Finite-height Square Research Articles

On the flow dynamics around a surface-mounted cube and boundary layer effects

Motivated by contradicting or insufficient information regarding the large-scale flow dynamics around surface-mounted finite-height square prisms of small aspect ratio, the present study investigates the dominant vortex shedding and low-frequency dynamics around a surface-mounted cube. These flow modes were obtained from the spectral proper orthogonal decomposition of large-eddy simulation results, at a Reynolds number of $\textit {Re}=1\times 10^4$ and two different types of boundary layer: a thin and laminar boundary layer with thickness $\delta /D=0.2$ and a thick and turbulent boundary layer with $\delta /D=0.8$ . The main antisymmetric mode pair revealed a new flow pattern with the alternate shedding of streamwise flow structures, indicating a transition from the half-loops of taller prisms to only streamwise strands (i.e. no vertical core) for smaller aspect ratio. The formation process of the streamwise structures is due to a reorientation of the vorticity of the arch vortex in the streamwise direction characteristic of the shed structures. The low-frequency drift mode affected the length of the recirculation region, the strength of vortex shedding, and the near-wall flow field and pressure distribution on the cube's faces, leading to low-frequency variations in the fluctuating drag and normal force coefficients. These large-scale flow dynamics were similar for both boundary layers, but minor differences were identified, related mostly to the occurrence of flow attachment and the formation of a headband vortex for the thicker boundary layer.

Control of the flow around a finite-height square cylinder with slot blowing near its free-end side edges

This paper describes an active control technique that uses symmetric downward slot blowing from the free-end side edges of a finite-height square cylinder to suppress the aerodynamic forces. The width (d) of the tested cylinder is 40 mm and the aspect ratio H/d is 5. The Reynolds number based on the oncoming flow velocity U∞ and d is 2.67 × 104. The tested blowing ratio Cb (=Ub/U∞, where Ub is the blowing velocity at the slot exit) ranges from 0 to 4, and two typical included angles of θ = 5° and 45° are considered. The experimental results indicate that free-end slot blowing effectively suppresses the aerodynamic forces on the cylinder. The maximum reduction in the aerodynamic forces occurs with θ = 5° and Cb = 3.0, whereupon the mean drag, fluctuating drag, and fluctuating lateral force are reduced by 6.80%, 48.52%, and 69.38%, respectively. Furthermore, slot blowing control introduces a strong downward entrainment into the near wake of the cylinder, weakening its spanwise vortex shedding. This successfully converts the alternating spanwise vortex shedding into symmetric shedding, especially near the free end from which the downward blowing issues.

Revisiting the surface-mounted cube: An updated perspective of the near wake and near-wall flow field

The flow around a surface-mounted cube has been investigated for decades, yet the fundamentals of the mean flow have not been updated to reflect the latest advances regarding the flow around surface-mounted finite-height square prisms in general. One of the main gaps is the flow field very near the cube walls, especially the sides, and its relationship to the near wake. To investigate these features, large-eddy simulations of the flow around a surface-mounted cube were carried out at a Reynolds number Re =1×104. Two boundary layers were considered: a thin and laminar boundary layer and a thick and turbulent one, to provide an overview of the flow around the cube for contrasting boundary layers. The major flow structures in the mean wake were the horseshoe vortex, the arch vortex and the dipole structures, with other regions of vorticity also present. The time-averaged flow fields presented similar flow features for both boundary layers, but the thicker and turbulent one caused the horseshoe vortex to be located closer to the cube, the wake to become narrower and shorter, the coherent structures and downwash to weaken, the pressure to decrease around the sides and top of the cube, the drag force coefficient to decrease, the normal force coefficient to increase, and the trailing edge vortices to weaken. Intermittent flow reattachment on the top and side faces of the cube, as well as corner vortices, were found for both boundary layers, while the side and free end vortices were found exclusively with the thicker boundary layer, yielding a headband vortex. The three-dimensional flow structures and features were related to the near-wall flow field on the cube and ground plane surfaces, giving a complete and updated description of the mean flow characteristics.

