Streamwise oscillations of cylinders near the critical Reynolds number

Abstract

The purpose of the research reported here is to attempt to clarify the conditions under which in-line oscillations of a circular cylinder occur, and to establish the oscillation characteristics. A mathematical model has been developed which attempts to represent a cylinder vibrating in the streamwise direction. This mathematical model is based on the Van der Pol equation and is similar in many respects to one series of models which exists for cross-flow oscillations. Solutions to the mathematical model indicate the possibility of in-line oscillations and the results so obtained have been fitted to experimental data, thus evaluating the free parameters in the mathematical model. An experiment was carried out to establish the effects of reduced velocity, Reynolds number, surface roughness, and freestream turbulence on the stability of a circular cylinder to in-line oscillations in the critical Reynolds number range. Results obtained from the test program indicate that, within the range of conditions covered, in-line oscillations occur when the Reynolds number is in the critical range, and then only when free-stream turbulence exists. Surface roughness of the test cylinders did not appear to play a significant role. No attempt was made to investigate in-line oscillations at subcritical Reynolds numbers.