Flow Separation Line Research Articles

Investigation on formation mechanism of cavitation channel vortex in the runner of Francis turbine

Abstract Cavitation channel vortices generally cause flow state more complex in the runner, leading to the work efficiency is reduced and the cavitation erosion on flow components is enhanced. In this paper, simulation of cavitation flow is carried out for a Francis turbine model, and the evolution of vortices in the runner during cavitation development is analyzed under partial load conditions. The results show that cavitation has a great influence on the morphology and distribution of attached vortices between blades, trailing vortices at the outlet edge of the blades, and vortex near the cone in the runner. With the gradual development of cavitation, the invasion effect of vortex rope in draft tube on the runner is enhanced, and the vortex near runner cone is gradually connected as a whole. Under the effect of the downstream reverse pressure gradient in local low-pressure area, the flow separation area gradually expands to the blade and upstream, and more singular points evolve on flow separation lines, which leads to more trailing vortices at the outlet of the blade and cavitation channel vortices are formed in serious cavitation stage.

A large eddy simulation of flow over a circular cylinder with circumferential triangular riblets: Effects of spanwise coverage ratio

Flow over circular cylinders covered with circumferential riblets of triangular shape with spanwise coverage ratios from 0 (bare cylinder) to 1 (fully covered) is investigated by large eddy simulation at three subcritical Reynolds numbers (2000, 3000 and 3900 respectively). The bare cylinder is considered as a reference case and for validation purpose. Detailed flow structures and boundary layer characteristics are described. For the fully covered cylinder, it is found that flows on the two sides of each riblet interact, forming a structure with stronger turbulent fluctuations and leading to a significantly shorter recirculation length compared to the other cases. The turbulent fluctuations are attenuated to various degrees for the partly covered cylinders. Two semicircular-shaped flow zones with distinct spanwise flows are observed around the riblets adjacent to the bare sections. Among the three partly covered cases under consideration (with spanwise coverage ratios of 0.25, 0.5 and 0.75 respectively), the half-covered cylinder has the largest semicircular-shaped flow zones, associated with the lowest turbulence in the flow field. A zigzag flow separation line is observed on all sections covered with riblets. The variations of the flow behaviours result in different characteristics of the hydrodynamic forces acting on the various cylinders. It is revealed that the lift fluctuation is the lowest for the half-covered cylinder and the highest for the fully covered cylinder. An examination of the sectional hydrodynamic forces further reveals that the sectional drag is higher at the riblet tip than that in the valley.

Spanwise-Discontinuous Grooves for Separation Delay and Drag Reduction of Bodies with Vortex Shedding

Suitably shaped grooves, placed transverse to the flow, can delay flow separation over curved surfaces. When grooves are fully extruded in the spanwise direction, they may reduce the drag of boat-tailed bodies with vortex shedding, but with the drawback of increasing the spanwise correlation of the vortex shedding. We investigate herein the effect of spanwise-discontinuous grooves through Large Eddy Simulations. A systematic analysis is carried out on the effect of the number, N, of grooves that are present for N equally long portions of the total spanwise length of the boat-tail. Discontinuous grooves further reduce the drag compared with the full-spanwise-extruded groove. Increasing N produces an improvement of the flow-control-device performance, whose maximum value is reached for N=3, corresponding to a spanwise extension of the groove roughly equal to the body crossflow dimension. Above this value, no further improvements are found. The maximum drag reduction is equal to 25.7% of the drag of the boat-tail without grooves and to 17.7% of the one of the boat-tail with the full-spanwise-extruded groove. The lowest drag value occurs for the least correlated vortex-shedding in the spanwise direction. The reduction in the correlation is mainly related to a flow separation line that is less regular in the spanwise direction.

A study of drag reduction with textile roughness on a cyclist model

Efforts were made to examine the effect of textile roughness for the reduction of aerodynamic drag experienced on a cyclist model. First of all, flow visualization experiments were conducted in a water channel with a 1/5 scale cyclist model to identify the flow separation lines on the contoured surface. Subsequently, based on the information learned, the idea of delaying flow separation on the model surface was implemented by means of sport suits. Seven sport suits featuring different textile materials and local roughness patterns were tested on a full-scale cyclist model in wind tunnel experiments, in addition to a reference case without a sport suit. From the CD data deduced, we identified a critical condition in most of the cases studied, featuring a least drag coefficient occurred at a Reynolds number within the flow speed range studied. For the best case found, the drag coefficient is amounted 7.5% less than that of the reference case at the same Reynolds number. Furthermore, the Cp and Cprms values reduced from the pressure measurements on the cyclist model with the sport suits unveil a trend that the reduction of drag actually infers the retreat of the local flow separation lines toward the rear side of the body accompanied with less severe the flow unsteadiness.