Mean wake and aerodynamic forces for surface-mounted finite-height square prisms of very small aspect ratio

The mean flow field, aerodynamic forces, bending moment and Strouhal number (St) were investigated for isolated surface-mounted finite-height square prisms of very small aspect ratio (AR). The Reynolds number was Re =7.5×104 for the velocity measurements and 9×104 for the force, bending moment and St measurements. Prisms with AR = 0.5, 0.7 and 1 were considered, under two different boundary layer thicknesses of δ/D=0.7–0.8 (thin) and δ/D=1.3 (thick). For both boundary layers, the mean drag force coefficient showed a sharper increase with AR compared with taller prisms, and the mean normal force coefficient increased smoothly, with a lower magnitude than pressure-based normal force coefficients. An approximately constant point of action of the drag force was found for AR < 1. While the thick boundary layer caused the spectral peaks to weaken and St to decrease, some periodicity was still found for all AR. These features were connected to the changes in the mean wake of the prisms with AR and δ/D. A smaller AR and larger δ/D had similar effects, causing the wake to shorten, the probability and type of reattachment of the flow on the free end to change, and the mean wake structure to transition from a streamwise wake vorticity pattern to an inner vorticity pattern. The prism with AR = 1 showed a dipole wake structure similar to that of taller prisms, while the unique wake topology of prisms with AR < 1 was found to be responsible for the different force and St trends identified in this range of AR.

Simulation study on flow behavior around a wall-mounted finite height square cylinder with corner chamfer

Current work aims to investigate the effect of applying corner chamfer on the wake of the square cylinder and understand the effect that various chamfer sizes have on the flow characteristics. The study also involves the understanding of the weakening of the wake, thus, possible improvement in structural integrity. The result of applying various corner chamfer on flow, mainly the plate cylinder juncture region, the tip region, and the wake region around the wall-mounted finite height square cylinder are investigated. The Aspect Ratio (AR) is kept at 4. The investigation employed the Improved Delayed Detached Eddy Simulation (IDDES) turbulence model in Fluent. Flow characteristics for the square cylinder without chamfer were validated against wind tunnel experimental results at a Reynolds number of 12,000 involving a similar geometry. Three cylinders with increasing corner chamfer were studied, and their results, as well as a comparison with the simple square cylinder, are discussed in this paper. The results in the wake region for various vertical and horizontal planes of the bluff body were analyzed. By applying a corner chamfer, a decrease in the wake was observed. By increasing the chamfer, improvement in the flow was observed, i.e., a reduction in drag coefficient, a smaller horseshoe vortex zone, wake region behind the cylinder was reduced, Strouhal number increased, and vortex structure diminish quicker.

The mean pressure distribution on the free end of a square prism

In this experimental study, the mean pressure distribution was measured on the free end of a surface-mounted finite-height square prism for different aspect ratios, incidence angles, and boundary layer thicknesses. The Reynolds number based on the width of the prism was kept constant at Re = 6.5 × 104, the aspect ratio of the prism was changed from AR = 1 to 11, and the incidence angle was varied in small increments from α = 0° to 45°. The thickness of the boundary layer on the ground plane relative to the prism width was either δ/D = 0.8 or δ/D = 2.6, representing a thin or thick boundary layer. When the prism was oriented at α = 0°, distinct mean pressure distributions were observed for prisms nearly or completely immersed in the boundary layer, and also for the very slender high-aspect ratio prisms. The mean normal force coefficient steadily increased with the aspect ratio but its value decreased in the presence of the thicker boundary layer. When the prism was oriented at α = 45°, strong pressure gradients were encountered near the leading edges for prisms nearly or completely immersed in the boundary layer, and the conical vortex angles increased with aspect ratio. For intermediate aspect ratios, these pressure gradients weakened and the vortex angles became insensitive to AR. When the incidence angle was between 0° and 45°, the asymmetric mean pressure distribution meant that the conical vortices were located at different angles. The position of the conical vortex located more centrally above the free end was more sensitive to changes in aspect ratio. The influence of the boundary layer on the vortex angles was more pronounced for smaller aspect ratios. In addition, the behaviour of the normal force coefficient with incidence became more complex for higher aspect ratios.

