A Description of Eddying Motions and Flow Patterns Using Critical-Point Concepts

Perry, and A E; Chong, M. S.

doi:10.1146/annurev.fl.19.010187.001013

Cited by 677 publications

(317 citation statements)

References 14 publications

Supporting

Mentioning

307

Contrasting

Order By: Relevance

“…critical points), the behaviour of the streamlines in the vicinity of these points, and the manner in which the critical points are connected by the dividing streamlines. An exhaustive description of the theory of critical points for compressible three-dimensional unsteady laminar or turbulent flows can be found in several sources (Dallmann 1982;Perry & Chong 1987;Chong, Perry & Cantwell 1990;Dallmann et al 1997); for completeness, the main aspects concerning incompressible flows are summarized next.…”

Section: Topological Considerationsmentioning

confidence: 99%

“…Critical point concepts emerged in the context of fluid flow in the early eighties of last century and have since become a powerful tool in describing exact local solutions of the equations of motion; such local solutions may then be used in order to reconstruct the entire (laminar or turbulent) three-dimensional flow fieldthe interested reader is referred to Dallmann (1982), , , Perry & Chong (1987) and Dallmann, Vollmers & Su (1997) for the fundamentals of the reconstruction and classification of separated flow topologies and, for example, to Vorobieff & Rockwell (1996) for one application of the theory to a concrete flow control problem. According to critical point theory, the two-dimensional flow structure of the laminar separated basic field is described by means of centre and node-saddle points.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Structural changes of laminar separation bubbles induced by global linear instability

Rodríguez

Theofilis

2010

J. Fluid Mech.

View full text Add to dashboard Cite

The topology of the composite flow fields reconstructed by linear superposition of a two-dimensional boundary layer flow with an embedded laminar separation bubble and its leading three-dimensional global eigenmodes has been studied. According to critical point theory, the basic flow is structurally unstable; it is shown that in the presence of three-dimensional disturbances the degenerate basic flow topology is replaced by a fully three-dimensional pattern, regardless of the amplitude of the superposed linear perturbations. Attention has been focused on the leading stationary eigenmode of the laminar separation bubble discovered by Theofilis et al. (Phil. Trans. R. Soc. Lond. A, vol. 358, 2000, pp. 3229-3324); the composite flow fields have been fully characterized with respect to the generation and evolution of their critical points. The stationary global mode is shown to give rise to a three-dimensional flow field which is equivalent to the classical U-shaped separation, defined by Hornung & Perry (Z. Flugwiss. Weltraumforsch., vol. 8, 1984, pp. 77-87), and induces topologies on the surface streamlines that are resemblant to the characteristic stall cells observed experimentally. IntroductionThe instability of a laminar separation bubble (LSB), embedded inside a boundary layer and arising as a consequence of an adverse free-stream pressure gradient on a flat surface, or induced by changes of the surface curvature, constitutes a problem of prime technological significance: in an aeronautical context related applications include lifting surfaces, low-pressure turbines and wind-turbine blades. The presence of a separated shear layer as an integral part of the LSB suggests that the instability properties of the shear layer should play a decisive role in the reattachment of the separated boundary layer. The one-dimensionality of the model shear-layer profile and its resulting amenability to classic, ordinary-differential-equation-based analysis (Michalke 1964; Blumen 1970 and subsequent work in this 'local' vein) has generated a wealth of knowledge on the problem of shear-layer instability perse and as applied to the LSB flow. On the other hand, Gaster postulated (H. Fasel, private communication November 2004) that, besides paying attention to the amplification of incoming disturbances by solution of the local instability problem, analysis of LSB flows 'in the true sense' should also be performed, by which a global instability analysis of the entire separated boundary layer flow is implied.

show abstract

Section: Topological Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structural changes of laminar separation bubbles induced by global linear instability

Rodríguez

Theofilis

2010

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Topology-based visualization of two-dimensional vector fields offers insight into the structure of flow [9]. In order to capture the essential topological structure of the separation bubble upstream of the rib, two methods are applied in this section to improve the quality of the velocity data.…”

