0
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.

<>

## References

Sekiguchi, H., and Asami, T., 1983, “Fundamental Investigation of an Oil Damper (2nd Report, Analyses Based on the Unsteady Flow Assumption),” Bull. JSME, 26(215), pp. 856–863.
Asami, T., and Sekiguchi, H., 1984, “Fundamental Investigation on an Oil Damper (3rd Report, Comparison of Analyses Based on Cylindrical Coordinates and Cartesian Coordinates),” Bull. JSME, 27(224), pp. 309–316.
Asami, T., Sekiguchi, H., and Taniguchi, S., 1985, “Study on the Oil Damper With Variable Damping Mechanism (1st Report, Damping Characteristics of the Damper With a Piston Having Cylindrical Orifices),” Bull. JSME, 28(246), pp. 2978–2985.
Nakane, Y., 1966, Springs, Absorbers and Brakes (in Japanese), Seibundo Shinkosha, Tokyo, p. 196.
Sadaoka, N., and Umegaki, K., 1994, “Numerical Method to Calculate Flow-Induced Vibration in a Turbulent Flow (1st Report, Derivation and Analysis of Oscillating Circular Cylinder),” Trans. JSME B, 60(570), pp. 409–416. (in Japanese)
Ichioka, T., Kawata, Y., Nakamura, T., Izumi, H., Kobayashi, T., and Takamatsu, H., 1995, “Research on Fluidelastic Vibration of Cylinder Arrays by Computational Fluid Dynamics (1st Report, Analysis on Two Cylinders and a Cylinder Row),” Trans. JSME B, 61(582), pp. 503–509. (in Japanese)
Matsumoto, H., Maekawa, S., and Kamemoto, K., 2000, “Three-Dimensional Analysis of Incompressible Flow Around an In-line Forced Oscillating Circular Cylinder,” Trans. JSME B, 66(644), pp. 1004–1012. (in Japanese)
Takato, K., Tsutsui, T., Akiyama, M., and Sugiyama, H., 1998, “Numerical Analysis of Flow Around a Vibrating Elastic Plate (An Approach Considered With Interaction of Distortion),” Trans. JSME B, 64(627), pp. 3720–3728. (in Japanese)
Sekiguchi, H., and Asami, T., 1982, “Fundamental Investigation of an Oil Damper (1st Report, Case of Its Analysis as Steady Flow),” Bull. JSME, 25(205), pp. 1135–1142.
Hirt, C. W., Amsden, A. A., and Cook, J. L., 1974, “An Arbitrary Lagrangian–Eulerian Computing Method for All Flow Speeds,” J. Computat. Phys., 14, pp. 227–253.
Donea, J., Huerta, A., Ponthot, J.-Ph., and Rodriguez-Ferran, A., 2004, Arbitrary Lagrangian–Eulerian Methods, Encyclopedia of Computational Mechanics, volume 1: Fundamentals, John Wiley & Sons Ltd., New York, Ch. 14.
Kim, J., and Moin, P., 1985, “Application of a Fractional-Step Method to Incompressible Navier–Stokes Equations,” J. Computat. Phys., 59, pp. 308–323.
Kawamura, T., and Kuwahara, K., 1984, “Computation of High Reynolds Number Flow Around Circular Cylinder With Surface Roughness,” AIAA Paper, 84-0340.
Izumi, H., Taniguchi, N., Kawata, Y., Kobayashi, T., and Adachi, T., 1994, “Three-Dimensional Flow Analysis Around a Circular Cylinder (1st Report, In the Case of a Stationary Circular Cylinder),” Trans. JSME B, 60(579), pp. 3797–3804. (in Japanese)
Ohba, H., and Kuroda, S., 1992, “Numerical Study of Flows Around a Rotating Square Cylinder,” Trans. JSME B, 58(549), pp. 1446–1451.
Inomoto, T., and Matsuno, K., 2004, “A Moving-Grid Finite-Volume Method for Three Dimensional Incompressible Flows,” Proceedings of the 18th Computational Fluid Dynamics Symposium, D2-3.

## 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)

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections