Karman Vortex Shedding Research Articles

Effects of sinusoidal streamwise gust on the vortex-induced force on an oscillating 5:1 rectangular cylinder

In the present study, the vortex-induced force was investigated for an oscillating rectangular cylinder with the side ratio of 5 ( B/D ​= ​5, B : breadth of the cylinder, D : depth of the cylinder) encountering a sinusoidal streamwise gust by wind tunnel tests and computational fluids dynamics (CFD) simulations. For the experiments part, a multiple-fan active-controlled wind tunnel was used to generate the sinusoidal streamwise gust and the vortex-induced force was measured. The results show that the component of total vortex-induced force caused by Karman vortex shedding (denoted as Karman-vortex-induced force) almost disappeared in the sinusoidal streamwise gust, while another component caused by motion-induced vortices (denoted as motion-induced force) remained almost unchanged, regardless of the gust frequency and amplitude. The CFD simulations were performed to shed light on the flow mechanism of vortex-induced force variation. It was found that the flow structure around rectangular cylinder is sensitive to the oncoming flow condition. The alternative vortex shedding in the near wake was suppressed due to the unsteady effects of sinusoidal streamwise gust, which is responsible for the disappearance of Karman-vortex-induced force. However, the vortices induced by the rectangular cylinder motion still exist and lead to the Karman vortex street in the far wake. • Experimental and numerical studies on the sinusoidal streamwise gusts over an oscillating 5:1 rectangular cylinder. • The unsteady effects of sinusoidal streamwise gusts on the vortex-induced force are investigated. • The Karman-vortex-induced force almost disappears in the sinusoidal streamwise gust. • The alternative vortex shedding in the near wake was suppressed as in the sinusoidal streamwise gust.

Experimental investigation of flame fluctuation reduction in distributed combustion

Analysis of dynamic combustor stability is essential for the development of practical devices that employ distributed reaction zones. The fluctuation of reaction zone (RZ) was studied to compare normal air combustion and distributed combustion at an equivalence ratio of 0.9 in a swirl-stabilized burner using methane fuel. Distributed combustion was fostered by diluting the inlet air stream with carbon dioxide that resulted in a gradual drop in the adiabatic flame temperature (Tad). High-speed broadband chemiluminescence at 3 kHz was used to study the global combustion dynamics. Vortex shedding observed along the shear layers influenced the oscillation of flame base in normal air combustion. However, relatively stable bases were observed in distributed combustion. Fast Fourier Transformation performed on RZ base fluctuation data supported the observations from chemiluminescence signatures. Proper orthogonal decomposition (POD) analysis indicated various vortex-shedding patterns as the dominant structures in conventional swirl flames. The power spectral density (PSD) of POD modes showed the rotational effect of RZ and weak von Karman vortex shedding to influence fluctuation in distributed combustion. The self-sustained flame oscillations in normal swirl flames were investigated from the acoustic and heat release fluctuation signals. Both acoustic and heat release fluctuations gradually reduced when approaching the distributed combustion. The PSD of these signals demonstrated a common peak at ~ 174 Hz (in normal swirl flames) with possible thermo-acoustic coupling. This peak was consistent with the peaks obtained from the base fluctuation and POD spectra. The peak gradually diminished when approaching the state of distributed combustion. A similar observation of gradually decreasing acoustic and heat release fluctuation was made with a constant Tad. However, the drop in chemiluminescence signal intensity with CO2 dilution was relatively low in case of constant Tad compared to the variable Tad case. The local and global Rayleigh index obtained for the variable Tad cases at different dilution levels showed positive values at O2 = 21 and 20%, which signified self-sustained instability. However, the distributed combustion possessed a negative Rayleigh index indicating dampening of instability. These results support the gradual decline of thermo-acoustic instability when approaching the distributed combustion condition.

Experimental investigation of the vortex-induced vibration of tapered light poles

To investigate the vortex-induced vibration (VIV) of a tapered light pole with a weld, experimental tests were carried out using a simplified aeroelastic model and a static sectional model in a wind tunnel. The VIV characteristics and aerodynamic performance of the light pole were investigated with and without considering the weld on the surface. It was found that the light pole can experience second-order mode VIV and multi-mode vibrations at different incoming wind speeds. For the second-order mode VIV, the cross wind vibration amplitudes were approximately twice that of the along wind, and the motion trajectory exhibited a steady ellipse shape. For the multi-mode vibration, no stable vibration trajectory was observed in the time history, and the higher modes vibration tended to occur at higher wind speeds. The weld had a dramatic effect on the VIV characteristics and aerodynamic performance of the light pole. The weld could increase or depress the VIV of the light pole, depending on its position relative to the wind direction. Furthermore, the aerodynamic force, Karman vortex shedding, Strouhal number, and distribution of the wind pressure were highly sensitive to the weld position. Different flow patterns could be triggered when the weld is located in certain positions, which may eventually result in different aerodynamic performance of light poles in the field.

Temporal evolution of lift in a pure cruciform system for energy harvesting

We investigated the displacement and lift time series of a circular cylinder - strip plate cruciform system for energy harvesting in the Reynolds number range 1.1×103≤Re≤14.6×103, numerically using the open source C++ library: OpenFOAM. The Karman vortex-induced vibration (KVIV) regime was identified between reduced velocity, U*, 2.3 and 13.6, while the streamwise vortex-induced vibration (SVIV) regime was identified between 18.2≤U*≤29.5. We analysed the cylinder displacement and lift time series using the Hilbert-Huang transform (HHT). Within this range of U*, Karman vortex shedding contributes nearly as much as streamwise vortex shedding to the root-mean-square amplitude of total lift, while between 25.0≤U*≤29.5, the Karman component contribution is on average twice that of the streamwise component. These findings hint at the possibility to improve the power output of the harvester by a factor of two between 18.2≤U*≤22.7 and by a factor of three between 25.0≤U*≤29.5, if we can unite the contribution to the root-mean-square amplitude of the total lift under a single vibration-driving mechanism: the shedding of streamwise vortex.

Experimental and numerical investigation of turbulent wake flow around wall-mounted square cylinder of aspect ratio 2

The turbulent wake velocity fields around a short wall-mounted square cylinder of aspect ratio 2 fully immersing into a thick turbulent boundary layer are obtained experimentally with PIV and numerically with LES. Comparison between the two sets of data is made on the time-averaged mean velocities, turbulent fluctuating velocities, and the detailed characteristics of energetic large-scale coherent structures. It is noted that a good comparison of the low-order statistics of velocity fields does not guarantee a satisfactory reproduction of the coherent structures. These flow structures show great similarities in the spatial patterns and dynamic performance between PIV and LES, but apparent differences in turbulent kinetic energy contribution. On the horizontal plane parallel to the wall, the dominant antisymmetric spatial mode pair illustrates the evolution process of Karman vortex shedding with a clear spectral peak around the characteristic frequency while three extra frequency peaks are found in the symmetric spatial modes. Further investigation on the velocity field on the central vertical plane reveals the connection between the unsteadiness of shear layer flow at the free end and the spanwise symmetric vortex shedding activities. It is confirmed that the flapping motion and vortex convection mechanisms observed for the present cylinder could modulate the symmetric wake dynamics. The three-dimensional extreme wake patterns, available from LES results, are related to the most energetic Karman vortex shedding demonstrate upward flow in the vortex weakening side. Meanwhile, the downwash flow at the extreme time instants is found to become stronger always for this kind of short cylinder with a dipole wake pattern.

Experimental investigation on vortex-induced vibrations of a hang-off evacuated drilling riser

A model experiment has been conducted for a hang-off evacuation riser considering the lower marine riser package (LMRP) based on the strain gauge test technology. The finite element eigenvalue method is used to analyze the natural frequency and mode shapes of the hang-off riser considering the axial tension force and the weight of LMRP. The modal analysis method is used to restructure the motion and analyze the vortex-induced vibration characteristics of the hang-off riser. Then, the influence of evacuation velocity is discussed. Results indicate that the mode shapes amplitude of the experimental riser with LMRP is significantly larger than that of the ordinary cantilever. The dominant frequency of each measuring point is the same, and the end-cell-induced vibration small frequency is observed near the bottom end. The vortex shedding in the cross-flow (CF) direction produced a large lift force, which resulted in the vibration frequency of in-line direction dominated by the CF direction. When the reduced velocity (Vr) is less than 40, the frequency response of the hang-off riser model increased with the evacuation velocity, which was subjected to the Karman vortex shedding frequency. When the frequency response of the riser model reached, the second-order natural frequency with Vr exceeds 40. Consequently, the “lock-in” phenomenon was observed and the riser exhibited vibrations with the second-order model.

