VM282

VM282
Mode-Superposition Response Analysis of a Piston-Fluid System

Overview

Reference:

Axisa, F., Antunes, J., Modelling Mechanical Systems: Fluid-Structure Interaction, 2006, p. 486

Analysis Type(s):
Modal Analysis (ANTYPE = 2)
Mode-Superposition Harmonic Analysis (ANTYPE = 3)
Element Type(s):
3D Acoustic Fluid Element (FLUID30)
Structural Mass (MASS21)
Spring-Damper Element (COMBIN14)
3D 8-Node Surface-to-Surface Contact Element (CONTA174)
3D Target Segment Element (TARGE170)
Input Listing: vm282.dat

Test Case

A simple piston-fluid system is modeled using a spring damper element (COMBIN14) for the piston, fluid elements (FLUID30) for the fluid column, and a mass element (MASS21) for the mass of the piston, as shown in Figure 488: Schematic Representation of a Spring-Mass Damper System Coupled to a Compressible Fluid Column in a Tube. The contact between the piston and the fluid column is established using the surface-to-surface contact element (CONTA174).

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

Figure 488: Schematic Representation of a Spring-Mass Damper System Coupled to a Compressible Fluid Column in a Tube

Schematic Representation of a Spring-Mass Damper System Coupled to a Compressible Fluid Column in a Tube

Figure 489: Finite Element Representation of a Spring-Mass Damper System Coupled to a Compressible Fluid Column in a Tube

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

Material PropertiesGeometric Properties Loading
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
Modal damping ratios[a]corresponding to : 2.0453 x 10-2, 3.6948 x 10-3, 7.0040 x 10-4, 2.2468 x 10-4, 9.8247 x 10-5
Tube radius, R = 12.5 cm
Tube length, L = 24 m
F0 = 1000 N
f = 0-100 Hz

[a] The modal damping ratios were obtained in a separate modal analysis using the damped eigensolver.

Analysis Assumptions and Modeling Notes

The piston is modeled as a 1D 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 MPC-based contact pairs are established using CONTA174 elements (KEYOPT(2) = 2) between the piston and the fluid column. The fluid-structure interaction (FSI) condition is defined using the SF,,FSI command at the interface between the piston and the fluid column.

A modal analysis of the piston-fluid system is performed using the unsymmetric eigensolver. The frequencies obtained from this simulation are compared with the analytical solution.

After performing the modal solve, the response of the piston-fluid system is evaluated using a mode-superposition harmonic analysis for a frequency range of excitation between 0-100 Hz. The damping in the piston is considered by specifying modal damping ratios (MDAMP). These results are then compared with the analytical solution.

Results Comparison

Modal FrequencyTargetMechanical APDLRatio
f1, Hz9.9169.8770.996
f2, Hz24.58324.3050.989
f3, Hz43.72943.5260.995
f4, Hz63.89563.7600.998
f5, Hz84.39584.2920.999
 TargetMechanical APDLRatio
Piston displacement amplitude at 1.0 Hz, m0.000250.000261.052
Piston displacement amplitude at f1, m0.005760.005750.998
Fluid pressure amplitude at 1.0 Hz, MPa10300.00010881.0031.056
Fluid pressure amplitude at f1, MPa264000.000263403.9170.998

The nodal solution plot (NSOL) shows the response with respect to the frequency of excitation.

Figure 490: Piston Displacement Response

Piston Displacement Response

Figure 491: Fluid Pressure Response at Mid-Column

Fluid Pressure Response at Mid-Column