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Horseshoe Vortex Formation Around a Cylinder
Abstract
An experimental investigation was conducted to characterize a symmetrical horseshoe vortex system in front of and a around a single large-diameter right cylinder centered between the sidewalls of a wind tunnel. Surface flow visualization anad surface static pressure measurements as well as extensive mean velocity and pressure measurements in and around the vortex system were acquired. The results lend new insight into the formation and development of the vortex system. Contrary to what has been assumed previously, a strong vortex was not identified in the streamwise plane of symmetry, but started a significant angular distance away from it. Rather than the multiple vortex systems reported by others, only a single primary vortex and saddle point were found. The scale of the separation process at the saddle point was much smaller than the scale of the approaching bundary layer thickness. Results of the present study not only shed light on such phenomena as the nonsymmetrical endwall flow in axial turbomachinery but can also be used as a test case for three-dimensional computational fluid mechanics computer codes.
... The flow behaviour around this type of foundation has been experimented with at different Reynolds numbers in previous studies, like [11][12][13]. Those research works presented a basis for other studies, like [14,15], as well as [16,17], who investigated the production of a horseshoe vortex around the structure and near the bottom. The authors of [18] studied the three-dimensional flow in the wake according to the Reynolds number and the generation of the von Kármán vortex streets downstream of the pile. ...
Offshore Wind Farm (OWF) foundations are considered to have a potential impact on the larval dispersion of benthic species. This study focused on OWFs’ impacts on larval dispersion, considering factors such as the foundation type, flow velocity, flow direction, and release type using numerical modelling. At the scale of monopile and gravity-based foundations, a combination of two numerical models was used: the Eulerian model (OpenFOAM), solving the 3D Navier–Stokes equations for computing the hydrodynamics, and the Lagrangian model (Ichthyop), solving the advection–diffusion equation for the larval dispersion simulations. The validation model tests were evaluated with experimental data as a first step of the study. Accurate results were achieved, yielding a Turbulent Kinetic Energy (TKE) Root-Mean-Squared Error (RMSE) in the range of 6.82–8.27 ×10−5kg/m·s2 within the refined mesh, with a coefficient of determination (R2) approaching unity. For the second phase, more-realistic simulations were modelled. Those simulations demonstrated turbulent wakes downstream of the foundations and horseshoe vortex formations near the bottom. A larval dispersion was simulated using passive particles’ motion. Vertical flumes in the wake with particles experiencing both upward and downward motions, impacting the fall velocities of the particles, were observed. The influence of gravity-based foundations might lead to a stepping-stone effect with a retention time of up to 9 min, potentially allowing the settlement of competent larvae. In a similar geometry with an angular spring tide velocity, 0.4% of particles were trapped.
... There seems to be some uncertainty over the relationship between these velocity fields and the visualised surface flow. Eckerle and Langston [31] also presented measurements of a turbulent horseshoe vortex. They also reported a single vortex although they report that the vortex was weaker on the symmetry plane than at 15 degrees. ...
p>The flow over a finite-height cylinder of height/diameter ratio of 1, with one end mounted on a ground plane, and the other end free, is studied experimentally and numerically. The context of the work is the investigation of numerical simulation methods for marine hydrodynamics, the aims being to test various simulation methods on a complex three-dimensional separated flow.
The experiments add to the sparse knowledge of this flow, particularly through the particle velocimetry (PIV) measurements which provide more detailed measurements of the flow. The surface flow visualisation images illustrate many features of the flow. Other measurements taken include hot-wire anemometry of the velocity fluctuations in the wake, surface pressure measurements, and force measurements.
A logical progression through different simulation techniques has been followed, starting with a basic Reynolds-Averaged Navier-Stokes (RANS) solution of the flow, using the k- ε model, which gave a poor prediction of the flow. Large-eddy simulations (LES) were performed which give better agreement with the experiments but fail in the modelling of the boundary layer flow on the ground plane. The next step was a detached-eddy (DES) simulation, which is hybrid RANS/LES model. This gives a better prediction of the flow near the wall, while retaining the benefits of an LES simulation away from the wall. These are believed to be the first LES and DES simulations of this flow.
In the context of marine hydrodynamics, which typically involves high Reynolds number flows, the DES methodology appears to offer a promising way forward. Particular attention has been focused on the flow around a typical tanker hullform where the flow in the propeller plane is highly turbulent. It is proposed that DES would be useful in this situation to obtain information about the turbulent flow here.