Effects of leading-edge separation on the vortex shedding and aerodynamic characteristics of an elongated bluff body

Wind-tunnel experiments were conducted on an elongated bluff body to investigate the effects of leading-edge separation on its vortex shedding and aerodynamic characteristics. Solid wind barriers of various heights were fixed at the leading edge to adjust the flow separation and reattachment. The flow field, particularly the upper-surface boundary layer, was investigated by employing a high-resolution particle image velocimetry (PIV) system. According to the PIV results, it was found that the critical height-to-thickness ratio for the leading-edge separated flow to reattach to the surface is h/t ​= ​0.5. The streamwise length of the reverse flow region increases with an increase in the height of the wind barrier. The effects of leading-edge separation on the vortex evolution and shedding were analysed. As h/t ​≤ ​0.5, the leading-edge separated shear layer is stable and reattaches to the surface. There exists only Karman vortex shedding in the wake when h/t ​≤ ​0.2, while the vortex evolution becomes random when 0.3 ​≤ ​h/t ​≤ ​0.5. However, when h/t ​> ​0.5, the leading-edge separated shear layer becomes unstable, thus resulting in free vortex shedding, convecting downstream, and interacting with the lower shear layer. Moreover, the Strouhal number of the vortex in the wake decreases from h/t ​= ​0 to h/t ​= ​0.5 and then increases from h/t ​= ​0.6 to h/t ​= ​1.0.

Sediment-laden flow and erosion modeling in a Pelton turbine injector

Abstract A major challenge in the operation and development of the high-head water resources, especially in the mountains with high sediment yield, is the erosion of Pelton turbine components. In this work, a numerical study was carried out based on sediment properties measured in field conditions, such as particle distributions and concentrations, to analyze the erosion mechanism of a prototype Pelton turbine injector. The Volume of Fluid (VOF) method was combined with a Lagrangian particle tracking approach to simulate the air-water-sediment flow, followed by the application of Mansouri’s model to estimate the erosion. The predicted erosion patterns were in good agreement with field observations, especially in physically reproducing the asymmetrical erosion distribution on the needle surface. To elucidate this asymmetry, fundamental analysis of the flow patterns including the vortex structures and the secondary flow on the particle behaviors was carried out. Interestingly results were found about the secondary flow induced by the von Karman vortex shedding, which increased the particle separations, and consequently, enhanced the erosion in shedding areas. The current work may provide important engineering insights to reduce erosion of components with inner obstructions.

Numerical investigations on drag reduction of a civil light helicopter fuselage

The paper presents the numerical investigations for a light civil helicopter fuselage with the purpose of reducing the helicopter drag. Two numerical methods: Reynolds-Averaged Navier-Stokes (RANS) and a hybrid RANS-LES method: improved delayed detached-eddy simulation (IDDES) method are performed for the simulation of a prototype helicopter fuselage. The RANS method is validated by a modular helicopter fuselage with experimental data, while the IDDES method has already been used in other studies and good results have been achieved. The numerical results of the civil helicopter in terms of the aerodynamic coefficients obtained by the two methods are consistent with each other. Compared to the RANS method, the IDDES approach is capable of predicting the large separation flow of the fuselage/components and the small-scale vortices in the flow field. It is found that the hybrid method captures the periodically detached separating vortices behind the skid struts, while the flow at the same position simulated by the RANS method is still attached. Moreover, separating vortices, which develop diagonally upwards, are captured at fuselage/tail-boom junction by the hybrid method, whereas RANS simulation doesn't predict. Subsequently, the design of the helicopter drag reduction is carried out at α=0 deg angle of attack and 0.2 Mach number through shape optimization based on the numerical simulations, and the numerical results are verified by the force tests. It shows that the optimization of the landing skids aims at reducing the strong Karman vortex shedding effect induced by the skids, which greatly decreases the total drag. Combined with the optimization of the fuselage/tail-boom transition, this approach suppresses the separation flow of the fuselage and reduces the pressure drag, and the adjustment of transition slope benefits of up to 1.18% drag reduction, while the extension of transition reduces the drag by 2.64%. The optimization of tail-boom layout demonstrates that lower tail-boom layout can contribute to a drag reduction by 4.37% (RANS) and 3.89% (test), respectively, when compared to the original tail-boom layout.

Evaluating the applicability of a phase-averaged processing of skin-friction field measurement using an optical flow method

The phase-averaged skin-friction analysis based on global luminescent oil film (GLOF) was conducted for periodically fluctuating unsteady phenomena at the frequency of approximately 150 Hz which is estimated based on Karman vortex shedding. An unsteady pressure transducer and a camera were synchronized, and the time-averaged and phase-averaged skin-friction fields were investigated. The time-series image pair data obtained by the camera were decomposed into eight intervals of a phase angle of $$\pi /4$$ with synchronizing the signal of the unsteady pressure. The phase-averaged result shows the periodical pattern corresponding to the vortices structure generated from the edge of the test model which was not resolved by the time-averaged result. The phase-averaged processing was successfully applied to the GLOF measurement, and the results showed the detail information of skin friction at each phase.

