Parametric Study on the Near-Wall Wake Flow of a Circular Cylinder: Influence of Gap Ratio and Reynolds Number

Abstract

Near-wall flow around circular cylinders is commonly encountered in various engineering applications, such as submarine pipelines and river-crossing conduits. The wake structure significantly influences local flow stability and has become a critical focus in fluid dynamics research. Specifically, when the gap ratio (G/D) ranges from 0.1 to 1.0, the interaction mechanism between the wall and the wake structure remains poorly understood. Moreover, the combined effects of the Reynolds number (Re) and gap ratio on the flow field require further investigation. In this study, a series of experimental measurements were conducted using two-dimensional, two-component particle image velocimetry (2D–2C PIV) to examine the influence of G/D and Re on the near-wall wake characteristics. The results indicate that, at a gap ratio of G/D = 0.1, the gap flow exhibits pronounced curling into the recirculation region, where the lower vortex is entrained and actively participates in wake evolution. When G/D ≥ 0.3, an increase in Re leads to a reduction in the lengths of both the upper and lower shear layers, a delayed attenuation of the wall-side shear layer, and a gradual symmetrization and contraction of the recirculation region behind the cylinder. Further analysis reveals that the evolution of the secondary vortex is strongly influenced by the combined effects of Re and G/D. Specifically, at Re = 3300 and G/D ≤ 0.3, the secondary vortex migrates away from the wall toward the upper shear layer, where it merges with the upper vortex. For 0.5 ≤ G/D ≤ 0.7, it interacts with the lower vortex, while at G/D = 1.0, it evolves independently downstream along the wall. At G/D = 0.5, the secondary vortex merges with the upper vortex at Re = 1100, whereas at Re = 5500, it interacts with the lower vortex instead. These findings contribute to a deeper understanding of the complex flow structures associated with near-wall cylinder wakes and offer valuable theoretical insights for engineering applications involving submarine pipelines in bottom-mounted or partially suspended configurations.

1. Introduction

The flow around near-wall circular cylinders is a classical topic in fluid mechanics and holds significant importance in various engineering applications. In submarine pipeline engineering, for instance, oil and gas transmission pipelines are commonly laid along riverbeds or traverse seabed terrains, often in close proximity to the seafloor [1,2]. However, due to local scour or uneven sediment backfilling, these pipelines frequently encounter non-ideal conditions, such as local free spans [3,4,5]. In such cases, the flow field surrounding the pipeline closely resembles that of a near-wall cylinder, making it a representative model for investigating the associated hydrodynamic phenomena. This type of flow involves not only variations in primary vortex shedding but also intricate interactions between the gap flow and the near-wall boundary layer. These flow characteristics have direct implications for structural safety, vortex-induced vibrations, local scour, and the long-term operational stability of the pipeline. Particularly under small gap ratio conditions, the flow exhibits highly complex wake dynamics, including asymmetric vortex structures and interference between shear layers [6,7,8,9].

In submarine pipeline engineering, the wake structure formed downstream of the pipeline plays a critical role in determining the hydrodynamic loading characteristics, including pressure, shear stress, and their fluctuations. These unsteady loads are major contributors to flow-induced vibrations, fatigue damage, and local scour-induced instability [10]. A detailed investigation into the wake dynamics of near-wall circular cylinders—specifically the generation, shedding, and evolution of wake vortices—can provide more accurate predictions of vortex-induced vibrations (VIV) and flow-induced vibrations (FIV), including their amplitude and frequency responses. Such insights are essential for informing pipeline design, optimizing support span arrangements, developing anti-scour strategies, and evaluating structural service life [11]. Furthermore, understanding the wake behavior of near-wall cylinders offers a theoretical foundation for optimizing the configuration and parametric design of protective structures, such as guide vanes and vortex suppression devices. This helps mitigate the risk of VIV and localized scouring, thereby enhancing the operational safety and reliability of submarine pipelines [12,13,14].

From a broader energy infrastructure perspective, the expansion of initiatives such as the “Belt and Road” has led to the rapid development of China’s oil and gas pipeline network, characterized by a “three vertical, four horizontal, and globally connected” configuration. A substantial portion of this network crosses aquatic environments, where pipelines are frequently subjected to complex hydrodynamic forces [15]. Therefore, a comprehensive understanding of near-wall cylinder flow mechanisms is essential for ensuring the safe and efficient operation of submarine pipelines. Such insights offer critical theoretical support for the design of protective structures and the optimization of pipeline layout and maintenance strategies in challenging underwater environments.

The study of flow around circular cylinders has a long history spanning over a century, with its fundamental characteristics primarily influenced by parameters such as the Reynolds number (Re), gap ratio (G/D), and boundary layer thickness (δ/D) [16,17]. For cylinders positioned far from a wall, the wake typically evolves into a well-organized von Kármán vortex street [18]. However, when a cylinder is placed in close proximity to a wall, the wall’s boundary layer significantly modifies the flow behavior—suppressing vortex shedding on one side while simultaneously inducing complex secondary vortex structures on the other [19].

