Strouhal Vortex Research Articles

Study of unsteady separated fluid flows using a multi-block lattice Boltzmann method

PurposeNumerical simulations are performed for studying the vorticity dynamics of a dipole colliding with the wall in a bounded flow and the wake structure and separated flow properties past a circular cylinder at the values of Reynolds numbers.Design/methodology/approachThe near wake statistics of separated fluid flows are investigated by using the lattice Boltzmann method (LBM) in a two-dimensional framework. A multi-block technique is applied to accurately resolve the flow characteristics by the grid refinement near the wall and preserve the stability of the numerical solution at relatively high Reynolds numbers.FindingsThe results show that the rolling-up of the boundary layer occurs due to the shear-layer instabilities near the surface which causes a boundary layer detachment from the wall and consequently leads to the formation of small-scale vortices. These shear-layer vortices shed at higher frequencies than the large-scale Strouhal vortices which result in small-scale high-frequency fluctuations in the velocity field in the very near wake. The present study also demonstrates that the efficiency of the multi-block LBM used for predicting the statistical features of flow problems is comparable with the solvers based on the Navier-Stokes equations.Practical implicationsStudying the separated flow characteristics in aerospace applications.Originality/valueApplying a multi-block lattice Boltzmann method (LBM) for simulation of separated fluid flows at high-Reynolds numbers. Studying of the near wake statistics of unsteady separated fluid flows using the multi-block LBM. Comparison of flow characteristics obtained based on the LBM with those of reported based on the Navier-Stokes equations.

Effect of Lateral End Plates on Flow Crossing a Yawed Circular Cylinder

Numerical simulation is carried out to investigate the effect of the boundary condition of two lateral end-plate walls on the flow structure in the wake of a flow crossing a yawed circular cylinder. Two typical boundary conditions, nonslip and periodic, are investigated. It is revealed that the boundary condition of the two end-plates has a significant effect on the flow behaviors in the wake. Under the nonslip boundary condition, the vortex structure in the wake exhibits a tapering shape to the tip end. The flow pattern is formed in the wake as the streamlines on the tip side are becoming denser while the streamlines on the base end are becoming sparser. Spectral power analysis of the local lift coefficient shows that the frequency distribution exhibits axial variation. On the base side, the frequency distribution is broadband. On the tip side, there are two peak frequencies: the larger one corresponds to the value predicted by the independence principle, and the smaller one is generated by the secondary axial flow separation from the rear cylinder wall. Under the periodic condition, the numerical results show that organized Strouhal vortex is shed in the wake in the same way as to the flow orthogonally passing a cylinder and the independence principle is still applicable.

Scaling of swimming performance in baleen whales.

The scale dependence of locomotor factors has long been studied in comparative biomechanics, but remains poorly understood for animals at the upper extremes of body size. Rorqual baleen whales include the largest animals, but we lack basic kinematic data about their movements and behavior below the ocean surface. Here, we combined morphometrics from aerial drone photogrammetry, whale-borne inertial sensing tag data and hydrodynamic modeling to study the locomotion of five rorqual species. We quantified changes in tail oscillatory frequency and cruising speed for individual whales spanning a threefold variation in body length, corresponding to an order of magnitude variation in estimated body mass. Our results showed that oscillatory frequency decreases with body length (∝length-0.53) while cruising speed remains roughly invariant (∝length0.08) at 2 m s-1 We compared these measured results for oscillatory frequency against simplified models of an oscillating cantilever beam (∝length-1) and an optimized oscillating Strouhal vortex generator (∝length-1). The difference between our length-scaling exponent and the simplified models suggests that animals are often swimming non-optimally in order to feed or perform other routine behaviors. Cruising speed aligned more closely with an estimate of the optimal speed required to minimize the energetic cost of swimming (∝length0.07). Our results are among the first to elucidate the relationships between both oscillatory frequency and cruising speed and body size for free-swimming animals at the largest scale.

