Intermittency as a codimension-three phenomenon

We analyze the interaction of three Hopf modes and show that locally a bifurcation gives rise to intermittency between three periodic solutions. This phenomenon can occur naturally in three-parameter families. Consider a vector fieldf with an equilibrium and suppose that the linearization off about this equilibrium has three rationally independent complex conjugate pairs of eigenvalues on the imaginary axis. As the parameters are varied, generically three branches of periodic solutions bifurcate from the steady-state solution. Using Birkhoff normal form, we can approximatef close to the bifurcation point by a vector field commuting with the symmetry group of the three-torus. The resulting system decouples into phase amplitude equations. The main part of the analysis concentrates on the amplitude equations in R³ that commute with an action ofZ ₂+Z ₂+Z ₂. Under certain conditions, there exists an asymptotically stable heteroclinic cycle. A similar example of such a phenomenon can be found in recent work by Guckenheimer and Holmes. The heteroclinic cycle connects three fixed points in the amplitude equations that correspond to three periodic orbits of the vector field in Birkhoff normal form. We can considerf as being an arbitrarily small perturbation of such a vector field. For this perturbation, the heteroclinic cycle disappears, but an invariant region where it was is still stable. Thus, we show that nearby solutions will still cycle around among the three periodic orbits.     

External Intermittency Simulation in Turbulent Round Jets

Direct numerical and large eddy simulation (DNS and LES) are applied to study passive scalar mixing and intermittency in turbulent round jets. Both simulation techniques are applied to the case of a low Reynolds number jet with Re = 2,400, whilst LES is also used to predict a high Re = 68,000 flow. Comparison between time-averaged results for the scalar field of the low Re case demonstrate reasonable agreement between the DNS and LES, and with experimental data and the predictions of other authors. Scalar probability density functions (pdfs) for this jet derived from the simulations are also in reasonable accord, although the DNS results demonstrate the more rapid influence of scalar intermittency with radial distance in the jet. This is reflected in derived intermittency profiles, with LES generally giving profiles that are too broad compared to equivalent DNS results, with too low a rate of decay with radial distance. In contrast, good agreement is in general found between LES predictions and experimental data for the mixing field, scalar pdfs and external intermittency in the high Reynolds number jet. Overall, the work described indicates that improved sub-grid scale modelling for use with LES may be beneficial in improving the accuracy of external intermittency predictions by this technique over the wide range of Reynolds numbers of practical interest.     

Transition Modeling Using Two Different Intermittency Transport Equations

The accurate numerical simulation of the flow through turbomachinerydepends on the correct prediction of boundary-layer transitionphenomena. Especially heat transfer and skin friction investigationsdemand a reliable simulation of the transition process. Therefore, in this work two different one-equation transport modelsfor a transitional weighting factor are selected and modified for theimplementation into a Reynolds-averaged Navier–Stokes solver. Thisfactor is used to modify the eddy viscosity obtained from a turbulencemodel to simulate the transition process. The first model was originallydeveloped by Steelant and Dick [1] to simulate by-passtransition for high free-stream turbulence. The second model wasproposed by Huang and Suzen [2] as a blending of two modelsfor near-wall intermittency and cross-stream variation of intermittency.In contrast to one-dimensional transition models, the new approachesmodel the transition process not only in flow direction but also acrossthe boundary-layer and thus provide a more realistic prediction of thetransition process. Whereas the Steelant and Dick model (SD) allowsturbulent quantities in the free-stream prior and after transition, thesecond model by Huang and Suzen (HS) sets the free-stream turbulence tozero in the whole flowfield. The models are validated on transitional skin friction experimentson a flat plate (T3 test cases of ERCOFTAC SIG 10), on heat transfermeasurements in a linear turbine cascade done at the VKI and on laservibrometer measurements of a linear turbine cascade. Both models showgood agreement with the skin friction data, but the heat transfer canonly be predicted correctly by the Steelant and Dick model due to itsability to consider the free-stream turbulence.     

Intermittency and scaling in turbulent convection

Both the velocity and temperature measurements taken in turbulent Rayleigh-B‘‘enard convection experiments have been analyzed. It is found that both the velocity and temperature fluctu-ations are intermittent and can be well-described by the She-Leveque hierarchical structure. A positive correlation between the vertical velocity and the temperature differences is found both at the center, near the sidewall and near the bottom of the convection cell, supporting that buoyancy is significant in the Bolgiano regime. Moreover, the intermittent nature of the temperature fluctuations in the Bol-giano regime can be attributed to the variations in the temperature dissipation rate. However, the relations between the velocity and temperature structure functions and their correlations implied by the Bolgiano-Obukhov scaling are not supported by experimental measurements.     

