How does flow in a pipe become turbulent?

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by threedimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs.     

Transition to turbulence in a shear flow

We analyze the properties of a 19-dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations shows a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition scenario in shear flows.     

Statistical analysis of the transition to turbulence in plane Couette flow

We argue on general grounds that the transition to turbulence in plane Couette flow is best studied experimentally at a statistical level. We present such a statistical analysis of experimental data guided by a parallel investigation of a simple coupled map lattice model for spatiotemporal intermittency. We confirm that this generic type of spatiotemporal chaos is relevant in the context of plane Couette flow, where the linear stability of the laminar regime at all Reynolds numbers insures the necessary local subcriticality. Using large ensembles of similar experiments, we show the existence of a well-defined threshold Reynolds number above which a unique, turbulent, intermittent attractor coexists with the laminar flow. Furthermore, our data reveals that this transition to spatiotemporal intermittency is discontinuous, i.e. akin to a first-order phase transition. Received: 10 April 1998 / Revised: 22 June 1998 / Accepted: 24 June 1998     

Pattern Fluctuations in Transitional Plane Couette Flow

In wide enough systems, plane Couette flow, the flow established between two parallel plates translating in opposite directions, displays alternatively turbulent and laminar oblique bands in a given range of Reynolds numbers R. We show that in periodic domains that contain a few bands, for given values of R and size, the orientation and the wavelength of this pattern can fluctuate in time. A procedure is defined to detect well-oriented episodes and to determine the statistics of their lifetimes. The latter turn out to be distributed according to exponentially decreasing laws. This statistics is interpreted in terms of an activated process described by a Langevin equation whose deterministic part is a standard Landau model for two interacting complex amplitudes whereas the noise arises from the turbulent background.     

Turbulence regeneration in pipe flow at moderate Reynolds numbers

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.     

Stability and angular-momentum transport of fluid flows between corotating cylinders

Turbulent transport of angular momentum is a necessary process to explain accretion in astrophysical disks. Although the hydrodynamic stability of disklike flows has been tested in experiments, results are contradictory and suggest either laminar or turbulent flow. Direct numerical simulations reported here show that currently investigated laboratory flows are hydrodynamically unstable and become turbulent at low Reynolds numbers. The underlying instabilities stem from the axial boundary conditions, affect the flow globally, and enhance angular-momentum transport.     

Rheology of blood by NMR

Pipe flow of blood in tubes of 1 and 7 mm inner diameter, respectively, was investigated employing two-dimensional NMR velocity imaging and PFG propagator measurements at different Reynolds numbers between 10 and 3500. The results are compared to flow of a water/glycerol mixture of matching viscosity under identical conditions. The transition from laminar to turbulent flow is observed by both a flattening of the velocity profile and a change of the propagator shape. For blood flow this transition is found to be shifted toward higher Reynolds numbers as compared to the transition of the water/glycerol mixture. This observation is in agreement with predictions from hydraulic measurements and is a consequence of the non-Newtonian flow characteristics of blood as a suspension of erythrocytes and plasma. Likewise, a deviation from the laminar flow condition is observed for blood at low Reynolds numbers between 10 and 100. This phenomenon is unknown for Newtonian liquids and is explained by the onset of a geometrical arrangement of the erythrocytes, the so-called rouleaux effect.     

Influence of initial conditions at the nozzle exit on the structure of round jet

Experimental data concerning the influence of initial conditions at the nozzle exit on the structure and development characteristics of round jets are reported. Features in the development of laminar and turbulent round jets emanating from variously elongated nozzles at identical Reynolds numbers are revealed. Smoke visualization pictures obtained for jets formed under different initial conditions (with different distributions of mean and pulsating flow velocities at the nozzle exit) are discussed. It is shown possible to make the zone of laminar flow in the jet stream more extended, and to delay the jet turbulization process in space, by making the flow-velocity profile more parabolic at the exit of elongated nozzle. Features in the development of vortical structures in a jet under an acoustic action are identified. It is shown that, for a turbulent round jet to be produced right at the nozzle exit, the nozzle length must be increased in excess of a certain value so that to provide for spatial growth of turbulent boundary layer thickness, finally ending in the formation of a fully turbulent flow velocity profile across the channel. This work was supported by the Russian Foundation for Basic Research (Grant No. 08-01-00027), the Ministry of Education and Science of the Russian Federation (project RNP 2.1.2.3370), and by the grants of President of the Russian Federation (NSH-454.2008.1 and. MK-420.2008.1).     

Laminar-Turbulent Transition: The Change of the Flow State Temperature with the Reynolds Number

Representing the fluid flow as a collection of coherent structures of various size, the statistical temperature of the flow state is determined as a function of the Reynolds number. It is shown that at small Reynolds numbers, associated with laminar states, the temperature is positive, while at large Reynolds numbers, associated with turbulent states, it is negative. At intermediate Reynolds numbers, the temperature changes from positive to negative as the size of the coherent structures increases, similar to what was predicted by Onsager for a system of parallel point-vortices in an inviscid fluid. It is also shown that in the range of intermediate Reynolds numbers the temperature exhibits a critical divergence.     

