Dynamics and mixing of vortex rings in crossflow

2008 ◽  
Vol 604 ◽  
pp. 389-409 ◽  
Author(s):  
RAJES SAU ◽  
KRISHNAN MAHESH
Keyword(s):  
Boundary Layer ◽  
Vortex Ring ◽  
Nozzle Exit ◽  
Velocity Ratio ◽  
Leading Edge ◽  
Vortex Rings ◽  
Low Velocity ◽  
Hairpin Vortices ◽  
Stroke Length ◽  
Asymmetric Vortex

Direct numerical simulation is used to study the effect of crossflow on the dynamics, entrainment and mixing characteristics of vortex rings issuing from a circular nozzle. Three distinct regimes exist, depending on the velocity ratio (ratio of the average nozzle exit velocity to free-stream crossflow velocity) and stroke ratio (ratio of stroke length to nozzle exit diameter). Coherent vortex rings are not obtained at velocity ratios below approximately 2. At these low velocity ratios, the vorticity in the crossflow boundary layer inhibits roll-up of the nozzle boundary layer at the leading edge. As a result, a hairpin vortex forms instead of a vortex ring. For large stroke ratios and velocity ratio below 2, a series of hairpin vortices is shed downstream. The shedding is quite periodic for very low Reynolds numbers. For velocity ratios above 2, two regimes are obtained depending upon the stroke ratio. Lower stroke ratios yield a coherent asymmetric vortex ring, while higher stroke ratios yield an asymmetric vortex ring accompanied by a trailing column of vorticity. These two regimes are separated by a transition stroke ratio whose value decreases with decreasing velocity ratio. For very high values of the velocity ratio, the transition stroke ratio approaches the ‘formation number’. In the absence of trailing vorticity, the vortex ring tilts towards the upstream direction, while the presence of a trailing column causes it to tilt downstream. This behaviour is explained. In the absence of crossflow, the trailing column is not very effective at entrainment, and is best avoided for optimal mixing and entrainment. However, in the presence of crossflow, the trailing column is found to contribute significantly to the overall mixing and entrainment. The trailing column interacts with the crossflow to generate a region of high pressure downstream of the nozzle that drives crossflow fluid towards the vortex ring. There is an optimal length of the trailing column for maximum downstream entrainment. A classification map which categorizes the different regimes is developed.

Passive scalar mixing in vortex rings

2007 ◽  
Vol 582 ◽  
pp. 449-461 ◽  
Author(s):  
RAJES SAU ◽  
KRISHNAN MAHESH
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Nozzle Exit ◽  
Passive Scalar ◽  
Rate Of Change ◽  
Vortex Rings ◽  
Ambient Fluid ◽  
Stroke Length ◽  
Formation Number

Direct numerical simulation is used to study the mixing of a passive scalar by a vortex ring issuing from a nozzle into stationary fluid. The ‘formation number’ (Gharibet al. J. Fluid Mech.vol. 360, 1998, p. 121), is found to be 3.6. Simulations are performed for a range of stroke ratios (ratio of stroke length to nozzle exit diameter) encompassing the formation number, and the effect of stroke ratio on entrainment and mixing is examined. When the stroke ratio is greater than the formation number, the resulting vortex ring with trailing column of fluid is shown to be less effective at mixing and entrainment. As the ring forms, ambient fluid is entrained radially into the ring from the region outside the nozzle exit. This entrainment stops once the ring forms, and is absent in the trailing column. The rate of change of scalar-containing fluid is found to depend linearly on stroke ratio until the formation number is reached, and falls below the linear curve for stroke ratios greater than the formation number. This behaviour is explained by considering the entrainment to be a combination of that due to the leading vortex ring and that due to the trailing column. For stroke ratios less than the formation number, the trailing column is absent, and the size of the vortex ring increases with stroke ratio, resulting in increased mixing. For stroke ratios above the formation number, the leading vortex ring remains the same, and the length of the trailing column increases with stroke ratio. The overall entrainment decreases as a result.

The behaviour of circular synthetic jets in a laminar boundary layer

2005 ◽  
Vol 109 (1100) ◽  
pp. 461-470 ◽  
Author(s):  
S. Zhong ◽  
F. Millet ◽  
N. J. Wood
Keyword(s):  
Boundary Layer ◽  
Velocity Ratio ◽  
Synthetic Jets ◽  
Operating Conditions ◽  
Vortex Rings ◽  
Hairpin Vortices ◽  
Vortical Structures ◽  
Flow Separation Control ◽  
Wall Flow ◽  
Near Wall