Zhang et al. [20], at Re = 350, observed that increasing G/D from 0.2 to 1.0 results in a more symmetric surface pressure distribution and a transition from suppressed to fully developed vortex shedding. Using large eddy simulation (LES) at Re = 1440, Sarkar et al. [21] further demonstrated that the gap ratio has a decisive impact on shear layer development and vortex formation. Ovchinnikov et al. [22], through direct numerical simulations (DNS) at Re = 385, 1155, and 3900, identified the emergence of banded wake structures in the cylinder’s wake. Samani et al. [23] employed large eddy simulation (LES) to investigate the influence of wall proximity on the wake structure behind a square cylinder. Their results showed that when the cylinder is placed very close to the wall, the near-wake region exhibits strong asymmetry. In particular, when the square cylinder is directly mounted on the bottom wall, the wake is dominated by a large and elevated recirculation zone, and vortex shedding is completely suppressed. Quro et al. [24] conducted both experimental and LES-based numerical studies on the near-wake dynamics of a circular cylinder in the presence of a wall. Their work focused on gap ratios of 0.5 and 1.0 and Reynolds numbers of 6666, 10,000, and 13,333. Notably, their investigation considered not only the influence of the bottom wall boundary layer on the cylinder wake but also the effects of a free surface above the flow field. Both the experimental and numerical results revealed a significant wall-induced wake elevation effect. Additionally, at relatively high Reynolds numbers, Kelvin–Helmholtz (KH) instabilities were observed in the shear layers on both the upper and lower sides of the cylinder.

Experimental investigations have also provided valuable insights. Price et al. [25] conducted systematic experiments over a Reynolds number range of 200–4960 and gap ratios from 0 to 2, establishing transition thresholds between different flow regimes. At Re = 1500, Zhou et al. [26] employed particle image velocimetry (PIV) and vortex identification techniques to reveal the evolution of wake structures. Lin et al. [27] showed that for G/D < 0.5, a pronounced upstream recirculation region forms ahead of the cylinder, playing a critical role in modulating the gap flow.

Kyriakides et al. [28] experimentally demonstrated that when a cylinder is placed parallel to the leading edge of a flat plate, the induced flow significantly alters the near-wall flow field, leading to the formation of distinct secondary vortices downstream of the gap. He et al. [29,30] conducted experimental investigations on a near-wall circular cylinder within a flat-plate boundary layer using particle image velocimetry (PIV) and flow visualization techniques. Due to the complexity of leading-edge receptivity effects (e.g., the influence of upstream geometry and disturbances), the cylinder was positioned directly above the downstream boundary layer to minimize such uncertainties. Their results demonstrated that when the cylinder is sufficiently close to the wall, direct interactions occur between the secondary vortices and the lower wake vortices. Khabbouchi et al. [31] employed PIV to study the jet flow within the gap between a circular cylinder and a solid wall, as well as its influence on the wake dynamics. The Reynolds number, based on the characteristic length and freestream velocity, was approximately 8700. The results showed that under large-gap flow conditions, vortex shedding was nearly symmetric, with minimal wall effects. At intermediate gap ratios, shear layer transition induced intermittent vortex shedding and the emergence of small-scale structures. In contrast, at small gap ratios, the jet flow disrupted the lower shear layer significantly. Wang et al. [32], through PIV experiments, found a strong dependence of vortex shedding behavior on the gap ratio. When the gap ratio was sufficiently small, it notably altered the vortex shedding patterns in the wake of the cylinder.

Despite the considerable progress made in previous studies, several key limitations persist in the current literature: (1) Most previous studies have primarily focused on relatively large gap ratios, with insufficient refinement in gap-ratio classification or investigations restricted to a single gap ratio. Consequently, experimental studies on the wake-structure characteristics of cylinder flows under small gap-ratio conditions (0.1 ≤ G/D ≤ 1.0) remain limited [22,26,31]; (2) systematic studies addressing the coupled effects of Reynolds number (Re) and gap ratio are lacking; and (3) the evolution pathways of secondary vortices and their interactions with primary vortices are not yet fully understood. Addressing these gaps is of critical scientific significance for advancing the understanding of near-wall cylinder flow dynamics.

To this end, the present study employs high-resolution physical model experiments using advanced two-dimensional, two-component particle image velocimetry (2D-2C PIV) techniques. A series of tests is conducted across a range of gap ratios (G/D = 0.1, 0.3, 0.5, 0.7, and 1.0) and Reynolds numbers (Re = 1100–5500). The primary objective is to comprehensively analyze the evolution characteristics of wake structures, with the ultimate goal of providing robust theoretical support for engineering applications such as submarine oil and gas pipeline design and assessment.

