7 results
Unsteady two-dimensional jet with flexible flaps at the channel exit
- Prashant Das, R. N. Govardhan, J. H. Arakeri
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- Journal:
- Journal of Fluid Mechanics / Volume 845 / 25 June 2018
- Published online by Cambridge University Press:
- 26 April 2018, pp. 462-498
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The present work studies the effect of passive exit flexibility on a two-dimensional starting jet. The exit flexibility is introduced by attaching two flexible (deformable) flaps at the jet exit of a high aspect ratio rectangular duct with the flaps initially being parallel to the channel walls. A controlled piston motion is used to generate the starting jet, which is composed of a rapid acceleration to a constant velocity ($U_{p}$) that is maintained for a given duration of time, after which it is brought to rest impulsively. The parameters which are varied include the flexural rigidity ($EI$) of the flaps, flap length ($L_{f}$) and piston speed ($U_{p}$), with measurements of the flap kinematics and flow field in each case. The flaps initially bulge due to the acceleration of the piston from rest, with this bulge growing in size and moving downstream as the flow develops, culminating in a large opening at the flap exit. Subsequently, the flaps return to their initial parallel position and remain there as long as the piston is in motion. Once the piston stops, the flaps collapse inwards due to fluid deceleration causing additional flow out of the flap region in the form of a jet that adds to the net amount of fluid pushed by the piston. We find that the flap kinematics is affected by the flap $EI$ and $L_{f}$ besides $U_{p}$. We define a non-dimensional flexural rigidity $EI^{\ast }=EI_{eq}/(1/2\unicode[STIX]{x1D70C}U_{p}^{2}L_{f}^{2}d)$, where $EI_{eq}$ is an equivalent flexural rigidity which takes the self-weight of the flaps into account ($d=\text{channel width}$; $\unicode[STIX]{x1D70C}=$ fluid density). We find that across different $EI_{eq}$, $L_{f}$, and piston speeds, the maximum opening of the flap tip and the time taken to reach this maximum opening in terms of $L/L_{f}$ (where $L=\text{fluid slug length}$) fall on a single curve for all the cases studied, when plotted with $EI^{\ast }$. Particle image velocimetry measurements show that the motion of the flaps results in the formation of additional pairs of vortices when compared to the single vortex pair formed in the absence of flaps. The total final circulation coming out of the flap region remains nearly the same as that of the rigid exit case. However, the final fluid impulse is always found to be higher in the flap cases, with the fluid impulse in most flap cases being approximately two times the fluid impulse of the rigid exit case. This increase in impulse is shown to be linked to the fact that the centroids of vorticity get spread out more in the lateral direction due to the opening of the flaps. The increased impulse and the higher time rate of change of impulse, which is linked with force, suggest that introduction of flexible flaps can help improve thrust performance when looked at from a propulsion point of view.
The kinematic genesis of vortex formation due to finite rotation of a plate in still fluid
- M. Jimreeves David, Manikandan Mathur, R. N. Govardhan, J. H. Arakeri
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- Journal:
- Journal of Fluid Mechanics / Volume 839 / 25 March 2018
- Published online by Cambridge University Press:
- 02 February 2018, pp. 489-524
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We present a combined experimental and numerical study of an idealized model of the propulsive stroke of the turning manoeuvre in fish. Specifically, we use the framework of Lagrangian coherent structures (LCSs) to describe the kinematics of the flow that results from a thin plate performing a large angle rotation about its tip in still fluid. Temporally and spatially well-resolved velocity fields are obtained using a two-dimensional, incompressible finite-volume solver, and are validated by comparisons with experimentally measured velocity fields and alternate numerical simulations. We then implement the recently proposed variational theory of LCSs to extract the hyperbolic and elliptic LCSs in the numerically generated velocity fields. Detailed LCS analysis is performed for a plate motion profile described by $\dot{\unicode[STIX]{x1D703}}(t)=\unicode[STIX]{x1D6FA}_{max}\sin ^{2}(\unicode[STIX]{x1D714}t)$ during $0\leqslant t\leqslant t_{o}$ and zero otherwise. The stopping time $t_{o}$ is given by $t_{o}=\unicode[STIX]{x03C0}/\unicode[STIX]{x1D714}=10~\text{s}$, the value of $\unicode[STIX]{x1D6FA}_{max}$ chosen to give a stopping angle of $\unicode[STIX]{x1D703}_{max}=90^{\circ }$, resulting in a Reynolds number $Re=c^{2}\unicode[STIX]{x1D6FA}_{max}/\unicode[STIX]{x1D708}=785.4$, where $c$ is the plate chord length and $\unicode[STIX]{x1D708}=10^{-6}~\text{m}^{2}~\text{s}^{-1}$ the kinematic viscosity of water. The flow comprises a starting and a stopping vortex, resulting in a pair of oppositely signed vortices of unequal strengths that move away from the plate in a direction closely aligned with the final plate orientation at $t/t_{o}\approx 2$. The hyperbolic LCSs are shown to encompass the fluid material that is advected away from the plate for $t>t_{o}$, henceforth referred to as the advected bulk. The starting and stopping vortices, identified using elliptic LCSs and hence more objective than Eulerian vortex detection methods, constitute only around two thirds of the advected bulk area. The advected bulk is traced back to $t=0$ to identify five distinct lobes of fluid that eventually form the advected bulk, and hence map the long-term fate of various regions in the fluid at $t=0$. The five different lobes of fluid are then shown to be delineated by repelling LCS boundaries at $t=0$. The linear momentum of the advected bulk region is shown to account for approximately half of the total impulse experienced by the plate in the direction of its final orientation, thus establishing its dynamical significance. We provide direct experimental evidence for the kinematic relevance of hyperbolic and elliptic LCSs using novel dye visualization experiments, and also show that attracting hyperbolic LCSs provide objective characterization of the spiral structures often observed in vortical flows. We conclude by showing that qualitatively similar LCSs persist for several other plate motion profiles and stopping angles as well.
