Stability Analysis of Slowly Divergent Swirling Flow(Ⅰ)──Theory

The stability of inviscid incompressible swirling flow with slowly divergence is investigated A multiple scale expansion is used to develop a linear stability study of slowly divergent swirling flow with non-axisymmetric disturbances The differental equations of zero-order and first-order disturbance module and governing equation of amplitude variation due to slowly divergent flow are derved The plaschko s equation for slowly divergent swirl-free jet has been extended to slowly divergent flow with swirlin the present study.

Discussion on Stability Criterion of Inviscid Compressible Swirling Flow

The stability condition for compressible and incompressible swirling flow is discussed and compared. It is found that Eckhoff and Storesletten's necessary condition for stability of inviscid compressible swirling flow seems incorrect.

Numerical prediction of vortex flow and thermal separation in a subsonic vortex tube

This work was aimed at gaining understanding of the physical behaviours of the flow and temperature separation process in a vortex tube. To investigate the cold mass fraction’s effect on the temperature separation, the numerical calculation was carried out using an algebraic Reynolds stress model (ASM) and the standard k-ε model. The modelling of turbulence of com-pressible, complex flows used in the simulation is discussed. Emphasis is given to the derivation of the ASM for 2D axisymmet-rical flows, particularly to the model constants in the algebraic Reynolds stress equations. The TEFESS code, based on a staggered Finite Volume approach with the standard k-ε model and first-order numerical schemes, was used to carry out all the computations. The predicted results for strongly swirling turbulent compressible flow in a vortex tube suggested that the use of the ASM leads to better agreement between the numerical results and experimental data, while the k-ε model cannot capture the stabilizing effect of the swirl.

Tomographic particle image velocimetry measurement on three-dimensional swirling flow in dual-stage counter-rotating swirler

Three-Dimensional(3D)swirling flow structures,generated by a counter-rotating dualstage swirler in a confined chamber with a confinement ratio of 1.53,were experimentally investigated at Re=2.3×10^(5)using Tomographic Particle Image Velocimetry(Tomo-PIV)and planar Particle Image Velocimetry(PIV).Based on the analysis of the 3D time-averaged swirling flow structures and 3D Proper Orthogonal Decomposition(POD)of the Tomo-PIV data,typical coherent flow structures,including the Corner Recirculation Zone(CRZ),Central Recirculation Zone(CTRZ),and Lip Recirculation Zone(LRZ),were extracted.The counter-rotating dual-stage swirler with a Venturi flare generates the independence process of vortex breakdown from the main stage and pilot stage,leading to the formation of an LRZ and a smaller CTRZ near the nozzle outlet.The confinement squeezes the CRZ to the corner and causes a reverse rotation flow to limit the shape of the CTRZ.A large-scale flow structure caused by the main stage features an explosive breakup,flapping,and Precessing Vortex Core(PVC).The explosive breakup mode dominates the swirling flow structures owing to the expansion and construction of the main jet,whereas the flapping mode is related to the wake perturbation.Confinement limits the expansion of PVC and causes it to contract after the impacting area.

On the Vortex Sheets of Compressible Flows

This paper provides a review of the recent results on the stability of vortex sheets in compressible flows.Vortex sheets are contact discontinuities of the underlying flows.The vortex sheet problem is a free boundary problem with a characteristic boundary and is challenging in analysis.The formulation of the vortex sheet problem will be introduced.The linear stability and nonlinear stability for both the two-dimensional two-phase compressible flows and the two-dimensional elastic flows are summarized.The linear stability of vortex sheets for the three-dimensional elastic flows is also presented.The difficulties of the vortex sheet problems and the ideas of proofs are discussed.

STABILITY OF VORTEX STREET IN GAS-LIQUID TWO-PHASE FLOW

The stability of the Karmen vortex street in gas-liquid two-phase flow wasstudied experimentally and theoretically. The values of the parameter h/l characterizing the vortexsirect structure (i. e. , the ratio of the vortex street width to the distance between two vortexes)for a stable vortex street in gas-liquid two-phase flow were obtained for the first lime. Theparameter h/l was proved to be a variable, not a constant as in single-phase flow, h/l is related tothe upstream fluid void fraction. In gas-liquid two-phase fluid flow to form a steady vortex streetis more difficult than in a single-phase fluid flow. Because in the unsteady vortex shedding thevortex shedding band frequency is broader than the one in the single phase fluid flow, so it iseasier to induce the cross-cylinder resonance than in the single phase fluid flow, and this caseshould give rise to the attention of engineers.

