Understanding evolution of vortex rings in viscous fluids
01 Nov 2017-
TL;DR: In this article, the evolution of vortex rings in isodensity and isoviscosity fluid has been studied analytically using a novel mathematical model, which predicts the spatiotemporal variation in peak vorticity, circulation, vortex size and spacing based on instantaneous vortex parameters.
Abstract: 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 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 , where is the vortex half-spacing and denotes the standard deviation of the Gaussian vorticity profile, governs the regime of vortex evolution. For higher values of , evolution follows short-time behaviour, while for , long-time behaviour is prominent. Using this theory, many reported anomalous observations have been explained.
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01 Feb 2019-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, a parametric study of the tapping process and its analysis confirmed that the threshold height for drain vortices is strongly influenced by the nozzle diameter and marginally influenced by residual inertia of the liquid.
Abstract: In a modern integrated steel plant, slag-free tapping during transfer of liquid steel from the BOF vessel to the ladle is prerequisite to produce ultraclean steel for high-end critical applications. The present investigation aims to examine the drain vortices during the liquid steel tapping process. The tapping experiments were conducted in a geometrical down-scaled Perspex BOF cold model, which was more akin to the industrial practice than the other geometries previously reported in the literature. The study highlights the influence of the complex BOF shape on drain vortices during the tapping process. It is observed that vorticity behavior during liquid steel tapping from the BOF vessel is different from the earlier observations reported for the teeming process. The parametric study of the tapping process and its analysis confirmed that the threshold height for drain vortices is strongly influenced by the nozzle diameter (ND) and marginally influenced by the residual inertia of the liquid. The carryover ratio (COR) for the water-oil experiments is in agreement with the values obtained in industrial practice. Yield loss tends to increase with the increase in ND. The onset of drain vortices in the presence of overlying phase (oil/slag) during the BOF tapping process could be principally controlled by the vessel design. The physical properties of the overlying phase had negligible influence on the drain vortices. The critical times for vortex and drain sink formation were predicted based on dimensional analysis coupled with the mathematical formulation for the tapping process. A strategy to control the slag carryover during the tapping process in industry is also discussed and postulated based on the understanding developed from water modeling experiments.
8 citations
TL;DR: In this paper, the formation and evolution of vortex rings in both unconfined and confined configurations was investigated in dense suspensions with volume fractions up to, and it was shown that vortex-ring circulation and non-dimensional vortex-core radius remain higher than those in pure water at the same equivalent Reynolds number.
Abstract: An experimental study of particle–vortex interactions has been undertaken in suspensions with volume fractions up to . Time-resolved particle image velocimetry measurements using a refractive index matching technique were performed to characterize the formation and evolution of vortex rings in both unconfined and confined configurations. It is shown that vortex rings in dense suspensions are more diffuse, which results in larger vortex cores and lower maximum vorticity. Furthermore, these vortex rings remain stable during their evolution, whereby the primary vortex breakdown and the formation of secondary vortices are inhibited. Although similar to vortex rings generated at lower Reynolds numbers in pure water, further results demonstrate that the vortex-ring circulation and non-dimensional vortex-core radius in dense suspensions remain higher than those in pure water at the same equivalent Reynolds number. Thus, the modification of vortex-ring behaviour in dense suspensions cannot be described solely through a variation in the effective viscosity. Finally, unlike in pure water, the confinement does not impact the non-dimensional vortex-core radius, vortex-ring circulation and maximum vorticity in dense suspensions. This unusual result demonstrates that the dynamics of vortex rings in dense suspensions are strongly insensitive to the effect of confinement.
7 citations
TL;DR: A novel, cost-effective, portable, complex flow phantom is proposed and the design specifications are provided, which employs a piston/cylinder system for vortex ring generation, coupled to an imaging tank full of fluid, for vortex propagation.
Abstract: Cardiovascular fluid dynamics exhibit complex flow patterns, such as recirculation and vortices. Quantitative analysis of these complexities supports diagnosis, leading to early prediction ...