Effect of inclined angle on a wall-mounted finite-height square cylinder with a passive vertical suction

Drilling a vertical cavity from the bottom to the free-end surface has been a passive method of controlling wake flow around a wall-mounted square cylinder. The mean flow field around a wall-mounted finite-height square cylinder with a vertical rectangular cavity was studied experimentally in a water tunnel to explore the effects of inclined angle α. Measurements were conducted using an acoustic Doppler velocimeter at the Reynolds number of Reh = 17,525, in which the incidence angles of the cylinder were α = 0, 10°, 30°, and 45°. Results depict the presence of a recirculation zone in the cavity and a near-wake zone. As α increases from 0 to 10°, the mean wake behind the cylinder shifts in the opposite position, and a single peak is observed. When α changes from 10° to 45°, the mean wake regains its symmetry, and two peaks are observed at the wake. Self-similarity in terms of the streamwise velocities and Reynolds shear stress can be achieved by properly selecting the velocity and length scales irrespective of the angle of incidence. For the wake flow with a higher value of α, the length of the mean recirculation zone, momentum exchange, and turbulence kinetic energy increase, whereas the mean and variance values of the vortex shedding frequency reach a smaller one. In this study, the cavity flow and wake flow are also observed in terms of velocity distribution, turbulent kinetic energy budget, and turbulent events.

Mean and Dynamic Aspects of the Wakes of a Surface-Mounted Cube and Block

Abstract The flow downstream of surface-mounted finite height square prisms with aspect ratio AR = 1 (cube) and 0.5 (block) was investigated experimentally in a low-speed wind tunnel, to determine the overall structure and dynamic behavior of the wake and the source of the streamwise vorticity. The Reynolds number based on the prisms' width D was Re =7.5×104 and the boundary layer thickness at the location of the prisms was δ/D=0.73. A vortex shedding frequency was found in the wake of the cube, but no periodicity was found in the wake of the block. The mean wake of the cube showed features of prisms below the critical AR, but the wake of the block had a distinct behavior due to the dominant shear flow from the boundary layer. The shear changed the downwash and, consequently, the streamwise vorticity distribution in the wake, in addition to reducing the magnitude of the Reynolds stresses. The phase-average analysis for the cube revealed the alternate shedding of inclined structures related to the streamwise vorticity in the upper part of the wake. These vorticity regions were caused by the alternate bending and entrainment of the side flow, caused by the downwash. The periodic component of the total Reynolds stresses was, however, significantly smaller than the turbulence-related stresses. This study showed that the wake had a transitional behavior for the cube, but became fundamentally different for the block when compared with prisms of higher AR.

Wind loading of a finite prism: aspect ratio, incidence and boundary layer thickness effects

A systematic set of low-speed wind tunnel experiments was performed at Re = 6.5x104 and 1.1x105 to study the mean wind loading experienced by surface-mounted finite-height square prisms for different aspect ratios, incidence angles, and boundary layer thicknesses. The aspect ratio of the prism was varied from AR = 1 to 11 in small increments and the incidence angle was changed from α = 0° to 45° in increments of 1°. Two different boundary layer thicknesses were used: a thin boundary layer with δ/D = 0.8 and a thick boundary layer with δ/D = 2.0–2.2. The mean drag and lift coefficients were strong functions of AR, α, and δ/D, while the Strouhal number was mostly influenced by α. The critical incidence angle, at which the prism experiences minimum drag, maximum lift, and highest vortex shedding frequency, increased with AR, converged to a value of αc = 18° ± 2° once AR was sufficiently high, and was relatively insensitive to changes in δ/D. A local maximum value of mean drag coefficient was identified for higher-AR prisms at low α. The overall behaviour of the force coefficients and Strouhal number with AR suggests the possibility of three flow regimes.

