On the formation and propagation of vortex rings and pairs of vortex rings

1997 ◽  
Vol 332 ◽  
pp. 121-139 ◽  
Author(s):  
S. L. Wakelin ◽  
N. Riley
Keyword(s):  
Similarity Theory ◽  
Laminar Flows ◽  
Plane Boundary ◽  
Vortex Rings ◽  
Single Vortex ◽  
Circular Annulus ◽  
Circular Orifice ◽  
High Reynolds ◽  
Two Parameters ◽  
Gap Width

Axisymmetric high-Reynolds-number laminar flows are simulated numerically. In particular, we consider the formation and propagation of single vortex rings from a circular orifice in a plane boundary, and pairs of vortex rings from a circular annulus in a plane boundary. During formation, single rings grow within an essentially potential flow, as in the similarity theory of Pullin (1979). When released they are shown to propagate in an almost inviscid manner, as described by Saffman (1970). Pairs of vortex rings, formed at a circular annulus, have been studied by Weidman & Riley (1993), both experimentally and computationally. They conclude from their observations that the behaviour of the rings depends primarily upon two parameters, namely the impulse applied to the fluid, during ring formation, and the gap width of the annulus. The results we present in this paper confirm the dependence of the flow on these parameters.

Effective boundary conditions for compressible flows over rough boundaries

2015 ◽  
Vol 25 (07) ◽  
pp. 1257-1297 ◽  
Author(s):  
Giulia Deolmi ◽  
Wolfgang Dahmen ◽  
Siegfried Müller
Keyword(s):  
Boundary Conditions ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Laminar Flows ◽  
Small Scale ◽  
Reynolds Number Flow ◽  
Effective Boundary ◽  
Effective Boundary Conditions ◽  
High Reynolds ◽  
Rough Boundaries

Simulations of a flow over a roughness are prohibitively expensive for small-scale structures. If the interest is only on some macroscale quantity it will be sufficient to model the influence of the unresolved microscale effects. Such multiscale models rely on an appropriate upscaling strategy. Here the strategy originally developed by Achdou et al. [Effective boundary conditions for laminar flows over periodic rough boundaries, J. Comput. Phys. 147 (1998) 187–218] for incompressible flows is extended to compressible high Reynolds number flow. For proof of concept a laminar flow over a flat plate with partially embedded roughness is simulated. The results are compared with computations on a rough domain.

Micro Pulsatile Jets for Thrust Optimization

2004 ◽  
Author(s):  
Tiffany J. Finley ◽  
Kamran Mohseni
Keyword(s):  
Actuation Voltage ◽  
Orifice Diameter ◽  
Vortex Rings ◽  
Wave Shape ◽  
Electromagnetic Actuation ◽  
Thrust Generation ◽  
Circular Orifice ◽  
Formation Number ◽  
Cylindrical Cavities ◽  
Maximum Thrust

Thrust optimization of micro-synthetic pulsatile jets is studied. Cylindrical cavities with a small circular orifice at one end, and a vibrating diaphragm at the other are used for thrust generation. The governing parameters are identified and the tradeoffs between electrostatic, piezoelectric, and electromagnetic actuation methods are investigated. Optimization of the micro jets requires a solution that gives maximum diaphragm displacement while minimizing voltage. The size of the orifice diameter is chosen to maintain a formation number of 4, at which the length of an expelled slug of fluid from the exit orifice is four times the diameter of orifice. This relationship maximizes the circulation and impulse in the leading vortex rings generated by the actuator. To examine the effects of cavity dimensions, a number of actuators are constructed out of aluminum with various cavity diameter, cavity height, and orifice diameters. Piezoelectric disks bonded to brass shims are used for actuation. The jets are tested in air at various actuation voltage and wave-shape functions. Maximum thrust generation is achieved at the resonant frequency of the cavity. Hot wire anemometry is used to further characterize the jet flow field. An investigation into electrostatic, piezoelectric, and electromagnetic diaphragm actuation methods revealed that electromagnetic actuation provides the maximum diaphragm displacement using a constant voltage.

