Subcritical Reynolds Number Research Articles

Flow-induced cross-flow vibrations of long flexible cylinder with an upstream wake interference

Flow-induced vibration (FIV) of a flexible cylinder with an upstream wake interference at a subcritical Reynolds number is numerically investigated in this study. Two cylinders are installed in a tandem arrangement with the tandem separation between the cylinder centers set at 5.0 diameters. The downstream cylinder is flexible and placed in the wake of the stationary rigid upstream cylinder. A quasi-three-dimensional fluid-structure interaction (FSI) numerical methodology that couples the strip theory-based Lagrangian discrete vortex method with the finite-element method (FEM) for structural dynamics is developed to simulate the FIV response of the flexible cylinder with the upstream wake interference. The vortex-induced vibration (VIV) of an identical isolated cylinder is also numerically simulated as a contrast. This numerical study characterizes the dynamic response of the cylinder FIV with the upstream wake interference and sheds light on the FSI mechanisms responsible for the structural dynamic response. With the upstream wake interference, the cylinder FIV response shows two features distinct from the isolated VIV response: the vibration of large amplitude during the modal resonance branch transition and the extension of the modal resonance branch. The hydrodynamic coefficients database is constructed by the rigid cylinder forced vibration experiment to help explain the FSI properties of the FIV dynamic response. The lower added mass coefficient for the FIV with the upstream wake interference than the VIV of the isolated cylinder guarantees the synchronization between the vortex shedding frequency and the “true” natural frequency of the structure persisting to higher reduced velocity in a certain modal resonance response branch. The excitation coefficient distribution indicates that the cylinder FIV with the upstream wake interference reaches higher amplitude at high reduced velocity, instead of ceasing resonance as the isolated cylinder. The numerical wake visualization is shown and used to explain the correlation between the distribution of hydrodynamic coefficients along the cylinder span and the wake vortex mode. It is found that the upstream wake interference effect is strongly correlated with the vortex–structure interaction pattern between the upstream wake vortices and the downstream motion. When the upstream vortex impinges on the downstream cylinder and splits into subvortices, the effect of the upstream wake interference acting on the downstream cylinder reduces. When the downstream cylinder enters the gap between the upstream vortices over the entire vibration process, the upstream wake has a stronger interference effect on the downstream FIV response.

Numerical VIV analysis of a single elastically-mounted cylinder: Comparison between 2D and 3D URANS simulations

In this paper the numerical simulations of the flow around an elastically-mounted circular cylinder with one degree of freedom (1-DOF) with small damping parameter and small mass ratio are presented. The simulations are performed for subcritical Reynolds numbers (2.0⋅103<Re<1.3<104), using the URANS (Unsteady Reynolds Averaged Navier Stokes) approach in combination with the SST (Shear Stress Transport) turbulence model. The simulations are carried out on 3D as well as 2D meshes. From the overall results it seems that the bi-dimensional approach could be effectively applied in the lower branch, while major discrepancies are present in the upper branch. The detailed analysis of the wake flow characteristics shows that the three dimensionality of the flow is stronger in the transition zones between the different branches. The extensive comparison between the computational simulations and the experimental results presented in this paper could be considered the “start point” in order to select the proper grid model depending on the requested accuracy.

Investigations on high-fidelity low-dissipation scheme for unsteady turbulent separated flows

Unsteady turbulent separated flow widely exists in aerospace vehicles and has become a major research topic. For the precise turbulent flow prediction, efficient and accurate numerical methods are the premise and foundation. However, most shock-capturing schemes designed for compressible flows have some difficulties in low-speed flow regions, and reduce the reliability when simulating unsteady turbulent separated flow with rich low Mach number features. Thus, the paper proposes a high-fidelity low-dissipation scheme termed LD-Roe2 and investigates the performances of the novel approach in unsteady turbulent separated flow simulations using the Hybrid Reynolds Averaged Navier-Stokes Equations/Large Eddy Simulation Approach (Spalart-Allmaras Delayed Detached Eddy Simulation). Numerical results including flow over a circular cylinder at subcritical Reynolds number and flow over tandem cylinders, demonstrate that the novel low-dissipation scheme can better simulate the unsteady separated flow and depicts finer smaller-scale vortical structures compared with traditional numerical schemes. It is expected to provide a more accurate and applicable numerical solution for the refined turbulent prediction.

