Comparison of flow structures in the downstream region of a cylinder and sphere

An experimental investigation of flow structures downstream of a circular cylinder and sphere immersed in a free-stream flow is performed for Re = 5000 and 10,000 using qualitative and quantitative flow visualization techniques. The obtained results are presented in terms of time-averaged velocity vectors, patterns of streamlines, vorticity, Reynolds stress correlations and turbulent kinetic energy distributions. Flow data reveal that the size of wake flow region, the location of singular and double points, the peak values of turbulence quantities, such as Reynolds stress correlations, vorticity fluctuations and turbulent kinetic energy vary as a function of models’ geometry and Reynolds Numbers. The concentration of small scale vortices is more dominant in the wake of the sphere than that of the cylinder. The maximum value of turbulent kinetic energy (TKE) occurs close to the saddle point for the cylinder case while two maximum values of TKE occur along shear layers for the sphere one because of the 3-D flow behavior.     

Numerical investigation of flow structures around a sphere

A numerical investigation of flow around a sphere is performed and compared with previous studies. Here, a second-order accurate, finite volume method is used in order to predict the instantaneous and time-averaged flow characteristics using large eddy simulation (LES) on the multi-block grid system. Namely, the objectives of this article are: (i) the presentation of flow structures in the wake region downstream of the sphere with a wide variety of flow properties such as the distribution of velocity vectors, patterns of streamlines, Reynolds stress correlations, root mean square of velocity components and other time-averaged flow data in order to reveal the vortical flow structures in detail and (ii) to demonstrate the abilities of computational methods in simulation of vortical flow data. Finally, it has been concluded that there are good agreements between the experimental results and numerical predictions.     

Characterization by proper-orthogonal-decomposition of the passive controlled wake flow downstream of a half cylinder

This study focuses on the flow modifications generated by a flat plate stabilizer placed downstream of a half-cylinder compared to the wake formation without the plate. For moderate Reynolds number, a snapshot proper-orthogonal-decomposition method based on particle-image-velocimetry (PIV) is used to analyze the complex dynamics of the flows and to highlight typical swirl formation mechanisms. Using this tool, the near-wake structures, the kinetic aspects, the energy contributions, the degree of organization of the structures and their temporal behaviour are identified. A strong link between the Strouhal number, the mean vorticity and the Total Energy is observed. The interference of the shear layer with the stabilizer has an atypical influence on the wake characteristics.     

A comparative assessment of fluid flow and heat transfer parameters in laminar flow around a circular cylinder and a sphere

Theoretical studies have been carried out for a comparative assessment of hydrodynamic boundary layer thickness, displacement thickness and shear stress at the wall for laminar flow around a circular cylinder and a sphere with the help of the approximate method due to Karman and Pohlhausen for two dimensional flow and the method as applied to bodies of revolution based on the work of F. W. Scholkemeier, respectively. Thermal boundary layer thickness and Nusselt number have been evaluated around the surface of the solids. Comparison is made with available solutions. The graphical presentation of the results depicts a concise and relative assessment of fluid flow and heat-transfer parameters for flow around cylinder and sphere.     

Measurement and decomposition of periodic flow structures downstream of a test turbine

The temperature dissipation rate inferred from the balance of $\overline{\theta^{2}}/2$ budget is used for the purpose of studying different methods employed to directly measure dissipation. The terms involved in the budget equation of temperature variance are measured with laser Doppler velocimetry and cold-wire thermometry used simultaneously. This study focuses on the centerline of a turbulent round jet, in the far field, at high Reynolds number (x/D = 30, Re _D  = 1.5 × 10⁵ and Re _λ  = 548). Particular attention is devoted to statistical convergence of second- and third-order moments of velocity and temperature fluctuations. Temperature dissipation obtained by Taylor’s hypothesis and radial temperature derivative spectra confirm local isotropy. A high level of low wave number content is reported for the longitudinal derivative spectra, probably due to transverse mode spectral aliasing and noise contamination for small wire separation. A parallel is drawn between finite difference formulations and the behavior of the autocorrelation coefficient for small wire separations. The temperature dissipation estimates found are close to the budget reference value, but spectral analysis cast doubts on the validity of the streamwise derivative obtained with a pair of probes.     

