Understanding evolution of vortex rings in viscous fluids

2017 ◽  
Vol 836 ◽  
pp. 873-909 ◽  
Author(s):  
Aashay Tinaikar ◽  
S. Advaith ◽  
S. Basu
Keyword(s):  
High Speed ◽  
Initial Conditions ◽  
Operating Conditions ◽  
Force Balance ◽  
Vortex Rings ◽  
Time Behaviour ◽  
Theoretical Predictions ◽  
Long Time ◽  
Vortex Size ◽  
Short Time

The evolution of vortex rings in isodensity and isoviscosity fluid has been studied analytically using a novel mathematical model. The model predicts the spatiotemporal variation in peak vorticity, circulation, vortex size and spacing based on instantaneous vortex parameters. This proposed model is quantitatively verified using experimental measurements. Experiments are conducted using high-speed particle image velocimetry (PIV) and laser induced fluorescence (LIF) techniques. Non-buoyant vortex rings are generated from a nozzle using a constant hydrostatic pressure tank. The vortex Reynolds number based on circulation $(\unicode[STIX]{x1D6E4}/\unicode[STIX]{x1D708})$ is varied in the range 100–1500 to account for a large range of operating conditions. Experimental results show good agreement with theoretical predictions. However, it is observed that neither Saffman’s thin-core model nor the thick-core equations could correctly explain vortex evolution for all initial conditions. Therefore, a transitional theory is framed using force balance equations which seamlessly integrate short- and long-time asymptotic theories. It is found that the parameter $A=(a/\unicode[STIX]{x1D70E})^{2}$, where $a$ is the vortex half-spacing and $\unicode[STIX]{x1D70E}$ denotes the standard deviation of the Gaussian vorticity profile, governs the regime of vortex evolution. For higher values of $A$, evolution follows short-time behaviour, while for $A=O(1)$, long-time behaviour is prominent. Using this theory, many reported anomalous observations have been explained.

scholarly journals Free radially expanding liquid sheet in air: time- and space-resolved measurement of the thickness field

2015 ◽  
Vol 764 ◽  
pp. 428-444 ◽  
Author(s):  
C. Vernay ◽  
L. Ramos ◽  
C. Ligoure
Keyword(s):  
High Speed ◽  
Liquid Sheet ◽  
Radial Position ◽  
Maximum Diameter ◽  
Time And Space ◽  
Level Measurement ◽  
Time Regime ◽  
Long Time ◽  
Short Time ◽  
Thickness Field

AbstractThe collision of a liquid drop against a small target results in the formation of a thin liquid sheet that extends radially until it reaches a maximum diameter. The subsequent retraction is due to the air–liquid surface tension. We have used a time- and space-resolved technique to measure the thickness field of this class of liquid sheet, based on the grey-level measurement of the image of a dyed liquid sheet recorded using a high-speed camera. This method enables a precise measurement of the thickness in the range $10{-}450~{\rm\mu}\text{m}$, with a temporal resolution equal to that of the camera. We have measured the evolution with time since impact, $t$, and radial position, $r$, of the thickness, $h(r,t)$, for various drop volumes and impact velocities. Two asymptotic regimes for the expansion of the sheet are evidenced. The scalings of the thickness with $t$ and $r$ measured in the two regimes are those that were predicted by Rozhkov et al. (Proc. R. Soc. Lond. A, vol. 460, 2004, pp. 2681–2704) for the short-time regime and Villermaux and Bossa (J. Fluid Mech., vol. 668, 2011, pp. 412–435) for the long-time regime, but never experimentally measured before. Interestingly, our experimental data also provide evidence for the existence of a maximum of the film thickness $h_{max}(r)$ at a radial position $r_{h_{max}}(t)$ corresponding to the cross-over of these two asymptotic regimes. The maximum moves with a constant velocity of the order of the drop impact velocity, as expected theoretically. Thanks to our visualization technique, we also provide evidence of an azimuthal thickness modulation of the liquid sheets.