Further Development of a Dynamic Intermittency Model For Wake-Induced Transition

The transition model studied in this paper uses an equation for free-stream intermittency and one for near-wall intermittency, combined with the SST turbulence model. The model was already assessed in earlier work for wake-induced transition in boundary layers in separated state and in attached state. For separated state transition, the model predicts the start and growth of transition very well, except for the impossibility to describe the breakdown of the roll-up vortices in a 2D RANS simulation. In attached state transition, the model has the tendency to generate a delayed start of transition and a too slow growth rate in the initial phase of transition. We demonstrate that a delayed start of transition is inherent for a RANS simulation. We propose a repair for the too slow growth rate in the initial stage of the transition. Additionally, both for wake-induced transition in separated state and in attached state, the original model has the tendency to predict a state too near to laminar in between wakes at the trailing edge. We demonstrate that this is caused by the too rapid destruction of the near-wall intermittency during relaminarization and in the lack of activation of near-wall intermittency for low turbulence level in the free stream. We propose a repair for both deficiencies. The fourth improvement is that we take into account the influence of the free stream turbulence length scale in the criteria for onset of transition. We demonstrate the high quality of the improved model for wake-induced transition on a steam turbine stator blade for outlet Reynolds number 600,000 and two levels of turbulence in the background flow: 3% and 0.4%.     

A Bypass Transition Model Based on the Intermittency Function

An intermittency model that is formulated in local variables is proposed for representing bypass transition in Reynolds-Averaged Navier-Stokes (RANS) computations. No external data correlation is used to fix transition. Transition is initiated by diffusion, and a source term carries it to completion. A sink term is created to predict the laminar region before transition, then it vanishes in the turbulent region. Both the source and sink are functions of a wall-distance Reynolds number and turbulence scale. A modification is introduced to predict transition in separated boundary layers. The transition model is incorporated with the k?ω RANS model. The present model is implemented into a general purpose, computational fluid dynamics (CFD) code. The model is validated with several test cases. Decent agreement with the available data is observed in a range of flows.     

Possible Effects of Small-Scale Intermittency in Turbulent Reacting Flows

It is now well established that quantities such as energy dissipation, scalar dissipation and enstrophy possess huge fluctuations in turbulent flows, and that the fluctuations become increasingly stronger with increasing Reynolds number of the flow. The effects of this small-scale “intermittenc” on various aspects of reacting flows have not been addressed fully. This paper draws brief attention to a few possible effects on reaction rates, flame extinction, flamelet approximation, conditional moment closure methods, and so forth, besides commenting on possible effects on the resolution requirements of direct numerical simulations of turbulence. We also discuss the likelihood that large-amplitude events in a given class of shear flows are characteristic of that class, and that, plausible estimates of such quantities cannot be made, in general, on the hypothesis that large and small scales are independent. Finally, we briefly describe some ideas from multifractals as a potentially useful tool for an economical handling of a few of the problems touched upon here.     

Intermittency in a cantilever plate in a randomly fluctuating fluid flow

Fluid–elastic systems nearing dynamic instabilities are known to be sensitive to fluctuations in fluid flow. A cantilever plate in axial flow with random temporal fluctuations, is examined numerically for its dynamical behaviour. The numerical model comprises of a nonlinear structural model for the flexible plate, coupled with unsteady lumped vortex model for the fluid forces. As the mean flow velocity is increased, the system transitions to limit cycle oscillations from a state of rest, through a regime of intermittent oscillations. The conditions for onset and disappearance of intermittency are discussed and are interpreted using stochastic bifurcation theories. While the onset of intermittency is found to be unaffected by the time scales of the flow fluctuations, they are observed to affect the length of the intermittency regime. The effect of plate flexibility on intermittency is also discussed.     

Intermittency and multiscale dynamics in milling of fiber reinforced composites

We have analyzed the variations in cutting force during milling of a fiber-reinforced composite material. In particular, we have investigated the multiscale dynamics of the cutting force measured at different spindle speeds using multifractals and wavelets. The multifractal analysis revealed the changes in complexity with varying spindle speeds. The wavelet analysis identified the coexistence of important periodicities related to the natural frequency of the system and its multiple harmonics. Their nonlinear superposition leads to the specific intermittent behavior. The workpiece used in the experiment was prepared from an epoxy-polymer matrix composite reinforced by carbon fibers.     

A case of strong nonlinearity: Intermittency in highly turbulent flows

It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We discuss the effect of a small viscosity on the self-similar solution to the Euler equations for inviscid fluids. Then we show that single-point records of velocity fluctuations in the Modane wind tunnel display correlations between large velocities and large accelerations in full agreement with scaling laws derived from Leray's equations (1934) for self-similar singular solutions to the fluid equations. Conversely, those experimental velocity–acceleration correlations are contradictory to the Kolmogorov scaling laws.     

