Upstream Stagnation Point Research Articles

Modified stable methods and effect of artificial diffusion in the numerical study of viscoelastic fluid flow

The trace of the polymer conformation tensor in numerical simulations is bounded by applying a logarithmic transformation to the elastic force in the finitely extensible nonlinear elastic-Peterlin model. This method, called elastic stress logarithmic transformation (EL), is combined with the artificial diffusion (AD) and square-root conformation reformulation (SRCR) methods to establish EL-AD and EL-SRCR methods, respectively. The accuracy and stability of these methods have been investigated by conducting direct numerical simulations of viscoelastic laminar flows around a circular cylinder at a Reynolds number Re = 100, considering a wide range of rheological parameters: the maximum polymer extensibility L = 10 and 100, and the Weissenberg number Wi=1−80. Specifically, effects of artificial diffusion coefficients measured by dimensionless Schmidt number Scc=10−106 on the flow are studied. The results indicate that the EL method can effectively ensure the boundedness and accuracy of the conformation tensor trace, making the EL-AD method a valuable modification of the AD method for simulations with larger L and Wi. The impact of the polymer stress diffusion on the simulation is complex. It can stabilize the simulation by reducing sharp gradients and peak positions of elastic stress. However, inappropriate artificial diffusion coefficients lead to flow artifacts when L is large (L = 100). One consequence is an amplification of the solid-like phenomenon caused by polymer near the upstream stagnation point of the cylinder. Another consequence is an enhanced suppression of vortices by polymer downstream of the cylinder. The challenge in determining a suitable AD coefficient emphasizes the superiority of the EL-SRCR method in terms of stability and accuracy.

Effect of blockage ratio on flow of a viscoelastic wormlike micellar solution past a cylinder in a microchannel.

We present experiments on the flow of a viscoelastic wormlike micellar solution around cylinders (radius R) confined in straight microchannels (width W). Thirteen flow geometries are tested where the blockage ratio is varied over a wide range 0.055 ≤ BR = 2R/W ≤ 0.63. Experiments are performed at negligible Reynolds number, and for Weissenberg numbers Wi = λU/R up to 1000, where U is the average flow speed and λ is the relaxation time of the fluid. Micro-particle image velocimetry is used to characterise the flow state at each BR and Wi. In all of the geometries, a first critical Weissenberg number marks a transition from symmetric flow to an asymmetric but time-steady flow state, while a second higher critical Weissenberg number marks the onset of time-dependent flows. However, we report a clear shift in behaviour over a narrow intermediate range of 0.33 ≲ BR ≲ 0.41. Channels with BR ≤ 0.33 fall in a 'low' BR regime, with instabilities that originate from the downstream stagnation point, while those with BR ≥ 0.44 fall in a 'high' BR regime, with instabilities developing at the upstream stagnation point. Behaviour within the newly-identified intermediate BR regime is complex due to the competing influence of the two stagnation points. We summarise all our results in a flow state diagram covering Wi-BR parameter space, clearly defining the different regimes of blockage ratio for the first time. Our results contribute to the understanding of the complexities of viscoelastic flow in this benchmark geometry.

Viscous free-surface flows past cylinders

Free-surface flows of viscous liquid down an inclined plane and past cylinders of various cross-sections are studied theoretically and experimentally. For relatively wide cylinders, a pond of nearly stationary fluid forms upstream of the cylinder, and a dry region without fluid occurs downstream of it. The flow structure in the pond region depends on the cylinder cross-section and curvature at the upstream stagnation point. The theory is used to deduce simplified asymptotic expressions of the force on the cylinders. The work is relevant to volcanic lava flow deflection by barriers.

Central recirculation zone induced by the DBD plasma actuation

Central recirculation zone (CRZ) is commonly formed in the near field of the injector exit by the vane swirler and used to stabilize the flame. In our experiment, a CRZ induced by the DBD plasma actuation was observed in the low swirl burner configuration for the first time, which clearly demonstrated that the mechanism of the combustion control by the plasma swirler is mainly through the aerodynamic effect. Three dielectric barrier discharge (DBD) actuators are placed in a circular array around the axis to generate ionic wind in the circumferential direction of the injector. Characteristics of the flow field have been measured using Laser Doppler Anemometry. It is found that a central recirculation zone with the shape of an ellipsoid is formed in the non-reacting flow field with the plasma actuation. The position of the upstream stagnation point was determined by the strength of the actuation. Although the CRZ disappears in the reacting flow field as the result of combustion heat release, the influence of the discharge on the flame lift-off height is noticeable. The results demonstrate that swirl enhancement by the plasma swirler is feasible, flexible and effective as a non-intrusive measure for flow control.

