Direct numerical simulation of low Reynolds number flows in an open‐channel with sidewalls

A direct numerical simulation of low Reynolds number turbulent flows in an open‐channel with sidewalls is presented. Mean flow and turbulence structures are described and compared with both simulated and measured data available from the literature. The simulation results show that secondary flows are generated near the walls and free surface. In particular, at the upper corner of the channel, a small vortex called inner secondary flows is simulated. The results show that the inner secondary flows, counter‐rotating to outer secondary flows away from the sidewall, increase the shear velocity near the free surface. The secondary flows observed in turbulent open‐channel flows are related to the production of Reynolds shear stress. A quadrant analysis shows that sweeps and ejections are dominant in the regions where secondary flows rush in toward the wall and eject from the wall, respectively. A conditional quadrant analysis also reveals that the production of Reynolds shear stress and the secondary flow patterns are determined by the directional tendency of the dominant coherent structures. Copyright © 2009 John Wiley & Sons, Ltd.     

A bypass wake induced laminar/turbulent transition

The process of laminar to turbulent transition induced by a von Karman vortex street wake, was studied for the case of a flat plate boundary layer. The boundary layer developed under zero pressure gradient conditions. The vortex street was generated by a cylinder positioned in the free stream. An X-type hot-wire probe located in the boundary layer, measured the streamwise and normal to the wall velocity components. The measurements covered two areas; the region of transition onset and development and the region where the wake and the boundary layer merged producing a turbulent flow. The evolution of Reynolds stresses and rms-values of velocity fluctuations along the transition region are presented and discussed. From the profiles of the Reynolds stress and the mean velocity profile, a ‘negative' energy production region along the transition region, was identified. A quadrant splitting analysis was applied to the instantaneous Reynolds stress signals. The contributions of the elementary coherent structures to the total Reynolds stress were evaluated, for several x-positions of the near wall region. Distinct regions in the streamwise and normal to the wall directions were identified during the transition.     

Vortex structure of turbulence over permeable walls

In order to understand the effect of the wall permeability on the turbulent vortex structure near porous walls, based on PIV experimental data, a probability density analysis of fluctuating velocities, statistical quadrant and quadrant-hole analyses of the Reynolds shear stress are performed. The investigated flow fields are turbulent channel flows whose bottom walls are made of porous media. The porous media used are three kinds of foamed ceramics which have almost the same porosity (∼0.8) but different permeability. From the discussions on those analyses, a conceptual scenario of the development of the vortex structure near a permeable wall is proposed for a moderate permeability Reynolds number case. It explains the reason why the near-wall long streaky structure tends to vanish near a porous wall with increasing wall permeability.     

Evidences of persisting thermal structures in Couette flows

DNS of passive thermal turbulent Couette flow at several friction Reynolds numbers (180, 250, and 500), and the Prandtl number of air are presented. The time averaged thermal flow shows the existence of long and wide thermal structures never described before in Couette flows. These thermal structures, named CTFS (Couette Thermal Flow Superstructures), are defined as coherent regions of hot and cold temperature fluctuations. They are intrinsically linked to the velocity structures present in Couette flows. Two different 2D symmetries can be recognized, which get stronger with the Reynolds number. These structures do not affect the mean flow or mean quantities as the Nusselt number. However, turbulent intensities and thermal fluxes depend on the width of the structures, mainly far from the walls. Since the width of the structures is related to the channel width, the statistics of thermal Couette flow are to some point box-dependent.     

Flow structures of a separating,reattaching, and recovering boundary layer for a large range of Reynolds number

Flow structures of a separating, reattaching, and recovering boundary layer over a smoothly contoured ramp are examined for an order of magnitude range of Reynolds number, which is achieved by increasing the wind tunnel pressure by up to 8 atm and varying the tunnel speed by a factor of three. The study was performed using instantaneous velocity vector plots and two-point correlations measured by PIV. The present paper discusses length scales of large-scale motions of the flow and roller vortices in the separated shear layer and their dependence on the Reynolds number or the flow geometry. Two-point correlation profiles show that the Reynolds number effects on the correlations vary strongly from region to region within the flow. Downstream of reattachment, correlation profiles show that the inner portion of the boundary layer recovers more rapidly than the outer portion, where excessively active eddies still persist. The Reynolds number effects seen at reattachment diminish in the recovery region, and the correlation profiles start to take on ordinary boundary layer characteristics.     

