Global stability of buoyant jets and plumes

Chakravarthy, R. V. K.; Lesshafft, Lutz; Huerre, Patrick

doi:10.1017/jfm.2017.764

Cited by 38 publications

(32 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These observations were corroborated by the DNS results of Jiang & Luo (2000) and of Satti & Agrawal (2006). This is also consistent with the recent theoretical analysis of Chakravarthy et al (2018) based on global modes. However, the local stability analysis by Chakravarthy et al (2015) found that the dominant and only absolutely unstable perturbation is helical rather than axisymmetric.…”

Section: Introductionsupporting

confidence: 91%

From a steady plume to periodic puffs during confined carbon dioxide dissolution

Meunier

Nadal

2018

J. Fluid Mech.

View full text Add to dashboard Cite

In this paper, the stability of a laminar plume due to solutal convection is addressed from experimental, numerical and theoretical points of view. A topless vertical tube containing water is put in a pressure cell filled with carbon dioxide ( $\text{CO}_{2}$ ). The diffusion of $\text{CO}_{2}$ at the free surface creates a thin layer of heavy fluid underneath the surface. This unstable density gradient generates a steady laminar plume which goes downward through the entire tube. A quasi-steady flow settles in the tube, filling gradually the bottom of the tube with heavy fluid. During this laminar regime, the velocity of the plume slowly decreases due to the build-up of the background density gradient. Surprisingly, despite the decrease of the Reynolds number, the laminar plume suddenly destabilises via a varicose mode into periodic pulsed puffs after an onset time which depends on the height of the tube and on the solutal Rayleigh number $Ra$ . This periodic regime is followed by an aperiodic regime, which lasts until the complete saturation of the solution. The observed destabilisation is explained as a result of the interplay between the feedback of the global recirculating flow and the progressive density stratification of the background fluid. The wavelength, frequency, onset time and phase velocity of the instability are explored using particle image velocimetry (PIV) measurements over two decades of Rayleigh number. The characteristics of the instability appear to be almost independent of the Bond number but strongly dependent on the solutal Rayleigh number and the aspect ratio. The phase velocity is very close to the fluid velocity of the plume before the instability, which has been predicted in various works to scale as $Ra^{2/3}(\ln \,Ra)^{1/3}$ . The wavelength is close to 4.5 times the radius of the cylinder (independent of aspect ratio, Bond number and Rayleigh number) such that the frequency scales as the phase velocity. The onset time, which is proportional to the height of the cylinder, scales as $Ra^{-0.55}$ and depends on the Bond number. A simplified model inspired from Lorenz’ waterwheel is proposed to explain the destabilisation process after partial fill-up of the cylinder. Although very qualitative, the model captures the key features of the experimental observations.

show abstract

Section: Introductionsupporting

confidence: 91%

From a steady plume to periodic puffs during confined carbon dioxide dissolution

Meunier

Nadal

2018

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Such a flow configuration is typical of previous experimental studies [15,11,9,16]. Global instability has also been observed in buoyant jets [17], but is not examined in this study.…”

Section: Flow Configurationmentioning

confidence: 53%

Passive control of global instability in low-density jets

Qadri

Chandler

Juniper

2018

European Journal of Mechanics - B/Fluids

View full text Add to dashboard Cite

Many studies have shown that low-density jets exhibit self-excited varicose oscillations. We use direct numerical simulation of the low Mach number Navier-Stokes equations to perform a linear global stability analysis of a helium jet at the threshold of onset of these oscillations. We calculate the direct and adjoint global modes and overlap these to obtain the structural sensitivity. We find that the structural sensitivity has high magnitudes in the shear layer downstream of the entrance plane, where the flow is absolutely unstable. We use the direct and adjoint global modes to calculate the effect of a control force on the growth rate and frequency of the unstable mode. We produce maps of the regions of the flow that are most sensitive to localized open loop steady forcing in the form of a body force and a heat source. We find that the most sensitive location for

show abstract

“…1), referred to as the 'arc branch' from here on, was found to present features that suggest a resonance between the inflow and outflow boundaries. Such branches are in fact ubiquitous in many, if not all, global spectra of truncated open shear flows found in the literature: boundary layers [10,11,1], cylinder wakes [24,20], jets [22,12], plumes [4], three-dimensional boundary layers with roughness elements [19,17] -all these and many others present similar characteristic branches of eigenvalues that are often described as being highly dependent on the type or position of outflow boundary conditions. Typically, no convergence with respect to the length of the numerical box can be attained for such modes.…”

Section: Introductionmentioning

confidence: 92%

Artificial eigenmodes in truncated flow domains

Lesshafft

2017

Theor. Comput. Fluid Dyn.

Self Cite

View full text Add to dashboard Cite

Whenever linear eigenmodes of open flows are computed on a numerical domain that is truncated in the streamwise direction, artificial boundary conditions may give rise to spurious pressure signals that are capable of providing unwanted perturbation feedback to upstream locations. The manifestation of such feedback in the eigenmode spectrum is analysed here for two simple configurations. First, explicitly prescribed feedback in a Ginzburg-Landau model is shown to produce a spurious eigenmode branch, named the 'arc branch', that strongly resembles a characteristic family of eigenmodes typically present in open shear flow calculations. Second, corresponding mode branches in the global spectrum of an incompressible parallel jet in a truncated domain are examined. It is demonstrated that these eigenmodes of the numerical model depend on the presence of spurious forcing of a local k+ instability wave at the inflow, caused by pressure signals that appear to be generated at the outflow. Multiple local k+ branches result in multiple global eigenmode branches. For the particular boundary treatment chosen here, the strength of the pressure feedback from the outflow towards the inflow boundary is found to decay with the cube of the numerical domain length. It is concluded that arc-branch eigenmodes are artifacts of domain truncation, with limited value for physical analysis. It is demonstrated, for the example of a non-parallel jet, how spurious feedback may be reduced by an absorbing layer near the outflow boundary.Comment: to appear in Theoretical and Computational Fluid Dynamics (2017 or 2018

show abstract

Global stability of buoyant jets and plumes

Cited by 38 publications

References 36 publications

From a steady plume to periodic puffs during confined carbon dioxide dissolution

From a steady plume to periodic puffs during confined carbon dioxide dissolution

Passive control of global instability in low-density jets

Artificial eigenmodes in truncated flow domains

Contact Info

Product

Resources

About