Flow past a sphere in density-stratified fluid

Stratified flow past a three-dimensional obstacle such as a sphere has been a long-lasting subject of geophysical, environmental and engineering fluid dynamics. In order to investigate the effect of the stratification on the near wake, in particular, the unsteady vortex formation behind a sphere, numerical simulations of stratified flows past a sphere are conducted. The time-dependent Navier–Stokes equations are solved using a three-dimensional finite element method and a modified explicit time integration scheme. Laminar flow regime is considered, and linear stratification of density is assumed under Boussinesq approximation. The effects of stratification is implemented by density transport without diffusion. The computed results include the characteristics of the near wake as well as the effects of stratification on the separation angle. Under increased stratification, the separation on the sphere is suppressed and the wake structure behind the sphere becomes planar, resembling that behind a vertical cylinder. With further increase in stratification, the wake becomes unsteady, and consists of planar vortex shedding similar to von Karman vortex streets.     

Investigation of the variability of the structure of a stratified wake behind a horizontal cylinder using optical and acoustic methods

The shadow flow pattern behind a horizontal cylinder uniformly towed in a stratified fluid with constant buoyancy frequency (in the imbedded vortex and turbulent wake regime) is recorded synchronously with acoustic echo sounding (basic frequency equal to 1 MHz) in a laboratory tank. Using computer processing, the illumination profiles in the schlieren pattern are constructed on scales comparable with the sounding acoustic ray width. Although the optical and acoustic profiles are not similar, nevertheless they enable the basic structural elements of the wake, including its high-gradient core to be identified, and their time variability traced. The features of the integral acoustic scattering characteristic, in particular, the volume scattering strength, allow this characteristic to be used, together with optical images of the flow pattern, to distinguish the flow regime identification criteria. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 5–17, May–June, 1998. The work was partly financed by the Russian Foundation for Basic Research (projects Nos. 96-05-64004 and 97-01-01013) and by INTAS Grant No. 93-1584.     

Recurrence and Reconnection Effect in an Attached Two-Dimensional Internal Wave Field

The shadow pattern of the wake behind a horizontal cylinder uniformly towed in a linearly stratified fluid is analyzed. In the “imbedded turbulent vortex” and “narrow turbulent wake” regimes the structure of the attached internal waves with fairly large amplitudes in the neighborhood of the body satisfactorily agrees with calculations based on the linear theory. As the distance from the source increases, the pattern becomes more complex. The internal waves radiated by the body itself and by the isolated vortices in the wake interfere and nonlinearly interact with each other and with the other flow elements. At large ages τ=t/T_b > 5.8 — time is normalized with respect to the buoyancy period) recurrence (spatial structure restored) and restructuring (phase surfaces reconnected) of a group of longest internal waves (of the attached type) are observed. The recurrent waves penetrate through the wake. These effects are associated with a general restructuring of the stratification modulated by a particular wave scale.     

Method of calculating subsonic gas flow with separation past wings

The steady nonlinear problem of subsonic compressible gas flow past a wing of arbitrary shape in plan is considered. A numerical method was devized for solving the problem; this is a further development of the method of discrete vortices. The surface of the body and the vortex wake behind it are simulated by systems of discrete vortex sections, but, in contrast to the case of an incompressible medium, it is necessary in this case for the sources to be distributed outside the wing. The circulations of the attached vortices, the strengths of the sources, and the shape of the wake are determined by iterations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 140–147, July–August, 1984.     

Micro-scale instability in a continuously stratified fluid

Experimental observations of small-scale structures caused by flow instabilities at layers of high density gradient in the wake behind a cylinder in a fluid with a continuous salt concentration stratification are reported. In the density wake it is possible to discern a number of structures such as wedge-like structures or cusps; small-scale instabilities (breakers) in the zones of interaction of attached internal waves and the high-gradient wake envelope; small-scale instability of the density boundary layer with a complicated density gradient pattern superimposed on a smooth velocity profile, and small-scale wake structures behind attached vortices in the case of a closed (central) wake envelope.Translated from Izvestiya RossiiskoiAkademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–10, May–June, 1995.     

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.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

Numerical solution for the flow of viscoelastic fluids around an inclined circular cylinder.

