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Research Papers: Fundamental Issues and Canonical Flows

# Numerical Study of the Damped Oscillation of Liquid Column in U-Tube With Particle Method

[+] Author and Article Information
Zhongguo Sun

e-mail: sun.zg@mail.xjtu.edu.cn
Department of Fluid Machinery and Engineering,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
Xi'an, Shaanxi 710049, PRC

1Corresponding author.

Manuscript received August 3, 2011; final manuscript received March 1, 2013; published online April 12, 2013. Assoc. Editor: Meng Wang.

J. Fluids Eng 135(6), 061202 (Apr 12, 2013) (9 pages) Paper No: FE-11-1311; doi: 10.1115/1.4023944 History: Received August 03, 2011; Revised March 01, 2013

## Abstract

The damped oscillation process of the liquid column in a U-tube is simulated and studied using the moving particle semi-implicit (MPS) method. The oscillation process is well reproduced and the effect of liquid properties as the density and viscosity is investigated, as well as the size effect of the U-tube. As key parameters, the amplitude and the period of the oscillation are calculated and analyzed when the flow conditions are changed. The results show that the amplitude and the average period of the oscillation process decrease when the liquid viscosity increases, and that the liquid density has a minor influence on the damping process. A critical finding for the size effect is that the oscillation process almost changes linearly with the size of the U-tube larger than the critical point, but nonlinearly when the size is scaled down. Larger viscosity results in shorter equilibrium time and viscosity plays a more important role in damping, especially for a smaller size of the U-tube. These versatile numerical protocols can present useful qualitative suggestions on the applications of a U-tube in many industrial fields.

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## Figures

Fig. 1

Motion of the leading edge with time in collapse of a water column

Fig. 2

Geometry of the U-tube

Fig. 5

The height of liquid column in time series with different densities (μ = 0.05 kg/(m s), ρ = 8×102 kg/m3, 1×103  kg/m, 1.2 × 103 kg/m3)

Fig. 3

The damped oscillation of liquid column in the U-tube in time series (ν = 5×10-5 m2/s, ρ = 1×103 kg/m3)

Fig. 4

The height of liquid column in time series with different particle distances

Fig. 6

The height of liquid column in time series with different viscosities (ν = 5 × 106 m2/s, 1 × 105 m2/s, 5 × 105 m2/s, and 1 × 104 m2/s)

Fig. 8

The definition of damped oscillation period T of liquid column in the U-tube (ν = 5 × 10−5 m2/s, ρ = 1 × 103 kg/m3)

Fig. 9

The period of damped oscillation in time series with different viscosities

Fig. 10

The height of liquid column in time series with different particle distances in case 1

Fig. 11

The height of liquid column in time series with different particle distances in case 2

Fig. 12

The height of liquid column in time series with different sizes (ν = 5 × 105 m2/s, ρ = 1 × 103 kg/m3)

Fig. 7

The amplitude of damped oscillation in time series with different viscosities

Fig. 13

The amplitude (left) and period (right) of damped oscillation in time series with different sizes (ν = 5 × 105 m2/s, ρ = 1 × 103kg/m3)

Fig. 14

The variation of nondimensional amplitude values with different viscosities of liquid and different sizes of liquid column (a) front view, (b) side elevation, (c) planform, (d) 3D view

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