Transitions and blowoff of unconfined non-premixed swirling flame

The present experimental work reports the first observations of primary and secondary transitions in the time-averaged flame topology in a non-premixed swirling flame as the geometric swirl number SG (a non-dimensional number used to quantify the intensity of imparted swirl) is varied from a magnitude of zero till flame blowout. First observations of two transition types viz. primary and secondary transitions are reported. The primary transition represents a transformation from yellow straight jet flame (at SG = 0) to lifted flame with blue base and finally to swirling seated (burner attached) yellow flame. Time-averaged streamline plot obtained from 2D PIV in mid-longitudinal plane shows a recirculation zone (RZ) at the immediate vicinity of burner exit. The lifted flame is stabilized along the vortex core of this RZ. Further, when SG ∼ 1.4–3, the first occurrence of vortex breakdown (VB) induced internal recirculation zone (IRZ) is witnessed. The flame now stabilizes at the upstream stagnation point of the VB-IRZ, which is attached to the burner lip. The secondary transition represents a transformation from a swirling seated flame to swirling flame with a conical tailpiece and finally to a highly-swirled near blowout oxidizer-rich flame. This transition is understood to be the result of transition in vortex breakdown modes of the swirling flow field from dual-ring VB bubble to central toroidal recirculation zone (CTRZ). The physics of transition is described on the basis of modified Rossby number (Rom). Finally, when the swirl intensity is very high i.e. SG ∼ 10, the flame blows out due to excessive straining and due to entrainment of large amount of oxidizer due to partial premixing. The present investigation involving changes in flame topology is immensely important because any change in global flame structure causes oscillatory heat release that can couple with dynamic pressure and velocity fluctuations leading to unsteady combustion. In this light, understanding mechanisms of flame stabilization is essential to tackle the problem of thermo-acoustic instability.

Effect of initial vortex core size on the coherent structures in the swirling jet near field

This study investigates the sensitivity to initial conditions of swirling jets undergoing vortex breakdown. Emphasis is placed on the recirculation bubble and on the helical coherent structures that evolve in its periphery. It is proposed that the vortex core size of the incoming swirling jet is the critical parameter that determines the dynamics of these coherent structures. This proposition is assessed with Stereo Particle-Image-Velocimetry (PIV) measurements of the breakdown region of two swirling jet configurations with different vortex core sizes at very similar overall swirl intensities. The swirling jets were generated by radial vanes entering a mixing tube, and the vortex core size was adjusted by using different center-body geometries. The time-averaged flow fields in the breakdown region reveal substantial differences in the jet spreading and the size of the recirculation bubble. Proper Ortogonal Decomposition (POD) was applied to the anti-axisymmetric and axisymmetric velocity fluctuations, to reconstruct the dynamics of the helical instability and the breakdown bubble, respectively. We find that the mode shape of the helical instability is not affected by the vortex core size. The frequency is found to coincide with the vortex core rotation rate, which relates inversely to the core size. The shape and dynamics of the non-periodic breakdown bubble are significantly affected by a change in vortex core size. The POD reveals that the energy content of the dominant non-periodic structure is changed markedly with the vortex core size. The bubble dynamics are further investigated by tracking the upstream stagnation point from the PIV snapshots. It is shown that a larger vortex core promotes smooth fluctuations of the recirculation bubble, while a small initial vortex core is linked to bimodal fluctuations of the recirculation bubble. The conclusions drawn from this study are relevant for fundamental swirling jet studies, as well as for the design of swirl-stabilized combustors, where the investigated coherent structures influence combustion performance.

