An experimental study of the decay of turbulent puffs in pipe flow

As reported in a number of recent studies, turbulence in pipe flow is transient for Re<2000 and the flow eventually always returns to the laminar state. Generally, the lifetime of turbulence has been observed to increase rapidly with Reynolds number but there is currently no accord on the exact scaling behaviour. In particular, it is not clear whether a critical point exists where turbulence becomes sustained or if it remains transient. We here aim to clarify if these conflicting results may have been caused by the different experimental and numerical protocols used to trigger turbulence in these studies.     

Transition to Turbulence in Pipe Flow

We review the results of recent experimental investigations into transition to turbulence in fluid flow through a circular straight pipe, at room temperature. The stability of Hagen–Poiseuille flow was investigated using impulsive perturbations by either injecting or sucking small amounts of fluid through holes in the wall of the pipe. The evolution of the induced patches of disturbed flow were observed using flow visualization and laser Doppler velocimetry. The principle result obtained was a finite amplitude stability curve where the critical amplitude of the disturbance required to cause transition is found to be inversely proportional to the Reynolds number. Estimates for the lower threshold value of Reynolds number which is required to sustain turbulence were also measured.     

Dynamical systems and the transition to turbulence in linearly stable shear flows

Plane Couette flow and pressure-driven pipe flow are two examples of flows where turbulence sets in while the laminar profile is still linearly stable. Experiments and numerical studies have shown that the transition has features compatible with the formation of a strange saddle rather than an attractor. In particular, the transition depends sensitively on initial conditions and the turbulent state is not persistent but has an exponential distribution of lifetimes. Embedded within the turbulent dynamics are coherent structures, which transiently show up in the temporal evolution of the turbulent flow. Here we summarize the evidence for this transition scenario in these two flows, with an emphasis on lifetime studies in the case of plane Couette flow and on the coherent structures in pipe flow.     

微管道内湍流转捩的实验研究

研究旨在确定微管道内流动从层流到湍流转捩的临界雷诺数。利用微观粒子图像测速技术(Micro-PIV)研究了去离子水在内径为230μm的圆形截面玻璃微管道内的流场结构,得到了从层流到充分发展湍流各流动状态下的轴向平均速度分布和湍流度分布,实验雷诺数为1020~3145,同时研究了微管道内的流动阻力特性。平均速度场和脉动速度场的实验结果表明微管道内从层流到湍流的转捩发生在Re=1800~1900左右,与流动阻力的测量结果一致,与宏观流动比较,并未发现微管道内的流动转捩有明显提前。实验结果还显示,当Re>2700时,微管道内的平均流速分布和相对湍流度分布呈现典型的充分发展湍流状态特征。     

单声道超声水表测量特性分段校正方法的研究

当管道内流体处于不同雷诺数测量条件时,超声水表的线平均流速v_L与面平均流速v_S之间存在着显著的非线性。根据管道内被测流体介质流动分布状态不同,提出了一种分段流量测量特性校正新方法,在其临界处设立校正分界点,当层流时,采用常系数校正;湍流与过渡流时,分别采用拟合直线方程校正。经实验验证,该方法是可行的。     

An optimal path to transition in a duct

This paper is concerned with the transition of the laminar flow in a duct of square cross section. As in the similar case of pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate for a study of the 'bypass' path to turbulence. It has already been shown that the classical linear optimal perturbation problem, yielding optimal disturbances in the form of longitudinal vortices, fails to provide an 'optimal' path to turbulence, i.e. optimal perturbations do not elicit a significant nonlinear response from the flow. Previous simulations have also indicated that a pair of travelling waves generates immediately, by nonlinear quadratic interactions, an unstable mean flow distortion, responsible for rapid breakdown. By the use of functions quantifying the sensitivity of the motion to deviations in the base flow, the optimal travelling wave associated with its specific defect is found by a variational approach. This optimal solution is then integrated in time and shown to display a qualitative similarity to the so-called 'minimal defect', for the same parameters. Finally, numerical simulations of an 'edge state' are conducted, to identify an unstable solution that mediates laminar-turbulent transition and relate it to results of the optimization procedure.     

