Burgers Vortex Model Research Articles

Entrainment, detrainment and enstrophy transport by small-scale vortex structures

The interaction of small-scale vortical structures with the surrounding fluid are studied using a fully resolved three-dimensional experimental data set of homogeneous turbulence measured at the centre of a von Kármán mixing flow facility and a direct numerical simulation (DNS) data set of forced isotropic turbulence. To identify the small-scale vortices and their boundaries, an objective observer-independent definition was implemented to avoid arbitrariness and is the first implementation applied to experimental measurements of small-scale turbulence. Volume-averaged and conditional statistics are presented to demonstrate consistency between the experimental and DNS data sets. To examine the interaction of the structures with the surrounding flow field, we examine the flow across the boundary of vortex structures by adopting a similar methodological approach to that used to investigate the local entrainment and detrainment across the turbulent–non-turbulent interface. The probability density function (p.d.f.) of entrainment velocity conditioned on the vortex boundary exhibited a non-Gaussian distribution that skewed slightly in favour of entrainment and is remarkably similar to the p.d.f.s of entrainment velocity observed in boundary layers and jets. We analyse the enstrophy transport equation conditioned on radial and axial coordinates of the vortices to quantify the inviscid and viscous components of the entrainment/detrainment process. A comparison with Burgers vortices is made and it is found that the Burgers vortex model captures the vortex structure average size and the mechanisms of enstrophy transport in the radial direction, but is unable to capture local statistics and describe the governing physics along the axes of the vortices.

Numerical and experimental investigation on the effect of heat release rate in the evolution of fire whirls

Buildings with large internal spaces, such as vertical shafts or atria, are widespread nowadays. In the case of fire, internal air currents may generate devastating fire whirls that can cause severe damage due to intensive heat release rate (HRR) and temperatures. This work presents the generation and evolution of fire whirls in a full-scale atrium experiment and their comparison with a numerical approach. A set of numerical models using FDS 6.7.5 are tested to assess the influence of the HRR curve and the impact of intrusive methods of temperature measurements on the prediction of whirls. The results show that the Burgers vortex model is well reproduced, although the continuous flame and plume regions can only be distinguished with fine grids. However, the periodic evolution of the whirls is better predicted with a time-averaged HRR curve, showing its influence on the flame height. The use of the experimental HRR curve presents more accurate results only in the temperatures far from the flame, with errors lower than 8.5% even for coarse grids. In addition, a small obstacle above the flame is observed to affect the formation of the whirls, which consequently impacts the grid sensitivity and computational cost.

Gas entrainment in the mock-up of the upper plenum of a sodium cooled reactor

The CEA intends to develop 4th generation sodium fast neutron reactors. From the state of art of the former operating sodium reactors PHENIX and SUPER-PHENIX and the past program EFR (European Fast Reactor) most global and the local thermal–hydraulic issues have been identified. However, the results of those previous projects do not fulfill for the current development requirement and safety standard. New experimental means are needed, especially for both validation of numerical codes and specific studies. In this way, a thermal–hydraulic loop, the PLATEAU facility, was developed and erected at the CEA Cadarache research center in 2012. Since experiments with sodium are complex to carry out, the tests are led in models using water as simulant fluid. Different mock-ups can be connected to this loop to study the different issues at various reactor conditions. The first model connected to the PLATEAU facility is MICAS, mock-up of the hot plenum. This one is dedicated to study the flow regime, both for code validation and engineering design development. It was designed at 1/6 scale from a 600MWe reactor design and was built in transparent polymer to carry out optical measurements as laser velocimetry and fast imaging.Gas entrainment by vortex is one of the issues identified and can have an impact on the vessel design. Gas occurrence in the core induces neutron effects which may lead to core reactivity variation. Gas entrainment was investigated at the MICAS free surface using fast imaging. A tendency regarding the geometry and the operating parameters was identified. More investigations were focused on the velocity field around the vortices in the way to develop a gas entrainment criterion. Two types of vortex occur at the free surface: those which induce gas entrainment, and those which do not. By the used of the Burgers vortex model, the downward velocity gradient and the circulation are identified as parameters influencing the gas entrainment. From the tangential velocity measured by particles image velocimetry around various types of vortex, the downward velocity gradient and the circulation were calculated using the Burgers model. Results showed that the Burgers model fit the experimental tangential velocity. Depending on the gas entrainment occurrence among the different studied vortex, a value for the gas entrainment criterion was found.