Flow visualization over a thick blunt trailing-edge airfoil with base cavity at low Reynolds numbers using PIV technique

In this study, the effect of cutting the end of a thick airfoil and adding a cavity on its flow pattern is studied experimentally using PIV technique. First, by cutting 30% chord length of the Riso airfoil, a thick blunt trialing-edge airfoil is generated. The velocity field around the original airfoil and the new airfoil is measured by PIV technique and compared with each other. Then, adding two parallel plates to the end of the new airfoil forms the desired cavity. Continuous measurement of unsteady flow velocity over the Riso airfoil with thick blunt trailing edge and base cavity is the most important innovation of this research. The results show that cutting off the end of the airfoil decreases the wake region behind the airfoil, when separation occurs. Moreover, adding a cavity to the end of the thickened airfoil causes an increase in momentum and a further decrease in the wake behind the trailing edge that leads to a drag reduction in comparison with the thickened airfoil without cavity. Furthermore, using cavity decreases the Strouhal number and vortex shedding frequency.Graphical abstract

Analysis of Flow Timescales on a Periodically Pitching/Surging Airfoil

Time-resolved velocity fields around a pitching and surging NACA 0018 airfoil were analyzed to investigate the influence of three independent timescales associated with the unsteady flowfield. The first of these timescales, the period of the pitch/surge motion, is directly linked to the development of dynamic stall. A simplified model of the flow using only a time constant mode and the first two harmonics of the pitch surge frequency has been shown to accurately model the flow. Full stall and leading-edge flow separation, however, were found to take place before the maximum angle of attack, indicating that a different timescale was associated with leading-edge vortex formation. This second, leading-edge vortex, timescale was found to depend on the airfoil convection time and compare well with the universal vortex formation time. Finally, instantaneous non-phase-averaged measurements were investigated to identify behavior not directly coupled to the airfoil motion. From this analysis, a third timescale associated with quasi-periodic Strouhal vortex shedding was found before flow separation. The interplay between these three timescales is discussed in detail, particularly as they relate to the periodic velocity and angle-of-attack change apparent to the blades of a vertical axis wind turbine.

Flow past a cylinder close to a free surface

Two-dimensional flow past a cylinder close to a free surface at a Reynolds number of 180 is numerically investigated. The wake behaviour for Froude numbers between 0.0 and 0.7 and for gap ratios between 0.1 and 5.0 is examined. For low Froude numbers, where the surface deformation is minimal, the simulations reveal that this problem shares many features in common with flow past a cylinder close to a no-slip wall. This suggests that the flow is largely governed by geometrical constraints in the low-Froude-number limit.At Froude numbers in excess of 0.3–0.4, surface deformation becomes substantial. This can be traced to increases in the local Froude number to unity or higher in the gap between the cylinder and the surface. In turn, this is associated with supercritical to subcritical transitions in the near wake resulting in localized free-surface sharpening and wave breaking. Since surface vorticity is directly related to surface curvature, such high surface deformation results in significant surface vorticity, which can diffuse and then convect into the main flow, altering the development of Strouhal vortices from the top shear layer, affecting wake skewness and suppressing the absolute instability. The variations of parameters such as Strouhal number and formation length are provided for Froude numbers spanning the critical range.At larger Froude numbers, good agreement is obtained with recently published experimental investigations. The previously seen metastable wake states are observed to occur for similar system parameters to the experiments despite the difference in Reynolds numbers by a factor of about 40. The wake state switching appears to be controlled by a feedback loop. Important elements of the feedback loop include the cyclic generation and suppression of the absolute instability of the wake, and the role of surface vorticity and vortices formed from the bottom shear layer in controlling vortex formation from the top shear layer. The proposed mechanism is presented. Shedding ceases at very small gap ratios (–0.2). This behaviour can be explained in terms of the fluid flux through the gap, vorticity diffusion into the surface and opposite-signed surface vorticity from the strong surface deformation.