Mitigation of Vortex-Induced Vibration of Cylinders Using Cactus-Shaped Cross Sections in Subcritical Flow

Flexible cylinders, such as marine risers, often experience sustained vortex-induced vibrations (VIVs). Installing helical strakes on a riser is the most widely used technique to mitigate VIVs. This study was inspired by the giant Saguaro Cacti which can withstand strong wind with a shallow root system. In this study, numerical simulations of flow past a stationary cylinder of a cactus-shaped cross-section in a two-dimensional flow field at a subcritical Reynolds number of 3900 were performed. Results show that cylinders of a cactus-shaped cross-section have a lower lift coefficient without increasing drag compared to those of a circular cylinder. VIV experiments on a single flexible pipe as well as on a set of two tandem-arranged flexible pipes were conducted at different reduced velocities to investigate the effects of the streamwise spacing and wake of the cactus-like body shape on VIV mitigation. Experimental results show that the cactus-like body shape can mitigate VIV responses of the cylinder at upstream position with no cost of increased drag; however, similar to helical strakes, the efficiency of VIV mitigation for the cylinder at downstream position is reduced. Although the cactus-like body shapes tested in this study were not optimized for oscillation suppression, still this study suggests that modification of the cross-sectional shape to a well-designed cactus-like shape has potentials to be used as an alternative technology to mitigate VIV of marine risers.

Early evolution of optimal perturbations in a viscosity-stratified channel

Abstract

Experimental Measurements of the Wake of a Sphere at Subcritical Reynolds Numbers

Abstract This work experimentally investigated the flow phenomena and vortex structures in the wake of a sphere located in a water loop at Reynolds numbers of Re = 850, 1,250, and 1,700. Velocity fields in the wake region were obtained by applying the time-resolved stereoscopic particle image velocimetry (TR-SPIV) technique. From the acquired TR-SPIV velocity vector fields, the statistical values of mean and fluctuating velocities were computed. Spectral analysis, two-point velocity–velocity cross-correlation, proper orthogonal decomposition (POD) and vortex identification analyses were also performed. The velocity fields show a recirculation region that decreases in length with an increase of Reynolds numbers. The power spectra from the spectral analysis had peaks corresponding to a Strouhal number of St = 0.2, which is a value commonly found in the literature studies of flow over a sphere. The two-point cross-correlation analysis revealed elliptical structures in the wake, with estimated integral length scales ranging between 12% and 63% of the sphere diameter. The POD analysis revealed the statistically dominant flow structures that captured the most flow kinetic energy. It is seen that the flow kinetic energy captured in the smaller scale flow structures increased as Reynolds number increased. The POD modes contained smaller structure as the Reynolds number increased and as mode order increased. In addition, spectral analysis performed on the POD temporal coefficients revealed peaks corresponding to St = 0.2, similar to the spectral analysis on the fluctuating velocity. The ability of POD to produce low-order reconstructions of the flow was also utilized to facilitate vortex identification analysis, which identified average vortex sizes of 0.41D for Re1, 0.33D for Re2, and 0.32D for Re3.

Numerical study on wake galloping of tandem circular cylinders considering the effects of mass and spacing ratios

The mass and spacing ratios of parallel circular cylinder structures change over a wide range in engineering applications. In this study, the effects of mass ratio, spacing ratio and helical wires on the wake galloping of tandem circular cylinders are investigated by LES turbulence model at the subcritical Reynolds number regime. The upstream cylinder is fixed and the downstream one is free to respond in the transverse direction. The characteristics of wake galloping of tandem circular cylinders are systematically studied for the cases of mass ratios m∗ ​= ​1.8, 200 and spacing ratios x0/D ​= ​4, 8 and 12. A critical velocity of wake galloping is derived as a function of mass ratio and lift coefficient slope using a wake-stiffness-based model. The suppression of wake galloping by the 4-start helical wires is examined and the maximum amplitude of vibration is found to decrease by 63% because of the positive added damping generated by helical wires.