Finite difference solutions have been obtained by the perturbation method to investigate the influence of shear thinning and elasticity on the flow around an inclined circular cylinder of finite length in a uniform flow. In this numerical analysis a generalized upper-convected Maxwell model, in which the viscosity changes according to the Cross model, has been used.The local flow over the cylinder is only slightly deflected. However, in the wake flow behind the cylinder the particle path is remarkably influenced by the axial flow and rapidly flows up parallel to the cylinder's axis. Then it gradually rejoins direction of the incoming flow. It is found that viscoelastic fluids are prone to flow axially in the vicinity of the cylinder. The numerical predictions generally agree with the flow visualization results.The numerical solutions also demonstrate that elasticity has a strong effect on the velocity profile especially around both ends of the cylinder; elasticity increases the asymmetric profiles of both circumferential velocity and axial velocity with respect to equal to 90° and decreases a difference in the circumferential velocity between the windward end and the leeward end.For non-Newtonian fluids, the length of the wake flow is influenced by not only the Reynolds number but also the cylinder diameter and it is larger for the cylinder with the smaller diameter at the same Reynolds number.Partly presented at the 9th Australasian Fluid Mechanics Conference, University of Auckland, New Zealand, 8–12 December, 1986     

Calculation of flow around a lifting surface in the case of large deformations

Many studies have been made of the nonstationary flow of an ideal incompressible fluid around a lifting surface. The present state of the numerical methods of solution of this problem is reviewed in [1]. The present paper studies three-dimensional nonstationary flow around a lifting surface which undergoes deformation and behind which a wake vortex surface is formed. The lifting and wake vortex surfaces are represented in parametric form. The metrics of these surfaces are used, and the introduced vortex function is approximated by bicubic splines. For the convenient application of the theory developed here to the flapping flight of insects, for which it is sometimes difficult to distinguish the lateral and trailing edges of the wings, the following terminology is introduced. The part of the edge of the lifting surface from which the wake vortex surface is shed is called the trailing edge. The remaining part is called the leading edge. On the leading edge, the velocity has a singularity. Test calculations have demonstrated the effectiveness of the method.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 72–79, July–August, 1980.     

Transient behaviors of a flame over a Tsuji burner

The present study investigated numerically the physical mechanisms underlying the transient behaviors of the flame over a porous cylindrical burner. The numerical results showed that a cold flow structure at a fixed inflow velocity of Uin = 0.6 m/s in a wind tunnel could be observed in two co-existing recirculation flows. Flow variations occur repeatedly until t = 4.71 s, and then a vortex existed steadily behind the burner and no shading occurred. The ignition of flammable mixture led to a rapid rise in gas temperature and a sudden gas expansion. When it reached the stable envelope flame condition, Uin is adjusted to an assigned value. Two blow-off mechanisms were identified. It was also found in the study flame shapes with buoyancy effects agreed with the ones observed experimentally by Tsai. Furthermore, the lift-off flame would appear briefly between the envelopes and wake ones, and was stabilized as a wake flame.     

Measurement and analysis of unsteady flow structures in rotor blade wakes

Time-variant data are obtained to investigate the exit flow field from a rotor in a research compressor. In the free-stream region, the instantaneous data are analogous to one another and to the ensemble averaged free-stream results. However, in the wake region, some of the instantaneous signals are similar to one another and to the ensemble averaged wake, but others differ significantly. These variations in the instantaneous data are interpreted and shown to be due to a vortex street structure in the wake. This is accomplished by: (1) developing a mathematical model of the rotor blade exit flow field based on a wake vortex street structure analogous to the unsteady flow field behind bluff bodies due to classical von Karman vortex shedding; and (2) correlating predictions of both the ensemble averaged and instantaneous rotor blade exit flow fields as well as the velocity probability density distributions from this vortex wake flow field model with the corresponding data. The correlation of the ensemble averaged rotor blade exit flow fields is very good and the flow angle distribution correlation excellent. The predicted instantaneous rotor blade exit flow field exhibits many of the flow features found in the data. Also, the probability density distributions for the data and the vortex wake flow field model are analogous to one another.List of symbols N number of rotor revolutions - S _w rotor blade wake width - S _x vortex core horizontal spacing - S _y vortex core vertical spacing - u velocity component parallel to vortex street motion - v velocity component normal to vortex street motion - W instantaneous relative velocity - W _i velocity induced by vortex street - W free-stream relative velocity - W _s velocity of vortex street - x coordinate parallel to vortex street motion - y coordinate normal to vortex street motion - free-stream relative flow angle - _inst instantaneous relative flow angle - vortex strength     

