2 results
Scaling of the puffing Strouhal number for buoyant jets and plumes
- N. T. Wimer, C. Lapointe, J. D. Christopher, S. P. Nigam, T. R. S. Hayden, A. Upadhye, M. Strobel, G. B. Rieker, P. E. Hamlington
-
- Journal:
- Journal of Fluid Mechanics / Volume 895 / 25 July 2020
- Published online by Cambridge University Press:
- 21 May 2020, A26
-
- Article
- Export citation
-
Prior research has shown that buoyant jets and plumes ‘puff’ at a frequency that depends on the balance of momentum and buoyancy fluxes at the inlet, as parametrized by the Richardson number. Experiments have revealed the existence of scaling relations between the Strouhal number of the puffing and the inlet Richardson number, but geometry-specific relations are required when the characteristic length is taken to be the diameter (for round inlets) or width (for planar inlets). Similar to earlier studies of rectangular buoyant jets and plumes, in the present study we use the hydraulic radius of the inlet as the characteristic length to obtain a single Strouhal–Richardson scaling relation for a variety of inlet geometries over Richardson numbers that span three orders of magnitude. In particular, we use adaptive mesh numerical simulations to compute puffing Strouhal numbers for circular, rectangular (with three different aspect ratios), triangular and annular high-temperature buoyant jets and plumes over a range of Richardson numbers. We then combine these results with prior experimental data for round, planar and rectangular buoyant jets and plumes to propose a new scaling relation that describes puffing Strouhal numbers for various inlet shapes and for hydraulic Richardson numbers spanning over four orders of magnitude. This empirically motivated scaling relation is also shown to be in good agreement with prior results from global linear stability analyses.
Azimuthal vorticity gradient in the formative stages of vortex breakdown
- M. KUROSAKA, C. B. CAIN, S. SRIGRAROM, J. D. WIMER, D. DABIRI, W. F. JOHNSON, J. C. HATCHER, B. R. THOMPSON, M. KIKUCHI, K. HIRANO, T. YUGÉ, T. HONDA
-
- Journal:
- Journal of Fluid Mechanics / Volume 569 / 25 December 2006
- Published online by Cambridge University Press:
- 15 November 2006, pp. 1-28
-
- Article
- Export citation
-
This paper is motivated by an observation: in the nascent state of vortex breakdown before it develops into a full-grown radial expansion, an initially straight vortex core first swells, and does so even in a straight pipe for no apparent reason. Although this initial swelling may be explained in many ways according to the perspectives chosen, we offer our own interpretation framed solely within vorticity dynamics: the radial swelling as well as the subsequent growth are induced by the azimuthal vorticity gradient decreasing downstream. The negative azimuthal vorticity gradient first appears at start-up and moves eventually into the region where the circulation reaches its steady-state value. The vorticity gradient can become negative without necessarily being accompanied by a sign-switch of the azimuthal vorticity itself.
The key point – that the negative azimuthal vorticity gradient induces initial radial swelling and its growth – is demonstrated in two analyses. First, a kinematic analysis results in an equation for the radial velocity where the azimuthal vorticity gradient appears as a source term. Its solution shows, in general and explicitly, that the negative azimuthal vorticity gradient does induce radially outward velocity. Two heuristic examples serve to illustrate this point further. In the second analysis, using the equation of motion in the streamline coordinates, the negative azimuthal vorticity gradient is shown to diverge the meridional streamlines radially. A numerical simulation using a modified vortex filament method not only corroborates this role of the azimuthal vorticity gradient in initiating and promoting the radial expansion, but also adds details to track the formation process. Both analyses and simulation support our interpretation that the initial radial swelling and its subsequent growth are induced by the negative azimuthal vorticity gradient.