Aerodynamic forces and three-dimensional flow structures in the mean wake of a surface-mounted finite-height square prism

Different flow models have been proposed for the flow around surface-mounted finite-height square prisms, but there is still a lack of consensus about the origin and connection of the streamwise tip vortices with the other elements of the wake. This numerical study was performed to address this gap, in addition to clarifying the relationship of the near-wake structures with the far wake and the near-wall flow, which is associated with the fluid forces. A large-eddy simulation approach was adopted to solve the flow around a surface-mounted finite-height square prism with an aspect ratio of AR = 3 and a Reynolds number Re = 500. The mean drag and normal forces and the bending moment for the prism were quantitatively compared in terms of skin-friction and pressure contributions, and related to the near-wall flow. Both three-dimensional visualizations and planar projections of the time-averaged flow field were used to identify, qualitatively, the main structures of the wake, including the horseshoe vortex, corner vortices and regions of high streamwise vorticity in the upper part of the wake. These features showed the same qualitative behavior as reported in high Reynolds number studies. It was found that some regions of high streamwise vorticity magnitude, like the tip vortices, are associated with the three-dimensional bending of the flow, and the tip vortices did not continuously extend to the free end of the prism. The three-dimensional flow analysis, which integrated different observations of the flow field around surface-mounted finite-height square prisms, also revealed that the mean near-wake structure is composed of two sections of different origin and location of dominance.

The effect of incidence angle on the mean wake of surface-mounted finite-height square prisms

The mean wake of a surface-mounted finite-height square prism was studied experimentally in a low-speed wind tunnel to explore the combined effects of incidence angle (α) and aspect ratio (AR). Measurements of the mean wake velocity field were made with a seven-hole pressure probe for finite square prisms of AR=9, 7, 5 and 3, at a Reynolds number of Re=3.7×104, for incidence angles from α=0° to 45°. The relative thickness of the boundary layer on the ground plane, compared to the prism width, was δ/D=1.5. As the incidence angle increases from α=0° to 15°, the mean recirculation zone shortens and the mean wake shifts in the direction opposite to that of the mean lift force. The downwash is also deflected to this side of the wake and the mean streamwise vortex structures in the upper part of the wake become strongly asymmetric. The shortest mean recirculation zone, and the greatest asymmetry in the mean wake, is found at the critical incidence angle of αcritical≈15°. As the incidence angle increases from α=15° to 45°, the mean recirculation zone lengthens and the mean streamwise vortex structures regain their symmetry. These vortices also elongate in the wall-normal direction and become contiguous with the horseshoe vortex trailing arms. The mean wake of the prism of AR=3 has some differences, such as an absence of induced streamwise vorticity near the ground plane, which support its classification as lying below the critical aspect ratio for the present flow conditions.

Influence of aspect ratio on the mean flow field of a surface-mounted finite-height square prism

The flow around surface-mounted, finite-height square prisms at a Reynolds number of Re = 4.2 × 104 was investigated experimentally in a low-speed wind tunnel using particle image velocimetry. The thickness of the boundary layer on the ground plane relative to the width of the prism was δ/D = 1.5. Four prism aspect ratios were tested, AR= 9, 7, 5, and 3, to study how the aspect ratio influences the flow field close to the prism. Upstream of the prism, lowering the aspect ratio from AR= 9 to AR= 3 causes the stagnation point on the upstream face to move closer to the free end, but there is no influence on the location and strength of the horseshoe vortex. Lowering the aspect ratio from AR= 9 to AR = 3 causes the cross-stream vortices in the upper and lower halves of the wake to move downstream and upstream, respectively; the latter vortex is absent for AR = 3, suggesting this prism sits below the critical aspect ratio. Above the free end of the prism, within the region of separated flow, lowering the aspect ratio from AR = 9 to AR = 3 shifts the location of the cross-stream vortex farther downstream. For the prism of AR = 3, reverse flow above the free end is stronger yet more unsteady compared to the more slender prisms, while the streamwise edge vortices are smaller and weaker.

