TIME-DOMAIN EDGE DIFFRACTION MODEL

Sound diffraction by edges is an important aspect in the study of sound propagation around solid obstacles. Time-domain models, in particular, can be useful in several practical problems such as diffraction of sonic booms by buildings. An extension of the Directive Line Source Model (DLSM), one of the models that predict the diffraction field produced by a sound wave incident on a half plane, is presented. The enhanced model is formulated in the time domain and renders the original DLSM valid close to shadow boundaries, where it was not valid before. Appropriate frequency-domain analytical solutions for plane, cylindrical, and spherical incident waves are transformed in the time domain, re-formulated, unified and re-interpreted. It is shown that for all types of incident radiation the diffracted signal can be interpreted as being radiated from a directional line source (as stipulated by the original DLSM) irrespective of the proximity to a shadow boundary, provided that the directivity of the virtual line source is appropriately modified. The proposed reformulation of the diffraction solution enables the application of the model to two cases of practical interest: diffraction by edges of finite length, and diffraction by wedges of both infinite and finite length. Predictions of the model compare favorably with other analytical solutions. Finally, the application of the model is demonstrated for the practical noise problem of sonic booms incident on buildings. Predictions agree reasonably well with 2006 NASA flight test measurements, while it is illustrated that edge diffraction by buildings (modeled as wedges) can significantly affect the noise field. As opposed to other time-domain diffraction models, which are applicable to a single type of incident radiation (mainly spherical), the presented method is applicable to all types of simple incident radiation (plane, cylindrical, spherical). Moreover, it provides theoretical insight, while it involves explicit and fast calculations.