Nonlinear development of acoustical instabilities in supersonic jets

In contrast with the roll-up of fluid interfaces through Kelvin-Helmholtz instability, recent numerical simulations with small amplitude perturbations of supersonic jets reveal another very different coherent mode of nonlinear acoustical instability of jets through the appearance of regular zig-zag shock patterns which traverse the interior of the jet and amplify as time evolves. In this paper, through a combination of appropriate ideas from linear and nonlinear high frequency geometric optics, the authors develop a quantitative theory which predicts the nonlinear development of zig-zag modes with a structure like those observed in the numerical simulations. The perturbation analysis is developed via a systematic application of nonlinear small amplitude high frequency geometric optics to the complex free surface problem defined by the perturbed jet; this procedure automatically yields simplified asymptotic equations which are analyzed explicitly and lead to the development of regular amplifying “zig-zag” shock structures in the jet. For a given streamwise period, Mach number, and jet width, the asymptotic theory gives explicit criteria for the number and structure of different regular zig-zag shock patterns which amplify with time. For Mach numbers M < 1, there are no amplifying acoustic zig-zig modes while for M > 1, there are a finite number of such modes depending on Mach number, jet width, and streamwise period. Explicit criteria to select the most destabilizing of these nonlinear eigenmodes are developed as well as several new quantitative predictions regarding the nonlinear development of acoustical instabilities in supersonic jets including the phenomenon of “super-resonance” for special values of the streamwise period.     

射流抛光多相紊流流场的数值模拟

 理论分析了射流抛光的紊动冲击射流特点,构建了射流抛光的垂直冲击射流模型和斜冲击射流模型。根据射流抛光冲击射流的特点,比较各种流体模型后,采用RNG k-e 模型应用于射流抛光模型的计算。利用计算流体力学理论的二阶迎风格式对抛光模型方程离散,用SIMPLEC数值计算方法对射流抛光过程的紊动冲击射流和离散相磨粒分布进行数值模拟,得到了射流抛光过程的连续流场和离散相磨粒与水溶液的耦合流场,同时计算出了抛光液射流在工件壁面上的压力、速度、紊动强度、剪切力分布和磨粒体积质量分布,分析了垂直射流抛光模型和斜冲击射流抛光模型紊流流场的特点。     

Quasi-radial wall jets as a new concept in boundary layer flow control

This work aims to introduce a novel concept of wall jets wherein the flow is radially injected into a medium through a sector of a cylinder, called quasi-radial (QR) wall jets. The results revealed that fluid dynamics of the QR wall jet flow differs from that of conventional wall jets. Indeed, lateral and normal propagations of a conventional three-dimensional wall jet are via shear stresses. While, lateral propagation of a QR wall jet is due to mean lateral component of the velocity field. Moreover, discharged Arrays of conventional three-dimensional wall jets in quiescent air lead to formation of a combined wall jet at large distant from the nozzles, while QR wall jet immediately spread in lateral direction, meet each other and merge together very quickly in a short distance downstream of the jet nozzles. Furthermore, in discharging the conventional jets into an external flow, there is no strong interaction between them as they are moving parallel. While, in QR wall jets the lateral components of the velocity field strongly interact with boundary layer of the external flow and create strong helical vortices acting as vortex generators.     

Axes and scalar measures of two-jet and three-jet events

In a comparison of the jet measures sphericity, spherocity and thrust we find that the spherocity axis exhibits strong instabilities against small changes of particle directions and points in many cases in the direction of a single particle rather than describing the events as a whole. Sphericity does not allow the unique association of particles with jets. Thrust yields such an association and can easily be computed in a non-iterative way. We generalize the concept of thrust for application to triple-jets and present a non-iterative procedure for computing the three axes as well as a scalar quantity measuring the three-jet structure of individual events.     

Next-to-leading-order results for five, six, and seven jets in electron-positron annihilation

We present next-to-leading order corrections in the leading color approximation for jet rates in electron-positron annihilation up to seven jets. The results for the two-, three-, and four-jet rates agree with known results. The NLO jet rates have been known previously only up to five jets. The results for the six- and seven-jet rate are new. The results are obtained by a new and efficient method based on subtraction and numerical integration.     