Simulation of laminar–turbulent transition in compressible Taylor–Green flow basing on quasi-gas dynamic equations

We report the results of numerical simulation of laminar–turbulent transition in the Taylor–Green vortex for viscous compressible gas flow basing on quasi-gas-dynamic (QGD) equations. Here the QGD system is obtained by a temporal averaging of the Navier–Stokes equations. The additional dissipative terms in QGD system serve to model the effects of the unresolved subgrid scales. Comparison with direct numerical simulation and large eddy simulation reference data demonstrates that QGD numerical algorithm provides a uniform and adequate simulation of both laminar and turbulent evolution of the vortex for Reynolds numbers from 100 up to 5000, including transition.     

FRICTION AND CONVECTION STUDIES OF R-134a IN MICROCHANNELS WITHIN THE TRANSITION AND TURBULENT FLOW REGIMES

Fluid flow and heat transfer characteristics of single-phase flows in microchannels for refrigerant R-134a were experimentally investigated. Experiments were conducted using rectangular channels micromilled in aluminum with hydraulic diameters ranging from approximately 112 to 210 w m and aspect ratios that varied from 1.0 to 1.5. Using overall temperature, flow rate, and pressure drop measurements, friction factors and convective heat transfer coefficients were experimentally determined for steady flow conditions. Effects of Reynolds number, relative roughness, and channel aspect ratio are examined in predicting friction factor and Nusselt number for the experiments. Experiment results indicated that transition from laminar to turbulent flow occurred between a Reynolds number of 2,000 and 4,000. Friction factor results were consistently lower than values predicted by macroscale correlations but exhibited the same trends with Reynolds numbers of macroscale correlations. Nusselt number results also exhibited a similar pattern of lower values obtained in the experiments than those predicted by commonly used macroscale correlations. Nusselt number results also indicated that channel size may suppress turbulent convective heat transfer and surface roughness may affect heat transfer characteristics in the turbulent regime.     

Direct numerical simulation of the flow around a wall-mounted square cylinder under various inflow conditions

The flow around a wall-mounted square cylinder of side d is investigated by means of direct numerical simulation (DNS). The effect of inflow conditions is assessed by considering two different cases with matching momentum-thickness Reynolds numbers Re_θ ? 1000 at the obstacle: the first case is a fullyturbulent zero pressure gradient boundary layer, and the second one is a laminar boundary layer with prescribed Blasius inflow profile further upstream. An auxiliary simulation carried out with the pseudo-spectral Fourier–Chebyshev code SIMSON is used to obtain the turbulent time-dependent inflow conditions which are then fed into the main simulation where the actual flow around the cylinder is computed. This main simulation is performed, for both laminar and turbulent-inflows, with the spectral-element method code Nek5000. In both cases the wake is completely turbulent, and we find the same Strouhal number St ? 0.1, although the two wakes exhibit structural differences for x > 3d downstream of the cylinder. Transition to turbulence is observed in the laminar-inflow case, induced by the recirculation bubble produced upstream of the obstacle, and in the turbulent-inflow simulation the streamwise fluctuations modulate the horseshoe vortex. The wake obtained in our laminar-inflow case is in closer agreement with reference particle image velocimetry measurements of the same geometry, revealing that the experimental boundary layer was not fully turbulent in that dataset, and highlighting the usefulness of DNS to assess the quality of experimental inflow conditions.     

Flow and Heat Transfer in Rough Micro Steel Tubes

Abstract

This article investigates the flow and heat transfer characteristics in micro steel tubes with inner diameters of 168 μm, 399 μm and relative roughness of 3.5% and 2.7%, respectively, by measuring the friction factors and the Nusselt number from laminar state to transitional state. Experiments show that the experimental Nusselt numbers are less than those predicted by the classical laminar correlation due to the effect of the variation of the thermophysical properties with temperature when Reynolds number is low. As the Reynolds number is higher than 800, the experimental Nusselt number are 25–50% higher than the predictions of the classical laminar and transitional correlations due to the effects of the roughness and the entrance length. The transition from laminar to turbulent flow occurs at the Reynolds number of 1,100–1,500.     

Effects of spanwise system rotation on turbulent stripes in a plane Poiseuille flow

In the transitional channel flow, the large-scale intermittent structure of localised turbulence, which is called the turbulent stripe pattern, can be found in the form of stripe arrangement. The structure of the turbulent stripe pattern is an oblique laminar–turbulent banded pattern and is inclined with respect to the streamwise direction. We performed direct numerical simulation at a transitional Reynolds number and very low-rotation numbers, and focused on the turbulent stripe pattern in the plane Poiseuille flow subjected to spanwise system rotation. We captured the turbulent stripe pattern in a rotating channel flow and found the augmentation and diminution of the turbulent stripe pattern were affected by the spanwise rotation. The contents of the discussion are the spatial size of the turbulent stripe pattern on the basis of the instantaneous flow fields, the energy spectra, and various statistics relating to the spanwise velocity component that characterise the turbulent stripe pattern. The turbulent stripe pattern was found to contain kinetic energy that was larger in very weakly rotating flows than in the static system. It was also found that the magnitude of the spanwise secondary flow increases, while the quasi-laminar region is wider at a very lowrotation number.     

