“…For and all values of , figures 11( a – c ) show that each PSD has a distinct peak at , indicating that the puffing frequency is slightly below that predicted by Wimer et al. (2020) (there are also smaller peaks at higher harmonics of the puffing frequency). For each of the cases, by contrast, we do not observe as clear a peak in the PSD.…”
Section: Resultsmentioning
confidence: 74%
“…Each of the PSDs has been normalized by the maximum magnitude, and the Strouhal number is normalized by the expected value based on Wimer et al. (2020) and . Figure 11.Normalized power spectral densities (PSDs) of along the centreline at for ( a – c ) and ( d – f ) , at ( a , d ) , ( b , e ) , and ( c , f ) .…”
Section: Resultsmentioning
confidence: 99%
“…These criteria were shown to be sufficient for simulating buoyant jets and plumes in Wimer et al. (2020, 2021), and we provide additional convergence tests in Appendix A.…”
Section: Methodsmentioning
confidence: 94%
“…This result was later generalized by Wimer et al. (2020), leading to a proposed relationship for axisymmetric round plumes of the form where is the density of the injected fluid, is the density of the surrounding fluid, is the gravitational acceleration, and is the velocity of the injected fluid. Equation was further substantiated using data from prior experiments (O'Hern et al.…”
Section: Introductionmentioning
confidence: 92%
“…Figure 16.( a – c ) Centreline density discrepancy , ( d – f ) centreline velocity , ( g – i ) the flow width using helium mass fraction , and ( j – l ) the flow width using streamwise velocity , for various maximum levels of AMR of ( a , d , g , j ) , , ( b , e , h , k ) , , and ( c , f , i , l ) , . We next consider the turbulent kinetic energy to assess convergence of the averages of second-order fluctuating moments, which have been shown previously to be important for ensuring that the puffing frequency is converged (Wimer et al. 2020, 2021). In figure 17, we show – planes of for each of the convergence test cases.…”
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
${Ri}_0$
.
“…For and all values of , figures 11( a – c ) show that each PSD has a distinct peak at , indicating that the puffing frequency is slightly below that predicted by Wimer et al. (2020) (there are also smaller peaks at higher harmonics of the puffing frequency). For each of the cases, by contrast, we do not observe as clear a peak in the PSD.…”
Section: Resultsmentioning
confidence: 74%
“…Each of the PSDs has been normalized by the maximum magnitude, and the Strouhal number is normalized by the expected value based on Wimer et al. (2020) and . Figure 11.Normalized power spectral densities (PSDs) of along the centreline at for ( a – c ) and ( d – f ) , at ( a , d ) , ( b , e ) , and ( c , f ) .…”
Section: Resultsmentioning
confidence: 99%
“…These criteria were shown to be sufficient for simulating buoyant jets and plumes in Wimer et al. (2020, 2021), and we provide additional convergence tests in Appendix A.…”
Section: Methodsmentioning
confidence: 94%
“…This result was later generalized by Wimer et al. (2020), leading to a proposed relationship for axisymmetric round plumes of the form where is the density of the injected fluid, is the density of the surrounding fluid, is the gravitational acceleration, and is the velocity of the injected fluid. Equation was further substantiated using data from prior experiments (O'Hern et al.…”
Section: Introductionmentioning
confidence: 92%
“…Figure 16.( a – c ) Centreline density discrepancy , ( d – f ) centreline velocity , ( g – i ) the flow width using helium mass fraction , and ( j – l ) the flow width using streamwise velocity , for various maximum levels of AMR of ( a , d , g , j ) , , ( b , e , h , k ) , , and ( c , f , i , l ) , . We next consider the turbulent kinetic energy to assess convergence of the averages of second-order fluctuating moments, which have been shown previously to be important for ensuring that the puffing frequency is converged (Wimer et al. 2020, 2021). In figure 17, we show – planes of for each of the convergence test cases.…”
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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