Effects of vortexes in feed header on air flow distribution of PEMFC stack: CFD simulation and optimization for better uniformity

Distribution uniformity is critical to achieve high performance for proton exchange membrane fuel cell (PEMFC) stacks. In this work, air flow distribution of a 30 kW “U-type” stack of 100 unit cells is investigated by computational fluid dynamics (CFD) simulation, Burgers vortex model is introduced to describe the mechanism of flow maldistribution. Three cases are presented to evaluate the effects of vortexes on the distribution uniformity under various average current densities, and obtain optimized design for better uniformity. The results show that the vortexes usually generate in the feed header, the flow vortex structures are governed by the feed header’s configuration. The distribution uniformity reduces dramatically with the increase of current density and the generation of vortexes. The cells that locate in the positions of vortexes get less flow allocation than other cells, distribution uniformity can improve by optimizing the feed header’s configuration to change the vortex structure of flow field.

Understanding droplet collisions through a model flow: Insights from a Burgers vortex.

We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significantly enhances sharp inhomogeneities in spatial particle densities, related to the rapid ejection of particles from intense vortices. Furthermore our work shows how such spatial clustering leads to an enhancement of collision rates and extreme statistics of collisional velocities. We also study the role of polydisperse suspensions in this enhancement. Our work uncovers an important principle, which, if valid for realistic turbulent flows, may be a factor in how small nuclei water droplets in warm clouds can aggregate to sizes large enough to trigger rain.

Experimental study on the 3D-flow field of a free-surface vortex using stereo PIV

ABSTRACTIn order to analyse the flow characteristics of free-surface vortexes and to validate the Burgers vortex model by using stereo particle image velocimetry, experiments are conducted in a 600 mm diameter vortex tank. Measured axial velocities indicate that 10–25% of the flow is transported through the vortex core. The velocity profiles show that the axial flow is concentrated in a domain bounded by two times the core radius. Despite Burgers’ assumption of radially independent axial velocity profiles, the model quantifies the tangential velocity profile within a relative uncertainty of circa 10%. The measurements show that it seems valid to use Burgers’ model to obtain an estimate for the core radius by taking the average axial velocity over a radial domain of approximately 2.2 times the core radius. The Burgers model quantifies the air core depth with an uncertainty of 20% relative to the measurements. When compared with the magnitude of vorticity diffusion by molecular viscosity, the experiments show that there is no significant diffusion by radial turbulence.

Evaluation of vortex identification methods based on two- and three-dimensional swirling strengths

Analytical solutions for two-dimensional (2D) and three-dimensional (3D) swirling strengths were derived and were used to simulate the detection of 3D vortices in planar Particle Image Velocimetry (PIV). Based on Euler’s rotation theorem and the Burgers vortex model, a general equation for the 2D swirling strength of a 3D vortex having an arbitrary inclination angle with the analyzed plane was proposed. Vortices were classified into two categories: strong vortices and weak vortices. When focusing only on strong vortices, previous studies reported that the ratio of the two swirling strengths varies as a sine function; however, we found that this ratio is a function of both circulation and inclination angle, and the relative deviation between the ratio function and the sine function exhibits a monotonous decrease with increasing circulation. When vortices are classified into different categories according to the circulation, the analytical solution fits well with data points in each category. Theoretical analysis reveals that the detection of a 3D vortex in planar PIV has a dependence on two factors (circulation and inclination angle) and the detection probability of a 3D vortex with a certain inclination angle in planar PIV was simulated. For example, detection probabilities of 3D vortices with inclination angles of 10°, 30°, 50°, and 90° are 10%, 46%, 81%, and 100%, respectively. To the best of author’s knowledge and study, the universally recognized assumption that only vortices with large inclination angles can be detected in planar PIV needs to be revised. For vortices with small inclination angles, as long as their circulation is sufficiently large, they can also be detected.