Abstract Dye flow visualisation of circular synthetic jets was carried out in laminar boundary layers developing over a flat plate at a range of actuator operating conditions and freestream velocities of 0·05 and 0·1ms–1. The purpose of this work was to study the interaction of synthetic jets with the boundary layer and the nature of vortical structures produced as a result of this interaction. The effects of Reynolds number (Re), velocity ratio (VR ) and Strouhal number (St) on the behaviour of synthetic jets were studied. At low Re and VR , the vortical structures produced by synthetic jets appear as highly stretched hairpin vortices attached to the wall. At intermediate Re and VR , these structures roll up into vortex rings which experience a considerable amount of tilting and stretching as they enter the boundary layer. These vortex rings will eventually propagate outside the boundary layer hence the influence of the synthetic jets on the near wall flow will be confined in the near field of the jet exit. At high Re and VR , the vortex rings appear to experience a certain amount of tilting but no obvious stretching. They penetrate the edge of the boundary layer quickly, producing very limited impact on the near wall flow. Hence it is believed that the hairpin vortices produced at low Re and VR are likely to be the desirable structures for effective flow separation control. In this paper, a vortex model was also described to explain the mechanism of vortex tilting.

Effect of velocity ratio on the interaction between plasma synthetic jets and turbulent cross-flow

2019 ◽  
Vol 865 ◽  
pp. 928-962 ◽  
Author(s):  
Haohua Zong ◽  
Marios Kotsonis
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
Velocity Ratio ◽  
Vortex Pair ◽  
Synthetic Jets ◽  
Low Energy ◽  
Vortex Rings ◽  
Wall Region ◽  
Mean Velocity ◽  
Counter Rotating Vortex Pair

Plasma synthetic jet actuators (PSJAs) are particularly suited for high-Reynolds-number, high-speed flow control due to their unique capability of generating supersonic pulsed jets at high frequency (${>}5$  kHz). Different from conventional synthetic jets driven by oscillating piezoelectric diaphragms, the exit-velocity variation of plasma synthetic jets (PSJs) within one period is significantly asymmetric, with ingestion being relatively weaker (less than $20~\text{m}~\text{s}^{-1}$) and longer than ejection. In this study, high-speed phase-locked particle image velocimetry is employed to investigate the interaction between PSJAs (round exit orifice, diameter 2 mm) and a turbulent boundary layer at constant Strouhal number (0.02) and increasing mean velocity ratio ($r$, defined as the ratio of the time-mean velocity over the ejection phase to the free-stream velocity). Two distinct operational regimes are identified for all the tested cases, separated by a transition velocity ratio, lying between $r=0.7$ and $r=1.0$. At large velocity and stroke ratios (first regime, representative case $r=1.6$), vortex rings are followed by a trailing jet column and tilt downstream initially. This downstream tilting is transformed into upstream tilting after the pinch-off of the trailing jet column. The moment of this transformation relative to the discharge advances with decreasing velocity ratio. Shear-layer vortices (SVs) and a hanging vortex pair (HVP) are identified in the windward and leeward sides of the jet body, respectively. The HVP is initially erect and evolves into an inclined primary counter-rotating vortex pair ($p$-CVP) which branches from the middle of the front vortex ring and extends to the near-wall region. The two legs of the $p$-CVP are bridged by SVs, and a secondary counter-rotating vortex pair ($s$-CVP) is induced underneath these two legs. At low velocity and stroke ratios (second regime, representative case $r=0.7$), the trailing jet column and $p$-CVP are absent. Vortex rings always tilt upstream, and the pitching angle increases monotonically with time. An $s$-CVP in the near-wall region is induced directly by the two longitudinal edges of the ring. Inspection of spanwise planes ($yz$-plane) reveals that boundary-layer energization is realized by the downwash effect of either vortex rings or $p$-CVP. In addition, in the streamwise symmetry plane, the increasing wall shear stress is attributed to the removal of low-energy flow by ingestion. The downwash effect of the $s$-CVP does not benefit boundary-layer energization, as the flow swept to the wall is of low energy.

Substructures in a turbulent spot

1988 ◽  
Vol 197 ◽  
pp. 389-414 ◽  
Author(s):  
R. Sankaran ◽  
M. Sokolov ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Leading Edge ◽  
Simple Relation ◽  
Sufficient Evidence ◽  
Streamwise Direction ◽  
Geometrical Construction ◽  
Turbulent Spot ◽  
Hairpin Vortices ◽  
Streamwise Distance

Substructures within a turbulent spot which develops in a slightly heated laminar boundary layer have been identified using arrays of cold wires aligned in either a streamwise direction or in a direction normal to the wall. At any given streamwise distance from the spot origin, histograms of the number of detected substructures exhibit a peak, defining the most probable spot or the spot with the most likely number of substructures. The number of substructures in the most probable spot increases with streamwise distance but all substructures are convected at approximately the same velocity for any given distance from the wall. This velocity is approximately equal to that of the leading edge of the spot and increases slightly with distance from the wall. The increase in the number of substructures accounts for the streamwise growth of the spot. A simple relation is derived for determining the number of substructures at a particular streamwise station and a geometrical construction is proposed for identifying the origin of a new substructure. There is sufficient evidence for suggesting that the new substructures are formed near the trailing edge of the spot. The convection velocity, inclination and lengthscales of the substructures compare favourably with the corresponding characteristics of hairpin vortices.