Thrust generation from pitching foils with flexible trailing edge flaps
- M. Jimreeves David, R. N. Govardhan, J. H. Arakeri
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- Journal:
- Journal of Fluid Mechanics / Volume 828 / 10 October 2017
- Published online by Cambridge University Press:
- 31 August 2017, pp. 70-103
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In the present experimental study, we investigate thrust production from a pitching flexible foil in a uniform flow. The flexible foils studied comprise a rigid foil in the front (chord length $c_{R}$) that is pitched sinusoidally at a frequency $f$, with a flexible flap of length $c_{F}$ and flexural rigidity $EI$ attached to its trailing edge. We investigate thrust generation for a range of flexural rigidities ($EI$) and flap length to total chord ratio ($c_{F}/c$), with the mean thrust ($\overline{C_{T}}$) and the efficiency of thrust generation ($\unicode[STIX]{x1D702}$) being directly measured in each case. The thrust in the rigid foil cases, as expected, is found to be primarily due to the normal force on the rigid foil ($\overline{C_{TN}}$) with the chordwise or axial thrust contribution ($\overline{C_{TA}}$) being small and negative. In contrast, in the flexible foil cases, the axial contribution to thrust becomes important. We find that using a non-dimensional flexural rigidity parameter ($R^{\ast }$) defined as $R^{\ast }=EI/(0.5\unicode[STIX]{x1D70C}U^{2}c_{F}^{3})$ appears to combine the independent effects of variations in $EI$ and $c_{F}/c$ at a given value of the reduced frequency ($k=\unicode[STIX]{x03C0}fc/U$) for the range of $c_{F}/c$ values studied here ($U$ is free-stream velocity; $\unicode[STIX]{x1D70C}$ is fluid density). At $k\approx 6$, the peak mean thrust coefficient is found to be about 100 % higher than the rigid foil thrust, and occurs at $R^{\ast }$ value of approximately 8, while the peak efficiency is found to be approximately 300 % higher than the rigid foil efficiency and occurs at a distinctly different $R^{\ast }$ value of close to 0.01. Corresponding to these two optimal flexural rigidity parameter values, we find two distinct flap deflection shapes; the peak thrust corresponding to a mode 1 type simple bending of the flap with no inflection points, while the peak efficiency corresponds to a distinctly different deflection profile having an inflection point along the flap. The peak thrust condition is found to be close to the ‘resonance’ condition for the first mode natural frequency of the flexible flap in still water. In both these optimal cases, we find that it is the axial contribution to thrust that dominates ($\overline{C_{TA}}\gg \overline{C_{TN}}$), in contrast to the rigid foil case. Particle image velocimetry (PIV) measurements for the flexible cases show significant differences in the strength and arrangement of the wake vortices in these two cases.
Effect of hinged leaflets on vortex pair generation
- Prashant Das, R. N. Govardhan, J. H. Arakeri
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- Journal:
- Journal of Fluid Mechanics / Volume 730 / 10 September 2013
- Published online by Cambridge University Press:
- 02 August 2013, pp. 626-658
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We experimentally study the effect of having hinged leaflets at the jet exit on the formation of a two-dimensional counter-rotating vortex pair. A piston–cylinder mechanism is used to generate a starting jet from a high-aspect-ratio channel into a quiescent medium. For a rigid exit, with no leaflets at the channel exit, the measurements at a central plane show that the trailing jet in the present case is never detached from the vortex pair, and keeps feeding into the latter, unlike in the axisymmetric case. Passive flexibility is introduced in the form of rigid leaflets or flaps that are hinged at the exit of the channel, with the flaps initially parallel to the channel walls. The experimental arrangement closely approximates the limiting case of a free-to-rotate rigid flap with negligible structural stiffness, damping and flap inertia, as these limiting structural properties permit the largest flap openings. Using this arrangement, we start the flow and measure the flap kinematics and the vorticity fields for different flap lengths and piston velocity programs. The typical motion of the flaps involves a rapid opening and a subsequent more gradual return to its initial position, both of which occur when the piston is still moving. The initial opening of the flaps can be attributed to an excess pressure that develops in the channel when the flow starts, due to the acceleration that has to be imparted to the fluid slug between the flaps. In the case with flaps, two additional pairs of vortices are formed because of the motion of the flaps, leading to the ejection of a total of up to three vortex pairs from the hinged exit. The flaps’ length (${L}_{f} $) is found to significantly affect flap motions when plotted using the conventional time scale $L/ d$, where $L$ is the piston stroke and $d$ is the channel width. However, with a newly defined time scale based on the flap length ($L/ {L}_{f} $), we find a good collapse of all the measured flap motions irrespective of flap length and piston velocity for an impulsively started piston motion. The maximum opening angle in all these impulsive velocity program cases, irrespective of the flap length, is found to be close to 15°. Even though the flap kinematics collapses well with $L/ {L}_{f} $, there are differences in the distribution of the ejected vorticity even for the same $L/ {L}_{f} $. Such a redistribution of vorticity can lead to important changes in the overall properties of the flow, and it gives us a better understanding of the importance of exit flexibility in such flows.
