Thermal characteristics of the wake shear layers from a slightly heated circular cylinder

In this paper, we investigate the thermal characteristics of wake shear layers generated by a slightly heated circular cylinder. Measurements of the fluctuating temperature were made in the region x/d = 0.6 to x/d = 3 (where x is the downstream distance from the cylinder axis and d is the cylinder diameter) using a single cold-wire probe. The Reynolds number Re was varied in the range 2,600–8,600. For Re = 5,500, simultaneous measurements were made with a rake of 16 cold wires, aligned in the direction of the mean shear, at x/d = 2 and 3. The results indicate that the passive temperature can be an effective marker of various instabilities of the wake shear layers, including the Kelvin–Helmholtz (KH) instability. The temperature data have confirmed the approximate Re ^m dependence of the KH instability frequency (f _KH) with different values of m over different ranges of Re, as reported previously in the literature. However, it is found that this power-law dependence is not exact, and a third-order polynomial dependence appears to fit the data well over the full range of Re. Importantly, it is found that the wake shear-layer instabilities can be grouped into three categories: (1) one with frequencies much smaller than the Bénard–Kármán-vortex shedding frequency, (2) one associated with the vortex shedding and (3) one related to the KH instability. The low-frequency shear-layer instabilities from both sides of the cylinder are in-phase, in contrast to the anti-phase high-frequency KH instabilities. Finally, the observed streamwise decrease in the mean KH frequency provides strong support for the occurrence of vortex pairing in wake shear layers from a circular cylinder, thus implying that both the wake shear layer and a mixing layer develop in similar fashion.     

Flow around a circular cylinder—structure of the near wake shear layer

The separated shear layer in the near wake of a circular cylinder was investigated using a single hot wire probe, with special attention given to the shear layer instability characteristics. Without end plates to force parallel vortex shedding, the critical Reynolds number for the onset of the instability was 740. The present data, together with all previously published data, show that the ratio of the instability frequency f_sl to the vortex shedding frequency f_v varies as Re^0.65, which is in agreement with the Re^0.67 dependence obtained by Prasad and Williamson [1997, J Fluid Mech 333:375–402]. However, the distribution of f_sl/f_v and the spectra of the longitudinal velocity fluctuation (u) suggest that, on either side of Re=5,000, the shear layer exhibits lower and upper subcritical regimes, in support of the observations by Norberg [1987, publication no. 87/2, Chalmers University of Technology, Sweden] and Prasad and Williamson [1997, J Fluid Mech 343:235–265]. The spectra of u provide strong evidence for the occurrence of vortex pairing in wake shear layers, suggesting that the near wake develops in a similar manner to a mixing layer.     

Flow past a cylinder: shear layer instability and drag crisis

Flow past a circular cylinder for Re=100 to 10⁷ is studied numerically by solving the unsteady incompressible two‐dimensional Navier–Stokes equations via a stabilized finite element formulation. It is well known that beyond Re ～ 200 the flow develops significant three‐dimensional features. Therefore, two‐dimensional computations are expected to fall well short of predicting the flow accurately at high Re. It is fairly well accepted that the shear layer instability is primarily a two‐dimensional phenomenon. The frequency of the shear layer vortices, from the present computations, agree quite well with the Re^0.67 variation observed by other researchers from experimental measurements. The main objective of this paper is to investigate a possible relationship between the drag crisis (sudden loss of drag at Re ～ 2 × 10⁵) and the instability of the separated shear layer. As Re is increased the transition point of shear layer, beyond which it is unstable, moves upstream. At the critical Reynolds number the transition point is located very close to the point of flow separation. As a result, the shear layer eddies cause mixing of the flow in the boundary layer. This energizes the boundary layer and leads to its reattachment. The delay in flow separation is associated with narrowing of wake, increase in Reynolds shear stress near the shoulder of the cylinder and a significant reduction in the drag and base suction coefficients. The spatial and temporal power spectra for the kinetic energy of the Re=10⁶ flow are computed. As in two‐dimensional isotropic turbulence, E(k) varies as k^?5/3 for wavenumbers higher than energy injection scale and as k^?3 for lower wavenumbers. The present computations suggest that the shear layer vortices play a major role in the transition of boundary layer from laminar to turbulent state. Copyright © 2004 John Wiley & Sons, Ltd.     

