Specification of replication length in quasi-two-dimensional integral surface method

This paper focuses on quasi-two-dimensional integral surface method in order to estimate the propagation of two-dimensional acoustic waves. In this approach, the required surface data is generated by replication of a two-dimensional data curve along the third out-of-plane dimension. For this purpose, a two-dimensional monopole acoustic source is employed and the Farassat integral surface approach is implemented. It is observed that the estimated sound pressure at far-field converges to the two-dimensional solution as the number of replications increases. The convergence trend shows an oscillatory behavior in terms of replication length and amplitude decay in each cycle. The impact of different parameters such as frequency of acoustic waves, free stream Mach number, distance, and the location of observer on convergence trend is investigated. Based on these results, a methodology to specify the replication length for the required level of convergence is proposed. The capability of the developed method is investigated by studying the cavity flow noise. The estimated noise at far-field for two oscillation modes, namely shear-layer and wake mode, reveals an error of 3.1% and 2.8% in comparison with the reference values, respectively, which indicates that the presented method is capable of predicting the far-field noise with a very good accuracy. •Assessment of the propagated waves w.r.t the replication length.•Introducing a methodology to specify the replication length.•Verifying the capability of the methodology through the study of cavity flow.