4 citations
TL;DR: In this article, high-speed imaging was used to investigate the heat transfer and melting dynamics of spherical ice particles impacting heated water baths of varying temperatures (23-70°C) with velocities ranging from 0.8 to 2.1
4 citations
TL;DR: In this paper, the evolution of a vortex ring generated by drop impinging on a liquid pool is examined in terms of its ring radius, core radius, translational velocity, vorticity, and circulation.
Abstract: The evolution of a vortex ring generated by drop impinging on a liquid pool is experimentally, numerically, and analytically investigated. The effect of impingement heights and shapes of the drops on the evolution of the vortex ring are examined in terms of its ring radius, core radius, translational velocity, vorticity, and circulation. We develop a novel analytical model for a finite vortex core to study its evolution in terms of the aforementioned parameters. We verify the proposed model and compare the other existing models with the corresponding experimental results obtained from the drop impingement method. The mathematical model is suitable for predicting both short-time and long-time behavior of the vortex ring in a unified manner. The analytical study unveils the controlling parameters that govern the viscous diffusion-driven evolution of the vortex ring. The circulation dynamics of the ring for the drop impingement method, which has received very little attention, is also experimentally investigated. The Lagrangian particle tracking method is used to study the circulation dynamics of the vortex ring. The combined study of experimental and numerical results, in conjunction with the analytical approach, provides useful insights into the formation of the vortex ring and its viscous diffusion process.
4 citations
References
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01 Jan 1967TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Abstract: Preface Conventions and notation 1. The physical properties of fluids 2. Kinematics of the flow field 3. Equations governing the motion of a fluid 4. Flow of a uniform incompressible viscous fluid 5. Flow at large Reynolds number: effects of viscosity 6. Irrotational flow theory and its applications 7. Flow of effectively inviscid liquid with vorticity Appendices.
11,187 citations
TL;DR: An index of the potential destructiveness of hurricanes based on the total dissipation of power, integrated over the lifetime of the cyclone, is defined and shows that this index has increased markedly since the mid-1970s, due to both longer storm lifetimes and greater storm intensities.
Abstract: Theory and modelling predict that hurricane intensity should increase with increasing global mean temperatures, but work on the detection of trends in hurricane activity has focused mostly on their frequency and shows no trend. Here I define an index of the potential destructiveness of hurricanes based on the total dissipation of power, integrated over the lifetime of the cyclone, and show that this index has increased markedly since the mid-1970s. This trend is due to both longer storm lifetimes and greater storm intensities. I find that the record of net hurricane power dissipation is highly correlated with tropical sea surface temperature, reflecting well-documented climate signals, including multi-decadal oscillations in the North Atlantic and North Pacific, and global warming. My results suggest that future warming may lead to an upward trend in tropical cyclone destructive potential, and--taking into account an increasing coastal population--a substantial increase in hurricane-related losses in the twenty-first century.
3,518 citations
TL;DR: The formation of vortex rings generated through impulsively started jets is studied experimentally in this paper, where the velocity and vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet.
Abstract: The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.
1,042 citations
TL;DR: In this paper, dynamique des : fluides reference record created on 2005-11-18, modified on 2016-08-08 was used for dynamique de fluides Reference Record.
Abstract: Keywords: dynamique des : fluides Reference Record created on 2005-11-18, modified on 2016-08-08
804 citations
TL;DR: In this paper, a set of six non-dimensional parameters that are the most significant in optimizing particle image velocimeter performance are identified, which are the data validation criterion, the particle image density, the relative in-plane image displacement, a velocity gradient parameter, and the ratio of the mean image diameter to the interrogation spot diameter.
Abstract: The spatial resolution, detection rate, accuracy and reliability of a particle image velocimeter (PIV) depend critically upon the careful selection of a number of parameters of the PIV system and the fluid motion. An analytical model and a Monte Carlo computer simulation have been developed to analyse the effects of experimental parameters and to optimize the system parameters. A set of six nondimensional parameters that are the most significant in optimizing PIV performance are identified. They are the data validation criterion, the particle image density, the relative in-plane image displacement, the relative out-of-plane displacement, a velocity gradient parameter, and the ratio of the mean image diameter to the interrogation spot diameter. These parameters are studied for the case of interrogation by autocorrelation analysis. By a single transformation, these results can be applied to interrogation by two-dimensional Fourier transform analysis of the Young's fringes.
762 citations