2. Preparation for the Experiment

2.1. Experimental Design

The experiments were conducted using a particle image velocimetry (PIV) system at the National Research Center for Inland Waterway Regulation Engineering, Chongqing Jiaotong University. The experimental setup comprised a water tank, a recirculation pump, a two-dimensional, two-component (2D-2C) PIV system, and a data acquisition unit. The main body of the tank was constructed from transparent acrylic to enable full-field flow visualization. The tank dimensions were 12 m in length, 0.25 m in width, and 0.25 m in height. A 5LN-33A drainage pump (AERCO International, Inc., Blauvelt, NY, USA) provided circulating flow, with a maximum discharge of 0.025 m³/s.

The velocity field measurements were conducted using a 2D-2C Particle Image Velocimetry (PIV) system jointly developed by Chongqing Jiaotong University and Tsinghua University. The system consists of a high-speed imaging unit, a laser illumination and optical system, and a dedicated software suite for data acquisition and processing. The high-speed camera employed was the MotionXtra-NS5S2 model (manufactured by Integrated Design Tools, Pasadena, CA, USA), a high-frequency CCD camera with a light sensitivity of ISO 3000 and 5 GB of internal memory. The lens used was a Canon f1.0/50 mm (manufactured by Canon Inc., Tokyo, Japan), providing an optical resolution of 1920 × 1080 pixels. The frame rate was set to 500 Hz, which was sufficient to ensure flow field stability and allowed accurate tracking of particle trajectories even at relatively high Reynolds numbers. The Motion Studio software(Version2.14.01) developed by Integrated Design Tools (IDT), USA, was employed to control the high-speed camera for data acquisition, and it was also used to configure camera parameters to optimize imaging quality.

The laser source used for illumination was a dedicated PIV laser manufactured by Beijing Laser wave OptoElectronics Tech. Co., Ltd., Beijing, China, with a wavelength of 532 nm, adjustable output power ranging from 0 to 10 W, and a power stability error of less than 1%. After passing through a cylindrical lens and a slit aperture, the laser beam was formed into a light sheet approximately 1 mm thick, oriented vertically along the streamwise direction of the test section. The laser sheet fully covered the core region of the flow around the cylinder, approximately 100 mm × 80 mm in size. The CCD camera was mounted on the side of the water channel, with its optical axis orthogonal to the laser sheet plane. Image pairs were acquired at a time interval of 2 ms to ensure high temporal resolution for the capture of flow velocity vectors. It should be noted that while continuous-wave (CW) lasers offer simplicity and stability, they do have certain limitations compared to pulsed lasers. Specifically, the lower light intensity and potential attenuation in fluid media may lead to blurred particle images, thereby limiting the achievable spatial resolution of the velocity field. However, in this study, the relatively shallow water depth allowed the laser sheet to effectively penetrate the test section and adequately illuminate the measurement region, meeting experimental requirements. A schematic of the PIV experimental setup is shown in Figure 1.

The PIV image data were processed using a multi-pass iterative cross-correlation algorithm based on Fast Fourier Transformation (FFT). A two-level interrogation window scheme was applied, consisting of initial 64 × 64 pixel windows followed by refined 32 × 32 pixel windows, with a 50% overlap ratio at each stage. This approach enabled accurate velocity vector estimation across the measurement domain. During the image preprocessing stage, contrast-limited adaptive histogram equalization (CLAHE) was first employed to correct non-uniform illumination within the images. This method effectively enhanced particle visibility in low-light regions, particularly near the wall where laser sheet intensity tends to decrease. Subsequently, a high-pass filter was applied to enhance the contrast of particle images, followed by Gaussian smoothing with a kernel size of 3 × 3 and a standard deviation of σ = 0.8 to suppress high-frequency noise. After time-averaging 1000 frames, the instantaneous velocity field reached convergence. Subsequently, outliers that significantly deviated from the primary flow velocity region were identified and removed using a standard deviation filter in combination with a local median filter. In the CLAHE process, a window size of 64 pixels was used. This window size provided a good balance between enhancing particle visibility and avoiding image distortion. A smaller window size may excessively amplify noise, whereas a larger window may fail to sufficiently improve local contrast, especially in regions near the wall.

The test section was located 5 m downstream from the inlet to ensure fully developed flow. To minimize the influence of the tank bottom, a smooth flat plate (2000 mm × 250 mm × 10 mm, length × width × thickness) was installed 30 mm above the bottom. The plate’s leading edge was contoured to suppress flow separation and reduce upstream disturbances. A smooth circular cylinder (diameter D = 10 mm) was horizontally mounted above the plate. Both ends were supported by rectangular end plates (15 mm × 15 mm × 2 mm) with beveled leading edges to minimize wake interference. The cylinder aspect ratio was L/D = 25, ensuring a quasi-two-dimensional near-wake core. To avoid receptivity effects near the plate’s front, the cylinder was placed 150 mm (15D) downstream, following prior studies [34].

Neutrally buoyant hollow glass spheres (mean diameter 20 μm, density 1.03 g/cm³) were used as tracer particles. Before each run, tracer particles were evenly dispersed via mechanical stirring to ensure uniform concentration. By maintaining a constant ambient temperature over an extended period, the water temperature during the experiments was stabilized at approximately 24 °C, corresponding to a kinematic viscosity of about 0.91 mm²/s. Freestream velocities were set at U_∞ = 0.1, 0.2, 0.3, 0.4 and 0.5 m/s, yielding Reynolds numbers Re = U_∞D/v = 1100, 2200, 3300, 4400, and 5500, respectively.

