Linear instability of plane Couette and Poiseuille flows

It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers Re > Re_th ≈ 139, which agrees with the experimental value of Re_th ≈ 150 ± 5 [16, 17]. This new result of the linear theory of hydrodynamic stability is obtained by abandoning traditional assumption of the longitudinal periodicity of disturbances in the flow direction. It is established that previous notions about linear stability of this flow at arbitrarily large Reynolds numbers relied directly upon the assumed separation of spatial variables of the field of disturbances and their longitudinal periodicity in the linear theory. By also abandoning these assumptions for plane Poiseuille flow, a new threshold Reynolds number Re_th ≈ 1035 is obtained, which agrees to within 4% with experiment—in contrast to 500% discrepancy for the previous estimate of Re_th ≈ 5772 obtained in the framework of the linear theory under assumption of the “normal” shape of disturbances [2].     

Local bifurcations of synchronization in self-excited and forced unidirectionally coupled micromechanical resonators

A unidirectionally coupled system of Microelectromechanical Systems (MEMS) resonators is investigated. Local bifurcations of both the single resonator and the coupled system are analyzed in the design of the coupled system. We discuss the behavior of the coupled system according to the change in the coupling parameter and the excitation force. Phenomena such as quasiperiodic oscillations and synchronization are shown by numerical simulations and studied analytically through perturbation methods. The coupled system shows oscillatory behavior without the excitation force. In the presence of the excitation force the coupled system exhibits complex behavior which can be beneficial in the design of the coupled system as a sensor.     

The sharkskin instability of polymer melt flows

Flows of polymeric liquids undergo instabilities whose origins are quite different from those of Newtonian flows, due to their elastic character and the complexity of the fluid/solid boundary condition. This article reviews recent studies of one such instability, the sharkskin phenomenon observed during extrusion of many linear polymers. Key experimental observations are summarized; one important fact that has become clear is the importance of the interaction between the molten polymer and the solid walls of the flow channel, especially near the contact line at the exit of the channel. Recent developments in understanding the relationship between wall slip and disentanglement of wall-adsorbed polymers from the bulk flow are briefly described, and putative heuristic mechanisms relating the instability to slip and contact line motion are presented. Finally, we review mathematical analyses of the stability of viscoelastic shear flows with slip boundary conditions. Some recent analyses yield instability predictions that are consistent with experiments, but further work is required to discriminate between the various mechanisms that have been proposed. (c) 1999 American Institute of Physics.     

Small-scale-velocity-induced linear instability of large-scale turbulent flows

Analysis of a simplified equation derived previously for small-scale velocity components shows that any turbulent flow of an incompressible liquid becomes unstable against infinitesimal perturbations of small-scale velocity components if the strain rate tensor for the large-scale velocity is high. Such a statement comes into conflict with the classical stability theory, which specifically asserts that the Poiseuille flow in a circular tube is linearly stable against infinitesimal perturbations.     

On the baroclinic instability of nonplanar flows

Summary Different ocean models with one or two layers having constant static stability and supporting constant-shear flows, whose directions are allowed to change with depth, are examined in the frame-work of the linear nonzonal baroclinic stability theory and in the absence of the β-effect. The analysis is reduced to solving a simple Sturm-Liouville boundary value problem in one dimension. A fairly general dispersion relation is found which correctly reproduces several special cases analysed by other authors. This relation shows a fair variety of possible behaviours for stability curves of two-layer models. The results show that the presence of a nonplanar shear-flow may have profound consequences on the stability character of the stationary geostrophic flow. In fact, it appears that the stability properties are strongly dependent on the propagation angle of the disturbance so that wave numbers which appear stable in the usual zonal theory may result unstable on such a nonzonal flow andvice versa. Paper presented at the 1^o Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 19–22, 1984, Rome.     

Local plasma parameters and integral characteristics of a magnetogasdynamic channel under conditions of ionization instability

Results are presented from an experimental investigation of the onset of ionization instability in a disk-shaped Faraday magnetogasdynamic channel attached to a shock tube. The experiments were carried out in a pure inert gas (xenon) without alkaline additives. A relation is found between the integral plasma characteristics of a nonequilibrium magnetogasdynamic channel and the local parameters of a plasma that is unstable against the ionization instability. Mechanisms for amplifying perturbations and increasing the effective conductivity are revealed. It is concluded that these effects stem mainly from the features of three-body recombination in rare gases.     

