Relaxation oscillations in the turbulent near wake

The method of [2] is used to examine the interaction of a shock or an expansion wave in the outer plane supersonic stream with a turbulent near wake. It is shown that the flow in the disturbed near wake may be two-valued, and for fixed conditions in the outer stream quasisteady transitional flows between these two steady states are possible. Under the influence of some external disturbing mechanism (believed to be turbulent pulsations of the large-vortex type) these quasi-steady flows become relaxation oscillations which lead to the experimentally observed base-pressure oscillations.The theoretical conclusions are confirmed by an experimental study of the base-pressure fluctuations which develop in a two-dimensional expansion-deflection nozzle with interaction of the off-design shock with the near wake.In conclusion the author wishes to thank G. G. Chernyi and G. N. Abramovich for helpful discussions of the study and L. V. Kapranova, T. S. Soboleva, and Z. A. Donskova for assistance in performing the calculations.     

An experimental study on unsteady turbulent near wake of a rectangular cylinder in channel flow

 Unsteady turbulent near wake of a rectangular cylinder in channel flow has been studied experimentally with a laser Doppler velocimetry (LDV). The time-averaged and phase-averaged statistics were measured for the cylinders having various width-to-height ratios, b/h. It is shown that the turbulent intensities on the centerline of the channel have their maxima near the rear stagnation point of a recirculation region. The contours of coherent vorticity and streamline reproduce clearly the shed vortices from the cylinder observed by the flow visualization. The characteristics of the flow field, which depends on b/h, are discussed and the significant contribution of the coherent structure to the flow field is clarified. Moreover, the turbulent kinetic energy budget has been examined. Received: 19 January 1998/Accepted: 21 July 1998     

The velocity field of the turbulent very near wake of a circular cylinder

Hot-wire measurements were conducted in the very near wake (x/d10) of a circular cylinder at a Reynolds number based on cylinder diameter, Re _d of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.This study has been funded by the NASA-Ames University Consortium Cooperative Agreement, NCC2-5003. We wish to thank Patrick Beaudan for providing us with the LES results for comparison and Parviz Moin for his interest in and encouragement of this experiment to provide validation data for the LES. We also wish to thank loseph Murray for his help with the look-up-table data reduction program.     

Interaction of a turbulent wake with the outer flow

The integral methods of boundary-layer theory are used to examine the interaction of a turbulent wake with the outer flow for the example of planar flow.In contrast with the known Crocco-Lees theory [1], the turbulent layer in the gas is described with the aid of an appropriate family of velocity profiles rather than by means of a Dorodnitsyn-type transformation of the incompressible turbulent layer. The selection of the simplest among the possible systems of first order interaction equations is justified; this system reduces to a single differential equation and an estimate is given of the influence of the arbitrariness in the equation selection on the final results.The hydrodynamic meaning of the singular and nonsingular integral curves and the singular point of the interaction equation is clarified on the basis of an examination of the interaction of compression and rarefaction waves in the outer supersonic stream with the wake. The effect of blowing (suction) and the initial boundary layer on the base pressure and the supersonic interaction flow as a whole is examined on the basis of the integral conditions for the splicing of the interaction flow with the isobaric mixing flow behind the corner. It is shown that, with proper selection of the single constant in the turbulent viscosity formula, the computational results are in satisfactory agreement with experiment.In conclusion, the authors wish to thank G. G. Chernyi for helpful discussions of the study, and L. V. Kapranova and Z. A. Donskova for assistance in the calculations.     