The selected range of Reynolds numbers spans the transitional regime from laminar to turbulent flow. Investigating this regime offers insight into the influence of flow regime transitions on the wake characteristics of the pipeline. Moreover, this range encompasses the critical Reynolds number region where near-wall effects significantly alter the flow around the cylinder. Regarding the choice of gap ratios (G/D), five representative values—0.1, 0.3, 0.5, 0.7, and 1.0—were selected for comparative analysis. This selection was made to avoid excessively large gap ratios, which may cause the pipeline model to behave similarly to an isolated cylinder, thereby diminishing the influence of the wall boundary. By systematically varying the gap ratio across this range, the study aims to capture the evolution of near-wall interference and its impact on wake development.

2.2. Verification of Experimental Flow Rate

Prior to analyzing the more complex transitional and turbulent flow characteristics, the measurement of mean velocity serves as a fundamental validation for the experimental setup and flow conditions. This procedure not only ensures the accuracy and repeatability of the Reynolds number, but also verifies that the measured results are not affected by instrumental or measurement errors, thereby eliminating potential uncertainties caused by improper velocity acquisition. Accordingly, five different free-stream velocities—0.1 m/s, 0.2 m/s, 0.3 m/s, 0.4 m/s, and 0.5 m/s—were prescribed under undisturbed flow conditions (i.e., in the absence of the cylinder) to acquire corresponding two-dimensional velocity field data. Each set of velocity data was then subjected to time-averaging to eliminate instantaneous fluctuations and obtain a stable distribution of mean flow velocity. This approach provides a reliable baseline for subsequent analysis of flow behavior in the presence of the cylinder.

From each time-averaged field, three representative points were selected for local velocity extraction. These points were located at least 0.05 m above the flat plate to minimize the influence of near-wall effects. The velocity data extracted from the PIV measurements were compared with the average flow velocity obtained from an electromagnetic flowmeter. This flowmeter, designed based on Faraday’s law of electromagnetic induction, consists of an electromagnetic sensor, a converter, and a power supply system. It is capable of measuring flow velocities ranging from 0.005 m/s to 10 m/s, with an accuracy of ±1.0%. The comparison provides an additional verification of the accuracy and reliability of the PIV velocity measurements. The spatial coordinates of the measurement points and the associated PIV-derived velocities are summarized in

Table 1. Comparison between PIV flow velocity value and measured value of flow velocity meter.

Flow Velocity Meter (m/s)	Distance from the Forefront of the Tablet 150D (mm)	Distance from the Forefront of the Tablet 160D (mm)	Distance from the Forefront of the Tablet 170D (mm)
0.10	0.10	0.11	0.11
0.19	0.20	0.21	0.19
0.30	0.31	0.31	0.31
0.41	0.41	0.40	0.40
0.50	0.50	0.51	0.51

. The comparison results demonstrate that the velocities measured by the PIV system at the selected points closely match those obtained from the electromagnetic flowmeter, with the error within ±2%. This consistency confirms the high measurement accuracy and reliability of the PIV system under the experimental conditions adopted in this study.

To further validate the effectiveness of the PIV system in capturing boundary layer development, streamwise velocity profiles were acquired at the streamwise location corresponding to the cylinder centerline in the flume. Figure 2 illustrates the measured velocity distributions under five different freestream velocities (U_∞ = 0.1, 0.2, 0.3, 0.4, and 0.5 m/s). The results indicate that the measurement error decreases with increasing Reynolds number. The maximum error was observed at Re = 1100, with a mean absolute error (MAE) of 0.0465, while the minimum error occurred at Re = 5500, with an MAE of 0.0183. Despite these minor discrepancies, the velocity profiles under all flow conditions exhibit distributions that closely resemble the theoretical Blasius solution for laminar boundary layers. The observed deviation near the wall at low Reynolds numbers is primarily attributed to the effects of non-uniform illumination, which could not be entirely eliminated during the experiments.

Across all flow conditions, the velocity profiles exhibit features characteristic of the theoretical Blasius solution for a laminar boundary layer, indicating that the PIV system is capable of resolving fine-scale flow gradients near the wall. The corresponding boundary layer thicknesses (δ) were determined to be 9.23 mm, 8.93 mm, 8.31 mm, 7.25 mm, and 6.38 mm, respectively, revealing a gradual decrease with increasing freestream velocity. This trend is consistent with the theoretical inverse relationship between boundary layer thickness and freestream velocity in laminar flow regimes.

Meanwhile, Figure 3a presents the mean velocity profile at the location of x/D = 2.5 in the wake region downstream of the cylinder. The measured data exhibit an overall shape that is consistent with the experimental results reported by He et al. [30] in Figure 3b, with minor discrepancies likely attributed to differences in the gap ratio. The mean velocity profile provides a clear representation of the longitudinal flow structure in the near-wake region, which aligns well with the characteristic features of the recirculation zone.

