Von Karman Vortex Shedding Research Articles

A Simulation Study on von Karman Vortex Shedding with Navier-Stokes and Shallow-Water Models

This study aims to investigate the advantages of employing numerical models based on Shallow-water equations for simulating von Karman vortex shedding. Furthermore, a comparative analysis with Navier-Stokes equations will be conducted to assess their effectiveness. In addition to Reynolds number (Re), Froude number (Fr), relevant to water depth, plays an important role in the Shallow-Water modeling of the von Karman vortex. In this study, simulations of 2D von Karman vortex shedding are performed using the Navier-Stokes model and Shallow-Water model, employing the least-squares finite-element method for space discretization and θ-method for time integration. The computed vortices characteristics, including the recirculation zone behind the cylinder, vortices size, and frequency, are presented. In the Navier-Stokes modeling, the computed results indicate that the size of vortices in space decreases and the Strouhal number increases as Re increases. In the Shallow-Water modeling for the same Re condition, the size of vortices increases and the Strouhal number decreases as Fr increases.

A Comprehensive Analytical Model for Vortex Shedding From Low-Speed Axial Fan Blades

Abstract The paper presents a comprehensive analytical model for the characterization of von Karman vortex shedding in the wake of models of low-speed axial fan blades. The elaborated minimal model is based on the Reynolds-averaged Navier–Stokes and continuity equations. For validation purposes, hot-wire measurements have been carried out in a wind tunnel on representative blade profiles. The measurement data obtained for various streamwise positions downstream of the blade trailing edge, i.e., transversal profiles of mean velocity as well as root-mean-square of fluctuating velocity, are evaluated. As the experimental validation demonstrates, the minimal model fairly localizes the transversal position of the vortex centers and represents the motion of the vortices along the wake. The validated minimal model serves the following benefits: (a) an extensive understanding of the underlying physics related to the flow field featuring vortex shedding in the near-wake region (easy-to-use quantitative correlation among the characteristics of wake flow affected by the shed vortices); (b) extension of the literature-based methodology for determination of the transversal distance between the shed vortex rows, being used as a scaling parameter for the Strouhal number utilized in calculation of vortex shedding frequency; and (c) modeling the behavior of rows of shed vortices farther away from the trailing edge. Such behavior may influence the acoustic signature of VS, and, as such, it is to be considered in fan noise modeling.

Numerical investigation on the effects of wake-induced vibration fluid flow over airfoil geometries

Currently, many companies are looking to innovate and decrease economic and environmental impacts in the aerospace, energy, and marine sectors. As companies continue to innovate, airfoil designs used in the aerospace, wind turbine, commercial, and military marine industries, the lighter materials used are more susceptible to fatiguing failures due to vibrations. When these geometries encounter unsteady flow, the airfoil creates a vibration response. If the vibration response is near the natural frequency of the airfoil geometry, catastrophic failure can occur. This paper analyzes the correlation between geometry and frequency response for NACA symmetric airfoils in unsteady flow due to von Karman vortex shedding. The correlation between the shedding frequency of the cylinder and the frequency response of the airfoil is also considered. The paper also aims to determine if there is a correlation between geometry and frequency response amplitude across the frequency spectrum and at the natural frequency of each airfoil. These results were compared to the airfoil natural frequency, determined through Finite Element Analysis (FEA).

Solution of Shallow-Water Equations by a Layer-Integrated Hydrostatic Least-Squares Finite-Element Method

A multi-layer hydrostatic shallow-water model was developed in the present study. The layer-integrated hydrostatic nonlinear shallow-water was solved with θ time integration and the least-squares finite element method. Since the least-squares formulation was employed, the resulting system of equations was symmetric and positive–definite; therefore, it could be solved efficiently by the preconditioned conjugate gradient method. The model was first applied to simulate the von Karman vortex shedding. A well-organized von Karman vortex street was reproduced. The model was then applied to simulate the Kuroshio current-induced Green Island vortex street. A swirling recirculation was formed and followed by several pairs of alternating counter-rotating vortices. The size of the recirculation, as well as the temporal and spatial scale of the vortex shedding, were found to be consistent with ADCP-CDT measurements, X-band radar measurements, and analysis of the satellite images. It was also revealed that Green Island vortices were affected by the upstream Orchid Island vortices.

