Subcritical Reynolds Number Range Research Articles

Numerical investigation of flow past a cylinder using cumulant lattice Boltzmann method

This paper presents simulations of flow past a circular cylinder within the subcritical Reynolds number (Re) range from 3900 to 2 × 105, utilizing the parameterized cumulant lattice Boltzmann model. In this study, a three-dimensional characteristic boundary condition for incompressible flow has been integrated into the lattice Boltzmann method at the outflow boundary to minimize spurious reflection. The flow field, wake statistics, hydrodynamic force, and power spectra results of Re = 3900 from the cumulant lattice Boltzmann model are exhaustively compared with the laboratory data and other numerical models. Relative to other numerical models employing turbulence closure, the cumulant lattice Boltzmann simulations demonstrate enhanced agreement with the experimental data even with relatively coarser grid resolution. The resolution-spanning feature for the cumulant lattice Boltzmann model in turbulent flows, without using explicit turbulence model, aligns with the previous benchmark case studies. The stability-preserving regularization process in the present model is analyzed. Results indicate that the influence of the regularization parameter is mitigated with improved grid resolution. A specific regularization parameter for flow around cylinder simulations is recommended. Variations in flow properties and hydrodynamic forces within the subcritical Reynolds number range of 3900 to 2 × 105 are analyzed. The results confirm that the parameterized cumulant lattice Boltzmann model can accurately simulate practical engineering flows, characterized by complex separation and recirculation, within the subcritical range. Moreover, the computational efficiency and parallel scalability are compared with other numerical methods.

Aeroacoustic simulation of bluff bodies with protrusions at moderate Reynolds number

This paper presents an evaluation of passive control methods that employ surface protrusions to mitigate the aerodynamic sound generated from a cylinder wake flow. Building on previous designs optimized for low Reynolds numbers (Re = 150) through adjoint-based aeroacoustic shape optimization, this study investigated the performance under a moderate Reynolds number (Re = 67 000) condition typical of mechanical engineering applications using aeroacoustic simulations based on the lattice Boltzmann method. Three configurations of surface protrusions were tested, all of which were found to significantly reduce the mean drag by at least 45% compared with that of an unmodified circular cylinder. Designs featuring rear protrusions outperformed the conventional splitter plate in terms of the sound reduction performance, with symmetrical protrusions on both the front and rear surfaces achieving a tonal sound reduction of 13 dB. However, a specific protrusion design increased the low-frequency sound owing to the intensified large-scale flow separation. These findings highlight the effectiveness of rear protrusions in suppressing wake oscillations and dipole sound generation in the subcritical Reynolds number range. Moreover, the study revealed the need to tailor the front protrusion shape to the Reynolds number for performance optimization.

Effect of a bioinspired upstream extended surface profile on flow characteristics and a drag coefficient of a circular cylinder

<abstract> <p>In the current work, the passive drag reduction of a circular cylinder for the subcritical Reynolds number range of 5.67×10<sup>4</sup> to 1.79×10<sup>5</sup> was computationally and experimentally investigated. First, inspired by nature, the aerodynamic drag coefficient of a whole Peregrine Falcon was measured in a subsonic wind tunnel for various angles of attack and Reynolds numbers (<italic>Re</italic>) and compared with the bare cylinder. At a 20° angle of attack and <italic>Re</italic> = 5.67×10<sup>4</sup>, the whole falcon model had a 75% lower drag coefficient than the bare cylinder. Later, with the moderate Falcon model, in which the falcon's beak and neck were linked to the cylinder as an extended surface, the drag coefficient decreased up to 72% in the subcritical Reynolds number zone. Finally, the extended surface with a falcon beak profile was connected to the cylinder with a stem and investigated both numerically and experimentally for various stem lengths, angles of attack, and Reynolds numbers. It was found that at low <italic>Re</italic>, the drag coefficient can be reduced by up to 47% for the stem length of 80 mm (<italic>L</italic>/<italic>D</italic> = 1.20) with an angle of attack 10°. The computational investigation yielded precise flow characteristics, and it was discovered that the stem length and the <italic>Re</italic> had a substantial influence on vortex generation and turbulent kinetic energy between the beak and cylinder, as well as downstream of the cylinder. Investigation revealed that percentile drag reduction was much lower for the whole Falcon model over a wide range of Reynolds numbers and positive angles of attack, which exist in nature. Similarly, when compared to the other stem lengths, the 60 mm stem length (<italic>L</italic>/<italic>D</italic> = 0.97) produced similar results to the whole Falcon model. The numerical results were well validated with the experimental results.</p> </abstract>

