Acoustic power balance in lined ducts

AbstractThis study investigates the suppression of the sound produced when a jet, issued from a circular nozzle or hole in a plate, goes through a similar hole in a second plate. The sound, known as a hole tone, is encountered in many practical engineering situations. The mean velocity of the air jet $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}u_0$ was $6\text {--}12\ \mathrm{m}\ {\mathrm{s}}^{-1}$. The nozzle and the end plate hole both had a diameter of 51 mm, and the impingement length $L_{im}$ between the nozzle and the end plate was 50–90 mm. We propose a novel passive control method of suppressing the tone with an axisymmetric obstacle on the end plate. We find that the effect of the obstacle is well described by the combination ($W/L_{im}$, $h$) where $W$ is the distance from the edge of the end plate hole to the inner wall of the obstacle, and $h$ is the obstacle height. The tone is suppressed when backflows from the obstacle affect the jet shear layers near the nozzle exit. We do a direct sound computation for a typical case where the tone is successfully suppressed. Axisymmetric uniformity observed in the uncontrolled case is broken almost completely in the controlled case. The destruction is maintained by the process in which three-dimensional vortices in the jet shear layers convect downstream, interact with the obstacle and recursively disturb the jet flow from the nozzle exit. While regions near the edge of the end plate hole are responsible for producing the sound in the controlled case as well as in the uncontrolled case, acoustic power in the controlled case is much lower than in the uncontrolled case because of the disorganized state.

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Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

Electronics ◽

10.3390/electronics10121452 ◽

2021 ◽

Vol 10 (12) ◽

pp. 1452

Author(s):

Cristian Mateo Castiblanco-Pérez ◽

David Esteban Toro-Rodríguez ◽

Oscar Danilo Montoya ◽

Diego Armando Giral-Ramírez

Keyword(s):

Genetic Algorithm ◽

Objective Function ◽

Programming Model ◽

Distribution Networks ◽

Optimization Method ◽

Optimal Placement ◽

Mixed Integer ◽

Power Balance ◽

Continuous Version ◽

Discrete Part

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

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