Flow and heat transfer in the wake of a triangular arrangement of spheres

This research work seeks to investigate the influence of spacing and heat transfer on the wake behavior of a triangular arrangement of spheres. Four experimental configurations have been investigated at three Reynolds numbers, Re1 = 350, Re2 = 700, and Re3 = 1050. Two isothermal cases were investigated with spacing between the spheres of zero and one sphere diameter, and two cases were investigated with an applied heat flux at the same spacing conditions. The time resolved particle image velocimetry results revealed various flow phenomena including flow separations, von Karman vortex shedding, and Kelvin–Helmholtz instabilities. The turbulent statistics reveal the effect of proximity and heat transfer on the time averaged values of the wake size, turbulent strengths, and Reynolds shear stress in the wake of each sphere, namely, the laminarization effects from the addition of heat and the suppression of the lead sphere wake from the proximity of the trailing spheres. These results are complemented by the application of proper orthogonal decomposition (POD) to the flow fields, which extracts the coherent structures from the flow. The modes that describe the coherent structures are extracted and described in detail, which provide further insight into effects of the experimental conditions on the temporal behavior of the flow. Many of the low order modes are found to be associated in pairs, corresponding to asymmetric structures or advection of a given structure downstream. The capability of POD to produce reduced order models of the flow is then utilized to facilitate vortex identification analysis. A turbulent kinetic energy based mode truncation criteria, which has been found to enhance vortex identification capability, is applied to select the POD modes and temporal coefficients to be used in the reduced order modeling. The reconstructed velocity fields are then analyzed with vortex identification algorithms to extract the vortex cores and boundaries. The combination of these approaches allows the study of the effect of proximity and heat transfer on the vortex characteristics, such as size, strength, and distribution.

Robust Mode Analysis

In this paper, we introduce a model-free algorithm, robust mode analysis (RMA), to extract primary constituents in a fluid or reacting flow directly from high-frequency, high-resolution experimental data. It is expected to be particularly useful in studying strongly driven flows, where nonlinearities can induce chaotic and irregular dynamics. The lack of precise governing equations and the absence of symmetries or other simplifying constraints in realistic configurations preclude the derivation of analytical solutions for these systems; the presence of flow structures over a wide range of scales handicaps finding their numerical solutions. Thus, the need for direct analysis of experimental data is reinforced. RMA is predicated on the assumption that primary flow constituents are common in multiple, nominally identical realizations of an experiment. Their search relies on the identification of common dynamic modes in the experiments, the commonality established via proximity of the eigenvalues and eigenfunctions. Robust flow constituents are then constructed by combining common dynamic modes that flow at the same rate. We illustrate RMA using reacting flows behind a symmetric bluff body. Two robust constituents, whose signatures resemble symmetric and von Karman vortex shedding, are identified. It is shown how RMA can be implemented via extended dynamic mode decomposition in flow configurations interrogated with a small number of time-series. This approach may prove useful in analyzing changes in flow patterns in engines and propulsion systems equipped with sturdy arrays of pressure transducers or thermocouples. Finally, an analysis of high Reynolds number jet flows suggests that tests of statistical characterizations in turbulent flows may best be done using non-robust components of the flow.

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.

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.

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.

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.

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.

A numerical study on the enhanced drag reduction and wake regime control of a square cylinder using dual splitter plates

In this paper, a dual splitter plate flow separation control device is introduced for a low Reynolds number flow (Re = 100) around the square cylinder of length L to achieve higher drag reduction and improved wake regime control compared to the conventional single splitter plate control devices. Here, two splitter plates of the same length W (ranging from 0.25 L to 2.50 L) are symmetrically attached on the rear surface along the horizontal centerline of the square cylinder with a spacing H (ranging from 0.0 L to 1.0 L) between them. The numerical study is performed using the in-house developed flexible forcing immersed boundary-lattice Boltzmann solver [1] to investigate the effects of dual splitter plate on the flow regime and flow-induced forces. The shear layer interaction with the splitter plates, as well as the vorticity and pressure distribution in the near wake region, are significantly modified by varying W and H, and four different flow regimes (Type I to Type IV) are identified from the observations. Among these flow types, the Type III flow pattern displays an accelerating flow in the wake region that is found to be most beneficial for higher base pressure recovery and drag reduction. Furthermore, dual splitter plates suppress von-Karman vortex shedding and lift force fluctuation, and produce higher drag reduction (≈ 21%) at less than half of the plate length of a single splitter plate. It is also noticed that a dual splitter plate configuration seems to be an optimum arrangement, since adding more splitter plates (up to 5 numbers were tested) on the rear surface of the square cylinder does not change the wake characteristics nor shows any improvements in the drag reduction.

