Large Eddy Simulations of Swirling Nozzle-Jet Flow Undergoing Vortex Breakdown

We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier-Stokes equations in cylindrical coordinates using high-order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0 ) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point-flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up- and downstream. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The critical cross-section of a vortex

Summary This paper discusses the problem of critical-flow cross-sections in vortex flows. It is shown that there are two different types of vortex flows, A-type and B-type vortices (say). An A-type vortex approaches its critical flow state as its cross-sectional area increases and departs from the critical state as the cross-sectional area is decreased. This property is associated with the particular dependence of total pressure and circulation on the stream function, and it holds for both subcritical and supercritical A-type vortices. On the other hand, both subcritical and supercritical B-type vortices approach their critical flow states as their cross-sectional areas are decreased and depart from their critical states for increasing cross-sectional area. As was shown by Benjamin, setting the first variation of the flow force with respect to the stream function equal to zero leads to Euler's equation of motion. The second variation also vanishes if the corresponding flow state is critical. In this case the sign of the third variation decides whether the flow is an A-type or a B-type vortex. Within the framework of inviscid-fluid flow theory the type of a vortex is preserved unless vortex breakdown occurs. Making use of the knowledge that vortex flows are controlled by two different types of critical-flow cross-sections a variety of vortex flow phenomena are investigated, including the two types of inlet vortices that are observed upstream of jet engines, the behavior of vortex valves, the flow characteristics of liquid-fuel atomizers and the bath tub vortex.     

A Parallel Code for LES of Compressible Swirling Jet Flow Undergoing Vortex Breakdown

Swirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners, turbines and jet engines. To simulate the highly nonlinear dynamics of the flow, it is necessary to use high-order numerical methods, leading to increased computational cost. To be able to perform simulations in acceptable turn-around time, an available LES code for solving the filtered compressible Navier-Stokes equations in cylindrical coordinates using compact finite-difference schemes was parallelized for massively-parallel architectures. The parallelization was done following the ghost-cell approach for filtering in the three spatial directions. The inter-process communication is handled using the message passing interface (MPI). The weak and strong scaling properties of the code indicate that it can be used for massively parallel simulations using several thousand processors. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Oblique Shock‐Vortex Interaction

Breakdown of a slender vortex caused by an oblique (OSVI) shock is studied using numerical solutions of the Euler equations for unsteady three‐dimensional flow. A Burgers vortex with a given circulation and axial velocity distribution is prescribed at the inflow boundary. The calculations show that like in incompressible flows supersonic breakdown is primarily controlled by pressure forces. The shock is deformed into an ‘s’‐shaped part near the vortex core where the shock becomes normal. The results indicate that initiation of breakdown is more sensitive to variations in the axial velocity than in the circulation, and that the .ow structure is clearly time‐dependent.     

The effects of non-uniform density and stagnation pressure on the breakdown characteristics of a vortex

Summary This paper is concerned with the extension of the theory of vortex breakdown, that was presented in previous publications by the present author and others, to cases of non-uniform density and non-uniform stagnation pressure outside the vortex core. The effects of radial density and velocity variations play an essential role for the layout of modern low-emission burners for premixed combustion. Furthermore, these effects turn out to be important with respect to an improved understanding of the formation of zones of flow recirculation in tornado-like vortices. With the help of the extension of a variational principle for axisymmetric flow to the case of non-uniform density it is possible to discuss inviscid flows of non-uniform density and stagnation pressure in great generality. A numerical solution method is given for general axisymmetric vortex flows, including flows that undergo vortex breakdown. The influences of density and stagnation pressure variations on vortex breakdown are analyzed in detail, for the special case of a generalized Rankine vortex. It is found that a radially increasing density leads to a reduction of the swirl number at which vortex breakdown occurs, whereas a radially decreasing axial velocity component in the approach flow of a vortex breakdown bubble leads to a substantially enlarged bubble. Finally, a Richardson number criterion is proposed for the scaling of a vortex breakdown bubble in a tornado.