Surface-pressure pattern of separating flows over inclined slender bodies

Surface-pressure measurements and literature review of crossflows over inclined slender bodies at high Reynolds numbers (4.2 × 106 to 17 × 106, based on body length and freestream velocity) show that the constructed pressure maps have a distinct pattern, which relates to large-scale separation. The separation envelope is defined by a pair of primary and secondary surface-bifurcation lines as described by Lee [“Longitudinal development of flow-separation lines on slender bodies in translation,” J. Fluid Mech. 837, 627–639 (2018)]. The present study shows that the separation envelope falls in a “plateau” region in the circumferential distribution of the mean pressure. In the distribution of circumferential pressure gradient, there are two local maxima, where one is located on the windward side of the separation envelope and the other is located on the leeward side. Pattern tracking identifies that the locus of maximum circumferential pressure gradient resembles the locus of separation, but is located further upstream along the slender body.

Effect of Surface Groove Structure on the Aerodynamics of Soccer Balls

Soccer balls have undergone dramatic changes in their surface structure that can affect their aerodynamics. The properties of the soccer ball surface such as the panel shape, panel orientation, seam characteristics, and surface roughness have a significant impact on its aerodynamics and flight trajectory. In this study, we performed wind-tunnel tests to investigate how the introduction of grooves on the surface of a soccer ball affects the flight stability and aerodynamic forces on the ball. Our results show that for soccer balls without grooves, changing the panel orientation of the ball causes a significant change in the drag coefficient. Soccer balls with grooves exhibited a smaller change in air resistance (Cd) in the supercritical region (20 to 30 m/s; 3.0 × 105 ≤ Re ≤ 4.7 × 105), compared to the ungrooved ball where only the panel orientation was changed. Furthermore, at power-shot speeds (25 m/s), the grooved ball exhibited smaller variations in lift force and side force than the ungrooved ball. These results suggest that a long groove structure on the surface of the soccer ball has a significant impact on the air flow around the ball in the supercritical region, and has the effect of keeping the air flow separation line constant.

Experimental study of a pitching and plunging wing

PurposeThe complex flow behavior over an oscillating aerodynamic body, e.g. a helicopter rotor blade, a rotating wind turbine blade or the wing of a maneuvering airplane involves combinations of pitching and plunging motions. As the parameters of the problem (Re, St and phase difference between these two motions) vary, a quasi-steady analysis fails to provide realistic results for the aerodynamic response of the moving body, whereas this study aims to provide reliable experimental data.Design/methodology/approachIn the present study, a pitching and plunging mechanism was designed and built in a subsonic closed-circuit wind tunnel as well as a rectangular aluminum wing of a 2:1 aspect-ratio with a NACA64-418 airfoil, used in wind turbine blades. To measure the pressure distribution along the wing chord, a number of fast responding transducers were embedded into the mid span wing surface. Simultaneous pressure measurements were conducted along the wing chord for the Reynolds number of 0.85 × 106 for both steady and unsteady cases (pitching and plunging). A flow visualization technique was used to detect the flow separation line under steady conditions.FindingsElevated pressure fluctuations coincide with the flow separation line having been detected through surface flow visualization and flattened pressure distributions appear downstream of the flow separation line. Closed hysteresis loops of the lift coefficient versus angle of attack were measured for combined pitching and plunging motions.Practical implicationsThe experimental data can be used for improvement of unsteady fluid mechanics problem solvers.Originality/valueIn the present study, a new installation was built allowing the aerodynamic study of oscillating wings performing pitching and plunging motions with prescribed frequencies and phase lags between the two motions. The experimental data can be used for improvement of computational fluid dynamics codes in case that the examined aerodynamic body is oscillating.