Flow-induced vibration of a flexibly mounted circular cylinder in the proximity of a larger cylinder downstream

A flexibly mounted circular cylinder is placed upstream of a stationary cylinder twice as large. Flow-induced vibration response of the small cylinder is measured with the interfering cylinder placed at 57 relative locations. In most situations, reduced-amplitude vibration or even no vibration is observed. Lock-in resonance remains the dominant vibration behavior, but the reduced velocity of peak lock-in is found to shift to a value higher or lower than the isolated cylinder value, depending on the lateral separation between the two cylinders. When the flexible cylinder is located just in front of the large cylinder, galloping-type vibration of very large amplitude occurs at reduced velocities above 12. Mechanisms of flow-induced vibration are discussed with the aid of flow visualizations. The present study supplements a previous paper reporting amplified vibration of the flexible cylinder with the interfering cylinder placed in various upstream locations.     

Experimental and high-order LES analysis of the flow in near-wall region of a square cylinder

A coupled experimental/numerical analysis of turbulent flow past a square cylinder is performed at the ERCOFTAC Reynolds number Re = U_∞D/ν = 21,400, where U_∞ is the inflow velocity and D the cylinder height. Complementary Laser Doppler Velocimetry (LDV) and high-order large-eddy simulations (LES) approaches, based on a spectral vanishing technique (SVV-LES), provide a comprehensive data base including both instantaneous data and post-processed statistics. Beyond these results, an achievement of the paper is to investigate the coherent structures developing on the sides and in the wake of the cylinder with a special focus on the flow features in the near-wall region. The flow is found to separate at the leading edge of the cylinder with the occurence of three-dimensional Kelvin-Helmholtz (KH) pairings localized in the separating shear layer. The interaction between these KH vortical structures and Von Kármán vortex shedding (VK) in the near wake is discussed based on both visualisations and frequency analysis. In particular, signatures of VK and KH vortical structures are found on velocity time samples.     

Fluid flow through a narrow sphere - cylinder meatus with very close diameter values

Summary Results are reported of an experimental hydraulic study on a centering system for the basis of fuel elements in a nuclear reactor. The system employs a cylindrical seat as a guide and a spherical centering element integral with the rod. Tests have been carried out for several values of the thikness of the meatus between sphere and cylinder, and, for every value of the thikness, with the perfectly centred sphere and with the totally eccentric sphere (touching the cylinder internally). Hydraulic characteristics of the system were obtained, in terms of dimensionless Euler-Reynolds numbers. Cavitation threshold has been determined for all the tested cases. A simple formula is further proposed, of very general validity, for approximate evaluation of the correction factor of the Stokes formula for a sphere in slow motion in a viscous fluid on the axis of an indefinite cylinder.

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Sommario Si riportano i risultati di un'indagine idraulica sperimentale effettuata su un sistema di centraggio per il piede di elementi di combustibile in un reattore nucleare. Il sistema è fondato sull'impiego di una sede cilindrica di guida e di un elemento sferico di centraggio solidale con la barra. Le esperienze condotte per vari valori dello spessore dell'intercapedine sfera-cilindro e, per ogni spessore, con riferimento sia all'assetto perfettamente centrato sia a quello totalmente eccentrico, hanno condotto alla determinazione delle caratteristiche idrauliche del sistema in termini di numero di Eulero - numero di Reynolds. Sono state condotte prove per la determinazione della soglia di cavitazione per i vari casi sperimentati. Viene inoltre proposta una formula approssimata di validità molto generale per la stima del coefficiente di correzione della formula di Stokes per il caso di moto lento di una sfera in un fluido viscoso lungo l'asse di un cilindro infinitamente lungo.

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Research supported by CNEN - PRV (Fast Reactor Project).     