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Zusammenfassung Die vorliegende Arbeit befasst sich mit der Erweiterung der vom gleichen Autor und anderen entwickelten Theorie für Vortex Breakdown auf den Fall ungleichförmiger Dichte und ungleichförmigen Gesamtdrucks ausserhalb des Wirbelkerns. Diese Effekte spielen eine grundlegende Rolle für die Auslegung moderner emissionsarmer Vormischbrenner. Ausserdem spielen die Effekte ungleichförmiger Dichte- und Gesamtdruckverteilungen eine wichtige Rolle für ein verbessertes Verständnis der Rückströmblasen in tornadoartigen Wirbelströmungen. Mit Hilfe der Erweiterung eines Variationsprinzips für rotationssymmetrische Strömungen auf den Fall ungleichförmiger Dichte wird es möglich, rotationssymmetrische Strömungen ungleichförmiger Dichte in grosser Allgemeinheit zu untersuchen. Im besonderen kann auch das Verhalten von Vortex-Breakdown-Strömungen analysiert werden. Die Einflüsse ungleichförmiger Dichte- und Gesamtdruckverteilungen auf das Vortex-Breakdown-Phaenomen werden im speziellen Fall eines verallgemeinerten Rankine'schen Wirbels eingehend untersucht. Es zeigt sich, dass eine in radialer Richtung zunehmende Dichte zu einer Verkleinerung der Drallzahl führt, bei der Vortex-Breakdown auftritt. Eine in radialer Richtung abnehmende axiale Geschwindigkeitskomponente führt zu einer massiven Vergrösserung der Vortex-Breakdown-Blase. Schliesslich wird ein Richardsonzahl-Kriterium als Skalierungsgesetz für Vortex-Breakdown-Blasen in Tornadoströmungen vorgeschlagen.

     

Analysis of Sound Radiated by Axisymmetric Vortex Ring

A theoretical and numerical study using the unsteady, 3D Navier-Stokes equations to generate axisymmetric vortex rings is reported. Increasing the vorticity, the vortex ring transition to a turbulent state are analyzed. After transition to a turbulent stage, the self-similarity of the temporal evolution of the flow is observed. Then we can compare sound radiated by the vortex ring to jet noise, at similar Reynolds number and low Mach number. The agreement between the simulation results and the simplified model is good. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The limiting vortex in the similarity solution for a swirling flow

It is known that the similarity solution for a viscous swirling flow over a stationary disk does not exist if the driving vortex far away from the disk is a potential vortex, while the solution exists for a rigid body vortex. Previously, the breakdown has been determined to occur if the azimuthal velocity of the driving vortex decreases faster than a certain power of the radial distance from the axis of symmetry. The decay parameter at which the similarity solution ceases to exist is computed here by a more direct method, and the reason for the breakdown becomes apparent. The analysis confirms (and slightly improves) the known value of the parameter. The case where the fluid, now assumed to be conducting, is subject to an axial magnetic field and the asymptotic behavior of the solution far away from the axis are also briefly discussed.     

Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.     

The effects of vortex breakdown bubbles on the mixing environment inside a base driven bioreactor

The bubble-type vortex breakdown inside a cylinder with flow driven by rotation of the base, has applications in mixing. We investigate this phenomena and its effect on the environment inside an open cylinder, with potential application as a tissue-engineering bioreactor, with tissue-scaffolds of two different geometries immersed in the fluid. Addition of scaffolds induces a blockage effect, hindering the flow in the central vortex core returning to the rotating base. This promotes early onset of vortex breakdown and alters the final shape of vortex breakdown bubbles. Placement of the scaffolds centrally on the cylinder axis yields almost identical levels and distributions of shear stress between the upper and lower surfaces of scaffolds. A change from a disk shaped to an ellipsoidal scaffold, of the same size, reduces the intensity of the maximum shear stresses at the scaffold surface by up to 50%. There is a range of Reynolds numbers where increasing Reynolds number, and hence possibly increasing mixing efficiency, leads to a decrease in the maximum levels of fluid forces at the scaffold surfaces. This is an important conclusion for scaffold based tissue engineering where improved mixing is sought, but often sacrificed in favor of minimizing fluid forces.     

Formation of a jet in case of non-stationary flow of a perfect fluid from a slit

The problem of flow of a perfect fluid from a slit separating two parallel planes is given a mathematical formulation for the case of a submerged jet, as well as for the case of a flow with a free boundary. Various types of flow are classified. The results of numerical solutions are compared with experimental data. The phenomenon of reversal of the vortex sheet which occurs when the flow rate through the slit is reduced, is discussed. The self-modelling problem is solving using the method of matching the asymptotic expansions. A cumulative effect is discovered, namely that the rate of penetration of a narrow central part of the self-modelling jet exceeds the rate of flow of the main part of the jet by one order of magnitude.     

