Rear stagnation point location in a subsonic near-wake

1976 ◽  
Vol 13 (5) ◽  
pp. 319-320 ◽  
Author(s):  
R. A. Merz ◽  
R. H. Page ◽  
C. E. G. Przirembel
Keyword(s):  
Stagnation Point ◽  
Point Location ◽  
Near Wake ◽  
Rear Stagnation Point

On the singular points in the laminar two-dimensional near wake flow field

1968 ◽  
Vol 33 (1) ◽  
pp. 39-63 ◽  
Author(s):  
Sheldon Weinbaum
Keyword(s):  
Stagnation Point ◽  
Series Solution ◽  
Wake Flow ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Near Wake ◽  
Type Series ◽  
Stagnation Points ◽  
Insight Into ◽  
Rear Stagnation Point

It is shown that useful information concerning the flow in the neighbourhood of the various separation and stagnation points in the laminar near wake of a blunt-based two-dimensional wedge can be learned from the locally valid Stokes type series solutions to the incompressible Navier-Stokes vorticity equation derived previously by Dean & Montagnon (1949) and Moffatt (1964). This theory, which is in qualitative agreement with the experiments of Hama (1967) and Donaldson (1967), shows that the flow separates from the base of a blunt-based body and not from its trailing edge. The series solution for the two-dimensional stagnation point is treated in detail and compared with Howarth's (1934) numerical solution in order to study the convergence and conditions for completeness of the Stokes type series solution. Finally, the wake rear stagnation point is examined to provide insight into the problem of wake closure.

Mechanisms in the hypersonic laminar near wake of a blunt body

2018 ◽  
Vol 839 ◽  
pp. 33-75 ◽  
Author(s):  
W. Schuyler Hinman ◽  
Craig T. Johansen
Keyword(s):  
Stagnation Point ◽  
Control Volume ◽  
Empirical Relationship ◽  
Theoretical Framework ◽  
Stagnation Pressure ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Near Wake ◽  
Entropy Transport ◽  
Rear Stagnation Point

A new theoretical framework, based on the analysis of Navier–Stokes solutions for the hypersonic laminar near wake of two-dimensional and axisymmetric blunt bodies, is presented. A semi-empirical relationship is derived between the free-stream Mach and Reynolds numbers and a characteristic wake Reynolds number. A control volume analysis was performed to assess the validity of some common assumptions used in the literature. Analysis of the momentum and vorticity equations is used to assess the dominant mechanisms of momentum transfer along and across the dividing streamline and centreline which enclose the near wake. An observed stagnation pressure gain along the dividing streamline is explained using the entropy transport equation, demonstrating an unbalance between entropy generation due to viscous dissipation and entropy diffusion. The rear-stagnation point flow is analysed using an analogy to a reversed flow jet which allows for the centreline Mach number to be solved. A new viscous–inviscid interaction theory is presented for the reattachment shock formation process for both planar and axisymmetric wakes. Finally, all of the sub-mechanisms are combined into an overall wake mechanism. The resulting equations constitute the first overall theoretical framework of the laminar near-wake mechanism including separation, reattachment, rear-stagnation point flow and dividing streamline stagnation pressure gain for both planar and axisymmetric near wakes. Scaling arguments are presented throughout the work for each of the key sub-mechanisms. Recommendations are made for how experimental and numerical results for the near wake should be presented. The equations and recommendations presented here are then used to perform a detailed disambiguation of laminar capsule studies in the literature.

Oscillatory flow past a circular cylinder in a rotating frame

1997 ◽  
Vol 345 ◽  
pp. 101-131
Author(s):  
M. D. KUNKA ◽  
M. R. FOSTER
Keyword(s):  
Circular Cylinder ◽  
Steady Flow ◽  
Stagnation Point ◽  
Oscillatory Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Temporal Integration ◽  
Oncoming Flow ◽  
Flow Past ◽  
Rear Stagnation Point

Because of the importance of oscillatory components in the oncoming flow at certain oceanic topographic features, we investigate the oscillatory flow past a circular cylinder in an homogeneous rotating fluid. When the oncoming flow is non-reversing, and for relatively low-frequency oscillations, the modifications to the equivalent steady flow arise principally in the ‘quarter layer’ on the surface of the cylinder. An incipient-separation criterion is found as a limitation on the magnitude of the Rossby number, as in the steady-flow case. We present exact solutions for a number of asymptotic cases, at both large frequency and small nonlinearity. We also report numerical solutions of the nonlinear quarter-layer equation for a range of parameters, obtained by a temporal integration. Near the rear stagnation point of the cylinder, we find a generalized velocity ‘plateau’ similar to that of the steady-flow problem, in which all harmonics of the free-stream oscillation may be present. Further, we determine that, for certain initial conditions, the boundary-layer flow develops a finite-time singularity in the neighbourhood of the rear stagnation point.