Flow past a transversely oscillating square cylinder in free stream at low Reynolds numbers

This paper reports simulation results for free‐stream flow past an oscillating square cylinder at Re=100 and 150, for oscillating‐to‐natural‐shedding frequency ratios of 0.5?f_r?3.0 at a fixed oscillation amplitude of 0.2 of the cylinder width. The transformed governing equations are solved in a non‐inertial frame of reference using the finite volume technique. The ‘lock‐in’ phenomena, where the vortex shedding becomes one with the oscillation frequency, is observed near the natural shedding frequency (f_r≈1). Beyond the synchronization band, downstream recovery of the wake to its stationary (natural) state (frequency) is observed in cross‐stream velocity spectra. At higher forcing frequencies, a phase lag between the immediate and the far wake results in a shear layer having multi‐polar vortices. A ‘Vortex‐switch’ accompanied by a change in the direction of energy transfer is identified at the ‘lock‐in’ boundaries. The variation of aerodynamic forces is noticed to be different in the lock‐in regime. The velocity phase portrait in the far wake revealed a chaotic state of flow at higher excitation though a single (natural) frequency appears in the spectra. Copyright © 2008 John Wiley & Sons, Ltd.     

Coherent Structures and their Frequency Signature in the Separated Shear Layer on the Sides of a Square Cylinder

The purpose of the present work is to study the various specific time scales of the turbulent separating flow around a square cylinder, in order to determine the Reynolds number effect on the separating shear layer, where occurs a transition to turbulence. Unsteady analysis based on large eddy simulation (LES) at intermediate Reynolds numbers and laser doppler velocimetry (LDV) measurements at high Reynolds numbers are carried out. The Reynolds number, based on the cylinder diameter D and the inflow velocity U _o , is ranging from Re?=?50 to Re?=?300,000. A special focus is performed on the coherent structures developing on the sides and in the wake of a square cylinder. For a large Reynolds number range above Re?≈?1,000, both signatures of Von Karman (VK) and Kelvin–Helmholtz (KH) type vortical structures are found on velocity time samples. The combination of their frequency signature is studied based on Fourier and wavelet analysis. In the present study, We observe the occurrence of KH pairings in the separating shear layer on the side of the cylinder, and confirm the intermittency nature of such a shear flow. These issues concerning the structure of the near wake shear layer which were addressed for the round cylinder case in a recent experimental publication (Rajagopalan and Antonia, Exp Fluids 38:393–402, 2005) are of interest in the present flow configuration as well.     

Effect of self-issuing jets along the span on the near-wake of a square cylinder

The study herein focuses on the vortex shedding characteristics and near-wake vorticity patterns of a square cylinder having self-issuing jets through holes along its span. Three different values of spacing between the consecutive holes λ with respect to the cylinder diameter D, i.e., λ/D = 1.5, 3 and 4 are studied experimentally via Digital Particle Image Velocimetry for the Reynolds number range extending from 200 to 1,000. It has been observed that the three-dimensionality of the wake flow depends on the spacing between the holes and Re number. For sufficiently low Reynolds numbers, the jet flows issuing from the holes yield a non-uniform distribution of mean flow characteristics like the shedding frequency and the formation length of vortices along the span of the cylinder when the spacing between jets along centerline is close to wavelength of the naturally existing three-dimensional wake instability. Additionally, for Re number up to 500, the self-issuing jets emanating from the holes show an indirect interaction with shear layers originating from upper and lower separation lines of the cylinder. However, for higher Re numbers of 750 and 1,000, they directly interact with and modify the vortices forming from the cylinder.     

