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Research Papers: Flows in Complex Systems

# Numerical Analysis of the Internal Flow in an Annular Flow Channel Type Oil Damper

[+] Author and Article Information
Toshihiko Asami

Professor
Mem. ASME
e-mail: asami@eng.u-hyogo.ac.jp

Itsuro Honda

Professor

Atsushi Ueyama

Department of Mechanical Engineering,
University of Hyogo,
2167 Shosha, Himeji,
Hyogo 671-2280, Japan

Equations (9) and (10) provide a solution derived in Cartesian coordinates, so the error due to expansion of the flow channel may occur when the difference between the radii of the cylinder and the piston is large. The analytical solution shown in Fig. 4 is derived in cylindrical coordinates so as not to cause such error. No visible difference due to the Cartesian and cylindrical coordinates occurs in the case of $Rr=0.8$ but does occur in the case of $Rr=0.5$ (1). A more accurate solution based on the cylindrical coordinates is represented by the Bessel functions and is not shown here because the solution is quite long.

Excluding the symbols listed in Eq. (11).

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 30, 2013; final manuscript received November 10, 2013; published online December 24, 2013. Assoc. Editor: D. Keith Walters.

J. Fluids Eng 136(3), 031101 (Dec 24, 2013) (8 pages) Paper No: FE-13-1404; doi: 10.1115/1.4026057 History: Received June 30, 2013; Revised November 10, 2013

## Abstract

The purpose of the present study is to clarify the fluid flow of an oil damper through numerical analysis in order to obtain an exact value of the damping coefficient of an oil damper. The finite difference method (FDM) was used to solve the governing equation of the fluid flow generated by a moving piston. Time steps evolved according to the fractional step method, and the arbitrary Lagrangian–Eulerian (ALE) method was adopted for the moving boundary. In order to stabilize the computation in the moving boundary problem, a masking method with a single block grid system was used. In other words, algebraic grid generation using a stretching function was used for the moving piston in the cylinder of the oil damper. The time-dependent coordinate system in the physical domain, which coincides with the contour of the moving boundary, is transformed into a fixed rectangular coordinate system in the computational domain. The computational results were compared with experimentally obtained results and the approximate analytical solution. The results of the present analysis exhibit good agreement with the experimental results over various widths of the annular flow channel between the piston and cylinder.

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## Figures

Fig. 1

Moving piston problem

Fig. 2

Velocity profile at the outlet of the pipe

Fig. 3

Cross-sectional view of an oil damper

Fig. 4

Velocity profile through the flow channel (a) Radius ratio Rr = 0.5, (b) Radius ratio Rr = 0.8

Fig. 5

Pressure drag acting on the piston (a) Radius ratio Rr = 0.5, (b) Radius ratio Rr = 0.8

Fig. 6

Friction drag acting on the piston (a) Radius ratio Rr = 0.5, (b) Radius ratio Rr = 0.8

Fig. 7

Relation between the damping coefficient and the piston length (a) Piston diameter: 26 mm, (b) Piston diameter: 30 mm, (c) Piston diameter: 32 mm, (d) Piston diameter: 34 mm

Fig. 8

Comparison of the numerically and experimentally obtained streamlines (a) Numerical (ωt=π/2), (b) Experimental (ωt=π/2), (c) Numerical (ωt=3π/2), (d) Experimental (ωt=3π/2)

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