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Generative mechanism of air column oscillations in a Hartmann-Sprenger tube excited by an air jet issuing from a convergent nozzle

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Summary

In this paper, a theory of the origin of the air column oscillations in the Hartmann-Sprenger (HS) tube excited by an air jet issuing from a convergent nozzle is presented.

For the analysis, the following basic configuration is assumed. The air jet issuing from a nozzle forms a steady stagnation flow between the nozzle and the open end of the tube, and the air column in the tube remains at rest. A massless hypothetical membrane is assumed at the open end of the tube. When a sinusoidal vibration of the membrane with very small amplitude is assumed, its radiation impedance is obtained by calculating the reactive forces of the flow field acting on the membrane on each side. If the real part of the radiation impedance is negative, the field is unstable, and the air column in the HS tube will be excited to oscillation.

The analytical results can explain well the experimental observations.

Zusammenfassung

Im vorliegenden Bericht wird der Schwingungsmechanismus der Luftsäule im Hartmann-Sprenger Rohr betrachtet für den Fall, dass diese durch einen Gasstrahl von einer konvergenten Düse angeregt wird. Für die Analysis wird die folgende Fundamentalkonfiguration angenommen: Der Gasstrahl der Düse bildet die stationäre Stauströmung zwischen der Düse und der Mündung des HS Rohres, und die Luftsäule im HS Rohr ist in Ruhe. An der Rohrmündung wird eine hypothetische Membrane angenommen. Wenn diese Membrane mit einer kleinen Amplitude sinusförmig schwingt, dann ist die Strahlungsimpedanz dieser Membrane durch die Gegenkräfte auf die Membrane gegeben. Wenn der Realteil der Strahlungsimpedanz negativ ist, ist das System selbsterregend und die Luftsäuleschwingung im HS Rohr wird erzeugt.

Das analytische Resultat stimmt mit dem experimentellen gut überein.

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, University of Saitama, Urawa, Japan

    M. Kawahashi & M. Suzuki

Authors
  1. M. Kawahashi
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  2. M. Suzuki
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Kawahashi, M., Suzuki, M. Generative mechanism of air column oscillations in a Hartmann-Sprenger tube excited by an air jet issuing from a convergent nozzle. Journal of Applied Mathematics and Physics (ZAMP) 30, 797–810 (1979). https://doi.org/10.1007/BF01590688

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  • DOI: https://doi.org/10.1007/BF01590688

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