Vortex characteristics and flow-induced forces of the wavy cylinder at a subcritical Reynolds number

The three-dimensional vortex characteristics behind the wavy cylinders are studied by Large Eddy Simulation (LES) at Re = 3900. The wavelength ratios (λ/Dm = 1.8–5.0) and amplitude ratios (a/Dm = 0.05–0.2) are mainly considered. The spanwise waviness is analyzed for the wavy cylinder on the flow control effect and the results of the unmodified cylinder (UC) are introduced for the comparison. The results show that there is a strong three-dimensional effect in the flow field distribution between the node and the saddle. The phenomenon of the multi-scale and the rib-like vortices are observed in the wake region. Boundary vortex flux of the cylinder reveals the vortex generation mechanism, the conversion of streamwise vortices further explain that mechanism. In addition, the length of vortex formation behind the wavy cylinder is longer than that of the UC. The mean streamwise velocity distribution exhibits a semi-symmetrical U-shaped to V-shaped transformation with the different characteristic positions. With the increment of the amplitude ratio, the statistical average of fluid force coefficients gradually reduces and reaches its minimum value at a/Dm = 0.2. The effect of the flow control is close to that of the UC at λ/Dm = 2.75. Finally, the wake control of the wavy cylinder is mainly related to vortex characteristics.

A novel drag reduction and vortex shedding mitigation measure for a circular cylinder in the subcritical regime

A novel aerodynamic measure, an arch mounted leeward of a circular cylinder, is proposed to reduce drag and mitigate vortex shedding for a circular cylinder. To confirm the validity of the proposed measure, the aerodynamic forces were measured through a force meter at the end of a cylinder, the wind pressure was measured at seven cross-sections of the cylinder, and elastically mounted cylinders were also tested. The results show that the arch significantly reduces drag and fluctuating lift by mitigating the vortex shedding in the subcritical Reynolds number range when the proper central angle is selected for the arch. The arch creates a higher base pressure at the leeward side and induces a pressure exchange and spanwise axial flow. This influence is extended along the length of the cylinder by the axial flow due to the strong correlation in the wake in the subcritical regime. Therefore, the arch lowers the base pressure and disrupts the formation of vortex shedding.

Transverse flow-induced vibrations of a sphere in the proximity of a free surface: A numerical study

In this paper, we present a numerical study on the transverse flow-induced vibration (FIV) of an elastically mounted sphere in the vicinity of a free surface at subcritical Reynolds numbers. We assess the interaction dynamics and the vibration characteristics of fully submerged and piercing spheres that are free to vibrate in the transverse direction. We employ the recently developed three-dimensional two-phase flow–structure interaction solver to investigate fully and partially submerged configurations of an elastically mounted sphere. To begin, we examine the vortex-induced vibration (VIV) phenomenon and the vortex-shedding modes of a fully-submerged sphere vibrating freely in all three spatial directions. We systematically verify and analyze the mode transitions and the motion trajectories in the three degrees-of-freedom (3-DOF) for the Reynolds number up to 30000. We next simulate the transversely vibrating (1-DOF) full-submerged sphere over a wide range of reduced velocities 3≤U∗≤20, whereby the reduced velocity is adjusted by changing the freestream Reynolds number. The VIV response amplitude and the topology of the wake structure are compared with the measurements for the mode I and mode II response branches. We further look into the effect of the free surface on the FIV response of a transversely vibrating sphere in the proximity of a free surface. The response dynamics of the sphere is studied for three representative values of normalized immersion ratio (h∗=h∕D, where h is the distance from the top of the sphere to undisturbed free-surface level and D is the sphere diameter), at h∗=1 (fully submerged sphere with no free-surface effect), h∗=0 (where the top of the sphere touches the free surface) and h∗=−0.25 (where the sphere pierces the free surface). At the lock-in range, we observe that the amplitude response of the sphere at h∗=0 is decreased significantly compared to the case at h∗=1. It is found that the vorticity flux is diffused due to the free-surface boundary and the free surface acts as a sink of energy that leads to a reduction in the transverse force and amplitude response. When the sphere pierces the free surface at h∗=−0.25, the amplitude response at the lock-in state is found to be greater than all the submerged cases studied with the maximum peak-to-peak amplitude of ∼2D. We find that the interaction of the piercing sphere with the air–water interface causes a relatively large surface deformation and has a significant impact on the synchronization of the vortex shedding and the vibration frequency. The streamwise vorticity contours and pressure distribution are employed to understand the VIV characteristics and wake dynamics. Increased streamwise vorticity gives rise to a relatively larger transverse force to the piercing sphere at h∗=−0.25, resulting in greater positive energy transfer per cycle to sustain the large-amplitude vibration. Lastly, we study the sensitivity of large-amplitude vibration on the mass ratio, m∗, and, Froude number, Fr, at the lock-in state.

