﻿ 水下变孔距定孔径分布二维排气开孔模式研究
 舰船科学技术  2023, Vol. 45 Issue (19): 94-98    DOI: 10.3404/j.issn.1672-7649.2023.19.017 PDF

Research on underwater two-dimensional exhaust vent mode based on variable-pitch / constant-size distribution
SUO Jun, TANG Si-mi, XU Fei, WANG Hong-bin
Naval Research Institute, Beijing 100161, China
Abstract: The scale parameters of bubbles produced by underwater exhaust influence the effect of the acoustic insulation. According to the dynamic characteristics in the process of underwater gas exhaust and the design criteria of equal flow per unit area, the two-dimensional exhaust equation of underwater gas is established. The analytical expressions of the opening position and geometric parameters of the two-dimensional exhaust device of underwater gas are obtained. The finite element models are established to compare the two vent patterns of uniform distribution and variable-pitch / constant-size distribution. The exhaust effect is verified by circulating flume test. The simulation and experimental results show that the variable-pitch / constant-size distribution mode can effectively control the distribution of bubbles scale parameters, and enhance the acoustic insulation effect of bubbles.
Key words: underwater exhaust     two-dimension     vent size distribution     acoustic insulation
0 引　言

1 气泡幕声衰减模型对声传播的影响 1.1 气泡谱分布特性分析

 $n\left( R \right) = {N_0}{R^E}{e^{ - \frac{{ER}}{{{R_0}}}}} \text{，}$ (1)
 ${N_0} = \frac{{{\tau _N}}}{{\displaystyle\int_0^\infty {\frac{4}{3}{\text{π}} {R^{3 + E}}{e^{ - ER/{R_0}}}dR} }} 。$ (2)

1.2 气泡幕声学性能分析

 $IR = \frac{{\left( {1 - k_1^2} \right)({e^{ - jk^{*}d}} - {e^{jk^{*}d}})}}{{{{(1 - {k_1})}^2}{e^{ - jk^{*}d}} - {{(1 + {k_1})}^2}{e^{jk^{*}d}}}}，$ (3)

 $\begin{split} ID = & \frac{1}{2}\left\{ \left[ {{k_1}\left( {1 - IR} \right) + (1 + IR)} \right]{e^{ - jk^{*}d}} -\right.\\ & \left. \left[ {{k_1}(1 - IR) - (1 + IR)} \right]{e^{jk^{*}d}} \right\}{e^{j{k_0}d}}。\end{split}$ (4)

 图 1 气泡半径变化对插入损失的影响 Fig. 1 Influence of bubble radius change on insertion loss

 图 2 气泡尺度分布特性对插入损失的影响 Fig. 2 Influence of bubble size distribution characteristics on insertion loss

2 气泡幕发生装置变距定积设计 2.1 基本假设

2.2 理论推导

i行、第j列孔的喷气流速为：

 ${v_{ij}} = \mu \sqrt {\frac{2}{{{\rho _{Hi}}}}\left( {{P_{ij}} - {P_{Hi}}} \right)}。$ (5)

 ${\rho _{Hi}} = W{P_{Hi}}，$ (6)

 $a = \frac{{{h_{ij}}{w_{ij}}}}{{hw}} \cdot \frac{{{Q_0}}}{{{v_{ij}}}}，$ (7)

 ${P_{ij}} = \left( {1 + Dh_{ij}^2w_{ij}^2} \right){P_{Hi}}，$ (8)

 ${P_{i + 1,j}} + \frac{{{\rho _{i + 1,j}}V_{i + 1,j}^2}}{2} = {P_{ij}} + \frac{{{\rho _{ij}}V_{ij}^2}}{2} + \Delta {P_{ij}} 。$ (9)

 $\begin{split} & {V_{ij}} = \frac{{{Q_{ij}}}}{{{A_i}}} = \frac{{\displaystyle\sum\limits_{s = 1}^i {{h_{sj}}} \cdot \displaystyle\sum\limits_{t = 1}^j {{w_{it}}} }}{{hw}} \cdot \frac{{{Q_0}}}{{{A_i}}}，\\ & {V_{i + 1,j}} = \frac{{{Q_{i + 1,j}}}}{{{A_{i + 1}}}} = \frac{{\displaystyle\sum\limits_{s = 1}^{i + 1} {{h_{sj}}} \cdot \displaystyle\sum\limits_{t = 1}^j {{w_{i + 1,t}}} }}{{hw}} \cdot \frac{{{Q_0}}}{{{A_{i + 1}}}}。\end{split}$ (10)

 $\begin{split} \Delta {P_{ij}} & = \int_0^{{h_{ij}}} {\frac{\lambda }{{{d_i}}}} \cdot \frac{{{\rho _{ij}}V_{ij}^2}}{2}{\rm{d}}x = \frac{{\lambda W{P_{ij}}Q_0^2{{\left( {\displaystyle\sum\limits_{s = 1}^i {{h_{sj}}} } \right)}^2}{{\left( {\displaystyle\sum\limits_{t = 1}^j {{w_{it}}} } \right)}^2}{h_{ij}}}}{{2{d_i}A_i^2{h^2}{w^2}}}=\\ & \frac{\lambda }{{{d_i}}} \cdot \frac{{D{\mu ^2}{a^2}}}{{A_i^2}}{\left( {\sum\limits_{s = 1}^i {{h_{sj}}} } \right)^2}{\left( {\sum\limits_{t = 1}^j {{w_{it}}} } \right)^2}{h_{ij}}{P_{ij}} 。\\[-21pt] \end{split}$ (11)