Numerical investigation of scale resolved turbulence models (LES, ELES and DDES) in the assessment of wind effects on supertall structures

Scale resolved turbulence models, such as large eddy simulation (LES), have been increasingly utilised in applications of computational wind engineering (CWE) for tall buildings, due to their proven numerical accuracy. The demand for computational time and resources in LES is still a concern in practical applications of CWE, where it is necessary to explore alternative modelling techniques. The main objective of this study is to critically investigate the possibility of using a computationally efficient hybrid RANS/LES approach, specifically embedded-LES (ELES), to predict wind effects on a supertall 406 m slender tower of non-standard geometry. Numerical predictions of LES and ELES are compared and critically analysed with experimental results obtained by performing boundary layer wind tunnel (BLWT) tests. It was shown that the choice of sub-grid scale (SGS) modelling in LES has an impact on the wind effects predicted on the structure. Out of the five SGS models tested, the wall adapting local eddy viscosity (WALE) model was the most suitable due to its treatment of the near wall region. An optimum domain configuration based on a parametric study was proposed for the application of ELES. The importance of overall mesh quality and its impact on fluctuating pressures and dynamic properties of wind is presented. Wind flow behaviour on the structure, such as Von-Karman vortex shedding and its dynamic implications, is also discussed. Finally, using the proposed modelling techniques, ELES can generate similar numerical accuracy to that of an LES model at a lower computational cost.

Prediction of vibration amplitudes on hydraulic profiles under von Karman vortex excitation

The shedding of von Karman vortices on the trailing edges of turbine hydraulic profiles such as stay vanes, guide vanes and runner blades is a well-known mechanism of excitation for high frequency structural vibrations. Most commonly problems occur on stay vanes because the flow across the trailing edges is relatively uniform, and structural damping is low. Our analysis of the excitation mechanism under von Karman vortex shedding shows that in the vicinity of resonance the hydrodynamic damping becomes a non-linear function of amplitude potentially resulting in unacceptable limit amplitudes. Past studies have focused on frequency prediction, resonance avoidance and special trailing edge shapes to reduce dynamic forcing. On modern low head turbines resonance cannot always be avoided without undue hydraulic performance penalties. In our paper we demonstrate the applicability of a fluid structure interaction based approach to predict vibration amplitudes under von Karman vortex shedding. This type of prediction can be used to ensure that permissible amplitudes are not exceeded. We also present a strategy to achieve low vibration amplitudes.

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.

The lowest Reynolds number of vortex-induced vibrations

It is well known that the occurrence of vortex-induced vibration (VIV) at a subcritical Reynolds number, which is lower than 47, is induced by fluid-structure interaction. However, for the free flow, this phenomenon disappears at a Reynolds number about 20. The current study provides an explanation to the disappearance of the VIV by capturing the evolution of the purely fluid modes at Reynolds numbers between 12 and 55. To ensure accurate mode extraction, the dynamic mode decomposition technique is utilized. Results show that the stable von Kármán vortex shedding mode exists in a subcritical flow regime but becomes less distinct as the Reynolds number decreases. When the Reynolds number is lower than 18, this mode nearly vanishes, characterizing the lower boundary of fluid-structure instability.

