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Experimental and numerical investigation of flow instability in a transient pipe flow
- Avinash Nayak, Debopam Das
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- Journal:
- Journal of Fluid Mechanics / Volume 920 / 10 August 2021
- Published online by Cambridge University Press:
- 14 June 2021, A39
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This paper describes the study of instability in a transient pipe flow of decaying nature, considering variation of the base flow with time. Linear stability analysis on the decaying base flow is carried out and the effect of wavenumber on the perturbation energy growth is studied. Non-modal optimal-mode analysis, with time integration, utilising adjoint equations, is found to be suitable for the study of instability in such transient flows. The range of wavenumbers, sensitive to perturbation in providing maximum perturbation energy growth, and the magnitude of the order of growth supports the conjecture that the transient growth of the optimal perturbation is responsible for the observed instability. The findings regarding stability mechanism are substantiated by an experimental investigation accompanied by a numerical study. In an unsteady experiment, where a piston with trapezoidal velocity variation drives the flow, an impulsively blocked duct flow is emulated. Particle image velocimetry (PIV) measurement provides the velocity data; the analytical velocity profiles are obtained using a series solution available in the literature, with a trapezoidal flow-rate-variation approximation. The analytical profiles capture the centreline velocities, various time scales and the reverse-flow regions, which the experiment fails to resolve. Observation of the vorticity fields confirms the appearance of instability waves close to the reverse-flow boundary layer near the wall, and the growth and transformation of the instability waves into fully grown vortices. The coherent wave structures and their associated wavenumbers are extracted quantitatively through spatial dynamic mode decomposition (DMD) analysis. This comprehensive analysis recognises the dynamics of the flow-field development, which suggests that the loss of mean-flow energy and the perturbation energy growth compensate each other, with the remaining energy losses accounted for by viscous dissipation.
Early transition, relaminarization and drag reduction in the flow of polymer solutions through microtubes
- Bidhan Chandra, V. Shankar, Debopam Das
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- Journal:
- Journal of Fluid Mechanics / Volume 885 / 25 February 2020
- Published online by Cambridge University Press:
- 10 January 2020, A47
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Experiments are performed to investigate the onset of early transition and drag reduction in the flow of polymer (polyacrylamide and polyethylene oxide) solutions through rigid microtubes of diameters in the range 0.49–2.84 mm. We measure friction factor variation with Reynolds number for varying polymer concentrations and tube diameters, and the Reynolds number, $Re_{t}$, at which the experimental data deviate from the laminar value represents the onset of transition. Crucially, owing to the high shear rates encountered in our experiments, we show that it is important to account for shear thinning of the fluid in the theoretical estimation of the friction factor in the laminar regime. We accomplish this using a Carreau model, and show that the use of laminar friction factor calculated without shear thinning leads to an erroneous overestimation of $Re_{t}$. The $Re_{t}$ obtained from friction factor data in the present study is in good agreement with that inferred using micro particle image velocimetry analysis in Chandra et al. (J. Fluid Mech., vol. 844, 2018, pp. 1052–1083). For smaller concentrations of the added polymer, there is a marginal delay in the onset of turbulence, but as the concentration is increased further, the transition Reynolds number decreases much below $2000$, the usual value at which transition occurs in Newtonian pipe flows. Thus, the present study further corroborates the phenomenon of early transition leading to an ‘elasto-inertial’ turbulent state in the flow of polymer solutions. For concentrations such that there is a delay in transition, if $Re$ is maintained above the $Re_{t}$ for Newtonian fluids, the flow is transitional or turbulent in the absence of polymers. At such a fixed $Re$, if the concentration of the polymer is increased gradually, the friction factor decreases and the flow relaminarizes. With further increase in polymer concentration, the flow undergoes a transition due to elasto-inertial instability. The effect of addition of small amounts of polymer on turbulent drag reduction in the flow of water through microtubes is also investigated. Increase in polymer concentration, molecular weight and decrease in tube diameter causes an increase in drag reduction. The friction factor data for different polymer concentrations, molecular weights, tube diameters and $Re$, when plotted with $Wi(1-\unicode[STIX]{x1D6FD})$, show a reasonable collapse, where $Wi$ is the Weissenberg number defined as the product of the longest relaxation time of the polymer solution and the average shear rate in the tube and $\unicode[STIX]{x1D6FD}$ is the ratio of solvent to total solution viscosity. Interestingly, the onset of the maximum drag reduction asymptote, for experiments using varying tube diameters and polymer concentrations, appears to occur at $Wi(1-\unicode[STIX]{x1D6FD})\sim O(1)$.
