The influence of inlet flow condition on the frequency of self-excited jet precession

Abstract

A precessing jet flow can be generated naturally by a fluidic nozzle comprising a cylindrical nozzle-chamber with a large sudden expansion at its inlet and a small lip at its outlet. Such a precessing jet flow is offset with respect to the chamber axis, about which it rotates. The aim of the present study is to investigate the influence of the chamber-inlet configuration on the frequency of such precession. Three different inlet configurations, classified as long pipe, smooth contraction, and sharp-edged orifice plate, are tested. It is found that the frequency of precession from the orifice is highest, whereas that of the pipe jet is lowest. These differences appear to result partly from the distinct differences in their respective initial boundary layers.

Introduction

A continuous precession of an initially axisymmetric jet has been observed within a short cylindrical chamber following a large sudden expansion (Hallett and Gunther, 1984; Dellenback et al., 1988; Nathan et al., 1998). Distinct from a swirling motion, the precession of a jet refers to a “gyroscopic-like” motion of the entire jet about an axis in space other than its own centerline. The patented, wholly axisymmetric nozzle to generate such a precessing jet (PJ) flow, see Fig. 1, is characterized by a small inlet (diameter=d), a large chamber (diameter=D; length=L) and an outlet lip (Luxton and Nathan, 1988; Nathan et al., 1998). The configuration of the device must be within specific geometric ratios, namely $D/d⩾4$ and L/D=2–3.5 to enable the jet precession. The flow within the chamber is nevertheless bistable, so that an axisymmetric flow mode can also be generated, and the probability, or prevalence, of the precessing mode depends upon these ratios (Nathan et al., 1998). However, when an axisymmetric center-body (C-B) is mounted upstream of the outlet lip (Wong et al., 2003), the probability of precession is effectively unity, provided that the Reynolds number $\mathrm{Re}\equiv U_{b}d/v$ (where U_b is the bulk mean velocity of the jet at the inlet exit) is sufficiently high.

The PJ flow within the nozzle chamber is complex. Any alteration to the chamber configuration is expected to cause a significant change to the flow behavior such as the precession frequency (f_p). Mi et al. (1999) and Mi and Nathan (2000) have investigated the effect of various geometric parameters on f_p. They observed that f_p increases significantly with increasing L (or L_c). It was also revealed that the precession frequency is even more sensitive to the distance between the C-B and the outlet exit. By comparison, the outlet diameter has little influence on f_p.

Wong et al. (2004) have demonstrated that the characteristics of the inlet flow to the chamber influences the probability of precession. Specifically the probability of precession depends on the type of inlet, and is greater with a sharp-edged orifice plate than with a long pipe, and least with a smooth contraction inlet. This indicates the importance of the inflow condition for the occurrence of jet precession. However, the effect of the inlet flow on the precession frequency f_p has yet to be investigated, prompting the present study.

In this Brief communication, the effect of different inlet configurations on the precession frequency and Strouhal number is examined. We use three different types of inlet: i.e., smooth contraction, which generates a ‘top-hat’ velocity profile, sharp-edged orifice, which leads to a near-field vena contracta, and a long straight pipe, through which fully developed turbulent pipe flow emerges. Previous investigations of an axisymmetric free jet [e.g., Mi et al., 2001a, Mi et al., 2001b] have shown significant differences between the near-field structures from similar configured nozzles. For instance, there are well-defined large-scale coherent structures in the near field from a smooth contraction, while such structures are considerably smaller and less coherent in the pipe jet. Likewise, the coherent structures in the orifice jet are formed at a considerably higher rate than in the contraction jet. Similar trends are anticipated to occur with such jets confined in a circular chamber. If this is true, the frequency of jet precession could be expected to be different for the three cases. Present measurements of f_p will check this speculation.