An investigation on near wall transport characteristics in an adiabatic upward gas–liquid two-phase slug flow

The near-wall transport characteristics, inclusive of mass transfer coefficient and wall shear stress, which have a great effect on gas–liquid two-phase flow induced internal corrosion of low alloy pipelines in vertical upward oil and gas mixing transport, have been both mechanistically and experimentally investigated in this paper. Based on the analyses on the hydrodynamic characteristics of an upward slug unit, the mass transfer in the near wall can be divided into four zones, Taylor bubble nose zone, falling liquid film zone, Taylor bubble wake zone and the remaining liquid slug zone; the wall shear stress can be divided into two zones, the positive wall shear stress zone associated with the falling liquid film and the negative wall shear stress zone associated with the liquid slug. Based on the conventional mass transfer and wall shear stress characteristics formulas of single phase liquid full-pipe turbulent flow, corrected normalized mass transfer coefficient formula and wall shear stress formula are proposed. The calculated results are in good agreement with the experimental data. The shear stress and the mass transfer coefficient in the near wall zone are increased with the increase of superficial gas velocity and decreased with the increase of superficial liquid velocity. The mass transfer coefficients in the falling liquid film zone and the wake zone of leading Taylor bubble are lager than those in the Taylor bubble nose zone and the remaining liquid slug zone, and the wall shear stress associated falling liquid film is larger than that associated the liquid slug. The mass transfer coefficient is within 10⁻³ m/s, and the wall shear stress below 10³ Pa. It can be concluded that the alternate wall shear stress due to upward gas–liquid slug flow is considered to be the major cause of the corrosion production film fatigue cracking.     

倾斜吹吸控制下湍流边界层减阻的直接数值模拟

雷诺切应力是壁湍流高摩擦阻力的重要来源, 有理论认为可以通过壁面生成负雷诺应力(数值上为正)的方式来削弱湍流流场中雷诺应力的分布, 以此获得流动减阻. 而通过对雷诺平均运动方程的法向二次积分, 可以发现壁面生成正雷诺应力(数值上为负)对壁面摩擦阻力系数才有负贡献. 文中在湍流边界层流动的控制区域下边界设置一系列倾斜狭缝, 利用该装置通过周期性吹吸的方法产生壁面生成正(负)雷诺应力, 并采用直接数值模拟方法考察和验证上文提到的减阻理论. 文中采用的湍流边界层流动模型, 其流动雷诺数(基于外流速度及动量损失厚度)从300 发展到860. 文中通过多组数值模拟算例, 考察了射流强度和频率对壁面摩擦阻力系数的影响, 并对比了壁面生成正或负雷诺应力对流动的影响. 研究表明, 壁面生成正雷诺应力控制的减阻率能达到3.26, 而壁面生成负雷诺应力控制的减阻效果较壁面生成正雷诺应力控制的要差; 壁面生成的正雷诺应力对壁面摩擦阻力有负贡献, 而壁面生成的负雷诺应力对壁面摩擦阻力有正贡献; 通过考察控制的收支比, 发现控制方案不能获得能量净收益.      

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.     

Self-preservation of rough-wall turbulent boundary layers

It is proposed that all fully rough-wall boundary layers should satisfy self-preservation more closely than a smooth-wall boundary layer. Previous work has shown that the self-preserving forms of the momentum and turbulent kinetic energy equations for a zero pressure gradient turbulent boundary layer, at sufficiently high Reynolds number, require that the wall shear stress is constant with x, and the layer thickness increases linearly with x. Measurements in two rough wall boundary layers suggest these conditions are met without assuming a form for the mean velocity distribution, and are more likely to exist in a fully rough wall layer than a smooth wall layer.     

Inner-outer decomposition of wall shear stress fluctuations in turbulent channels

Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components. The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent motions, and the small-scale one is obtained by subtracting the large-scale one from the total, which fully remove the outer influences. We show that the statistics of the small-scale fluctuating wall shear stress is Reynolds number independent at the friction Reynolds number larger than 1000, while which is Reynolds number dependent or the low-Reynolds-number effect exists at the friction Reynolds number smaller than 1000. Therefore, a critical Reynolds number that defines the emergence of universal small-scale fluctuating wall shear stress is proposed to be 1000. The total and large-scale fluctuating wall shear stress intensities approximately follow logarithmic-linear relationships with Reynolds number, and empirical fitting expressions are given in this work.     

The measurement of ?U?, ?V? and ?uv? inside the turbulent spot using conditionally sampled hot-wire anemometer signals

By means of a tripping wire turbulent spots are generated in a conditionally stable laminar boundary layer along a flat plate in a low-turbulence windtunnel. At several vertical and lateral positions the streamwise (U) and vertical (V) velocity components of the spot are measured using anX-shaped hot wire anemometer. The spot's leading edge (LE) and trailing edge (TE) are determined by a high frequency detection criterion.The derived ensemble averaged shear stress uv shows a remarkable plateau over the last 3/4 of the spot length and over about 1/2 of the spot width, approximately independent of the height above the plate. The measurements suggest that the velocities of the LE and the TE can be explained by simple advection of the active turbulent region. Other mechanisms seem to be responsible for the lateral spread of the spot, as is suggested by the measurements outside the plane of symmetry.     

Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes

The results of direct numerical simulation of turbulent flows of non-Newtonian pseudoplastic fluids in a straight pipe are presented. The data on the distributions of the turbulent stress tensor components and the shear stress and turbulent kinetic energy balances are obtained for steady turbulent flows at the Reynolds numbers of 10⁴ and 2×10⁴. As distinct from Newtonian fluid flows, the viscous shear stresses turn out to be significant even far from the wall. In power-law fluid flows the mechanism of the energy transport from axial to transverse component fluctuations is suppressed. It is shown that with decrease in the fluid index the turbulent transfer of the momentum and the velocity fluctuations between the wall layer and the flow core reduces, while the turbulent energy flux toward the wall increases. The earlier-proposed models for the average viscosity and the non-Newtonian one-point correlations are in good agreement with the data of direct numerical simulation.     

A time-resolved hot-wire shear stress probe for turbulent flow: use of laminar flow calibration

A specially-designed rotating rig for producing near Couette flow was used in the calibration of a marginally elevated hot-wire shear stress probe. The probe was then used for measurements in both the turbulent boundary layer and pipe flows. Results showed that the mean wall shear stress can be accurately predicted and the near wall statistical quantities of intensity, skewness and flatness of shear stress fluctuations concurred well with previous works, thereby supporting the notion of a time-resolved shear stress probe for turbulent flows.     

Characterization of near-bed coherent structures in turbulent open channel flow using synchronized high-speed video and hot-film measurements

High-speed video recordings (500 Hz) of flow visualizations in the near wall region of a turbulent open channel flow were synchronized with hot-film measurements of flow velocity and bed shear stress. Analysis of the video images provided information about the main characteristics of coherent flow structures associated with the occurrence of low-speed streak ejections near the bed. These structures consisted mainly of oscillating shear layers that were converted in the downstream direction and lifted away from the bed. A visual detection criterion was developed to obtain ensemble averaged profiles of the velocity and shear stress data during ejection events, allowing for the characterization of the associated flow field during the occurrence of coherent structures. Conditional averaging suggests that the occurrence of such coherent patterns affects mainly the turbulence structure in the wall region, and that the observed events reveal a plausible mechanism by which energy is extracted from the mean flow by large scale turbulent fluctuations, and then further transferred towards smaller eddies, while the structures lose their coherence. The intermittent nature of production and dissipation of turbulent energy becomes noticeable, taking place about 21% of the time. The results obtained also provide evidence that seems to link the structures responsible for the turbulent vertical transport of momentum, and for the maintenance of the turbulent state, with the mechanism that triggers the entrainment of sediment into suspension. Comparison of present results with other experiments conducted in different types of flows strongly confirms a universal structure of coherent events in wall bounded flows.The support of the Fluid, Hydraulic, and Paniculate System Program of the National Science Foundation (Grant CTS-9210211) and the donors of the Petroleum Research Fund of the American Chemical Society (Grant PRF 24328-G2) is gratefully acknowledged.     

Break-Up of Aerosol Agglomerates in Highly Turbulent Gas Flow

Agglomerate aerosols in a turbulent flow may be subjected to very high turbulent shear rates which through the generation of lift and drag can overcome the adhesive forces binding the constituents of an agglomerate together and cause it to break-up. This paper presents an analysis of the experimental measurements of the breakup of agglomerates between 0.1?C10???m in size, in a turbulent pipe flow followed by an expansion zone with a Reynolds numbers in the range 10⁵ to 10⁷. The analysis shows that even in wall bounded turbulence, the high turbulent shear stresses associated with the small scales of turbulence in the core can be the main source of breakup preceding any break-up that may occur by impaction at the wall. More importantly from these results, a computationally fast and efficient solution is obtained for the General Dynamic Equation (GDE) for agglomerate transport and breakup in highly turbulent flow. Furthermore the solution for the evolution of the aerosol size distribution is consistent with the experimental results. In the turbulent pipe flow section, the agglomerates are exposed continuously to turbulent shear stresses and experience more longer term breakup than in the expansion zone (following the pipe flow) where the exposure time is much less and break-up occurs instantaneously under the action of very high local turbulent shear stresses. The validity of certain approximations made in the model is considered. In particular, the inertia of the agglomerates characterised by a Stokes Number from 0.001 for the smallest particles up to 10 for 10???m particles and the fluctuations of the turbulent shear stresses are important physical phenomena which are not accounted for in the model.     