Core-pressure alleviation for a wall-normal vortex by active flow control

We consider the application of active flow control to modify the radial pressure distribution of a single-phase wall-normal vortex. The present flow is based on the Burgers vortex model but with a no-slip boundary condition prescribed along its symmetry plane. The wall-normal vortex serves as a model for vortices that emerge upstream of turbomachinery, such as pumps. This study characterizes the baseline vortex unsteadiness through numerical simulation and dynamic mode decomposition. The insights gained from the baseline flow are used to develop an active flow control technique with rotating zero-net-mass blowing and suction with the objective of modifying the core-pressure distribution. The effectiveness of the control strategy is demonstrated by achieving a widened vortex core with increased pressure. This change in the flow field weakens the local strength of the wall-normal vortex core, potentially inhibiting the formation of hollow-core vortices, commonly encountered in liquids.

Numerical evaluation of gas core length in free surface vortices

The formation and evolution of free surface vortices represent an important topic in many hydraulic intakes, since strong whirlpools introduce swirl flow at the intake, and could cause entrainment of floating matters and gas. In particular, gas entrainment phenomena are an important safety issue for Sodium cooled Fast Reactors, because the introduction of gas bubbles within the core causes dangerous reactivity fluctuation. In this paper, a numerical evaluation of the gas core length in free surface vortices is presented, according to two different approaches. In the first one, a prediction method, developed by the Japanese researcher Sakai and his team, has been applied. This method is based on the Burgers vortex model, and it is able to estimate the gas core length of a free surface vortex starting from two parameters calculated with single-phase CFD simulations. The two parameters are the circulation and the downward velocity gradient. The other approach consists in performing a two-phase CFD simulation of a free surface vortex, in order to numerically reproduce the gas- liquid interface deformation. Mapped convergent mesh is used to reduce numerical error and a VOF (Volume Of Fluid) method was selected to track the gas-liquid interface. Two different turbulence models have been tested and analyzed. Experimental measurements of free surface vortices gas core length have been executed, using optical methods, and numerical results have been compared with experimental measurements. The computational domain and the boundary conditions of the CFD simulations were set consistently with the experimental test conditions.

Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets

Direct numerical simulations of a planar jet and of shear free turbulence at Reλ = 115–140 using very fine resolutions allow the first direct identification and characterisation of the viscous superlayer (VSL) that exists at the edges of mixing layers, wakes, jets, and boundary layers, adjacent to the turbulent/non-turbulent interface. For both flows the VSL is continuous with higher local thicknesses forming near the larger intense vorticity structures. The mean thickness of the VSL is of the order of the Kolmogorov micro-scale and agrees well with an estimate based on the Burgers vortex model.

Development of vortex model with realistic axial velocity distribution

A vortex is considered as one of significant phenomena which may cause gas entrainment (GE) and/or vortex cavitation in sodium-cooled fast reactors. In our past studies, the vortex is assumed to be approximated by the well-known Burgers vortex model. However, the Burgers vortex model has a simple but unreal assumption that the axial velocity component is horizontally constant, while in real the free surface vortex has the axial velocity distribution which shows large gradient in radial direction near the vortex center. In this study, a new vortex model with realistic axial velocity distribution is proposed. This model is derived from the steady axisymmetric Navier-Stokes equation as well as the Burgers vortex model, but the realistic axial velocity distribution in radial direction is considered, which is defined to be zero at the vortex center and to approach asymptotically to zero at infinity. As the verification, the new vortex model is applied to the evaluation of a simple vortex experiment, and shows good agreements with the experimental data in terms of the circumferential velocity distribution and the free surface shape. In addition, it is confirmed that the Burgers vortex model fails to calculate accurate velocity distribution with the assumption of uniform axial velocity. However, the calculation accuracy of the Burgers vortex model can be enhanced close to that of the new vortex model in consideration of the effective axial velocity which is calculated as the average value only in the vicinity of the vortex center.