The Comparison of Various Turbulence Models of the Flow around a Wall Mounted Square Cylinder

The flow past a wall mounted square cylinder, a typical and basic shape of building, bridge or offshore structure, was simulated using URANS computation through adoption of three turbulence models, namely, the k-e model, k-ω model, and the v2-f model. It is well known that this flow is naturally unstable due to the Karman vortex shedding and exhibits a complex flow structure in the wake region. The mean flow field including velocity profiles and the dominant frequency of flow oscillation that was from the simulations discussed earlier were compared with the experimental data observed by Wang et al. (2004; 2006). Based on these comparisons it was found that the v2-f model is most accurate for the URANS simulation; moreover, the k-ω model is also acceptable. However, the k-e model was found to be unsuitable in this case. Therefore, v2-f model is proved to be an excellent choice for the analysis of flow with massive separation. Therefore, it is expected to be used in future by studies aiming to control the flow separation.

Low-frequency unsteadiness in the flow around a square cylinder with critical angle of [formula omitted] at the Reynolds number of [formula omitted

Numerical simulations with high grid resolutions are conducted to investigate the flow past a square cylinder at the Reynolds number of 2.2×104 and the critical angle of attack of 14°. The focus is on the unsteadiness with a much lower frequency than that of von Karman vortex shedding. This study confirms the existence of low-frequency unsteadiness even for the square cylinder. The qualitative and quantitative features of low-frequency unsteadiness are systematically analyzed in terms of forces, vortex shedding and separation bubble. The low frequency with the outstanding peak is much lower than the frequency of von Karman vortex shedding; specifically, it is about 0.14fvK, where fvK is the vortex-shedding frequency. The low-frequency unsteadiness can be “felt” in the time series of forces and in the dynamics of vortex shedding and separation bubble. For both drag and lift, the unsteadiness is manifested by the low-frequency modulation of force amplitude and by the low-frequency periodic variation between the high and low values of the mean drag and lift over a vortex shedding cycle. The smaller force amplitude is accompanied simultaneously by the vortex shedding with longer formation length and weaker spanwise correlation, together with longer separation bubble on the flow-reattachment side of the cylinder.

Unsteady skin-friction field estimation based on global luminescent oil-film image analysis

A global luminescent oil-film (GLOF) image analysis method to estimate unsteady skin-friction fields in an unsteady flow field is proposed and demonstrated. A governing equation describing the dynamics of the oil film (the thin-oil-film equation) is employed for the unsteady oil-film images. The frequency response of the oil-film movement is analyzed, and a cutoff frequency is defined as a function of the oil-film thickness and the kinematic oil viscosity. The estimating skin-friction vector is defined along with a spatiotemporal weighted window and obtained by solving the overdetermined system of the thin-oil-film equation. The system can be solved by using the weighted linear least-squares method, and the time-resolved skin-friction field can be estimated. The time-resolved GLOF image analysis method is demonstrated on an experiment of a junction flow on a flat surface with a square cylinder. The GLOF images in the Karman vortex shedding bounding the flat surface were acquired, and the time-resolved skin-friction fields were obtained. The results showed that fluctuation in the skin-friction vectors corresponds to the shedding frequency, and the vortices bounding the surface were extracted. The averaged skin-friction field is compared with the result of the previous study based on the time-independent model. The normalized skin friction from both methods showed good agreement, which indicates that the quantitative value will be obtained when a calibration process is involved in a future study.

Flow/noise control of a rod–airfoil configuration using “natural rod-base blowing”: Numerical experiments