Finite Volume Study of Flow Separation Phenomena for Steady Flow over a Circular Cylinder at Low Reynolds Number

Flow separation is one of the major distinguishing phenomena between the potential flow and actual fluid flow and circular cylinder has long been considered as the simplest form of bluff body for analyzing flow separation characteristics. Here in this article, different flow separation phenomena such as onset of separation, angular position of separation point, size of separation bubble, drag due to the separation and effect of blockage ratio on position of separation point for steady flow over a smooth circular cylinder are studied numerically using finite volume method of solving the Navier-Stokes equations at very low Reynolds number up to 50. The trends of change of these phenomena with increasing Reynolds number are expressed in form of some empirical equations and compared with results of previously published literatures. The separation starts at Reynolds number as low as 2.0 and the starting-separation angle is 146.557o from the upstream stagnation point and with increasing Reynolds number, the point of separation travels upstream while the separation bubble length increases with increasing Reynolds number. Profound effect of the blockage ratio on the location of separation point is evident in this numerical analysis.

English

Flow separation is one of the major distinguishing phenomena between the theoretical or potential flow and actual fluid flow that introduces several aerodynamic forces and other renowned phenomena. Here in this article, different flow separation phenomena such as onset of separation, angular position of the separation point, size of the separation bubble, drag due to the separation and effect of the blockage ratio on the position of the separation point for steady flow over a smooth circular cylinder are studied numerically using the finite volume method at very low Reynolds number up to 50, and the trends of change of these phenomena with increasing Reynolds number are expressed in the form of some empirical equations and compared with results of previously published literature. The separation starts at Reynolds numbers as low as 2.0 and the starting-separation angle is 146.557° from the upstream stagnation point, while with increasing Reynolds number, the point of separation travels upstream and the separation bubble length increases. The profound effect of the blockage ratio on the location of the separation point is evident in this numerical analysis. Favre-averaged Navier-Stokes equations, a k-ɛ turbulence model and the finite volume method are used for numerical analysis, in which heat transfer or generation, and buoyancy effects are not taken in account.

The dynamics of intrusions into a density-stratified crossflow

Buoyant fluid from a steady source (such as a volcanic eruption) in a stratified environment (such as the atmosphere) rises to an equilibrium level where it spreads as a homogenous intrusion. Here the dynamics of such an intrusion in the presence of a mean ambient flow are examined with semi-analytical models. The intrusive flow is irrotational, and is governed by mass conservation and a form of the Bernoulli equation that relates the intrusion velocity and its thickness. Two types of source are considered—one in which the initial flow from the source is radially symmetric, which is appropriate for weak crosswinds, and another in which it is unidirectional, which also applies to strong crosswinds. In the absence of wind, the outward flow from the radial source is radially uniform and supercritical in the hydraulic sense, with decreasing thickness and increasing speed with distance from the source. In the presence of a crosswind, however, unless the crosswind is very strong a stagnation point exists on the upstream side of the radial source, where the intrusion thickness reaches a maximum. There are two types of flow solution: those where the flow is wholly subcritical, and others where the flow is “transcritical,” being subcritical on the upstream side of the source, and supercritical on the downstream side. It is these transcritical solutions with a supercritical spreading tail that are relevant to flows from isolated sources. For these flows, the upstream stagnation point is quite close to the source, and its position is remarkably insensitive to the strength of the crossflow, relative to that of the source. As a consequence, the position of this stagnation point gives a direct measure of the strength of the source. The external flow is mostly directed horizontally around the intrusion, much as if the latter were a rigid obstacle. The behaviour of the flow in the far-field tail of the intrusion is analysed for both the inviscid case, and for the more realistic one in which the intrusive flow is affected by the drag of its motion relative to that of the environment. The second type of flow, from the unidirectional source, has the same asymptotic behaviour, but the near-field flow changes with increasing distance, from one with maximum thickness on the centerline to one with minimum thickness there. Apart from the fluid dynamical aspects, the results have potential significance for interpretation of geological sediments.

Visualization by discharge illumination technique and modification by plasma actuator of rarefied Mach 2 airflow around a cylinder

The use of plasma actuators for flow control has received considerable attention in recent years. This kind of device seems to be an appropriate means of raising abilities in flow control thanks to total electric control, no moving parts and a fast response time. The experimental work presented here shows, firstly, the non-intrusive character of the visualization of the density field of an airflow around a cylinder obtained using a plasma luminescence technique. Experiments are made in a continuous supersonic wind tunnel. The static pressure in the flow is 8 Pa, the mean free path is about 0.3 mm and the airflow velocity is 510 m s−1. Pressure measurements obtained by means of glass Pitot tube without the visualization discharge are proposed. Measured and simulated pressure profiles are in good agreement in the region near the cylinder. There is good correlation between numerical simulations of the supersonic flow field, analytical model predictions and experimental flow visualizations obtained by a plasma luminescence technique. Consequently, we show that the plasma luminescence technique is non-intrusive. Secondly, the effect of a dc discharge on a supersonic rarefied air flow around a cylinder is studied. An electrode is flush mounted on the cylinder. Stagnation pressure profiles are examined for different electrode positions on the cylinder. A shock wave modification depending on the electrode location is observed. The discharge placed at the upstream stagnation point induces an upstream shift of the bow shock, whereas a modification of the shock wave shape is observed when it is placed at 45° or 90°.

