﻿ 新型蓄能器浮标上浮运动水动力性能研究
 舰船科学技术  2018, Vol. 40 Issue (3): 42-48 PDF

Research on the dynamic performance of floating motion of a new type float with energy accumulator
ZOU Yi-lin, CAO Jun-jun, YAO Bao-heng, LIAN Lian, REN Ping
The State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: Because of the importance of the deep ocean in the earth climate system, a series of research projects which take the deep ocean as the core have been put forward and implemented in the world. The float has been generally used in deep ocean observation research in consideration of its high-resolution observation ability. In order to broaden the variation range of the volume of the float, a new type float named N2 float which is equipped with N2 energy accumulator basing the normal APEX float has been devised. The schematic diagram of this float would be proposed. The formulation of the uniform motion of the float would be given by doing mechanical analysis, and the volume of the float needed for floating would be calculated, the figures of accelerated velocity-time history and velocity-time history of the normal type and new type float would be deduced, the figures would be compared and the influence of the energy accumulator would be analyzed.
Key words: N2 float     profile detection     energy accumulator     mechanical analysis
0 引　言

1 剖面探测浮标结构 1.1 国外浮标简介

1.2 算例浮标结构组成介绍

 图 1 氮气浮标结构简图及工作原理 Fig. 1 The sketch of the structure and thefundamental diagram of N2 float
2 浮标阻力系数的计算

 图 2 外域网格 Fig. 2 The mesh of external area

 图 3 内域网格 Fig. 3 The mesh of internal area

 $c = \frac{{8\pi }}{{Re\left( {2 - \ln Re} \right)}},$ (1)

3 浮标运动过程研究 3.1 浮标上浮的基本方程

 ${F_D} + mg = \rho g{V_{{\text{浮}}}},$ (2)

 ${F_D} = {C_D}\frac{\rho }{2}{u_0}^2A,$ (3)

 ${C_D}\frac{\rho }{2}{u_0}^2A + mg = \rho g{V_{{\text{浮}}}}{\text{。}}$ (4)

 ${V_{{\text{浮}}}} = \frac{{{C_D}\frac{\rho }{2}{u_0}^2A + 2mg}}{{\rho g}}{\text{。}}$ (5)

3.3 浮标上浮过程中浮力保持不变 3.3.1 浮标上浮过程瞬时加速度建立

 ${{m}}\frac{{{ d}u}}{{{ d}t}} = \rho g{V_{{\text{浮}}}} - mg - {C_D}\frac{\rho }{2}{u^2}A,$ (6)

 $\frac{{{ d}u}}{{{ d}t}} = \frac{\rho }{m}g{V_{{\text{浮}}}} - g - {C_D}\frac{\rho }{{2m}}{u^2}A{\text{。}}$ (7)
3.3.2 浮标加速过程速度方程的建立

 $\!\!\! \frac{m}{{\sqrt 2 \left( {\rho g{V_{{\text{浮}}}} \!-\! mg} \right){C_D}\rho A}} \cdot \ln \left| {\left. {\frac{{u \!-\! \sqrt {2\left( {\frac{{\rho g{V_{{\text{浮}}}} \!-\! mg}}{{{C_D}\rho A}}} \right)} }}{{u \!+\! \sqrt {2\left( {\frac{{\rho g{V_{{\text{浮}}}} \!-\! mg}}{{{C_D}\rho A}}} \right)} }}} \right|} \right. \!=\! t \!+\! C{\text{。}}\!\!\!\!\!$ (8)
3.4 浮标上浮过程中浮力随压力变化

 $V = \frac{{nRT}}{P},$ (9)

 ${P_{{\text{海}}}} = \rho g\left( {4\ 000 - y} \right),$ (10)

 ${P_0} = {\left. {{P_{{\text{海}}}}} \right|_{y = 0}},$ (11)
 ${V_0} = \frac{{nRT}}{{{P_0}}}{\text{。}}$ (12)

 ${V_1} - {V_0} = \frac{{nRT}}{{\rho g\left( {4\ 000 - y} \right)}} - {V_0}{\text{。}}$ (13)

 $\frac{{{{ d}^2}y}}{{{ d}{t^2}}}\! =\! \frac{\rho }{m}g\left( {\frac{{nRT}}{{\rho g\left( {4\ 000 \!-\! y} \right)}} \!-\! {V_0} \!+\! {V_{{\text{浮}}}}} \right) \!-\! g \!-\! {C_D}\frac{\rho }{{2m}}{u^2}A{\text{。}}$ (14)

3.5 浮标上浮过程能源效率分析

 ${W_1} = \left( {{{\rho g}}{V_{{\text{浮}}}} - mg} \right){y_1}{\text{。}}$ (15)

 ${P_1} = \frac{{{W_1}}}{t}{\text{。}}$ (16)

 ${W_2} = \left( {{{\rho g}}\left( {\frac{{nRT}}{{\rho g\left( {4000 - {y_2}} \right)}} - {V_0} + {V_{{\text{浮}}}}} \right) - mg} \right){y_2},$ (17)