Computational kinematic characterization of flow past a bluff body for type 304 stainless steel material using ANSYS workbench

Current computational Analysis deals with the velocity analysis of G/D 0.5 at different time frames. Type 304 stainless steel is used as it is an austenitic steel with excellent corrosion resistant properties. Finite size vortex has been made by translating circular cylinder that was permitted to move at a consistent speed over a zero pressure-gradient shear layer. The regulated vortex makes an extremely powerless stream astute pressure gradient that destabilized the level plate shear layer at subcritical Reynolds number. 2D fluid domain of 0.5 G/D is designed, modeled, meshed and the effective boundary conditions are applied. Different Models are highlighted in the current research such as Mass Conservation Equation, Momentum Conservation Equation, Energy equation, k –ω Model and Shear Stress Transport Turbulence Model. The governing equations are also elaborated. The Velocity Comparison at Point 1,2,3,4 for G/D 0.5 at different time steps is analysed. Also the Velocity Contour for different locations like front, left, right and mid view is computationally analysed. It is finally concluded that the disturbance in flow with lower G/D (less than 0.5) ratio in near wall zone is suppressed completely over the time and steady condition can be achieved after sufficient amount of time. The magnitude of the change in the kinematic properties are analysed and discussed. Specifically, the 304 stainless steel material is used in order to work on product development just after the positive results. The major significance of the current research is to provide all the governing equations, proper methodology, process and finally the trend at different locations based on computational techniques. Fluid flow is simulated in all the three cases with uniform velocity 1.76 m/s by using ANSYS Fluent Solver. The Future scope for the current computational Analysis is to change the G/D values and take different time step size for micro or even Nano kinematic analysis.

Comparative study of mass transfer distributions and oil-flow visualizations with image analysis on long and short 90° elbows

To understand the mass transfer mechanism of 90° elbows, a comparative study of mass transfer measurements and oil-flow visualization with image analysis is carried out for long and short 90° elbows in the Reynolds numbers Re = 5 × 104 –2 × 105. The mass transfer distributions are evaluated by using the plaster-dissolution method, while the oil-flow fields are quantitatively visualized by oil-flow technique combined with cross-correlation image analysis, which allows observation of the oil-flow velocity magnitude and direction on the elbow walls. The mass transfer evaluations in the sub-critical Reynolds number indicate an increase in mass transfer distribution along the center wall of the long elbow and a further increase in the downstream of the short elbow. These are highly suppressed on the center wall as the Reynolds number increases, and the mass transfer distributions become almost independent of the elbow curvatures in the post-critical Reynolds number. These observations of mass transfer distributions are well correlated with the oil-flow visualizations with image analysis, which indicate formation of low oil-flow-velocity on the center wall of the long elbow, occurrence of flow separation and reverse flow downstream of short elbow at sub-critical Reynolds number. These features of oil-flow fields on the elbows are highly suppressed and becomes independent of the elbow curvature in the post-critical Reynolds number.