Low Pressure Turbine Relaminarization Bubble Characterization using Massively-Parallel Large Eddy Simulations

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Shriram Jagannathan ◽  
Markus Schwänen ◽  
Andrew Duggleby
Keyword(s):  
Boundary Layer ◽  
Reverse Flow ◽  
Leading Edge ◽  
Suction Side ◽  
Low Pressure ◽  
Surface Boundary ◽  
Suction Surface ◽  
Hairpin Vortices ◽  
Low Pressure Turbine ◽  
Large Eddy

The separation and reattachment of suction surface boundary layer in a low pressure turbine is characterized using large-eddy simulation at Ress = 69000 based on inlet velocity and suction surface length. Favorable comparisons are drawn with experiments using a high pass filtered Smagorinsky model for sub-grid scales. The onset of time mean separation is at s/so = 0.61 and reattachment at s/so = 0.81, extending over 20% of the suction surface. The boundary layer is convectively unstable with a maximum reverse flow velocity of about 13% of freestream. The breakdown to turbulence occurs over a very short distance of suction surface and is followed by reattachment. Turbulence near the bubble is further characterized using anisotropy invariant mapping and time orthogonal decomposition diagnostics. Particularly the vortex shedding and shear layer flapping phenomena are addressed. On the suction side, dominant hairpin structures near the transitional and turbulent flow regime are observed. The hairpin vortices are carried by the freestream even downstream of the trailing edge of the blade with a possibility of reaching the next stage. Longitudinal streaks that evolve from the breakdown of hairpin vortices formed near the leading edge are observed on the pressure surface.

Effect of Upstream Shear on Flow and Heat (Mass) Transfer Over a Flat Plate

2008 ◽  
Author(s):  
Kalyanjit Ghosh ◽  
R. J. Goldstein
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Flow Direction ◽  
Velocity Ratio ◽  
Leading Edge ◽  
Surface Velocity ◽  
Freestream Velocity ◽  
Inner Region

A parametric study is conducted to investigate the effect of wall shear on a two-dimensional turbulent boundary layer. The shear is imparted by a moving belt, flush with the wall, translating in the flow direction. Velocity and mass transfer experiments have been performed for four surface-to-freestream velocity ratios (0, 0.38, 0.52, 0.65) with a Reynolds number based on the momentum thickness between 770 and 1776. The velocity data indicate that the location of the ‘virtual origin’ of the turbulent boundary layer ‘moves’ downstream towards the trailing edge of the belt with increasing surface velocity. The highest velocity ratio represents a case which is responsible for the removal of the inner region of the boundary layer. Mass transfer measurements downstream of the belt show the presence of a local minimum in the variation of the Stanton vs. Reynolds number for the highest velocity ratio. Downstream of this minimum, approximately 1 cm from the leading edge of the mass transfer plate, the characteristics of the turbulent boundary layer are restored and the data fall back on the empirical variation of the Stanton number with Reynolds number.

On the scaling of propagation of periodically generated vortex rings

2018 ◽  
Vol 853 ◽  
pp. 150-170 ◽  
Author(s):  
H. Asadi ◽  
H. Asgharzadeh ◽  
I. Borazjani
Keyword(s):  
Vortex Ring ◽  
Empirical Relation ◽  
Vortex Rings ◽  
Hairpin Vortices ◽  
Pulsed Jets ◽  
Pulsed Jet ◽  
Vortex Pairing ◽  
Periodic State ◽  
Periodic Rings ◽  
Definition Of