Concentration-Based Decomposition of the Flow around a Confined Cylinder in a UV Disinfection Reactor

The proper orthogonal decomposition (POD) is applied to spatial concentration data, obtained using laser-induced fluorescence (LIF), for the flow around a confined circular cylinder (R=4,900 R=4,900) and compared with their corresponding velocity and vorticity fields. The velocity, vorticity, and concentration modes identify the dominating coherent structures, i.e., shear layer rollup, instantaneous recirculation and von Karman vortex shedding. In the velocity and vorticity decomposition, instantaneous recirculation, and von Karman vortex shedding are represented in the highest energy modes. However, in the concentration decomposition, the most energetic modes represent the regions with strong concentration intermittency, i.e., where no dye is present, whereas the coherent structures, which are identified in the highest modes in the velocity and vorticity decomposition, are only found in the less energetic modes. The concentration-based decomposition identifies the shear layer around the cylinder, which is only partially captured by its vorticity-based counterpart.

Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Part I: Experimental and numerical investigation

Three-dimensional Direct Numerical Simulations combined with Particle Image Velocimetry experiments have been performed on a hemisphere-cylinder at Reynolds number 1000 and angle of attack 20°. At these flow conditions, a pair of vortices, so-called “horn” vortices, are found to be associated with flow separation. In order to understand the highly complex phenomena associated with this fully three-dimensional massively separated flow, different structural analysis techniques have been employed: Proper Orthogonal and Dynamic Mode Decompositions, POD and DMD, respectively, as well as critical-point theory. A single dominant frequency associated with the von Karman vortex shedding has been identified in both the experimental and the numerical results. POD and DMD modes associated with this frequency were recovered in the analysis. Flow separation was also found to be intrinsically linked to the observed modes. On the other hand, critical-point theory has been applied in order to highlight possible links of the topology patterns over the surface of the body with the computed modes. Critical points and separation lines on the body surface show in detail the presence of different flow patterns in the base flow: a three-dimensional separation bubble and two pairs of unsteady vortices systems, the horn vortices, mentioned before, and the so-called “leeward” vortices. The horn vortices emerge perpendicularly from the body surface at the separation region. On the other hand, the leeward vortices are originated downstream of the separation bubble, as a result of the boundary layer separation. The frequencies associated with these vortical structures have been quantified.

Dynamical-systems analysis and unstable periodic orbits in reacting flows behind symmetric bluff bodies

Dynamical systems analysis is performed for reacting flows stabilized behind four symmetric bluff bodies to determine the effects of shape on the nature of flame stability, acoustic coupling, and vortex shedding. The task requires separation of regular, repeatable aspects of the flow from experimental noise and highly irregular, nonrepeatable small-scale structures caused primarily by viscous-mediated energy cascading. The experimental systems are invariant under a reflection, and symmetric vortex shedding is observed throughout the parameter range. As the equivalence ratio-and, hence, acoustic coupling-is reduced, a symmetry-breaking transition to von Karman vortices is initiated. Combining principal-components analysis with a symmetry-based filtering, we construct bifurcation diagrams for the onset and growth of von Karman vortices. We also compute Lyapunov exponents for each flame holder to help quantify the transitions. Furthermore, we outline changes in the phase-space orbits that accompany the onset of von Karman vortex shedding and compute unstable periodic orbits (UPOs) embedded in the complex flows prior to and following the bifurcation. For each flame holder, we find a single UPO in flows without von Karman vortices and a pair of UPOs in flows with von Karman vortices. These periodic orbits organize the dynamics of the flow and can be used to reduce or control flow irregularities. By subtracting them from the overall flow, we are able to deduce the nature of irregular facets of the flows.

Far-field vortex structures in mountain wakes

Laboratory experiments on scaled mountain wakes have provided the first demonstration that indicates the existence of two distinct mechanisms for the formation of the long-lived vortex structures that have been frequently observed in satellite imagery. In a series of laboratory experiments the well-known von Karman vortex shedding mechanism has been observed at low values of Froude number (corresponding to low speed flow and strong stratification). At high Froude numbers the initial highly turbulent wake evolves into a vortex pattern similar to the far-wake dipole eddies previously observed in laboratory studies of submerged stratified wakes. In satellite imagery vortex structures have been observed to persist for hundreds of kilometers. In the present laboratory experiments far-wake dipole eddies were observed to persist for at least 200 diameters downstream, which corresponds to ~4,000 km when scaled to actual mountains. When generated at multiple sites along a continental mountain chain, these eddy structures could play a significant role in the development and variability of multi-scale weather and climate patterns.