Numerical analysis of self-excited tangential combustion instability for an MMH/NTO rocket combustor

This study presented the numerical simulation of the tangential combustion instability in a hypergolic liquid bipropellant rocket thrust chamber, which applied fuel liquid film cooling method and unlike impinging injectors. The liquid spray was modeled using Lagrangian approach, while the gas was regarded as Euler phase. Stress-blended eddy simulation and finite rate/eddy–dissipation model were adopted to simulate the turbulent combustion process. Consistent with the experiment results, this work successfully simulated the transformation of tangential combustion instability from standing mode to spinning mode. The mean pressure, amplitude and frequency of limit cycle oscillation were in good agreement with the experiment. There was a detailed analysis about the flow field, Rayleigh index, and driving mechanism of the combustion instability. It was found that the oscillation began with hot spots of heat release rate due to the interaction between the spray of impinging injectors and cooling fuel jet. More than that, cooling fuel jet also contributed to drive the oscillation. In the standing mode, injectors in the inner and outer rings drive the oscillation together, while the spinning mode is mainly driven by injectors in the outer ring. The pressure wave is subsonic and its Mach number is close to 1. It was shown that the pressure wave contained a complex structure divided into three parts. This led to the in-phase of the pressure along the axial direction and the double-peak characteristic of the downstream pressure signal. Besides, a positive feedback closed-loop system associated with periodic oxidizer/fuel ratio was believed to sustain the combustion instability. The oscillation can be maintained when pressure, heat release and oxidizer/fuel ratio are coupled together. The analysis results indicate that rotating detonation is an implication to tangential combustion instability.     

Nonlinear stability and instability of transonic flows through a nozzle

We study transonic flows along a nozzle based on a one-dimensional model. It is shown that flows along the expanding portion of the nozzle are stable. On the other hand, flows with standing shock waves along a contracting duct are dynamically unstable. This was conjectured by the author based on the study of noninteracting wave patterns. The author had shown earlier that supersonic and subsonic flows along a duct with various cross sections are stable. Basic to our analysis are estimates showing that shock waves tend to decelerate along an expanding duct and accelerate along a contracting duct.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041. This material is based upon work supported by the National Science Foundation under Grant No. MCS 7802202 and by the Sloan Foundation     

Computational investigations of the coupling between transient flame dynamics and thermo-acoustic instability in a self-excited resonance combustor

Combustion instability due to thermo-acoustic interactions is a critical combustion problem that requires a thorough understanding because of its adverse impact on stable and reliable operation of combustors in high-speed propulsion devices like gas turbines and rockets. This work conducts computational investigations of the coupling between the transient flame dynamics such as the ignition delay and local extinction and the thermo-acoustic instability developed in a self-excited resonance combustor to gain deep insights into the mechanisms of thermo-acoustic instability. A 2D modelling framework that employs different flamelet models (the steady flamelet model and the flamelet/progress variable approach) is developed to enable the examination of the effect of the transient flame dynamics caused by the strong coupling of the turbulent mixing and finite-rate chemical kinetics on the occurrence of thermo-acoustic instability. The models are validated by using the available experimental data for the pressure signal. Parametric studies are performed to examine the effect of the occurrence of the transient flame dynamics, the effect of artificial amplification of the Damköhler number, and the effect of neglecting mixture fraction fluctuations on the predictions of the thermo-acoustic instability. The parametric studies reveal that the occurrence of transient flame dynamics has a strong influence on the onset of the thermo-acoustic instability. Further analysis is then conducted to localise the effect of a particular flame dynamic event, the ignition delay, on the thermo-acoustic instability. The reverse effect of the occurrence of the thermo-acoustic instability on the transient flame dynamics in the combustor is also investigated by examining the temporal evolution of the local flame events in conjunction with the pressure wave propagation. The above observed two-way coupling between the transient flame dynamics (the ignition delay) and the thermo-acoustic instability provides a plausible mechanism of the self-excited and sustained thermo-acoustic instability observed in the combustor despite the fact that the results are obtained from 2D simulations. The same analysis is expected to be extensible to fully 3D simulations.     

