Absolute and convective instabilities of two-dimensional bluff body wakes in ground effect

Local and global instabilities are investigated of wakes of general two-dimensional bluff bodies placed near and parallel to a plane boundary or ground. A spatio-temporal linear stability analysis is first applied to a four-parameter family of local wake profiles to investigate the fundamental local stability characteristics of the wake in ground effect. The analysis shows significant dependencies of the stability characteristics of the wake on the distance from the wake centreline to the ground (normalised by the wake width), and also on the velocity ratio of the near- and far-ground sides of the wake. The analysis is then compared with earlier experiments on a circular cylinder to examine, according to the transition scenario of the steep global modes, the streamwise variation of the local stability characteristics of the wake in ground effect. The comparison indicates that the near wake region of the cylinder changes from being absolutely unstable to being convectively unstable when the cylinder comes down into the near-ground range in which the von Kármán-type vortex shedding from the cylinder is suppressed, being qualitatively consistent with the transition scenario for general wake-type flows. A possible explanation is also given for the counter-intuitive relation between the thickness of the boundary layer on the ground and the critical gap distance for the cessation of the von Kármán-type vortex shedding in ground effect.     

Temporal and spatial instability of an inviscid compound jet

This paper examines the linear hydrodynamic stability of an inviscid compound jet. We perform the temporal and the spatial analyses in a unified framework in terms of transforms. The two analyses agree in the limit of large jet velocity. The dispersion equation is explicit in the growth rate, affording an analytical solution. In the temporal analysis, there are two growing modes, stretching and squeezing. Thin film asymptotic expressions provide insight into the instability mechanism. The spatial analysis shows that the compound jet is absolutely unstable for small jet velocities and admits a convectively growing instability for larger velocities. We study the effect of the system parameters on the temporal growth rate and that of the jet velocity on the spatial growth rate. Predictions of both the temporal and the spatial theories compare well with experiment.Dedicated to the memory of Professor Tasos C. Papanastasiou     

Nonlinear instability of a liquid jet in the presence of a uniform electric field

The nonlinear electrohydrodynamic stability of an irrotational jet in the presence of capillary force and weak viscous stress on the surface has been studied. Two nonlinear modified Schrödinger equations are obtained. Neglecting the viscous stress, the classic Schrödinger equations are obtained. The stability conditions of steady state solutions are investigated, using the modulation concept. It is found that the viscous stress produces a resonance (say a viscous resonance) away from the critical point. For the progressive waves, we obtained modified transition curves inserting the viscous stress. The classic nonlinear cutoff wave number is obtained and this means that the viscous stress has a fluctuating effect on the perturbed jet, away from the critical points.     

流动聚焦及射流不稳定性

流动聚焦是一种有效的微细射流产生方法,其原理可以描述为从毛细管流出的流体由另一种高速运动的流体驱动,经小孔聚焦后形成稳定的锥–射流结构,射流因不稳定性破碎成单分散的液滴.自从1998年流动聚焦被提出以来,陆续发展了单轴流动聚焦、电流动聚焦、复合流动聚焦和微流控流动聚焦等毛细流动技术.这些技术稳定、易操作、没有苛刻的环境条件的要求,能够制备单分散性较好的微纳米量级的液滴、颗粒和胶囊,在科学研究和实际应用中具有重要价值.流动聚焦涉及了多尺度、多界面和多场耦合的复杂流体力学问题,其中稳定的锥形是形成稳定射流的先决条件,过程参数是影响射流界面扰动发展的关键因素,而射流不稳定性分析是揭示射流破碎的最主要理论工具.该文回顾了近二十年来不同结构流动聚焦的研究进展,概述这些技术涉及的过程控制、流动模式、尺度律和不稳定性分析等关键力学问题,总结射流不稳定性的研究方法和已取得的成果,最后展望流动聚焦的研究方向和应用前景.     

Flow focusing and jet instability

流动聚焦是一种有效的微细射流产生方法,其原理可以描述为从毛细管流出的流体由另一种高速运动的流体驱动,经小孔聚焦后形成稳定的锥–射流结构,射流因不稳定性破碎成单分散的液滴.自从1998年流动聚焦被提出以来,陆续发展了单轴流动聚焦、电流动聚焦、复合流动聚焦和微流控流动聚焦等毛细流动技术.这些技术稳定、易操作、没有苛刻的环境条件的要求,能够制备单分散性较好的微纳米量级的液滴、颗粒和胶囊,在科学研究和实际应用中具有重要价值.流动聚焦涉及了多尺度、多界面和多场耦合的复杂流体力学问题,其中稳定的锥形是形成稳定射流的先决条件,过程参数是影响射流界面扰动发展的关键因素,而射流不稳定性分析是揭示射流破碎的最主要理论工具.该文回顾了近二十年来不同结构流动聚焦的研究进展,概述这些技术涉及的过程控制、流动模式、尺度律和不稳定性分析等关键力学问题,总结射流不稳定性的研究方法和已取得的成果,最后展望流动聚焦的研究方向和应用前景.     

