VM-WB-MECH-103

VM-WB-MECH-103
Harmonic Response Analysis of a Piston-Fluid System

Overview

Reference: Axisa, F., & Anutes, J. (2006). Modelling of Mechanical Systems: Fluid-Structure Interaction (p. 486). Butterworth-Heinemann.
Solver(s):

Ansys Mechanical

Analysis Type(s): Harmonic Analysis
Element Type(s): Solid

Test Case

A simple piston-fluid system is modeled using a spring attached to a mass moving in a frictionless fluid filled cylinder.

The piston is driven by a harmonic force F0eiωt along the axial direction. A full harmonic analysis is performed to investigate the displacement of the piston and the pressure amplitude at mid-column.

This problem is also presented in VM282

Figure 138: Finite Element Representation of a Spring-Mass System Coupled to a Compressible Fluid Column in a Tubet

Finite Element Representation of a Spring-Mass System Coupled to a Compressible Fluid Column in a Tubet

Material PropertiesGeometric PropertiesLoading

Fluid Properties:

Density, ρf = 1000 kg/m3
Effective speed of sound, ce = 1000 m/s
Scaling factor of the stiffness of the fluid column, Kf = 2 x 106 N/m
Mass, Mf = 1178 kg

Structural Properties:

Mass, Ms = Mf / 2
Stiffness, Ks = Kf

Tube radius, R = 12.5 cm

Tube length, L = 24 m

F0 = 1000 N

f = 0 - 100 Hz

Analysis Assumptions and Modeling Notes

The piston is modeled as a spring-mass system with one end fixed. The fluid column is modeled as a straight tube of constant cross-sectional area filled with a compressible fluid. The tube is closed at the outlet. The contact region is defined as the interface between the mass and the fluid in the tube.

A modal acoustics analysis of the piston-fluid system is performed to obtain the first five frequencies.

A harmonic acoustics analysis is performed with the applied force to determine the piston-displacement amplitude and the fluid-pressure amplitude.

Ansys Mechanical does not support mode-superposition harmonic-acoustic analysis as performed in VM282. The portion of that analysis including damping is not reproduced in this test.

Results Comparison

Modal FrequencyTargetMechanicalError (%)
f1, Hz9.9169.895-0.213
f2, Hz24.58324.6030.081
f3, Hz43.72943.7340.011
f4, Hz63.89563.9050.016
f5, Hz83.39584.3941.198
ResultTargetMechanicalError (%)
Piston displacement amplitude at 1.0 Hz, m0.000250.00024988-0.048
Fluid pressure amplitude at 1.0 Hz, MPa10300104221.18