Numerical simulation of the effect of upstream swirling flow on swirl meter performance

Flow measurement is important in the fluid process and transmission system. For the need of accuracy measure- ment of fluid, stable flow is acquired. However, the elbows and devices as valves and rotary machines may pro- duce swirling flow in the natural gas pipeline networks system and many other industry fields. In order to reveal the influence of upstream swirling flow on internal flow fields and the metrological characteristics, numerical si- mulations are carried out on the swirl meter. Using RNG k-e turbulent model and SIMPLE algorithm, the flow field is numerically simulated under swirling flows generated from co-swirl and counter-swirl flow. Simulation results show fluctuation is enhanced or weakened depending on the rotating direction of swirling flow. A coun- ter-swift flow increases the entropy production rate at the inlet and outlet of the swirler, the junction region between throat and divergent section, and then the pressure loss is increased. The vortex precession dominates the static pressure distributions on the solid walls and in the channel, especially at the end region of the throat.

Analytical Solution of the Flow Field Induced by the Uniformly Moving Double Helical Vortex Filaments

The analytical expressions was deduced for the inviscid flow field induced by the double vortex filaments that move uniformly and rigidly without change of its form in a cylindrical tube, where the vortex filaments rotate around its axial with a constant angular velocity and translates along its axial with a constant transferal velocity. It is a key of solving problem to set up a moving cylindrical coordinate system together with the vortex filaments motion, in which the relative velocity field is presumed to be time-independent and with helical symmetry. The result shows that the absolute velocity field and pressure field are all time-periodic functions, and may degenerate into a time-independent field when the helical vortex filaments slip along the filaments themselves or is immobile. The calculation results at the location of pressure peaks and valleys on pipe wall are accordant with experimental results. When the cylindrical pipe radius tends to infinitely large quantity, it is also concluded that the double helical vortex filaments induce flow field in an unbound space.

Analytical Solutions to the Flow Field Induced by Uniformly Moving Multiple Helical Vortex Filaments

This paper presents analytic solutions for the flow field of inviscid fluid induced by uniformly and rigidly moving multiple helical vortex filaments in a cylindrical pipe. The relative coordinate system is set on the moving vortex filaments. The analytical solutions of the flow field are obtained on the assumption that the relative velocity field induced is time-independent and helically symmetrical. If the radius of the cylindrical pipe approaches infinity, these solutions are also available for unbounded space. The results show that both the absolute velocity field and pressure field are periodical in time, and may reduce to time-independent when the helical vortex filaments are immobile or slip along the filaments themselves. Furthermore, the solution of velocity field is reduced to Okulov's formula for the case of a single static vortex filament in a cylindrical pipe. The calculated locations of pressure peak and valley on the pipe wall agree with experimental results.

Detached eddy simulation on the structure of swirling jet flow field

The improved delayed detached eddy simulation method with shear stress transport model was used to analyze the evolution of vortex structure,velocity and pressure fields of swirling jet.The influence of nozzle pressure drop on vortex structure development and turbulence pulsation was investigated.The development of vortex structure could be divided into three stages:Kelvin-Helmholtz(K-H)instability,transition stage and swirling flow instability.Swirling flow could significantly enhance radial turbulence pulsation and increase diffusion angle.At the downstream of the jet flow,turbulence pulsation dissipation was the main reason for jet velocity attenuation.With the increase of pressure drop,the jet velocity,pulsation amplitude and the symmetry of velocity distribution increased correspondingly.Meanwhile the pressure pulsation along with the axis and vortex transport intensity also increased significantly.When the jet distance exceeded about 9 times the dimensionless jet distance,the impact distance of swirling jet could not be improved effectively by increasing the pressure drop.However,it could effectively increase the swirl intensity and jet diffusion angle.The swirling jet is more suitable for radial horizontal drilling with large hole size,coalbed methane horizontal well cavity completion and roadway drilling and pressure relief,etc.

Instability characteristics of a co-rotating wingtip vortex pair based on bi-global linear stability analysis

The Stereo Particle Image Velocimetry(SPIV)technology is applied to measure the wingtip vortices generated by the up-down symmetrical split winglet.Then,the temporal biglobal Linear Stability Analysis(bi-global LSA)is performed on this nearly equal-strength corotating vortex pair,which is composed of an upper vortex(vortex-u)and a down vortex(vortex-d).The results show that the instability eigenvalue spectrum illustrated by(ωr,ω_(i))contains two types of branches:discrete branch and continuous branch.The discrete branch contains the primary branches of vortex-u and vortex-d,the secondary branch of vortex-d and coupled branch,of which all of the eigenvalues are located in the unstable half-plane ofω_(i)>0,indicating that the wingtip vortex pair is temporally unstable.By contrast,the eigenvalues of the continuous branch are concentrated on the half-plane ofω_(i)<0 and the perturbation modes correspond to the freestream perturbation.In the primary branches of vortex-u and vortex-d,Mode P_(u) and Mode Pd are the primary perturbation modes,which exhibit the structures enclosed with azimuthal wavenumber m and radial wavenumber n,respectively.Besides,the results of stability curves for vortex-u and vortex-d demonstrate that the instability growth rates of vortex-u are larger than those of vortex-d,and the perturbation energy of Mode P_(u) is also larger than that of Mode Pd.Moreover,the perturbation energy of Mode P_(u) is up to 0.02650 and accounts for 33.56%percent in the corresponding branch,thereby indicating that the instability development of wingtip vortex is dominated by Mode P_(u).By further investigating the topological structures of Mode P_(u) and Mode Pd with streamwise wavenumbers,the most unstable perturbation mode with a large azimuthal wavenumber of m=5-6 is identified,which imposes on the entire core region of vortex-u.This large azimuthal wavenumber perturbation mode can suggest the potential physical-based flow control strategy by manipulating it.

