An Empirical Model of the Motion of Turbulent Vortex Rings
An Empirical Model of the Motion of Turbulent Vortex Rings
复制标题
湍流涡环运动的经验模型
DOI：
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发表时间：
1971
期刊：
影响因子：
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通讯作者：
G. M. Johnson
中科院分区：
文献类型：
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作者：
G. M. Johnson
D IMENSIONAL arguments indicate that the motion of both axial turbulent puffs (strongly turbulent masses of fluid moving through surroundings with which they readily mix)1 and turbulent vortex rings2 will remain similar at all distances from their virtual sources if their spreading rates are linear and their translational velocities decay as the inverse cube of the distance from their respective virtual sources. This hypothesis appears to be well substantiated for the case of the rapidly spreading turbulent puffs.1-3 However, the validity of the model is much more difficult to determine for the case of the vortex ring, where the extremely slow ring growth leads to the prediction of very large virtual origins. In fact, recent experiments4 indicate that measurements would be required at least 1000 diam from the discharging orifice, in order to satisfactoril y test the similarity model. Since such measurements have not been made and do not appear to be in the offing, the following empirical model is proposed for use in engineering calculations. Quantitative agreement with experimental results is good to distances on the order of 70 diam from the discharging orifice. The model is based on measurements of air vortex rings, seeded with a mist of dioctyl phthalate droplets, traveling through quiescent air. The time of flight was recorded by using the signal from a hot-wire anemometer to stop an electronic event timer as the vortex passed the anemometer. The hot-wire circuitry was also used to flash a stroboscope, thereby illuminating the vortex to an open-lensed camera, which recorded its geometry. All measurements were repeated at least thirty times and the mean values were used in further computations. It was apparent from the data that the behavior of the rings is very accurately described by (t - tv)/to = C[(x - x (D