Numerical analysis of gas-dynamic instabilities during the laser drilling process

The use of high-pressure gas jets in the laser-drilling process has significant influence on the melt ejection mechanism. These jets are highly unstable and this directly relates to the gas pressure and the geometry of the hole being drilled. The evolution of gas-dynamic instabilities during the laser-drilling process was investigated numerically. A minimum length nozzle (MLN) with a 300 μm throat diameter was modelled at various gas pressures, with the gas jet impinging on a range of simulated holes with different aspect ratios. The simulations predict the formation of surface pressure fluctuations that have a broad spectrum due to both the turbulent nature of the jet and the blunt shock oscillation on the surface. The surface pressure variations and the blunt shock oscillation govern the gas dynamic conditions inside the hole, which strongly influence the melt ejection phenomena during the laser-drilling process.     

Detonation simulations in supersonic flow under circumstances of injection and mixing

The unsteady, reactive Navier-Stokes equations with a detailed chemical mechanism of 11 species and 27 steps were employed to simulate the mixing, flame acceleration and deflagration-to-detonation transition (DDT) triggered by transverse jet obstacles. Results show that multiple transverse jet obstacles ejecting into the chamber can be used to activate DDT. But the occurrence of DDT is tremendously difficult in a non-uniform supersonic mixture so that it required several groups of transverse jets with increasing stagnation pressure. The jets introduce flow turbulence and produce oblique and bow shock waves even in an inhomogeneous supersonic mixture. The DDT is enhanced by multiple explosion points that are generated by the intense shock wave focusing of the leading flame front. It is found that the partial detonation front decouples into shock and flame, which is mainly caused by the fuel deficiency, nevertheless the decoupled shock wave is strong enough to reignite the mixture to detonation conditions. The resulting transverse wave leads to further mixing and burning of the downstream non-equilibrium chemical reaction, resulting in a high combustion temperature and intense flow instabilities. Additionally, the longitudinal and transverse gradients of the non-uniform supersonic mixture induce highly dynamic behaviors with sudden propagation speed increase and detonation front instabilities.     

Jets

This is a discussion of concentrated large-scale flows in planetary atmospheres and oceans, argued from the viewpoint of basic geophysical fluid dynamics. We give several elementary examples in which these flows form jets on rotating spheres. Jet formation occurs under a variety of circumstances: when flows driven by external stress have a rigid boundary which can balance the Coriolis force, and at which further concentration can be caused by the beta effect; when there are singular lines like the line of vanishing windstress or windstress-curl, or the Equator; when compact sources of momentum, heat or mass radiate jet-like beta plumes along latitude circles; when random external stirring of the fluid becomes organized by the beta effect into jets; when internal instability of the mass field generates zonal flow which then is concentrated into jets; when bottom topographic obstacles radiate jets, and when frontogenesis leads to shallow jet formation. Essential to the process of jet formation in stratified fluids is the baroclinic life cycle described in geostrophic turbulence studies; there, conversion from potential to kinetic energy generates eddy motions, and these convert to quasibarotropic motions which then radiate and induce jet-like large-scale circulation. Ideas of potential vorticity stirring by eddies generalize the notion of Rossby-wave radiation, showing how jets embedded in an ambient potential vorticity gradient (typically due to the spherical geometry of the rotating planet) gain eastward momentum while promoting broader, weaker westward circulation. Homogenization of potential vorticity is an important limit point, which many geophysical circulations achieve. This well-mixed state is found in subdomains of the terrestrial midlatitude oceans, the high-latitude circumpolar ocean, and episodically in the middle atmosphere. Homogenization expels potential vorticity gradients vertically to the top and bottom of the fluid, and sideways to the edges of flow domains or gyres; in both these ways is jet formation enhanced.     

Absolute instability of a liquid jet in a coflowing stream

Cylindrical liquid jets are inherently unstable and eventually break into drops due to the Rayleigh-Plateau instability, characterized by the growth of disturbances that are either convective or absolute in nature. Convective instabilities grow in amplitude as they are swept along by the flow, while absolute instabilities are disturbances that grow at a fixed spatial location. Liquid jets are nearly always convectively unstable. Here we show that two-phase jets can breakup due to an absolute instability that depends on the capillary number of the outer liquid, provided the Weber number of the inner liquid is >O(1). We verify our experimental observations with a linear stability analysis.     

