Theory of laminar near wake of blunt bodies in hypersonic flow.

Lees, Lester; Reeves, Barry L.

doi:10.2514/3.3316

Cited by 92 publications

(8 citation statements)

References 10 publications

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“…And in this sense, from the point of view of transition development in the boundary layer-free viscous layer-wake system, the free viscous layer is stable. The data obtained correspond to the statements of Reeves & Lees (1965) that in a viscous free layer (up to the throat of a wake) at M > 3 there is laminar flow. The development of disturbances in the wake (regular wake) is shown in figures 7 and 8, where the spectra of energy of fluctuations, measured in the layer close to the critical one (with the maximum level of disturbances), and in the plane of symmetry of the wake y = 0, are presented (at x = 40, 60, 80 mm and 40, 50, 60 mm).…”

Section: Stability Of the Wake At Mach Number M ∞ =supporting

confidence: 82%

Experimental studies of stability and transition in high-speed wakes

Lysenko

1999

J. Fluid Mech.

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The investigation undertaken deals with the development of disturbances in a supersonic wake (free viscous layer and regular wake) behind a flat plate both in its linear and nonlinear stages. The influence of a number of factors (Mach and Reynolds numbers, temperature factor, thickness of the plate, length of its stern) on the wake stability and transition was studied. The development of the artificial disturbances in a wake at Mach number M∞ = 2 was investigated also.It was found that compressibility of the flow (increasing Mach number) stabilizes the wake disturbances – their amplification rates decrease, and the transition point moves away from the model plate. Cooling of the model surface at M∞ ≈ 7 has a destabilizing influence on the development of disturbances in the wake. With increase of unit Reynolds number the beginning of transition in the wake moves forward to a rear critical point. It was confirmed that a distinctive maximum in the spectral distribution of fluctuations appears, corresponding to Strouhal number (based on frequency of this maximum) of 0.3. With the growth of the model thickness the disturbance amplification rates in the wake increase, which results in earlier transition of a laminar wake into turbulent one. With the growth of length of the plate stern, the position of the wake transition moves back accordingly, while the wake stability increases a little (though very unsignificantly). In the nonlinear stage of development of disturbances, the occurrence of a triad of waves, satisfying the resonant correlation of frequencies, and the growth of harmonics are observed. A monochromatic packet of waves of Tollmien–Schlichting type, rather narrow (in the transversal coordinate) in the boundary layers on a flat plate with an opposite wedge at the stern, was found to extend in the wake. The wake disturbances have a complex wave structure. At the Mach number of free flow 2.0, the three-dimensional disturbances are the most unstable in the wake.

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Section: Stability Of the Wake At Mach Number M ∞ =supporting

confidence: 82%

Experimental studies of stability and transition in high-speed wakes

Lysenko

1999

J. Fluid Mech.

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“…One chooses a trial value of M,; the corresponding value of V, is then obtained from (4.8); the boundary conditions for (4.6) are split between 7 = 0 and 7 = 03. One finds that, for each trial initial value of fq(0) or x, t Reeves & Lees (1965, p. 2094, state that the only similar solution for B compressible free shear layer is for adiabatic flow, in which case the Cohen-Reshotko (1956) equations for non-adiabatic flow reduce to (4.6) above.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Equation (3.9) is more general: it applies to adiabatic and non-adiabatic flows of arbitrary Prandtl number, and is far simpler than the equivalent expression that emerges from the approximate integral techniques (e.g. compare with equation (3.6) in Reeves & Lees 1965).…”

Section: (I) the Pressure-area Relationmentioning

confidence: 99%

“…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%

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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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“…The external flow above the rear stagnation point is not parallel to the axis, and undergoes further compression beyond this point. Reeves and Lees (18) have established that the length over which recompression takes place, and hence the amount of departure from isentropic behaviour, is primarily a function of the free shear layer thickness at the start of recompression. With increasing Re, the efficiency of recompression increases, leading to a higher base pressure, an effect just the opposite of that arising from conservation of angular momentum in the recirculation region.…”

Section: Reynolds Number Effectsmentioning

confidence: 99%

A Survey of Hypersonic Near Wake Studies

Crane

1969

Aeronaut. j.

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The complicated time-dependent flow in the wake of a blunt based body at low speeds is a well known phenomenon, but drastic changes in the wake structure occur as speeds increase. Somewhere in the transonic regime, the periodic vortex shedding ceases, and at supersonic Mach numbers a steady flow pattern is established. The boundary layer on the body separates to form a free shear layer, the two layers from opposite sides of the body meeting at the so-called neck of the wake. Downstream of this point, the viscous wake persists for many hundreds of body diameters, and the term “far wake” is usually taken to refer to downstream distances greater than about ten body diameters. The neck of a hypersonic wake occurs typically one or two diameters from the base, and marks the downstream end of what is often known as the base flow region; this region includes a low speed, recirculating flow bounded by the shear layers and the base wall. Between the base and somewhere a few body diameters beyond the neck, the flow field is known as the near wake, and forms the subject of this survey.

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Theory of laminar near wake of blunt bodies in hypersonic flow.

Cited by 92 publications

References 10 publications

Experimental studies of stability and transition in high-speed wakes

Experimental studies of stability and transition in high-speed wakes

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

A Survey of Hypersonic Near Wake Studies

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