Turbulence in a three‐dimensional wall‐bounded shear flow

A new turbulent flow with distinct three‐dimensional characteristics has been designed in order to study the impact of mean‐flow skewing on the turbulent coherent vortices and Reynolds‐averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette–Poiseuille flow enabled in‐depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8° away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non‐alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three‐dimensional shear flows. Coherent flow structures, which are known to be associated with the Reynolds shear stress in near‐wall regions, were identified by the λ₂‐criterion. Instantaneous and ensemble‐averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean‐flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean‐flow three‐dimensionality. The turning of the coherent vortices and the accompanying symmetry‐breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble‐averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near‐wall structures and the Reynolds‐averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two‐dimensional turbulent boundary layers remains valid also in flows with moderate mean three‐dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.     

Vortex dynamics and scalar transport in the wake of a flat-plate controlled by a vibrating trailing-edge flap

We investigate the onset and development of vortical flow disturbances introduced into the wake of a horizontally fixed flat-plate by means of the controlled motion of a trailing edge flap. The vibrating mechanics of the flap allows for the introduction of both impulsive and harmonic weak amplitude velocity disturbances which are propagated downstream into the wake flow of the flat-plate. Quantitative experimental and numerical predictions of both steady and unsteady wake flow velocity resulting from different flapping frequencies are made at low Reynolds numbers (Re < 10⁴). Frequency response tests of the wake confirmed the existence of two dominant frequencies where the wake flow organises with a particular arrangement of downstream moving vortex structures. Numerical predictions of steady (unforced) and forced wake velocity profiles and kinetic energy profiles are in good agreement with the experimental results. In order to understand practical implications of the dominant vortex structures in scalar transport, we have extended the numerical part of the study solving for the concentration equation of a passive scalar being injected in particular regions of the physical domain. A spatial correlation between the trajectory of vortex structures and the scalar concentration downstream the wake is observed. Moreover, the onset of tip vortex structures produced during the forcing cycle seems to be responsible of a local increase of scalar concentration near the span wise flap ends.     

Three-dimensional instability of two counter-rotating vortices in a rectangular cavity driven by parallel wall motion

The linear stability of two counter-rotating vortices driven by the parallel motion of two facing walls in a rectangular cavity is investigated by a finite volume method. Critical Reynolds and wave numbers are calculated for aspect ratios ranging from 0.1 to 5. This range is sufficient to find the asymptotic behavior of the critical parameters when the aspect ratio tends to zero and infinity, respectively. The critical curve is smooth for all aspect ratios and, hence, the character of the instability changes continuously. When the moving walls are far apart the mechanism is centrifugal, as in the classical lid-driven cavity. For aspect ratios near unity a combined mechanism, also involving strain near the vortex cores, leads to the instability which tends to asymmetrically displace the vortex cores, very similar to the cooperative short-wave instability of a free counter-rotating vortex pair. In the limit when plane Poiseuille flow is approached in the bulk, the three-dimensional perturbations are strongly localized near both downstream ends of the moving walls.     

单柱单锥型液—液旋流分离管内流场的LDV诊断

应用二维激光多普勒仪（ＬＤＶ）对一种单柱单锥型液－液旋流分离管内流场进行了测量,考察了流量、溢流比、压力比和气芯等参数对流场的影响。测量结果表明：切向速度分布呈典型的Ｒａｎｋｉｎｅ涡结构,沿轴向衰减很少,表明所用锥角是合适的;因该旋流管的水力直径较大,切向速度的总体水平较低,由于对了离特性带来了不利影响。此外,没有观察到切向速度分布的的双峰分布现象。轴向速度的总体水平较低,尤其是在锥形管的上游更为     

Measurements of velocity,temperature and velocity fluctuation distributions in falling liquid films

The velocity, temperature and velocity fluctuation distributions within falling spindle oil films in an inclined rectangular channel were measured using hot-wire techniques and thin thermocouples. The interfacial shear was caused by cocurrent air flow.The results indicate that the liquid films are as a whole much more laminar-like than turbulent in a range of Reynolds numbers (4γ/μ) up to the experimental limit of 6000. Mixing motion occurs in the vicinity of the interface; however, the flow near the wall surface exhibits no sign of such eddy motions, as predicted by the wall law for single phase turbulent flow. Although velocity fluctuation is observed within films with interfacial shear, mean velocity profiles are approximately the same as those obtained by the laminar film prediction.     

