On Boussinesq and non-Boussinesq starting forced plumes

Abstract

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.