Area rule for the wake behind a three-dimensional body

In three-dimensional flows, the local characteristics of the medium in the wake behind a supersonic body at Reynolds numbers Re 5·10⁴ depend in a complicated manner on the coordinates. However, in a number of cases it is important to know only the parameters of the medium averaged over the transverse section of the wake. For example, for the diagnostics of the plasma of the wake behind a body by means of microwave resonators the electron density averaged over the section is used [1]. The chemiluminescent radia tion of the wake is also obtained in an averaged form [2]. It is therefore worthwhile obtaining the average characteristics of the medium without detailed study of the local parameters. In the present paper, a rule is established that makes it possible to use the results obtained for the far viscous wake behind an axisymmetric body in the case of the wake behind a three-dimensional body that is nearly axisymmetric, the flow conditions being similar. The three-dimensional wake is considered to the distances until it degenerates into an axisymmetric wake.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 148–150, May–June, 1980.We thank G. Yu. Stepanov and É. Z. Apshtein for helpful advice in a discussion of the results.     

Swirling turbulent wake behind a self-propelled body

The development of the swirling turbulent axisymmetric wake of a self-propelled body is modeled numerically. The flow pattern is calculated within the framework of the thin shear layer approach for nonclosed system of the motion and continuity equations. The closed system of equations is written for two different formulations of the closure relations. The numerical solution of the problem is performed with the use of the finite-difference algorithm realised on moving grids. The algorithm is conservative with respect to the laws of conservation of the momentum and the angular momentum. The experimentally measured distributions are used as the initial conditions. Both the models described agree well with the experimental data of Gavrilov N., Demenkov A., Kostomakha V., Chernykh G. (2000), Experimental and numerical modelling of turbulent wake behind self-propelled body, J. Appl. Mech. Tech. Phys., 41 (4), 619–627. It is demonstrated that at the large distances downstream from the body the solution of the problem approaches the self-similar one.     

Laser-sheet flow visualization of the confined wake behind a ring

The flow over a ring model situated axisymmetrically in a circular pipe has been studied by the laser-sheet flow visualization technique. Over 25 rings of different sizes are investigated. The flow characteristics are observed and summarized into six regimes, in terms of the two geometrical parameters G/W and . Here, W is the width of the ring, is the mean diameter of the ring, and G is the gap width between the pipe wall and the outer edge of the ring. It is interesting to point out that vortex-shedding structures produced by a ring model can persist over a considerable distance downstream in three of the six regimes which correspond to different physical processes of shedding.     

Self-similar degeneration of the turbulent wake behind a body towed in a passively stratified medium

A mathematical model of the far turbulent wake behind a towed body in a passively stratified medium, based on the known semi-empirical e-? model of turbulence, is considered. A grouptheoretical analysis of the model is performed. With the help of the method of B-determining equations, the model is reduced to a system of ordinary differential equations, which is solved numerically. The resultant solution is compared with a self-similar solution obtained by direct numerical integration of the differential equations at large distances from the body.     

The wake flow control behind a circular cylinder using ion wind

Active and passive flow control methods have been studied for decades, but there have been only a few studies of flow control methods using ion wind, which is the bulk motion of neutral molecules driven by locally ionized air from a corona discharge. This paper describes an experimental study of ion wind wake control behind a circular cylinder. The experimental conditions consisted of a range of electrohydrodynamic numbers—the ratio of an electrical body force to a fluid inertial force—from 0 to 2 and a range of Reynolds numbers from 4×10³ to 8×10³. Pressure distributions over the cylinder surface were measured and flow visualizations were carried out using a smoke-wire method. The flow visualizations confirmed that ion wind significantly affects the wake structure behind a circular cylinder, and that the pressure drag can be dramatically reduced by superimposing ion wind.List of symbols BR blockage ratio - C _d coefficient of the pressure drag - C _p coefficient of the surface pressure, 2(p–p ₀)/(U ₀ ²) - C _pb coefficient of the base surface pressure, 2(p _b–p ₀)/(U ₀ ²) - D diameter of the cylinder - D _P pressure drag - d _p diameter of particle - E the electric field - F _e Coulombian force (qE) - F _v viscous force - H wire-to-cylinder spacing - I total electric current (A) - L the axial length of cylinder (m) - N _EHD electrohydrodynamic number - p _b base pressure of cylinder at =180° - p ₀ reference static pressure at 10D upstream - q the charge on the particle - R radius of the cylinder - V applied voltage (kV) - U ₀ mean flow velocity (m/s) - ion mobility in air (m²/(s V)) - ₀ permittivity of free space - viscosity of fluid (kg/ms) - density of fluid (kg/m³) - installation angle of a wire electrode (°)     

Structure of wake of a sharp-edged bluff body in a shallow channel flow

The flow field downstream of a bluff body in a typical open channel flow was explored by two-dimensional particle image velocimetry. Measurements are obtained in horizontal planes at the near-bed, mid-depth and near-surface locations downstream of the body up to a streamwise distance of 10D, where D is the width of the body. The dimensionless streamwise defect velocity profile of the wake flow matches well with the data of a previous investigation and does not reflect any dependency on the distance from the bed. However, the nature of development of the recirculation region is found to be different at the three vertical locations. The time-averaged streamline pattern indicates the existence of a unique nodal pattern close to the bed. The variation of the half-width is also found to be affected by the presence of the bed and the free surface. The bed friction arrests the transverse growth of the shear layer, and the free-surface helps to redistribute the turbulent kinetic energy in the streamwise and transverse directions. Swirling strength analysis is carried out to compare the behavior and statistics of the vortex population in the vertical direction. The prevailing magnitude of the swirling strength is found to be different at the three vertical locations. Bed friction assists to dissipate vorticity rapidly, and therefore reduces the probability of appearance of strong vortices close to the bed.     

