energies Article Numerical Simulation of Acoustic Resonance Enhancement for Mean Flow Wind Energy Harvester as Well as Suppression for Pipeline Liuyi Jiang 1 , Hong Zhang 2,*, Qingquan Duan 1 and Xiaoben Liu 2 1 College of Safety and Ocean Engineering, China University of Petroleum, Beijing 102249, China; [email protected] (L.J.); [email protected] (Q.D.) 2 National Engineering Laboratory for Pipeline Safety, MOE Key Laboratory of Petroleum Engineering, Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing 102249, China; [email protected] * Correspondence: [email protected] Abstract: Acoustic resonance in closed side branches should be enhanced to improve the efficiency of wind energy harvesting equipment or thermo-acoustic engine. However, in gas pipeline trans- portation systems, this kind of acoustic resonance should be suppressed to avoid fatigue damage to the pipeline. Realizable k-# delayed detached eddy simulations (DDES) were conducted to study the effect of different branch pipe shapes on acoustic resonance. At some flow velocities, the pressure amplitude of the simulation results is twice as large as that of the experimental results, but the simulation can accurately capture the flow velocity range where acoustic resonance occurs. The results prove the feasibility of the method of the equivalent diameter of the circular cross-section pipe and the square cross-section pipe to predict acoustic resonance. The pressure pulsation amplitude of acoustic resonance in a square cross-section pipe is significantly increased than that in a circular Citation: Jiang, L.; Zhang, H.; Duan, square cross-section pipe, indicating that the square cross-section branch configuration can be more Q.; Liu, X. Numerical Simulation of conducive to improving the efficiency of wind energy harvesting. The influence of the angle between Acoustic Resonance Enhancement for the branch and the main pipe on the acoustic resonance was studied for the first time, which has Mean Flow Wind Energy Harvester an obvious influence on the acoustic resonance. It is found that the design of a square wind energy as Well as Suppression for Pipeline. harvester is better than that of a circular one; meanwhile, changing the branch angle can increase Energies 2021, 14, 1725. https:// doi.org/10.3390/en14061725 or suppress the acoustic resonance, which can improve the utilization efficiency of the acoustic resonance and provide a new method for suppressing the acoustic resonance. Academic Editor: Dibin Zhu Keywords: acoustic resonance; closed side branch; DDES; wind energy harvester Received: 23 December 2020 Accepted: 15 March 2021 Published: 19 March 2021 1. Introduction Publisher’s Note: MDPI stays neutral Acoustic resonance occurs as a gas flows through a closed side branch at a certain with regard to jurisdictional claims in velocity. In industry, this kind of acoustic resonance may exhibit the two sides like a coin, a published maps and institutional affil- valuable side and a harmful side. iations. 1. For wind-energy harvesting, acoustic resonance can output standing waves in the closed side branch without moving parts, providing continuous pressure fluctuation for wind harvesting equipment [1–4] or temperature difference for thermo-acoustic engines [5,6], the acoustic resonance, in this case, needs to be strengthened to improve Copyright: © 2021 by the authors. utilization efficiency [7]. Licensee MDPI, Basel, Switzerland. This article is an open access article 2. Closed side branches exist widely in industry, such as natural gas transmission distributed under the terms and pipelines [8,9], safety valves of the steam pipeline in nuclear power plant [10–15], conditions of the Creative Commons a vertical-lift system of fighters [16–18]. Acoustic resonance in these cases can in- Attribution (CC BY) license (https:// duce severe vibration and noise, cause fatigue damage to the pipeline, threaten the creativecommons.org/licenses/by/ safe operation of the pipeline, and even cause safety accidents, which need to be 4.0/). Energies 2021, 14, 1725. https://doi.org/10.3390/en14061725 https://www.mdpi.com/journal/energies Energies 2021, 14, 1725 2 of 17 avoided or suppressed. Therefore, it is of practical significance to enhance or suppress acoustic resonance. The mechanism of acoustic resonance has been clarified [19,20]. When the gas flows through the branch mouth, the wall friction of the main pipe disappears, and the shear layer falls off from the upstream wall, forming periodic vortices, which spread to the downstream of the main pipe into the branch. As the vortex reattaches to the downstream wall, the acoustic energy accumulates into the branch pipe, and the vortex interacts with the gas in the branch, which further promotes to form of a large vortex. The sound wave generated by the vortex propagates to the branch and reflects at the bottom of the branch. The incident wave and the reflected waveform a standing wave in the closed side branch, resulting in great pressure fluctuations [21–27] (Figure1). From the