Detached flow over a step with the formation of a turbulent wake

A method of calculating the plane turbulent layer behind a step interacting with a free potential flow of incompressible fluid is developed. The method includes consideration of the initial boundary layer and injection (or suction) in the isobaric bottom region. Friction on the wall behind the step is neglected, which corresponds to symmetric quasisteady flow behind the straight edge of a plate. The inviscid flow is represented by the Keldysh-Sedov integral equations; the flow in the wake with a one-parameter velocity profile is represented by three first-order differential equations—the equations of momentum for the wake and motion along its axis and the equation of interaction (through the displacement thickness) of the viscous flow with the external potential flow. The turbulent friction in the wake is given, accurate to the single empirical constant, by the Prandtl equation. The different flow regions — on the plate behind the step, the isobaric bottom region, and the wake region — are joined with the aid of the quasi-one-dimensional momentum equation for viscous flow. The momentum equation for the flow as a whole serves as the closure condition. The obtained integrodifferential system of equations is approximated by a system of nonlinear finite-difference equations, whose solution is obtained on a computer by minimization of the sum of the squares of the discrepancies. The results of the calculations agree satisfactorily with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1977.We are grateful to V. I. Kuptsov for consultation and help in programming and to Z. A. Donskova who assisted in the calculations and preparation of the paper.     

A study of flow properties near critical points in the near wake of a circular cylinder

By applying the phase-plane technique to velocity data in the near-wake of a circular cylinder, three types of critical points are identified. Foci and saddle points occur most frequently, but a significant number of nodes is also found. Flow topology and properties associated with these points are examined in some detail. While foci and saddle points are associated with maxima of local vorticity and strain rate respectively, nodes are associated with a strong local divergence, indicating significant local three-dimensionality. The relative probability of time delay between critical points is also discussed.     

Laminar near wake of a sharp wedge in hypersonic perfect-gas flow

The laminar near wake behind a sharp wedge with the semi-vertex angle of 10° and a flat base section placed at zero incidence in a Mach 6 uniform perfect-gas flow with the specific heat ratio 1.4 at Reynolds numbers ranging from 3 × 10² to 10⁵ is considered. The study is carried out on the basis of the numerical solution of the Navier-Stokes equations. The results on the base pressure and the pressure and local stagnation temperature distributions along the plane of symmetry and in several cross-sections in the near wake are compared in detail with the data [1].     

An experimental study of a turbulent wing-body junction and wake flow

Extensive measurements were conducted in an incompressible turbulent flow around the wing-body junction formed by a 3∶2 semi-elliptic nose/NACA 0020 tail section and a flat plate. Mean and fluctuating velocity measurements were performed adjacent to the wing and up to 11.56 chord lengths downstream. The appendage far wake region was subjected to an adverse pressure gradient. The authors' results show that the characteristic horseshoe vortex flow structure is elliptically shaped, with ? (W)/?Y forming the primary component of the streamwise vorticity. The streamwise development of the flow distortions and vorticity distributions is highly dependent on the geometry-induced pressure gradients and resulting flow skewing directions. The primary goal of this research was to determine the effects of the approach boundary layer characteristics on the junction flow. To accomplish this goal, the authors' results were compared to several other junction flow data sets obtained using the same body shape. The trailing vortex leg flow structure was found to scale on T. A parameter known as the momentum deficit factor (MDF = (Re _T)² (θ/T)) was found to correlate the observed trends in mean flow distortion magnitudes and vorticity distribution. Changes in δ/T were seen to affect the distribution of u′, with lower ratios producing well defined local turbulence maxima. Increased thinning of the boundary layer near the appendage was also observed for small values of δ/T.     

Turbulent flow near the base and in the near wake with free flow vorticity taken into account

The method of integral relations is used to calculate the basic flow parameters behind sharp and blunted cones. Similar investigations have been carried out in many papers, for example, [1–3]. In contrast to the assumptions made in other computational methods, the present paper includes the vorticity of the flow off the rear edge of the body, and the inviscid free flow is calculated by the method of characteristics with separation of the attached compressive shocks into an edge and a trailing shock. In the general case the wall ahead of the base is assumed to be heat conducting. Calculated results are given for a wide range of the parameters governing the problem. It is shown that the vorticity of the flow off the rear edge has a considerable effect on the base pressure. The agreement between the calculated results and the available experimental data is satisfactory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 122–130, March–April, 1976.     