Intermittency in pitch-plunge aeroelastic systems explained through stochastic bifurcations

Nonlinear Dynamics - Aeroelastic systems with hardening nonlinearity exhibit supercritical Hopf bifurcation when the flow velocity exceeds a critical velocity leading to self-sustaining large...     

微动诱发的触点电接触间歇失效现象研究

金属触点是电气电子工程领域中导通电流、传递信号的关键,机械振动应力环境产生的微动将使系统的电接触性能逐步退化,并诱发触点间发生间歇失效现象.借助电动振动台设计了触点微动磨损测试分析系统,以铜镀金触点为研究对象,获得了接触电阻全寿命周期内的退化过程.结合接触电阻与SEM/EDX分析结果确定了微动频率、微动幅值对触点磨损发生间歇失效的条件及电接触间歇失效机理.     

Modelling of Unsteady Transition in Low-Pressure Turbine Blade Flows with Two Dynamic Intermittency Equations

A transition model for describing wake-induced transition is presented based on the SST turbulence model by Menter and two dynamic equations for intermittency: one for near-wall intermittency and one for free-stream intermittency. In the Navier-Stokes equations, the total intermittency factor, which is the sum of the two, multiplies the turbulent viscosity computed by the turbulence model. The quality of the transition model is illustrated on the T106A test cascade for two Reynolds numbers, using experimental results by Stieger and Hodson for transition mainly due to kinematic wake impact on a separation bubble. The quality of the model is also revealed on the T106D test cascade using experimental results from Hilgenfeld, Stadtmuller and Fottner for wake turbulence induced transition. The test cases differ in pitch to chord ratio, Reynolds number and inlet free-stream turbulence intensity, causing different transition mechanisms. The unsteady results are presented in space-time diagrams of shape factor and wall shear stress on the suction side. The results show the capability of the model to capture the physics of unsteady transition in separated state. Inevitable shortcomings are revealed as well.     

Comparison of Two Unsteady Intermittency Models for Bypass Transition Prediction on a Turbine Blade Profile

The present paper evaluates two unsteady transition modelling approaches: the prescribed unsteady intermittency method PUIM, developed at Cambridge University and the dynamic unsteady intermittency method developed at Ghent University. The methods are validated against experimental data for the N3-60 steam turbine stator profile for steady and for unsteady inlet flow conditions. The characteristic features of the test case are moderately high Reynolds number and high inlet turbulence intensity, which causes bypass transition. The tested models rely both on the intermittency parameter and are unsteady approaches. In the prescribed method, the time-dependent intermittency distribution is obtained from integral relations. In the dynamic method, the intermittency distribution follows from time-dependent differential equations. For unsteady computations, self-similar wake profiles are prescribed at the inlet of the computational domain. Joint validation of the prescribed and the dynamic unsteady intermittency models against experimental data shows that both methods are able to reproduce the global features of the periodical evolution of the boundary layer under the influence of a periodically impinging wake. The overall quality of the dynamic method is better than that of the prescribed method.     

Intermittency and stochastic modeling of hydrodynamic pressure fluctuations in the near field of compressible jets

The intermittent statistics of the pressure fluctuations measured in the near field of a compressible jet are investigated under several flow conditions. An experiment is carried out in a semi-anechoic chamber on a single stream compressible jet at Mach numbers varying from 0.5 to 0.9 and measuring the fluctuating pressure in several positions in the near field. The main quantities analyzed are the intermittent time and the energy amplitude of events that are extracted from the experimental data through a wavelet-based tracking algorithm. As an extension of a previous paper (Camussi et al., 2017), low order statistical moments (mean and variance) and Probability Distribution Functions are parametrized in terms of three relevant quantities characterizing the jet flow physics: the Mach number, the radial distance from the jet axis and the axial position. It is observed that the non-dimensional statistical quantities are weakly dependent upon the flow conditions allowing for simple stochastic models to be introduced on the basis of suitable fittings of averaged statistical properties and of the Probability Distribution Functions.     