Jet charge in high-energy nuclear collisions

The averaged jet charge characterizes the electric charge of the initiating parton and provides a powerful tool to distinguish quark jets from gluon jets.We predict,for the first time,the medium modification of the averaged jet charge in the heavy-ion collisions at the LHC,where jet productions in p+p collisions are simulated by PYTHIA6,and the parton energy loss in QGP is calculated with two Monte Carlo models of jet quenching:PYQUEN and JEWEL.We found that the distribution of averaged jet charge is significantly suppressed by initial state isospin effects due to the participation of neutrons with zero electric charge during nuclear collisions.The considerable enhancement of the averaged jet charge in central Pb+Pb collisions is observed relative to peripheral collisions,since the jet quenching effect is more pronounced in central collisions.The distinct feature of the averaged jet charge between quark and gluon jets,along with the sensitivity of medium modifications on the jet charge to flavor dependence of the parton energy loss,could be very useful to discriminate the energy loss pattern between quark and gluon jets in heavy-ion collisions.     

The influence of fragmentation models in the production of hadron jets in electron–positron annihilation

The analysis of electron–positron annihilations to hadrons at high energies shows that apart from two-jet events, there are also signs of three-jet events which are interpreted according to the QCD, as a gluon radiated by a quark. In this paper, we investigate the fragmentation of quarks and gluons to hadron jets. We show that gluon jets have a higher multiplicity compared to quark jets of the same energy. Furthermore, inclusion of different flavours in the distributions shows that quark jets are flavour-dependent, but gluon jets are not. The differences between quark and gluon jets also manifest themselves in the fragmentation functions. We observe that the fragmentation for gluon jet is softer than that for quark jet, because the radiation of soft gluons is larger for gluon jets and that gluon cannot be present as a valence parton inside a produced hadron. We provide possible explanations for these features in this paper.     

Research on the mechanics of underwater supersonic gas jets

An experimental research was carried out to study the fluid mechanics of underwater supersonic gas jets. High pressure air was injected into a water tank through converging-diverging nozzles (Laval nozzles). The jets were operated at different conditions of over-, full- and under-expansions. The jet sequences were visualized using a CCD camera. It was found that the injection of supersonic air jets into water is always accompanied by strong flow oscillation, which is related to the phenomenon of shock waves feedback in the gas phase. The shock wave feedback is different from the acoustic feedback when a supersonic gas jet discharges into open air, which causes screech tone. It is a process that the shock waves enclosed in the gas pocket induce a periodic pressure with large amplitude variation in the gas jet. Consequently, the periodic pressure causes the jet oscillation including the large amplitude expansion. Detailed pressure measurements were also conducted to verify the shock wave feedback phenomenon. Three kinds of measuring methods were used, i.e., pressure probe submerged in water, pressure measurements from the side and front walls of the nozzle devices respectively. The results measured by these methods are in a good agreement. They show that every oscillation of the jets causes a sudden increase of pressure and the average frequency of the shock wave feedback is about 5–10 Hz.     

Noise generation by instabilities in low Reynolds number supersonic jets

An experimental investigation of noise generation by instabilities in low Reynolds number supersonic air jets has been performed. Sound pressure levels, spectra and acoustic phase fronts were measured with a traversing condenser microphone in the acoustic field of axisymmetric, perfectly expanded, cold jets of Mach numbers 1·4, 2·1 and 2·5. Low Reynolds numbers in the range from Re = 3700 to Re = 8700 were obtained by exhausting the jets into an anechoic vacuum chamber test facility. This contrasts with Reynolds numbers of over 10⁶ for similar jets exhausting into atmospheric pressure. The flow fluctuations of the instability in all three jets have been measured with a hot-wire and the results are documented in a previous paper by Morrison and McLaughlin. Acoustic measurements show that the major portion of the sound radiated by all three jets is produced by the instability's rapid growth and decay that occurs near the end of the potential core. This takes place over a relatively short distance (less than two wavelengths of the instability) in the jet. In the lower two Mach number jets the instability has a phase velocity less than the ambient acoustic velocity. In the Mach number 2·5 jet the instability phase speed is 1·11 times the ambient acoustic velocity. In this case the acoustic phase fronts indicate the possibility of a Mach wave component. It was also determined that low level excitation at the dominant frequency of the instability actually decreased the radiated noise by suppressing the broad band component.     

