### Abstract

A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier-Stokes (N-S) equations by firstly taking fluid-structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow's Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.

Original language | English |
---|---|

Pages (from-to) | 2034-2049 |

Number of pages | 16 |

Journal | Applied Mathematical Modelling |

Volume | 31 |

Issue number | 9 |

Early online date | 3 Nov 2006 |

DOIs | |

Publication status | Published - Sep 2007 |

### Keywords

- three-dimensional viscous flow
- N-S equations
- numerical simulation
- fluid-structure interaction
- differential quadrature method
- Navier-Stokes equations
- liquid-filled pipes
- vibration analysis
- DNS
- models
- number

### Cite this

*Applied Mathematical Modelling*,

*31*(9), 2034-2049. https://doi.org/10.1016/j.apm.2006.08.007

**Numerical simulation of three-dimensional incompressible fluid in a box flow passage considering fluid-structure interaction by differential quadrature method.** / Zhang, Lixiang; Guo, Yakun; He, Shihua.

Research output: Contribution to journal › Article

*Applied Mathematical Modelling*, vol. 31, no. 9, pp. 2034-2049. https://doi.org/10.1016/j.apm.2006.08.007

}

TY - JOUR

T1 - Numerical simulation of three-dimensional incompressible fluid in a box flow passage considering fluid-structure interaction by differential quadrature method

AU - Zhang, Lixiang

AU - Guo, Yakun

AU - He, Shihua

PY - 2007/9

Y1 - 2007/9

N2 - A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier-Stokes (N-S) equations by firstly taking fluid-structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow's Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.

AB - A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier-Stokes (N-S) equations by firstly taking fluid-structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow's Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.

KW - three-dimensional viscous flow

KW - N-S equations

KW - numerical simulation

KW - fluid-structure interaction

KW - differential quadrature method

KW - Navier-Stokes equations

KW - liquid-filled pipes

KW - vibration analysis

KW - DNS

KW - models

KW - number

U2 - 10.1016/j.apm.2006.08.007

DO - 10.1016/j.apm.2006.08.007

M3 - Article

VL - 31

SP - 2034

EP - 2049

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 9

ER -