Trailing vortices in a free-surface flow

The free-surface effect on two-dimensional flow structures, especially on the trailing vortices, is investigated numerically in this paper. The solution procedure employs a higher-order semi-implicit projection method. The numerical results have been compared with experimental data on wave elevation disturbed by a submerged translating hydrofoil with a positive angle of attack. The schematic computations reveal some interesting and unique characteristics of the trailing-vortex development in a laminar flow beneath a free surface. Based on the computational data, an empirical Strouhal–Reynolds–Froude number relationship is proposed for the purely laminar vortex shedding in a free-surface flow. Moreover, the numerical findings also indicate that the presence of a free surface accelerates the Strouhal vortex frequency, yet delays not only the onset of a large-scale Kármán instability but also the occurrence of transitional behaviors. The shedding frequency downshifts drastically or even becomes discontinuous when the secondary vortex grows on the suction side. A metastable transition frequency emerges at the same time and becomes distinct with increasing Reynolds number. The variation of the vortex-shedding Strouhal number with respect to both Reynolds and Froude numbers is obtained. The power spectra of the trailing wake consist of harmonics of the vortex-shedding and transition frequencies (mfs,nft), as well as their combinations (mfs±nft).

At the Upper Transition of Subcritical Regime of a Circular Cylinder

The present study establishes the transition between the lower and upper subcritical regime of flow over a circular cylinder at 7×103<Re<2×104. Based on a new sampling technique, it is shown that the small-scale secondary vortices, especially those of high energy, play an important role in the transition. Within a primary vortex shedding period, the secondary vortices appear in groups. In a group, the streamwise velocity of secondary vortices exhibits the increase, peak, and decrease pattern associated with the formation of Strouhal vortices. In the lower subcritical regime, the Group I of singular group occurs most frequently, while in the upper subcritical regime, the Group III of three groups is the most frequent. Pairings of successive secondary vortices are found, and the paired vortices also appear in groups. The present model of transition involves the excitation of the separated shear layer at the most amplified mode by the disturbances associated with the secondary and paired vortices. Due to their mutual interference, the higher-energy small-scale vortices affect the primary vortex sheet, which in turn amplifies the former. These higher-energy vortices have enhanced pairings, which also play a dominant role in the later stage of transition.

Turbulent Flow Past an Array of Bluff Bodies Aligned Along the Channel Axis

Computations and measurements of time mean velocities, total fluctuation intensities, and Reynolds stresses are presented for spatially periodic flows past an array of bluff bodies aligned along the channel axis. The Reynolds number based on the channel hydraulic diameter and cross-sectional bulk mean velocity, the pitch to rib-height ratio, and the rib-height to channel-height ratio were 2 × 104, 10, and 0.13, respectively. The unsteady phase-averaged Navier-Stokes equations were solved using a Reynolds stress model with wall function and wall-related pressure strain treatment to reveal the feature of examined unsteady vortex shedding flow. Laser Doppler velocimetry measurements were performed to measure the velocity field. Code verifications were performed through comparisons with others’ measured developing single-rib flow and our measured fully developed rib-array flow. The possible causes for the differences between the experiments and computations are discussed. The calculated phase-averaged flow field clearly displays the vortex shedding behind the rib and is characterized in terms of shedding Strouhal number, vortex trajectory, vortex celerity, and vortex travelling distance in a phase cycle. Furthermore, the difference between the computed developing single-rib flow and fully developed rib-array flow is addressed.

Wake structure of a single bubble rising in a two-dimensional column

The formation-shedding mechanism of the turbulent wake induced by a single gas bubble rising in a two-dimensional column has been experimentally studied. Both qualitative flow visualization and quantitative full-field measurements using particle tracking technique have been conducted. The topological characteristics of phase-averaged and time-mean flow fields are studied in terms of the critical point theory. Contours for phase-averaged vorticity and time-mean Reynolds stresses are presented. The continuous supplies of small-scale shear layer vortices and turbulent stresses from the free shear layer to the wake are evident. Variation of circulation with the phase is given. Except at the time when the entrained free stream cuts through one side of the wake boundary and results in shedding of the Strouhal vortex, the supply-dispersion of positive and negative shear layer vortices from both sides of the free shear layer is found to be nearly equivalent. The descending velocity of Strouhal vortex in the near wake is examined to be less than $ {1 \\over 3}$ of the bubble rising velocity.