Wake dynamics of external flow past a curved circular cylinder with the free-stream aligned to the plane of curvature

The fundamental mechanism of vortex shedding past a curved cylinder has been investigated at a Reynolds number of 100 using three-dimensional spectral/hp computations. Two different configurations are presented herein: in both cases the main component of the geometry is a circular cylinder whose centreline is a quarter of a ring and the inflow direction is parallel to the plane of curvature. In the first set of simulations the cylinder is forced to transversely oscillate at a fixed amplitude, while the oscillation frequency has been varied around the Strouhal value. Both geometries exhibit in-phase vortex shedding, with the vortex cores bent according to the body's curvature, although the wake topology is markedly different. In particular, the configuration that was found to suppress the vortex shedding in absence of forced motion exhibits now a primary instability in the near wake. A second set of simulations has been performed imposing an oscillatory roll to the curved cylinder, which is forced to rotate transversely around the axis of its bottom section. This case shows entirely different wake features from the previous one: the vortex shedding appears to be out-of-phase along the body's span, with straight cores that tend to twist after being shed and manifest a secondary spanwise instability. Further, the damping effect stemming from the transverse planar motion of the part of the cylinder parallel to the flow is no longer present, leading to a positive energy transfer from the fluid to the structure.     

Effect of blockage on critical parameters for flow past a circular cylinder

The effect of location of the lateral boundaries, of the computational domain, on the critical parameters for the instability of the flow past a circular cylinder is investigated. Linear stability analysis of the governing equations for incompressible flows is carried out via a stabilized finite element method to predict the primary instability of the wake. The generalized eigenvalue problem resulting from the finite element discretization of the equations is solved using a subspace iteration method to get the most unstable eigenmode. Computations are carried out for a large range of blockage, 0.005?D/H ?0.125, where D is the diameter of the cylinder and H is the lateral width of the domain. A non‐monotonic variation of the critical Re with the blockage is observed. It is found that as the blockage increases, the critical Re for the onset of the instability first decreases and then increases. However, a monotonic increase in the non‐dimensional shedding frequency at the onset of instability, with increase in blockage, is observed. The increased blockage damps out the low‐frequency modes giving way to higher frequency modes. The blockage is found to play an important role in the scatter in the data for the non‐dimensional vortex shedding frequency at the onset of the instability, from various researchers in the past. Copyright © 2005 John Wiley & Sons, Ltd.     

Issue Information

Three‐dimensional direct numerical simulation results of flow past a circular cylinder are influenced by numerical aspects, for example the spanwise domain length and the lateral boundary condition adopted for the simulation. It is found that inappropriate numerical set‐up, which restricts the development of intrinsic wake structure, leads to an over‐prediction of the onset point of the secondary wake instability (Re_cr). A best practice of the numerical set‐up is presented for the accurate prediction of Re_cr by direct numerical simulation while minimizing the computational cost. The cylinder span length should be chosen on the basis of the intrinsic wavelength of the wake structure to be simulated, whereas a long span length is not necessary. For the wake transitions above Re_cr, because the wake structures no longer follow particular wavelengths but become disordered and chaotic, a span length of more than 10 cylinder diameters (approximately three times the intrinsic wavelength) is recommended for the simulations to obtain wake structures and hydrodynamic forces that are not strongly restricted by the numerical set‐up. The performances of the periodic and symmetry lateral boundary conditions are compared and discussed. The symmetry boundary condition is recommended for predicting Re_cr, while the periodic boundary condition is recommended for simulating the wake structures above Re_cr. The general conclusions drawn through a circular cylinder are expected to be applicable to other bluff body configurations. Copyright © 2017 John Wiley & Sons, Ltd.     

Role of the shear layer instability in the near wake behavior of two side-by-side circular cylinders

Wakes, and their interaction behind two parallel cylinders lying in a plane perpendicular to the flow, have been investigated experimentally in the sub-critical Reynolds number regime. The experiments were performed in a water channel using laser Doppler velocimetry. The gap between the two cylinders was less than the cylinder diameter, a geometry referred to as strong interaction configuration. In this case the blockage is strong and a gap-jet appears between the cylinders. Two flow regimes of the near wake region have been identified: one below a critical Reynolds number Re _c ]1000;1700[, where the gap jet is stably deflected to one side and the double near-wake becomes asymmetric; the other, above Re _c, where the gap-jet deflection is unstable and a random flopping phenomenon takes place. When Re<Re _c, two different Strouhal numbers are identified, related to the Kármán vortex shedding behind each cylinder. When Re>Re _c, a third frequency appears in the near wake, related to the development of Kelvin-Helmholtz vortices in the separated shear layer of the cylinders [Prasad A, Williamson CHK (1997) J Fluid Mech 333:375]. The observed flopping behavior is attributed to the birth of these Kelvin-Helmholtz instabilities and their intermittent nature. Further downstream, beyond about five cylinder diameters, the random flopping flow phenomena disappear while a slightly asymmetric single wake persists. It is characterized by a Strouhal number St=0.13, a value that one would normally measure behind a single cylinder of twice its diameter.     