Section: Topology Of the Upstream Separation Bubblementioning

confidence: 99%

“…Depending on whether streamlines are attracted to or emanate from critical points, critical points are classified into stable and unstable types. A detailed description of critical-point theory can be found in [9]. In addition, another important topological feature is the so-called bifurcation line towards which other trajectories converge asymptotically.…”

Section: Introductionmentioning

confidence: 99%

Turbulent flow in a ribbed channel: Flow structures in the vicinity of a rib

Wang

Salewski

Sundén

2010

Experimental Thermal and Fluid Science

View full text Add to dashboard Cite

PIV measurements are performed in a channel with periodic ribs on one wall. The emphasis of this study is to investigate the flow structures in the vicinity of a rib in terms of mean velocities, Reynolds stresses, probability density functions (PDF), and two-point correlations. The PDF distribution of u is bimodal in the separated shear layer downstream of the rib. The maximum Reynolds shear stresses occur at the leading edge of the rib. Based on quadrant analysis, it is found that ejection motions make a dominant contribution to the Reynolds shear stress in this region. Moreover, topology-based visualization is applied to the separation bubble upstream of the rib. Salient critical points and limit cycles are extracted, which gives clues to the physical processes occurring in the flow.

show abstract

“…In the the case of isothermal laminar shear flows numerous examples exist were exploration of the effects of local flow structure on the global picture has proved extremely informative -see for example Gaskell et al (1997), Wilson et al (2005), Perry and Chang (1987), Jeffrey and Sherwood (1980), Scholle et al (2006). What unifies all of these problems is that, even in the absence of inertia, the irregular confining geometry is a catalyst for eddy formation.…”

Section: Introductionmentioning

confidence: 99%

The effect of locally induced flow structure on global heat transfer for plane laminar shear flow

Scholle

Haas

Aksel

et al. 2009

International Journal of Heat and Fluid Flow

View full text Add to dashboard Cite

Heat transfer in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one, which is fixed, has a regular sinusoidally varying profile. A closed form analytical solution for velocity, based on lubrication theory, together with a semi-analytic one for temperature, from application of Ritz's direct method, is derived for creeping flow. In addition, detailed numerical solutions are obtained from a finite element formulation of the weak form of the governing equations for mass, momentum and energy (temperature) conservation, enabling the effects of inertia to be explored. It is shown that changes in the mean plate separation, that is the geometry, and the level of inertia present affect the local hydrodynamic flow structure in the form of kinematically and inertially induced eddies, respectively. These in turn impact on the local "laminar thermal mixing", and consequently enhance the global heat transfer. Results are reported for a wide range of Peclét, Reynolds and Nusselt numbers with agreement between the two methods of solution, for the case of creeping flow, found to be extremely good. The key flow features that emerge are:(i) For creeping flow and varying Peclét number, the thermal field is asymmetric for all values of the Peclét number other than the limiting conditions of zero and infinity, at which extremes the corresponding thermal field is symmetric. In the limit of infinite Peclét number the eddy becomes a basin of fluid at uniform temperature.(ii) Global heat transfer in the case of creeping flow, expressed in terms of the Nusselt number, for a given Peclét number increases as the mean plate separation decreases, that is as the local kinematically induced eddy structure becomes more pronounced. Preprint submitted to Elsevier 11 December 2008(iii) There exists a subtle inter-play between variations in the mean plate separation and the level of inertia imposed, in that both influence the presence or otherwise of eddies. Starting from a creeping flow condition the introduction of inertia can in addition both enlarge and skew an existing eddy. When this information is condensed to a series of Nusselt number curves the indication is that it should be possible, from a practical standpoint, to find a critical mean plate separation, for a given Peclét number, for which local inertially influenced eddy effects on the global heat transfer are at a minimum.

show abstract

A Description of Eddying Motions and Flow Patterns Using Critical-Point Concepts

Cited by 677 publications

References 14 publications

Structural changes of laminar separation bubbles induced by global linear instability

Structural changes of laminar separation bubbles induced by global linear instability

Turbulent flow in a ribbed channel: Flow structures in the vicinity of a rib

The effect of locally induced flow structure on global heat transfer for plane laminar shear flow

Contact Info

Product

Resources

About