A criterion of similarity and transition to turbulence for electric arc flows

A method is suggested for determining the similarity criterion and the criterion of transition of an electric arc flow in a plasmatron channel from a laminar regime to a turbulent one (equivalent Reynolds number) that does not require using any reference temperature. Application of this method to the available experimental data on the transition to turbulence demonstrates its correctness and efficiency. The critical value of the proposed similarity criterion corresponding to the boundary of the transition from a laminar regime to a turbulent one has been revealed. A marginal curve separating the regions of the laminar and turbulent regimes of the plasma flow has been plotted in the space of the operating plasmatron parameters. A phenomenon of a double change of the electric arc flow regime with electric current rise upon constant plasma-forming gas flow rate has been discovered.     

Rotating Couette flow of helium II

An experimental study of He II Couette flow is reported. Using second-sound measurements (Doppler effect, attenuation), we show the existence of different regimes and study their dependence on temperature and gap between the cylinders. We propose a simple model which allows a qualitative understanding of our experimental results. According to this model, the transition from laminar to turbulent flow takes place in two stages by a series of instabilities. First, the laminar regime vortex array is disorganized. Then, normal fluid instabilities lead to turbulence of the whole He II.Laboratoire associé au Centre National de la Recherche Scientifique.     

Boundary layer on a permeable wall with suction of gas

The differential model of turbulence, supplemented with transport equation for turbulent heat flux, is used to perform a numerical investigation of the boundary layer on a permeable wall with suction of gas. It is demonstrated that the protraction of transition from laminar to turbulent mode of flow and the laminarization of the initial turbulent boundary layer occur under conditions of suction of gas. This is evidenced both by the behavior of integral and local characteristics of flow and heat transfer and by the degeneracy of turbulence when the suction of laminar turbulent layer becomes asymptotic. The critical values of the suction parameter are determined.     

Laminar-to-Turbulence Transition Revealed Through a Reynolds Number Equivalence

Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence γ (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where γ = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y⁺ = 1, where y⁺ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of γ against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, γ ≈ 25, and for plate flow, γ ≈ 151.5. These findings suggest that a certain combination of γ and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.     

翼形表面流动激励载荷特征试验研究

为了研究水下航行体翼形表面流动激励载荷特征,采用柔性基底微型传感器阵列,建立风洞中翼形结构表面流动激励载荷测试方法。分析了翼形表面层流、转捩、湍流发展过程中激励力试验特征,试验结果表明:翼形表面经过层流、转捩、湍流发展过程,随着来流速度的增大,翼形表面转捩区位置逐渐前移直至完全湍流。提出了转捩点预报修正方法,修正后预报值与试验值偏差在 10 % 以内,为水下航行体翼形流动激励力相关研究提供试验基础。     

Normal Fluid Velocity Profile and Transition from T-1 to T-2 State of Superfluid Turbulence

It has been known for many years that in a circular counterflow pipe there exist two different states of turbulence of helium II: the T-1 state, which appears at low values of heat flux, and the T-2 state, which appears suddenly at higher heat flux and is characterized by a much higher density of quantized vortex lines. Until now the nature of the two turbulent states has been a mystery. To understand this problem we have addressed the issue of the velocity profile of the normal fluid and its stability. The computed critical heat flux of the transition from the T-1 state to the T-2 state is found to be in good agreement with the observations. The result indicates that in the T-1 state the superfluid is turbulent but the normal fluid is still laminar. The T-1 to T-2 transition corresponds to the onset of normal fluid turbulence.     