Turbulization of the wake behind a single roughness element on a blunted body at a hypersonic Mach number

The influence of a cylinder-shaped single roughness element on the laminar–turbulent transition in the presence of an entropy layer is experimentally studied. The experiments are performed on a blunted cone model at the Mach number M = 5. The roughness element is located on the blunted tip of the model. Information about the mean and fluctuating parameters of the boundary layer in the wake behind the roughness element is obtained by using hot-wire anemometry. It is shown that flow turbulization behind the roughness elements occurs at the local Reynolds number calculated on the basis of the roughness element height and equal to 400–500. It is found that the presence of the roughness element exerts a significant effect on the unsteady characteristics of the boundary layer if the roughness element height is smaller than the effective value.     

Flow field in the wake of a bluff body driven through a steady recirculating flow

The wake produced by a bluff body driven through a steady recirculating flow is studied experimentally in a water facility using particle image velocimetry. The bluff body has a rectangular cross section of height, \(H\), and width, \(D\), such that the aspect ratio, AR = H/D, is equal to 3. The motion of the bluff body is uniform and rectilinear, and corresponds to a Reynolds number based on width, Re _D  = 9,600. The recirculating flow is confined within a hemicylindrical enclosure and is generated by planar jets emanating from slots of width, \(h\), such that \(Re_h=500\). Under these conditions, experiments are performed in a closed-loop facility that enables complete optical access to the near-wake. Velocity fields are obtained up to a distance of \(13D\) downstream of the moving body. Data include a selection of phase-averaged velocity fields representative of the wake for a baseline case (no recirculation) and an interaction case (with recirculation). Results indicate that the transient downwash flow typically observed in wakes behind finite bodies of small aspect ratio is significantly perturbed by the recirculating flow. The wake is displaced from the ground plane and exhibits a shorter recirculation zone downstream of the body. In summary, it was found that the interaction between a bluff body wake and a recirculating flow pattern alters profoundly the dynamics of the wake, which has implications on scalar transport in the wake.     

Coherent structure in the turbulent wake behind a circular cylinder

A wake behind a circular cylinder at Reynolds number 850–1700 was visualized by the smoke-wire method. The observations of the How together with the results of quantitative measurements, such as various velocity correlation coefficients, illustrated the formation process of spoon-shaped large eddies in the region 90 ⩽x/d⩽ 230 attained through the deformation and rearrangement of the regular Karman vortices. A spoon vortex was likely to pair with the counterpart on the opposite side of the wake. The large-scale bulges of the turbulent and non-turbulent interface of the wake were shown to correspond to these spoon vortices.These results indicate that some coherent structures are organized by rearrangement and deformation of initially regular vortices in turbulent flow.     

A numerical study of the wake behind a blunt‐trailing‐edged body. Part 2: the topology of the flow

This project focuses on the wake behind a two‐dimensional blunt‐trailing‐edged body. The body has an elliptical nose followed by a straight section that ends in a blunt base. For this geometry, the boundary layer separation points are defined and fixed. This permits a better assessment of the vital influence of the boundary layers upon the wake. It is hoped that the study of this special geometry will contribute to a better understanding of the wake flow. The main aim of this article is to study the topology of the wake by means of direct numerical simulation (DNS). The idea is to mimic some experimental work techniques. In an experiment, by means of proper synchronization, one is able to arrive at the mean‐in‐the‐phase fields. In the present work, similar data are obtained through the use of numerical tools. The topology of the wake flow in terms of the movement of the coherent structures, fields of Reynolds stresses, position of saddles and centers, is obtained for certain values of the body's aspect ratio. A comparison with the circular cylinder experimental data is also provided. An important result is the finding of some specific stress distributions around the main structures. The stress level lines are a hint of where the energy transfer of the mean flow to the turbulence is more intense. Copyright © 2011 John Wiley & Sons, Ltd.     

Criteria of negative wake generation behind a cylinder

It was demonstrated by simulation in our previous study that both the normal stress and its gradient are responsible for the negative wake generation (overshoot in the axial velocity) and streamline shifting. Extensional properties of the fluids dominate the generation of the negative wake, while other factors strengthen or weaken the formation of velocity overshoot. In this study, the criteria for the negative wake generation are discussed in detail for various fluid models, including the PTT, the FENE-CR, the FENE-P, and the Giesekus models. With the FENE-CR fluid, it is easier to generate negative wake than with the FENE-P fluid. This confirms that the constant shear viscosity FENE-CR fluid enhances the velocity overshoot, and that the shear-thinning viscosity FENE-P fluid delays the negative wake generation. The Giesekus fluid has a similar behaviour to the PTT fluid with regarding to the critical conditions of negative wake generation when appropriate fluid parameters are selected. The mechanism of wall proximity in enhancing the negative wake generation is also demonstrated with the analysis for the first time.