Experimental verification and numerical simulation of a vortex flowmeter at low Reynolds numbers

This study presents experimental verification and numerical simulations of a vortex flow meter in the Reynolds number range between 8300 and 50,000. A custom-designed bluff body with a wedge back shape was used in the flowmeter. A shedding frequency of the flowmeter was measured in an air duct using a hot-film probe. To evaluate the accuracy of the flowmeter, a measurement uncertainty analysis was performed. Numerical simulations of the vortex flowmeter were performed with the open source code OpenFOAM. Transient simulations of periodic vortex shedding behind the bluff body were performed using different simulation methods depending on the pipe Reynolds number, such as Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and Unsteady Reynolds Averaged Navier Stokes (URANS) method. The simulated vortex shedding frequencies matched the experimental data very well. Experiments and simulations demonstrated a clear linear dependence of the shedding frequency on the volumetric flow rate over the entire range of Reynolds numbers. In addition, numerical simulations were used to study the main mechanisms of vortex formation and shedding behind the considered bluff body.     

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.     

卧式半圆柱型涡流发生器的传热与阻力特性及场协同理论分析

为研究卧式半圆柱型涡流发生器的特性,通过数值模拟方法对安装有卧式半圆柱型涡流发生器的矩形通道进行了传热和流阻特性的研究。结果表明:在相同雷诺数Re下,安装有卧式半圆柱型涡流发生器的矩形通道的换热效果明显优于矩形光滑通道,但阻力系数也均大于矩形光滑通道。对比综合性能指标表明,6/8H楞长处的综合特性PEC值最大。通过对场协同理论分析得出,矩形光滑通道和四种不同楞长的卧式半圆柱型涡流发生器的协同数Fc均随着雷诺数Re的增大而减小,而且其变化趋势也越来越平缓,最终逐渐趋近于定值。相同雷诺数Re下,楞长为6/8H时的协同数Fc最大。     

Three dimensional aerodynamic characteristics of weis-fogh mechanism

The three-dimensional flows in the Weis-Fogh mechanism are studied by flow visualization and numerical simulation by the discrete vortex method. The vortex method, especially the vortex stick method, is employed to investigate the vortex structure in the wake of the two wings. The pressure is estimated by the Bernoulli equation, and the lift on the wing is also obtained. For the results, the eddies near the leading edge of each wing in the fling stage take a convex shape because the eddies shed from both tips entrain the flows, and the downwash in the rotating stage is deflected toward the outside because the outside tip vortex is stronger than the inside one. The lift coefficient on the wings in this mechanism is almost independent of the Reynolds number. This paper was recommended for publication in revised form by Associate Editor Haecheon Choi Ki-Deok Ro received his B.S. degree in Marine Engineering from Pukyong National University, Korea, in 1977. He then received his M.S. and Ph.D. degrees from Kobe University, Japan, in 1986 and 1989, respectively. Dr. Ro is currently a Professor at the School of Mechanical Engineering at Gyeongsang National University in Gyeongnam, Korea. He serves as an Editor of Journal of the Korean Society of Marine Engineering. Dr. Ro’s research interests include fluid mechanics, CFD, and vortex method.     

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.     

Wake suppression behind two slightly non-coplanar cylinders

We here have found when the two parallel cylinders are arranged slightly non-coplanar, the vortex shedding could be significantly suppressed above Reynolds number of 6000. This finding is unlike the common understanding that the Karman vortex formation behind the structure can be manipulated when a structure located within the inherently unstable near wake of another structure. It is particularly important for flow control, since the flow-induced vibration of two parallel cylinders can be suppressed effectively with only slightly non-coplanar arrangement.     

Investigation of different aspects of laminar horseshoe vortex system using PIV

Juncture flow is a classical fluid mechanics problem having wide applications in both aero and hydro dynamics. The flow separates upstream of the obstacle due to the adverse pressure gradient generated by it, with the formation of the vortical structure called “horseshoe vortex.” The current study is carried out for an elliptical leading edge obstacle placed on a flat plate to investigate the horseshoe vortex for a range of Reynolds number (Re_W) based on maximum width (W) for which the incoming boundary layer is laminar. Four different types of horseshoe vortex systems were found: the steady, amalgamation, transition and breakaway. The transition vortex system is one after which the vortex system changes from amalgamation to breakaway. In this phase the vortex system alternatively undergoes both amalgamation and breakaway vortex cycles. The effect of variation in the chord wise shape of the obstacle is investigated. The quantitative measurements of PIV show that the vortex system does not undergo any significant change for different chord lengths of the model with the fixed aspect ratio and maximum width. The most upstream saddle point is also studied for steady horseshoe vortex region and found that it is the “saddle of attachment” where flow attaches to the plate surface instead of separating from it.     

