Numerical investigation of fluid flow past a square cylinder using upstream,downstream and dual splitter plates

A two-dimensional numerical study is carried out to analyze the drag reduction and vortex shedding suppression behind a square cylinder in presence of splitter plate arranged in upstream, downstream and both upstream and downstream location at low Reynolds number (Re = 160). Computations are performed using a Single relaxation time lattice Boltzmann method (SRT-LBM). Firstly, the code is validated for flow past a single square cylinder. The obtained results are compared to those available in literature and found to be in good agreement. Numerical simulations are performed in the ranges of 1 ≤ L ≤ 4 and 0 ≤ g ≤ 7, where L and g are the length of splitter plate and gap spacing between the splitter plate and main square cylinder, respectively. The effect of these parameters on the vortex shedding frequency, time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficient, vorticity contours visualization and force exerted on the cylinder are quantified together with the observed flow patterns around the main cylinder and within the gap spacings. The observed results are also compared with a single square cylinder without splitter plate. We found that at some combinations of L and g, the mean drag coefficient and Strouhal number reach either its maximum or minimum value. It is found that the drag is reduced up to 62.2 %, 13.3 % and 70.2 % for upstream, downstream and dual splitter plates, respectively as compared to a single square cylinder (without splitter plate). In addition, in this paper we also discussed the applications of SRT-LBM for suppression of vortex shedding and reduction of the drag coefficients.     

Numerical investigation of wake flow control by a splitter plate

Unsteady separated flow around a square cylinder is simulated by using vortex tracing method to investigate the wake flow control by a splitter plate attached to the base of a bluff body. The numerical method is evaluated with selected numerical parameters for the case without the splitter plate. Then the method is applied to computations for different splitter plate lengths. Instantaneous flow patterns are scrutinized to see how the splitter plate affects the vortex formation behind the body and the downstream shedding. It is confirmed that the drag and the frequency are significantly reduced by the splitter plate, suppressing vortex shedding in the wake.     

Numerical study of fluid force reduction on a circular cylinder using tripping rods

A numerical investigation on the effects of small tripping rods on the fluid force reduction on a big structure has been carried out using finite volume method where a configuration of a circular cylinder with two small tripping rods symmetrically placed very near to its front surface is studied. The diameter ratio of the rods and the cylinder is set at 0.08, 0.10 and 0.12, and the gap between the rods and the cylinder is fixed at 0.08 of the cylinder diameter. The angular position of the rods varies from 20° to 60°. The effects of the tripping rods on force reduction, vortex shedding frequency and flow separation have been examined for various arrangements of the rods with Reynolds number focused on 200 for laminar flow and 5.5×10⁴ for a turbulent flow. The results reveal that there exits an optimum position where the time averaged force coefficients acting on the cylinder all reach their minimum values and at the same time Strouhal number meets its maximum. At the optimum position the drag coefficient is reduced by 18% for Re=200 and 59% for Re=5.5×10⁴. Further investigation with tripping rods placed near the separation points is also carried out for Re=5.5×10⁴ and a considerable drag reduction is found.     

Comparison of flow characteristics around an equilateral triangular cylinder via PIV and Large Eddy Simulation methods

The flow structures around an equilateral triangular cylinder, which is commonly used as a vortex shedder in the vortex flowmeter, were investigated experimentally and numerically. Flow characteristics such as vorticity contours, patterns of sectional streamlines, velocity vectors, velocity fields, Reynolds stress correlations, Strouhal numbers and drag coefficients were examined using the Particle Image Velocimetry (PIV) technique and the Large Eddy Simulation (LES) turbulence model. Experimental studies were performed in an open water channel for Re=2.9×10³, Re=5.8×10³ and Re=1.16×10⁴ based on the equilateral triangle edge. A sharp-tip corner of the cylinder with a triangle cross-section was exposed to the upstream side while the other two sharp-tip corners were placed on the downstream side. Numerical studies were also completed at Reynolds numbers in the range of 2.9×10³≤Re≤1.16×10⁵ to obtain the changes in the Strouhal numbers and drag coefficients. When the results of PIV and LES are considered in the same interval of Reynolds numbers, the maximum and minimum values of each flow pattern were nearly the same. The time-averaged patterns had considerable symmetry with respect to the axis line passing through the sharp-tip corner of the cross-section of the triangular cylinder. The Strouhal number was independent of the Reynolds number and was found to be approximately 0.22. The drag coefficient decreased with increasing Reynolds numbers while increasing the Power Spectral Density (PSD) and the vortex shedding frequency. For the same Reynolds numbers, the experimental and numerical results were in good agreement. Therefore, the LES turbulence model is recommended for applications of flow around this type of bluff body that is generally used in the design of vortex flowmeters to generate vortex shedding.     