Flow around two elastically-mounted cylinders with different diameters in tandem and staggered configurations in the subcritical Reynolds number regime

Flow around two cylinders with different diameters undergoing Flow-Induced Vibrations (FIV) in the subcritical flow regime is investigated using two-dimensional Unsteady Reynolds Averaged Navier-Stokes (URANS) approach. Physical parameters of the system are chosen to represent the free spanning pipelines laid in proximity. The two cylinders are initially placed at various tandem and staggered positions with one in the wake of the other, and subject to steady current flows. The two cylinders are free to respond in both in-line and transverse directions. The investigated Reynolds numbers (Re) are Re1=1.4×105 based on the diameter of the larger cylinder and Re2=1.15×105 based on the diameter of the smaller cylinder. A parametric study investigating the effects of relative spacing of the cylinders on the vibration response of the system is performed. First and second order statistics of the flow, frequency domain analysis and flow field visualizations are used to characterize the dynamic behavior of the system. It is found that the motion trajectories of the downstream cylinder show a qualitative difference depending upon whether it is in tandem with the upstream cylinder or in the wake with a transverse offset. A large amplification of the in-line response is observed in the positions with a transverse offset. The vibration response of the upstream cylinder is affected by the presence of the downstream cylinder only when the horizontal center-to-center distance is small (L/D1=2.06 where D1 is the diameter of the larger cylinder) and is largely unaffected when the horizontal distance is increased to L/D1=3.22.

Study of Surface Roughness Effect on a Bluff Body—The Formation of Asymmetric Separation Bubbles

Turbulent flows around bluff bodies are present in a large number of aeronautical, civil, mechanical, naval and oceanic engineering problems and still need comprehension. This paper provides a detailed investigation of turbulent boundary layer flows past a bluff body. The flows are disturbed by superficial roughness effect, one of the most influencing parameters present in engineering applications. A roughness model, recently developed by the authors, is here employed in order to capture the main features of these complex flows. Starting from subcritical Reynolds number simulations (Re = 1.0 × 105), typical phenomena found on critical and supercritical flow regimes are successfully captured, like non-zero lift force and its direction change, drag crisis followed by a gradual increase on this force, and separation and stagnation points displacement. The main contribution of this paper is to present a wide discussion related with the temporal history of aerodynamic loads of a single rough circular cylinder capturing the occurrence of asymmetric separation bubbles generation. The formation of asymmetric separation bubbles is an intrinsic phenomenon of the physical problem, which is successfully reported by our work. Unfortunately, there is a lack of numerical results available in the literature discussing the problem, which has also motivated the present paper. Previous study of our research group has only discussed the drag crisis, without to investigate its gradual increase and the change on lift force direction. Our results again confirm that the Lagrangian vortex method in association with Large-Eddy Simulation (LES) theory enables the development of two-dimensional roughness models.

Large Eddy Simulation of Flow Pasta Twisted Cylinder

The wavy cylinder has a sinusoidal variation incross sectional area along the spanwise direction and the twistedcylinder has been newly designed by rotating the elliptic crosssection along the spanwise direction, so that the cylinder surfacehas a twisted spiral pattern. A twisted cylinder is investigated toobserve the effect of twisted spiral pattern of the flow fields. Itguarantees the accuracy of the present numerical methods thatthe excellent comparisons with previous studies for the cases of asmooth circular cylinder. The effect of surface torsion which isnewly designed in here has been predicted and assessed in termsof the mean drag and root-mean-square (RMS) value offluctuating lift at the subcritical Reynolds number of 3000.Subsequently, the mechanisms of enhancing the aerodynamicperformance and passive control of vortex-induced vibrations arealso investigated by careful analysis with the flow structures. Theiso-surface of swirling strength has been imposed to identify thevortical structures in the turbulent wake

Influence of the center cylinder on the flow characteristics of four- and five-cylinder arrays at subcritical Reynolds number