A Large-Eddy Simulation of the Near Wake of a Circular Cylinder

The formation and the downstream transport of the Strouhal vortices in the near wake of a circular cylinder are investigated using the large-eddy simulation (LES) method. The governing equations are formulated in curvilinear coordinates to accommodate a nonorthogonal grid with formal development of a dynamic model to account for the subgrid turbulent scales. Results were produced with and without use of the model. The focus of the investigation is at a subcritical Reynolds number of 5600. Using the dynamic model, the LES results compared best to the published experimental data in terms of both the global and local wake characteristics such as the drag and base pressure coefficients, shedding and detection frequencies, peak vorticity, and the downstream mean velocity-defect and Reynolds stresses. The results further showed streamwise filaments that connect subsequent Strouhal vortices. Qualitatively, the time-averaged Reynolds stresses of the formation region revealed similar symmetric characteristics over the range 525 ≤ Re ≤ 140,000.

Turbulent Near Wake Behind a Partially Grooved Circular Cylinder

The near wake of a partially V-grooved circular cylinder is investigated. The flow over the smooth half is within the high subcritical regime, while that over the grooved half is within the transcritical regime. Secondary and Strouhal vortices are found in the near wakes of both halves. The formation of the secondary vortices, due to the separated shear layers, is coupled to the formation of the Strouhal vortices. These secondary vortices of the two halves are of the horse shoe type. On the grooved half, another type of secondary vortices is found to be caused by the flow over the triangular blunt end of the V grooves.

Three-dimensional subharmonic waves during transition in the near-wake region of a cylinder

Detailed quantitative measurements of three-dimensional subharmonic waves have been obtained with a scanning laser anemometer in the near-wake region of a circular cylinder. A spatial decomposition technique has been used to separate the secondary three-dimensional flow from the primary Strouhal vortex flow. The appearance of subharmonic frequencies in the spectrum of the secondary instability field at Reynolds numbers of 300 and above provides experimental evidence consistent with the scenario of a period-doubling route to turbulence. The basic flow structure of the secondary field responsible for producing the subharmonics is shown to be pairs of counter-rotating streamwise vortices, which alternate the direction of rotation every Strouhal period.

Numerical analysis of incompressible flow over smooth and grooved circular cylinders

The viscous incompressible flow fields around smooth and grooved circular cylinders are simulated by solving two-dimensional time-dependent Navier-Stokes equations. The numerical scheme used is the MAC method in finite-volume discretization with pressure and velocity as variables. New boundary conditions on the grooved cylinder surface are proposed such that the Navier-Stokes solver code, originally developed for smooth cylinder flow, can be slightly modified to simulate the flow field around a grooved cylinder. Detailed comparison between smooth and grooved cylinder flows indicates that the grooves affect the flow characteristics on the cylinder surface as well as the flow structures in space. The phenomena of Strouhal vortex shedding and transition waves in the near wake are predicted. By using spectral analysis, the frequency ratio of the transition wave to the Strouhal vortex of the smooth cylinder flow field is shifted due to the presence of the grooves. The increase in this frequency ratio with Reynolds number at 10 3 ⩽ Re ⩽ 5 × 10 3 qualitatively agrees with the experimental results. The interaction processes like vortex pairing and merging in the near wake of both smooth and grooved cylinder flows are also predicted.

Shear layer vortices and longitudinal vortices in the near wake of a circular cylinder

Results are presented on (1) the shear layer vortices developing in the free shear layers located between the separation point and the first shed Strouhal vortex of a circular cylinder and (2) the longitudinal vortices developing in the braid region of the Strouhal vortices in the wake. Evidence based on flow visualization shows that the longitudinal vortices develop independently at low Reynolds numbers. An analysis is developed to show that the spanwise length scale of the longitudinal vortices in the separated shear layers and the longitudinal vortices in the Strouhal vortices are comparable near Re ≈ 1000. At higher Reynolds number, with increasing Re, the spanwise scale of the former reduces faster than that of the latter.