Study on the unsteady wakes past a square cylinder near a wall

Experimental and numerical studies on the unsteady wake field behind a square cylinder near a wall were conducted to find out how the vortex shedding mechanism is correlated with gap flow. The computations were performed by solving unsteady 2-D Incompressible Reynolds Averaged Navier-Stokes equations with a newly developed ε-SST turbulence model for more accurate prediction of large separated flows. Through spectral analysis and the smoke wire flow visualization, it was discovered that velocity profiles in a gap region have strong influences on the formation of vortex shedding behind a square cylinder near a wall. From these results. Strouhal number distributions could be found, where the transition region of the Strouhal number was atG/D=0.5 - 0.7 above the critical gap height. The primary and minor shedding frequencies measured in this region were affected by the interaction between the upper and the lower separated shear layer, and minor shedding frequency was due to the separation bubble on the wall. It was also observed that the position(y/G) and the magnitude of maximum average velocity (u/u∞) in the gap region affect the regular vortex shedding as the gap height increases.     

Experimental study on the confined flow over a circular cylinder with a splitter plate

An experimental study was carried out to investigate the effect of a splitter plate on wake flows downstream of a circular cylinder symmetrically placed in a confined channel. A particle image velocimetry (PIV) measurement was applied to visualize the flow structure and analyze changes in the vortex shedding process. The control elements of the splitter plate length, L/D (D is the cylinder diameter) was varied from 0 to 1.5 and Reynolds number, Re_D was considered at 2400 and 3000. The experimental results showed that the splitter plate had an influence on stabilization of wake turbulences in a confined channel. For shorter splitter plate length of L/D=0.5 and 0.75 cases, flow structures were significantly modified and the vortex shedding frequency decreased as compared with bare cylinder cases. For longer splitter plate length of L/D=1, 1.25 and 1.5 cases, the generation of a secondary vortex was observed based on the snapshot proper orthogonal decomposition (snapshot POD) analysis. In addition, turbulent characteristics corresponding to turbulent kinetic energy (TKE) and Reynolds shear stress correlations took the lowest values and the dominant vortex shedding frequency disappeared. There was an optimal value of the splitter plate length at L/D=1 on suppression of velocity fluctuations. Moreover, the stabilizing effect of a splitter plate was more obvious at Reynolds number of Re_D=3000 than that at Re_D=2400.     

Numerical simulation of flow past rectangular cylinders with different aspect ratios using the incompressible lattice Boltzmann method

This paper presents a numerical study of a uniform flow past a rectangular cylinder using the incompressible lattice Boltzmann method (ILBM). Firstly, we use the ILBM to simulate the flow past a square cylinder symmetrically placed in a two-dimensional channel and results are validated against the well-resolved results obtained using finite-difference method and finite-volume method. Secondly, the effects of the aspect ratio defined as R = width/height on the fluid forces, vortex shedding frequency and the flow structures in the wake are investigated. Aspect ratios ranging from 0.15 to 4.00 and four Reynolds numbers Re = 100, 150, 200 and 250 are selected for the investigation. The results show that the effects of aspect ratio on physical quantities such as drag and lift coefficients, Strouhal number and the vortex shedding mechanism are very notable in the range between 0 and 2. In general, the drag coefficient decreases with the aspect ratio and the decreasing rate is more distinct in the range of 0.15 ≤ R ≤ 2.0. There is no local maximum found at around R = 0.6 in the drag coefficient as reported for higher Reynolds numbers in the literature. However the root-mean-square value of the lift coefficient shows a maximum value at R ≈ 0.5 for all Reynolds numbers selected. The variation of Strouhal number with R appears to be different for four selected Reynolds numbers. Especially for Re = 250, a discontinuity in St, as has been observed for higher Reynolds numbers, is observed at around R = 1.45 where multiple peaks are found in the result of Fourier spectrum analysis of the lift force and irregular vortex shedding behavior with no fixed shedding frequency is observed from the instantaneous vorticity contours. Such discontinuity is not observed for Re = 100, 150 and 200. The present results using the LBM are compared with some existing experimental data and numerical studies. The comparison shows that the LBM can capture the characteristics of the bluff body flow well and is a useful tool for bluff body flow studies.     