High-Precision Numerical Scheme for Vortical Flow

In this study, a new high-precision numerical simulation scheme for vortical flows (vortex-based scheme) is proposed. This scheme identifies a vortical flow in each computational cell, and then, reconstructs a vortical velocity distribution based on the Burgers vortex model. In addition, a pressure distribution in the vicinity of the vortex center is also reconstructed. The momentum transfer is calculated with the reconstructed velocity and pressure distributions, and therefore, the vortex-based scheme can simulate vortical flows more accurately than the conventional schemes. In fact, as the simulation result of inviscid vortex attenuation problem, the vortex-based scheme shows lower simulation error compared to the conventional discretization schemes. Moreover, also in the numerical simulation of the quasi-steady vortical flow, the simulation accuracy of the vortex-based scheme is superior to those of the conventional schemes.

The intense vorticity structures near the turbulent/non-turbulent interface in a jet

AbstractThe characteristics of the intense vorticity structures (IVSs) near the turbulent/non-turbulent (T/NT) interface separating the turbulent and the irrotational flow regions are analysed using a direct numerical simulation (DNS) of a turbulent plane jet. The T/NT interface is defined by the radius of the large vorticity structures (LVSs) bordering the jet edge, while the IVSs arise only at a depth of about $5\eta $ from the T/NT interface, where $\eta $ is the Kolmogorov micro-scale. Deep inside the jet shear layer the characteristics of the IVSs are similar to the IVSs found in many other flows: the mean radius, tangential velocity and circulation Reynolds number are $R/ \eta \approx 4. 6$, ${u}_{0} / {u}^{\ensuremath{\prime} } \approx 0. 8$, and ${\mathit{Re}}_{\Gamma } / { \mathit{Re}}_{\lambda }^{1/ 2} \approx 28$, where ${u}_{0} $, and ${\mathit{Re}}_{\lambda } $ are the root mean square of the velocity fluctuations and the Reynolds number based on the Taylor micro-scale, respectively. Moreover, as in forced isotropic turbulence the IVSs inside the jet are well described by the Burgers vortex model, where the vortex core radius is stable due to a balance between the competing effects of axial vorticity production and viscous diffusion. Statistics conditioned on the distance from the T/NT interface are used to analyse the effect of the T/NT interface on the geometry and dynamics of the IVSs and show that the mean radius $R$, tangential velocity ${u}_{0} $ and circulation $\Gamma $ of the IVSs increase as the T/NT interface is approached, while the vorticity norm $\vert \omega \vert $ stays approximately constant. Specifically $R$, ${u}_{0} $ and $\Gamma $ exhibit maxima at a distance of roughly one Taylor micro-scale from the T/NT interface, before decreasing as the T/NT is approached. Analysis of the dynamics of the IVS shows that this is caused by a sharp decrease in the axial stretching rate acting on the axis of the IVSs near the jet edge. Unlike the IVSs deep inside the shear layer, there is a small predominance of vortex diffusion over stretching for the IVSs near the T/NT interface implying that the core of these structures is not stable i.e. it will tend to grow in time. Nevertheless the Burgers vortex model can still be considered to be a good representation for the IVSs near the jet edge, although it is not as accurate as for the IVSs deep inside the jet shear layer, since the observed magnitude of this imbalance is relatively small.

Effect of Experimental Conditions on Gas Core Length and Downward Velocity of Free Surface Vortex in Cylindrical Vessel

This paper deals with characteristics of surface vortex in a cylindrical vessel. One of the characteristics is a gas core length, which is important to estimate the onset condition of the gas entrainment but influenced easily by the experimental condition. In the experiment using water, the effects of the water temperature, water level, and the surface tension on the gas core length were investigated. The onset condition of the gas entrainment is sometimes estimated by using the Burgers vortex model but the real flow in the vessel is different from the model. The velocity fields were measured by particle image velocimetry (PIV) and the velocity gradient of the downward flow was discussed. The proper flow conditions for the Burgers vortex model are a high water level and a high flow rate.

