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.

Numerical analysis of bluff body wakes under periodic open-loop control

2013 ◽  
Vol 739 ◽  
pp. 94-123 ◽  
Author(s):  
Derwin J. Parkin ◽  
M. C. Thompson ◽  
J. Sheridan
Keyword(s):  
Strouhal Number ◽  
Cross Section ◽  
Vortex Shedding ◽  
Open Loop ◽  
Wake Flow ◽  
Dynamic Mode ◽  
Two Dimensional ◽  
Near Wake ◽  
Recirculation Bubble ◽  
Number Range

AbstractLarge eddy simulations at$Re= 23\hspace{0.167em} 000$are used to investigate the drag on a two-dimensional elongated cylinder caused by rear-edge periodic actuation, with particular focus on an optimum open-loop configuration. The 3.64 (length/thickness) aspect-ratio cylinder has a rectangular cross-section with rounded leading corners, representing the two-dimensional cross-section of the now genericAhmed-body geometry. The simulations show that the optimum drag reduction occurs in the forcing Strouhal number range of$0. 09\leq S{t}_{act} \leq 0. 135$, which is approximately half of the Strouhal number corresponding to shedding of von Kármán vortices into the wake for the natural case. This result agrees well with recent experiments of Henninget al. (Active Flow Control, vol. 95, 2007, pp. 369–390). A thorough transient wake analysis employing dynamic mode decomposition is conducted for all cases, with special attention paid to the Koopman modes of the wake flow and vortex progression downstream. Two modes are found to coexist in all cases, the superimposition of which recovers the majority of features observed in the flow. Symmetric vortex shedding in the near wake, which effectively extends the mean recirculation bubble, is shown to be the major mechanism in lowering the drag. This is associated with opposite-signed vortices reducing the influence of natural vortex shedding, resulting in an increase in the pressure in the near wake, while the characteristic wake antisymmetry returns further downstream. Lower-frequency actuation is shown to create larger near-wake symmetric vortices, which improves the effectiveness of this process.

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.

The Interaction of Porous Metal Coating With the Near Wake of Bluff Body

2012 ◽  
Author(s):  
Hanru Liu ◽  
Jinjia Wei ◽  
Zhiguo Qu
Keyword(s):  
Circular Cylinder ◽  
Bluff Body ◽  
Porous Metal ◽  
Metal Coating ◽  
Wake Flow ◽  
Navier Stokes ◽  
Aerodynamic Forces ◽  
Near Wake ◽  
Drag Forces ◽  
Flow Induced Noise

The flow around a circular cylinder with porous metal coating (PMC) is numerically investigated based on an approach of unsteady Reynolds Averaged Navier-Stokes (URANS) at subcritical Reynolds number. The model validation is carried out through comparison with some available experimental results in the literatures. It is found that the simulated results in the present work coincide well with the experimental data. The interaction of PMC with the near wake of circular cylinder such as streamline, vorticity and shear stress are studied in detail. The result reveals that PMC has capability of manipulating the wake flow so that the near wake of PMC cylinder is substantially different from that of smooth one. In addition, the fluctuations of aerodynamic forces are mitigated effectively. Varying the thickness of porous metal coating causes various velocity distributions and aerodynamic performance of bluff body. When the thickness is appropriate, the drag forces can be reduced to a certain extent. It is expected that the modification of flow characteristic and aerodynamic forces also produces the suppression of flow-induced noise generated by bluff body. These studies on wake flow and analysis of its relationship to flow-induced noise will be useful to understand the mechanism of controlling bluff body flow-induced noise by using PMC and to optimize the PMC for controlling flow and flow-induced noise.

Suppression of Unsteady Vortex Shedding From a Circular Cylinder by Using a Passive Jet Flow Control Method

2014 ◽  
Author(s):  
Wenli Chen ◽  
Hui Li ◽  
Hui Hu
Keyword(s):  
Circular Cylinder ◽  
Flow Control ◽  
Stagnation Point ◽  
Vortex Shedding ◽  
Control Method ◽  
Aerodynamic Force ◽  
Jet Flow ◽  
Wake Flow ◽  
Cylinder Model ◽  
Rear Stagnation Point

A passive jet flow control method was employed to suppress the unsteady vortex shedding from a circular cylinder at the Reynolds number level of Re = (0.18∼1.1)×105. The passive jet flow control was achieved by blowing jets from the holes near the rear stagnation point of the cylinder, which are connected to the in-take holes located near the front stagnation point through channels embedded inside the cylinder. Since a part of the oncoming flow would inhale into the in-take holes, flow through the embedded channels, and blow out from the holes near the rear stagnation point to suppress/manipulate the alternating vortex shedding in the wake flow behind the circular cylinder, the present passive jet flow control method does not require any additional energy inputs for the flow control. In the present study, the aerodynamic force (i.e., both lift and drag) acting the circular cylinder model with and without the passive jet flow control were compared quantitatively at different Reynolds numbers (i.e., different inlet mean speed). It was found that, in addition to almost eliminating the fluctuations of the lift forces acting on the cylinder, the passive jet flow control method was also found to reduce the mean drag acting on the cylinder model greatly. The instantaneous vorticity distributions and corresponding streamline patterns were used to reveal the underlying physics about why and how the passive jet flow control method can be used to suppress the alternating vortex shedding and induce a symmetrical wake pattern behind the cylinder model.

scholarly journals Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Ali Shokrgozar Abbassi ◽  
Asghar Baradaran Rahimi
Keyword(s):  
Heat Transfer ◽  
Strain Rate ◽  
Flat Plate ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Variable Velocity ◽  
Two Dimensional ◽  
Flow And Heat Transfer ◽  
Energy Equations

General formulation and solution of Navier–Stokes and energy equations are sought in the study of two-dimensional unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration toward main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces an unsteady two-dimensional flow in which the plate moves along z-direction with variable velocity and acceleration in general. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. Velocity and pressure profiles, boundary layer thickness, and surface stress-tensors along with temperature profiles are presented for different examples of impinging fluid strain rate, selected values of plate velocity, and Prandtl number parameter.

scholarly journals Unsteady Reversed Stagnation-Point Flow over a Flat Plate

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Vai Kuong Sin ◽  
Chon Kit Chio
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Asymptotic Solution ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Total Flow ◽  
Navier Stokes Equations

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. Robins and Howarth (1972) stated that this is not true in neglecting the viscous terms within the total flow field. Viscous terms in this analysis are now included, and a similarity solution of two-dimensional reversed stagnation-point flow is investigated by solving the full Navier-Stokes equations.

A Vortex Model of the Darrieus Turbine: An Analytical and Experimental Study

1979 ◽  
Vol 101 (4) ◽  
pp. 500-505 ◽  
Author(s):  
J. H. Strickland ◽  
B. T. Webster ◽  
T. Nguyen
Keyword(s):  
Experimental Study ◽  
Prediction Model ◽  
Vortex Lattice ◽  
Three Dimensional ◽  
Wake Flow ◽  
Two Dimensional ◽  
Lattice Method ◽  
Near Wake ◽  
Vortex Lattice Method ◽  
Vortex Model

An aerodynamic prediction model has been formulated for two- and three-dimensional Darrieus turbines using a vortex lattice method of analysis. Experiments were conducted on a series of two-dimensional rotor configurations in a water tow tank. The agreement between analysis and experiment was in general found to be good. This model should allow one to make accurate predictions of instantaneous aerodynamic blade forces and to characterize the near wake flow behind the rotor.

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