Gap-flow patterns behind twin-cylinders at low Reynolds number

The flow structures, drag coefficients (C _d ) and vortex shedding characteristics around a single square cylinder and twin side-by-side square cylinders were experimentally investigated with various Reynolds numbers (Re) and gap ratios (g*) in a vertical water tunnel. The Reynolds number (Re) and gap ratio (g*) were 178 < Re < 892 and 0 ≤ g* ≤ 2.5, respectively. The flow patterns and vortex shedding frequency were determined using the particle tracking flow visualization (PTFV). The flow structures, velocity properties, and drag coefficients were calculated using the particle image velocimetry (PIV). The topological flow patterns of vortex evolution processes were plotted and analyzed based on critical point theory. Furthermore, the flow structures behind twin side-by-side square cylinders were classified into three modes — single vortex-street mode, gap-flow mode and couple vortex-streets mode. The maximum C _d occurred in the single vortex-street mode, and the minimum C _d occurred in the gap-flow mode. The highest Strouhal number (St) occurred in the single vortex-street mode, and the lowest St occurred in the gap-flow mode.     

The effect of serrated fins on the flow around a circular cylinder

An experimental study is performed to investigate the characteristics of near wake flow behind a circular cylinder with serrated fins using a constant temperature anemometer and flow visualization. Various vortex shedding modes are observed. Fin height and pitch are closely related to the vortex shedding frequency after a certain transient Reynolds number. The through-velocity across the fins decreases with increasing fin height and decreasing fin pitch. Vortex shedding is affected strongly by the velocity distribution just on top of the finned tube. The weaker gradient of velocity distribution is shown as increasing the freestream velocity and the fin height, while decreasing the fin pitch. The weaker velocity gradient delays the entrainment flow and weakens its strength. As a result of this phenomenon, vortex shedding is decreased. The effective diameter is defined as a virtual circular cylinder diameter taking into account the volume of fins, while the hydraulic diameter is proposed to cover the effect of friction by the fin surfaces. The Strouhal number based upon the effective diameters seems to correlate well with that of a circular cylinder without fins. After a certain transient Reynolds number, the trend of the Strouhal number can be estimated by checking the ratio of effective diameter to inner diameter. The normalized velocity and turbulent intensity distributions with the hydraulic diameter exhibit the best correlation with the circular cylinder’s data.     

Simulation of vortex shedding from a square cylinder in oscillating channel flow

Laminar vortex shedding of a square cylinder mounted between two parallel walls are numerically simulated by using a finite volunme method based on a linear upwind differencing scheme and SIMPLER algorithm. The unsteady terms are approximated by a two-step fully-implicit backward scheme. The lock-on phenomena in an oscillating flow as well as the vortex shedding in a steady flow are investigated. The values of Strouhal number in the steady uniform flow are reasonably predicted with accuracy by the present numerical method. The frequency range of the incoming flow for the lock-on appear is well simulated. When the flow is loked-on, the shedding frequency is half of the incoming flow frequency. The structural characteristics of shedding vortex in the lock-on range is discussed in the present paper.     

Numerical simulation of vortex-induced vibration of a square cylinder

Vortex-induced vibration (VIV) of a square cylinder in a cross flow is examined numerically. Both the rigid and elastic cases are simulated at a low Reynolds number of 100. The approach solves the unsteady flow field using a finite element method with a deforming grid to accommodate the moving cylinders. As for the cylinder motions, a two-degree-of-freedom structural dynamics model is invoked. Fluid-structure interactions are resolved through iteration at the same time step. The calculated results for the case of rigid cylinder indicated that the non-dimensional vortex shedding frequency (or the Strouhal frequency) of a square cylinder at rest is 0.13, which is in good agreement with the published results. For the elastic case, with the change of the cylinder’s natural frequency, “lock-in” and “beat” phenomena were successfully captured. The phenomena of resonance and galloping can also be indicated.     