Numerical Simulation of Polymer Injection in Turbulent Flow Past a Circular Cylinder

Using a code developed to compute high Reynolds number viscoelastic flows, polymer injection from the upstream stagnation point of a circular cylinder is modeled at Re=3900. Polymer stresses are represented using the FENE-P constitutive equations. By increasing polymer injection rates within realistic ranges, significant near wake stabilization is observed. Rather than a turbulent detached shear layer giving way to a chaotic primary vortex (as seen in Newtonian flows at high Re), a much more coherent primary vortex is shed, which possesses an increased core pressure as well as a reduced level of turbulent energy.

Experimental and Numerical Modeling of the Bow Shock Interaction with Pulse-Heated Air Bubbles

The influence of various parameters characterizing the single- and double-pulse energy deposition (ED) upstream of a blunt body (distance between the deposition point and the body, amount of the energy and time delay between the pulses) on the topology of the supersonic flow at Mach 2 is studied experimentally and numerically. The obtained pressure-time diagram at the upstream stagnation point of the body as well as some significant topological properties of the bow-shock / heated-bubble interaction, like shock deformation and reflection, as well as the evolution of the heated bubble into the vortex ring downstream, are analyzed as resulting from the shock-decelerated spherical light-gas inhomogeneity. The evolution and topology of the interfering heated bubbles by double-pulse ED show the significance of vorticity generation initiated by blast-waves coming from the neighboring bubbles.

2333 高分子溶液のヘルショウ流れに対する弾性の影響(S42-6 複雑流体の流動現象(6),S42 複雑流体の流動現象)

Effect of elasticity on the potential flow pattern in a Hele-Shaw cell is investigated by using three polymer solutions. While the inertia effect of Newtonian fluid causes the streamline separate from the body at its rear side, the elasticity of polymer solutions generates recirculating bubble around the upstream stagnation point. Regions for the potential flow, the inertia-affected and the elasticity-affected patterns are presented on the Re-We plane.

Effect of elasticity of a polymer solution on the Hele-Shaw flow

In this study, the Hele-Shaw cell is used to examine the effect of fluid elasticity on the flow patterns of two-dimensional potential flow. Flows around a circular cylinder, a square cylinder and flows through abruptly converging-diverging channels (slits) with different throat lengths are tested for water and 0.2 wt % polyacrylamide aqueous solution (PAA-solution). The viscosity of the latter is well modeled by the power law, and the first normal stress difference in the steady shear flow is around ten times higher than the shear stress. Although the PAA-solution is highly shear-thinning, the flows of PAA-solution well reproduce the two-dimensional potential flow patterns that correspond to the respective flow configurations when the flow rate is very low. The potential flow patterns of PAA solution are disturbed in the opposite way of inertia effect observed for water. The streamlines near the upstream stagnation point of cylinders are shifted upstream separating from the cylinder surface when the flow rate is higher, while streamlines in the wake approach closer to the downstream stagnation point. Streamlines of flow through the slit at flow rates higher than the potential flow region show that a pair of vortices is formed upstream the slit entrance, while the streamlines remain attached to the downstream wall after passing the slit.

B112 乱流促進装置による高迎角翼のはく離制御

The aim of this investigation is to develop the high performance vertical axis wind turbine (VAWT) with turbulence promoters. An angle of attack of turbine blades in VAWT changes from a plus to a minus broadly. Symmetric vortex generators are therefore required to develop the turbulence promoters for VAWT. A thin tripping wire introduces at upstream stagnation point as symmetric turbulence promoters. In order to evaluate an effect of the turbulence promoters, wind tunnel experiments and numerical simulations were carried out. As a result, turbulence promoter restrains the flow separation at high angle of attack. Lifting force is 38 % larger than that of conventional airfoil by using the turbulence promoter. It reveals that the turbulence promoter is effective device to improve performance of the VAWT.

