A simple exact solution of the Prandtl boundary layer equations containing a point of separation

Liu, Ching Shi; Wan, Yieh-Hei

doi:10.1007/bf00282331

Cited by 9 publications

(8 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Subsequently, by using Lagrangian coordinates, Van Dommelen (1981) and Van Dommelen & Shen (1982) overcame the computational difficulties seen earlier in the Eulerian frame. Analytic results show, however, that separation in the boundary layer equations has no direct connection with velocity singularities (Liu & Wan 1985). Furthermore, these methods are inapplicable to physical two-dimensional Navier-Stokes flows, which do not exhibit singularities.…”

Section: Prior Work On Flow Separationmentioning

confidence: 99%

“…The first category views separation as the appearance of a singularity in the boundary layer equation (Sears & Telionis 1971, 1975. As examples of both separation without such singularities and singularities without separation are known (Liu & Wan 1985), this view practically associates separation with one's inability to solve the boundary layer equations accurately. The second category views separation as ejection of material from the boundary due to the presence of wall-based non-hyperbolic invariant manifolds in the Lagrangian dynamics (Haller 2004).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact theory of material spike formation in flow separation

2018

View full text Add to dashboard Cite

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. Based on the exact curvature evolution of near-wall material lines, our theory identifies both fixed and moving flow separation, is effective also over short time intervals, and admits a rigorous instantaneous limit. As a byproduct, we derive explicit formulae for the evolution of material line curvature and the curvature rate for general compressible flows. The material backbone that we identify acts first as the precursor and later as the centrepiece of unsteady Lagrangian flow separation. We also discover a previously undetected spiking point where the backbone of separation connects to the boundary, and derive wall-based analytical formulae for its location. Finally, our theory explains the perception of off-wall separation in unsteady flows and provides conditions under which such a perception is justified. We illustrate our results on several analytical and experimental flows.

show abstract

Section: Prior Work On Flow Separationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact theory of material spike formation in flow separation

2018

View full text Add to dashboard Cite

show abstract

“…Peridier 1995;Cassel, Smith & Walker 1996;Degani, Walker & Smith 1998), and formal asymptotic expansions are available for Van Dommelen's singularity in the boundary-layer equations (Cowley 1983;. Analytic results show, however, that separation in the boundary-layer equations has no direct connection with velocity singularities (Liu & Wan 1985).…”

Section: Prior Work On Unsteady Separationmentioning

confidence: 99%

Exact theory of unsteady separation for two-dimensional flows

2004

View full text Add to dashboard Cite

We use a dynamical systems approach to extend Prandtl's steady separation criterion to two-dimensional unsteady flows with no-slip boundaries. Viewing separation profiles as non-hyperbolic unstable manifolds in the Lagrangian frame, we obtain explicit Eulerian formulae for the location of flow separation and reattachment on fixed and moving boundaries. We also derive high-order approximations for the unsteady separation profile in the vicinity of the boundary. Our criteria and formulae only use the derivatives of the velocity field along the boundary, and hence are of use in monitoring and controlling separation. In particular, we predict unsteady flow separation points and separation angles from distributed pressure and skin-friction measurements along the wall. As an example, we predict and verify separation points and separation profiles in variants of a two-dimensional oscillating separation-bubble flow.

show abstract

“…As an alternative, Van Dommelen 5 and Van Dommelen and Shen 7 proposed that separation takes place at singularities in the solution of the boundary layer equations. Analytic results show, however, that separation in the boundary layer equations has no direct connection with velocity singularities 8 . In addition, physical velocity fields display no singularities, making Van Dommelen's principle inapplicable to Navier-Stokes flows.…”

Section: Introductionmentioning

confidence: 95%

Experimental Validation of the Kinematic Theory of Unsteady Separation

Peacock

Coral

Haller

2005

35th AIAA Fluid Dynamics Conference and Exhibit

View full text Add to dashboard Cite

We present a study of a new kinematic theory of unsteady separation. The approach allows for the determination of both the location and orientation of separation in a twodimensional unsteady fluid flow based solely upon surface shear-stress and pressure measurements. The experimental results obtained for a rotor-oscillator flow are compared with complementary numerical simulations. It is clearly identified that in both periodic and certain aperiodic unsteady fluid flows, separation does not occur at a point of instantaneous zero skin-friction, but rather at a point where the time-averaged skin-friction is zero.

show abstract

A simple exact solution of the Prandtl boundary layer equations containing a point of separation

Cited by 9 publications

References 13 publications

Exact theory of material spike formation in flow separation

Exact theory of material spike formation in flow separation

Exact theory of unsteady separation for two-dimensional flows

Experimental Validation of the Kinematic Theory of Unsteady Separation

Contact Info

Product

Resources

About