Experimental investigation of a confined flow downstream of a circular cylinder centred between two parallel walls

In this work, we present an experimental study of the wall confinement effect on the wake formation behind a circular cylinder of diameter d_c=10 mm and of length L_c=30d_c. The experiments were performed in a water tunnel with the dimensions (length=300d_c, height=3d_c, span L_c=30d_c). The confinement rate was r=1/3 and the Reynolds number was in the range of 30–277. The experiments were done using 2-D PIV measurements. The first instability was delayed by the confinement and the von Kármán vortices characteristics are different from the unconfined case. Proper orthogonal decomposition (POD) of the flow was used for a filtering purpose and to extract the energetic contribution of the different modes. A low-order representation of the flow, constructed from the first pair of modes in the well-defined region of the flow, shows that von Kármán vortices are equivalent to vanishing progressive waves. Measurements done above the cylinder show the presence of 3-D span instabilities showing great similarities with “Mode A” and “Mode B” found in the unconfined case.     

Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

Summary An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time. Received 15 January 1996; accepted for publication 21 November 1996     

Study of gas flow in region of incidence of a shock on a cylinder in high supersonic flow

Some results are presented of a study on the effect of incident shock intensity on the flow field and force effects of a shock incident on a cylinder in the vicinity of the point of incidence (V. K. Kutlikov assisted in obtaining part of the experimental data).     

Establishment of circumfluence (steady-state flow) when a shock wave strikes a cylinder or a sphere

The problem of the diffraction of a shock wave at a stationary sphere or cylinder is considered. The finite-difference method proposed by S. K. Godunov [1, 2] is employed Numerical solutions are obtained for the stage of the diffraction of the shock wave and for the subsequent steady state of flow around the object (circumfluence). Cases of sub-, trans-, and supersonic flow behind the shock wave are considered. When strong shock waves undergo diffraction, zones of reverse flow appear in the neighborhood of the tail part of the obstacle.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 97–103, September–October, 1972.     

Numerical modeling of three-dimensional vortex structures in hypersonic transverse flow past a cylinder

A new mechanism of the formation of spatially periodic structures on the nose surfaces of cylindrically blunted bodies in a hypersonic transverse flow is investigated. According to this mechanism, a curved shock wave produces a vortex flow, while the vortex, which is conserved in the presence of weak dissipation, acts on the shock and maintains its curved shape. The realizability of this vortex formation mechanism is verified by direct numerical simulation using the FLUENT software package. It is confirmed that in the case of uniform hypersonic freestream both plane and three-dimensional modes of the steady flow past the cylinder nose can exist. The three-dimensional mode is characterized by periodic-in-span vortex structures and considerable heat flux peaks on the nose surface. The calculated results are compared with the experimental data.     

Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature.     

Streakline visualization of the structures in the near wake of a circular cylinder in sinusoidally oscillating flow

A numerical investigation of three-dimensional sinusoidally oscillating flow around a circular cylinder was conducted to examine mushroom-type structures in the near wake that are manifestations of the Honji instability. The focus of this paper is to examine the flow structure through the analysis of the streaklines in the flow. Through the use of streakline visualizations and their correlation with vorticity in the flow field, the onset and development of the mushroom-type structures is followed. The parameter value range is 0.1<KC<2.0 and β=1035, 6815, and 9956. The streakline patterns in several axial planes are examined and used to describe the various mechanisms that sustain the mushroom-type structure during the oscillatory cycle.     

Comparison between two finite-difference schemes for computing the flow around a cylinder

Separated flow past a circular cylinder is computed from two finite-difference Navier–Stokes models. Stream functions are calculated using a successive-over-relaxation (SOR) procedure. Alternating-direction-implicil (ADI) and ‘upwind’ directional difference explicit (DDE) numerical schemes for solving the vorticity-transport equation are compared. The ‘upwind’ differencing technique produces artificial viscosity which damps the wake and suppresses vortex shedding. It is shown to be unreliable and so the ADI approach is recommended.