On the flow behaviour of confined finite-length wavy cylinders

Confined aspect-ratio of 6 wavy cylinders with a mean blockage-ratio of 0.5 were studied using time-resolved particle-image velocimetry at a sub-critical Reynolds number of 2700. Wavelengths and wave amplitudes of 2–4 and 0.1–0.3 mean diameters respectively were investigated. Results show that vortices are generally shed from the wavy cylinder and channel walls regularly, reminiscent of the unsteady symmetric flow configuration in confined non-wavy cylinders. Furthermore, vortex formation lengths for confined wavy cylinders are generally shorter than their unconfined counterparts, though their variations with respect to geometrical changes remain consistent with unconfined flow conditions. Gross cross-stream flow behaviour does not differ significantly between confined and unconfined wavy cylinders, indicating that finite-length effects are independent of the present confinement. Confined wavy cylinder wake regions are more sensitive towards geometrical changes and a combination of small wavelength and large wave amplitude leads to significant suppression of coherent cylinder and wall vortex-shedding. This is supported by phase-averaged flow reconstructions derived from Proper Orthogonal Decomposition analysis. Lastly, larger wave amplitudes lead to redistributions of dominant flow energy further downstream and to higher mode numbers, which suggests a causal link to the formation of stronger and more coherent streamwise vortices.     

Effects of jet velocity profiles on a round jet in cross-flow

This paper reports the results of an experimental investigation on the effects of jet velocity profiles on the flow field of a round jet in cross-flow (JICF) using laser-induced fluorescence and digital particle-image velocimetry techniques (DPIV). Tophat and parabolic jets were considered, with the momentum ratios (MRs) ranging from 2.3 to 5.8. Results show that the thicker shear layer associated with a parabolic JICF is able to delay the formation of leading-edge and lee-side vortices when compared to the tophat JICF at the corresponding MR. As a result, there is an increase in jet penetration and a reduction in the near-field entrainment of cross-flow fluid by a parabolic JICF. Also, the less coherent nature of the leading-edge and lee-side vortices in a parabolic JICF is more likely to break up sporadically into smaller-scaled vortices. In addition, DPIV results show that a parabolic JICF exhibits not only a faster velocity recovery of cross-flow fluid at the jet lee-side than the corresponding tophat JICF, it also consistently registers a higher magnitude of the peak average vorticity than the tophat JICF for all MR considered. Despite these differences, the time-averaged flow topology for both cases share many salient features.     

Tomographic PIV investigation of coherent structures in a turbulent boundary layer flow

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in the logarithmic region of the turbulent boundary layer in a water tunnel.The Reynolds number based on momentum thickness is Reθ = 2 460.The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low speed fluid,which is flanked on either side by highspeed ones.Statistical support for the existence of hairpins is given by conditional averaged eddy within an increasing spanwise width as the distance from the wall increases,and the main vortex characteristic in different wall-normal regions can be reflected by comparing the proportion of ejection and its contribution to Reynolds stress with that of sweep event.The pre-multiplied power spectra and two-point correlations indicate the presence of large-scale motions in the boundary layer,which are consistent with what have been termed very large scale motions(VLSMs).The three dimen-sional spatial correlations of three components of velocity further indicate that the elongated low-speed and highspeed regions will be accompanied by a counter-rotating roll modes,as the statistical imprint of hairpin packet structures,all of which together make up the characteristic of coherent structures in the logarithmic region of the turbulent boundary layer(TBL).     

Linear stability of two-dimensional steady flow in wavy-walled channels

Linear stability of fully developed two-dimensional periodic steady flows in sinusoidal wavy-walled channels is investigated numerically. Two types of channels are considered: the geometry of wavy walls is identical and the location of the crest of the lower and upper walls coincides (symmetric channel) or the crest of the lower wall corresponds to the furrow of the upper wall (sinuous channel). It is found that the critical Reynolds number is substantially lower than that for plane channel flow and that when the non-dimensionalized wall variation amplitude is smaller than a critical value (about 0.26 for symmetric channel, 0.28 for sinuous channel), critical modes are three-dimensional stationary and for larger , two-dimensional oscillatory instabilities set in. Critical Reynolds numbers of sinuous channel flows are smaller for three-dimensional disturbances and larger for two-dimensional disturbances than those of symmetric channel flows. The disturbance velocity distribution obtained by the linear stability analysis suggests that the three-dimensional stationary instability is mainly caused by local concavity of basic flows near the reattachment point, while the critical two-dimensional mode resembles closely the Tollmien–Schlichting wave for plane Poiseuille flow.     