Perturbation dynamics in unsteady pipe flows

2007 ◽  
Vol 570 ◽  
pp. 129-154 ◽  
Author(s):  
M. ZHAO ◽  
M. S. GHIDAOUI ◽  
A. A. KOLYSHKIN
Keyword(s):  
Growth Mechanism ◽  
Flow Instability ◽  
Initial Conditions ◽  
Laminar Flows ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Transient Growth ◽  
Energy Growth ◽  
Long Time ◽  
Short Time

This paper deals with perturbed unsteady laminar flows in a pipe. Three types of flows are considered: a flow accelerated from rest; a flow in a pipe generated by the controlled motion of a piston; and a water hammer flow where the transient is generated by the instantaneous closure of a valve. Methods of linear stability theory are used to analyse the behaviour of small perturbations in the flow. Since the base flow is unsteady, the linearized problem is formulated as an initial-value problem. This allows us to consider arbitrary initial conditions and describe both short-time and long-time evolution of the flow. The role of initial conditions on short-time transients is investigated. It is shown that the phenomenon of transient growth is not associated with a certain type of initial conditions. Perturbation dynamics is also studied for long times. In addition, optimal perturbations, i.e. initial perturbations that maximize the energy growth, are determined for all three types of flow discussed. Despite the fact that these optimal perturbations, most probably, will not occur in practice, they do provide an upper bound for energy growth and can be used as a point of reference. Results of numerical simulation are compared with previous experimental data. The comparison with data for accelerated flows shows that the instability cannot be explained by long-time asymptotics. In particular, the method of normal modes applied with the quasi-steady assumption will fail to predict the flow instability. In contrast, the transient growth mechanism may be used to explain transition since experimental transition time is found to be in the interval where the energy of perturbation experiences substantial growth. Instability of rapidly decelerated flows is found to be associated with asymptotic growth mechanism. Energy growth of perturbations is used in an attempt to explain previous experimental results. Numerical results show satisfactory agreement with the experimental features such as the wavelength of the most unstable mode and the structure of the most unstable disturbance. The validity of the quasi-steady assumption for stability studies of unsteady non-periodic laminar flows is discussed.

Effects of heat conduction in a wall on thermoacoustic-wave propagation

2012 ◽  
Vol 697 ◽  
pp. 60-91 ◽  
Author(s):  
N. Sugimoto ◽  
H. Hyodo
Keyword(s):  
Wave Propagation ◽  
Heat Conduction ◽  
Asymptotic Expansions ◽  
Wave Equations ◽  
Solid Wall ◽  
Time Behaviour ◽  
Dynamical Equations ◽  
Long Time Behaviour ◽  
Long Time ◽  
Short Time

AbstractThis paper examines the effects of heat conduction in a wall on thermoacoustic-wave propagation in a gas, as a continuation of the previous paper (Sugimoto, J. Fluid Mech., 2010, vol. 658, pp. 89–116), enclosed in two-dimensional channels by a stack of plates or in a periodic array of circular tubes, both being subject to a temperature gradient axially and extending infinitely. Within the narrow-tube approximation employed previously, the linearized system of fluid-dynamical equations for the ideal gas coupled with the equation for heat conduction in the solid wall are reduced to single thermoacoustic-wave equations in the respective cases. In this process, temperatures of the gas and the solid wall are sought to the first order of asymptotic expansions in a small parameter determined by the square root of the product of the ratio of heat capacity of gas per volume to that of the solid, and the ratio of thermal conductivity of the gas to that of the solid. The effects of heat conduction introduce into the equation two hereditary terms due to triple coupling among viscous diffusion, thermal diffusion of the gas and that of the solid, and due to double coupling between thermal diffusions of the gas and solid. While the thermoacoutic-wave equations are valid always for any form of disturbances generally, approximate equations are derived from them for a short-time behaviour and a long-time behaviour. For the short-time behaviour, the effects of heat conduction are negligible, while for the long-time behaviour, they will affect the propagation as a wall becomes thinner. It is unveiled that when the geometry of the channels or the tubes, and the combination of the gas and the solid satisfy special conditions, the asymptotic expansions exhibit non-uniformity, i.e. a resonance occurs, and then the thermoacoustic-wave equations break down. Discussion is given on modifications in the resonant case by taking full account of the effects of heat conduction, and also on the effects on the acoustic fields.

scholarly journals Dynamic Coefficients Identification of Water-Lubricated Hybrid Bearings Used in High-Speed Spindles with Different Excitation Methods

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Lin Wang ◽  
Xianzhi Xiong ◽  
Hua Xu
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Harmonic Excitation ◽  
Operating Conditions ◽  
Rotating Speed ◽  
Dynamic Coefficients ◽  
Supply Pressure ◽  
Theoretical Predictions ◽  
Coefficients Identification ◽  
Excitation Method

Rotor stability and rotation accuracy, which are highly dependent on the dynamic coefficients of supporting hybrid bearings, are two important issues of high-speed water-lubricated spindles. To improve the spindles’ performance, the dynamic coefficients of high-speed water-lubricated hybrid bearings were experimentally identified by the noncontact harmonic excitation method and the additional unbalance excitation method, respectively. Comparisons between experimental results and theoretical predictions were made. The experimental technique and the identification model were validated to be effective. Besides, the influence of supply pressure and rotating speed on dynamic coefficients was also presented. As for different operating conditions, valuable guides were provided to investigate the dynamic performance of high-speed and ultra-high-speed spindles.