Near-field pressure and wake velocity coherence of a circular cylinder

Aerodynamic noise and unsteady loads resulting from the vortex shedding of a circular cylinder pose significant challenges in engineering applications. Understanding these challenges is closely related to pressure fluctuations on the cylinder surface. This experimental study conducted simultaneous measurements of surface pressure and velocity fluctuations within the subcritical Reynolds number range (14.7×103≤Re≤30×103) to investigate the influence of vortex shedding on near-field pressure. The experiments utilized a highly instrumented cylinder with mini-pressure transducers. The results revealed that surface pressure fluctuations exhibit maximum energy content near the cylinder's shoulders at the fundamental vortex shedding frequency (f0), aligning with pronounced lift fluctuations. The analysis of pressure–velocity coherence indicated that the most energetic flow structures resulting from vortex shedding significantly contribute to generating surface pressure fluctuations at the f0-peak frequency, extending over a considerable distance from the near- to far-wake regions. Additionally, the pressure fluctuations responsible for drag fluctuations are predominantly imposed at the base of the cylinder, primarily at the second harmonic (2f0), arising from flow structures shed at the end of the vortex formation region. Wavelet analysis provided insights into the temporal characteristics of surface pressure fluctuations, revealing amplitude modulation over time with multiple repetitive patches around the f0-peak frequency and close to the cylinder's shoulders, where the highest energy level predominates due to vortex shedding.

Acquiring high-resolution wind measurements by modifying radiosonde sounding procedures

Abstract. High-resolution wind measurements are crucial for the understanding of dynamic processes in the atmosphere. In the troposphere and lower stratosphere, radiosondes provide a good vertical resolution of a few metres, but the wind data are usually low-pass filtered by the manufacturer in order to suppress disturbances in the data caused by the spurious motions of the sonde. As an example, the filter within the standard processing of Vaisala radiosondes becomes effective at vertical scales below 300 m for an ascent rate of 5 m s−1. We describe a method for increasing the usable resolution of radiosonde wind measurements. The main ideas are to avoid self-induced motions of the balloon by keeping it in the subcritical Reynolds number range, to avoid typical pendulum motions of a 15 s period by using a shorter string, and to use data from a descending balloon in order to avoid disturbances from the wake of the balloon affecting temperature and humidity measurements due to the decreased string length. We demonstrate that our changes in hardware and software allow for artefact-free wind data down to scales of 50 m, while the remaining disturbances on even smaller scales are removed. Accordingly, the usable resolution of the wind data has been increased by a factor of 6, compared to the standard data output, at relatively low cost.

Numerical study on the flow-induced vibrations of two elastically mounted side-by-side cylinders at subcritical Reynolds numbers

Two-degree-of-freedom (2DOF) flow-induced vibrations (FIV) of an elastically mounted circular cylinder pair arranged in parallel are numerically investigated in a subcritical Reynolds number range of 1470–10320. The two cylinders are identical with mass ratios of m⁎ = 2.6 and mass-damping parameters of (m⁎ + Ca)ζ = 0.013. The transverse centre-to-centre spacing ratio (Sy/D) between them is varied from 4.0 to 10.0 with an increment of 2.0. The effect of Sy/D on the FIV responses, hydrodynamic features and wake patterns is evaluated. It is found that the response amplitudes of the two cylinders show similar variation trends and both drop to smaller values earlier than an isolated cylinder when Sy/D = 4.0, 6.0 and 10.0. Whereas, their response characteristics are different at Sy/D = 8.0. Cylinder #1 reaches its peak in-line (IL) and cross-flow (CF) amplitudes equivalent to those of the single cylinder, while the vibration amplitudes of Cylinder #2 experience decreases at Vr = 8.0. Moreover, the results suggest that the interference between the two cylinders is nonnegligible for all the Sy/D values considered in the present study. Six wake patterns are identified including the asymmetric long period flip-flopping (ALFF), asymmetric shear layer (ASL), biased in-phase synchronised (BIS), asymmetric shedding (A-Shed), in-phase synchronised (IS) and anti-phase synchronised (AS) patterns. The asymmetric wake patterns give rise to the distinct vibration modes of the two cylinders.