An Experimental Investigation of Streamwise Vortices in the Wake of a Bluff Body

Three-dimensional near-field wake structures behind a circular cylinder were investigated at Reynolds numbers ranging from 50 to 1800 based on cylinder diameter. The main feature of the three-dimensional structure of the wake behind the cylinder is the formation of streamwise vortices superimposed on the Strouhal vortex street. Flow visualization experiments were conducted to illustrate the relationship between the streamwise vortices and the Strouhal vortices. The formation of the streamwise vortices in the wake is discussed and it is emphasized that the stretching effect in the saddle region formed by the spanwise vortices plays a major role in the development of the streamwise vortices. Spanwise wavelengths of the streamwise vortices were measured using flow visualization and a digital imaging method. Spanwise perturbations were introduced to study the wavelength selectivity of the streamwise vortices.

Quantitative measurements of three-dim ensional structures in the wake of a circular cylinder

The fine scale three-dimensional structures usually associated with streamwise vortices in the near wake of a circular cylinder have been studied at Reynolds numbers ranging from 170 to 2200. Spatially continuous velocity measurements along lines parallel to the cylinder axis were obtained with a scanning laser anemometer. To detect the streamwise vortices in the amplitude modulated velocity field, it was necessary to develop a spatial decomposition technique to split the total flow into a primary flow component and a secondary flow component. The primary flow is comprised of the mean flow and Strouhal vortices, while the secondary flow is the result of the three-dimensional streamwise vortices that are the essence of transition to turbulence. The three-dimensional flow amplitude increases in the primary vortex formation region, then saturates shortly after the maximum amplitude in the primary flow is reached. In the near-wake region the wavelength decreases approximately like Re−0.5, but increases with downstream distance. A discontinuous increase in wavelength occurs below Re = 300 suggesting a fundamental change in the character of the three-dimensional flow. At downstream distances (x/D = 10-20), the spanwise wavelength decreases from 1.42D to 1.03D as the Reynolds number increases from 300 to 1200.

An experimental investigation of streamwise vortices in the wake of a bluff body

Three-dimensional near-field wake structures behind a circular cylinder were investigated at Reynolds numbers ranging from 50 to 1800 based on cylinder diameter. The main feature of the three-dimensional structure of the wake behind the cylinder is the formation of streamwise vortices superimposed on the Strouhal vortex street. Flow visualization experiments were conducted to illustrate the relationship between the streamwise vortices and the Strouhal vortices. The formation of the streamwise vortices in the wake is discussed and it is emphasized that the stretching effect in the saddle region formed by the spanwise vortices plays a major role in the development of the streamwise vortices. Spanwise wavelengths of the streamwise vortices were measured using flow visualization and a digital imaging method. Spanwise perturbations were introduced to study the wavelength selectivity of the streamwise vortices.

The Mechanics of Separated Flows about Cylinders

The development of the separated shear flows about rectangular and circular cylinders is investigated in the Reynolds number range 3000 less than 9000 by means of flow visualisation with hydrogen bubbles and velocity measurement with a hot-film anemometer. The results elucidate some interesting features of the three-dimensional flow in the nonlinear stage of the transition to turbulence. The small-scale spanwise vortices formed in the separated flow undergo strong distortion and merge into a large-scale Strouhal vortex. The interaction between spanwise vortices is closely associated with the spectral properties of velocity fluctuations. The pair of the counter-rotation streamwise vortices are detected between the large-scale spanwise vortices in the near wake of the cylinder.

Secondary vortices in the wake of circular cylinders

Using both the hydrogen-bubble flow-visualization technique and hot-wire-anemometry measurements, secondary vortices have been detected in the near-wake of circular cylinders and their characteristics studied over a Reynolds-number range of 1200–11000. The vortex-shedding characteristics of these secondary vortices clearly indicate that ‘transition waves’, detected in the cylinder near wake by Bloor (1964), and secondary vortices are identical phenomena. It is established that the non-dimensional shedding frequency of the secondary vortices demonstrates a 0.87 power-law relationship relative to Reynolds number, contrary to the 0.5 power-law reported by Bloor. The results suggest that the vortices result from a near-wake, free-shear instability which causes the separated cylinder boundary layer to roll up into the secondary vortices. Visual observations indicate that immediately following their formation the vortices undergo a strong three-dimensional distortion, which may provide the mechanism for the transition from laminar to turbulent Strouhal vortices.