In summary, both the comparative evaluation of pointwise velocity measurements and the analysis of boundary layer development confirm that the PIV system employed in this study accurately captures the velocity distribution within the flume. These findings underscore the system’s high reliability and suitability for investigating complex flow structures in near-wall and wake regions.

3. Experimental Analysis

3.1. Flat Velocity Profile

Figure 4 illustrates the time-averaged streamwise velocity distributions for different gap ratios (G/D = 0.1, 0.3, and 0.5) within the Reynolds number range of 1100 ≤ Re ≤ 5500. These distributions provide a more intuitive depiction of the velocity deficit along the mainstream direction and the wake development characteristics, thereby enabling precise determination of the recirculation zone location. Based on these characteristics, the evolution mechanism of the flow structures in the wake region of a cylinder with a small gap ratio in water can be further elucidated. The results indicate that for G/D ≤ 0.5, the wake dynamics exhibit pronounced sensitivity to Reynolds number variations. Under small-gap conditions, the confined flow environment significantly amplifies local shear effects, causing the gap flow to develop rapidly within the boundary layer adjacent to the flat plate.

This gap flow is subjected to the combined influence of the wall-induced boundary layer and the intensified shear stress, resulting in an upward deflection of the gap jet along the wall. The deflected jet eventually separates from the surface, generating substantial disturbances in the cylinder’s wake region. At this stage, strong interactions occur between the upper free shear layer—originating from the cylinder’s upper surface—and the upward-deflected gap flow below. This interaction leads to the formation of a prominent recirculating vortex structure in the wake.

In parallel, the viscous effects of the wall boundary layer impose considerable resistance on the main flow, promoting flow separation near the trailing edge of the gap-flow passage. This separation results in the formation of symmetric or asymmetric separation bubbles, further complicating the near-wake flow behavior and enhancing both unsteadiness and asymmetry.

To further validate and visualize these flow features observed in the time-averaged velocity distributions, particle trajectory fields are examined, providing complementary insight into the wake development and the interaction between gap flow and cylinder shear layers. Figure 5 presents the time-averaged particle trajectory fields behind the cylinder for the case of G/D = 0.5, over the Reynolds number range of 1100 < Re < 5500. Consistent with the instantaneous velocity fields shown in Figure 4, a clear spatial correlation is observed between the low-velocity region and the wall-attached separation bubbles, confirming the persistent influence of gap flow interactions on the wake structure. At the intersection of the gap flow and the upper shear layer of the cylinder, as well as on the downstream side of the separation bubble, minor discrepancies arise due to the relatively low local flow velocities and the differences in data processing methods employed in the two figures.

At Re = 1100, two distinct separation bubbles are formed on the flat plate surface, with the primary separation bubble located approximately at x/D = 4. As the Reynolds number increases to 2200, both separation bubbles shift upstream along the wall, with the primary bubble advancing to x/D = 3 and simultaneously reducing in size. When Re reaches 3300, the smaller separation bubble disappears, and the primary separation bubble becomes further compressed. Finally, at Re = 5500, the separation bubble vanishes completely, indicating a substantial transition in the near-wall flow structure with increasing Reynolds number.

These changes are primarily driven by the enhanced inertial effects of the gap flow at higher Reynolds numbers, which reduce its deflection angle and consequently weaken the adverse pressure gradient along the wall, thereby effectively suppressing boundary layer separation. As the separation bubbles shrink and eventually disappear, the deflection of the recirculation region behind the cylinder gradually weakens. Consequently, the wake structure becomes increasingly symmetric with respect to the cylinder’s centerline, and the overall size of the recirculation region significantly diminishes as Reynolds number increases.

In addition to Reynolds number, the gap-to-diameter ratio (G/D) exerts a significant influence on the wake structure. This effect is especially pronounced at small gap ratios, where the interaction between wall-induced shear forces and the near-wall flow around the cylinder leads to complex flow characteristics, including pronounced asymmetry and the formation of multi-scale vortex structures.

When the gap ratio is G/D = 0.1, the extremely narrow clearance between the cylinder base and the wall causes dual confinement of the flow, which significantly reduces the gap flow rate. This weakened gap flow is not only strongly deflected upward due to wall effects but also exhibits intensified vortex curling, which is markedly more intense compared to larger gap ratios. Notably, in contrast to the case with G/D ≥ 3, when G/D = 1, the recirculation region behind the cylinder contains two vortices of distinctly different scales. The primary vortex is mainly generated by the curled gap flow, while the secondary, smaller vortex originates from interactions between the primary vortex and the free shear layer above the cylinder. This dual-vortex structure remains relatively stable across different Reynolds numbers, indicating a weak dependence on Reynolds number under narrow-gap conditions.