 $\begin{split} &{P_{H,i + 1}}\left( {1 + Dh_{i + 1,j}^2w_{i + 1,j}^2} \right)\left[ 1 + \frac{{D{\mu ^2}{a^2}}}{{A_{i + 1}^2}}{{\left( {\sum\limits_{s = 1}^i {{h_{sj}} + {h_{i + 1,j}}} } \right)}^2}\times \right.\\ & \left.{{\left( {\sum\limits_{t = 1}^j {{w_{i + 1,t}}} } \right)}^2} \right] = {P_{Hi}}\left( {1 + Dh_{ij}^2w_{ij}^2}\right)\times \\ & \left[ {1 + \frac{{D{\mu ^2}{a^2}}}{{A_i^2}}{{\left( {\sum\limits_{s = 1}^i {{h_{sj}}} } \right)}^2}{{\left( {\sum\limits_{t = 1}^j {{w_{it}}} } \right)}^2}\left( {1 + \frac{\lambda }{{{d_i}}}{h_{ij}}} \right)} \right]。\\[-21pt] \end{split}$ (12)

 $\begin{split}&\scriptsize {h_{i + 1,j}} = \\ &\scriptsize\sqrt {\frac{{{P_{Hi}}}}{{{P_{H,i + 1}}}}\left( {\frac{1}{{Dw_{i + 1,j}^2}} + h_{ij}^2} \right)\frac{{1 + \frac{{D{\mu ^2}{a^2}}}{{A_i^2}}{{\left( {\displaystyle\sum\limits_{s = 1}^i {{h_{sj}}} } \right)}^2}{{\left( {\displaystyle\sum\limits_{t = 1}^j {{w_{it}}} } \right)}^2}\left( {1 + \frac{\lambda }{{{d_i}}}{h_{ij}}} \right)}}{{1 + \frac{{D{\mu ^2}{a^2}}}{{A_{i + 1}^2}}{{\left( {\displaystyle\sum\limits_{s = 1}^i {{h_{sj}} + {h_{i + 1,j}}} } \right)}^2}{{\left( {\displaystyle\sum\limits_{t = 1}^j {{w_{i + 1,t}}} } \right)}^2}}} - \frac{1}{{Dw_{i + 1,j}^2}}} 。\end{split}$ (13)

 $\begin{split} & \scriptsize{w_{i,j + 1}} =\\ & { \scriptsize\sqrt {\left( {\dfrac{1}{{Dh_{i,j + 1}^2}} + w_{ij}^2} \right)\dfrac{{1 + \dfrac{{D{\mu ^2}{a^2}}}{{A_j^2}}{{\left( {\displaystyle\sum\limits_{s = 1}^i {{h_{sj}}} } \right)}^2}{{\left( {\displaystyle\sum\limits_{t = 1}^j {{w_{it}}} } \right)}^2}\left( {1 + \dfrac{\lambda }{{{d_j}}}{w_{ij}}} \right)}}{{1 + \dfrac{{D{\mu ^2}{a^2}}}{{A_{j + 1}^2}}{{\left( {\displaystyle\sum\limits_{s = 1}^i {{h_{s,j + 1}}} } \right)}^2}{{\left( {\displaystyle\sum\limits_{t = 1}^j {{w_{it}} + {w_{i,j + 1}}} } \right)}^2}}} - \dfrac{1}{{Dh_{i,j + 1}^2}}}}。\end{split}$ (14)

3 排气过程相分布、排气孔压力有限元计算分析 3.1 基本思路

3.2 均匀分布排气孔模型

 图 3 4 kg/s进气流速均匀分布排气孔方案网格模型 Fig. 3 Grid model of exhaust hole scheme with uniform distribution of 4 kg/s intake flow rate

 图 4 均匀分布排气孔模型纵向气相分布情况 Fig. 4 Longitudinal gas phase distribution of the uniformly distributed vent model

3.3 变距定积排气孔模型 3.3.1 开孔总面积接近原则

3.3.2 进气初始位开孔压力接近原则

 图 5 4 kg/s流速进气口压力接近原则变距定积方案网格模型 Fig. 5 Grid model of the variable-pitch / constant-size scheme at 4 kg/s flow rate under the principle of inlet pressure close

 图 6 进气初始位开孔压力接近原则变距定积模型纵向气相分布情况 Fig. 6 Longitudinal gas phase distribution of the variable-pitch / constant-size model under the principle of inlet pressure close at the initial-positioning vent

4 排气试验验证

 图 7 均匀分布排气模型 Fig. 7 Uniformly distributed vent model

5 结　语

1）水中气泡群分布函数基本符合Poisson分布。通过调控气泡幕中气泡尺度参数，可提高气泡幕的隔声效果。

2）依据单位面积排气量相等原则开展变孔间距定孔面积设计。在进气初始位开孔压力接近条件下，与均匀开孔排气方案相比，进气口压力约低0.96%，最近排气孔压力高出约0.48%。

3）在相同排气条件下，变距定积排气模型排气效果明显优于均匀排气模型。

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