泄爆诱导的湍流、旋涡和外部爆炸

基于k-ε湍流模型和Eddy-dissipation燃烧模型,采用同位网格SIMPLE算法,对充满甲烷-氧气预混气的带导管柱形泄爆容器向空气中泄爆的情形进行了数值模拟．根据计算结果,分析了泄爆后外流场中可燃云团、火焰和压力的变化过程．结果表明,外部爆炸是因射流火焰点燃高压区中的可燃云团,从而引起的剧烈湍流燃烧所致．同时还讨论了外流场湍流和涡量的分布特征．射流火焰进入外部可燃云团后,湍流主要分布在平均动能梯度较大的区域,而不在火焰阵面上．涡量分布主要受斜压效应的影响,在压力和密度梯度斜交区域,其值较大．     

Numerical study on the dynamics of a jet-vortex interaction

The interaction of a vortex and a jet plays an important role for many industrial processes such as carbon black formation or combustion in diesel engines. The knowledge of physics of these phenomena is crucial for engineers, but also for scientists who wish to study this complex flow pattern. In this research, we numerically investigate cases where a cylindrical reactor is charged with gas injected through five ports. The first one is located along the main axis of the cylinder and this leads to the formation of the main jet. The other four ports are situated along the side walls such that the gas entering the cylinder tangentially through them causes a vortex to be formed. The objective of this paper is to show the fundamental physical phenomena and also how the initial and boundary conditions influence the results. It is shown how the process is influenced not only by modifying the velocity of injected gas, but also by the orientation and position of the vortex inlet nozzles.     

三角翼大迎角流场结构和气动力特性的计算分析研究

采用数值计算方法对亚音速三角翼纵向及带有小侧滑和横侧小扰动情况下的流场结构进行了计算,利用数值计算所得到的大迎角流动流场数据,结合相关的实验研究结果,建立了对大迎角旋涡流场结构进行定量分析的方法．给出了三角翼大迎角情况下相应的气动力、力矩系数,以及机翼前缘分离涡轴线位置和旋涡破裂位置随迎角的变化规律,并对带有小侧滑和横侧小扰动情况下对横侧力矩的影响进行了计算与分析．计算结果表明,在前缘分离涡破裂前的上游旋涡区内,前缘分离涡轴线基本保持为直线,且随着迎角增加,前缘分离涡轴线位置愈靠近翼根,并远离翼面;在前缘分离涡破裂的初始阶段,于旋涡轴线处,压力系数会迅速增加,沿涡轴线方向速度迅速减小,在垂直于流向的截面内,愈靠近涡轴线处,沿涡轴线方向速度愈小,甚至出现负值,说明沿涡轴线方向出现回流．当绕机翼上表面前缘分离涡破裂后,将会导致横侧运动不稳定,如果受到小扰动,将产生横侧力矩发散．     

Vortex breakdown as a fundamental element of vortex dynamics

Summary Keller et al. (1985) have shown that, in analogy to the theory of gravity currents, there exist two types of force-free transitions (i.e. vortex breakdown phenomena) between axisymmetric vortex-flow states in tubes.This paper presents an extension of our earlier analysis, which is based on a variational principle and does not account for viscous effects and shear layer instabilities, to axisymmetric vortex flows in tubes with varying cross-sectional area.A broad investigation into the properties of steady axisymmetric vortex flows is given, in so far as they can be represented by perfect-fluid theory and simple extensions of it. It is argued that the basic physics of such flows, including vortex breakdown phenomena, can be explained with the help of the relatively simple theoretical concepts proposed. Numerical results are presented which show complete flow fields of loss-free transition in diffusers for various types of vortex flows. LDA-measurements and flow visualization experiments proove the existence of two types of transitions, as proposed by the analysis, and show the significance of critical cross-sections in the flow.

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Zusammenfassung Keller et al. (1985) haben gezeigt, daß in Analogie zur Theorie der Schwereströmungen zwei Arten von impulserhaltenden Übergängen (i.e. Vortex-Breakdown-Phänornene) zwischen axisymmetrischen Wirbelströmungszuständen existieren.Diese frühere Theorie, die auf einem einfachen Variationsprinzip basiert und Reibungseffekte sowie Scherschichtsinstabilitäten nicht berücksichtigt, wird in dieser Arbeit auf axisymmetrische Wirbelströmungen in Rohren mit veränderlicher Querschnittsfläche erweitert. Die Eigenschaften axisymmetrischer Wirbelströmungen werden in ihrer vollen Breite untersucht, soweit sie der Theorie der idealen Strömungen und ihren einfachsten Verallgemeinerungen zugänglich sind. Wie es scheint, kann mit hinreichender Rechtfertigung festgestellt werden, daß die grundlegende Physik solcher Strömungen (einschließlich der Vortex-Breakdown-Phänome) mit den relativ einfachen theoretischen Konzepten erklärt werden kann, die in dieser Arbeit diskutiert werden. Es werden numerische Ergebnisse gezeigt, welche die vollständigen Strömungsfelder verlustfreier Übergänge in Diffusoren für verschiedenartige Wirbelströmungen beinhalten. LDA-Messungen und Strömungsbeobachtungen beweisen die Existenz der von der Theorie vorausgesagten übergangsarten und zeigen die zentrale Bedeutung der kritischen Strömungsquerschnitte.

