3 results
A second-order integral model for buoyant jets with background homogeneous and isotropic turbulence
- Adrian C. H. Lai, Adrian Wing-Keung Law, E. Eric Adams
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- Journal:
- Journal of Fluid Mechanics / Volume 871 / 25 July 2019
- Published online by Cambridge University Press:
- 20 May 2019, pp. 271-304
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Buoyant jets or forced plumes are discharged into a turbulent ambient in many natural and engineering applications. The background turbulence generally affects the mixing characteristics of the buoyant jet, and the extent of the influence depends on the characteristics of both the jet discharge and ambient. Previous studies focused on the experimental investigation of the problem (for pure jets or plumes), but the findings were difficult to generalize because suitable scales for normalization of results were not known. A model to predict the buoyant jet mixing in the presence of background turbulence, which is essential in many applications, is also hitherto not available even for a background of homogeneous and isotropic turbulence (HIT). We carried out experimental and theoretical investigations of a buoyant jet discharging into background HIT. Buoyant jets were designed to be in the range of $1<z/l_{M}<5$, where $l_{M}=M_{o}^{3/4}/F_{o}^{1/2}$ is the momentum length scale, with $z/l_{M}<\sim 1$ and $z/l_{M}>\sim 6$ representing the asymptotic cases of pure jets and plumes, respectively. The background turbulence was generated using a random synthetic jet array, which produced a region of approximately isotropic and homogeneous field of turbulence to be used in the experiments. The velocity scale of the jet was initially much higher, and the length scale smaller, than that of the background turbulence, which is typical in most applications. Comprehensive measurements of the buoyant jet mixing characteristics were performed up to the distance where jet breakup occurred. Based on the experimental findings, a critical length scale $l_{c}$ was identified to be an appropriate normalizing scale. The momentum flux of the buoyant jet in background HIT was found to be conserved only if the second-order turbulence statistics of the jet were accounted for. A general integral jet model including the background HIT was then proposed based on the conservation of mass (using the entrainment assumption), total momentum and buoyancy fluxes, and the decay function of the jet mean momentum downstream. Predictions of jet mixing characteristics from the new model were compared with experimental observation, and found to be generally in agreement with each other.
On Boussinesq and non-Boussinesq starting forced plumes
- JIAOJIAN AI, ADRIAN WING-KEUNG LAW, S. C. M. YU
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- Journal:
- Journal of Fluid Mechanics / Volume 558 / 10 July 2006
- Published online by Cambridge University Press:
- 04 July 2006, pp. 357-386
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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.
Second-order integral model for a round turbulent buoyant jet
- HONGWEI WANG, ADRIAN WING-KEUNG LAW
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- Journal:
- Journal of Fluid Mechanics / Volume 459 / 25 May 2002
- Published online by Cambridge University Press:
- 17 June 2002, pp. 397-428
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The development of a second-order integral model for a round turbulent buoyant jet is reported based on new experimental data on turbulent mass and momentum transport. The mean and turbulent characteristics of a round vertical buoyant jet covering the full range from jets to plumes were investigated using a recently developed combined digital particle image velocimetry (DPIV) and planar laser-induced fluorescence (PLIF) system. The system couples the two well-known techniques to enable synchronized planar measurements of flow velocities and concentrations in a study area. The experimental results conserved the mass and momentum fluxes introduced at the source accurately with closure errors of less than 5%. The momentum flux contributed by turbulence and streamwise pressure gradient was determined to be about 10% of the local mean momentum flux in both jets and plumes. The turbulent mass flux, on the other hand, was measured to be about 7.6% and 15% of the mean mass flux for jets and plumes respectively. While the velocity spread rate was shown to be independent of the flow regime, the concentration-to-velocity width ratio λ varied from 1.23 to 1.04 during the transition from jet to plume. Based on the experimental results, a refined second-order integral model for buoyant jets that achieves the conservation of total mass and momentum fluxes is proposed. The model employs the widely used entrainment assumption with the entrainment coefficient taken to be a function of the local Richardson number. Improved prediction is achieved by taking into account the variation of turbulent mass and momentum fluxes. The variation of turbulent mass flux is modelled as a function of the local Richardson number. The turbulent momentum flux, on the other hand, is treated as a fixed percentage of the local mean momentum flux. In addition, unlike most existing integral models that assume a constant concentration-to-velocity width ratio, the present model adopts a more accurate approach with the ratio expressed as a function of the local Richardson number. As a result, smooth transition of all relevant mean and turbulent characteristics from jet to plume is predicted, which is in line with the underlying physical processes.