Evolution of an improved vortex generator

This paper reviews the process, stretching over several years and with contributions from several workers, by which an improved body shape for use in vortex shedding meters was designed and tested. A priori knowledge of the fluid mechanics involved in vortex shedding, supplemented by information obtained from observation (flow visualization) and measurement (spectral analysis), was used to direct the design process. Particular attention was focused on stabilizing the vortex sheddind so that signal dropout and unnecessary limitations to the operating range could be attacked at their source. After examination of the performance of a number of different cylinder cross-sections, and experiments involving splitters and afterbodies, a detailed study of a generator consisting of a circular cylinder split across its lateral diameter was undertaken. Subsequently, it was found that the performance of this (already good) generator could be improved still further by shaping the rear surface of the cylinder. The split cylinder with concave rear surface resulting from this design process was shown to provide the strongest and most regular vortex shedding of all the shapes tested. Moreover, the performance benefits of this shape can now be explained in terms of the flow structure in the near wake.     

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 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.     

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.     

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 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.     

Numerical assessment of turbulent models at a critical regime on unstructured meshes

The present study mainly aims to investigate the performances of different turbulent models for the flow simulation around a circular cylinder at a critical Reynolds number regime (Re = 8.5×10⁵, Tu = 0.7%). A hybrid RANS/LES model (SAS model), a correlation-based transition model ( $\gamma - \widetilde{\operatorname{Re} }_{\theta t} $ model), and a fully turbulent RANS model (SST model) were used to simulate various flow features, such as laminar-turbulence transition inside the boundary layer and the unsteady vortex shedding in the wake region, and their feasibilities for the flow simulation at a critical Reynolds number regime were demonstrated. A vertex-centered finite-volume method was used to discretize the incompressible Navier-Stokes equations, and an unstructured mesh technique was used to discretize the computational domain. The inviscid fluxes were evaluated using 2^nd-order Roe??s flux difference splitting, and the viscous fluxes were computed based on central differencing. A dual time-stepping method and the Gauss-Seidel iteration were used for unsteady time integration. The parallelization strategy using METIS and MPI libraries was used to reduce computational costs. The unsteady characteristics and the time-averaged quantities of the flow fields were compared between turbulent models. The numerical results were also compared with experimental results. The turbulent models showed quite different results at the critical regime because of the different abilities of each model to predict various flow features, such as laminar-turbulence transition and unsteady vortex shedding.     

Response characteristics of a vortex-excited circular cylinder in laminar flow

This paper presents numerical simulation results for vortex-induced vibration of a circular cylinder in laminar flow. A vortex method is implemented to solve the two-dimensional Navier-Stokes equations in terms of vorticity. In order to validate the numerical code, the flow past a fixed cylinder is first investigated for which enough experimental and numerical results are available. Basic characteristics of the dynamic response and vortex shedding for an elastically mounted circular cylinder are then investigated for 70 < Re < 170. The lock-in phenomenon is captured at certain reduced velocities where the lift coefficient takes a considerable value associated with a high amplitude response. The wake structure exhibits the 2S or C (2S) modes of vortex shedding in this range of Reynolds numbers, as opposed to the 2P mode which is observed in the turbulent flow regime. The numerical results are in acceptable agreement with available experimental and numerical data.     

Characteristics of flow past a circular cylinder with a rectangular groove

In the present study, features of the flow past a circular cylinder with single longitudinal groove pattern placed on its surface were investigated. Six different rectangular groove sizes were tested for angular position of the groove from the forward stagnation point of the circular cylinder within 0°≤θ≤150°. The particle image velocimetry (PIV) technique were employed to measure flow field downstream of the cylinder immersed in a uniform flow field with the Reynolds number, Re=5000. Time-averaged flow data such as vorticity, 〈ω〉 streamline, 〈Ψ〉, streamwise, 〈u′u′〉 and transverse, 〈v′v′〉 Reynolds normal stresses, turbulent kinetic energy, TKE and RMS of streamwise, u_rms and transverse, v_rms velocity components were obtained from PIV data to demonstrate flow features. Moreover, frequency of Karman vortex shedding was explored using single point spectral analysis. It is concluded that presence of the groove on a cylinder surface significantly affects the near wake flow structure and turbulence statistics. Karman vortex shedding frequency, f_k strongly depends on the groove size. Moreover, the shear layer instability is induced on the grooved side with additional frequencies.     