Wind tunnel tests of aerodynamic interference effects on two iced vertical circular cylinders in a tandem arrangement

The aerodynamic characteristics of the two iced vertical circular cylinders in a tandem arrangement, due to the shape change by icing, are complex, and lack systematical investigation. Therefore, a set of wind tunnel tests were carried out to study the aerodynamic characteristics of the leeward vertical cylinder, with ice shape, icing thickness, cylinder spacing, and icing relative position of cylinders varied in the subcritical Reynolds number range in this study. Results show that the icing thicknesses had a greater impact on the lift coefficients of D-shaped ice leeward cylinder at the same angle of attack. The aerodynamic characteristics of the iced leeward cylinder were stable when the ratio (L/D) of cylinder spacing was within the range of 4.8–6.2. The change of flow field should be considered in the stability analysis of two circular vertical cylinders. The drag coefficients of the iced leeward cylinder varied significantly due to the shielding effects, especially within the range of 9° attack angle and L< 6.2D. The results of this work can provide an experimental reference for future research on wind resistance of two circular cylindrical structures in engineering practice.

Hydrodynamic regimes and drag on horizontally pulled floating spheres

We use high-speed imaging to investigate the movement of a floating sphere pulled horizontally along a water surface. The model sphere is 10 cm in diameter and has half of the water density resulting in a half-submerged static sphere. By varying the pulling force, we investigate the flow dynamics in the subcritical Reynolds number range, of Re ≈ 2 × 104 to 2 × 105. We characterize three hydrodynamic regimes with the increase in the pulling force, to which we refer to as: low Froude number, Fr &amp;lt; 0.6, intermediate, 0.6 &amp;lt; Fr &amp;lt; 1.2 and high Froude number, Fr &amp;gt; 1.2 regimes. In the low Fr regime, the sphere moves with little disturbance of the water surface and the drag is close to half of the drag on a fully submerged sphere. In the intermediate Fr regime, a pronounced wave pattern is developed which together with the dipping of the sphere below the water level leads to an increase in the drag force. Based on a potential flow approximation for the downward force on the sphere moving along the surface, we derive a semiempirical relation for the sphere dipping as a function of the Froude number. Finally, in the high Fr regime, the sphere movement switches to a mode of periodic dipping below and surfacing above the water surface. The periodic vertical motion portrays a decrease in the average drag force.

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.

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.

The dynamic evolution of fluid strouhal number under flow fields around flexible vertical pipe groups

In this paper, a Strouhal-Reynolds number evolution region for the pipe groups within the subcritical Reynolds number range is established and a Strouhal-Reynolds number relation curve in root mean square terms is yielded for the first time. A Strouhal-Reynolds number model for flow around flexible pipes under 180 sets of test is presented. The least squares method is used to fit the Strouhal numbers among the pipes within their flow velocity intervals; isolated pipe is introduced as reference cases for examining how the Strouhal numbers of the pipes vary with Reynolds number. The results indicate that, when in tandem arrangement, the Strouhal number of the three-pipe group showed a gradual reduction from upstream to downstream whereas both vortex shedding enhancement and suppression occurred in the five-pipe group; interferences contributed to the vortex shedding in the wake flow of the pipes in side-by-side arrangement. It is also found that interferences significantly changed the vortex shedding frequencies on both rear sides of the pipes; only 16.9% of the Strouhal numbers of the three-pipe and five-pipe group fell within [0.185,0.20], which is largely different from conventional cognition of the Strouhal number within the subcritical Reynolds number range.

Flow past a bluff body subjected to lower subcritical Reynolds number

The paper aimed to study the flow structure at the wake of the bluff body with altered blockage ratio (BR) keeping the fixed aspect ratio (AR). The study was conducted by a finite volume technique using commercial software Ansys-Fluent. The CFD analysis of the bluff body is mainly subjected to the lower subcritical Reynolds number range (5000 to 15,000) along with blockage ratio as an important factor. The flow parameters such as drag coefficient, pressure, and kinetic energy variations are analyzed here for the Reynolds number (Re) and BR. It was observed that at fixed Re, the drag coefficient (CD) increases with an increase in the BR while decrease with increasing Re for a fixed value of BR.

An Experimental Investigation of the Surface Pressure Fluctuations for Round Cylinders

An experimental study is carried out to investigate the unsteady pressure exerted on the surface of a round cylinder in the subcritical Reynolds number range. Results are presented for the surface pressure fluctuations, spanwise coherence, lateral correlation length, and peripheral coherence. Discussions are provided for the dominance of the first three vortex shedding tones at different regions of the cylinder and the size of the flow structures around the cylinder. The dataset provided have shed new light on the unsteady aerodynamic loading acting on cylinders and provides the impetus for further research on the aerodynamics and aeroacoustics of bluff bodies.