Biosensor Capture Kinetics Model of Nanocube-Augmented Carbon Nanotube Networks

AbstractAu-coated Pd (Au/Pd) nanocubes (˜250 nm in width) connected via a network of single-walled carbon nanotubes (SWCNTs) have been employed as an electrochemical biosensor. As previously reported, these in situ Au/Pd nanocube SWCNT networks are capable of ultrasensitive amperometric sensing of glucose, with a sensitivity, detection limit, and linear sensing range greater than similar CNT-based glucose biosensors. The 3D mass diffusion of glucose molecules to the Au/Pd nanocube surfaces, forced convection environment of the testing vial, and Brownian motion of the Au/Pd nanocubes are all likely factors contributing to the strong electrochemical performance of the Au/Pd-SWCNT biosensor. In an effort to elucidate the effects of these contributing factors, this work demonstrates an analytical biosensor capture kinetics model that analyzes the analyte-biosensor mass transfer by molecular diffusion and convection due to both the fluid motion within the test vial and the Brownian motion of the Au/Pd nanocubes themselves.The biosensor capture kinetics model incorporates a quasi steady-state integrated incident flux equation to model mass diffusion of biomolecules to the surface of a 1D planar, 2D nanowire, and 3D nanosphere surface in Cartesian, cylindrical, and spherical coordinates respectively. A Burgers vortex model is introduced to analyze the biosensor diffusion boundary layer within a test vial that experiences fluid downwelling and upwelling within the vial center and boundaries due to the rotation of a magnetic stir bar. Finally the convection-diffusion equation simplified by Stokes flow is utilized to model the diffusion boundary layer of the Au/Pd nanocubes experiencing Brownian motion.Several key conclusions can be interfered from this model. First, a biosensor experiencing 3D mass diffusion will exhibit a greater analyte concentration flux of at least one order of magnitude greater than a biosensor experiencing 2D diffusion and 1D mass diffusion in quiescent and convective fluid environments. Additionally, mass transfer by convection increases the concentration flux to the biosensor by inhibiting the continued advancement of the analyte depletion layer around the biosensor. Furthermore, the Brownian motion model of the Au/Pd nanocubes is shown to improve the mass transfer to the biosensor surface, portraying a substantial increase in amperometric current signal output as compared to a similar electrochemical-based biosensor with stationary Au/Pd nanocubes. In summary, the results of the biosensor capture kinetics model corroborate the high sensitivities and low detection limits previously observed experimentally by Au/Pd nanocube-SWCNT biosensors.

Stretched vortices in a compressible fluid

Stretched vortices in a compressible fluid are considered. A modified Burgers vortex model is considered for which the flow associated with the vortex is perpendicular to the plane of uniform straining flow, a situation that is well suited to modeling a mixing-layer flow or a jet flow.

Correlations of vorticity and material line elements with strain in decaying turbulence

Correlations of the vorticity and the passive material line element with strains in decaying turbulence are investigated. The mean principal rates of the strain and the growth rates of the vorticity and the material line element due to the nonlinear stretching are all found to be proportional to the square-root-mean enstrophy. The ratios of the principal rates are 4:1:−5. It is shown how these ratios help determining the values of free parameters in the phenomenological models of turbulence such as the Burgers vortex model proposed by Ashurst (private communication) and the Lundgren–Townsend vortex model by Pullin and Saffman [Phys. Fluids A 5, 126 (1993); 6, 3010 (1994)]. The mean growth rate of material line elements is slightly larger than the intermediate principal rate, but much less than the most positive one. Numerical results show that the material line element has nearly the same preferences in aligning with the principal directions of the strain corresponding to the mostly positive and the intermediate principal rates. The growth rate is approximately linearly correlated with the strain magnitude but almost uncorrelated with the vorticity magnitude. Conditional statistics and a simple model flow have been used to explain the above observations.