Effect of vortex dynamics and instability characteristics on the induced drag of trailing vortices

In this paper, trailing vortices generated by three wingtip configurations, namely the M6wing and the M6 wing with a blended or split winglet, are experimentally investigated using the Stereo Particle Image Velocimetry(SPIV) technology. Then, linear stability analysis is performed to investigate instability characteristics. Three corresponding trailing vortex patterns, including the isolated trailing vortex without wake(pattern v) and with wake(pattern v-w), co-rotating vortex pair(pattern v-v), are observed in experiments. The strength of trailing vortices, characterized by circulation, is reduced after installing winglets as expected, and the strength of pattern v-v can be further suppressed compared with pattern v-w. Moreover, instability characteristics, such as the eigenvalue spectrum and perturbation mode, are distinctive among these three vortex patterns.The distribution of eigenvalue spectrums indicates that pattern v and pattern v-w are temporally“marginally stable”, while pattern v-v is temporally “unstable.” The primary perturbation mode of pattern v and pattern v-w is the m =-1 helical mode, while |m|>1 for the case of pattern v-v.The effect of vortex dynamics and instability characteristics can be concluded in two aspects.Firstly, the value of induced drag is polluted by about 3% from vortex wandering since vortex wandering affects the tangential velocity and streamwise vorticity of trailing vortices. Secondly, the growth rate and penetration depth perturbation mode affect trailing vortex evolution and further affect induced drag. Specifically, the larger the growth rate and penetration depth are, the more turbulence injects inside the vortex core, thus leading to a quicker and more intense attenuation of trailing vortex, as well as a smaller induced drag. This finding can guide us to manipulate the induced drag in flow control.

Flow Past an Accumulator Unit of an Underwater Energy Storage System： Three Touching Balloons in a Floral Configuration

An LES simulation of flow over an accumulator unit of an underwater compressed air energy storage facility was conducted. The accumulator unit consists of three touching underwater balloons arranged in a floral configuration. The structure of the flow was examined via three dimensional iso surfaces of the Q criterion. Vortical cores were observed on the leeward surface of the balloons. The swirling tube flows generated by these vortical cores were depicted through three dimensional path lines. The flow dynamics were visualized via time series snapshots of two dimensional vorticity contours perpendicular to the flow direction; revealing the turbulent swinging motions of the aforementioned shedding-swirling tube flows. The time history of the hydrodynamic loading was presented in terms of lift and drag coefficients. Drag coefficient of each individual balloon in the floral configuration was smaller than that of a single balloon. It was found that the total drag coefficient of the floral unit of three touching balloons, i.e. summation of the drag coefficients of the balloons, is not too much larger than that of a single balloon whereas it provides three times the storage capacity. In addition to its practical significance in designing appropriate foundation and supports, the instantaneous hydrodynamic loading was used to determine the frequency of the turbulent swirling-swinging motions of the shedding vortex tubes; the Strouhal number was found to be larger than that of a single sphere at the same Reynolds number.

综掘巷道径向涡旋运移对截割产尘污染的影响

为了掌握综掘巷道风幕运移动态过程对截割产尘污染的影响规律,以进一步提高风幕阻尘效率。采用数值模拟与现场实测相结合,研究分析不同径向涡旋强度和运移距离条件下综掘巷道流场结构演变和粉尘污染。研究结果表明:径向涡旋以贴壁旋流形式运移,随径向涡旋强度和运移距离增大,运移过程中分别形成偏向压风侧和轴向的支流,随后径向涡旋转变为均匀轴向流场,粉尘污染随之分别呈不断减小和先增大后减小的规律。掘进司机处粉尘质量浓度与径向涡旋强度和运移距离间分别满足玻尔兹曼分布Boltzmann模型和对数正态分布LogNormal模型。当径向涡旋强度为0.9,运移距离为30 m时,能够实现高效控尘,现场实测结果显示,掘进司机处总尘和呼吸性粉尘降尘率分别达到82.7%和78.3%,能够有效改善人员作业环境。研究结果可为煤矿综掘巷道粉尘污染高效控制与治理提供参考。

