﻿ 基于流固耦合的线性充液卡箍管路振动研究
 舰船科学技术  2016, Vol. 38 Issue (11): 87-90 PDF

Vibration research on linear liquid clamp pipe based on the fluid-solid coupling
SUN Huan
School of Architecture, Tianjin University, Tianjin 300072, China
Abstract: The liquid pipeline hydraulic system is widely used in aircraft, lathe, refrigeration and other large transport systems. Due to the effect of the vibration of the pipe is caused by the liquid flow conditions, the study of the need of fluid-structure interaction theory. In view of the linear liquid pipeline, fluid-solid coupling vibration model is established on the basis of the finite element theory. The pipe vibration modal and Von Misses stress distribution under the limit of symmetrical layout are studied. Results show that the clamp can be dramatically reduced amplitude. The more far away from the clamp set in vibration, the more obvious effect. The resonance condition obviously strengthen with the increase of vibration frequency; the maximum stress point as long as the layout inside the pipe. Pressure change is the macro performance of hydraulic effect and volatility curve reflects the charging process is a complex process, try to choose decorate liquid pipe of the shorter length.
Key words: liquid pipeline     finite element theory     modal analysis     vibration characteristics
0 引言

1 有限元模型

1.1 液体连续相湍流模型

 $\frac{{\partial \rho }}{{\partial t}} + \frac{{\partial (\rho {u_i})}}{{\partial {x_i}}} = 0,$

 $\begin{array}{l} \displaystyle\frac{{\partial (\rho {u_i})}}{{\partial t}} + \frac{{\partial ({u_i}{u_j})}}{{\partial {x_j}}} = - \frac{{\partial p}}{{\partial {x_i}}} + \frac{\partial }{{\partial {x_j}}}[\mu (\frac{{\partial {u_i}}}{{\partial {x_j}}} + \\ \quad \quad \quad \displaystyle\frac{{\partial {u_j}}}{{\partial {x_i}}} - \frac{2}{3}{\delta _{ij}}\frac{{\partial {u_k}}}{{\partial {x_k}}})] + \frac{\partial }{{\partial {x_j}}}( - \rho \overline {{{u'}_i}{{u'}_j}} )\text{，} \end{array}$

 $- \rho \overline {{{u'}_i}{{u'}_j}} = {\mu _t}(\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}) - \frac{2}{3}{\delta _{ij}}(\rho k + {\mu _t}\frac{{\partial {u_k}}}{{\partial {x_k}}})\text{，}$

 \begin{aligned} & \displaystyle \frac{\partial }{{\partial t}}(\rho k) + \frac{\partial }{{\partial {x_i}}}(\rho k{u_i}) = \frac{\partial }{{\partial {x_j}}}[(u + \frac{{{u_t}}}{{{\sigma _k}}})\frac{{\partial k}}{{\partial {x_j}}}] + \\ & \quad \quad \quad {G_k} + {G_b} - \rho \varepsilon - {Y_M} + {S_k}\text{，}\\ & \displaystyle \frac{\partial }{{\partial t}}(\rho \varepsilon ) + \frac{\partial }{{\partial {x_i}}}(\rho \varepsilon {u_i}) = \frac{\partial }{{\partial {x_j}}}[(u + \frac{{{u_t}}}{{{\sigma _\varepsilon }}})\frac{{\partial \varepsilon }}{{\partial {x_j}}}] + \\ & \quad \quad \quad {C_{1\varepsilon }}\frac{\varepsilon }{k}({G_k} + {C_{3\varepsilon }}{G_b}) - {C_{2\varepsilon }}\rho \frac{{{\varepsilon ^2}}}{k} + {S_\varepsilon }\text{。} \end{aligned}

1.2 固体管路力学位移模型

 $﻿$\mathit{\boldsymbol{M}}x'' + \mathit{\boldsymbol{C}}x' + \mathit{\boldsymbol{K}}x = \mathit{\boldsymbol{F}}(t),

1.3 耦合控制流程

1）从流体方程 $\mathop F\nolimits_f \left[ {\mathop X\nolimits_f ,\mathop \lambda \nolimits_d \mathop {\mathop d\nolimits_s }\nolimits^{k - 1} + \left( {1 - \lambda } \right)\mathop {\mathop d\nolimits_s }\nolimits^{k - 2} } \right] = 0$ 中得到流体解向量 $\mathop {\mathop X\nolimits_f }\nolimits^k$ 。运用给定的结构位移对流体模型求解才可以得出这个解。但计算中还需要观察到的是结构的位移运用了位移松弛因子 $\mathop \lambda \nolimits_d \left( {0 < \mathop \lambda \nolimits_d < 1} \right)$ ，因为流体和结构2个模型不在一个矩阵中求得解，所以像这样的处理会在做一些比较麻烦且繁杂的模型时会产生很好的帮助效果。迭代形成了收敛是因为有了松弛因子的帮助。

2）若只需要满足应力收敛条件，那么就要计算应力残量并和迭代容差做比较。若是将这个标准达到，那么就可以不再进行步骤3~步骤5。

3）从结构方程 $\mathop F\nolimits_s \left[ {\mathop {\mathop X\nolimits_s }\nolimits^k ,\mathop \lambda \nolimits_\tau \mathop {\mathop \tau \nolimits_f }\nolimits^{k - 1} } \right] = 0$ 中解出结构解向量 $\mathop {\mathop X\nolimits_s }\nolimits^k$ 流体应力同样运用了应力松弛因子 $\mathop \lambda \nolimits_\tau \left( {0 < \mathop \lambda \nolimits_\tau < 1} \right)$

4）流体的节点位移要用给定的边界条件 $\mathop {\mathop d\nolimits_f }\nolimits^k = \mathop \lambda \nolimits_d \mathop {\mathop d\nolimits_s }\nolimits^k + \left( {1 - \mathop \lambda \nolimits_d } \right)\mathop {\mathop d\nolimits_s }\nolimits^{k - 1}$ 计算。

5）假如说只满足位移收敛条件这一个条件，那么就要计算位移残量并和迭代容差做比较。当应力和位移的标准都要求满足时，则2个收敛条件都要检查。如果迭代不收敛，回到步骤1）继续下一个迭代，直到达到FSI迭代的最大数（这种情况下，程序停止，显示不收敛信息）。

6）保存而且输出流体和结构的结果。时间步和求解时间在这种解法当中是由流体模型所操控。但是，结构模型中定义的所有时间函数必须覆盖计算的时间范围。在耦合系统中，流体模型决定了这些控制收敛的参数，如应力和位移迭代容差、松弛因子、收敛标准等。

2 充液管路三维模态分析

 图 1 建模图 Fig. 1 Modeling figure

 图 2 6阶模态振型图 Fig. 2 Six order modal vibration mode

 图 3 管路中点的Von Misses应力云图 Fig. 3 Von Misses stress nephogram of line midpoint
3 充液管路长度对压力波动的影响

 图 4 充液管路出口的压力曲线 Fig. 4 Pressure curve of liquid pipeline export

4 结语

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