Spreading of Nonuniform Jets in Wind

The steady flow due to a nonuniform source in an otherwise uniform stream is studied, the source taking the form of an upstream-pointing and a downstream-pointing slender jet, or sheet-jet. The planar-model setting is described, along with applications, and then viscous flow computations are presented. The results show that the sheet-jet source together with the entrainment into the jets upstream and downstream induce an almost sink-like response in the overall flow, in contrast with the effects of a uniform source. The response yields a small eddy at the higher Reynolds numbers of the computations and suggests that large-scale eddies may occur for increased Reynolds numbers; yet the uniform-source model predicts the upstream stagnation point and some other features well.

Asymptotic structure of the stress field in flow past a cylinder at high Weissenberg number

We study the flow of an upper convected Maxwell fluid past a cylinder in the limit of high Weissenberg number. We make the simplifying assumption that the velocity field is given and similar to the Newtonian case (as discussed below, this assumption is likely to be wrong) and consider the integration of the stress equations. The asymptotic behavior at high Weissenberg number leads to boundary layers along the edge of the cylinder as well as stress concentration in the wake. The stresses in the boundary layer are of order W while the width of the boundary layer is of order W −1. The stresses in the wake are of order W 3, and the width of the wake is of order W −2. Just outside the boundary layer near the cylinder and wake, there is a region where the stresses are much larger (order W 3 near the cylinder and W 5 near the wake). The origin of these stresses is in the stretching flow near the upstream stagnation point.

A study of vortex magnetic separation (VMS) with a high-speed video system

This paper describes the work with a high-speed video system and an image processing computer system on the mechanisms involved in Vortex magnetic separation (VMS). The high-speed video system can clearly display individual particle trajectories at Reynolds Numbers of 6 – 40 which made it possible to measure and calculate particle position and velocity distribution with reference to a wire by means of an image processing computer system. Based on the analysis of variations of particle trajectories and velocity distribution around a single wire at different testing conditions in the process of vortex magnetic capture, it is revealed that the repulsive regions on the magnetized wire make magnetic particles separate from the wire surface at φ < 90°, where φ is the angle measured from the upstream stagnation point on the wire. Although some particles do follow the boundary layer flow to enter the vortex region behind the wire and be captured there, the probability for retention on the downstream side of the wire is reduced. When the repulsive regions on the wire is very small (e.g. H 0 < H s ), the trajectory is different, magnetic particles roll along the wire surface, enter the vortex region and are captured on the downstream of the wire. The nature of the boundary layer flow is another important factor in VMS process. Only those magnetic particles which can stay in the boundary layer can be involved in the downstream capture. The trajectory analysis also shows the inertia force acting on non-magnetic particles is the main factor which allows their escape from the boundary layer around the wire and this results in VMS process producing the secondary magnetic concentration of high grade.

Numerical modeling studies of lee mesolows, mesovortices and mesocyclones with application to the formation of Taiwan mesolows

Numerical experiments are performed for inviscid flow past an idealized topography to investigate the formation and development of lee mesolows, mesovortices and mesocyclones. For a nonrotating, low-Froude number flow over a bell-shaped moutain, a pair of mesovortices form on the lee slope move downstream and weaken at later times. The advection speed of the lee vortices is found to be about two-thirds of the basic wind velocity, which is due to the existence of a reversed pressure gradient just upstream of the vortices. The lee vortices do not concur with the upstream stagnation point in time, but rather form at a later time. It is found that a pair of lee vortices form for a flow withFr=0.66, but take a longer time to form than in lower-Froude number flows. Since the lee vortices are formed rather progressively, their formation may be explained by the baroclinically-induced vorticity tilting as the mountain waves become more and more nonlinear.

A Theoretical Remark about Waves on a Static Water Surface Beneath a Layer of Moving Air

Grundy and Tuck [J. Fluid Mech., 178 (1987), pp. 441–457] treat the problem of large-amplitude waves on an air–water interface where the air is a steady nonuniform flow and the water is stationary. They computed both periodic nonlinear Stokes-like waves far downstream and a configuration of the water surface from the edge region of a hovercraft. However, there is no work that treats the existence of such Stokes-like waves theoretically. The present work aims to prove the existence of such solutions in the case where the cushion pressure is low, that is, the depression $h_0 $ at the upstream stagnation point from the mean water level is small.