When the vortices shedding from an upstream rod impinge upon the surface of a downstream airfoil, the resultant vortex–body interaction noise can be significant. The use of “natural rod-base blowing” to reduce this interaction noise is investigated numerically using a 3D hybrid computational aeroacoustics approach. The natural blowing is generated through an internal slot that interconnects the stagnation and base region of the rod. Numerical simulation is performed for a straight blowing at blowing rates (BRs) between 6.4% and 16.3% and an oblique blowing with slot–incidence angles (θ) between 0° and 15°, respectively. Far-field noise evaluation demonstrates that the natural rod-base blowing under tested BRs can reduce significantly the noise emission, whereas loses its efficiencies gradually with the increase of angle θ. The most effective case is the straight blowing (θ=0°) at BR≥13.6% where the far-field tonal noise associated with the steady-periodic von Karman vortex shedding is annihilated. The changes in transient flow structures indicate that the natural blowing gradually attenuates the von Karman vortex shedding when BR increases, resulting in a mitigation of vortex–body​ interaction on the airfoil leading surface and hence a reduction of the unsteady lift. At BR=13.6%, as the angle θ reaches 15° from below, a new von Karman vortex street reforms in the flow field, leading to another tonal noise. Linear stability analysis based on a local concept of absolute/convective instability suggests that the absolutely unstable region in the near-wake of the rod elongates first and then shrinks with the increase of BR, while the local absolute growth rate decreases monotonously.

Dynamic mode decomposition analysis of flow characteristics of an airfoil with leading edge protuberances

A numerical investigation of the flow mechanisms and fluctuating aerodynamic performances of an airfoil with leading-edge protuberances is presented within post-stall regime at a Reynolds number of 1.2×105. In detail, a large eddy simulation (LES) has been conducted and then validated through quantitative comparisons with experimental and numerical results. Furthermore, dynamic mode decomposition (DMD) analysis has been carried out. Superior to the proper orthogonal decomposition (POD) method, DMD could extract mode with single-frequency characteristics. Therefore, the physical backgrounds of corresponding modes could be identified, and the flow control mechanisms could be uncovered, together with the influence on spanwise coherent structures. From the analysis at a streamwise section near laminar separation bubbles (LSBs), it has been found that the improved aerodynamic characteristics at peaks stem from the strong streamwise vortices induced by leading-edge protuberances, which lead to momentum transfer process from troughs to neighboring peaks. Meanwhile, DMD modes corresponding to the shear layers of LSBs have also been found, and the frequency characteristics are quantitatively depicted. On the other hand, from the analysis at selected lateral slices, the first DMD mode of smooth airfoil case is obviously related with Karman vortex shedding process according to the spatial distribution and frequency characteristics. Although wavy leading-edge causes the breakdown of spanwise coherent structures and the degradation of flow energy, Karman vortex shedding pattern could also be identified at particular troughs in modified airfoil case.

Experimental investigation of vortex shedding past a circular cylinder in the high subcritical regime

Vortex shedding in the near wake of a circular cylinder is investigated using surface pressure measurements and two component Particle Image Velocimetry (2C PIV) for 1.49 × 105 ≤ Re ≤ 5 × 105. Space-time distribution of surface pressure shows that regular vortex shedding is interspersed with bursts of weakened activity. Its occurrence increases with an increase in Re. As a result, the rms of the lift coefficient decreases significantly in the subcritical regime with an increase in Re. Proper Orthogonal Decomposition (POD) of the surface pressure data and the 2C PIV data at the midspan of the cylinder shows that most of the energy is contained within the antisymmetric (AS) and symmetric (S) modes. The AS mode is responsible for the regular von Karman vortex shedding, while the S mode is related to intermittent expansion and contraction of the vortex formation region. The energy of the AS mode decreases at a faster rate as compared to that of the S mode with an increase in Re. The S mode is the most dominant mode beyond Re ∼ 3.2 × 105. In the critical regime, the POD modes are modified due to the presence of the intermittent Laminar Separation Bubble (LSB). 2C PIV at the midspan of the cylinder reveals that the weakening of the AS mode is accompanied by an increase in the formation length, Lf. (Lf/d) increases from 1.4 in the low subcritical to 2.0 in the high subcritical regime, where d is the diameter of the cylinder. The weakening of the AS mode and increase in Lf/d collectively lead to a significant decrease in fluctuating lift with an increase in Re. 2C PIV of a spanwise section shows that weakening of vortex shedding is nearly uniform along the span of the cylinder.