Puffing in planar buoyant plumes: BiGlobal instability analysis and experiments
- Kuchimanchi K. Bharadwaj, Debopam Das
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- Journal:
- Journal of Fluid Mechanics / Volume 863 / 25 March 2019
- Published online by Cambridge University Press:
- 28 January 2019, pp. 817-849
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The present study investigates the puffing behaviour of planar buoyant plumes by employing linear BiGlobal stability analysis and experiments. The BiGlobal instability characteristics of two-dimensional plumes have been explored using stability analysis and compared with the puffing behaviour of both rectangular plumes and square plumes obtained from experiments. In the parameter space investigated, which spans a Richardson number range $0.03<Ri<960$, instability analysis reveals that planar plumes exhibit BiGlobal instability only for varicose perturbations, while they remain stable for sinuous perturbations. The BiGlobal frequency and growth rates of the unstable varicose mode are used to obtain Strouhal number correlation and stability curves. An investigation into the effect of the spanwise wavenumber on BiGlobal instability indicates that planar plumes are more unstable to two-dimensional perturbations than to three-dimensional perturbations. An increase in the spanwise wavenumber tends to stabilize planar plumes without affecting their oscillation frequencies. Experiments suggest that the puffing frequencies in rectangular plumes closely follow the power law obtained from two-dimensional instability analysis while exhibiting a weaker dependence on inlet aspect ratio. To further explore the effect of aspect ratio on puffing behaviour, experiments have been carried out in plumes of aspect ratio 1, i.e. square plumes. Square plumes are found to be more stable and to exhibit higher puffing frequencies than rectangular plumes. The reasons for these differences in puffing dynamics between rectangular and square plumes have been explored from the phase-locked streamwise and spanwise flow visualizations. In addition to puffing, spanwise visualizations in both rectangular and square plumes show the presence of secondary flows at their corners, similar to their constant-density jet counterparts. Finally, from experiments, we deduced a new universal puffing frequency correlation with the hydraulic diameter as the length scale which eliminates the aspect ratio dependence, and is valid for both square and low-aspect-ratio rectangular plumes.
Onset of transition in the flow of polymer solutions through microtubes
- Bidhan Chandra, V. Shankar, Debopam Das
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- Journal:
- Journal of Fluid Mechanics / Volume 844 / 10 June 2018
- Published online by Cambridge University Press:
- 16 April 2018, pp. 1052-1083
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Experiments are performed to characterize the onset of laminar–turbulent transition in the flow of high-molecular-weight polymer solutions in rigid microtubes of diameters in the range $390~\unicode[STIX]{x03BC}\text{m}{-}470~\unicode[STIX]{x03BC}\text{m}$ using the micro-PIV technique. By considering flow in tubes of such small diameters, the present study probes higher values of elasticity numbers ($E\equiv \unicode[STIX]{x1D706}\unicode[STIX]{x1D708}/R^{2}$) compared to existing studies, where $\unicode[STIX]{x1D706}$ is the longest relaxation time of the polymer solution, $R$ is the tube radius and $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the polymer solution. For the Newtonian case, our experiments indicate that the natural transition (without the aid of any forcing mechanism) occurs at Reynolds number ($Re$) $2000\pm 100$. As the concentration of polymer is increased, initially there is a delay in the onset of the transition and the transition Reynolds number increases to $2500$. Further increase in concentration of the polymer results in a decrease in the Reynolds number for transition. At sufficiently high concentrations, the added polymer tends to destabilize the flow and the transition is observed to happen at $Re$ as low as $800$. It is also observed that the addition of polymers, regardless of their concentration, reduces the magnitude of the velocity fluctuations after transition. Dye-stream visualization is further used to corroborate the onset of transition in the flow of polymer solutions. The present work thus shows that addition of polymer, at sufficiently high concentrations, destabilizes the flow when compared to that of a Newtonian fluid, thereby providing additional evidence for ‘early transition’ or ‘elasto-inertial turbulence’ in the flow of polymer solutions. The data for the transition Reynolds number $Re_{t}$ from our experiments (for tubes of different diameters, and for two different polymers at varying concentrations) collapse well according to the scaling relation $Re_{t}\propto 1/\sqrt{E(1-\unicode[STIX]{x1D6FD})}$, where $\unicode[STIX]{x1D6FD}$ is the ratio of solvent viscosity to the viscosity of the polymer solution.