Vortex growth in jets

1970 ◽  
Vol 44 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Gordon S. Beavers ◽  
Theodore A. Wilson
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Computer Experiments ◽  
Vortex Rings ◽  
Periodic Flow ◽  
Two Dimensional ◽  
Vortex Sheets ◽  
Vortex Pairs ◽  
Symmetric Pattern ◽  
Circular Orifice

Observations are reported on the growth of vortices in the vortex sheets bounding the jet emerging from a sharp-edged two-dimensional slit and from a sharp-edged circular orifice. A regular periodic flow is observed near the orifice for both configurations when the Reynolds number of the jet lies between about 500 and 3000. The two-dimensional jet produces a symmetric pattern of vortex pairs with a Strouhal number of 0·43. Vortex rings are formed in the circular jet with a Strouhal number of 0·63. Computer experiments show that a growing pair of vortices in two parallel vortex sheets produces a symmetric pattern of vortices upstream from the original disturbance.

Boundary-Layer Interaction Theory

1983 ◽  
Vol 50 (4b) ◽  
pp. 1104-1113 ◽  
Author(s):  
A. F. Messiter
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Laminar Flows ◽  
Local Interaction ◽  
Interaction Theory ◽  
Surface Geometry ◽  
Boundary Layer Interaction ◽  
Special Solutions ◽  
High Reynolds ◽  
Basic Ideas

Boundary-layer theory for flows at high Reynolds number fails locally in small regions with large gradients, where special solutions are required, with the pressure initially unknown. Examples include the flow near a discontinuity in surface geometry or near a separation point. During the past 15 years, local-interaction problems have been studied extensively for laminar flows, with particular attention to the description and prediction of separation, and a few examples have been worked out for turbulent flows. The basic ideas of asymptotic local-interaction theory are described, and applications are summarized for a variety of flows.

On the stability of high-Reynolds-number flows with closed streamlines

1989 ◽  
Vol 200 ◽  
pp. 19-38 ◽  
Author(s):  
A. J. Mestel
Keyword(s):  
Rotating Magnetic Field ◽  
Two Dimensional ◽  
Inviscid Flows ◽  
Stability Theorems ◽  
High Reynolds ◽  
The Stability ◽  
Two Parameters ◽  
Reynolds Number Flows ◽  
Flow Reversals ◽  
Entire Theory

In steady, two-dimensional, inertia-dominated flows it is well known that the vorticity is constant along the streamlines, which, in a bounded domain, are necessarily closed. For inviscid flows, the variation of vorticity across the streamlines is arbitrary, while for forced, weakly dissipitative flows, it is determined by the balance between viscous diffusion and the forcing. This paper discusses the linear stability of flows of this type to two-dimensional disturbances. Arnol'd's stability theorems are discussed. An alternative functional to Arnol'd's is found, which gives the same stability criteria and which permits a representation of the problem in terms of a Schrödinger equation. Conditions for stability are derived from this functional. In particular it is shown that total flow reversals are potentially unstable. The results are illustrated with respect to the geometrically simple case when the streamlines are circular and the forcing is due to a rotating magnetic field, for which case the stability regions are calculated as a function of two parameters. It is shown that the entire theory, including Arnol'd's theorems, applies also to poloidal axisymmetric flows.

scholarly journals Development of gravity currents on rapidly changing slopes

2017 ◽  
Vol 833 ◽  
pp. 70-97 ◽  
Author(s):  
M. E. Negretti ◽  
J.-B. Flòr ◽  
E. J. Hopfinger
Keyword(s):  
Similarity Theory ◽  
Boundary Layer Separation ◽  
Gravity Currents ◽  
Bottom Friction ◽  
Reynolds Stresses ◽  
Velocity Increase ◽  
Acceleration Parameter ◽  
Boundary Slope ◽  
Layer Velocity ◽  
High Reynolds

