The characteristics of Boussinesq and non-Boussinesq starting forced plumes were investigated in this study. Two distinct periods in the transient plume penetration are identified, namely, the period of flow development (PFD) and period of developed flow (PDF). Similarity solutions are developed in PDF by incorporating the behaviour of an isolated buoyant vortex ring and recent laboratory results on the trailing forced plume, and the temporal variation of the penetration rate is derived during the different phases of jet-like, transitional and plume-like flow. To verify the similarity solutions, experiments were conducted on vertical starting forced plumes using combined particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) with refractive index matching. The discharge Reynolds number was varied from 3773 to 7403 and the range of excess densities ($\Delta_0 \,{=}\, (\rho_\infty\,{-}\,\rho_0)/\rho_\infty$, where $\rho_0$ and $\rho_\infty$ are initial plume and ambient density, respectively) from 2.77% to 25.07%. The experimental results revealed distinct differences between plumes having an initial density difference of larger or smaller than 15% due to the non-Boussinesq effects. Thus, the value of 15% was employed as an approximate criterion to divide the plumes into Boussinesq versus non-Boussinesq cases. The measured penetration rates and the mean centreline axial velocity of the Boussinesq starting forced plumes agreed well with the analytical predictions at the fully developed stage. However, the behaviour was substantially more complex for the non-Boussinesq plumes. In the transient records, it was noted that the time scales for the penetration of the starting plumes and the velocity development in the trailing forced plume were similar, but the time scale for the Gaussian profile to become self-similar was somewhat longer.
The gravity-driven starting jet characteristics over the range of Reynolds numbers from 1179 to 10 611 have been investigated using planar laser induced fluorescence and particle image velocimetry. Of the 17 cases investigated, pinch off for the leading vortex was found to appear at Reynolds number above 3000. For those cases involving pinch off, limiting values for the nondimensional circulation for the leading vortex could be identified at around 1.26 and the nondimensional energy was at about 0.35Ϯ 0.01, respectively. The former agrees with the universal value proposed by Shusser et al. ͓Phys. Fluids 18, 033601 ͑2006͔͒ to within 9%, while the latter lies within the analytical result range ͑from 0.27 to 0.4͒ proposed by Gharib et al. ͓J. Fluid Mech. 360, 121 ͑1998͔͒. The results thus suggested that the pinched-off vortex ring would achieve similar characteristics and that may also be independent of the generation mechanism.
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.
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