A simple low order model of the forced Karman wake

The present work develops a very simple mathematical model for the 2D von Karman vortex shedding wake. The case where this wake is periodically excited at the vortex shedding frequency is considered. The goal is to arrive at an approximate model that is simple enough to allow a full analysis of the underlying nonlinear dynamics. Since such a simple model cannot be expected (and is not intended) to replicate the Navier-Stokes equations the comparison criteria is the ability of the model to replicate the sequence of bifurcations as the forcing amplitude parameter is varied. Such a model can be useful for flow control applications.Equivariant bifurcation theory is employed to obtain the low order discrete model for the dynamics of the Karman wake when ‘reflection-symmetrically’ forced at the vortex shedding frequency.The discrete dynamical system (amplitude equations) modeling the mode interactions is derived in Poincaré space. Model parameters are then determined via POD from numerical simulations of the simple stationary cylinder case.A quantitative analysis of the wake dynamics based on the model above is presented. For Re=1000, dynamics of the 2D cylinder wake are shown to be closely linked, via the Bogdanov-Takens bifurcation scenario to physical and mathematical systems having SO(2) symmetry. For Re=200, a torus breakdown following the Afraimovich-Shilnikov scenario is found. The result is a complex, possibly chaotic, wake flow.Experimental results, in the form of measured POD modes, are also presented. The results suggest that the 3D wake transition does not destroy the 2D Karman wake dynamics; the latter apparently remains dominant even at moderately higher Reynolds numbers.The goal of the present work is to show that much can be learnt from a very simple model of the wake dynamics when the role of symmetry is carefully considered. This could also be viewed the other way around; that the dynamical bifurcation behavior of the apparently complex forced wake flow can, somewhat surprisingly, be described by a fairly simple model.     

Installation effects on vortex shedding flowmeters

Numerous measurements of the effects of pipe fittngs on vortex shedding flowmeters are carried out as a contribution to flow metering standards. A water test line of 150 mm diameter is used in the experiments covering a Reynolds number range of about 2 × 10⁵ to 10⁶. The effects of six kinds of piping configurations are examined at various upstream straight pipe lengths and all four kinds of liquid vortex shedding flowmeters, which were commercially available in Japan, are tested. The vortex shedding flowmeters are compared with a turbine meter in experiments designed to evaluate reproducibility of measurements. The uncertainty of the measured data is estimated at about 0.1%. It is found that the magnitude of each installation effect strongly depends on the design of the flowmeter. The experimental results are presented in detail and a table is given of the minimum upstream straight pipe lengths needed to suppress the effects to less than 0.5% for each of the tested flowmeters. This can be used as guidance in the installation of vortex shedding flowmeters.     

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.     

Numerical simulation of trailed vortex alleviation through chipped wingtip shapes

The shedding of strong vortices generated during take-off and landing poses serious hazards for the following aircraft. To circumvent the vortex wake hazard, a chipped wingtip shape was suggested, and a series of numerical simulations were conducted to verify the conceptual validity of such shape. Numerical simulation was performed by using the incompressible Navier-Stokes solver with the pressure-based semi-implicit method for pressure linked equations algorithm. The Reynolds stressmodel was employed to evaluatethe turbulence effects.The trailed vortices of the chipped wingtip shapes were found to be more dissipative than those of the baseline wingtip shape. The counter-rotating vortices produced by the chipped wingtip shape can weaken the primary wingtip vortex strength in the far field. Regardless of the slightly increasing the drag, the chipped wingtip shape can successfully mitigate the tangential velocity of the vortices. These types of wingtip shapes had various design parameters, such as the aspect ratio, spacing, and area of each chip. Systematic numerical simulations were conducted to evaluate the effect of these parameters. According to the parametric study results, the aspect ratio was sensitive to the increase in the drag coefficient, and the area was susceptible to the moment coefficient. Evidently, a trade-off relationship existed between the tangential velocity reduction and the drag increase.