Propeller tip and hub vortex dynamics in the interaction with a rudder

In the present paper, the interaction mechanisms of the vortices shed by a single-screw propeller with a rudder installed in its wake are addressed; in particular, following the works by Felli et al. (Exp Fluids 6(1):1–11, 2006a, Exp Fluids 46(1):147–1641, 2009a, Proceedings of the 8th international symposium on particle image velocimetry: Piv09, Melbourne, 2009b), the attention is focused on the analysis of the evolution, instability, breakdown and recovering mechanisms of the propeller tip and hub vortices during the interaction with the rudder. To investigate these mechanisms in detail, a wide experimental activity consisting in time-resolved visualizations, velocity measurements by particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) along horizontal chordwise, vertical chordwise and transversal sections of the wake have been performed in the Cavitation Tunnel of the Italian Navy. Collected data allows to investigate the major flow features that distinguish the flow field around a rudder operating in the wake of a propeller, as, for example, the spiral breakdown of the vortex filaments, the rejoining mechanism of the tip vortices behind the rudder and the mechanisms governing the different spanwise misalignment of the vortex filaments in the pressure and suction sides of the appendage.     

Effect of homogeneous stratification of the fluid on the dynamics of a kármán vortex street behind a circular cylinder

The experimental results of studying the effect of homogeneous stratification of the fluid on the conditions of generation of a Kárman vortex street [1] developing in the wake of a cylinder in steady horizontal motion are described. In a homogeneous medium at Reynolds numbers Re >5 two symmetrical regions of vorticity of opposite sign are formed behind the cylinder and move together with the latter. As the speed of the cylinder increases, the link between the vortices and the cylinder grows weaker, the vortices are stretched out along the flow and at Re > 40 begin to separate alternately, forming a vortex street in the wake. At first, the frequency of vortex separation increases sharply with increase in Re, but then levels off. It is found that in a uniformly stratified fluid the onset of vortex separation from the moving cylinder is delayed. The dependence of the critical Reynolds number (onset of vortex separation) on the internal Froude number is obtained. The effect of stratification of the fluid on the frequency of separation of the vortices in the Kármán street is investigated. The effect of the Froude number on the dependence of the Strouhal number on the Reynolds number is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 83–86, January–February, 1986.In conclusion the authors wish to thank A. T. Onufriev for his interest in their work and useful discussions of the results.     

Aerodynamic loading on a cylinder behind an airfoil

The interaction between the wake of a rotor blade and a downstream cylinder holds the key to the understanding and control of electronic cooling fan noise. In this paper, the aerodynamic characteristics of a circular cylinder are experimentally studied in the presence of an upstream NACA 4412 airfoil for the cylinder-diameter-based Reynolds numbers of Re_d=2,100–20,000, and the airfoil chord-length-based Reynolds numbers of Re_c=14,700–140,000. Lift and drag fluctuations on the cylinder, and the longitudinal velocity fluctuations of the flow behind the cylinder were measured simultaneously using a load cell and two hot wires, respectively. Data analysis shows that unsteady forces on the cylinder increase significantly in the presence of the airfoil wake. The dependence of the forces on two parameters is investigated, that is, the lateral distance (T) between the airfoil and the cylinder, and the Reynolds number. The forces decline quickly as T increases. For Re_c<60,000, the vortices shed from the upstream airfoil make a major contribution to the unsteady forces on the cylinder compared to the vortex shedding from the cylinder itself. For Re_c>60,000, no vortices are generated from the airfoil, and the fluctuating forces on the cylinder are caused by its own vortex shedding.     

Investigations of wake flows of a flat plate in steady,oscillatory and combined flows

Numerical study on near wake flows of a flat plate in three kinds of oncoming flows is made by using the discrete vortex model and improved vorticity creation method. For steady oncoming flow, both gross and detailed features of the wake flow are calculated and discussed. Then, in harmonic oscillatory oncoming flow two different wake flow patterns withK _c=2,4 and 10 are obtained respectively. Our results present a new wake flow pattern for lowKc numbers (Kc<5) describing vortex shedding, pairing and moving in a period of the oscillatory flow starting from rest. The calculated drag and inertia force coefficients are closer to experimental data from the U-tube than the previous results of vortex simulation. For in-line combined oncoming flow the vortex lock-in and dynamic characteristics are simulated. The results are shown to be in good agreement with experiments. The project supported by National Natural Science Fundation of China and LNM of Institute of Mechanics. CAS     

Circulation flow at the front surface of a sphere in a supersonic wake

Several theoretical and experimental studies of supersonic flow past a blunt body located in the wake behind another body have been made [1–7]. It has been shown that a reverse-circulation flow can occur in the shock layer at the front surface. The possibility of such a flow forming depends on the nonuniformity of the freestream flow and the Reynolds number. This paper presents new results of the theoretical study of the structure of the shock wave at the front surface of such a sphere, obtained on the basis of numerical solution of Navier-Stokes equations. It is shown that for a fixed nonuniformity of the freestream flow, an increase in the Reynolds number and cooling of the surface of the body lead to the formation of a secondary vortex in the region where the contour of the body intersects the axis of symmetry. A study is made of the variations of the drag and heat transfer parameters over the front surface of a cooled and thermally insulated sphere. The possibility of numerical simulation of the flow on the basis of the Euler equations is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 143–148, May–June, 1985.     