Evolution and Turbulence Properties of Self-Sustained Transversely Oscillating Flow Induced by Fluidic Oscillator

2007 ◽  
Vol 129 (8) ◽  
pp. 1038-1047 ◽  
Author(s):  
Rong Fung Huang ◽  
Kuo Tong Chang
Keyword(s):  
Stagnation Point ◽  
Vortex Pair ◽  
Transverse Oscillation ◽  
Oscillating Flow ◽  
Near Wake ◽  
Fluidic Oscillator ◽  
Planar Jet ◽  
Oscillation Process ◽  
Gravity Driven ◽  
Flow Evolution

The evolution process and turbulence properties of a transversely oscillating flow induced by a fluidic oscillator are studied in a gravity-driven water tunnel. A planar jet is guided to impinge a specially designed crescent surface of a target blockage that is enclosed in a cavity of a fluidic oscillator. The geometric configuration of the cavity transforms the inherent stability characteristics of the jet from convective instability to absolute instability, so that the jet precedes the persistent back and forth swinging in the cavity. The swinging jet is subsequently directed through two passages and issued alternatively out of the fluidic oscillator. Two short plates are installed near the exits of the alternatively issuing pulsatile jets to deflect the jets toward the central axis. The deflected jets impinge with each other and form a pair of counter-rotating vortices in the near wake of the oscillator with a stagnation point at the impingement point. The stagnation point of the counter-rotating vortex pair moves back and forth transversely because of the phase difference existing between the two issued jets. The merged flow evolving from the counter-rotating vortices formed by the impingement of the two pulsatile jets therefore presents complex behavior of transverse oscillation. The topological models corresponding to the flow evolution are constructed to illustrate the oscillation process of the oscillating flow. Significant momentum dispersion and large turbulence intensity are induced by the transverse oscillation of the merged flow. The statistical turbulence properties show that the Lagrangian integral time and length scales of the turbulence eddies (the fine-scale structure) produced in the oscillating flow are drastically reduced.

An Experimental Study of a Symmetrical Aerofoil with a Rear Suction Slot and a Retractable Flap

1953 ◽  
Vol 57 (514) ◽  
pp. 627-645 ◽  
Author(s):  
D. M. Heughan
Keyword(s):  
Stagnation Point ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Large Change ◽  
Free Fluid ◽  
Stream Velocity ◽  
Suction Velocity ◽  
Suction Slot ◽  
Stable Flow ◽  
Rear Stagnation Point

SummaryExperiments were made on an aerofoil of 25 per cent, thickness with a suction slot at the rear and a flap that could be withdrawn into the slot. The main object of the work was to investigate the effect of withdrawing the flap when all the air in the boundary layer was sucked into the slot. In particular, as a test of the type of anti-gust device proposed by Thwaites, it was required to observe the change of lift that occurred during withdrawal of the flap and a subsequent change of incidence (with the flap still withdrawn).The flow was investigated by the use of smoke and tufts, by pressure plotting on the surface of the aerofoil, and by measurements of total and static pressures in the wake. The effects of varying incidence, flap position, and suction velocity were investigated.It was found that the provision of a flap downstream of the enclosing streamline, so that the rear stagnation point was not in the free fluid, was all important in relation to the behaviour of an aerofoil which had a suction slot at its rounded rear.With the flap extended beyond the enclosing streamline and with the ratio of suction-slot velocity to free stream velocity higher than the theoretical value, a stable flow was obtained within the theoretical incidence range. A favourable pressure gradient was observed in the slot entry and no measureable wake existed downstream of the flap. Smoke filaments, emitted from a tube projecting from the slot slightly beyond the enclosing streamline, travelled far downstream with apparently little diffusion.When the flap was placed so that its trailing edge was inside the enclosing streamline, i.e. so that there was in theory a stagnation point in the free fluid, an instability of a three-dimensional character occurred, with a wide wake and a large drag coefficient. The lift curves were unusual and it was found that movement of the flap caused a large change of lift coefficient. There was no evidence that the lift could be maintained constant, independent of incidence, when the flap was withdrawn into the slot.

Boundary-layer development at a two-dimensional rear stagnation point

1972 ◽  
Vol 56 (1) ◽  
pp. 161-171 ◽  
Author(s):  
A. J. Robins ◽  
J. A. Howarth
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Initial Value ◽  
Boundary Layer Development ◽  
Leading Term ◽  
Layer Development ◽  
Rear Stagnation Point ◽  
Good Agreement

This paper examines the nature of the development of two-dimensional laminar flow of an incompressible fluid at the rear stagnation point on a cylinder which is started impulsively from rest. Proudman & Johnson (1962) first examined this type of flow, andobtainedasimilarity solution of the inviscid form of the equations of motion. This solution describes the nature of the flow at large distances from the surface, for large times after the start of the motion. Here, the flow at the rear stagnation point is examined in greater detail. The solution found by Proudman & Johnson constitutes the leading term in an asymptotic expansion, valid for large times. Further terms in this expansion are now calculated, and the method of matched asymptotic expansions is used to obtain an inner solution describing the flow near the surface. A numerical integration of the full initial-value problem gives good agreement with the analytical solution.

On the differential equation governing the rear stagnation point in magnetohydrodynamics and Goldstein's ‘backward’ boundary layers

1967 ◽  
Vol 63 (4) ◽  
pp. 1327-1330 ◽  
Author(s):  
S. Leibovich
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Stagnation Point ◽  
Boundary Layers ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Stagnation Point Flow ◽  
Special Cases ◽  
Rear Stagnation Point

AbstractExistence and uniqueness proofs for a boundary-value problem associated with a magnetohydrodynamic Falkner–Skan equation are presented. Relevant special cases of the problem herein considered include the magnetohydrodynamic rear stagnation point flow, and the non-magnetic ‘backward boundary layers’ of Goldstein(2).

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