Gravity currents often occur on complex topographies and are therefore subject to spatial development. We present experimental results on continuously supplied gravity currents moving from a horizontal to a sloping boundary, which is either concave or straight. The change in boundary slope and the consequent acceleration give rise to a transition from a stable subcritical current with a large Richardson number to a Kelvin–Helmholtz (KH) unstable current. It is shown here that depending on the overall acceleration parameter$\overline{T_{a}}$, expressing the rate of velocity increase, the currents can adjust gradually to the slope conditions (small$\overline{T_{a}}$) or go through acceleration–deceleration cycles (large$\overline{T_{a}}$). In the latter case, the KH billows at the interface have a strong effect on the flow dynamics, and are observed to cause boundary layer separation. Comparison of currents on concave and straight slopes reveals that the downhill deceleration on concave slopes has no qualitative influence, i.e. the dynamics is entirely dominated by the initial acceleration and ensuing KH billows. Following the similarity theory of Turner 1973 (Buoyancy Effects in Fluids. Cambridge University Press), we derive a general equation for the depth-integrated velocity that exhibits all driving and retarding forces. Comparison of this equation with the experimental velocity data shows that when$\overline{T_{a}}$is large, bottom friction and entrainment are large in the region of appearance of KH billows. The large bottom friction is confirmed by the measured high Reynolds stresses in these regions. The head velocity does not exhibit the same behaviour as the layer velocity. It gradually approaches an equilibrium state even when the acceleration parameter of the layer is large.

scholarly journals About bubbles and vortex rings

2015 ◽  
Vol 780 ◽  
pp. 1-4 ◽  
Author(s):  
C. Martínez-Bazán
Keyword(s):  
Vortex Rings ◽  
Complex Mechanism ◽  
Complex Interplay ◽  
Single Vortex ◽  
Vortical Structures ◽  
Turbulent Eddies ◽  
Deformation Dynamics ◽  
Bubble Interaction ◽  
Elongation Process ◽  
Shed Light

Bubble interaction with turbulence has a number of applications in engineering processes and nature. The complex interplay between the vortical structures present in a turbulent flow and the bubbles drives their deformation dynamics, which may lead to bubble rupture under the appropriate conditions. Such a process includes nonlinear interaction among the turbulent eddies and between the eddies and the bubbles. Thus, the coupled evolution of a single vortex ring with a bubble represents an idealized scenario that can provide a framework to shed light on understanding such a common and complex mechanism. Jha & Govardhan (J. Fluid Mech., vol. 773, 2015, pp. 460–497) have performed elegant experiments generating controlled vortex rings and injecting bubbles of known volume. They have reported interesting results on the elongation process of the bubble and its impact on vortex dynamics.

Deformation and breakup of bubbles interacting with single vortex rings

2021 ◽  
pp. 103734
Author(s):  
F.J. Foronda-Trillo ◽  
J. Rodríguez-Rodríguez ◽  
C. Gutiérrez-Montes ◽  
C. Martínez-Bazán
Keyword(s):  
Vortex Rings ◽  
Single Vortex

scholarly journals Some observations regarding steady laminar flows past bluff bodies

2014 ◽  
Vol 372 (2020) ◽  
pp. 20130353 ◽  
Author(s):  
Bengt Fornberg ◽  
Alan R. Elcrat
Keyword(s):  
Numerical Methods ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
Laminar Flows ◽  
Bluff Bodies ◽  
The Past ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Steady Laminar

Steady laminar flows past simple objects, such as a cylinder or a sphere, have been studied for well over a century. Theoretical, experimental and numerical methods have all contributed fundamentally towards our understanding of the resulting flows. This article focuses on developments during the past few decades, when mostly numerical and asymptotical advances have provided insights also for steady, although unstable, high-Reynolds-numbers flow regimes.

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