Experimental study of the mean wake of a tidal stream rotor in a shallow turbulent flow

The mean wake of a three-bladed horizontal axis tidal stream turbine operating at maximum power coefficient has been investigated experimentally in a wide flume with width 11 times the depth, providing minimal restriction to transverse wake development and behaviour of large-scale horizontal turbulence structures. This is an important first stage for understanding wake interaction in turbine arrays and hence large-scale power generation. The rotor diameter has a typical value of 60% of the depth and the thrust coefficient is representative of a full-scale turbine. The shear layers originating from the rotor tip circumference show classic linear expansion downstream, with the rate of a plane shear layer vertically and 1.5 times that horizontally. These shear layers merge by around 2.5 diameters downstream forming a self-similar two-dimensional wake beyond eight diameters downstream with a virtual origin at two diameters downstream of the rotor plane. The spreading rate is somewhat less than that for solid bodies. The detailed velocity measurements made in the near wake show rotation and vorticity similar to that measured previously for wind and marine turbines although with asymmetry associated with bed and surface proximity. The longitudinal circulation in a transverse plane is conserved at about 1% of the swept circulation from the blade tip within two diameters downstream, the extent of detailed measurement. Turbines are usually designed using blade element momentum theory in which velocities at the rotor plane are characterised by axial and tangential induction factors and it is now possible to see how this idealisation relates to actual velocities. The axial induction factor corresponds to velocity deficits at 0.4–0.8 radii from the rotor axis across the near wake while the tangential induction factor at the rotor plane corresponds to velocities at 0.4–0.6 radii between 1–2 diameters downstream, indicating some general correspondence. For the two-dimensional self-similar far wake the two parameters defining the centreline velocity deficit and the transverse velocity profiles are likely to be insensitive to Reynolds number in turbulent conditions.     

Measurement of the turbulent kinetic energy budget of a planar wake flow in pressure gradients

Turbulent kinetic energy (TKE) budget measurements were conducted for a symmetric turbulent planar wake flow subjected to constant zero, favorable, and adverse pressure gradients. The purpose of this study is to clarify the flow physics issues underlying the demonstrated influence of pressure gradient on wake development, and provide experimental support for turbulence modeling. To ensure the reliability of these notoriously difficult measurements, the experimental procedure was carefully designed on the basis of an uncertainty analysis. Three different approaches were applied for the estimate of the dissipation term. An approach for the determination of the pressure diffusion term together with correction of the bias error associated with the dissipation estimate is proposed and validated with the DNS results of Moser et al (J Fluid Mech (1998) 367:255–289). This paper presents the results of the turbulent kinetic energy budget measurement and discusses their implications for the development of strained turbulent wakes.An erratum to this article can be found at     

Air flow aerodynamic on a wall-mounted hemisphere for various turbulent boundary layers

Air flow field around a surface-mounted hemisphere of a fixed height for two different turbulent boundary layers (thin and thick) are investigated experimentally and numerically. Flow measurements are performed in a wind tunnel using hot-wire anemometer and streamwise component of velocity fluctuation are calculated using a special developed program of the hardware system. Mean surface pressure coefficients and velocity field for the same hemisphere are determined by the numerical simulation. Turbulent flow field and intensity are measured for two types of boundary layers and compared at various sections in both streamwise and spanwise directions. Numerical scheme based on finite volume and SIMPLE algorithm is used to treat pressure and velocity coupling. Studies are performed for Reynolds number, Re_H = 32,000. Based on the numerical simulation using RNG k–ε turbulence model, flow pathlines, separation region and recirculation area are determined for the two types of turbulent boundary layer flows and complex flow field and recirculation regions are identified and presented graphically.     

Hypersonic viscous gas flow over a delta wing in the intermediate interaction regime with allowance for wake flow

The results of calculating the hypersonic flow over a plane delta wing of finite length with allowance for wake flow in the intermediate interaction regime are presented. A comparison is made with the data for flow over a delta wing with given pressure at the trailing edge.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 142–149, September–October, 1993.