Absolute and convective instability of a liquid sheet with transverse temperature gradient

The spatial–temporal instability behavior of a viscous liquid sheet with temperature difference between the two surfaces was investigated theoretically. The practical situation motivating this investigation is liquid sheet heated by ambient gas, usually encountered in industrial heat transfer and liquid propellant rocket engines. The existing dispersion relation was used, to explore the spatial–temporal instability of viscous liquid sheets with a nonuniform temperature profile, by setting both the wave number and frequency complex. A parametric study was performed in both sinuous and varicose modes to test the influence of dimensionless numbers on the transition between absolute and convective instability of the flow. For a small value of liquid Weber number, or a great value of gas-to-liquid density ratio, the flow was found to be absolutely unstable. The absolute instability was enhanced by increasing the liquid viscosity. It was found that variation of the Marangoni number hardly influenced the absolute instability of the sinuous mode of oscillations; however it slightly affected the absolute instability in the varicose mode.     

Flow instability of nanofuilds in jet

The flow instability of nanofluids in a jet is studied numerically under various shape factors of the velocity profile, Reynolds numbers, nanoparticle mass loadings,Knudsen numbers, and Stokes numbers. The numerical results are compared with the available theoretical results for validation. The results show that the presence of nanoparticles enhances the flow stability, and there exists a critical particle mass loading beyond which the flow is stable. As the shape factor of the velocity profile and the Reynolds number increase, the flow becomes more unstable. However, the flow becomes more stable with the increase of the particle mass loading. The wavenumber corresponding to the maximum of wave amplification becomes large with the increase of the shape factor of the velocity profile, and with the decrease of the particle mass loading and the Reynolds number. The variations of wave amplification with the Stokes number and the Knudsen number are not monotonic increasing or decreasing, and there exists a critical Stokes number and a Knudsen number with which the flow is relatively stable and most unstable,respectively, when other parameters remain unchanged. The perturbation with the first azimuthal mode makes the flow unstable more easily than that with the axisymmetric azimuthal mode. The wavenumbers corresponding to the maximum of wave amplification are more concentrated for the perturbation with the axisymmetric azimuthal mode.     

Effect of heat exchange on the interfacial instability of gas-liquid jet

IntroductionInrecentyears,theprosperityofmetalpowdermarket[1] andthedevelopmentofsprayformingtechniquesmakeitnecessarytostudythemechanismofjetatomization .Freelyfallinghightemperaturemetalliquid ,impactedbyhighspeedgasaround ,breaksintodropletsofdifferentsizes,whichprocedureiscalledair_blastatomizationorsprayatomization .Infact,thisprocesshasawiderengineeringapplications,rangingfromfuelinjectorsingasturbinesandjetengines,totwo_phaseflowchemicalreactors ,spraydrying ,andsoon .OnthebasisofKelvi…     

Absolute and convective instability of a supersonic boundary layer

Using the saddle-point method, asymptotics of time evolution for spatially localized three-dimensional intrinsic disturbances are determined. Criteria of absolute instability are established for the case of a branching dispersion relationship. Calculation results for the regions of existence of instability for a flat-plate boundary layer forRe→∞ andM=10 are presented. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika Vol. 40, No. 3, pp. 104–108, May–June, 1999.     

Surface instability and primary atomization characteristics of straight liquid jet sprays

Using the detailed numerical simulation data of primary atomization, the liquid surface instability development that leads to atomization is characterized. The numerical results are compared with a theoretical analysis of liquid–gas layer for a parameter range close to high-speed Diesel jet fuel injection. For intermittent and short-duration Diesel injection, the aerodynamic surface interaction and transient head formation play an important role. The present numerical setting excludes nozzle disturbances to primarily investigate this interfacial instability mechanism and the role of jet head. The first disturbed area is the jet head region, and the generated disturbances are fed into the upstream region through the gas phase. This leads to the viscous boundary layer instability development on the liquid jet core. By temporal tracking of surface pattern development including the phase velocity and stability regime and by the visualization of vortex structures near the boundary layer region, it is suggested that the instability mode is the Tollmien–Schlichting (TS) mode similar to the turbulent transition of solid-wall boundary layer. It is also demonstrated that the jet head and the liquid core play an interacting role, thus the jet head cannot be neglected in Diesel injection. In this study, this type of boundary layer instability has been demonstrated as a possible mechanism of primary atomization, especially for high-speed straight liquid jets. The effect of nozzle turbulence is a challenging but important issue, and it should be examined in the future.     