Experimental and numerical study of the adsorption performance of a vortex suction device using water-swirling flow

An electrically activated underwater suction device is designed to form an amazing amount of negative pressure by generating water swirling flow,which can make underwater wall-climbing robot stick to the wall surface allowing a ground clearance.For the purpose of a full understanding of the mechanism of the suction device,a series of experimental tests are carried out and a computational fluid dynamics(CFD)model is established.The results show that the suction force F is consistent between experimental tests and simulations.An insight into the flow phenomena of vortex suction device,including spatial velocity and pressure distribution,is given through numerical simulation analysis.Furthermore,the crucial parameters,i.e.,the rotation speedωand gap clearance h,are studied.Then the relationships of F-ωand F-h are clarified.It reveals that with the increasing of rotation speed,the suction force increases quadratically.And with the increasing of gap clearance,the suction force increases firstly and then decreases,so that a reasonable design interval of gap clearance can be got to obtain the required suction force for the engineering applications.

Effect of Non-Newtonian Viscosity for Surfactant Solutions on Vortex Characteristics in a Swirling Pipe Flow

Effects of non-Newtonian viscosity for surfactant solution on the vortex characteristics and drag-reducing rate in a swirling pipe flow are investigated by pressure drop measurements, velocity profile measurements and viscosity measurements. Non-Newtonian viscosity is represented by power-law model （t= kD^π）. Surfactant solution used has shear-thinning viscosity with n 〈 1.0. The swirling flow in this study has decay of swirl and vortex-type change from Rankin＇s combined vortex to forced vortex. It is shown that the effect of shear-thinning viscosity on the decay of swirl intensity is different by vortex category and the critical swirl number with the vortex-type change depends on shear-thinning viscosity.

基于环空流场特性的变径稳定器参数优化研究

变径稳定器径向活塞不同的伸缩状态对环空流场会产生影响。为此,采用流体动力学研究不同状态下的环空流场特性并在此基础上进行结构优化。建立变径稳定器的流体动力学数值模拟模型,结合现场应用的变径稳定器参数,分析不同螺旋带参数和流体参数下的流体特性。研究结果表明:螺旋升角为55°左右时最优,螺旋棱截面对应圆心角对环空流场影响不明显,螺旋棱侧面倾角在5°~10°范围内较好,径向活塞为伸出状态时旋流流场表现更好;钻井液排量与旋流长度之间呈正相关、近似线性关系,钻井液密度较大时可以改善旋流衰减流场,但对切向速度和旋流长度影响较小。研究结论可为变径稳定器的结构设计与优化提供技术支撑。

STRUCTURES OF CONFINED VORTEX BREAKDOWN IN CONSTANT DIAMETER PIPE FLOW

Numerical solutions of three-dimensional, incompressible and unsteady Navier-Stokes equations for constant diameter swirling pipe flows are used to study vortex breakdown, including the detailed flow structures in the bubble domain and the ＂tail＂ behind the bubble during the vortex breakdown, and a comparison is made between the numerical solutions and the experimental results.

跨声速转子机匣孔式非定常抽吸扩稳机理研究

为了研究跨声速转子机匣孔式非定常抽吸的扩稳机理,以Rotor 37为研究对象,针对机匣孔式抽吸方案进行了非定常数值对比研究,探讨了抽吸前后转子总性能和失速裕度的变化规律,详细分析了近失速工况下转子的三维流场结构,建立了相应的动叶通道内涡结构模型;此外,进一步分析了非定常抽吸对叶尖流场非定常特性的影响。结果表明:采用机匣孔式抽吸可实现对叶尖泄漏流的有效控制,在保证转子效率的同时,将近失速工况的转子压比提升2.1%,失速裕度提升6.86%;非定常抽吸使得近失速工况下叶尖泄漏涡的尺寸明显减小,改善了叶尖区域流场的非定常特性,缓解了流场内的二次流流动堵塞,提升了转子叶尖流场的稳定性。

3D FLOW INSIDE BUBBLE-TYPE VORTEX BREAKDOWN: AN EXPERIMENTAL INVESTIGATION VIA LDV

Bubble-type vortex breakdown of the swirling flow inside a closed cylindricalcontainer with a rotating upper endwall was experimentally investigated via LDV. 3D measurement ofthe steady bubble at H/R =1.5 was firstly carried out with very fine grid arrangement. Flow detailsinside the bubble and its Re -dependent structure were made clear. Abrupt waves of the azimuthalvelocity component were always found to be between the bottom stationary endwall and the upstreamstagnation point, which might be the reason of bubble formation. Variation of bubble structure andbubble center with the increasing Re gives the explanation for the disappearance of the breakdownregion.