The propagation of periodically generated vortex rings (period $T$) is numerically investigated by imposing pulsed jets of velocity $U_{jet}$ and duration $T_{s}$ (no flow between pulses) at the inlet of a cylinder of diameter $D$ exiting into a tank. Because of the step-like nature of pulsed jet waveforms, the average jet velocity during a cycle is $U_{ave}=U_{jet}T_{s}/T$. By using $U_{ave}$ in the definition of the Reynolds number ($Re=U_{ave}D/\unicode[STIX]{x1D708}$, $\unicode[STIX]{x1D708}$: kinematic viscosity of fluid) and non-dimensional period ($T^{\ast }=TU_{ave}/D=T_{s}U_{jet}/D$, i.e. equivalent to formation time), then based on the results, the vortex ring velocity $U_{v}/U_{jet}$ becomes approximately independent of the stroke ratio $T_{s}/T$. The results also show that $U_{v}/U_{jet}$ increases by reducing $Re$ or increasing $T^{\ast }$ (more sensitive to $T^{\ast }$) according to a power law of the form $U_{v}/U_{jet}=0.27T^{\ast 1.31Re^{-0.2}}$. An empirical relation, therefore, for the location of vortex ring core centres ($S$) over time ($t$) is proposed ($S/D=0.27T^{\ast 1+1.31Re^{-0.2}}t/T_{s}$), which collapses (scales) not only our results but also the results of experiments for non-periodic rings. This might be due to the fact that the quasi-steady vortex ring velocity was found to have a maximum of 15 % difference with the initial (isolated) one. Visualizing the rings during the periodic state shows that at low $T^{\ast }\leqslant 2$ and high $Re\geqslant 1400$ here, the stopping vortices become unstable and form hairpin vortices around the leading ones. However, by increasing $T^{\ast }$ or decreasing $Re$ the stopping vortices remain circular. Furthermore, rings with short $T^{\ast }=1$ show vortex pairing after approximately one period in the downstream, but higher $T^{\ast }\geqslant 2$ generates a train of vortices in the quasi-steady state.

scholarly journals EFFECT OF TIP CLEARANCE ON THE FLOW FIELD OF THE MIXED FLOW TURBOCHARGER TURBINE

2017 ◽  
Vol 79 (7-3) ◽  
Author(s):  
M. S. Kamarudin ◽  
M. Zulkeflee ◽  
M. H. Padzillah
Keyword(s):  
Flow Field ◽  
Combustion Engine ◽  
Velocity Ratio ◽  
Leading Edge ◽  
Tip Clearance ◽  
Optimum Operating ◽  
Low Velocity ◽  
Mixed Flow ◽  
Optimum Operating Condition ◽  
Design Speed

Turbocharger is a device comprising mainly of a turbine and a compressor. The demand of turbocharger in the automotive industry increases as it significantly enhances the output power of an Internal Combustion Engine and reduces emission. The use of mixed flow turbine to replace the conventional radial turbine gives better impact since the turbine transient response increases and operates more efficiently at low velocity ratio. The flow behaviour inside the turbine affects the torque generation by the turbine. It is necessary for the turbine to have a specified clearance between the rotor tip and the casing of the turbomachine. This undoubtedly will contribute to clearance loss and mixing of leaked flow which produce disturbance to the exhaust flow. In order to investigate this effect, the validated Computational Fluid Dynamics method is chosen in order to replicate the flow field inside the mixed flow turbine. The simulation is carried out at the optimum operating condition which is at turbine total-to-static efficiency of 79% with inlet mass flow rate of 0.5kg/s. The flow inside the passage is plotted into pressure and velocity contours which are compared at 50% (30000rpm) and 80% (48000rpm) of the turbine design speed. The comparison between having 0% (no leakage) and 3% shroud tip clearance are then compared. Through the analysis, it is suggested that clearance leakage and flow separation cause disruption to the desirable uniform flow inside the turbine passage. The presence of Coriolis effect that resists the clearance leakage flow only at near leading edge of the rotor is observed. Furthermore, a low pressure region is perceived at rotor hub which absent in the radial flow turbine. These factors eventually reduce the performances of the actual turbine.

Bifurcation and stability analysis of a jet in cross-flow: onset of global instability at a low velocity ratio

2012 ◽  
Vol 696 ◽  
pp. 94-121 ◽  
Author(s):  
Miloš Ilak ◽  
Philipp Schlatter ◽  
Shervin Bagheri ◽  
Dan S. Henningson
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Initial Growth ◽  
Low Velocity ◽  
Hairpin Vortices ◽  
Jet In Cross Flow ◽  
Periodic Behaviour ◽  
Set Up

AbstractWe study direct numerical simulations (DNS) of a jet in cross-flow at low values of the jet-to-cross-flow velocity ratio$R$. We observe that, as the ratio$R$increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi-periodic behaviour, before finally becoming turbulent, as seen in the simulation of Bagheriet al. (J. Fluid. Mech., vol. 624, 2009b, pp. 33–44). The value of$R$at which the first bifurcation occurs for our numerical set-up is found, and shedding of hairpin vortices characteristic of a shear layer instability is observed. We focus on this first bifurcation, and find that a global linear stability analysis predicts well the frequency and initial growth rate of the nonlinear DNS at the critical value of$R$and that good qualitative predictions about the dynamics can still be made at slightly higher values of$R$where multiple unstable eigenmodes are present. In addition, we compute the adjoint global eigenmodes, and find that the overlap of the direct and the adjoint eigenmode, also known as a ‘wavemaker’, provides evidence that the source of the first instability lies in the shear layer just downstream of the jet.

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