 ${P_2} = \frac{{{W_2}}}{t}{\text{。}}$ (18)
4 数值求解及结果分析 4.1 浮标上浮运动方程数值求解思路

ode45算法的求解思路为用4阶方法提供候选解，用5阶方法控制误差，它是单步解算命令，常用于求解非刚性中等精度的问题。考虑式（14），将龙格-库塔方法的一般形式表示如下[9]

 ${y_{n + 1}} = {y_n} + h\varphi \left( {{t_n},{y_n},h} \right),$ (19)

 $\varphi \left( {{t_n},{y_n},h} \right) = \mathop \sum \limits_{i = 1}^r {c_i}{K_i},$ (20)
 ${K_1} = f\left( {{t_n},{y_n}} \right),$ (21)
 ${K_i} = f({t_n} + {\lambda _i}h,{y_n} + h\mathop \sum \limits_{j = 1}^{i - 1} {\mu _{ij}}{K_j}),\;i = 2, \ldots ,r{\text{。}}$ (22)

 $\left\{ \begin{array}{l}{y_{n + 1}} = {y_n} + \frac{h}{6}\left( {{K_1} + 2{K_2} + 2{K_3} + {K_4}} \right),\\{K_1} = f\left( {{t_n},{y_n}} \right),\\{K_2} = f\left( {{t_n} + \frac{h}{2},{y_n} + \frac{h}{2}{K_1}} \right),\\{K_3} = f\left( {{t_n} + \frac{h}{2},{y_n}\frac{h}{2}{K_2}} \right),\\{K_4} = f\left( {{t_n} + h,{y_n} + h{K_3}} \right){\text{。}}\end{array} \right.$ (23)

 $y\left( {{t_{n + 1}}} \right) - y_{n + 1}^{\left( h \right)} \approx c{h^5},$ (24)

 $y\left( {{t_{n + 1}}} \right) - y_{n + 1}^{\left( {\frac{h}{2}} \right)} \approx 2c{\left( {\frac{h}{2}} \right)^5}{\text{。}}$ (25)

 $y\left( {{t_{n + 1}}} \right) - y_{n + 1}^{\left( {\frac{h}{2}} \right)} \approx \frac{1}{{15}}\left[ {y_{n + 1}^{\left( {\frac{h}{2}} \right)} - y_{n + 1}^{\left( h \right)}} \right]{\text{。}}$ (26)
4.2 Matlab数值计算结果分析

 图 4 有无蓄能器时速度随时间变化曲线 Fig. 4 The presence of speed changing over time with/without accumulator

 图 5 无蓄能器时加速度随时间变化图 Fig. 5 The presence of accelerated speed changing over time without accumulator

 图 6 有蓄能器时加速度随时间变化图 Fig. 6 The presence of accelerated speed changing over time with accumulator

 图 7 预定速度0.2 m/s时加速度比较 Fig. 7 The comparation of accelerated speed at the priming speed 0.2 m/s with/without accumulator

 图 8 预定速度0.3 m/s时加速度比较 Fig. 8 The comparation of accelerated speed at the priming speed 0.3 m/s with/without accumulator

 图 9 预定速度0.4 m/s时加速度比较 Fig. 9 The comparation of accelerated speed at the priming speed 0.4 m/s with/without accumulator

 图 10 预定速度0.5 m/s时加速度比较 Fig. 10 The comparation of accelerated speed at the priming speed 0.5 m/s with/without accumulator

 图 11 预定速度0.2 m/s时加速度差 Fig. 11 The velocity contrast at the priming speed 0.2 m/s

 图 12 预定速度0.3 m/s时加速度差 Fig. 12 The velocity contrast at the priming speed 0.3 m/s

 图 13 预定速度0.4 m/s时加速度差 Fig. 13 The velocity contrast at the priming speed 0.4 m/s

 图 14 预定速度0.5 m/s时加速度比较 Fig. 14 The velocity contrast at the priming speed 0.5 m/s

 图 15 有无蓄能器时功率随时间的变化 Fig. 15 The presence of power changing over time with/without accumulator
5 结　语

1）基于一种不同于普通浮标的上浮下沉的结构方法，即在传统的通过主浮力泵向外置油囊抽排油的基础上加装氮气蓄能器装置，通过因氮气罐内气体压力随海水压力的变化所储存的能量转变为额外浮力使浮标加速上浮，对这种新型浮标进行其性能的数值仿真计算；

2）用Fluent计算出浮标在各速度下匀速上浮的阻力系数，用力学分析的方法得到浮标在有蓄能器的情况下加速度的表达式并计算出浮标上浮所需要的最小体积；

3）用Matlab进行数值求解得到各种状况下的速度-时间曲线和加速度-时间曲线，并分析得到蓄能器对浮标上浮速度有一定影响；

4）用Matlab进行数值求解得到各种状况下功率-时间曲线，并分析得到安装蓄能器对提高浮标上浮功率有一定的作用。

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