The synthesis of experiments and simulations has shed new light on some of the key flow features around the truncated cylinder. In particular the horseshoe vortex system has been shown to consist of four vortices although they are not all visible in some experimental measurements. The flow over the free-end which was the subject of some debate has been shown to consist of a single vortex arching over the free-end rising from two swirl patterns on the surface. The wake is seen to consist of chaotic eddies with no dominant shedding frequency.</p
... Fig. 9 shows the wake vortex system generated when the unstable shear layers are detached from the surface of the pier (Breusers et al. 1977). The streamlines observed herein agree well with previous reports (Breusers et al. 1977;Baker 1980;Eckerle and Langston 1987;Roulund et al. 2005;Zhao et al. 2010); the streamlines that made their way around the upper portion of the cylinder are directed downwards, and lee-wake vortices are formed close to the bed surface. ...
... These eddies include well-known tip-leakage (TLV), tip-separation (TSV), induced (IV) and horseshoe (HSV) vortices. The mechanism of HSV formation in a flow around a cylinder or a bluff body bounded by a wall is thoroughly described in the literature (e.g., see Baker, 1980;Eckerle and Langston, 1987;Launay et al., 2017;Gazi and Afzal, 2020). In this paper, these are referred to as corner vortices (CV) which are registered over the suction side and under the pressure side of the hydrofoil and around its axis. ...
The paper deals with an experimental study of tip-clearance cavitation inception and development and its vortical structure coupled with dynamics of the main attached cavity on the suction side of a two-dimensional symmetric hydrofoil equipped with a rotation axis. The gap is formed by the end face of the model and a transparent sidewall of the test channel. The experiments were performed for attack angles of 3° and 9° and 0.4-, 0.8-, 1.75- and 3.75-mm gaps (or 1.8%–17% relative thickness) under various flow conditions on the cavitation number. In order to observe the tip-clearance cavitation occurrence, high-speed imaging was applied. The leakage flow velocity was measured inside the clearance by a modified Particle Tracking Velocimetry technique. It is shown that the mean velocity field of the leaking flow is split into eight distinctive zones where the flow direction and velocity magnitude substantially differ. Positions and extents of these zones are practically independent of the primary flow regime but are affected by the attack angle. Local velocity values of the leakage flow are unexpectedly found to be about 20% higher in the region of a gap cavity than the mean bulk velocity of the incoming flow. Cavitating cores of various vortices manifest themselves in the recorded images, showing that the vortex structure of the leakage flow associated with the tip-clearance cavitation is very complicated and the hydrofoil axis makes it even more complex by inducing new vortices and cavities. For the gaps considered, an increase of its size causes the tip-clearance cavitation to be initiated at higher cavitation numbers, i.e., this is favorable for its occurrence, while the development of the main cavity is hindered. In unsteady flow regimes, dynamics of the primary cavity on the hydrofoil suction side significantly influences the leakage flow direction and the tip-clearance cavitation evolution. Periods of oscillation cycles of the main and gap cavities coincide but the maximum size of the gap cavity is reached with a phase lag relative to the main one. At the small incidence angle, thicker gaps and unsteady flow conditions, extremely transient pressure waves are registered in the clearance, with their velocities ranging from 41 to 81 m/s.
... Fluid motion responsible for the development of secondary flow can be visualized in the form of vortex structures having the shape of a horseshoe placed in front of the protruding body, which are extending into the passage on either sides of the body, called horseshoe vortex. 1 Secondary flow occurs in a variety of practical systems such as turbomachine blade end-wall junction, aircraft wing-body junction, pier of a bridge, in large buildings, hull of ship etc. Horseshoe vortex, passage vortex and corner vortices constitute different forms of secondary flows. The energy of secondary flow is unavailable for useful purpose and in the case of turbomachines it contributes to nearly 30-40% of the total loss. 2 Secondary flow in turbomachine is largely influenced by the type of flow occurring in front of the body and the type of the flow topology in the symmetry plane. ...
The paper presents a numerical investigation on the junction flow occurring at the intersection between a wall and a protruding circular cylinder. Simulations of flow for Reynolds number (Re) in the range [125 - 20000] have been carried out using OpenFOAM, an open source CFD tool. Plots of stream tracers have been used to qualitatively characterize the flow topology as either attachment or separation based on the type of singular points, classified as nodes and saddle points. Quantitative variations of momentum flux have been applied to identify a key mechanism for the transition of topology using the relative momentum strength of the incoming and reverse flow. Effect of a thinner boundary layer has been assessed by (i) imposing a reduced wall shear stress, and (ii) increasing the Reynolds number. Features of a typical unsteady flow, in the transition regime, at Re = 20000 have been predicted using Large Eddy Simulation (LES) with a one-equation eddy viscosity sub-grid scale model. Description of the time evolution of the topology at Re = 20000 has been able to validate the one-equation model in OpenFoam as well as to further validate the key mechanism identified for topology transition.
