Two-dimensional Wake Research Articles

Deflection of a two-dimensional natural convection wake due to the presence of a vertical surface in close proximity

The interaction between a freely rising thermal plume and an unheated vertical surface in its neighbourhood has been investigated. The underlying transport mechanisms are of interest from a fundamental standpoint, as well as in a variety of practical problems, such as the cooling of electronic equipment and room fires. A detailed numerical and experimental study of the flow is carried out. The temperature and velocity gradients are expected to be large, particularly near the thermal source. Also, any constraints imposed on the entrainment into the flow in the vicinity of the source are expected to significantly affect the nature of the flow and the interaction. These considerations make it imperative to solve the full governing equations in the interaction region. These equations are solved numerically by finite-difference methods, employing the vorticity-stream function formulation. The important physical variables in the problem are the total thermal energy input by the source, the size of the source, and the distance of the source from the vertical wall which is taken as adiabatic or isothermal in the computation. The flow is found to be strongly deflected towards the vertical surface for the parametric ranges considered. As expected, the diffusion effects in the main flow direction are found to decay downstream and the flow to gradually approach the characteristics of a wall plume resulting from a concentrated line heat source with the same total heat input. Thus, the axial diffusion terms may be neglected far downstream, allowing the flow there to be approximated as a boundary, layer, with the full equations being solved in the interaction region. Finally, an experimental investigation is carried out to characterize the nature of the interaction. The flow is visualized by means of a shadowgraph and the temperature field is measured in the interaction region, downstream of the source. Numerical predictions agree with the experimental results, lending support to the numerical model for this interaction.

On the large-scale structure of the turbulent wake of a flat plate

A simple heat-tagging technique was used to isolate and analyze the large-scale coherent structures present in the two-dimensional wake of a flat plate. The results indicate the presence of these coherent structures even at 250 momentum thicknesses downstream of the trailing edge. These structures have a vortexlike topology and carry a significant amount of the total shear stress. The present results for the flat-plate wake seem to be in general agreement with those that have been obtained in cylinder wakes by other contemporary investigators using more complex techniques of eduction and signal enhancement.

Modal decomposition of velocity signals in a plane, turbulent wake

The Orr-Sommerfeld equation admits two solution modes for the two-dimensional plane wake. These are the sinuous mode with antisymmetric streamwise fluctuations and the varicose mode with symmetric streamwise fluctuations. The varicose mode is often ignored because its amplification rates are considerably less than those of the sinuous mode. An experimental investigation of the varicose mode in a two-dimensional turbulent wake was undertaken to determine if this mode of instability agrees as well with linear stability theory, as did the sinuous mode in previous experiments (Wygnanski, Champagne & Marasli 1986). The experiments demonstrated that, although it is possible to generate a nearly pure symmetric disturbance wave, it is very difficult to do as the flow is very sensitive to the slightest asymmetries which might be present in the experiments. These asymmetries are preferentially amplified, resulting in the eventual distortion of an initially prominent symmetric wave. It was therefore necessary to decompose phase-averaged measurements of the streamwise component of the velocity fluctuations into their symmetric and antisymmetric parts, and the results were compared with the appropriate theoretical eigenfunctions from linear stability theory. The lateral distribution of the amplitude and the phase of each mode agree reasonably well with their theoretical counterparts from the Orr-Sommerfeld equation. Slowly diverging linear theory predicts the streamwise variation of the sinuous mode quite well, but fails to do so for the varicose mode. An eddy-viscosity model, coupled with the slowly diverging linear equations, predicts the streamwise variation of both modes reasonably well and describes the transverse distributions of the perturbation amplitudes for both modes, but it fails to predict the distribution of phase for the varicose mode.

Local structure of turbulence in free plows with strong intermittency

The results of an experimental verification of the theory of locally homogeneous turbulence in a mixing layer, a boundary layer, two-dimensional and axisymmetric wakes and, moreover, in the three-dimensional wake of a cylinder of finite length are presented. Since the characteristic dimensions of most of the flows investigated were very large (integral scales of turbulence of up to 1 m), at very large Reynolds numbers high resolution was achieved. The measurements showed that the quantities C and ν characterizing the inertial interval of the turbulence spectrum are not universal constants, as previously assumed, and in the flows in question, irrespective of their type, are uniquely determined by the intermittency factor.

