Research Article

An Image Based Mathematical Model for the Propagation of Fan Noise in a Plenum with Large Side Openings

Table 1

Basic concept and novelties for group images method.

Steps in the group images methodTight-fitting enclosure in reference [10]Fan plenum enclosure in this paper

Define the source model relative to enclosureA machine surface comprising one side of enclosure modeled as uniformly and randomly distributed over the machine surface due to multimodal machine surface vibrationAxial fan(s) modeled as point source with directivity located at the ceiling area of the plenum

Select the main reverberation group as that between the closest set of parallel enclosure surfacesThe reverberation between the machine surface and its opposite wall located close to it with an integration over the machine source surfaceThe reverberation between the floor and ceiling (comprising the fans) from the point source fan(s)

Select the second group as the images of the first group due to the other one or two sets of parallel enclosure surfacesImages projected by the area source along the ceiling-floor and side wall-side wall sets; this results in single summationsImages projected by the point source along the bulkhead-bulkhead set as well as the four quadrants comprising floor-ceiling, bulkhead-bulkhead images; this results in double summations

Use of a factor for including the group of highest order or extra surfaces images that occurImages produced from the combination of the main group and second group, which lie in four quadrantsImages produced from solid portion of side wall areas containing the large openings and due to the main group and second group sets

Model for the directivity of the direct path from source to enclosure surface that would serve as the radiation area to external spaceThe directivity is inherent in the Hohenwarter [11] radiation model from an area sourceThe directivity is modeled using the analysis from Morse and Ingard [12] by considering the fan area as random radiation with directivity relative to a point source