Thermoacoustic-wave equations for gas in a channel and a tube subject to temperature gradient

2010 ◽  
Vol 658 ◽  
pp. 89-116 ◽  
Author(s):  
N. SUGIMOTO
Keyword(s):  
Temperature Gradient ◽  
Diffusion Layer ◽  
Acoustic Waves ◽  
Deborah Number ◽  
Span Length ◽  
Time Behaviour ◽  
Initial State ◽  
Long Time Behaviour ◽  
Long Time ◽  
Short Time

This paper develops a general theory for linear propagation of acoustic waves in a gas enclosed in a two-dimensional channel and in a circular tube subject to temperature gradient axially and extending infinitely. A ‘narrow-tube approximation’ is employed by assuming that a typical axial length is much longer than a span length, but no restriction on a thickness of thermoviscous diffusion layer is made. For each case, basic equations in this approximation are reduced to a spatially one-dimensional equation in terms of an excess pressure by making use of a method of Fourier transform. This equation, called a thermoacoustic-wave equation, is given in the form of an integro-differential equation due to memory by thermoviscous effects. Approximations of the equations for a short-time and a long-time behaviour from an initial state are discussed based on the Deborah number and the Reynolds number. It is shown that the short-time behaviour is well approximated by the equation derived previously by the boundary-layer theory, while the long-time behaviour is described by new diffusion equations. It is revealed that if the diffusion layer is thicker than the span length, the thermoviscous effects give rise to not only diffusion but also wave propagation by combined action with temperature gradient, and that negative diffusion may occur if the gradient is steep.

scholarly journals Dispersive shock waves in viscously deformable media

2013 ◽  
Vol 718 ◽  
pp. 524-557 ◽  
Author(s):  
Nicholas K. Lowman ◽  
M. A. Hoefer
Keyword(s):  
Shock Waves ◽  
Volume Fraction ◽  
Initial Conditions ◽  
Leading Edge ◽  
Wave Dispersion ◽  
Cross Sectional ◽  
Theoretical Predictions ◽  
Number Dynamics ◽  
Long Time ◽  
Constitutive Parameters

AbstractThe viscously dominated, low-Reynolds-number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behaviour when viewed appropriately. In these systems, nonlinear self-steepening competes with wave dispersion, giving rise to dispersive shock waves (DSWs). Example systems considered here include magma migration through the mantle as well as the buoyant ascent of a low-density fluid through a viscously deformable conduit. These flows are modelled by a third-order, degenerate, dispersive, nonlinear wave equation for the porosity (magma volume fraction) or cross-sectional area, respectively. Whitham averaging theory for step initial conditions is used to compute analytical, closed-form predictions for the DSW speeds and the leading edge amplitude in terms of the constitutive parameters and initial jump height. Novel physical behaviours are identified including backflow and DSW implosion for initial jumps sufficient to cause gradient catastrophe in the Whitham modulation equations. Theoretical predictions are shown to be in excellent agreement with long-time numerical simulations for the case of small- to moderate-amplitude DSWs. Verifiable criteria identifying the breakdown of this modulation theory in the large jump regime, applicable to a wide class of DSW problems, are presented.

scholarly journals Type II migration strikes back – an old paradigm for planet migration in discs

2019 ◽  
Vol 492 (1) ◽  
pp. 1318-1328 ◽  
Author(s):  
Chiara E Scardoni ◽  
Giovanni P Rosotti ◽  
Giuseppe Lodato ◽  
Cathie J Clarke
Keyword(s):  
Initial Conditions ◽  
Giant Planet ◽  
Type Ii ◽  
Standard Type ◽  
Planet Migration ◽  
Theoretical Predictions ◽  
Gap Opening ◽  
Long Time ◽  
Flow Through ◽  
Good Agreement