Geometry effects on mean wake topology and large-scale coherent structures of wall-mounted prisms

Turbulent wake behind five wall-mounted rectangular prisms is measured by time-resolved particle-image velocimetry with an aim to generalize the effects of prism geometry (in terms of aspect ratio, AR, and side ratio, SR) on the wake characteristics. For the time-averaged wake, the arch-type topology is well supported. With AR increasing from 1 to 4 for the square prisms, a transition process between the “dipole” and “quadrupole” wake patterns is observed. On the other hand, an increase in SR does not seem to greatly influence the mean wake structure behind rectangular prisms unless reattachment occurs on the side walls. The turbulent wake velocity fields are analyzed with a proper orthogonal decomposition method, considering the intrinsic symmetries of vortex shedding activities. In the extraction of dominant low-order flow structures, the low-frequency shift mode and periodic vortex shedding mode pair are always captured as the most important turbulent kinetic energy contributors but with significant nonlinear cross-superposition. A low-pass Gaussian filter is then introduced to achieve separation between these two types of coherent structures via new spatial modes, which maintain the same mode shape patterns. The size of the shift mode vortex is found closely related to the time-averaged wake structure, while the pattern of the Karman vortex shedding mode pair seems completely independent. The two separated pure modes develop continuously and compete with each other along the model height. The present study appears to be the first one to investigate the effects of prism geometry on large-scale coherent wake motions from this perspective.

Correlation between single-wire and multi-wire tripping of the flow past a circular cylinder

An experimental study is carried out to explore if the collective influence of multiple tripwires applied spanwise on a circular cylinder can be correlated to the well-known effects of single-wire tripping from previous studies. Constant Temperature Anemometry and Particle Image Velocimetry tests were conducted on single-wire- and two-wire-fitted cylinders in subcritical flow. Noting that a single tripwire can only influence the shedding frequency when it is within a certain range of locations on the cylinder surface, two scenarios for two-wire-fitted cylinders are noteworthy: (1) One of the two wires can fall within this range of locations. This is the case where flow features for the two-wire-fitted cylinder are identical to the single-wire-fitted one. In this category, the Karman vortex shedding loses its coherence and a bistable separation behavior sets in when the influential wire is at the first critical location (+/−θc1) of the single-wire application. (2) Both tripwires can be in the range of locations where the single tripwire application influences the shedding frequency. This is the scenario where flow is controlled by both tripwires. The most dominant influence comes from the tripwire that is closer to the θc location (another critical location identified by previous studies for single-wire applications). Furthermore, in this category, the drastic attenuation of the Karman instability and the onset of the bistable shear-layer separation occur when one of the wires is at a new θc1 location that is about 5°–7° larger than the θc1 reported for single-wire tripping by previous studies. This change in θc1 comes together with a large degree of near-wake contraction to satisfy the simultaneous entrainment demand needed for the early transition of both shear layers in the two-wire-fitted case. A shortage of fluid in satisfying such an increased entrainment demand is speculated to be the cause of the observed shift in θc1.

Cross-spectral analysis of PSP images for estimation of surface pressure spectra corrupted by the shot noise

We proposed applying the cross-spectrum analysis to the unsteady pressure-sensitive paint (PSP) images to eliminate the electronic shot noise component from the pressure fluctuation spectrum. The data of surface pressure fluctuation behind a square cylinder which measured by means of the polymer/ceramic PSP with a frequency response of approximately 5 kHz which is sufficiently high for studying the Karman vortex shedding was used for the validation of this analysis method. The cross spectrum is compared with the auto-spectrum of PSP images and that of the Kulite pressure transducer that corresponds to the reference signal. The cross spectrum can drastically reduce the electronic shot noise component in the pressure fluctuation spectrum. The second peak of vortex shedding which is not observed in the result of auto-spectrum can be observed thanks to the noise reduction. The convergence of calculation is faster as the size of the spatial area for calculating cross spectrum increases.

Low-frequency dynamics of the flow around a finite-length square cylinder

Fluctuating pressure on the side faces, lee-ward face and free end of a finite-length square cylinder is measured simultaneously, together with the velocity in its free-end shear flow, to reveal their inherent connection. The width (d) of the tested model is 40 mm, and the aspect ratio is 5. All experiments are conducted in a low-speed wind tunnel at an oncoming flow velocity (U∞) of 10 m/s. The corresponding Reynolds number based on U∞ and d is 27,000. It is found that, the fluctuating pressure on the side faces and free end has remarkable low-frequency instability with the frequency of about 1/10 of the well-known spanwise Karman vortex shedding. Besides, a high-frequency component, corresponding to Karman vortex shedding, is also found in the fluctuating pressure on cylinder side faces. The low-frequency instability is in phase over the entire cylinder span, while the high-frequency component tends to be out of phase, especially at the lower part of the cylinder. The free-end shear flow flaps at the low frequency and strongly correlates with the modes of spanwise vortex shedding. Particularly, when the free-end shear flow flaps to its lower position, alternate spanwise vortex shedding with high pressure fluctuation occurs; when it flaps to its upper position, the occurrence probability of co-shedding with low pressure fluctuation increases significantly especially near the cylinder free end.