Steady flow past a torus with aspect ratio less than 5

Steady flow past a torus with an aspect ratio less than 5 and its axis aligned with the flow is studied numerically by solving the steady, axisymmetric Navier–Stokes equations. The wake structure behind tori exhibits diverse behaviours. The detached recirculating zone on the axis, the attached recirculating zone, and the detached recirculating zone behind the torus tube may appear individually or concurrently, depending on the aspect ratio and the Reynolds number. A wake structure map is summarized based on the observed flow behaviours. Six flow regimes with different wake behaviours are identified and the corresponding flow regime map is plotted, which include the no-recirculating-zone regime, the single-detached-recirculating-zone regime, the single-attached-recirculating-zone regime, the two-recirculating-zone regime I, the two-recirculating-zone regime II, and the three-recirculating-zone regime. Over the range of aspect ratio 1.9<AR<2.4, the detached wake initially increases but then decreases in size with Reynolds number, and eventually disappears at Reynolds numbers beyond a critical value (depending on the aspect ratio). The underlying mechanisms of the onset and disappearance of the recirculating zones are discussed in terms of vorticity accumulation and base bleed. The recirculating zone first occurs when the maximum vorticity on the surface of the torus exceeds about 5. The detached recirculating zone on the axis of the torus disappears once the flow rate through the hole of the torus is beyond a certain threshold. In addition, the present results suggest that different transition modes to non-axisymmetric flow for tori with different aspect ratios reported in the literature may result from the wake structures prior to the transition.     

Mechanisms of wake deflection angle change behind a heaving airfoil

An immersed-boundary numerical method is applied to simulate the wake downstream of a two-dimensional heaving airfoil. A switch of vortex pattern is found to be the major reason that a deflected asymmetric wake reverses its deflection angle. Parameters of the heaving airfoil and flow that influence the onset and location of the vortex switching are discussed. While the previous literature deliberately discussed the wake deflection in the near wake region, this study shows that the deflection angle can change from the near wake to far wake regions. A cross-flow effective phase velocity is introduced to analyze the already-formed asymmetric wake behind the airfoil. A vortex dipole model and the related vortex dynamics analysis are developed to show that the change of the distance between the vortices is the primary factor that leads to the vortex pattern switching in the far wake.     

Experimental study of low precessing frequencies in the wake of a turbulent annular jet

This paper investigates the flow structure in the wake behind the centrebody of an annular jet using time-resolved stereoscopic PIV measurements. Although the time-averaged flow field is symmetric, the instantaneous wake is asymmetric. It consists of a central toroidal vortex (CTV), which closes downstream at the stagnation point. This stagnation point lies off-axis and hence the axis of the CTV is tilted with respect to the central axis of the geometry. The CTV precesses around the central axis, corresponding to a Strouhal number of 2.5 × 10⁻³. The phase averaging technique is used to study this large-scale motion as it can separate the precession from the turbulence in the flow field. It is found that the precession creates a highly three-dimensional flow field and for instance near the stagnation point, up to 45% of the rms velocity fluctuations are attributed to it.     

Volumetric reconstruction of the mean flow around circular cylinders fitted with strakes

The volumetric reconstruction technique presented in this paper employs a two-camera stereoscopic particle image velocimetry (SPIV) system in order to reconstruct the mean flow behind a fixed cylinder fitted with helical strakes, which are commonly used to suppress vortex-induced vibrations (VIV). The technique is based on the measurement of velocity fields at equivalent adjacent planes that results in pseudo volumetric fields. The main advantage over proper volumetric techniques is the avoidance of additional equipment and complexity. The averaged velocity fields behind the straked cylinders and the geometrical periodicity of the three-start configuration are used to further simplify the reconstruction process. Two straked cylindrical models with the same pitch (p = 10d) and two different heights (h = 0.1 and 0.2d) are tested. The reconstructed flow shows that the strakes introduce in the wake flow a well-defined wavelength of one-third of the pitch. Measurements of hydrodynamic forces, fluctuating velocity, vortex formation length, and vortex shedding frequency show the interdependence of the wake parameters. The vortex formation length is increased by the strakes, which is an important effect for the suppression of vortex-induced vibrations. The results presented complement previous investigations concerning the effectiveness of strakes as VIV suppressors and provide a basis of comparison to numerical simulations.