Turbulence and heat excited noise sources in single and coaxial jets

The generation of noise in subsonic high Reynolds number single and coaxial turbulent jets is analyzed by a hybrid method. The computational approach is based on large-eddy simulations (LES) and solutions of the acoustic perturbation equations (APE). The method is used to investigate the acoustic fields of one isothermal single stream jet at a Mach number 0.9 and a Reynolds number 400,000 based on the nozzle diameter and two coaxial jets whose Mach number and Reynolds number based on the secondary jet match the values of the single jet. One coaxial jet configuration possesses a cold primary flow, whereas the other configuration has a hot primary jet. Thus, the configurations allow in a first step the analysis of the relationship of the flow and acoustic fields of a single and a cold coaxial jet and in a second step the investigation of the differences of the fluid mechanics and aeroacoustics of cold and hot coaxial jets. For the isothermal single jet the present hybrid acoustic computation shows convincing agreement with the direct acoustic simulation based on large-eddy simulations. The analysis of the acoustic field of the coaxial jets focuses on two noise sources, the Lamb vector fluctuations and the entropy sources of the APE equations. The power spectral density (PSD) distributions evidence the Lamb vector fluctuations to represent the major acoustic sources of the isothermal jet. Especially the typical downstream and sideline acoustic generations occur on a cone-like surface being wrapped around the end of the potential core. Furthermore, when the coaxial jet possesses a hot primary jet, the acoustic core being characterized by the entropy source terms increases the low frequency acoustics by up to 5 dB, i.e., the sideline acoustics is enhanced by the pronounced temperature gradient.     

A comparison of b and uds quark jets to gluon jets

Symmetric three-jet events are selected from hadronic Z⁰ decays such that the two lower energy jets are each produced at an angle of about 150° with respect to the highest energy jet. In some cases, a displaced secondary vertex is reconstructed in one of the two lower energy jets, which permits the other lower energy jet to be identified as a gluon jet through anti-tagging. In other cases, the highest energy jet is tagged as a b jet or as a light quark (uds) jet using secondary vertex or track impact parameter and momentum information. Comparing the two lower energy jets of the events with a tag in the highest energy jet to the anti-tagged gluon jets yields a direct comparison of b, uds and gluon jets, which are produced with the same energy of about 24 GeV and under the same conditions. We observe b jets and gluon jets to have similar properties as measured by the angular distribution of particle energy around the jet directions and by the fragmentation functions. In contrast, gluon jets are found to be significantly broader and to have a markedly softer fragmentation function than uds jets. For the k _⊥ jet finder with y _cut=0.02, we find $${«ngle n^{? ch.}»ngle {? gluon}?er «ngle n^{? ch.}»ngle {? b} {? quark}}=1.089pm 0.024 ({? stat.})pm0.024 ({? syst.})$$ $${«ngle n^{? ch.}»ngle {? gluon}?er «ngle n^{? ch.}»ngle {? uds} {? quark}}=1.390pm 0.038 ({? stat.})pm0.032 ({? syst.})$$ as the ratios of the mean charged particle multiplicity in the gluon jets compared to the b and uds jets. Results are also reported using the cone jet finder.     