As the gap ratio increases to G/D ≥ 0.3, the dual-vortex structure persists. However, the size disparity between the two vortices significantly decreases. With increasing Reynolds number, the two vortices tend to evolve toward similar sizes, and their distribution gradually becomes symmetric along the cylinder’s central axis.

Further observations from Figure 4 indicate that under G/D ≥ 3 conditions and at a fixed Reynolds number, the recirculation region behind the cylinder and its interaction with the near-wall boundary layer undergo substantial changes. Specifically, as the gap ratio increases, the extent of the recirculation region contracts noticeably. For Re = 1100 and 2200, the size of the low-velocity region near the wall-boundary layer decreases with increasing gap ratio. These findings suggest that a larger gap ratio effectively reduces the near-wall influence on the wake structure, promoting a more symmetric and stable development of the wake region. As a result, the flow behavior increasingly resembles the canonical flow around an isolated circular cylinder in freestream conditions.

In summary, both the Reynolds number and gap ratio (G/D) significantly influence the structural evolution of the wake region behind the cylinder. Experimental results demonstrate that at G/D = 0.1, the highly confined narrow-gap channel causes the gap flow to undergo pronounced curvature as it enters the wake region, resulting in substantial disturbances to the local flow field. Under this condition, a distinct dual-vortex structure forms within the recirculation region, consisting of a large-scale primary vortex primarily generated by the upwardly curved gap flow, and a smaller secondary vortex produced through interactions between the primary vortex and the upper shear layer above the cylinder. The overall wake pattern at this gap ratio differs markedly from that observed under larger gap conditions.

As the gap ratio increases to G/D ≥ 0.3, the widening of the gap channel enhances the momentum of the gap flow, while the constraining effect of the wall diminishes. This change results in a more stable and symmetric wake structure. Moreover, with the combined effects of increasing Reynolds number and gap ratio, both the extent of the wake region and the size of the low-velocity zone near the wall-boundary layer exhibit a clear decreasing trend. At higher Reynolds numbers, the dual-vortex structure within the recirculation region becomes increasingly symmetric, the overall wake region contracts, and the size of the wall-attached separation bubbles is significantly reduced. These observations suggest a more organized and coherent evolution of the flow structure.

Thus, appropriately increasing both the gap ratio and Reynolds number is beneficial for mitigating wall-induced interference in the wake region, improving near-wall flow characteristics, and promoting the evolution of the wake structure toward that of a freestream cylinder wake.

3.2. Average Vorticity Distribution

Figure 6 illustrates the distribution characteristics of the time-averaged spanwise vorticity for four gap ratios (G/D = 0.1, 0.3, 0.5, and 0.7) across a range of Reynolds numbers. Analysis of the vorticity field evolution reveals distinct structural characteristics and developmental trends within the upper and lower shear layers of the cylinder, as well as within the boundary layer along the flat plate wall.

At a small gap ratio (G/D = 0.1), the strong geometric confinement between the cylinder and the wall significantly inhibits the development of both the lower shear layer and the wall-induced boundary layer. Due to the limited flow passage in the narrow gap, the lower shear layer exhibits prominent upward curling at the cylinder’s trailing edge, with some portions rolling into the recirculation zone. This mechanism induces considerable disturbances in the wake region, leading to a highly asymmetric wake structure, which contrasts sharply with the more symmetric patterns observed at larger gap ratios (G/D ≥ 3).

As the gap ratio increases to G/D = 0.3, 0.5, and 0.7, both the lower shear layer of the cylinder and the terminal region of the wall shear layer exhibit an upward deflection trend within the low Reynolds number range (Re ≤ 2200). Notably, as the Reynolds number increases, the deflection angles of both shear layers decrease significantly. Meanwhile, the spanwise vorticity within the wall boundary layer exhibits a clear attenuation trend, accompanied by a downward shift in its spatial position. At Re = 5500, the spanwise vorticity of the wall layer nearly disappears, indicating a substantial reduction in the separation tendency driven by the adverse pressure gradient. Furthermore, at higher Reynolds numbers (Re = 5500), the upper and lower shear layers around the cylinder display a well-defined symmetrical configuration, with significantly reduced streamwise extent. This shortening of the shear layer length scale enhances the periodic shedding of wake vortices, thereby increasing the evolution frequency of the wake structure.

3.3. Distribution Characteristics of Gap Flow

Figure 7 illustrates the distributions of dimensionless time-averaged velocity (U/U_∞) along the cylinder centerline for three gap ratios (G/D = 0.3, 0.5, and 0.7) under various Reynolds number conditions. The case with G/D = 0.1 is excluded from the analysis due to the presence of weak flow structures and poorly defined vorticity distributions in the wake region, which prevent the extraction of representative flow characteristics.