Longitudinal development of flow-separation lines on slender bodies in translation

This paper examines flow-separation lines on axisymmetric bodies with tapered tails, where the separating flow takes into account the effect of local body radius $r(x)$, incidence angle $\unicode[STIX]{x1D713}$ and the body-length Reynolds number $\mathit{Re}_{L}$. The flow is interpreted as a transient problem which relates the longitudinal distance $x$ to time $t^{\ast }=x\,\text{tan}(\unicode[STIX]{x1D713})/r(x)$, similar to the approach of Jeans & Holloway (J. Aircraft, vol. 47 (6), 2010, pp. 2177–2183) on scaling separation lines. The windward and leeward sides correspond to the body azimuth angles $\unicode[STIX]{x1D6E9}=0$ and $180^{\circ }$, respectively. From China-clay flow visualisation on axisymmetric bodies and from a literature review of slender-body flows, the present study shows three findings. (i) The time scale $t^{\ast }$ provides a collapse of the separation-line data, $\unicode[STIX]{x1D6E9}$, for incidence angles between $6$ and $35^{\circ }$, where the data fall on a power law $\unicode[STIX]{x1D6E9}\sim (t^{\ast })^{k}$. (ii) The data suggest that the separation rate $k$ is independent of the Reynolds number over the range $2.1\times 10^{6}\leqslant \mathit{Re}_{L}\leqslant 23\times 10^{6}$; for a primary separation $k_{1}\simeq -0.190$, and for a secondary separation $k_{2}\simeq 0.045$. (iii) The power-law curve fits trace the primary and secondary lines to a characteristic start time $t_{s}^{\ast }\simeq 1.5$.

Over-tip leakage flow and loss in a turbine cascade equipped with suction-side partial squealers

Over-tip leakage flow and loss in a turbine cascade equipped with suction-side partial squealer rims have been investigated for the squealer rim height-to-span ratios (hst/s) of 0.94%, 1.88%. 3.75%, and 5.63% in the case of a tip gap height-to-span ratio of h/s=1.36%. The casing wall and tip surface visualizations for hst/s=3.75% show that most of the incoming tip leakage flow tends to accelerate through a convergent (nozzle-like) tip gap flow channel and penetrates into the neighboring blade flow passage even upstream of the mid-chord in the form of a wall jet, whereas the rest of it is entrapped by the suction-side squealer rim, flows backward, and is separated from the tip surface along a backward flow separation line. Therefore, the tip surface can be divided into a separation bubble and a backward flow area by the backward flow separation line. A qualitative tip gap flow model for the suction-side squealer tip is suggested in this study. For the present suction-side squealer tip, the total pressure loss coefficient mass-averaged throughout the present measurement plane decreases consistently with increasing hst/s and is higher than that for the cavity squealer tip or the pressure-side squealer tip regardless of hst/s.

Numerical Simulation of Shock Induced Turbulence in a Nozzle Flow

In the present paper, a study has been conducted to investigate the shock induced turbulent flow fields and shock/turbulent-boundary layer interaction at the nozzle divergent. Experimental photographs and numerical images are used to investigate on laminar flow structures, transition phenomena, flow separation line as well as viscous boundary layer separation, turbulence structure development and shock/turbulent-boundary layer interaction. It is observed that transition from laminar to turbulent flow separation is shown earlier at the nozzle divergent for the weaker shock wave propagation and the fully developed turbulence is appeared with unsteady flow fluctuations at the end of the nozzle divergent. It is found that the pressure downstream of the separation point showed an unsteady behavior with strong oscillations, and finally jumped to values quite above the ambient pressure. By solving the 2D Navier–Stokes equations with k–e turbulence model, all turbulent parameters are determined at the end of the nozzle divergent and it is observed that turbulence intensities are almost uniform at the end of the nozzle divergent where slight decay phenomena are appeared along the downstream direction. The skewness of the velocity fluctuations indicates that the present flow appears to be isotropic at the end of the nozzle divergent.