Stability of flow past a cylinder: Energy budget of eigenmodes

Global linear stability analysis of the flow past a circular cylinder at the onset of primary wake instability is carried out. The real and imaginary parts of the most unstable eigenmode, responsible for vortex shedding, are very similar but associated with a spatial shift in the vortex structures. This shift results in the convection of vortices that are observed in the unsteady flow, which is actually a consequence of global absolute instability. The kinetic energy density, associated with the most unstable eigenmode, is studied. At the onset of the instability the energy density of the disturbance field is found to be stronger in the far wake compared with the near wake. With increase in Re the region where the disturbance is strong moves upstream closer to the cylinder. However, the maximum value of the kinetic energy density of the disturbance lies outside the recirculation zone even for Re upto 100. A linearized mechanical energy equation for the time evolution of the kinetic energy density of the disturbance is utilized to examine the energy budget of the most unstable eigenmode at various Re. It is found that the most significant contribution to the growth rate of the disturbance arises from the transfer of the energy due to the strain rate of the base flow to the perturbation. The stabilizing effect of the viscous dissipation increases with increase in Re, but saturates for Re beyond ～70. Copyright © 2009 John Wiley & Sons, Ltd.     

Wake transition for surface mounted rectangular cylinder due to incoming shear flow

Three-dimensional unsteady wake characteristics have been investigated numerically in flow past surface mounted finite-height rectangular cylinder using Open Source Field Operation and Manipulation. Effect of impinging shear (shear intensity, K) on transitional characteristics of wake flow has been studied using iso-Q surfaces for Reynolds number (Re) in the range from 150 to 250. Various flow regimes, such as steady flow, symmetric and asymmetric modes of vortex shedding have been identified based on the values of Re and K for different side ratios (SR) of the cylinder. Unsteady wake oscillations have been analyzed using time signal of transverse velocity component in the wake. These signals have been decomposed into different component signals using Hilbert-Huang transformation (HHT). Variation of frequency and energy density with time of the decomposed signals has been presented in the form of Hilbert spectra. Effects of Re, SR and K on wake oscillation frequency have been illustrated in the form of marginal spectra. Time-delay reconstructions and Poincare sections have been examined to study periodic and aperiodic nature of the wake flow. Non-stationarity associated with the wake fluctuation is quantified in terms of degree of stationarity. Symmetric and asymmetric modes have been confirmed using singular value decomposition of the vorticity field and presented using dynamic modes. Growth rate and frequency of the modes corresponding to symmetric shedding are found to be lower than those for asymmetric shedding. In addition, variation in mean drag coefficient has been reported with change in Re and K for each value of SR.     

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Adjoint formulation is employed for the optimal control of flow around a rotating cylinder, governed by the unsteady Navier–Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time‐dependent. Since the numerical control problem is ill‐posed, regularization is employed. An empirical logarithmic law relating the regularization coefficient to the Reynolds number was derived for 60?Re?140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re=60 to Re=1000. The results obtained by the computational optimal control method agree with previously obtained experimental and numerical observations. A significant reduction of the amplitude of the variation of the drag coefficient is obtained for the optimized values of the rotation rate. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of force and wake mode of an oscillating cylinder

The turbulent flow behind a circular cylinder subjected to forced oscillation is numerically studied at a Reynolds number of 5500 by using three-dimensional Large Eddy Simulations (3-D LES) technique with the Smagorinsky model. The filtered equations are discretised using the finite volume method with an O-type structured grid and a second-order accurate method in both time and space. Firstly, the main wake parameters of a stationary cylinder are examined and compared in the different grid resolutions. Secondly, a transversely oscillating cylinder with a constant amplitude in a uniform flow is investigated. The cylinder oscillation frequency ranges between 0.75 and 0.95 of the natural Kármán frequency, and the excitation amplitude is moderate, 50% of the cylinder diameter. The flow characteristics of an oscillating cylinder are numerically examined and the corresponding wake modes are captured firstly in 3-D LES at Re=5500. A transition between different wake modes is firstly investigated in a set of numerical simulations.     

