Shock regularization in dense gases by viscous–inviscid interactions

Kluwick, A.; Meyer, Georg

doi:10.1017/s0022112009992618

Cited by 14 publications

(24 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The shock layer problem for fluids with embedded negative Γ regions has been treated by Cramer and Crickenberger [8]. Lighthill's [41] work for shocks of small but finite amplitude was generalized by Cramer and Kluwick [7], Cramer and Crickenberger [8], while the structure of weak shocks in confined geometries was elucidated by Kluwick and Gittler [26], Kluwick, Braun and Gittler [27], Kluwick and Meyer [32,33].…”

Section: Discussionmentioning

confidence: 99%

“…The wave equation (37) is embedded in a boundary layer problem which provides a second relationship between p and the perturbation displacement thickness − A and closes the flow description, Gittler and Kluwick [12], Kluwick and Gittler [26], Kluwick, Braun and Gittler [27], Kluwick and Meyer [32,33]. We thus conclude that the physical mechanism for the formation of pseudo-shocks reflects a subtle interplay of disturbances propagating upstream inside the wall layers which are slowly convected downstream in the core region where the flow is nearly sonic.…”

Section: Shock Structurementioning

confidence: 99%

See 1 more Smart Citation

Shock discontinuities: from classical to non-classical shocks

Kluwick

2017

Acta Mech

View full text Add to dashboard Cite

The possibility of shocks was first suggested by Stokes in 1848, but no consistent theory emerged for another almost 30 years. Indeed, severe criticism by Lord Kelvin and Lord Rayleigh led him to finally discard this idea. In the meantime, algebraic shock conditions had been derived by Rankine and Hugoniot, and their names have come to be associated with the shock conditions generally. As Thompson (Compressiblefluid dynamics, McGraw-Hill, New York, 1972) concludes, "Stokes's claim to recognition for his discovery has been diverted by circumstance." Starting with a brief discussion of these early developments, the present review paper will then concentrate on the important question of how to select from all formally possible solutions of the Rankine-Hugoniot jump relations those which are physically realizable solutions. This is at the core of the so-called admissibility problem. Of course, a necessary condition is provided by the second law of thermodynamics which states that the entropy must not decrease during adiabatic changes of state. For perfect gases, this requirement is also a sufficient condition to rule out "impossible" shocks. For fluids with an arbitrary equation of state and/or situations where in addition to thermoviscous effects, dispersive effects also come into play this is not the case in general. The selection of physically admissible solutions is then found to be a more delicate matter and may result in new types of shocks which differ distinctively from their classical counterparts and, therefore, are termed non-classical shocks.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Shock Structurementioning

confidence: 99%

Shock discontinuities: from classical to non-classical shocks

Kluwick

2017

Acta Mech

View full text Add to dashboard Cite

show abstract

“…Because the channel is assumed to be symmetric with respect to its axis, it is sufficient to consider the lower half of the configuration. For large values of the Reynolds number considered here the local interaction process taking place is found to be given by the interplay of three regions (or decks) exhibiting significantly different flow behaviour and, as in the case of strictly two-dimensional flow [2,3], the relevant perturbation parameter is governed by…”

Section: Problem Formulationmentioning

confidence: 91%

“…Consequently, the stage at which strong interaction between predominantly inviscid and viscous flow regions comes into play can be identified by inspection analysis based on the triple-deck concept, which also provides the relevant geometrical scalings as well as the magnitude of the associated perturbations of the various field quantities. An interesting example is provided by flows through slender channels that were first investigated by Kluwick & Bodonyi [1] assuming supersonic conditions of perfect gases, whereas transonic effects including more general gas behaviour were also studied later [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Triple-deck analysis of transonic high Reynolds number flow through slender channels

Kluwick

Kornfeld

2014

Phil. Trans. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

“…Under supersonic flow conditions a first mathematical explanation for this effect was given by Lighthill [5]. For the two dimensional subsonic case Kluwick and Meyer [6] showed, that there is strictly no upstream influence. In contrast to these results one finds an upstream influence in the three dimensional case also under subsonic flow conditions.…”

mentioning

confidence: 99%

Local Interaction Theory for Laminar Transonic Flows in Slender Channels

Kluwick

Kornfeld

2009

Proc Appl Math and Mech

View full text Add to dashboard Cite

Transonic flows through channels so narrow that the classical boundary layer approach fails are considered. As a consequence the properties of the inviscid core and the viscosity dominated boundary layer region can no longer be determined in subsequent steps but have to be calculated simultaneously. The resulting viscous inviscid interaction problem for weakly three dimensional laminar flows is formulated for perfect gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes planar in the leading order approximation. Representative solutions for subsonic as well as for supersonic flows disturbed by three dimensional surface mounted obstacles will be presented. In the present paper viscous inviscid interactions of steady weakly three dimensional transonic flows in narrow channels are considered which are triggered, for example, by a shallow deformation of the channel walls. Using asymptotic analysis for large Reynolds number Re =ũ rL /ν 1 Kluwick and Gittler, assuming two dimensional steady flows of a perfect gas, showed that a consistent interaction theory can be formulated in which the flow inside the inviscid core region is almost one-dimensional, [2]. The former theory can be extended to the weakly three dimensional case if the heightsH andh of the channel and the surface mounted obstacle are of orders 3L and 7L and if the length ∆ X and width ∆ Z of the obstacle are of orders 3L and 2L with = Re −1/12 . Hereũ r ,L andν denote the flow velocity in the core region just upstream of the local interaction region, a characteristic length associated with the unperturbed boundary layer adjacent to the channel wall and a reference value of the kinematic viscosity. It turns out, that the flow in the core region is, in contrast to the two dimensional case, almost planar.The interaction region exhibits a triple deck structure. As in the classical triple deck theory, e.g. see [3], the role of the main deck is to transfer the displacement effects excerted by the lower deck unchanged to the upper deck and to transfer the resulting pressure disturbances again unchanged back to the lower deck. Here, the fluid motion is governed by a weakly three dimensional and incompressible form of the boundary layer equationswhere (X, Y, Z), (U, V, W ) and P denote Cartesian coordinates parallel to the free stream direction, normal to the channel wall and lateral to the free stream direction, the corresponding velocity components and the pressure. All quantities are suitable scaled. The boundary conditions include the no slip condition on the channel walls, the requirement that the unperturbed velocity profile is recovered in the limit X → −∞ and a matching condition between the lower and main deck for large Ywhere − A(X, Z) denotes the perturbation of the displacement thickness caused by the interaction process. The flow in the upper deck is a quasi planar flow weakly perturbed by the boundary layer displacement. As a result, pressure disturbances resulting from the bounda...

show abstract

Shock regularization in dense gases by viscous–inviscid interactions

Cited by 14 publications

References 35 publications

Shock discontinuities: from classical to non-classical shocks

Shock discontinuities: from classical to non-classical shocks

Triple-deck analysis of transonic high Reynolds number flow through slender channels

Local Interaction Theory for Laminar Transonic Flows in Slender Channels

Contact Info

Product

Resources

About