Computation of turbulent flows and radiated sound from axial compressor cascade

The losses at off-design points from a compressor cascade occur due to the deviation from a design incidence angle at the inlet of the cascade. The self-noise from the blade cascade at off-design points comes from a separated boundary layer and vortex sheddings. If the incidence angle to the cascade increases, stalling in blades may occur and the noise level increases significantly. This study applied Large-Eddy Simulations (LES) using deductive and deductive dynamic SGS models to low Mach-number, turbulent flow with each incidence angle to the cascade ranging from −40° to +20°, and compared numerical predictions with measured data. It was observed that the oscillating separation bubbles attached to the suction surface do not modify wake flows dynamically for cases of negative incidence angles. However, an incidence angle greater than 8° caused a separated vortex near the leading edge to be shed downstream and created stalling. The computed performance parameters such as drag coefficient and total pressure loss coefficient showed good agreement with experimental results. Noise from the cascade of the compressor is summarized as sound generated by a structure interacting with unsteady, turbulent flows. The hybrid method using acoustic analogy was observed to closely predict the measured overall sound powers and directivity patterns at design and off-design points of blade cascade.     

Passive control of circular cylinder wake in shallow flow

The control of vortex shedding of a circular cylinder in shallow water using a splitter plate located in the downstream of the circular cylinder was studied by employing particle image velocimetry (PIV) technique. Experiments were carried out in a water channel having a test section of 8000 mm × 1000 mm × 750 mm dimensions at a Reynolds number of 6250. The length of the splitter plate (L) was varied within the range of 0.5 ? L/D ? 2 with an increment of 0.5. The plate was submerged into water at different height ratios (h_p/h_w) such as 0.25, 0.5, 0.75 and 1.0. Mean velocity vector field, corresponding vorticity contours, streamline topologies and turbulent quantities were calculated using 300 instantaneous velocity vector field measured by PIV. As the ratio of h_p/h_w increases, the effect of the splitter plate on the suppression of the vortex shedding increases. Flow characteristics and examination of spectra indicate that Karman vortex shedding is attenuated pronouncedly for the cases of L/D ? 1 and h_p/h_w ? 0.75. The transverse Reynolds normal stress is more effective on the attenuation of turbulent kinetic energy than the streamwise Reynolds normal stress. The value of peak transverse Reynolds normal stress is reduced to 90% of that of the bare cylinder at most.     

Control of laminar vortex shedding behind a circular cylinder using tabs

Small, thin flat plates (called tabs hereafter) are attached to the upper and lower surfaces of a circular cylinder to control vortex shedding and reduce the mean drag and lift fluctuations at the Reynolds number of 100. We vary the location and size of the tabs and the distance between the adjacent tabs. The maximum amount of drag reduction by the tabs is 17%. It is found that the tabs perturb twodimensional vortex shedding and introduce spanwise mismatch of vortex shedding, which weakens the strength of vortex shedding or even annihilates vortex shedding. The present result suggests that these tabs are an effective passive device for the control of vortex shedding behind two-dimensional bluff bodies.     

Effect of Reynolds numbers on flow past four square cylinders in an in-line square configuration for different gap spacings

In this paper two-dimensional (2-D) numerical investigation of flow past four square cylinders in an in-line square configuration are performed using the lattice Boltzmann method. The gap spacing g = s/d is set at 1, 3 and 6 and Reynolds number ranging from Re = 60 to 175. We observed four distinct wake patterns: (i) a steady wake pattern (Re = 60 and g = 1); (ii) a stable shielding wake pattern (80 ≤ Re ≤ 175 and g = 1); (iii) a wiggling shielding wake pattern (60 ≤ Re ≤ 175 and g = 3) and (iv) a vortex shedding wake pattern (60 ≤ Re ≤ 175 and g = 6). At g = 1, the Reynolds number is observed to have a strong effect on the wake patterns. It is also found that at g = 1, the secondary cylinder interaction frequency significantly contributes for drag and lift coefficients signal. It is found that the primary vortex shedding frequency dominates the flow and the role of secondary cylinder interaction frequency almost vanish at g = 6. It is observed that the jet between the gaps strongly influenced the wake interaction for different gap spacing and Reynolds number combination. To fully understand the wake transformations the details vorticity contour visualization, power spectra of lift coefficient signal and time signal analysis of drag and lift coefficients also presented in this paper.     