Effect of acoustic disturbances on a free convective flow

A gas-dynamic flow in an axisymmetric convective jet is studied experimentally. It is demonstrated that the jet flow with Grashof numbers Gr = (0.4–2.0) · 10⁶ is self-similar. Acoustic oscillations directed perpendicular to the axis of symmetry transform the profiles of the gas-flow parameters; two temperature maximums located outside the axis can appear. The results obtained indicate that flow instability is generated in high-gradient regions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 27–33, September–October, 2006.     

Studies on stability and dynamics of a swirling jet

The temporal instability and nonlinear evolution of the swirling jet near a nozzle exit are studied by both normal-mode method and three dimensional direct numerical simulation (3D DNS). It is found that the swirl enhances the maximum linear growth rates for negative helical modes, while decreases the growth rate for axisymmetric mode. Numerical simulations show that the evolution in early stage is compared well with the linear stability theory. In nonlinear stage, the swirl promotes the breakup of 3D large scale organized structures in the flow into small eddies. The project supported by the National Natural Science Foundation of China (19772052)     

电场驱动射流的弯曲失稳分析

本文对电场驱动射流弯曲问题的动力模型作了理论推导和数值分析.在假定射流具有牛顿粘性并作一维流动的基础上,建立了射流运动的控制方程,采用此方程来研究当带电流体穿过电场时受小扰动而产生的失稳现象.将方程无量纲化后,利用简正模态法对控制方程进行了稳定性分析,而后采用伽辽金法求解方程.结果表明,外电场增强、表面电荷量进一步增多(电荷量较大时)、射流轴向流速增大(其值较大时)、射流半径减小以及电荷的分布不均匀性增大,都可以显著增强射流的短波不稳定性;射流偶数阶频率导致了不稳定性,而且阶数越高,不稳定性增长得越快;频率具有虚部,意味着模态中相差的存在;并且射流在短时问内会失去稳定性.     

Absolute inviscid instability of a ring jet with back-flow and swirl

The absolute instability of a ring jet with back-flow and swirl has been investigated on the basis of the inviscid linearized theory for incompressible flow. An axisymmetric disturbance mode is found to be only convectively unstable. The first azimuthal mode can become absolutely unstable, if the ring jet has a back-flow on the jet axis, and an additional swirl can increase the instability. However, for large swirl the absolute instability is suppressed. A ring jet without back-flow becomes absolutely unstable only in the presence of swirl.     

The breakup and atomization of a viscous liquid jet

Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet. With respect to the spatial growing disturbance mode, the numerical results obtained from the solution of the dispersion equation reveal that a dimensionless parameterJ _e exists. AsJ _e>1, the axisymmetric disturbance mode is most unstable; and whenJ _e<1, the asymmetric disturbances come into being, their growth rate increases with the decrease, ofJ _e, till one of them becomes the most unstable disturbance. The breakup of a low-speed liquid jet results from the developing of axisymmetric disturbances, whose instability is produced by the surface tension; while the atomization of a high-speed liquid jet is brought about by the evolution of nonaxisymmetric disturbance, whose instability is caused by the aerodynamic force on the interface between the jet and the ambient gas. The project supported by the National Natural Science Foundation of China     

Temporal stability of a particle-laden jet

The temporal instability of a particle-laden jet was investigated numerically which took into consideration the parametric effects of jet parameter, B, jet Reynolds number, Re_j, particle mass loading, Z and Stokes number, St. The linear stability theory was used to derive the instability equations of a viscous particle-laden jet flow. The single-phase instability of a top-hat jet was then calculated and compared with the available analytical theories. The numerical results agree well with the analytical results for both the axisymmetric (n = 0) and first azimuthal (n = 1) modes. The results show that the first azimuthal mode disturbance is usually more unstable than that of the axisymmetric mode. But the axisymmetric mode disturbance can be more unstable when Z is high enough (i.e., Z ? 0.1). The higher B and Re_j are, the more unstable the particle-laden jet will be. The existence of particles enhances the flow stability. With the increasing of Z, the jet flow will grow more stable. The inviscid single-phase jet is the most unstable. The wave amplification, c_i first decreases with the increasing of St and then increases afterwards. There exist certain values of St, at which the jet is the most stable.     

Design and operation of the free jet elongational rheometer

The controlled free jet instability is used for elongational rheometry of polymer solutions. The instantaneous elongational viscosity represents a convenient comparative parameter. Its dependence on the operating parameters and the conditions of operation will be discussed.