perspective of the acoustic resonance mechanism, the branch shape affects the shedding and reattachment of the acoustic vortex, so the branch shape can affect the acoustic resonance, which is worthy of in-depth study. Figure 1. The gas flows through a closed side branch. The cross-section shapes of the pipes studied before are square and circular. The square pipe is convenient for the visualization of research. After the tracer particles are injected into the flow, the flow mode can be directly captured, avoiding the influence of the intersection line at the T-shaped intersection of the circular pipe. In general, square pipes or circular pipes were studied separately. Both square and circular pipes were studied by Bruggeman et al. [28]. Bruggeman et al. pointed out that the mechanisms of acoustic resonance in square and circular pipes are the same and proposed that the results studied in a circular pipe can roughly evaluate whether acoustic resonance occurs in the range of Strouhal number in an equivalent square pipe, in which the equivalent diameter is calculated as deff = pd/4, where d is the circular branch diameter. The validity of this equivalence method means that the visualization results in a square pipe can be used to predict the acoustic resonance in an equivalent circular pipe. Moreover, there is no curve intersecting lines in the flow area of square pipes, so it is easier to obtain high-quality orthogonal grids. This not only saves the workload of grid generation in Computational Fluid Dynamics (CFD) preprocessing but also reduces the hardware resources and time cost in the computer solving process. However, the acoustic resonance characteristics of the equivalent diameter configurations have not been studied. The previous studies focus on the mechanism, characteristics, and suppression meth- ods of the acoustic resonance in closed side branches, in which all the branches are perpen- dicular to the main pipeline [8–11,13–20,23,24,26,27]. Some visualization studies of acoustic resonance in square cross-section pipe are to capture the acoustic vortex mode [9,13]. The mechanism and characteristics of acoustic resonance in the high-pressure natural gas trans- mission pipeline [29], the mean flow wind energy harvester (atmospheric air pipeline) [1,2], and the steam pipeline of nuclear power plant [10,12] are studied. The main purpose of changing the branch shape is to suppress acoustic resonance. Baldwin et al. [11] proposed that the internal structure of the safety valve should be designed out of the St-range at which acoustic resonance occurs. Jungbauer et al. [30] proposed to increase the diameter of Energies 2021, 14, 1725 3 of 17 the branch at the connection with the main pipe and use a reducer to connect the original branch pipe to change the St-range of acoustic resonance, thereby suppressing acoustic resonance. These two methods are effective, but the velocity in the main velocity is limited to a certain range once the pipeline structure is designed and constructed. Compared with the branch cross-section and the branch diameter, the branch angle has a greater influence on acoustic resonance and has more potential in suppressing or enhancing acoustic resonance. However, all the pipeline structures in the previous study are branch pipelines perpendicular to the main pipeline [19,20]. In the field of mean flow wind energy harvesting, all the research only focused on the structure of the circular cross- section and the branch perpendicular to the main pipe [2–6,31]. There is currently a lack of research on the influence of branch angle on acoustic resonance. Therefore, in this paper, the acoustic resonance of a circular pipe and an equivalent diameter square pipe are simulated with the realizable k-# DDES model. In addition, the influences of the intersecting line of the pipe on the acoustic resonance are discussed. Furthermore, the influence of the branch angle on acoustic resonance is studied. Current simulations show that these changes can improve mean flow wind harvesting and suppress the acoustic resonance in industrial pipelines. 2. Mathematical Methods The method workflow of the simulation is shown in Figure2. In this section, the CFD method is introduced in the order shown in Figure2. The higher the pressure potential energy, the more beneficial it is to improve the efficiency of the wind energy harvester. Therefore, the pressure distribution determines the installation position of piezoelectric devices in the wind energy harvester. The wider the velocity range and the more consistent the frequency are, the more convenient it is to harvest wind energy. Moreover, the velocity field can show the mechanism of pressure amplitude enhancement. Therefore, velocity, pressure and vorticity are analyzed. Figure 2. The method workflow of the simulation. 2.1. Geometry Model The geometric model is shown in Figure3, which is the flow area in the pipe. D is the main pipe internal diameter, L is the main pipe length, the left is the inlet, and the right is the outlet.