One-Dimensional Computer Analysis of Oscillatory Flow in Rigid Tubes

Abstract

The dynamic characteristics of catheter-transducer systems using rigid tubes with compliance lumped in the transducer and oscillatory flow of fluid in rigid tubes were analyzed. A digital computer model based on one dimensional laminar oscillatory flow was developed and verified by exact solution of the Navier-Stokes Equation. Experimental results indicated that the damping ratio and resistance is much higher at higher frequencies of oscillation than predicted by the one dimensional model. An empirical correction factor was developed and incorporated into the computer model to correct the model to the experimental data. Amplitude of oscillation was found to have no effect on damping ratio so it was concluded that the increased damping ratio and resistance at higher frequencies was not due to turbulence but to two dimensional flow effects. Graphs and equations were developed to calculate damping ratio and undamped natural frequency of a catheter-transducer system from system parameters. Graphs and equations were also developed to calculate resistance and inertance for oscillatory flow in rigid tubes from system parameters and frequency of oscillation.

An attempt to measure fluctuating local pressure in free turbulent flow in water

“…Probe -d Probe -air 15 Equation (4) has the same form as the conventional model equation of a system for the wall-pressure measurement (Donovan et al, 1991). Thus, the behavior of the pressure-measuring system is equivalent to that of a damped harmonic oscillator, and the damping ratio and the natural frequency (in rad/s) of the system are given as…”

“…Dynamic response of such a pressure-measuring system has been investigated in the previous studies (e.g., Geddes et al, 1984), and it was pointed out that the dynamic response was non flat mainly due to elasticity of the pressure sensor while effect of compressibility of the fluid is negligible. The methods to correct these effects have been studied in literatures (Donovan et al, 1991;Taylor and Donovan, 1992;Donovan et al, 1994;Aydin, 1998). In these studies, the behavior of the pressure-measuring system was modeled as that of a harmonic oscillator with one degree of freedom, and parameters in the model equation, the natural frequency and the damping factor, were determined by calibration.…”