Analytical and numerical modeling, sensitivity analysis, and multi-objective optimization of the acoustic performance of the herschel-quincke tube

Abstract This study presents the assessments of the acoustic performance of a Herschel-Quincke (HQ) tube, which includes sensitivity analysis and multi-objective optimization of its design variables. A proper model introduced using the flow characteristics of the HQ tube. Input variables were frequency (f), temperature (T), the ratio of areas (R), and tube length (L). These variables were chosen to be varied in a specified range to best characterize the exhaust flow in internal combustion engines. Then a proper multi-objective genetic algorithm (MOGA) was developed for the acoustic performance and geometry optimization of a two-duct HQ tube; the objectives were maximizing the transmission loss (TL) and at the same time minimizing the backpressure (BP). Besides, the local sensitivity analysis using numerical derivative and variance-based global sensitivity analysis (GSA) using Monte Carlo sampling was performed for the analytical model of the HQ tube. The results showed that the length of the bypass tube is a crucial factor for the maximum sensitivity index (SI) of the TL, while the SI of the BP was maximum for the ratio of areas. The proposed analytical model was proved to be reliable for the TL, showing low values of the error of the sensitivity index (eSI) and less reliable for the BP parameter, showing higher eSI values. For the evaluation of the TL sensitivity, Monte Carlo sampling is relatively inaccurate in the small sample size of 200. It was also observed that the Uniform distribution had lower eSI in lower sample sizes; however, Sobol sampling showed better performance in higher sample sizes. The MOGA optimization proved to be successful in maximizing the TL for the frequencies between 105.84 and 1981.11 Hz, with the TL greater than 20 dB, and the BP less than 0.1. The most efficient solution among the Pareto set after a tradeoff was at 105.84 Hz, for which the TL and the BP were 36.47 dB and 1.50E−02, respectively. The model with the best goodness of fit to represent the Pareto front was the power model with two terms. Then, the acoustic performance of the optimized geometry was investigated using computational aeroacoustics (CAA) in the presence of mean flow in Fluent software. Using the CAA approach, the maximum TL value was obtained for 104 0.4 Hz as 12.14 dB. The simulated TL by CAA had more broadband behaviors with fewer peaks than the analytical approach. The results of this study demonstrated the remarkable potential of the MOGA optimization and sensitivity analysis for acoustic performance and topology optimization for possible applications in internal combustion engines.