     

Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations

We study the interplay between the local geometric properties and the non-blowup of the 3D incompressible Euler equations. We consider the interaction of two perturbed antiparallel vortex tubes using Kerr's initial condition . We use a pseudo-spectral method with resolution up to 1536 × 1024 × 3072 to resolve the nearly singular behavior of the Euler equations. Our numerical results demonstrate that the maximum vorticity does not grow faster than doubly exponential in time, up to t = 19, beyond the singularity time t = 18.7 predicted by Kerr's computations , . The velocity, the enstrophy, and the enstrophy production rate remain bounded throughout the computations. As the flow evolves, the vortex tubes are flattened severely and turned into thin vortex sheets, which roll up subsequently. The vortex lines near the region of the maximum vorticity are relatively straight. This local geometric regularity of vortex lines seems to be responsible for the dynamic depletion of vortex stretching.     

A fully meshless method for ‘gas – evaporating droplet’ flow modelling

A meshless method for modelling two-phase flows with phase transition is described. The method is based on consideration of three systems: viscous-vortex blobs, thermal-blobs and droplets; and can be applied for numerical simulation of 2D non-isothermal flows of ‘gas-evaporating droplets’ in the framework of the one-way coupled two-fluid approach. The carrier phase is viscous incompressible gas. The dispersed phase is presented by a cloud of identical spherical droplets, and, due to evaporation, the radius and mass of droplets are time dependent. The carrier phase parameters are calculated using the viscous-vortex and thermal-blob method; the dispersed phase parameters are calculated using the Lagrangian approach. Two applications have been considered: (i) a standard benchmark – Lamb vortex; (ii) a cold spray injected into a hot quiescent gas. In the latter problem three cases corresponding to three droplet sizes were investigated. The smallest droplets (of the three cases considered) are more readily entrained by the carrier phase and form ring-like structures; the flow shows better mixing. Larger droplets evaporate less intensively. The medium sized droplets collect into two narrow bands stretched along the jet axis. The largest droplets form a two-phase jet, which remains close to the jet axis. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Localization of acoustic sources in subsonic jets

The sound in the acoustic far–field of a round jet is generated by a multitude of unsteady flow structures with different length and time scales. Most likely, different components of the noise spectrum are created by different structures in the jet which emit sound in different directions. Based on Lighthill's acoustic analogy, we present a method for relating flow structures of the jet with far–field noise spectra and their associated directivity patterns. The method allows to determine what kind of noise (with respect to frequency and emission direction) is generated at a given streamwise location. We illustrate the method with numerical results for a round isothermal jet. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

浅水横流中异重冲击射流的大尺度涡结构

采用RNG湍流模型对浅水横流中异重冲击射流的大尺度涡结构进行了详细的数值研究．分析了冲击区滞止点上游壁面涡结构和近区Scarf涡结构的尺度、形成机理和演化特征．计算得到了上游壁面涡的特征尺度,结果表明上游壁面涡具有高度的三维性,其特征尺度依赖于流速比和环境水深．近区Sarf涡结构对横流冲击射流的横向浓度分布具有重要的影响．当流速比相对较小时,在底层壁射流与环境横流的横向边界附近出现明显的高浓度聚集现象,计算结果表明Scarf涡结构对这一高浓度聚集区的形成起主导作用．     

Axisymmetrical rotating jets

The article presents computation results for a free jet emerging from a nozzle of radius R with Mach number M = 1 and nonrated value n = 3. The jet rotates at the nozzle outlet with constant angular velocity ω = 2 and corresponding circular velocity W = ωr (r < R ). The computation results for this jet are compared with those for a laminar (non-rotating) jet with the same fluid-dynamic parameters. The numerical results corroborate the theoretical conclusions concerning the effect of jet rotation on flow structure. Specifically, it is confirmed that the mixing of the jet with the surrounding gas is more intense and that a strongly twisted jet exhibits backflow toward the nozzle in the axial region. Translated from Prikladnaya Matematika i Informatika, No. 28, pp. 44–49, 2008.     

Lagrangian chaos and multiphase processes in vortex flows

We discuss experimental and numerical studies of the effects of Lagrangian chaos (chaotic advection) on the stretching of a drop of an immiscible impurity in a flow. We argue that the standard capillary number used to describe this process is inadequate since it does not account for advection of a drop between regions of the flow with varying velocity gradient. Consequently, we propose a Lagrangian-generalized capillary number C_L number based on finite-time Lyapunov exponents. We present preliminary tests of this formalism for the stretching of a single drop of oil in an oscillating vortex flow, which has been shown previously to exhibit Lagrangian chaos. Probability distribution functions (PDFs) of the stretching of this drop have features that are similar to PDFs of C_L. We also discuss on-going experiments that we have begun on drop stretching in a blinking vortex flow.