Estimation of roughness lengths and flow separation over compound bedforms in a natural-tidal inlet

The hydraulic effect of asymmetric compound bedforms on tidal currents was assessed from field measurements of flow velocity in the Knudedyb tidal inlet, Denmark. Large asymmetric bedforms with smaller superimposed ones are a common feature of sandy shallow water environments and are known to act as hydraulic roughness elements in dependence with flow direction. The presence of a flow separation zone on the bedform lee was estimated through analysis of the measured velocity directions and the calculation of the flow separation line. The Law of the Wall was used to calculate roughness lengths and shear velocities from log–linear segments sought on transect-averaged and single-location velocity profiles. During the ebb tide a permanent flow separation zone was established over the steep (10–20°) lee sides of the ebb-oriented primary bedforms, which generated a consequent drag on the flow. During the flood, no flow separation was induced by the gentle (2°) lee side of the primary bedforms except over the steepest (10°) part of the lee side where a small separation zone was sometimes observed. As a result, hydraulic roughness was only due to the superimposed bedforms. The parameterized flow separation line was found to underestimate the length of the flow separation zone of the primary bedforms. A better estimation of the presence and shape of the flow separation zone over complex bedforms in a tidal environment still needs to be determined; in particular the relationship between flow separation zone and bedform geometry (asymmetry, relative height or slope of the lee side) is unclear. This would improve the prediction of complex bedform roughness in tidal flows.

An Initial Investigation of Adjoint‐Based Unstructured Grid Adaptation for Vortical Flow Simulations

A computational fluid dynamics (CFDs) method utilizing unstructured grid technology has been employed to compute vortical flow around a 65° delta wing with sharp leading edge, which is specially known as the geometry of the second international vortex flow experiment (VFE‐2). In VFE‐2, 65° delta wings with different leading edges had been broadly investigated by experiments, which resulted in a special database for CFDs codes validation. The emphasis of this paper is to investigate the effectiveness of an adjoint‐base grid adaptation method for unstructured grid in capturing concentrated vortices generated at sharp edges or flow separation lines of lifting surfaces flying at high angles of attack. Earlier experiences in vortical flow simulations had indicated that the vortex behavior is highly dependent on the local grid resolution both on body surface and space. The adjoint‐based adaptation method used here is hoped to save grid points with a reasonable grid resolution for vortical flow simulations. The basic idea is to construct a new adaptive sensor in a grid adaptation process with the intent to tell where the elements should be smaller or larger by introducing an adjoint formulation to relate the estimated functional error to local residual errors of both the primal and adjoint solutions.

Flow-Separation Lines on Axisymmetric Bodies with Tapered Tails

a = local body radius amax = maximum body radius a = dimensionless body radius, a=amax jCfj = skin-friction magnitude, j wj=q Cpc = crossflow pressure coefficient, p p1 =qsin H = Heaviside unit step function l = body length p = pressure q = freestream dynamic pressure, U =2 Re = Reynolds number based on body length, Ul = t = time t = dimensionless time, tv =a U = freestream velocity magnitude u, v = longitudinal and lateral freestream velocity components = angle of incidence = angular position of separation point measured from the windward side o = initial angle of separation 1 = equilibrium angle of separation = normalized separation point, 1 = o 1 = longitudinal distance aft from the nose = dynamic viscosity = fluid density

Electric discharge control of flow separation on oblique airfoil

The possibility of controlling flow separation on an oblique airfoil using dielectric-barrier discharge has been experimentally studied. The experiments were performed at subsonic flow velocities in a broad range of the angle of attack. The results of measurements of the velocity and surface pressure fields and an analysis of the flow patterns show that the application of electric discharge allows the interval of the angles of attack for separation-free flow past the airfoil to be significantly increased. Various discharge regimes have been studied, including those with continuous activation by single voltage pulses with a frequency of 0.5–5 kHz and by pulse trains at a repetition rate of 1–100 Hz. The efficiency of the flow separation control has been studied as dependent on the electrical parameters, frequency characteristics, and position of the discharge relative to the flow separation line.