An experiment on the randomization process in the laminar-turbulent transition of a two-dimensional wake

An experiment on the randomization process in the laminar-turbulent transition of a two-dimensional wake

A reversed-flow singularity in interacting boundary layers

It is proposed that a singularity can occur in interacting boundary layers when reversed flow is present. The theoretical breakdown/singularity takes place in general at a critical point between separation and reattachment and it involves viscous-inviscid interaction between the sublayers that develop on either side of the critical point, because of a streamfunction behaviour like normal distance to the powerKnear the wall and possibly in mid-eddy. Moreover, the breakdown is for a value of the controlling parameter not much beyond the value that first produces separation. A study of the acceptableKrange tends to suggest that the singularity arises either for the valueK= 3/2, corresponding to the local pressure gradient and skin friction being singular like streamwise distance to the powers -3/5 and -1/5 respectively, subject to logarithmic modifications. or, more likely, for the limit valueK= 1, which is associated with a discontinuity appearing in the pressure and velocity profile. Comparisons with interactive-boundary-layer and Navier-Stokes computations seem fairly supportive. The occurrence of the singularity offers an explanation for the appearance of a pronounced second minimum in numerous computed skin-friction plots, the numerical difficulties encountered in all reversed-flow computations, and the start of airfoil stall. The theory of the breakdown (which is modified for unsteady motions in an allied paper) also has widespread application, being relevant toallthe interactive separating flows known to date, including internal and external two-dimensional or three-dimensional boundary layers and wakes.

Interaction of Two-Dimensional Wakes

First Page

Modulational instability of plane waves in a two-dimensional jet and wake

The modulational instability problem is reformulated by the amplitude expansion method. A generalized version of the Stewartson-Stuart equation is derived, which is applicable to any supercritical state as long as the amplitude of the disturbance is small. The modulational instability of plane waves in a two-dimensional jet and wake is investigated on the basis of this equation, and it is found that the plane waves are stable to side-band disturbances in supercritical states except in the close neighbourhood of the critical state.

The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers

The linear parallel and incompressible stability of a family of bluff-body wake profiles is studied at Reynolds numbers close to the onset of Kármán vortex shedding. The family of mean flow profiles allows for the variation of the wake depth as well as for a variable ratio of wake width to mixing layer thickness. The absolute or convective nature of the sinuous instability is determined as a function of the profile parameters and Reynolds number. A comparison of this survey with experimental data shows that in bluff-body near wakes a region of local absolute instability begins to form at a Reynolds number of approximately one-half the critical value for Kármán vortex shedding. Hence, at the onset of the global response (Kármán vortex shedding), a substantial region of local absolute instability already exists in the wake. This confirms the qualitative model prediction of Chomaz, Huerre, and Redekopp [submitted to Phys. Rev. Lett.] and also shows that the prediction of vortex shedding frequencies, when based on local stability properties alone, is somewhat arbitrary even at the critical Reynolds number.

A computational model for a symmetric turbulent wake

The study of wakes has many engineering applications. A wake is present behind any object placed in a fluid flow. The wake structure affects the pressure distribution on the object creating the wake. A wake is characterized by high turbulent intensities and mean velocity gradients in the lateral direction. The mathematical modeling of a general three-dimensional wake is very complicated. Work is therefore initiated by modeling a two-dimensional symmetric turbulent wake behind a flat plate. Another reason for choosing this simple flow situation is that very good quality experimental data can be produced for this simple flow. The results from the computational model and comparison with experimental data is the topic of this paper.

Curvature and pressure-gradient effects on a small-defect wake

A fully developed two-dimensional turbulent wake was deflected by an airfoil-like thin plate placed at small angles in the external flow. The response of the mean-flow and turbulence properties of the wake to the ‘mild’ pressure gradient and the ‘mild’ streamline curvature caused by the deflection is studied. Owing to the small defect velocity, the extra strain rates are large compared with the main shear strain and the Reynolds stresses are strongly influenced by both the pressure gradient and the streamline curvature. The defect velocity relative to an appropriately chosen ‘potential-flow velocity’, and the mean vorticity, however, are not as strongly influenced by the curvature. Changes in the magnitudes of the Reynolds-stress components are much larger than would be caused by the simple rotation of coordinates aligned with the wake path. Most turbulence-model parameters are influenced significantly, while some pure turbulence parameters, such as the Taylor microscale, are relatively uninfluenced. The rapid and lagged responses are apparent and the terms in the transport equation for turbulent kinetic energy indicate that the response of the production terms is almost instantaneous, while the diffusion and dissipation terms are delayed.