Experimental investigation of combustion instabilities of a mesoscale multinozzle array in a lean-premixed combustor

Self-excited combustion instabilities in a mesoscale multinozzle array, also referred to as a micromixer-type injector, have been experimentally investigated in a lean-premixed tunable combustor operating with preheated methane and air. The injector assembly consists of sixty identical swirl injectors of 6.5 mm inner diameter, which are evenly distributed across the combustor dump plane. Their flow paths are divided into two groups – inner and outer stages – to form radially stratified reactant stoichiometry for the control of self-excited instabilities. OH PLIF measurements of stable flames reveal that the presence of radial staging has a remarkable influence on stabilization mechanisms, reactant jet penetration/merging, and interactions between adjacent flame fronts. In an inner enrichment case, two outer (leaner) streams merge into a single jet structure, whereas the inner (richer) reactant jets penetrate far downstream without noticeable interactions between neighboring flames. The constructed stability map in the 〈?_i, ?_o〉 domain indicates that strong self-excited instabilities occur under even split and outer enrichment conditions at relatively high global equivalence ratios. This is attributed to large-scale flame surface deformation in the streamwise direction, as manifested by vigorous detachment/attachment movements. The use of the inner fuel staging method was found, however, to limit the growth of large-amplitude heat release rate fluctuations, because the center flames are securely anchored during the whole period of oscillation, giving rise to a moderate lateral motion. We demonstrate that the collective motion of sixty flames – rather than the individual local flame dynamics – play a central role in the development of limit cycle oscillations. This suggests that the distribution pattern of the injector array, in combination with the radial fuel staging scheme, is the key to the control of the instabilities.     

Visualization of jet mixing in a fluidic oscillator

The fluidic oscillator is a device that generates an oscillating jet when supplied with fluid at pressure. The oscillator has no moving parts — the creation of the unsteady jet is based solely on fluid-dynamic interactions. Fluidic oscillators can operate at frequencies ranging up to 20 kHz, and are useful for flow control applications. The fluidic oscillator evaluated in the current study is comprised of two fluid jets that interact in an internal mixing chamber, producing the oscillating jet at the exit. Both porous pressure-sensitive paint (PSP) and dye-colored water flow are used to visualize the internal and external fluid dynamics of the oscillator. Porous PSP formulations have been shown to have frequency responses on the order of 100 kHz, which is more than adequate for visualizing the fluidic oscillations. In order to provide high-contrast PSP data in these tests, one of the internal jets of the fluidic oscillator is supplied with oxygen, and the other with nitrogen. Results indicate that two counter-rotating vortices within the mixing chamber drive the oscillations. It is also shown that the fluidic oscillator possesses excellent mixing characteristics.     

Surface density of the polarization charge of a magnetic fluid jet in a uniform electric field

The behavior of magnetic fluid jets in electric and magnetic fields is investigated. A way of calculating the density of a charge forming on the jet’s surface is suggested, and a charge formation mechanism is put forward.     

A comparison of b and uds quark jets to gluon jets

Symmetric three-jet events are selected from hadronic Z⁰ decays such that the two lower energy jets are each produced at an angle of about 150° with respect to the highest energy jet. In some cases, a displaced secondary vertex is reconstructed in one of the two lower energy jets, which permits the other lower energy jet to be identified as a gluon jet through anti-tagging. In other cases, the highest energy jet is tagged as a b jet or as a light quark (uds) jet using secondary vertex or track impact parameter and momentum information. Comparing the two lower energy jets of the events with a tag in the highest energy jet to the anti-tagged gluon jets yields a direct comparison of b, uds and gluon jets, which are produced with the same energy of about 24 GeV and under the same conditions. We observe b jets and gluon jets to have similar properties as measured by the angular distribution of particle energy around the jet directions and by the fragmentation functions. In contrast, gluon jets are found to be significantly broader and to have a markedly softer fragmentation function than uds jets. For thek _⊥ jet finder withy _cut=0.02, we find as the ratios of the mean charged particle multiplicity in the gluon jets compared to the b and uds jets. Results are also reported using the cone jet finder.     

针板型大气压氦气冷等离子体射流的二维模拟

大气压冷等离子体射流的传播机理一直是人们研究的一个热点. 本文采用自洽的二维等离子体流体模型, 研究了大气压氦气冷等离子体射流在自身环境气体中以及在介质管中的传播问题. 得到了电子密度、电离速率、空间电场以及电子温度等参量的时空分布规律, 分析了介质管大小以及介质管介电常数对射流放电性质的影响, 得到了一种提高电子密度和射流尺寸的新方法. 关键词： 大气压冷等离子体射流 等离子体子弹 数值模拟 流体模型