An experimental study of an axisymmetric turbulent pulsed air jet
- I. CHOUTAPALLI, A. KROTHAPALLI, J. H. ARAKERI
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- Journal:
- Journal of Fluid Mechanics / Volume 631 / 25 July 2009
- Published online by Cambridge University Press:
- 17 July 2009, pp. 23-63
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An experimental study is carried out to elucidate the structure of a high Reynolds number (~105) turbulent pulsed jet. Particle image velocimetry measurements showed that the near flow field is dominated by a series of vortex rings with jet-like flows in between. The data show that the vortex rings convect at nearly constant speed of 0.6Uj (Uj: mean jet exit velocity) and the spacing between the rings assumes a value of about 0.6/St (St: Strouhal number=fd/Uj, where f is the pulsing frequency and d is the nozzle exit diameter). With increasing Strouhal number, the rings are closely spaced and the flow tends to assume a steady jet character at five diameters downstream of the nozzle exit. At lower Strouhal numbers there is a distinct region of jet flow in between the rings. Many of the global characteristics, entrainment, mass and momentum flux are essentially determined by the strength and spacing of the rings which, in turn, depend on St. We show that the increase in momentum is due to both increased momentum flux and overpressure at the exit in accordance with Krueger & Gharib (AIAA J., vol. 43 (4), 2005, p. 792). This increase in momentum comes at the expense of higher energy required to produce the jet. We also present results of organized and random components of the fluctuations and production of the random turbulence in a pulsed jet. The two regions of dominant turbulence production are identified with the ring and the trailing jet shear layers.
Instability-induced ordering, universal unfolding and the role of gravity in granular Couette flow
- MEHEBOOB ALAM, V. H. ARAKERI, P. R. NOTT, J. D. GODDARD, H. J. HERRMANN
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- Journal:
- Journal of Fluid Mechanics / Volume 523 / 25 January 2005
- Published online by Cambridge University Press:
- 21 January 2005, pp. 277-306
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Linear stability theory and bifurcation analysis are used to investigate the role of gravity in shear-band formation in granular Couette flow, considering a kinetic-theory rheological model. We show that the only possible state, at low shear rates, corresponds to a ‘plug’ near the bottom wall, in which the particles are densely packed and the shear rate is close to zero, and a uniformly sheared dilute region above it. The origin of such plugged states is shown to be tied to the spontaneous symmetry-breaking instabilities of the gravity-free uniform shear flow, leading to the formation of ordered bands of alternating dilute and dense regions in the transverse direction, via an infinite hierarchy of pitchfork bifurcations. Gravity plays the role of an ‘imperfection’, thus destroying the ‘perfect’ bifurcation structure of uniform shear. The present bifurcation problem admits universal unfolding of pitchfork bifurcations which subsequently leads to the formation of a sequence of a countably infinite number of ‘isolas’, with the solution structures being a modulated version of their gravity-free counterpart. While the solution with a plug near the bottom wall looks remarkably similar to the shear-banding phenomenon in dense slow granular Couette flows, a ‘floating’ plug near the top wall is also a solution of these equations at high shear rates. A two-dimensional linear stability analysis suggests that these floating plugged states are unstable to long-wave travelling disturbances.The unique solution having a bottom plug can also be unstable to long waves, but remains stable at sufficiently low shear rates. The implications and realizability of the present results are discussed in the light of shear-cell experiments under ‘microgravity’ conditions.
Bifurcation in a buoyant horizontal laminar jet
- JAYWANT H. ARAKERI, DEBOPAM DAS, J. SRINIVASAN
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- Journal:
- Journal of Fluid Mechanics / Volume 412 / 10 June 2000
- Published online by Cambridge University Press:
- 10 June 2000, pp. 61-73
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The trajectory of a laminar buoyant jet discharged horizontally has been studied. The experimental observations were based on the injection of pure water into a brine solution. Under certain conditions the jet has been found to undergo bifurcation. The bifurcation of the jet occurs in a limited domain of Grashof number and Reynolds number. The regions in which the bifurcation occurs has been mapped in the Reynolds number–Grashof number plane. There are three regions where bifurcation does not occur. The various mechanisms that prevent bifurcation have been proposed.