Development of pseudo-two-dimensional turbulent wakes

Pseudo-two-dimensional wakes are generated by introducing spanwise cellular structures in the otherwise plane turbulent wake by means of the castellated blunt trailing edges of different configurations. The transverse growths of these coflowing cellular wakes are found to be independent of each other without any noticeable spanwise interaction. This wake growth is examined in the light of the plane equilibrium wake analysis. Though these wakes are not found to be exactly self-similar, their growth shows a nonmonotonous approach toward the asymptotic state appropriate to that of a plane wake. The dye emission in the wakes illustrated a coherent vortical structure in the transverse plane, similar to that of the usual two-dimensional wake, in spite of the initial spanwise irregularities.

Structure of random velocity fluctuations in a two-dimensional vortex-street wake.

This paper describes experimentall the structure of random components of the velocity fluctuations in the vortex-street wake of a thin normal plate at a Reynolds number of 23 OOO. Measurements were made by a phase-averaging technique at positions eight heights downstream of the plate. The random components were defined as the corresponding instantaneous velocities subtracted by their phase-averaged values, viz. the periodic components. The random components were decomposed into several narrow-band frequency components, whose contributions to the Reynolds shearing stress are found to generally attain a maximum at saddles associated with the periodic components. Moreover the Reynolds shearing stress is dominated by the low-frequency components whose longitudinal length scale is greater than that of the periodic components. These facts raise a doubt as to the well·documented idea that most of Reynolds shearing stress is produced by the vortex stretching near the saddles. The low-frequency random components may possibly be produced by a modulation of the shape, strength and position of each realization of the periodic components.

Full-potential circular wake solution of a twisted rotor blade in hover

A solution for transonic flow past a twisted rotor blade in hover is obtained using a modified version of the full-potential code ROT22 and a circular wake. The flow is also evaluated for a fixed-wing-type straight wake. The solutions for the straight wake and circular wake, and the circular wake and a two-dimensional wake are compared. The data reveal that the circular wake and the general two-dimensional wake solutions have similar characteristics.

Large-scale structures visualization in a high Reynolds number, turbulent flat-plate wake at supersonic speed

A visual study is performed in a supersonic, two-dimensional wake; the high value of the Reynolds number ensures that the wake is turbulent from the trailing edge. The flow is seeded by fluid vaporization in one boundary layer upstream of the trailing edge; a light sheet is generated by a Q-switched, high energy ruby laser. The set of photographs taken from the trailing edge up to the far wake is then processed after digitization of the pictures. A progressive contamination of the lower part of the wake by the fluid initially present in the upper part can be observed. In the far wake region, well organized large scale structures can be visualized. Statistics are performed and the results are compared with previous hot-wire measurements and discussed in terms of downstream wake behaviour.

Spanwise Mixing in Multistage Axial Flow Compressors: Part I—Experimental Investigation

Spanwise mixing has been shown to be an essential feature of multistage compressor aerodynamics. The cause of spanwise mixing in multistage axial flow compressors has been investigated directly by using an ethylene tracer gas technique in two low-speed, four-stage machines. The results show that the dominant mechanism is that of turbulent type diffusion and not the radial convection of flow properties as has been previously suggested. The mixing was also found to be substantially uniform in magnitude all the way across the span with levels similar to those found in two-dimensional turbulent wakes.

Spatial Stability of a Reactive Wake

Abstract The spatial stability of a two-dimensional wake undergoing finite-rate kinetics is studied for both neutral and amplified antisymmetric disturbances. For inviscid flows, a gen-eralized stability equation is derived that reduces to the classical inviscid stability equation for non-reactive flows. Numerical calculations are presented for both non-reactive and reactive wakes and, for no chemical reactions, excellent agreement with calculations by Lees and Gold 1964) is obtained. For reactive flows, the neutral phase velocity is shown to be a function of both the free stream Mach number and the wake centerline temperature excess, in contrast to on-reactive flows, where it is independent of Mach number. The reactive stability problem is hown to be quite different from the non-reactive stability problem for both neutral and amplified isturbances.

The Weakly Nonlinear Stability of the Two-Dimensional Jet and Wake

The nonlinear stability of the two-dimensional jet and wake in slightly supercritical states is investigated by making use of the weakly nonlinear theory. Accurate values of the coefficients in the Stewartson-Stuart equation are calculated numerically. Both flows are shown to have supercritical equilibrium states. The side-band instability of the equilibrium solutions in the form of plane wave is examined, and they are shown to be unstable. But in numerical solution simulating an access to the equilibrium from smoothly localized initial values, any instability and chaotic behaviour have not been detected.

The dispersion of velocity fluctuation in a two-dimensional vortex wake.

The dispersion of velocity fluctuation in a two-dimensional vortex wake.

Errata: "The Two-Dimensional Laminar Wake with Initial Asymmetry"

Errata: "The Two-Dimensional Laminar Wake with Initial Asymmetry"