Facing the demands of the energy transition, gas turbines require continuous development to improve thermal efficiency. Since this can be achieved by further increasing the turbine inlet temperature, advanced cooling techniques are required to protect the highly loaded turbine components. This includes the first nozzle guide vane, which is located just downstream of the combustion chamber. Film cooling, i.e., injecting coolant into the hot-gas path, has been a cornerstone of turbine cooling. While the coolant film is typically supplied through discrete cooling holes, design-related gaps, e.g., the purge slot between the transition duct and the vane platform, can be utilized for injecting coolant. Since the coolant is drawn from the compressor, potentially offsetting thermal efficiency gains from increased turbine inlet temperatures, efficient use of the coolant is critical. In this context, experimental data obtained under engine-like flow conditions, i.e., matching the Mach and Reynolds numbers that are present in the engine, are indispensable for assessing the film cooling performance. Existing research on upstream slot injection has a blind spot, as all high-speed studies were conducted in linear cascades. This approach neglects, by principle, the influence of the radial pressure gradient that naturally occurs in swirling flows and potentially affects coolant propagation. Therefore, a high-speed annular sector cascade has been developed: It allows testing the film cooling performance and aerodynamic effects of coolant flows from various upstream slot configurations, not only at engine-like Mach and Reynolds numbers but also considering the radial pressure gradient. The cascade is equipped with nozzle guide vanes with contoured endwalls representing state-of-the-art turbine design. The results to be expected from the test rig are, therefore, of great relevance. The annular sector cascade is integrated into the existing high-speed turbine test facility at the Institute of Fluid Mechanics and Turbomachinery (University of Kaiserslautern-Landau), which was previously used for testing a linear cascade with the same nozzle guide vane design. It incorporates various measurement techniques such as five-hole probes, pressure-sensitive paint, and infrared thermography to investigate both the thermal and aerodynamic aspects of film cooling. This thesis provides a detailed description of the cascade development, starting from the aerodynamic design up to the structural implementation. It also includes the results of the previous measurements in the linear cascade, as they provided the basis for refining the measurement methods.
Longitudinal vortices have tremendous practical utility for flow control (control by vortices) and in some cases have exhibited tremendous potential for causing harm if uncontrolled (i.e. control of vortices is required). Vortex control has thus far been carried out via multitudinous approaches in an empirical fashion, aided by the essentially inviscid nature of much of longitudinal vortex behaviour. Further refinement and several applications of vortex flow control require knowledge regarding the detailed flow physics of longitudinal vortices such as transition, transitional flow regimes, turbulence structure and modelling, and interaction with shock waves, other vortices and surfaces. This paper summarises vortex control applications and extant techniques for the control of longitudinal vortices produced by bodies, leading edges, tips, and intersections.
The flows past a vertical surface-piercing finite circular cylinder at Re = 2.7 × 10⁵ and Fr = 1.1 are investigated numerically by means of delayed detached-eddy simulation and a geometric volume-of-fluid method based on piecewise-linear interface calculation. Good agreement with experimental data is achieved in various aspects, thereby demonstrating the reliability and accuracy of the present numerical model. On this basis, the characteristics of typical turbulent structures are analyzed thoroughly, as is the spanwise variation of the flow field caused by complex interactions. Because of the effects of the free surface and the free end, the velocity profile, separation angle, vorticity, and turbulent kinematic energy at different spanwise positions exhibit strong three-dimensionality, including the outward-spreading trend at the interface and the fluctuation induced by the upwash flow near the free end. By using the modified Omega–Liutex method Ω̃R, instantaneous and time-averaged primary turbulent structures are identified well with the iso-surfaces of proper thresholds. A complete necklace vortex and a pair of wave-induced vortices are observed below the free surface, while a pair of large-scale arch vortices and two pairs of tip vortices are generated near the free end. The Liutex lines and streamlines are then used to analyze the spatial formations and developments of these structures. Furthermore, by performing spectral analysis at different probes on the cylinder surface and in the wake region, the dominant frequencies for each primary turbulent structure are determined.
Impingement cooling is an effective method for removing heat from a high temperature target surface using sprayed jets oriented to impinge on the surface. Detailed local heat-/mass-transfer distributions are measured using the naphthalene sublimation method. The main parameters of this study are jet hole spacing (
$s/d = 4$
, 8) and crossflow rate. The heat-/mass-transfer coefficients on the target surface are significantly influenced by the crossflow volume and pin-fin structures, and the degree of this influence is affected by different jet hole spacings. The results indicate that a small hole spacing increases the heat/mass transfer by 15%–30% than a large hole spacing for the Reynolds number of 15 000.
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