Nonlinear dynamics of fully developed swirling jets

Douglas, Christopher M.; Emerson, Benjamin; Lieuwen, Timothy C.

doi:10.1017/jfm.2021.615

Cited by 13 publications

(56 citation statements)

References 70 publications

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“…Superficially, is indistinguishable from the weak form in Douglas et al. (2021 b ). However, the present work introduces one crucial but subtle distinction related to the discretisation that was necessary to ensure continuous dependence of the problem on the parameter .…”

Section: Problem Formulationmentioning

confidence: 68%

“…In the case of , the singularity distinguishes the annular configuration from the distinct case of a circular jet studied in Douglas et al. (2021 b ). Physically, the presence of an inner no-slip wall for any arbitrarily small always implies the existence of a stagnation point along the axis.…”

Section: Problem Formulationmentioning

confidence: 88%

“…Aside from the annular cross-section of the pipe, the configuration studied in this paper is essentially identical to that of our earlier investigation of circular swirling jets (Douglas et al. 2021 b ). As in that study, here we adopt a cylindrical coordinate system centred at the exit of the pipe such that , and reference all quantities to the outer diameter of the pipe and the volume-averaged velocity through the pipe.…”

Section: Problem Formulationmentioning

confidence: 92%

“… As in our previous work, a Neumann condition is enforced for the radial velocity component along to promote the transparency of the inlet to upstream-propagating disturbances and more closely approximate a very long pipe (Rusak 1998; Douglas et al. 2021 b ). Next, 3-D symmetry conditions are enforced along the central axis to ensure continuity of disturbances across the singularity at .…”

Section: Problem Formulationmentioning

confidence: 99%

“…Thus, as in Douglas et al. (2021 b ), we seek the appropriate spaces such that for all test functions , where is the standard spatial inner product. Superficially, is indistinguishable from the weak form in Douglas et al.…”

Section: Problem Formulationmentioning

confidence: 99%

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Dynamics and bifurcations of laminar annular swirling and non-swirling jets

2022

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This paper presents bifurcation analyses characterising the nonlinear dynamics of fully developed laminar annular jets with respect to the centrebody diameter ${ {d}}$ , Reynolds number ${ {Re}}$ , and swirl ratio ${ {S}}$ . Similar flows appear in numerous applications and feature a vibrant range of topological and dynamical characteristics associated with phenomena including shear layer separation and vortex breakdown. Our results begin by describing the non-monotonic evolution of the axisymmetric jet's steady topology under varying ${ {S}}$ . In accord with earlier reports, the jet progresses through a sequence of wake, breakdown and wall jet regimes in a qualitatively similar manner across a wide span of ${ {d}}$ and ${ {Re}}$ values. In the wake regime, the non-swirling jet bifurcates to a plane-symmetric, but not axisymmetric, steady flow pattern beyond a ${ {d}}$ -dependent critical ${ {Re}}$ value. With further increase in ${ {Re}}$ , the steady non-swirling jet destabilises subsequently via multiple distinct Hopf bifurcations. Introducing ${ {S}}>0$ to the jet also induces unsteadiness by twisting the singly azimuthally periodic ( $|m|=1$ ) asymmetric wake structure and causing it to precess periodically in time about the central axis. Intermediate swirl stabilises this unsteady dynamics and restores the jet's axisymmetry. This stabilising effect is then reversed in the breakdown regime at higher ${ {S}}$ , where a variety of different $|m|=1$ and $|m|=2$ instabilities bifurcate from the steady flow as ${ {S}}$ is increased. Several instances of hysteresis and subcritical behaviour are reported and discussed, including one that manifests precessing vortex core oscillations.

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Section: Problem Formulationmentioning

confidence: 68%

Section: Problem Formulationmentioning

confidence: 88%

Section: Problem Formulationmentioning

confidence: 92%

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

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Dynamics and bifurcations of laminar annular swirling and non-swirling jets

2022

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A balanced outflow boundary condition for swirling flows

Douglas

2024

Theor. Comput. Fluid Dyn.

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In open flow simulations, the dispersion characteristics of disturbances near synthetic boundaries can lead to unphysical boundary scattering interactions that contaminate the resolved flow upstream by propagating numerical artifacts back into the domain interior. This issue is exacerbated in flows influenced by real or apparent body forces, which can significantly disrupt the normal stress balance along outflow boundaries and generate spurious pressure disturbances. To address this problem, this paper develops a zero-parameter, physics-based outflow boundary condition (BC) designed to minimize pressure scattering from body forces and pseudo-forces and enhance transparency of the artificial boundary. This “balanced outflow BC” is then compared against other common BCs from the literature using example axisymmetric and three-dimensional open swirling flow computations. Due to centrifugal and Coriolis forces, swirling flows are known to be particularly challenging to simulate in open geometries, as these apparent forces induce non-trivial hydrostatic stress distributions along artificial boundaries that cause scattering issues. In this context, the balanced outflow BC is shown to correspond to a geostrophic hydrostatic stress correction that balances the induced pressure gradients. Unlike the alternatives, the balanced outflow BC yields accurate results in truncated domains for both linear and nonlinear computations without requiring assumptions about wave characteristics along the boundary.

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