Oscillation of Flexible Tubes - Onset and Subsequent Behaviour

Abstract

These experiments provide a detailed record of the oscillation of flexible rubber tubes as air flows through them. The tubes are mounted in an experimental rig illustrated in Oscillation of Flexible Tubes - Onset and Subsequent Behaviour.txt. Air suction is controlled by a voltage between 0 and 10 volts, which tells the suction fan to operate between its minimum and maximum power downstream of the flexible tube. During an experiment this voltage is set by a computer to ramp up slowly to a maximum value, before ramping slowly down again. The ramping speed is chosen so that any behaviour seen has time to reach a quasi-steady state. Throughout this pressure recordings are made at the 4 indicated locations (pu,p1,p2,pd) as well as an acoustic pressure reading close to the flexible tube and a video recording of the rotameter that records the flowrate. Pressures are measured relative to the external atmospheric pressure. The flexible tubes are held in place under a prescribed axial strain. For each experimental run we have recorded the unstrained tube diameter (d), the unstrained tube length (l0), the unstrained tube wall thickness (h), the tube length in the experiment (l), the sampling rate for pressure readings (fs), the pressure in the upstream plenum (pu), just upstream of the tube (p1), just downstream of the tube (p2), and in the downstream plenum (pd), and the acoustic pressure (pa). All pressures are measured relative to the environmental pressure, such that pressures below the environmental pressure are positive. From the video of the rotameter we extract a flowrate for each frame of the video. We then use the acoustic pressure and the sound recording from the video to synchronise these flowrate readings with the pressure readings (pa,p1,p2,pu, and pd are all recorded simultaneously). Hence we obtain a set of flowrate values over time, labelled Q. These readings need to have their own separate time vector. Hence we obtain the following vectors of experimental data; the time vector for pressure readings (time), the time vector for flowrate (time_Q), and the flowrate (Q). For each run we have traces of p1, p2, pu, pd, pa, and Q. These recordings generally reveal a complex set of self excited oscillations. One important metric that we explicitly extract is the onset frequency, denoted f. We define this as the first frequency that appears in p1, p2 and pa that is sustained for more than around 1 second. This is somewhat subjective, but we feel that it is worth having these figures recorded here. We also estimate the uncertainty in this frequency by looking at the variation in frequency seen at onset. Hence we again add the following data; frequency at onset (f), uncertainty in f (f_pm), flowrate at onset (Qo), uncertainty in Qo (Qo_pm), p1 at onset (p1o), uncertainty in p1o (p1o_pm), p2 at onset (p2o), uncertainty in p2o (p2o_pm). In runs where self excited oscillations were not observed (f, f_pm, Qo, Qo_pm, p1o, p1o_pm, p2o, p2o_pm) all have the value nan. We also store the upstream rigid tube length (lu), and the downstream rigid tube length (ld). Numerical data is stored in a separate csv file for each run, called runX.csv, which has been compressed, meaning that each file is stored as runX.tar.bz2. The csv file is arranged in rows. The first column contains the symbol for the variable, and all remaining columns contain the data. We also have a summary csv file called run_summary.csv. This contains 15 columns, arranged as follows; run_number, d, l0, h, l, f, f_pm, Qo, Qo_pm, p1o, p1o_pm, p2o, p2o_pm, lu, ld.