scholarly journals The Unsteady Flow of a Weakly Compressible Fluid in a Thin Porous Layer I: Two-Dimensional Theory

2009 ◽  
Vol 69 (4) ◽  
pp. 1084-1109
Author(s):  
D. J. Needham ◽  
S. Langdon ◽  
G. S. Busswell ◽  
J. P. Gilchrist
Keyword(s):  
Unsteady Flow ◽  
Porous Layer ◽  
Compressible Fluid ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Weakly Compressible ◽  
Layer I

Paper 29: Unsteady Flow Effects Downstream of an Annular Cascade of Self-Excited Blades

1969 ◽  
Vol 184 (7) ◽  
pp. 83-88
Author(s):  
V. G. Nabar
Keyword(s):  
Unsteady Flow ◽  
Boundary Layers ◽  
Large Concentration ◽  
Two Dimensional ◽  
Hot Wire ◽  
Dimensional Theory ◽  
Wall Boundary ◽  
Blade Tip ◽  
Flow Effects ◽  
Annular Cascade

This paper presents a two-dimensional theory for calculating streamwise perturbations in the flow downstream of a cascade of self-excited blades and gives details of hot-wire measurements of unsteadiness downstream of an annular cascade. The theoretical values show little variation from blade to blade, whereas the experiments exhibit a large concentration of perturbations near the hub and a comparatively smaller one near the tip. It is thought that periodic circulation is shed largely from the blade tip and root within the annulus wall boundary layers, in a manner similar to the shedding of steady circulation from the aeroplane wings.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

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