Laminar and Turbulent Transition of Fine-Grained Slurries

An experimental investigation of flow behavior of fine-grained highly concentrated slurries, i.e., water mixtures of kaolin and fly ash from a fluidic-type combustion chamber produced during the process of desulphurization, in horizontal straight pipes is presented. A pipe loop with hydraulically smooth stainless steel pipes was used to measure the slurry flow parameters. Kaolin slurry has time-independent, yield pseudo-plastic response for volume concentrations higher than about 6%. In contrast, fluidic fly ash-gypsum water mixture is time dependent and showed substantial decrease of flow resistance due to the effect of shearing during the initial period of pumping. An intensive shearing of concentrated fluidic fly ash-gypsum slurry results in a substantial reduction of the hydraulic gradient in the laminar region and in a marked shift of the laminar/turbulent transition point towards a lower velocity value. After shearing in a turbulent regime a reduction in the hydraulic gradient at the transition point reached about 50% of its original value. The transition from laminar to turbulent regime results in an abrupt increase of flow resistance. The flow patterns become fundamentally different for the two regimes. It was found that pressure fluctuation could well indicate the laminar/turbulent transition. The transition from laminar to turbulent flow is very important for accurate and efficient design and operation of dense slurry pipelining. The optimum operational condition is slightly above the laminar/turbulent transition point, where flow conditions are often very attractive from an economic point of view.     

Laminar and Turbulent Transition of Fine-Grained Slurries

An experimental investigation of flow behavior of fine-grained highly concentrated slurries, i.e., water mixtures of kaolin and fly ash from a fluidic-type combustion chamber produced during the process of desulphurization, in horizontal straight pipes is presented. A pipe loop with hydraulically smooth stainless steel pipes was used to measure the slurry flow parameters. Kaolin slurry has time-independent, yield pseudo-plastic response for volume concentrations higher than about 6%. In contrast, fluidic fly ash-gypsum water mixture is time dependent and showed substantial decrease of flow resistance due to the effect of shearing during the initial period of pumping. An intensive shearing of concentrated fluidic fly ash-gypsum slurry results in a substantial reduction of the hydraulic gradient in the laminar region and in a marked shift of the laminar/turbulent transition point towards a lower velocity value. After shearing in a turbulent regime a reduction in the hydraulic gradient at the transition point reached about 50% of its original value. The transition from laminar to turbulent regime results in an abrupt increase of flow resistance. The flow patterns become fundamentally different for the two regimes. It was found that pressure fluctuation could well indicate the laminar/turbulent transition. The transition from laminar to turbulent flow is very important for accurate and efficient design and operation of dense slurry pipelining. The optimum operational condition is slightly above the laminar/turbulent transition point, where flow conditions are often very attractive from an economic point of view.     

Formation and development of turbulence during movement of a disperse system in a round tube

The experimental results are presented for a study of the turbulence intensity, coefficient of intermittence, and average velocity profile during the transition of the laminar flow of an aqueous dispersion of bentonite clay to turbulent flow. A calculation of the critical value of the Reynolds number is offered.     

Superfluid turbulence in a nonuniform circular channel

We have measured the dissipation associated with superfluid turbulence in a nonuniform channel of circular cross section in order to further explore the discrepancies with theory discovered previously in a nonuniform rectangular channels. Our data show that the two turbulent states supported in uniform circular channels (TI andTII) are also present in our experiments for either diverging or converging flow, indicating that this two-state structure is quite robust. The transition from laminar flow to theTI state and the transition from theTI to theTII state each occur at stationary turbulent fronts in the channel. One consequence of this phenomenon is that theTI/TII transition is substantially broadened. Our data for theTI state, when analysed assuming local uniformity, are in excellent agreement with previous results from uniform channels. The broadenedTI/TII transition severely restricts our experimental access to theTII state. Nevertheless, our data are consistent with the same kind of modification to the vortex line density found for the nonuniform rectangular channels.     

