Similarity analysis of the flow-induced noise of a benchmark submarine

As one of the three major noise sources of submarines, flow-induced noise plays a key role for the stealth capability of submarines. Several research studies based on experiment or simulation have evaluated the sound radiation from the scale model; however, it is still a great challenge to efficiently evaluate the flow-induced noise of a large-scale prototype. In order to solve this problem, the flow-induced noise of different scale submarines is analyzed, and both the similarity law and the scale effect are discussed in the dimensionless frequency St = 10-1089. The fully appended DARPA SUBOFF, a famous benchmark submarine model, is used in our research. The relationship between the sound power, scale variables, and the speed and scale variables is obtained using the Buckingham Pi theorem. Then, the sound pressure level and the sound power level of the SUBOFF, with the scale ratio of 1:24 and 1:48 and the speed of 2, 4, and 8 m/s, are calculated based on the large-eddy simulation (LES)/Lighthill hybrid method. Finally, the scale effect between a hypothetical prototype (actually, a benchmark SUBOFF model with a scale ratio of 1:8) and its scale models are discussed at the same speed. The numerical results show that the submarine's sound power level conforms to the similarity relationship of dipole source within the cut-off frequency St = 100. The error of the sound power level is about 20 lg ( f ) caused by scale effect when the dimensionless frequency is greater than the cut-off frequency, where f is the scale ratio from the hypothetical prototype to the model. The scale error of the sound pressure level at different position and different frequency exist differently when extrapolating from model results to prototype according to the similarity law based on dipole source.