可压流体Rayleigh-Taylor不稳定性的离散Boltzmann模拟

使用离散Boltzmann模型模拟了可压流体系统中多模初始情况下的Rayleigh-Taylor不稳定性.该离散Boltzmann模型等效于一个Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.通过模拟Riemann问题:Sod激波管、冲击波碰撞和热Couette流问题验证模型的有效性,所得数值结果与解析解一致.利用该模型对界面间断随机多模初始扰动的可压Rayleigh-Taylor不稳定性进行数值模拟研究,得到不稳定性界面演化过程的基本图像.由于黏性和热传导共同作用,一开始扰动界面被"抹平",演化较慢;随着模式互相耦合而减少,演化开始加速,并经历非线性小扰动阶段和不规则非线性阶段,而后发展成典型的"蘑菇状",后期进入湍流混合阶段.由于扰动模式的耦合与发展,轻重流体的重力势能、压缩能与动能相互转化,系统先是趋于热动平衡态,而后偏离热动平衡态以线性形式增长,接着再次趋于热动平衡态,最后慢慢远离热动平衡态.     

Dissipative instability of charged aerosol flows in the mesosphere

We consider the possible mechanism of generation of charged-particle density irregularities and electric field in the middle atmosphere based on the development of the dissipative instability of a flow of large charged aerosols. A dispersion equation describing the properties of the spectral component of a quasi-static electric field with allowance for the aerosol charging inertia is obtained. This equation is used to study characteristics of the instability threshold. It is shown that the charging inertia and the presence of photoelectrons lead to an increase and a decrease in the threshold plasma frequency of the aerosols, respectively. It is found that there exist optimal combinations of such parameters as the radius of spherical aerosols and the mass of heavy ion clusters for which the instability threshold is minimum. It is also shown that the instability threshold is lower for the particles stretched along the motion direction. Quantitative estimates are given for medium parameters necessary for the excitation of instability in the region of existence of polar mesospheric summer echo as well as for spatial scales of unstable perturbations. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 11, pp. 942–957, November 2006.     

Self-organization of temporal structures in a multiequilibrium self-excited oscillator system with frequency control

An analysis is made of the nonlinear dynamics of a model of a self-excited oscillator system with automatic fine tuning of the frequency and possessing more than one equilibrium state. It is shown that, depending on the delay parameters of the control loop and the initial frequency detuning, various periodic and stochastic temporal structures may be formed, accompanied by the generation of various limit cycles and chaotic attractors in phase space. Reasons for the onset of self-modulation are set forth, and the position of the different oscillation regions is established. The main bifurcations are studied together with scenarios for the transformation of the oscillator self-modulation modes as a function of the parameters. Zh. Tekh. Fiz. 67, 1–8 (March 1997)     

Comparative analysis of the frequency noise in two distributed circuits of semiconductor self-excited oscillators

Kuibyshev State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 2, pp. 242–245, February, 1989.     

Structure and dynamics of edge flames in the near wake of unequal merging shear flows

We examine in this study the structure and dynamic properties of an edge flame formed in the near-wake of two initially separated shear flows, one containing fuel and the other oxidiser. A comprehensive study is carried out within the diffusive-thermal framework where the flow field, computed a-priori, is used for the determination of the combustion field. Our focus is on the effects of three controlling parameters: the Damköhler number controlling the overall flow rate, the oxidiser-to-fuel strain rate ratio of the supply streams that determines the extent of oxidiser entrainment towards the mixing zone, and the Lewis number, assumed equal for the fuel and oxidiser, that depends on the mixture composition. Response curves, representing the edge flame standoff distance as a function of Damköhler number, exhibit two distinct shapes: C-shaped and U-shaped curves characterising the response of low and high Lewis number flames, respectively. Stability considerations show that the upper solution branch of the C-shaped response curve is unstable and hence corresponds to physically unrealistic states, but due to heat conduction toward the cold plate the lower solution branch is always stable. The states forming this solution branch correspond to flame attachment, where the edge flame remains practically attached to the tip of the plate until it is blown off by the flow when the velocity exceeds a critical value. The U-shaped response, on the other hand, consists of equilibrium states that are globally stable. Thus, high Lewis number flames can be always stabilised near the splitter plate, with the edge held stationary or undergoing a back and forth motion, or lifted and stabilised downstream by the flow. Insight into the distinct stabilisation characteristics, exhibited by the different Lewis number cases, is given by examining the relationship between the local flow velocity and the edge propagation speed.