Effects of wavelength and amplitude of a wavy cylinder in cross-flow at low Reynolds numbers

Three-dimensional numerical simulations of laminar flow around a circular cylinder with sinusoidal variation of cross-section along the spanwise direction, named ‘wavy cylinder’, are performed. A series of wavy cylinders with different combinations of dimensionless wavelength (λ/Dm) and wave amplitude (a/Dm) are studied in detail at a Reynolds number of Re = U∞Dm/ν = 100, where U∞ is the free-stream velocity and Dm is the mean diameter of a wavy cylinder. The results of variation of mean drag coefficient and root mean square (r.m.s.) lift coefficient with dimensionless wavelength show that significant reduction of mean and fluctuating force coefficients occurs at optimal dimensionless wavelengths λ/Dm of around 2.5 and 6 respectively for the different amplitudes studied. Based on the variation of flow structures and force characteristics, the dimensionless wavelength from λ/Dm = 1 to λ/Dm = 10 is classified into three wavelength regimes corresponding to three types of wake structures. The wake structures at the near wake of different wavy cylinders are captured. For all wavy cylinders, the flow separation line varies along the spanwise direction. This leads to the development of a three-dimensional free shear layer with periodic repetition along the spanwise direction. The three-dimensional free shear layer of the wavy cylinder is larger and more stable than that of the circular cylinder, and in some cases the free shear layer even does not roll up into a mature vortex street behind the cylinder. As a result, the mean drag coefficients of some of the typical wavy cylinders are less than that of a corresponding circular cylinder with a maximum drag coefficient reduction up to 18%. The r.m.s. lift coefficients are greatly reduced to practically zero at optimal wavelengths. In the laminar flow regime (60 ≤ Re ≤ 150), the values of optimal wavelength are Reynolds number dependent.

Turbulent wake of an inclined cylinder with water running

This paper presents the results of an experimental study of fluid dynamics around an inclined circular cylinder with and without water running over its surface, covering water rivulet formation, fluid forces on the cylinder, near wake and their interrelationships. The cylinder inclination angle (α) with respect to incident flow was between 55° and 80°. It has been found that water running over the cylinder surface may behave quite differently, depending on the Reynolds number (Re), and subsequently impact greatly upon the fluid dynamics around the cylinder. As such, five flow categories are classified. CategoryA: one water rivulet was observed, irrespective of α, at the leading stagnation point at a smallRe. CategoryB: the rivulet splits into two, symmetrically arranged about the leading stagnation line, onceReexceeds a critical value that depends on α. The two rivulets may further switch back to one, and vice versa. CategoryC: two symmetrical straight rivulets occur. CategoryD: the two rivulets shift towards the flow separation line with increasingReand oscillate circumferentially. The oscillation reaches significant amplitude when the rivulets occur at about 70° from the leading stagnation point. This increased amplitude is coupled with a rapid climb in the mean and fluctuating drag and lift, by a factor of near 5 for the fluctuating lift at α = 80°. Meanwhile, the flow structure exhibits a marked variation. For example, Strouhal number and vortex formation length decrease, along with an increase in spanwise vorticity concentration, velocity deficit, and coherence between vortex shedding and fluctuating lift. All these observations point to the occurrence of a ‘lock-in’ phenomenon, i.e. the rivulet oscillation synchronizing with flow separation. A rivulet–vortex-induced instability is proposed to be responsible for the well reported rain–wind-induced vibration associated with the stay cables of cable-stayed bridges. CategoryE: the two rivulets shift further downstream just beyond the separation line; the shear layers behind the rivulets become highly turbulent, resulting in weakened vortex shedding, flow fluctuating velocities and fluctuating fluid forces. Based on the equilibrium of water rivulet weight, aerodynamic pressure and friction force between fluid and surface, an analysis is developed to predict the rivulet position on the cylinder, which agrees well with measurements.

Unsteady flow field in a square tube T-junction

This work constitutes an extension of two previous experimental studies, examining the flow field in a square tube T-junction with a time-dependent periodic inlet flow rate (zero to a maximum value) and equal branch flow rates. Based on numerical predictions, more details of the flow field are revealed, not being easily detectable by the experiment. Emphasis is given on the recirculation regions examining the velocity, pressure, and wall shear stress distributions as well as the limiting streamlines as a function of time. During acceleration an adverse pressure gradient builds up at the junction due to the streamlines curvature, causing flow separation before flow peak, which initiates at the corners of the tube cross section. Flow separation and reattachment lines, determined by the limiting streamline topology, move apart during deceleration. Streamwise cross-flow vortices appear in both branches, being much stronger in the 90° branch. The characteristics of the latter vortices, namely their circulation, swirl ratio, velocity distribution, as well as the process of their birth at the beginning of each cycle are examined in detail. Wall shear stress distributions exhibit maximum values at the entrance of the 90° branch, taking values proportional to the inlet time-dependent flow rate. Finally, comparisons with steady inlet conditions showed that in the unsteady case the flow can sustain much higher adverse pressure gradients before separating.