Global instability analysis and experiments on buoyant plumes
- Kuchimanchi K. Bharadwaj, Debopam Das
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- Journal:
- Journal of Fluid Mechanics / Volume 832 / 10 December 2017
- Published online by Cambridge University Press:
- 26 October 2017, pp. 97-145
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The present work investigates the puffing instability of circular buoyant plumes by performing global linear stability analysis and experiments. In the non-dimensional parameter space investigated, plumes exhibit global instability only for axisymmetric perturbations with two unstable modes, which are of oscillatory type. The frequencies of these two unstable global modes agree well with the experiments which suggest that puffing occurs in buoyant plumes as a result of linear global instability. A comprehensive investigation on the effect of various non-dimensional parameters and inlet velocity profiles on frequency and growth rates of the global modes is carried out. The results are used to delineate the stability boundaries for these global modes and to obtain scaling laws for the associated oscillation frequencies. The analysis demonstrates that the two buoyancy parameters, Froude number and source-to-ambient density ratio, play dominant roles in impacting plume transition and oscillation frequencies. Results from global linear stability analysis and earlier experiments have majorly differed in two aspects. The earlier experiments reported a switch in puffing frequency scaling in Richardson number range 100–500, while the instability analysis predicts this switch at around 6000. Also, the instability analysis predicts the occurrence of puffing at density ratios higher than the critical value 0.5–0.6 reported in earlier experiments. To address these differences and validate the results obtained from global linear stability analysis, experiments are performed in a set-up that has been carefully designed to minimize the settling chamber disturbances. The present experiments corroborate the findings of global linear stability analysis. The mechanisms responsible for global instability in plumes have been identified using perturbation vorticity transport equation.
Generation and characteristics of vortex rings free of piston vortex and stopping vortex effects
- Debopam Das, M. Bansal, A. Manghnani
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- Journal of Fluid Mechanics / Volume 811 / 25 January 2017
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- 06 December 2016, pp. 138-167
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This paper presents a novel method for generating vortex rings that circumvents some of the drawbacks associated with existing methods in producing them. The predominant effects that occur in previously used methods are due to the presence of some of the other vortices such as the stopping vortex, piston vortex, image vortex and orifice lip generated vortices in the early stage of development. These disturbances influence the geometric, kinematic and dynamic characteristics of a vortex ring and lead to mismatches with classical theoretical predictions. It is shown in the present study that the disturbance free vortex rings produced follow the classical theory. Flow visualization and particle image velocimetry experiments are carried out in the Reynolds number (defined as the ratio of circulation ($\unicode[STIX]{x1D6E4}$) and kinematic viscosity ($\unicode[STIX]{x1D708}$)) range, $2270<Re_{\unicode[STIX]{x1D6E4}}<6790$, to find the translational velocity, total and core circulation, core diameter, ring diameter and bubble diameter. In reference to the earlier studies, significant differences are noted in the variations of the vortex ring diameter and core diameter. A model for the core diameter during the formation stage is proposed. The translational velocity variation with time shows that the second-order accurate formula derived using Hamilton’s equation by Fraenkel (J. Fluid Mech., vol. 51, 1972, pp. 119–135) predicts it best.
