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Using numerical simulations, we investigate the near-field temporal variability of axisymmetric helium plumes as a function of inlet-based Richardson ( $${Ri}_0$$ ) and Reynolds ( $${Re}_0$$ ) numbers. Previous studies have shown that $${Ri}_0$$ plays a leading-order role in determining the frequency at which large-scale vortices are produced (commonly called the ‘puffing’ frequency). By contrast, $${Re}_0$$ dictates the strength of localized gradients, which are important during the transition from laminar to turbulent flow. The simulations presented here span a range of $${Ri}_0$$ and $${Re}_0$$ , and use adaptive mesh refinement to achieve high spatial resolutions. We find that as $${Re}_0$$ increases for a given $${Ri}_0$$ , the puffing motion undergoes a transition at a critical $${Re}_0$$ , marking the onset of chaotic dynamics. Moreover, the critical $${Re}_0$$ decreases as $${Ri}_0$$ increases. When the puffing instability is non-chaotic, time series of different variables are well-correlated, exhibiting only modest changes in the dynamics (including period doubling and flapping). Once the flow becomes chaotic, denser ambient fluid penetrates the core of the plume, similar to penetrating ‘spikes’ formed by Rayleigh–Taylor instabilities, leading to only moderately correlated flow variables. These changes result in a non-trivial dependence of the puffing frequency on $${Re}_0$$ . Specifically, at sufficiently low $${Re}_0$$ , the puffing frequency falls below the prediction from Wimer et al. ( J. Fluid Mech. , vol. 895, 2020). As $${Re}_0$$ increases beyond the critical $${Re}_0$$ , the puffing frequency increases and then drops back down to the predicted scaling. The dependence of the puffing frequency on $${Re}_0$$ provides a possible explanation for previously observed changes in the scaling of the puffing frequency for high $${Ri}_0$$ .
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Richardson and Reynolds number effects on the near field of buoyant plumes: flow statistics and fluxes
The near-field characteristics of highly buoyant plumes, commonly referred to as lazy plumes, remain relatively poorly understood across a range of flow conditions, particularly compared with our understanding of far-field characteristics. Here, we perform fully resolved three-dimensional numerical simulations of round helium plumes to characterize the effects of different inlet Richardson, $${Ri}_0$$ , and Reynolds, $${Re}_0$$ , numbers on first- and second-order statistical moments as well as average vertical fluxes in the near field. For sufficiently high $${Re}_0$$ at a particular $${Ri}_0$$ , heavy air can penetrate the core of the plume, reminiscent of spikes in the classical Rayleigh–Taylor instability. In the most turbulent simulation, this penetration becomes so strong that a recirculation zone forms along the centreline of the plume. Vertical fluxes are found to scale linearly with vertical distance from the plume inlet, consistent with experimental and numerical observations (Jiang & Luo, Flow Turbul. Combust. , vol. 64, 2000, pp. 43–69; Kaye & Hunt, Intl J. Heat Fluid Flow , vol. 30, 2009, pp. 1099–1105). We analytically derive this linear scaling from the governing equations by making a radial entrainment hypothesis whereby ambient fluid is entrained, on average, only in the radial direction at a finite distance from the inlet. Through this derivation, we identify physical mechanisms that can cause these relationships to remain only approximately valid for the present simulations. Lastly, we identify near-field power-law scaling relations for the flux magnitudes based on $${Ri}_0$$ , and also examine vertical profiles of the non-dimensional Richardson number flux. Ultimately, insights from the present simulations are used to define near-, intermediate- and far-field regions in buoyant plumes.
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- Award ID(s):
- 1847111
- PAR ID:
- 10425933
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 961
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.208
