Supersonic separated and reattaching laminar flows. i - general theory and application to adiabatic boundary-layershock-wave interactions

Lees, Lester; Reeves, Barry L.

doi:10.2514/3.2700

Cited by 186 publications

(7 citation statements)

References 14 publications

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“…Further, the viscous shear in the wake becomes increasingly more pronounced at higher speeds. With this physical background, an integral-moment method, derived by taking integral moments of the boundary-layer equations, has been actively developed in the past decade, notably by Lees and co-workers (Lees & Kubota 1957, Lees Reeves 1964, Reeves & Lees 1965, Grange et al 1967. At present, this is the method that is both rational and useful for engineering problems though various numerical methods have also been adopted.…”

Section: Complqessibility Effectmentioning

confidence: 99%

Cavity and Wake Flows

Wu¹

1972

Annu. Rev. Fluid Mech.

115

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The phenomenon of wake formation behind a body moving through a fluid, and the associated resistance of fluids, must have been one of the oldest experiences of man. From an analytical point of view, it is also one of the most difficult problems in fluid mechanics. Rayleigh, in his 1876 paper, observed that "there is no part of hydrodynamics more perplexing to the student than that which treats of the resistance of fluids." This insight of Rayleigh is so penetrating that the march of time has virtually left no mark on its validity even today, and likely still for some time to come.The first major step concerning the resistance of fluids was made over a century ago when Kirchhoff (1869) introduced an idealized inviscid-flow model with free streamlines (or surfaces of discontinuity) and employed (for steady, plane flows) the ingenious conformal-mapplng technique that had been invented a short time earlier by Helmholtz (1868) for treating twodimensional jets formed by free streamlines. This pioneering work offered an alternative to the classical paradox of D'Alembert (or the absence of resistance) and laid the foundation of the free-streamline theory. We appreciate the profound insight of these celebrated works even more when we consider that their basic idea about wakes and jets, baaed on a construction with surfaces of discontinuity, was formed decades before laminar and turbulent flows were distinguished by Reynolds (1883), and long before the fundamental concepts of boundary-layer theory and flow separation were established by Prandtl (1904a).However, there have been some questions raised in the past, and still today, about the validity of the Kirchhoff flow for the approximate calculation of resistance. Historically there is little doubt that in constructing the flow model Kirchhoff was thinking of the wake in a single-phase fluid, and not at all of the vapor-gas cavity in a liquid; hence the arguments, both for and against the Kirchhoff flow, should be viewed in this light. On this basis, an important observation was made by Sir William Thomson, later Lord Kelvin (see Rayleigh 1876) "that motions involving a surface of separation are unstable" (we infer that instability here includes the viscous effect). Regarding this comment Rayleigh asked "whether the calculations of resistance are materially affected by this circumstance as the pressures experienced must be nearly independent of what happens at some distance in the rear of the obstacle, where the instability would first begin to manifest itself." 243 8025 www.annualreviews.org/aronline Annual Reviews

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Section: Complqessibility Effectmentioning

confidence: 99%

Cavity and Wake Flows

Wu¹

1972

Annu. Rev. Fluid Mech.

115

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“…The very severe adverse pressure gradients of the present experiments provide a stringent test of any theory of compressible turbulent boundary layers. The momentum-integral technique, developed by Todisco & Reeves (1969) from the pioneering work of Lees & Reeves (1964) for laminar flow, seems capable of tackling this problem but further progress requires a detailed knowledge of velocity and temperature profile development in an adverse pressure gradient.…”

Section: Theorymentioning

confidence: 99%

Heat transfer from hypersonic turbulent flow at a wedge compression corner

Coleman

Stollery

1972

J. Fluid Mech.

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“…The integral techniques, first introduced by Crocco & Lees (1952) for adiabatic flow and since elaborated on and extended by a number of investigators (Glick 1962;Lees & Reeves 1964;Reeves & Lees 1965;Webb et al 1965;Go& Webb & Lees 1967;Ai 1967), have shown important qualitative similarities between the over-all behaviour of the one-dimensional and two-dimensional phenomena. I n these theories the viscous region, by virtue of the integral averaging process, is represented as an equivalent one-dimensional flow with dissipation.…”

Section: Introductionmentioning

confidence: 99%

On the two-dimensional viscous counterpart of the one-dimensional sonic throat

Weinbaum

Garvine

1969

J. Fluid Mech.

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An analysis of the full, compressible, non-adiabatic boundary-layer equations is presented to describe the so-called ‘throat’ formed when a two-dimensional viscous layer, interacting with a supersonic inviscid outer stream, is accelerated or decelerated through sonic velocity defined in some mean sense. The basic analysis differs from previous momentum integral theories in that the dynamics of the viscous layer is described by the exact local expressions for the streamwise gradients of the flow variables that obtain from the boundary-layer conservation equations, rather than on streamwise derivatives of integral properties of these equations. The theory is then used to develop an extensive analogy with the classical analysis of the throat in the inviscid quasi one-dimensional streamtube. The theory shows that a single integral constraint exists at the throat, which relates the velocity and temperature profiles in the viscous layer to the motion of the inviscid outer flow. One consequence of this constraint is that, for a one-parameter family of profile shapes, the solution can be started at the throat station by specifying only a single variable, the free stream Reynolds number based on the physical thickness of the viscous layer at the throat station. For the hypersonic near wake, this simplification permits one to obtain an approximate solution for the downstream flow without first solving the detailed motion in the base recirculation region. The paper ends with a discussion of the numerical results for the Stewartson family of wake-like profiles.

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Supersonic separated and reattaching laminar flows. i - general theory and application to adiabatic boundary-layershock-wave interactions

Cited by 186 publications

References 14 publications

Cavity and Wake Flows

Cavity and Wake Flows

Heat transfer from hypersonic turbulent flow at a wedge compression corner

On the two-dimensional viscous counterpart of the one-dimensional sonic throat

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