Vortex dynamics and energy transport of a plane jet impinging upon a small cylinder

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Abstract

This paper studies the self-sustained oscillating flow induced by a plane jet impinging upon a small circular cylinder located in the jet centerline within the potential-core region. The air jet is mainly operated at the exit velocity of 10 m/s with the Reynolds number of 1.04×104 based on the jet exit height H. The small cylinder diameter d over the jet exit height ratio, d/H, is 0.2. The flow characteristics and the energy transport processes in the jet–cylinder wake region are extensively investigated by means of hot-wire measurements and phase-averaging calculations. Experimental results indicate that the velocity fluctuations around the cylinder are mainly produced from the shedding vortices under the jet–cylinder interaction. Two types of shear flows, namely, the jet type and the wake type, are obtained behind the small cylinder. With the aid of the vortex formation and merging processes from the jet shear layers, the flow mixing is effectively enhanced after the jet–cylinder impingement.

Introduction

For most of impinging jet flow investigations, the obstacles in size selected for impingement are normally much larger than the jet exit height as discussed by Rockwell and Naudascher [1]. In our previous study on the jet–cylinder interaction [2], [3], a small cylinder with the diameter smaller than the jet exit height is used instead, where the cylinder is fully submerged within the potential core region of the jet flow. Therefore, the coherent structures in the jet shear layer region can no longer impinge upon the small cylinder directly as the usual case of impingement between a jet and a larger cylinder. However, the phenomenon of self-sustained flow oscillations can still be found under the jet and small cylinder impingement. It is noticed that after the impingement, the resonant frequency of the flow structures is different from the fundamental frequency of the natural jet, but is consistent with the shedding frequency of the wake behind the cylinder. The cylinder wake's shedding vortex instability then acts as an exciting source for the feedback mechanism in the flow field from the jet exit to the cylinder.

In the present study, two types of free shear layers simultaneously take place in the jet–small cylinder impinging flow field, namely, jet and wake. In practice, a basic free shear flow is composed of two parallel fluid streams with a significant velocity gradient in between. This velocity gradient can induce the so-called Kelvin–Helmholtz instability, which has been proven to be inviscidly unstable. Such instability would grow exponentially with the downstream direction, and then rolls up into organized vortical structures to govern the entire shear flow development. These large-scale, wave-like coherent structures can easily be observed in both wake and jet flow fields [4], [5].

According to Thomas [6], the jet flow consists of two shear layers divided by a core of irrotational flow region (i.e. the potential core region). The two shear layers spread transversely along downstream direction and then merge together to eventually engulf the potential core. During the developing process of the jet column, the energy content of the fundamental instability increases abruptly with downstream direction and then rolls up to form organized vortex structures. The neighboring vortices would further merge together as a result of subsequent evolution of the subharmonic instabilities. The locations of vortex formation and merging can be well identified by the relative energy exchange characteristics of the two velocity fluctuations (i.e. streamwise and transverse components) [7]. As for the cylinder wake flow, the evolving instabilities now produce a succession of shedding vortices, but no vortex merging process is observed. That is, the jet and wake perform distinct energy transport characteristics due to different mechanisms of formation and growth of the coherent structures.

For the current jet–small cylinder impinging flow, the resonant frequency of the induced self-sustained oscillation has been proven to be consistent with the shedding frequency of the cylinder wake [3]. In the early wake investigations, Bloor [8] had found that the instability evolution of the shedding vortices initiates near the separation point of the cylinder surface when the uniform flow passing it. The produced shedding vortices then lead to the occurrence of pressure fluctuations on the cylinder surface. The pressure fluctuations on the cylinder surface also exhibit similar characteristics to that on the leading edge of an obstacle when the vortices impinging on it, which were clearly studied by Kaykayoglu and Rockwell [9], [10]. Therefore, one of the major objectives in the present study is to examine the interacting mechanism between the vortex shedding processes and the jet shear flow, which will result in the self-sustained oscillation in the jet–small cylinder impinging flow field. By using the concept of hydrodynamic instability, the development of coherent structures can easily be investigated from the evolution of instabilities within the free shear layers. Thus, it is worthwhile to investigate the energy distribution of instabilities and their relative energy transfer processes of the interacting coherent structures. With different velocity patterns of the jet and wake, the combined jet–cylinder impinging flow field can be divided into the jet and the wake regions. The development of the coherent structures is individually investigated in the two regions, which is then used in comparison with their energy transport behaviors of the instabilities to further understanding the correlation between them. Furthermore, the jet flow with a small cylinder in the core region has many aspects of academic interests and practical applications, such as the flow meters where a needle is used as a throttle to vary the flow rate. The other objective of this paper will hence focus on the study of shear flow entrainment after the jet–cylinder impingement between a jet with 15 mm height at the exit and 3 mm small cylinder in diameter, which will be compared with that of the natural jet case.

Section snippets

Experimental apparatus and data treatment

The plane jet facility employed in the present study is an open-circuited blowing-down type wind tunnel. The air source is supplied by a 3 HP variable speed centrifugal blower, which is followed by a noise reduction chamber, a honeycomb, and screens for flow quality management. The jet nozzle is a fifth-order polynomial profile with a height (H) of 15 mm and an aspect ratio of 20 at the nozzle exit. The operating velocity throughout the experiment is fixed at 10 m/s, with the turbulence

On the mean velocity distributions

In the present experiment, the cylinder location is selected at Xcy=1.3H downstream of the jet exit such that a prominent resonant self-sustained oscillating flow field can be obtained. The operating velocity is fixed at U0=10 m/sec, and the cylinder diameter d is 3.0 mm. In the beginning, the streamwise mean velocity profiles and the corresponding velocity gradients are measured at different downstream locations. Fig. 2 presents the variations of the mean velocity profiles behind the cylinder

Practical significance and usefulness

The present paper studies the vortex dynamics and energy transport of a plane jet impinging upon a small cylinder located in the jet center. In practical sense, this is a problem concerning the flow impinging characteristics of jet interacting with a small cylinder located in the jet core to create flow mixing and enhancement. In reality, the small cylinder can also be deemed as a needle to actively serve as the flow throttle meter. This kind of apparatus is of great importance to both

Concluding remarks

The vortex dynamics and energy transport behaviors in the jet–cylinder interacting flow are experimentally studied by hot wire measurements. The small cylinder with diameter d is located within the jet potential core region with the exit height H, in which d/H=0.2 and the jet potential core provides an uniform flow impinging upon the submerged small cylinder to form a succession of shedding vortices. The jet in the present study is mainly operated at 10 m/s with the Reynolds number of 1.04×104

Acknowledgements

This work is supported by National Science Council, R.O.C., under contract number NSC 89-2212-E-006-078.

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