Jet-wave amplification in organ pipes

Abstract

An envelope-based method to estimate both the jet-wave amplification factor and the mouth-field strength in organ pipes is developed by using flow visualization of a smoked jet with a high-speed digital video camera. A theoretical envelope of wave growth, which is approximated using a negative displacement model of the jet drive, is compared with an experimental envelope derived from superposing many instantaneous shapes of jet deflection in the steady-state oscillation. The estimation results are presented in dimensional terms with respect to two particular models, where the flue-to-edge distances are, respectively, 15.8 and 10.2 mm, with a common flue thickness of 2.2 mm. In our experiment the jet velocity ranges from 7 to 33 m/s, the Reynolds number from 1000 to 5000, and the sounding frequency from 130 to 580 Hz. The amplification factor of organ pipe jets, estimated to lie in the 0.18–0.26-mm−1 range, tends to decrease and saturate with increasing blowing velocity in each oscillation mode; the mouth-field strength defined as the acoustic displacement amplitude, roughly estimated to be 0.5–1.5 mm, tends to increase and saturate with increasing blowing velocity. A hot-wire anemometer is then used to measure the mouth-field strength, whose value shows a good agreement with the estimated one. This result confirms the validity of our envelope-based method. A dimensionless representation of the experimental data is used to compare wave characteristics between an organ pipe jet and an acoustically perturbed free jet. The applicability of the spatial and temporal theories of jet instability is discussed to analyze them. If we can assume a Poiseuille flow at the flue exit and a subsequent Bickley jet, the spatial theory seems to be relevant to our organ pipe jets. However, for lack of a reliable experimental measurement of the jet half-thickness we cannot draw a definite conclusion about the wave characteristics of organ pipe jets.