基于有限积分法的输流直管轴向流固耦合有限积分法数值模拟

Numerical simulation on FSI characteristics of fluid-conveying straight pipe by finite integration method

针对弹性输流直管轴向耦合振动四方程模型,应用有限积分法分别配合隐式欧拉法和拉普拉斯数值反演法建立两种不同的数值模式,研究瞬时关阀时输流直管轴向耦合振动响应特性。采用径向基函数和多项式基函数组成的混合函数通过节点构造有限积分法的插值函数,将函数积分结果转换为节点函数值的线性累加,简单易行且稳定性好。将所提出的数值模式计算结果与前人的研究成果进行对比,吻合良好,表明有限积分法在处理间断波问题时具有较高的鲁棒性和稳定性,可精确地捕捉到水锤压力的非线性变化过程,但在时间项处理上,拉普拉斯数值反演法在间断处存在一定的数值振荡,隐式欧拉法并未出现,可见在水击问题上有限积分法配合隐式欧拉法的精度更高、稳定性更好。研究结果表明:在考虑泊松和连接耦合共同作用时,管道压力水头波动与经典水锤相比,相位出现延迟,与只有泊松耦合相比,由于管道的振动叠加了与液体产生的强迫振动,压力脉动明显加剧。

Based on the four-equation model of the elastic fluid-conveying straight pipe,the axial coupling vibration characteristics with water hammer effect are studied in this paper.Two numerical schemes were developed by combining the finite integration method (FIM) with the implicit Euler method (IEM) and with the numerical inversion of Laplace transform (NILT),respectively,to efficiently and accurately analyze the axial coupling vibration of the pipe.A mixed function,consisting of the radial basis function (RBF) and the polynomial basis function (PBF),is adopted to construct the interpolation function of the FIM at each node.Then,the integral value of a function can be discretized into linear combinations of the function values at the node.This feature makes the FIM easy to program,straightforward and efficient when it is applied to a complicated computational region.To evaluate the accuracy and robustness of the proposed scheme for dealing with the discontinuous wave problems,it was compared with other numerical methods and reasonable agreements were achieved.It indicates that FIM can accurately capture the nonlinear process with water hammer effect.Nevertheless,on processing the temporal term,the numerical oscillation occurs at the discontinuity for NILT while IEM does not have.Moreover,when considering the interaction of Poisson and connection coupling,the pipe pressure wave appears to have some delay in the phase compared with the classic water hammer.Due to the superposition of the pipe vibration and the forced vibrations produced by liquids,the pressure fluctuation increases significantly compared with the situation when only considering Poisson coupling.