The experimental results reveal that the interplay between gap ratio and Reynolds number strongly influences the velocity distribution in the cylinder’s wake. At G/D = 0.3 with Reynolds numbers Re = 1100 and 2200, the mean velocity distributions exhibit peak values at x/D = 3.35 with U/U_∞ = 0.68 and at x/D = 3.07 with U/U_∞ = 0.66, respectively. Similarly, at G/D = 0.5 with Re = 1100 and 2200, pronounced peaks appear at x/D = 3.09 with U/U_∞ = 0.70 and at x/D = 2.85 with U/U_∞ = 0.72, respectively. This is attributed to the pronounced upward deflection of the gap flow at low Reynolds numbers. As the deflected flow crosses the cylinder centerline, a localized maximum in velocity develops. With increasing Reynolds number, this velocity peak progressively shifts upstream, indicating a contraction in the streamwise development of the gap flow.

Downstream of the velocity peak, the presence of a separation bubble extending above the cylinder centerline induces a rapid decay in the time-averaged velocity. At higher Reynolds numbers (Re = 3300, 4400, and 5500), the flow exhibits significant changes: the deflection angle of the gap flow decreases, and the flow no longer crosses the cylinder centerline. The near-cylinder velocity distribution displays characteristic recirculation features, with the location of the minimum velocity shifting upstream as Re increases. This behavior reflects the dynamic evolution of the recirculation region, characterized by a reduction in size and upstream migration of its core with increasing Reynolds number.

For the case of G/D = 0.7, the time-averaged velocity along the cylinder centerline consistently shows a decrease followed by an increase over the entire Reynolds number range (Re = 1100 to 5500). This pattern indicates that a larger gap substantially weakens the wall-confinement effect, limiting the momentum of the gap flow and preventing it from crossing the cylinder centerline. The location of the minimum velocity corresponds to the recirculation core, whereas the downstream velocity increase reflects the gradual re-energization of the wake by the incoming mainstream flow.

Notably, similar to the trends observed for G/D = 0.3 and 0.5, the minimum velocity location for G/D = 0.7 also shifts upstream with increasing Reynolds number. This consistent behavior underscores the dynamic nature of the recirculation region and its sensitivity to Reynolds number across different gap configurations.

3.4. Evolution Characteristics of Vortex Structure

Figure 8 illustrates the evolution of the instantaneous vorticity field at Re = 3300 for various gap ratios. Regions where the vorticity magnitude exceeds a specified threshold delineate the coherent vortex structures [36]. The results reveal that the boundary layer along the lower wall exerts a strong suppressive influence on the vortex shedding process behind the cylinder. Under small gap ratio conditions, the wake vortex evolution deviates notably from the classical Kármán vortex street pattern. In addition, the near-wall flow exhibits significant changes not only in the distribution of shed wake vortices but also in vortex merging phenomena, both between successive wake vortices and between wake vortices and wall-induced vortices.

Under the gap ratio condition of G/D = 0.1, the flow over the upper surface of the cylinder remains largely unaffected by the presence of the near-wall boundary, resulting in the formation of a distinct positive vorticity shear layer and regular vortex shedding at the downstream end. In contrast, the lower surface is strongly influenced by the boundary layer blockage effect, leading to significant distortion of the negative vorticity shear layer and pronounced suppression of vortex shedding. Most of the vortices on the lower side are entrained into the recirculation zone instead of being convected downstream, while only a small portion develops in the streamwise direction. As a result, the wake structure deviates markedly from the canonical Kármán vortex street pattern, which typically features a periodic, alternate shedding of oppositely signed vortices into the downstream flow. At t = 0 s, vortices A and B form at the ends of the upper and lower shear layers, respectively. At t = 0.16 s, both vortices detach into the recirculation region and subsequently dissipate. More importantly, the separation of the lower shear layer, in conjunction with the blockage effect of the wall boundary layer, induces the formation of a secondary vortex with opposite rotation to that of the lower wake vortices. This secondary vortex migrates upward, merges with vortices from the upper shear layer, and is then transported downstream. It is noteworthy that although the wake does not exhibit a typical alternating vortex shedding pattern, the upper shear layer maintains a distinct periodic shedding behavior. This unique flow phenomenon highlights the complex interactions between wall-induced effects and the free shear layer under the G/D = 0.1 condition.

At G/D = 0.3, the experiment reveals a marked transition in flow behavior. The wall-induced blockage effect on the lower shear layer is significantly reduced, leading to increased strength of the lower shear layer and the elimination of strong curling behavior. As a result, the vortex shedding path shifts from the recirculation zone to the downstream region of the main flow. As shown in Figure 8b1,b2, the negative-vorticity vortex A, shed from the lower shear layer, forms a coupled structure with the positive-vorticity vortex B generated from the upper shear layer. These vortices are convected downstream together, but both experience a gradual reduction in intensity, with the negative-vorticity vortex decaying more rapidly.

At G/D = 0.5, the experimental observations indicate a further intensification of the gap flow, accompanied by an increase in the strength of both the lower wake vortices and the secondary vortices. At the same time, the deflection angles of the cylinder’s lower shear layer and the wall-induced shear layer are reduced. Although the lower wake vortices and secondary vortices still exhibit some degree of deflection during shedding, the deviation is no longer sufficient to enable coupling with the upper wake vortices. Instead, a distinct interaction system forms between the lower wake vortices and the secondary vortices, which enhances energy dissipation. As shown in Figure 8c1,c2, vortex pairs A–B and C–D evolve downstream at a shallow angle, reflecting the characteristics of this newly established vortex interaction regime.