Homoclinic tangle on the edge of shear turbulence

Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate between laminar and turbulent shear flow as their stable manifolds separate the two in state space. In this Letter we describe flows homoclinic to a time-periodic edge state that display the essential properties of turbulent bursting. During a burst, vortical structures and the associated energy dissipation are highly localized near the wall, in contrast with the familiar regeneration cycle.     

Numerical simulation of flow around a circular cylinder with curved sectional grooves

In a circular cylinder with uniform flow, a sudden decrease in the drag force occurs at a high Reynolds numbers; however, it is known that the same phenomenon occurs at a lower Reynolds number in the case where there exist grooves or roughness on the circular cylinder surface. To clarify the flow characteristics around a circular cylinder in the case of changing the shape of grooves we analyzed the drag coefficient, lift coefficient, turbulent kinetic energy, vorticity and pressure by applying the RNGk-ε turbulent model. The shapes of the grooves were arced, triangulated and curved. The results showed that the separation point for a circular cylinder with curved sectional grooves shifts to the most downstream side and the drag coefficient becomes the smallest among circular cylinders with grooves.     

Dynamics and structure of unstably stratified homogeneous turbulence

We characterise the properties of unstably stratified homogeneous turbulence by means of high-resolution direct numerical simulations and a two-point statistical spectral model based on a quasi-normal closure proposed by Burlot et al. Both approaches agree very well regarding the evolution of one- and two-point turbulent statistics, showing that the model is valid at even higher Reynolds numbers than previously considered. From a parametric study with different initial conditions, we confirm that the energy distribution at large scale influences strongly the late time dynamics of the flow. In particular, we assess the existence of backscatter transfer of energy, and evaluate its role in the growth rate of several turbulent quantities. Moreover, thanks to the statistical model, we analyse the scale-by-scale anisotropy of the flow through the decomposition of turbulent spectra in terms of directional anisotropy and polarisation anisotropy, for a refined characterisation of the structure of the flow which is strongly anisotropic in the large scales. This also allows us to study how isotropy is restored in the inertial scales.     

绕圆柱体自由表面磁流体流动和传热的研究

本文对在不同雷诺数下,绕圆柱体的磁流体自由表面流动及传热进行了模拟,分析了磁场对绕流圆柱尾迹和涡分离的影响,获得了两种雷诺数下的电磁力密度、流场和温度场分布。结果表明,磁场不仅影响了流动的形态,而且对湍流有抑制作用,降低了自由表面的更新机制,从而减少了传热能力;在相同的Hartmann数下,相比低雷诺数下的流动换热情况,高雷诺数下的湍流不能被完全抑制,自由表面与尾迹的相互作用也较强,因而自由表面换热也较强。     

基于温敏漆技术的圆锥高超声速大攻角绕流背风面流动结构实验研究

高超声速流动中, 大攻角下圆锥背风面边界层会存在流动分离与再附、边界层转捩等多种流动现象, 进而对圆锥表面温度分布产生显著的影响。为了对这一复杂流动规律及其对表面温升分布的影响进行讨论, 研究基于温敏漆技术, 得到了在Mach数为6的低湍流度来流条件下, 攻角为10°的圆锥背风面温升分布结果。通过对不同位置、不同方位角处温升分布曲线的分析, 对大攻角下圆锥背风面边界层流动发展过程及不同发展阶段的流动特征进行了讨论。同时, 通过对来流总压的调节, 得到了不同Reynolds数下的圆锥背风面温升分布结果, 总结了Reynolds数对流动的影响规律。研究发现, 高超声速大攻角圆锥背风面边界层流动发展过程中会依次出现层流分离、定常横流涡影响、转捩以及湍流分离与再附等流动特征, 而在不同的Reynolds数下, 各个流动特征产生影响的范围不同, 随着Reynolds数的降低, 层流范围和定常横流涡影响范围均有所增加, 而从观察到横流影响到转捩开始发生的范围基本相同。      

Calculation of the flow about a sphere and the drag of the sphere under laminar and strongly turbulent conditions

To investigate the influence of a strongly turbulent incoming flow on the hydrodynamic drag of a body and occurrence of the early crisis of drag, a numerical experiment is conducted in which a free gas flow about a sphere is simulated for two cases, namely, for a laminar flow and for a strongly turbulent flow. Turbulence is simulated by assuming a high kinematic coefficient of turbulent viscosity. Calculation data lead us to conclude that the early crisis of drag at Reynolds numbers near 100, which shows up as a considerable (four-to sevenfold) decrease in the hydrodynamic force and the drag coefficient of the body, can be explained by the strong turbulence of the incoming flow.