Numerical analysis of turbulent flow in a rotating U-bend with roughened walls

A numerical analysis has been performed for a developing turbulent flow in a rotating U-bend of strong curvature with rib-roughened walls using an anisotropic turbulent model. In this calculation, an algebraic Reynolds stress model is used to precisely predict Reynolds stresses, and a boundary-fitted coordinate system is introduced as a method of coordinate transformation to set the exact boundary conditions along the complicated shape of U-bend with rib-roughened walls. Calculated results for mean velocity and Reynolds stresses are compared to the experimental data in order to validate the proposed numerical method and the algebraic Reynolds stress model. Although agreement is certainly not perfect in all details, the present method can predict characteristic velocity profiles and reproduce the separated flow generated near the outer wall, which is located just downstream of the curved duct. The Reynolds stresses predicted by the proposed turbulent model agree well with the experimental data, except in regions of flow separation.     

圆柱绕流流场结构的大涡模拟研究

为进一步揭示绕流现象的形成机理,本文分别对处于层流稳态区、尾流过渡区、剪切层转换区Re分别为26、200、1.4×105的三种典型流态下的单圆柱绕流进行了二维数值模拟研究。Re为26时应用层流模型直接求解N-S方程,而Re分别为200、1.4×105时使用大涡模拟的方法进行计算。数值模拟很好地再现了稳定的涡旋结构、周期性交替脱落的卡门涡街结构、不规则的涡旋结构,在此基础上分析了尾流结构的基本特征及其压强分布规律、平均的流场特性、积分参数(如升力系数、阻力系数、斯特劳哈尔等),并与有关研究成果进行了对比。研究发现,采用不同流动介质时流场特性有所差异,空气为介质时的计算结果更符合实验的成果,而水为介质时计算结果偏差较大,这主要是由尾流涡旋产生的不合理负压造成的。     

Hydrodynamic instability of separated viscous flow around a circular cylinder

A uniform viscous flow around a circular cylinder is studied numerically in the Reynolds number range from 0 to 500. It is shown that the existence and the basic properties of self-oscillating regimes are specified by the evolution of their hydrodynamic instability. It is found that the vortex formation in a near wake is associated with the separation zone dynamics in the main flow. The values of critical Reynolds numbers for the four successive bifurcations of the self-oscillating regimes of flow are obtained. An interpretation of experimental data on the vortices in the near wake is discussed.     

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re_θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.     

Experimental study of the velocity field in a vortex-flow heat exchanger with isothermal conditions

The velocity field in a vortex heat cell was investigated experimentally using laser Doppler velocimetry for a wide range of flow conditions. Experimental results point out the three dimensionality of the exchanger's flow, which is composed into a main vortex flow developing along the side walls. The strength of the flow increases up to a limiting value reached for a Reynolds number ranging between 15,000 and 30,000; a secondary flow, caused by interaction between centrifugal and inertial forces, extends perpendicularly to the main flow and remains Reynolds number dependent. It is composed of multiple counter-rotating structures occurring at the exchanger periphery with low inlet Reynolds numbers, thus reducing the rate of centripetal momentum transfer. With increasing inlet Reynolds number, the secondary flow extends across the whole exchanger radius, thus increasing the rate of mixing of the treated fluid. The appearance of so-called Taylor–Görtler vortices tends to reduce the z- and r-axis vorticity transfer.     

Turbulent flow dynamics caused by a truncated cylinder

The turbulent flow field around a quite simple geometry has been analysed in detail based on a snapshot database taken from numerical simulation. Here, emphasis is placed on the dominant coherent motion and the flow dynamics in the separated wake. The method-based analysis is performed using POD, filtering and phase-averaging. The results obtained show a highly intermittent flow topology, which reveals different (at least three) recurring vortex arrangements, but with considerably stochastic character. Corresponding frequencies, the periodicity as well as correlation and interaction of predominant vortex motions are discussed. The methods employed are not limited to the configuration exemplarily chosen.