When the gap ratio increases to G/D = 0.7, the deflection of the wall-induced shear layer becomes negligible, and the vortex shedding process returns to a typical alternating pattern. However, due to the proximity between the lower shear layer and the wall boundary layer, approximately 40% of the lower wake vortices remain accompanied by secondary vortices during shedding, and are convected downstream as combined vortex structures. With a further increase in the gap ratio to G/D = 1.0, both the strength and size of the secondary vortices decrease substantially, and these vortices become completely detached from the wake system. At this stage, vortex shedding from the upper and lower shear layers becomes fully symmetric and alternates in a classical fashion. The resulting flow field closely resembles that of canonical flow past an isolated cylinder, indicating a near-complete suppression of wall-induced effects.

Figure 9 and Figure 10 systematically examine the evolution of vortex structures at G/D = 0.5 under varying Reynolds numbers. The experimental results show that at Re = 1100, the cylinder’s lower shear layer exhibits a pronounced upward deflection of approximately 40 degrees, leading to boundary layer separation on the flat wall and its subsequent movement toward the upper shear layer. The secondary vortices shed from the end of the wall shear layer then merge with the upper wake vortices. As the Reynolds number increases to 5500, the separation between the upper and lower shear layers becomes more compact, the vortex shedding frequency increases, and the size of shed vortices from both layers increases.

It is also noteworthy that the vortex evolution process in the wake region demonstrates distinctive vortex dynamics. First, as the shed vortices are convected downstream, they undergo multiple interactions, including the merging of upper wake vortices with secondary vortices and the amalgamation of adjacent, independent vortices. Second, under the influence of the mainstream shear flow, the vortex cores are significantly stretched and deformed. Simultaneously, the outer shear layers become unstable due to intensified velocity gradients, leading to fragmentation of coherent vortex structures and the formation of small-scale, disorganized vortices. Ultimately, these secondary vortex structures undergo progressive vorticity attenuation due to viscous dissipation and turbulent mixing, resulting in complete kinetic energy loss within the flow field.

4. Conclusions

In this study, high-resolution Particle Image Velocimetry (PIV) was employed to systematically investigate the flow characteristics around a near-wall circular cylinder at five gap ratios (G/D = 0.1–1.0) across a wide range of Reynolds numbers (Re = 1100–5500). The principal findings are summarized as follows:

(1)

Under the condition of G/D = 0.1, the mean spanwise vorticity of the gap flow is significantly smaller compared to that of the upper shear layer, particularly near the end of the gap curl, where the mean spanwise vorticity is nearly zero. In this state, the gap flow exhibits pronounced curling characteristics and penetrates deeply into the recirculation zone. The flow field structure demonstrates a strong Reynolds number independence. As the gap ratio increases to G/D ≥ 0.3, both the size of the recirculation region and the deflection angle of the gap flow decrease monotonically with increasing Reynolds number and gap ratio. Simultaneously, higher Reynolds numbers result in shorter wall separation bubbles and more compact development of the upper and lower shear layers. The wall-associated shear layer also weakens progressively and shifts downstream.

(2)

The dynamic behavior of the gap flow demonstrates a strong coupled dependence on Reynolds number and gap ratio. At Re = 1100 and 2200, within the range 0.3 ≤ G/D ≤ 0.5, the gap flow crosses the cylinder centerline, and the streamwise velocity along the centerline exhibits a non-monotonic trend—decreasing, increasing, and then decreasing again. However, for Re ≥ 3300, the intensified gap flow no longer crosses the centerline, and the velocity profile transitions to a decreasing-then-increasing pattern. Notably, at G/D = 0.7 across all Reynolds numbers, the streamwise velocity gradually recovers to the free-stream value downstream of the recirculation region, indicating a transition toward a semi-confined flow regime.

(3)

The vortex evolution process reveals a three-stage transition with increasing gap ratio:

(i)

At G/D = 0.1, the lower wake vortex is completely confined within the recirculation zone. Both the lower wake vortex and secondary vortices exhibit a significant weakening in vorticity compared to the upper wake vortex, with smaller vorticity dissipating more rapidly during the evolution process.

(ii)

For 0.3 ≤ G/D ≤ 0.5, the vorticity of the lower wake vortex is significantly enhanced compared to that at G/D = 0.1. Moreover, the secondary vortices shed in this range form a coupled system with the lower wake vortex, which collectively influences the evolution of the upper wake vortex.

(iii)

When G/D ≥ 0.7, the secondary vortices gradually detach from the wake vortex system, and the wake recovers a symmetric shedding pattern, approaching that of an isolated cylinder flow.

These results provide valuable theoretical insights into the complex flow mechanisms associated with near-wall circular cylinders and establish a foundation for the development of active flow control strategies in confined marine and engineering applications.