The effect of a splitter plate on the flow around a finite prism

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height square prism was investigated experimentally in a low-speed wind tunnel. Measurements of the mean drag force and vortex shedding frequency were made at Re=7.4×104 for square prisms of aspect ratios AR=9, 7, 5 and 3. Measurements of the mean wake velocity field were made with a seven-hole pressure probe at Re=3.7×104 for square prisms of AR=9 and 5. The relative thickness of the boundary layer on the ground plane was δ/D=1.5–1.6 (where D is the side length of the prism). The splitter plates were mounted vertically from the ground plane on the wake centreline, with a negligible gap between the leading edge of the plate and rear of the prism. The splitter plate heights were always the same as the heights of prisms, while the splitter plate lengths ranged from L/D=1 to 7. Compared to previously published results for an “infinite” square prism, a splitter plate is less effective at drag reduction, but more effective at vortex shedding suppression, when used with a finite-height square prism. Significant reduction in drag was realized only for short prisms (of AR≤5) when long splitter plates (of L/D≥5) were used. In contrast, a splitter plate of length L/D=3 was sufficient to suppress vortex shedding for all aspect ratios tested. Compared to previous results for finite-height circular cylinders, finite-height square prisms typically need longer splitter plates for vortex shedding suppression. The effect of the splitter plate on the mean wake was to narrow the wake width close to the ground plane, stretch and weaken the streamwise vortex structures, and increase the lateral entrainment of ambient fluid towards the wake centreline. The splitter plate has little effect on the mean downwash. Long splitter plates resulted in the formation of additional streamwise vortex structures in the upper part of the wake.

An Experimental Investigation of Aspect Ratio and Incidence Angle Effects for the Flow Around Surface-Mounted Finite-Height Square Prisms

The flow around a surface-mounted finite-height square prism was investigated using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re = 7.3 × 104 for prism aspect ratios of AR = 3, 5, 7, 9, and 11 and incidence angles from α = 0 deg to 45 deg. The thickness of the boundary layer on the ground plane relative to the side length was δ/D = 1.5. Measurements of the vortex shedding frequency were made with a single-component hot-wire probe, and measurements of the mean drag and lift forces were obtained with a force balance. For all aspect ratios and incidence angles, the mean drag coefficient and Strouhal number were lower than those of an infinite prism, while the mean lift coefficient was of nearly similar magnitude. As the aspect ratio was increased from AR = 3 to 11, the force coefficients and Strouhal number slowly approached the infinite-square-prism data. The mean drag coefficient and Strouhal number for the finite prism were less sensitive to changes in incidence angle compared to the infinite square prism. The critical incidence angle, corresponding to minimum mean drag coefficient, minimum (most negative) mean lift coefficient, and maximum Strouhal number, shifted to a higher incidence angle compared to the infinite square prism, with values ranging from αcritical = 15 deg to 18 deg; this shift was greatest for the prisms of higher aspect ratio. The behavior of the force coefficients and Strouhal number for the prism of AR = 3 was distinct from the other prisms (with lower values of mean drag coefficient and mean lift coefficient magnitude, and a different Strouhal number trend), suggesting the critical aspect ratio was between AR = 5 and AR = 3 in these experiments. In the wall-normal direction, the power spectra for AR = 11 and 9 tended to have weaker and/or more broad-banded vortex shedding peaks near the ground plane and near the free end at α = 0 deg and 15 deg. For AR = 7 to 3, well-defined vortex shedding peaks were detected along the entire height of the prisms. For AR = 11 and 9, at α = 30 deg and 45 deg, vortex shedding peaks were absent in the power spectra in the upper part of the wake.