Giant drag reduction on Leidenfrost spheres evaluated from extended free-fall trajectories

Vapor layer sustained on the surface of a heated sphere, by the means of the Leidenfrost effect, can dramatically reduce the hydrodynamic drag on a sphere due to an early drag crisis transition. Here we investigate the vapor layer effect on the free fall of heated metallic spheres in a fluorocarbon liquid, FC-72 (perfluorohexane), employing two tall liquid tanks: a 3 m tall 14 cm wide tank and a 2 m tall 20 × 20 cm cross-section tank with a heater device. These tanks are significantly larger than the tanks used in prior studies. We use high-speed video camera recordings to track extended fall trajectories and to compare the drag on room-temperature no-vapor-layer spheres to that of heated Leidenfrost vapor-layer spheres. Analysis of the extended free-fall trajectories and acceleration, based on the sphere dynamic equation of motion, enables the accurate evaluation of the vapor-layers-induced drag reduction, without the need for extrapolation. We demonstrate that the drag on the Leidenfrost sphere in FC-72, can be as low as CD = 0.04 ± 0.01, or an order of magnitude lower than the values for the no vapor layer spheres in the subcritical Reynolds number range. This drag reduction extends into the supercritical Reynolds number range. The analysis method developed herein, to describe the sphere trajectories, can be applied in other related studies. Results of this study are expected to stimulate the development on energy saving drag-reduction technologies based on lubricating gas layers.

An experimental study of a circular cylinder's two-degree-of-freedom motion induced by vortex

This paper presents results of an experimental investigation of vortex-induced vibration (VIV) of a flexibly mounted and rigid cylinder with two-degrees-of-freedom with respect to varying ratio of in-line natural frequency to cross-flow natural frequency, f∗, at a fixed low mass ratio. Combined in-line and cross-flow motion was observed in a sub-critical Reynolds number range. Three-dimensional displacement meter and tension meter were used to measure dynamic responses of the model. To validate the results and the experiment system, x and y response amplitudes and ratio of oscillation frequency to cross-flow natural frequency were compared with other experimental results. It has been found that the higher harmonics, such as third and more vibration components, can occur on a certain part of steel catenary riser under a condition of dual resonance mode. In the present work, however, due to the limitation of a size of circulating water channel, the whole test of a whole configuration of the riser at an adequate scale for VIV phenomenon was not able to be conducted. Instead, we have modeled a rigid cylinder and assumed that the cylinder is a part of steel catenary riser where the higher harmonic motions could occur. Through the experiment, we have found that even though the cylinder was assumed to be rigid, the occurrence of the higher harmonic motions was observed in a small reduced velocity (Vr) range, where the influence of the in-line response is relatively large. The transition of the vortex shedding mode from one to another was examined by using time history of x and y directional displacement over all experimental cases. We also observed the influence of in-line restoring force power spectral density with f∗.

Coherent and turbulent processes in the bistable regime around a tandem of cylinders including reattached flow dynamics by means of high-speed PIV

The turbulent flow around two cylinders in tandem at the sub-critical Reynolds number range of order of 105 and pitch to diameter ratio of 3.7 is investigated by using time-resolved Particle Image Velocimetry (TRPIV) of 1kHz and 8kHz. The bi-stable flow regimes including a flow pattern I with a strong vortex shedding past the upstream and the downstream cylinder, as well as a flow pattern II corresponding to a weak alternating vortex shedding with reattachment past the upstream cylinder are investigated. The structure of this “reattachment regime” has been analyzed in association with the vortex dynamics past the downstream cylinder, by means of POD and phase-average decomposition. These elements allowed interconnection among all the measured PIV planes and hence analysis of the reattachment structure and the flow dynamics past both cylinders. The results highlight fundamental differences of the flow structure and dynamics around each cylinder and provide the ‘gap’ flow nature between the cylinders. Thanks to a high-speed camera of 8kHz, the shear-layer vortices tracking has been possible downstream of the separation point and the quantification of their shedding frequency at the present high Reynolds number range has been achieved. This issue is important regarding fluid instabilities involved in the fluid–structure interaction of cylinder arrays in nuclear reactor systems, as well as acoustic noise generated from the tandem cylinders of a landing gear in aeronautics.