ABSTRACT In this paper, we analyse giant gap-opening planet migration in proto-planetary discs, focusing on the type II migration regime. According to standard type II theory, planets migrate at the same rate as the gas in the disc, as they are coupled to the disc viscous evolution; however, recent studies questioned this paradigm, suggesting that planets migrate faster than the disc material. We study the problem through 2D long-time simulations of systems consistent with type II regime, using the hydrodynamical grid code fargo3d. Even though our simulations confirm the presence of an initial phase characterized by fast migration, they also reveal that the migration velocity slows down and eventually reaches the theoretical prediction if we allow the system to evolve for enough time. We find the same tendency to evolve towards the theoretical predictions at later times when we analyse the mass flow through the gap and the torques acting on the planet. This transient is related to the initial conditions of our (and previous) simulations, and is due to the fact that the shape of the gap has to adjust to a new profile, once the planet is set into motion. Secondly, we test whether the type II theory expectation that giant planet migration is driven by viscosity is consistent with our simulation by comparing simulations with the same viscosity and different disc masses (or vice versa). We find a good agreement with the theory, since when the discs are characterized by the same viscosity, the migration properties are the same.

scholarly journals Impinging Fluid in Immersed Granular Material to Obtain Local Fluidization for Breaking Sedimentation

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Eko Yudiyanto ◽  
I. Nyoman Gede Wardana ◽  
Nurkholis Hamidi ◽  
Denny Widhiyanuriyawan
Keyword(s):  
Granular Material ◽  
High Speed ◽  
Reynold Number ◽  
Granule Size ◽  
Cavity Expansion ◽  
Cavity Formation ◽  
Long Time ◽  
Granular Behavior ◽  
Short Time ◽  
Fluidization Process

Granular material is the most abundant material type in industry. Efforts to improve the efficiency of handling of granular material are continually ongoing. Sedimentation is one of the problems in transporting this material; when sedimentation occurs, the flow of material is obstructed and requires significant energy to clean the pipelines. The problem of sedimentation in pipes is thus an issue that merits serious attention. To solve the sedimentation problem, it is proposed to use the impinging method, which is a shock flow that is inserted into the granular sediment. This experiment to impinge immersed granular material is proposed to solve this depositional problem. Shooting high-speed fluid in a short time is expected to be one of the methods of preventing sedimentation that occurs in handling granular material. The material used in this experiment varies in granule size: very fine, fine, and medium-sized granules. These experiments provide an overview of post-impinging granular behavior with fluidization movement. For very fine granular size, post-impinging fluid cavity expansion occurs, followed by slow fluidization. This fluidization movement occurs for a long time. For fine granules, fluid cavity formation happens much faster, and fluidization occurs immediately. For medium-sized granules, post-impinging fluidization occurs immediately. To measure the impinging process to produce fluidization, the Reynold Number of Impinging (Re*) is used. The fluidization process occurs at Re* < 4000. The internal fluidization movements occur mainly at Re* values 2000-4000 (i.e. transition regions).

scholarly journals Influence of angled dispersion gas on coaxial atomization, spray and flame formation in the context of spray-flame synthesis of nanoparticles

2021 ◽  
Vol 62 (5) ◽  
Author(s):  
M. Bieber ◽  
M. Al-Khatib ◽  
F. Fröde ◽  
H. Pitsch ◽  
M. A. Reddemann ◽  
...  
Keyword(s):  
High Speed ◽  
Gas Flow ◽  
Initial Conditions ◽  
Operating Conditions ◽  
Nozzle Geometry ◽  
Flame Stability ◽  
Final Particle ◽  
Synthesis Of Nanoparticles ◽  
Spray Formation ◽  
Spray Flame

Abstract Liquid atomization determines the initial conditions for flame formation and particle synthesis. Without a stable flame, high droplet velocities and thus short droplet residence time in the flame may lead to droplets being injected into an extinguished flame, which influences synthesis and final particle output. An experimental investigation of spray formation and flame stability is performed through high-speed visualization. Targeted variation of nozzle geometry is applied to improve spray-flame interaction and compared to a standardized burner. Timescales of spray density and flame fluctuations are quantified and compared, where the latter were significantly larger and hence not correlated. Instead, dispersion gas forms a barrier between spray phase and pilot flame; hence, ignition depends on large liquid lumps with high radial momentum to break through the dispersion gas for spray ignition. Angling of dispersion gas flow increases radial shear and turbulence and leads to refined atomization and improved flame stability. To investigate the nozzle influence on particle formation, particle characteristics are examined by online and offline analytics with focus on particle structures and product purity. The modified nozzle produced smaller primary particle sizes, thus indicating a sensitivity of sintering dominance on the nozzle geometry. Impurities impact the examination of particle structures and general particle functionality. Carbon contamination was apparent in synthesized particles and also indicated sensitivity to nozzle geometry. Discrepancies to literature data are discussed regarding differences in flame activity and droplet characteristics. The report highlights, how product characteristics can differ crucially due to changes in nozzle geometry despite comparable operating conditions. Graphic abstract

Sign in / Sign up

Export Citation Format

Share Document