Development of an Intermittency Equation for the Modeling of the Supersonic/Hypersonic Boundary Layer Flow Transition

An intermittency transport equation is developed in this study to model the laminar-turbulence boundary layer transition at supersonic and hypersonic conditions. The model takes into account the effects of different instability modes associated with the variations in Mach numbers. The model equation is based on the intermittency factor γ concept and couples with the well-known SST k–ω eddy-viscosity model in the solution procedures. The particular features of the present model approach are that: (1) the fluctuating kinetic energy k includes the non-turbulent, as well as turbulent fluctuations; (2) the proposed transport equation for the intermittency factor γ triggers the transition onset through a source term; (3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ, which are often cost-ineffective with the modern CFD methods; (4) in the fully turbulent region, the model retreats to SST model. This model is validated with a number of available experiments on boundary layer transition including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition with a reasonably wide range of Mach numbers.     

Wakes of thin flat plates: Intermittency,cessation of vortex shedding and the emergence of an intermediate-wake instability

The near and intermediate wake regions of thin flat plates with both sharp and circular trailing edges (TEs) are investigated with direct numerical simulations (DNSs). The TE is circular in two of the cases (IN & NS) and sharp in one of them (ST). The separating boundary layers are turbulent in all cases. The main objective here is to explore the effect of significantly reducing the Reynolds number (Re_D, based on circular TE diameter, D) on the flow in the TE region, in particular the vortex shedding process (Cases IN and NS). Intermittent shedding is observed in Case IN. Case NS, with half the TE diameter of Case IN, is an essentially non-shedding case. The second objective is to understand the reasons underlying the findings of an earlier experimental wake investigation (sharp TE) where a broadband peak was observed in centerline cross-stream velocity (v) spectra. Case ST from the present study showed a wake instability resulting in spanwise vortices. The instability is intermittent and contributes to a broadband peak in the centerline v spectrum. Cases IN & NS also exhibit a similar wake instability in the intermediate wake and a corresponding spectral (v) broadband peak. The third objective is to study the distributions of the time-averaged velocity statistics in thin plate wakes. The turbulent stresses and, the budget terms for the streamwise intensity, obtained in Case IN, are included and discussed here. All the budget terms contribute appreciably to the overall budget in the transport equation for streamwise normal intensity.     

Intermittency as a transition to turbulence in pipes: A long tradition from Reynolds to the 21st century

Intermittencies are commonly observed in fluid mechanics, and particularly, in pipe flows. Initially observed by Reynolds (1883), it took one century for reaching a rather full understanding of this phenomenon whose irregular dynamics (apparently stochastic) puzzled hydrodynamicists for decades. In this brief (non-exhaustive) review, mostly focused on the experimental characterization of this transition between laminar and turbulent regimes, we present some key contributions for evidencing the two concomittant and antagonist processes that are involved in this complex transition and were suggested by Reynolds. It is also shown that a clear explicative model was provided, based on the nonlinear dynamical systems theory, the experimental observations in fluid mechanics only providing an applied example, due to its obvious generic nature.     

Intermittency and Regularity Issues in 3<Emphasis Type="Italic">D</Emphasis> Navier-Stokes Turbulence

Two related open problems in the theory of 3D Navier-Stokes turbulence are discussed in this paper. The first is the phenomenon of intermittency in the dissipation field. Dissipation-range intermittency was first discovered experimentally by Batchelor and Townsend over fifty years ago. It is characterized by spatio-temporal binary behaviour in which long, quiescent periods in the velocity signal are interrupted by short, active ‘events’ during which there are violent fluctuations away from the average. The second and related problem is whether solutions of the 3D Navier-Stokes equations develop finite time singularities during these events. This paper shows that Leray’s weak solutions of the three-dimensional incompressible Navier-Stokes equations can have a binary character in time. The time-axis is split into ‘good’ and ‘bad’ intervals: on the ‘good’ intervals solutions are bounded and regular, whereas singularities are still possible within the ‘bad’ intervals. An estimate for the width of the latter is very small and decreases with increasing Reynolds number. It also decreases relative to the lengths of the good intervals as the Reynolds number increases. Within these ‘bad’ intervals, lower bounds on the local energy dissipation rate and other quantities, such as ||u(·, t)||_∞ and ||∇u(·, t)||_∞, are very large, resulting in strong dynamics at sub-Kolmogorov scales. Intersections of bad intervals for n≧1 are related to the potentially singular set in time. It is also proved that the Navier-Stokes equations are conditionally regular provided, in a given ‘bad’ interval, the energy has a lower bound that is decaying exponentially in time.Final version 17 March 05. Original version November 03.     

截尾Gauss概率密度函数中待定参数的确定

给出一种计算描述标量湍流脉动的截尾Gauss概率密度函数的待定参数的方法. 通过将关于待定参数的代数方程组表示成适于求解的形式，综合应用牛顿法、牛顿下山法和阻尼牛顿法等迭代算法，并恰当地选取待定参数的迭代初值，获得了在标量平均值及其脉动均方值的各种取值条件下待定参数的相应数值.