On starting square jets and forced plumes

Abstract

The present research focuses on the studies of the transitional stage of jets and plumes. It can be generally divided into two parts, namely, starting jets and starting forced plumes. The first part attempts to improve the understanding of the vortex dynamics in starting jets and to examine the differences between that of the circular jets and square jets. Based on the qualitative (via PLIF) and quantitative results obtained (via PIV), it was found that streamwise vortices generated at the corners of the square nozzle interacted with the primary vortices. The interactions had altered the downstream flow characteristics tremendously. Vortex pinch-off, leapfrogging, coalescence and axis-switching were observed in starting square jets and the mechanisms were analyzed. For starting forced plume, Boussinesq and non-Boussinesq cases had been investigated analytically and experimentally. An analytical model for the starting forced plume covering the entire range of jet-like, transitional and plume-like had been developed based on the understanding Wang & Law (2002) for forced plumes. The velocity ratio between the head vortex and the trailing buoyant jet was derived to vary from the jet-like to plume-like phases. The transitional changes for this ratio had also been quantified. Experimental results verified the analytical model. The quantative PIV results showed disorder behaviors in the near-field region for the non-Boussinesq cases (15% ∆ >). Virtual origin correction approach was utilized to compensate the non-Boussinesq effects.

The pinch-off process of the leading vortex ring in a starting jet

“…where C is a constant within the range of 3.15 to 4.08 for the best fitted line. Johari et al (1997) x tip /D = C(tU 0 /D) 1/2 (Re D = 5 × 10 3 ∼ 2 × 10 4 ) C = 2.14 ∼ 2.58 Lahbabi et al (1993) x tip /D = C(tU 0 /D) 1/2 (Re D = 2.6 × 10 3 ) C = 2.9 Cossali et al (2001) x tip /D = C(tU 0 /D) 1/2 (Re D = 1.26 × 10 4 ∼ 1.36 × 10 4 ) C = 3.41 Ai (2006) x which is normalized by the jet exit diameter D, for various cases. The boundary of the vortex ring is defined at the level 1.5 s −1 in the azimuthal vorticity contours for respective cases.…”

“…Experimental results of Ai (2006) on the gravity-driven starting jets using Planar Laser Induced Fluorescence (PLIF) and Digital Particle Image Velocimetry (DPIV) over a range of Reynolds number from 1, 179 to 10, 611 are analyzed and discussed. The following remarks can be extracted from the preceding texts.…”

“…It is noted that some modifications of these two basic configurations were also utilized in previous experimental studies in order to simulate actual starting jet applications, such as temporally exit diameter D = D(t) (Allen and Naitoh, 2005;Dabiri and Gharib, 2005), nozzles with vertical wall at exit plane (Gharib et al, 1998), and converging nozzle (i.e. 0 • < β < 90 • in figure 2.1(b)) (Ai, 2006). In studies of starting jets, dimensionless time of the flow is usually defined as…”

“…Finally, setup of the experiment performed by Ai (2006) is positioned perpendicular to the measurement plane and records an image se-quence of the particle fields with a spatial resolution of 1, 008 × 1, 016 pixels.…”

“…This analysis is based on the experimental results of Ai (2006) where u and v are the local axial and radial velocity, respectively, x and r are the streamwise distance from the nozzle exit and the radial distance from the axisymmetric centerline (see the cylindrical coordinates defined in figure 3.3), respectively. The total circulation is obtained by integrating the vorticity contained within the lowest detectable contours for either positive or negative values.…”