Local heat transfer around a wall-mounted cube at 45° to flow in a turbulent boundary layer

The flow and local heat transfer around a wall-mounted cube oriented 45° to the flow is investigated experimentally in the range of Reynolds number 4.2 × 10 3–3.3 × 10 4 based on the cube height. The distribution of local heat transfer on the cube and its base wall are examined, and it is clarified that the heat transfer distribution under the angled condition differs markedly to that for cube oriented perpendicular to the flow, particularly on the top face of the cube. The surface pressure distribution is also investigated, revealing a well-formed pair of leading-edge vortices extending from the front corner of the top face downstream along both front edges for Re>(1−2)×10 4. Regions of high heat transfer and low pressure are formed along the flow reattachment and separation lines caused by these vortices. In particular, near the front corner of the top face, pressure suction and heat transfer enhancement are pronounced. The average heat transfer on the top face is enhanced at Re>(1−2)×10 4 over that of a cube aligned perpendicular to the flow.

A vorticity dynamics theory of three-dimensional flow separation

A theory of three-dimensional incompressible flow separation is presented in terms of the on-wall signatures of the flow. Some long-standing controversial issues are revisited and answers given, such as the inconsistency of the separation criteria based on the topological theory and “open separation,” and whether a separation line is an asymptote or envelope of neighboring skin-friction lines. General criteria for identifying an “open” or “closed” flow separation zone and separation line (including the initial point of the latter), steady and unsteady, are obtained, which apply to a generic smooth curved wall at any Reynolds numbers. The criteria are found to be most clearly given in terms of on-wall signatures of vorticity dynamics. These are then specified to steady boundary layer separation at large Reynolds numbers. A scale analysis under mild assumptions leads to a three-dimensional triple-deck structure near a generic boundary layer separation line. Criteria are presented for “separation watch,” which tells that a boundary-layer may soon break away, and for “separation warning,” which identifies the vorticity characteristics in an already formed boundary-layer separation zone and along a boundary-layer separation line. Flow behavior and its dependence on outer flow conditions are examined qualitatively. A numerical example is given which confirms the predictions of the theory.

The Effects of the Island of Hawaii on Offshore Rainband Evolution

The diurnal cycle of airflow on the island of Hawaii and the structure of the low-level flow separation line between the island-induced offshore flow and incoming trade winds are reasonably well understood. This study examines the formation and organization of nocturnal and early morning offshore Hawaiian rainbands, the flow patterns associated with these rainbands, and their relationship to the flow separation line. This investigation uses the complete radar and aircraft dataset from the 1990 Hawaiian Rainband Project. The formation and evolution of nocturnal and early morning rainfall on the windward side of the island were found to be related to four major factors: (a) the existence or absence of trade wind cloud patches arriving from the northeast Pacific, (b) the effect of island blocking on the trade wind flow as it approaches the island, (c) the low-level convergence and thermal and moisture stratification near the flow separation line, and (d) the position of the flow separation line, controlled by both the Froude number and diabatic processes (nocturnal radiative cooling and evaporative cooling) occurring over the island. If trade wind cloud patches are absent over the ocean upstream of the island, rainbands normally will not form upstream of the flow separation line. Under normal Froude number conditions, if the ratio of the low-level trade wind speed to the Brunt–Väisälä frequency, U/N, is greater than the height of the level of free convection, rainbands will form offshore over the flow separation line. Otherwise, rainbands will not form at this location. When the Froude number is elevated (typically, strong trade wind cases) rainbands will form over the windward shore independent of this ratio. If trade wind cloud patches are present, which is the typical case, light rain normally falls far from the island. These rain regions are enhanced by the weak convergence associated with island blocking and are organized into shore-parallel linear features by the deformation flow induced by the island. The enhancement generally occurs about 35–50 km from the island. Rainbands undergo a second enhancement over the flow separation line. Rainbands will also form over the flow separation line if U/N is greater than the level of free convection.