Axial interaction of a vortex ring with a cylinder
- Debopam Das, Akash Manghnani, Mohit Bansal, Prafulla Sohoni
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- Journal of Fluid Mechanics / Volume 809 / 25 December 2016
- Published online by Cambridge University Press:
- 09 November 2016, pp. 1-30
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In this paper, axial interaction of a vortex ring with a thin circular cylinder has been studied. An apparatus to generate clean vortex rings, free of piston and stopping vortex effects, has been used. Flow visualization and particle image velocimetry (PIV) experiments are carried out to determine and compare the characteristics of free and interacting vortex rings in the Reynolds number (defined with the circulation of the free travelling vortex ring) range of $2270<Re_{\unicode[STIX]{x1D6E4}}<6790$. It is observed that due to the presence of the cylinder, there is an increase in the velocity of the vortex ring. Also, noticeable changes in the characteristic properties of vortex ring such as core circulation, core diameter and ring diameter have been observed. Changes in these parameters are explained by two changes in the flow field between the vortex ring and the cylinder due to axial interactions: (i) displacement of the streamlines and (ii) acceleration in the induced velocity field in this region. These two mutually opposing effects determine the changes in the primary vortex ring properties that take place during interaction. To justify these experimental observations quantitatively, an analytical study of the interaction under an inviscid assumption is performed. The inviscid analysis does predict the increase in velocity during the interaction, but fails to predict the values observed in the present experiments. However, when the theory is used to correct the velocity change through incorporation of the effects of an axisymmetric induced boundary layer region over the cylinder, modelled as an annular vortex sheet of varying strength, the changes in the translational velocities of the vortex rings match closely with the experimental values.
Role of slipstream instability in formation of counter-rotating vortex rings ahead of a compressible vortex ring
- C. L. Dora, T. Murugan, S. De, Debopam Das
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- Journal:
- Journal of Fluid Mechanics / Volume 753 / 25 August 2014
- Published online by Cambridge University Press:
- 16 July 2014, pp. 29-48
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Counter-rotating vortex rings (CRVRs) are observed to form ahead of a primary compressible vortex ring that is generated at the open end of a shock tube at sufficiently high Mach numbers. In most of the earlier studies, the embedded shock strength has been asserted as the cause for the formation of CRVRs. In the present study, particle image velocimetry (PIV) measurements and high-order numerical simulations show that CRVRs do not form in the absence of a Mach disk in the sonic under-expanded jet behind the primary vortex ring. Kelvin–Helmholtz-type shear flow instability of the slipstream originating from the triple point of the Mach disk and subsequent eddy pairing, as observed by Rikanati et al. (Phys. Rev. Lett., vol. 96, 2006, art. 174503) in shock-wave Mach reflection, is found to be responsible for CRVR formation. The growth rate of the slipstream in the present problem follows the model proposed by them. The parameters influencing the formation of CRVRs as well as their dynamics is investigated. It is found that the strength of the Mach disk and its duration of persistence results in an exit impulse that determines the number of CRVRs formed.
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.
Transition of unsteady velocity profiles with reverse flow
- DEBOPAM DAS, JAYWANT H. ARAKERI
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- Journal:
- Journal of Fluid Mechanics / Volume 374 / 10 November 1998
- Published online by Cambridge University Press:
- 10 November 1998, pp. 251-283
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This paper deals with the stability and transition to turbulence of wall-bounded unsteady velocity profiles with reverse flow. Such flows occur, for example, during unsteady boundary layer separation and in oscillating pipe flow. The main focus is on results from experiments in time-developing flow in a long pipe, which is decelerated rapidly. The flow is generated by the controlled motion of a piston. We obtain analytical solutions for laminar flow in the pipe and in a two-dimensional channel for arbitrary piston motions. By changing the piston speed and the length of piston travel we cover a range of values of Reynolds number and boundary layer thickness. The velocity profiles during the decay of the flow are unsteady with reverse flow near the wall, and are highly unstable due to their inflectional nature. In the pipe, we observe from flow visualization that the flow becomes unstable with the formation of what appears to be a helical vortex. The wavelength of the instability ≃3
δ whereδ is the average boundary layer thickness, the average being taken over the time the flow is unstable. The time of formation of the vortices scales with the average convective time scale and is ≃39/(Δ ū/δ ), where Δu=(umax−umin) and umax, umin and δ are the maximum velocity, minimum velocity and boundary layer thickness respectively at each instant of time. The time to transition to turbulence is ≃33/(Δ ū/δ ). Quasi-steady linear stability analysis of the velocity profiles brings out two important results. First that the stability characteristics of velocity profiles with reverse flow near the wall collapse when scaled with the above variables. Second that the wavenumber corresponding to maximum growth does not change much during the instability even though the velocity profile does change substantially. Using the results from the experiments and the stability analysis, we are able to explain many aspects of transition in oscillating pipe flow. We postulate that unsteady boundary layer separation at high Reynolds numbers is probably related to instability of the reverse flow region.