Two-degree-of-freedom VIV of circular cylinder with variable natural frequency ratio: Experimental and numerical investigations

Slender offshore structures possess multiple natural frequencies in different directions which can lead to different resonance conditions when undergoing vortex-induced vibration (VIV). This paper presents an experimental and numerical investigation of a two-degree-of-freedom VIV of a flexibly mounted circular cylinder with variable in-line-to-cross-flow natural frequency ratio. A mechanical spring-cylinder system, achieving a low equivalent mass ratio in both in-line and cross-flow directions, is tested in a water towing tank and subject to a uniform steady flow in a sub-critical Reynolds number range of about 2×103–5×104. A generalized numerical prediction model is based on the calibrated Duffing-van der Pol (structure-wake) oscillators which can capture the structural geometrical coupling and fluid-structure interaction effects through system cubic and quadratic nonlinearities. Experimental results for six measurement datasets are compared with numerical results in terms of response amplitudes, lock-in ranges, oscillation frequencies, time-varying trajectories and phase differences of cross-flow/in-line motions. Some good qualitative agreements are found which encourage the use of the implemented numerical model subject to calibration and the sensitivity analysis of empirical coefficients. Moreover, comparisons of the newly-obtained and published experimental results are carried out and discussed, highlighting a good correspondence in both amplitude and frequency responses. Various patterns of figure-of-eight orbital motions associated with dual two-to-one resonances are observed experimentally as well as numerically: the forms of trajectories are noticed to depend on the system mass ratio, damping ratio, reduced velocity parameter and natural frequency ratio of the two-dimensional oscillating cylinder.

VIV suppression of a two-degree-of-freedom circular cylinder and drag reduction of a fixed circular cylinder by the use of helical grooves

Experimental investigations have been carried out to examine the effects of triple-starting helical grooves on the drag of fixed circular cylinders and the vortex-induced vibration of elastically supported cylinders. For the elastically supported cylinder, the Reynolds number varied from 1.3×10 4 to 4.6×10 4, whilst for the fixed cylinder from 3.1×10 4 to 3.75×10 5. A comparative approach which allows direct comparisons of the results was adopted where two cylinders of identical dimensions and physical properties with or without helical surface grooves were tested in exactly same experimental set-ups. In the elastically supported cylinder tests, the cylinders were attached to a vertically cantilevered supporting rod and towed in a towing tank. Both the in-line and cross-flow vibrations were permitted. In the fixed cylinder tests, the cylinders were supported on rigid vertical struts and towed horizontally in the same towing tank. It is found that for the case investigated the helical grooves were effective in suppressing the vortex-induced cross-flow vibration amplitudes with the peak amplitude reduced by 64%. Drag reductions of up to 25% were also achieved in the sub-critical Reynolds number range tested in the study for the fixed cylinders.

An active flow control strategy for the suppression of vortex structures behind a circular cylinder

An algorithm is proposed to model, predict and control vortex shedding behind a circular cylindrical configuration. The main ingredients of the algorithm include multiple-feedback sensors, actuators (with zero net mass injection) and a control strategy. Along with the mass and momentum conservation equations, a control equation is implemented to enable the desired flow control goals. A number of sensors are chosen in the downstream of the body to report the state of the flow. The role of externally controllable actuators on the fluid flow patterns past a circular configuration is assessed. To enable, zero net mass injection, two simple rotary type mechanical actuators are located at 120°, right behind the main cylinder. The popular finite volume based SIMPLE scheme is employed for the numerical calculations. As a precursor, the scheme simulates flow past an isolated cylinder, which is validated over a moderate range of Reynolds numbers. The design parameters of interest such as Strouhal number, drag and lift coefficients etc are used for the purpose of validation. The simulated flow fields are compared against the flow visualization study, which clearly demonstrates the efficacy of the actuators at discrete levels of rotation. The basic character of the flow is completely modified at U c/ U ∞ = 2.0 and Re = 100, where a complete suppression of vortex shedding is observed. This is tantamount to complete control of all the global instability modes. Fictitious tracer particles are released to visualize the vortex structures in the form of streaklines. The results clearly demonstrate the effectiveness of a rather simple active control algorithm in suppressing the vortex structures. All the relevant fluid flow features of the bluff-body fluid mechanics under the influence of actuators are studied in the sub-critical Reynolds number range of Re = 100–300.

Simulation of cross-flow-induced vibration of tube bundle by surface vorticity method

A fluid-structure interaction model based on Surface Vorticity Method (SVM) was used to study flow-induced vibrations of tube bundles in medium space ratio. The flow-induced vibrations of four tubes in a rotated square and a staggered tube bundle in three-row and five-column arrangements were simulated in the high sub-critical Reynolds number (Re) range. The results on fluid forces, tube responses and vorticity maps were presented. The vorticity maps of the four rotated-square tubes changed dramatically when the rigid tubes were replaced by the flexible tubes. From the vorticity maps and vibration responses of the staggered tube bundle of different structural parameters, it was found that with the decrease of tube natural frequency, the maximal vibration response moved from the third row to the first. The results also showed that when more flexible tubes are used, the flow pattern changed drastically and the fluid-structure interaction imposed a dominant impact on the flow.