The three-dimensional flow around the four-cylinder and five-cylinder arrays are numerically studied at Re = 3900 by large eddy simulation (LES). By selecting eight spacing ratios (L/D = 2.0–7.0) and three incidence angles (α = 0°–45°), the influence of the center cylinder on the flow characteristics and interference effects of the four-cylinder array is discussed. Different spacing ratios can be divided into three categories with respect to flow regions of the multi-cylinder: small gap flow regime (L/D = 2.0–3.5), critical flow regime (L/D = 3.5–5.0) and large gap flow regime (L/D = 5.0–7.0). For cases with small spacing ratios, the influence of the center cylinder is very notable on the flow characteristics of the four-cylinder array. As the ratio increases, the influence of the center cylinder gradually decreases on the surrounding cylinders in the multi-cylinder array. On the other hand, the direction of the incoming flow also affects the flow characteristics of both four-cylinder and five-cylinder arrays. The development of the shear layer is strongly influenced by the center cylinder for the upstream cylinders at α = 45°. Boundary vortex flux components, flow characteristics and fluid force coefficients change significantly with adding the center cylinder for the four cylinders.

Characterization of coherent structures in turbulent wake of a sphere using partially averaged Navier–Stokes (PANS) simulations

The large-scale coherent structures in the wake of a sphere at subcritical Reynolds number (Re = 3700) are examined at different degrees of resolution (filter size) using scale-resolving simulations (SRS) of turbulence. The Partially averaged Navier–Stokes (PANS)-SRS method is employed to compute the wake flow at four levels of resolution marked by unresolved-to-total kinetic energy ratios: fk = 0.5, 0.3, 0.2, 0.1. The results from the four simulations are used to compute one-point statistics, frequency spectra, and spatio-temporal POD (proper orthogonal decomposition) modes. One-point statistics are reasonably well reproduced (in comparison with existing data) at all degrees of resolution. However, the frequency spectra and POD modes exhibit some degree of dependence on the level of resolution. It is demonstrated that accurate depiction of coherent structures is contingent upon adequately resolving key underlying instabilities. The finest resolution PANS simulation (fk = 0.1) is then used to characterize the large-scale coherent structures in the near-wake of the sphere. The main features of this wake, specifically azimuthal mode shapes, modal energy, and frequency content, are compared with experiments and numerical simulations of wakes of other axisymmetric bodies resulting in good agreement. Overall, the study demonstrates that PANS-SRS can capture key one-point statistics and coherent structure features of complex flows in a cost-efficient manner.

개선된 PANS 난류 모델을 이용한 높은 레이놀즈 수를 갖는 실린더 주위 난류 유동에 대한 수치 모사

Computational simulations of turbulent flows around a circular cylinder were performed to investigate the drag coefficient and Strouhal number at sub-critical and critical Reynolds numbers. Unstructured grids with 3.1 million cells including prism layers were used in the present study. Both RANS and PANS simulations using k-ω SST model failed to predict a transitional behavior of drag coefficient and vortex shedding frequency at sub-critical and critical Reynolds numbers due to the absence of laminar separation bubble. But a hybrid combination of unresolved turbulence viscosity in PANS and sub-grid scale turbulence viscosity in LES provided a good agreement of drag coefficient and vortex shedding frequency with previous results.

Modification and application of low Reynolds number k–ɛ turbulence model to vortex-induced vibration at subcritical Reynolds number range

In the study of the cross-flow vortex-induced vibration of the cylinder, it is found that with the increase in the Reynolds number, the upper branch of the vibration amplitude and the lock-in region show an increasing trend. Currently, there are relatively few studies on two-degree-of-freedom VIV at high Reynolds number. In this paper, the Launder and Sharma low Reynolds number k–ɛ turbulence model is modified by limiting the kinetic energy generation term and dissipation term, which is similar with the limiter used in SST k–ω model. Based on the modified turbulence model, the two-degree-of-freedom vortex-induced vibration of the cylinder with different Reynolds numbers is simulated with the two-dimensional RANS method. The accuracy of the improved turbulence model and its applicable Reynolds number range are verified by comparing with experiments and relevant numerical simulations. The effects of Reynolds number on the vibration characteristics of cylinder with low mass damping ratio are discussed, which provide a theoretical reference for the study of vortex-induced vibration under high Reynolds number.

Vortex-induced vibrations of a flexible cylinder at subcritical Reynolds number

Abstract