, the weather effect, the presence of obstacles, and the sound wave reflections on hard surfaces (all of which are addressed in another module of the SILDIS^® software).