A study of flow patterns for staggered cylinders at low Reynolds number by spectral element method

This study investigates the pattern of flow past two staggered array cylinders using the spectral element method by varying the distance between the cylinders and the angle of incidence (α) at low Reynolds numbers (Re = 100-800). Six flow patterns are identified as Shear layer reattachment (SLR), Induced separation (IS), Vortex impingement (VI), Synchronized vortex shedding (SVS), Vortex pairing and enveloping (VPE), and Vortex pairing splitting and enveloping (VPSE). These flow patterns can be transformed from one to another by changing the distance between the cylinders, the angle of incidence, or Re. SLR, IS and VI flow patterns appear in regimes with small angles of incidence (i.e., α ≤ 30° ) and hold only a single von Karman vortex shedding in a wake with one shedding frequency. SVS, VPE and VPSE flow patterns appear in regimes with large angles of incidence (i.e., 30° ≤ α ≤ 50° ) and present two synchronized von Karman vortices. Quantitative analyses and physical interpretation are also conducted to determine the generation mechanisms of the said flow patterns.     

Experimental characterization of the flow field of square prism with a detached splitter plate at high reynolds number

The characteristics of the flow field of a square prism with detached splitter plate in its wake were investigated by measuring the fluid force on the prism and by visualizing the flow field through particle image velocimetry (PIV) with a high Reynolds number (Re = 10,000). The experimental parameters included the ratios of the splitter and prism widths (H/B = 0.5–1.5) as well as the gap ratios (G/B = 0–2) between the prism and the splitter plate at a high Reynolds number (Re = 10,000). The drag reduction rate of the square prism increased with increasing H/B for the same G/B; meanwhile, it increased and then decreased with increasing G/B for the same H/B. When the detached splitter place was installed, vortices rotating in opposite directions were generated on its upper and lower sides. Reverse flow was caused by the vortices in the wake region of the square prism, and the prism drag was decreased by the reverse flow.     

A T-shaped vortex shedder for a vortex flow-meter

A configuration of a T-shaped vortex shedder is developed with the goal of improving the quality of the vortex shedding signal measured. This T-shaped vortex shedder comprises a trapezoidal cylinder which is fixed in shape and an extended plate attached behind whose length is variable. The vortex shedding frequency is deduced from the differential pressure signal measured, which corresponds to the pressure difference resulting from the two sides of the trapezoidal cylinder. By varying the length of the extended plate, the optimal situation is found to be when the length of the extended plate falls in the range of 1.56 to 2.0 times the width of the vortex shedder, when the low-frequency variations embedded in the pressure signal are significantly suppressed.     

Suppression of flow-induced vibration of a circular cylinder by means of a flexible sheet

In this study, the suppression of flow-induced vibration of an elastically supported circular cylinder by attachment of a flexible sheet was investigated experimentally. In particular, the dependence of flow-induced vibration characteristics of the circular cylinder upon the flow velocity was investigated in detail by axially attaching the flexible poly-ethylene sheet to the cylinder surface. The characteristics of the flow-induced vibration of the cylinder were investigated by changing the attachment angle ?? and the length l of the flexible sheet (rectangular type) as experimental parameters in various combinations. The angle ?? was set at five different angles, 90°, 45°, 0°, ?45° and ?90°. The angle??s base point was the back side stagnation point of the cylinder. The length l of the flexible sheet varied from 0.5 to 3.0 times of the cylinder??s diameter at the interval of 0.5 times. The width T of the flexible sheet along the span of the cylinder also varied in 7 cases from 1.0L to 0.4L (L is the length of the cylinder) in order to discover the minimum width of the sheet necessary to effectively suppress the flow-induced vibration of the cylinder. Furthermore, the flexible sheet of the minimum width was split into 2 to 5 pieces and attached to the cylinder, and changes in the flow-induced vibration characteristics were investigated. Also, vibration characteristics were investigated for a flexible sheet in the shape of an isosceles triangle. As a result, the optimal length l and minimum width T of the flexible rectangular sheet were found to be 2??2.5D and 0.7L, respectively, to suppress the flow-induced vibration of the cylinder. Most importantly, it was found that the sheet located at the back side stagnation point can suppress the flow-induced vibration generated by any directional flow to strike the front surface of the cylinder.