Vibroacoustic Modelling of a Periodic Assembly of Multi-Coupled Fins Based on Wave Decomposition

The prediction of the noise radiated by finned coils is necessary to design silent heat pumps. Finned coils are made of a huge number of parallel fins multi-coupled by tubes. Modelling the complete structure using Finite and Boundary Element Methods is practically impossible due to very-high computational costs. It seems thus relevant to exploit the periodicity of the structure to get a small-sized model independent of the number of fins. In this paper, the finned coil is reduced to a finite assembly of fins multi-coupled by springs. Using the transfer matrix formulation, the structure is divided into unit elements and propagating waves are identified. The main feature of the approach presented here is to use these waves to compute the acoustic response of the complete periodic structure from the acoustic response of only one unit element. For this purpose, the acoustic pressure radiated by the unit element is computed for each wave travelling in the structure using standard BEM software. The pressure fields are then duplicated according to the phase difference of each wave and all waves contributions are finally summed. A numerical comparison with the direct computation of a complete assembly with FEM and BEM showed a great accuracy with a low computational effort. This approach allows to consider finite structures made of numerous fins without a huge increase of calculation time.