Critical threshold in pipe flow transition

This study provides a numerical characterization of the basin of attraction of the laminar Hagen-Poiseuille flow by measuring the minimal amplitude of a perturbation required to trigger transition. For pressure-driven pipe flow, the analysis presented here covers autonomous and impulsive scenarios where either the flow is perturbed with an initial disturbance with a well-defined norm or perturbed by means of local impulsive forcing that mimics injections through the pipe wall. In both the cases, the exploration is carried out for a wide range of Reynolds numbers by means of a computational method that numerically resolves the transitional dynamics. For , the present work provides critical amplitudes that decay as Re(-3/2) and Re(-1) for the autonomous and impulsive scenarios, respectively. For Re=2875, accurate threshold amplitudes are found for constant mass-flux pipe by means of a shooting method that provides critical trajectories that never relaminarize or trigger transition. These transient states are used as initial guesses in a damped Newton-Krylov method formulated to find periodic travelling wave solutions that either travel downstream or exhibit a helicoidal advection.     

粘性液体对管道中扭转导波传播特性的影响研究

对带有液体的圆柱/管中的波传播进行了研究。在流动为层流的假设下,研究了有粘性液体管道中扭转导波的位移模式和传播特性。分析了波的频散和衰减曲线,得到了粘性、密度等和第一阶扭转模态衰减的关系,确定了粘性液体对扭转导波的影响,为扭转导波在损伤检测中应用做了一些理论工作。数值计算结果与某文献中实验结果符合较好,一定程度上证明了液体中的层流假设,说明了第一阶扭转模态在损伤探测中的优势。     

Aspects of linear and nonlinear instabilities leading to transition in pipe and channel flows

The failure of normal-mode linear stability analysis to predict a transition Reynolds number (Retr) in pipe flow and subcritical transition in plane Poiseuille flow (PPF) has led to the search of other scenarios to explain transition to turbulence in both flows. In this work, various results associated with linear and nonlinear mechanisms of both flows are presented. The results that combine analytical and experimental approaches indicate the strong link between the mechanisms governing the transition of both flows. It is demonstrated that the linear transient growth mechanism is based on the existence of a pair of least stable nearly parallel modes (having opposite phases and almost identical amplitude distributions). The analysis that has been applied previously to pipe flow is extended here to a fully developed channel flow predicting the shape of the optimized initial disturbance (a pair of counter-rotating vortices, CVP), time for maximum energy amplification and the dependence of the latter on Re. The results agree with previous predictions based on many modes. Furthermore, the shape of the optimized initial disturbance is similar in both flows and has been visualized experimentally. The analysis reveals that in pipe flow, the transient growth is a consequence of two opposite running modes decaying with an equal decay rate whereas in PPF it is due to two stationary modes decaying with different decay rates. In the first nonlinear scenario, the breakdown of the CVPs (produced by the linear transient growth mechanism) into hairpin vortices is followed experimentally. The associated scaling laws, relating the minimal disturbance amplitude required for the initiation of hairpins and the Re, are found experimentally for both PPF and pipe flow. The scaling law associated with PPF agrees well with the previous predictions of Chapman, whereas the scaling of the pipe flow is the same as the one previously obtained by Hof et al. indicating transition to a turbulent state. In the second nonlinear scenario, the base flow of pipe when it is mildly deviated from the Poiseuille profile by an axisymmetric distortion is examined. The nonlinear features reveal a Retr of approximately 2000 associated with the bifurcation between two deviation solutions.     

DNS of turbulent flows with intermittency formed in a spherical layer with modulated velocity of rotation of the outer spherical boundary

Turbulent flow regimes in a layer of a viscous incompressible fluid confined between counter-rotating spherical boundaries have been numerically simulated in the case of periodic variations in the velocity of outer sphere rotation at a constant velocity of the inner sphere. The obtained solutions reveal temporal alteration of the laminar and turbulent regimes occupying the entire spatial region of flow in the spherical layer. The numerical results agree with the available experimental data on the shape of the velocity profile and the relative duration of its laminar phase. Factors responsible for the transition to chaos and the appearance of intermittency during this transition are established.