Direct Computations of Boundary Layers Distorted by Migrating Wakes in a Linear Compressor Cascade

A Direct Numerical Simulation (DNS) of flow in the V103 Low-Pressure (LP) compressor cascade with incoming wakes was performed. The computational geometry was chosen largely in accordance with the setup of the experiments performed by Hilgenfeld and Pfitzner (J Turbomach 126:493–500, 2004) at the University of the Armed Forces in Munich. The computations were carried out on the NEC-SX8 in Stuttgart using 64 processors and 85 million grid points. The incoming wakes stemmed from a separate DNS of incompressible flow around a circular cylinder with a Reynolds number of Re _d  = 3300 (based on mean inflow velocity and cylinder diameter). The boundary layer along the suction surface of the blade was found to separate and roll up due to a Kelvin–Helmholtz instability triggered by the periodically passing wakes. Inside the rolls further transition to turbulence was found to occur. The boundary-layer flow along the pressure surface did not separate, instead it underwent by-pass transition.     

Tomographic and time resolved PIV measurements on a finite cylinder mounted on a flat plate

Tomographic and time resolved PIV measurements were performed to examine the 3D flow topology and the flow dynamic above the upper surface of a low-aspect ratio cylinder at Re ≈ 1 ×  10⁵. This generic experiment is of fundamental interest because it represents flow features which are relevant to many applications such as laminar separation bubbles and turbulent reattachment. At Re  ≈ 1 × 10⁵, laminar separation bubbles arise on the side of the cylinder. Furthermore, on the top of the cylinder a separation with reattachment is of major interest. The tomographic PIV measurement, which allows to determine all three velocity components in a volume instantaneously, was applied to examine the flow topology and interaction between the boundary layer and wake structures on the top of the finite cylinder. In the instantaneous flow fields the tip vortices and the recirculation region becomes visible. However, it is also observed that the flow is quite unsteady due to the large separation occurring on the top of the cylinder. In order to study the temporal behaviour of the separation, time resolved PIV was applied. This technique allows capturing the dynamic processes in detail. The development of vortices in the separated shear layer is observed and in addition regions with different dominant frequencies are identified.     

LES Study of Turbulent Boundary Layer Over a Smooth and a Rough 2D Hill Model

Large eddy simulation (LES) is carried out to investigate the turbulent boundary-layer flows over a hill-shaped model with a steep or relatively moderate slope at moderately high Reynolds numbers (Re = O(10³)) defined by the hill height and the velocity at the hill height. The study focuses on the effects of surface roughness and curvature. For Sub-grid Scale (SGS) modeling of LES, both the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) are applied. The behavior of the separated shear layer and the vortex motion are affected by the oncoming turbulence, such that the shear layer comes close to the ground surface, or the size of a separation region becomes small because of the earlier instability of the separated shear layer. Appropriate measures are required to generate the inflow turbulence. The methods of Lund et al. (J. Comput. Phys., 140:233–258, 1998) and Nozawa and Tamura (J. Wind Eng. Ind. Aerodyn., 90:1151–1162, 2002; The 4th European and African Conference on Wind Engineering, 1–6, 2005) are employed to simulate the smooth- and rough-wall turbulent boundary layers in order to generate time-sequential data of inflow turbulence. This paper discusses the unsteady phenomena of the wake flows over the smooth and rough 2D hill-shaped obstacles and aims to clarify the roughness effects on the flow patterns and the turbulence statistics distorted by the hill. Numerical validation is conducted by comparing the simulation results with wind tunnel experiment data for the same hill shape at almost the same Re. The applicability of DSM and DMM are discussed, focusing on the recirculation region behind a steep hill.     

PIV analysis of near-wake behind a sphere at a subcritical Reynolds number

The vortical structure of near-wake behind a sphere is investigated using a PIV technique in a circulating water channel at Re = 11,000. The measured velocity fields show a detailed vortical structure in the recirculation region such as recirculation vortices, reversed velocity zone, and out-of-plane vorticity distribution. The vorticity distribution of the sphere wake shows waviness in cross-sectional planes. The time-averaged turbulent structures are consistent with the visualized flow showing the onset of shear layer instability. The spatial distributions of turbulent intensities provide turbulent statistics for validating numerical predictions.