Wall shear stress prediction in three-dimensional turbulent boundary layers

A method is developed to infer the wall shear stress for three-dimensional turbulent boundary layers based on the assumption that the resultant surface shear stress and the effective velocity based on Prahlad's model correlates the velocity profile into its two-dimensional form. Existence of the near wall region similarity has been demonstrated for three-dimensional turbulent boundary layers.     

Wall shear stress modified by bubbles in a horizontal channel flow of silicone oil in the transition region

We performed laboratory experiments on bubbly channel flows using silicone oil, which has a low surface tension and clean interface to bubbles, as a test fluid to evaluate the wall shear stress modification for different regimes of bubble migration status. The channel Reynolds numbers of the flow ranged from 1000 to 5000, covering laminar, transition and turbulent flow regimes. The bubble deformation and swarms were classified as packing, film, foam, dispersed, and stretched states based on visualization of bubbles as a bulk void fraction changed. In the dispersed and film states, the wall shear stress reduced by 9% from that in the single-phase condition; by contrast, the wall shear stress increased in the stretched, packing, and foam states. We carried out statistical analysis of the time-series of the wall shear stress in the transition and turbulent-flow regimes. Variations of the PDF of the shear stress and the higher order moments in the statistic indicated that the injection of bubbles generated pseudo-turbulence in the transition regime and suppressed drag-inducing events in the turbulent regime. Bubble images and measurements of shear stress revealed a correlated wave with a time lag, for which we discuss associated to the bubble dynamics and effective viscosity of the bubble mixture in wall proximity.     

A film-based wall shear stress sensor for wall-bounded turbulent flows

In wall-bounded turbulent flows, determination of wall shear stress is an important task. The main objective of the present work is to develop a sensor which is capable of measuring surface shear stress over an extended region applicable to wall-bounded turbulent flows. This sensor, as a direct method for measuring wall shear stress, consists of mounting a thin flexible film on the solid surface. The sensor is made of a homogeneous, isotropic, and incompressible material. The geometry and mechanical properties of the film are measured, and particles with the nominal size of 11 μm in diameter are embedded on the film’s surface to act as markers. An optical technique is used to measure the film deformation caused by the flow. The film has typically deflection of less than 2% of the material thickness under maximum loading. The sensor sensitivity can be adjusted by changing the thickness of the layer or the shear modulus of the film’s material. The paper reports the sensor fabrication, static and dynamic calibration procedure, and its application to a fully developed turbulent channel flow at Reynolds numbers in the range of 90,000–130,000 based on the bulk velocity and channel full height. The results are compared to alternative wall shear stress measurement methods.     

Experimental study on near wall transport characteristics of slug flow in a vertical pipe

In this work, the wall shear stress and the mass transfer coefficient of the gas–liquid two-phase upward slug flow in a vertical pipe are investigated experimentally, using limiting diffusion current probes and digital high-speed video system. In experiments, the instantaneous and averaged characteristics of wall shear stress and mass transfer coefficient are concerned. The experimental results are compared with the numerical results in previous paper of the authors. Both experiment and numerical simulation show that the superficial gas and liquid velocities have an obvious influence on the instantaneous characteristics of the two profiles. The mass transfer coefficient has characteristics similar to the wall shear stress. The instantaneous wall shear stress and mass transfer coefficient profiles have the periodicity of slug flow. The averaged wall shear stress and mass transfer coefficient increase with increased superficial gas velocity. However, there is inconsistency in the variation trends of the averaged wall shear stress and mass transfer coefficient with superficial liquid velocity between experimental result and numerical simulation result, which can be attributed to the difference in flow condition. Moreover, the Taylor bubble length is also another impacting factor. The experimental and numerical results all shows that the product scale can not be damaged directly by the flow movement of slug flow. In fact, the alternative forces and fluctuations with high frequency acting on the pipe wall due to slug flow is the main cause for the slug flow enhanced CO₂ corrosion process.     

Numerical study of effects of pulsatile amplitude for transitional turbulent pulsatile flow in pipes with ring‐type constrictions

The effects of pulsatile amplitude on sinusoidal transitional turbulent flows through a rigid pipe in the vicinity of a sharp‐edged mechanical ring‐type constriction have been studied numerically. Pulsatile flows were studied for transitional turbulent flow with Reynolds number (Re) of the order of 10⁴, Womersley number (Nw) of the order of 50 with a corresponding Strouhal number (St) of the order of 0.04. The pulsatile flow considered is a sinusoidal flow with dimensionless amplitudes varying from 0.0 to 1.0. Transitional laminar and turbulent flow characteristics in an alternative manner within the pulsatile flow fields were observed and studied numerically. The flow characteristics were studied through the pulsatile contours of streamlines, vorticity, shear stress and isobars. It was observed that fluid accelerations tend to suppress the development of flow disturbances. All the instantaneous maximum values of turbulent kinetic energy, turbulent viscosity, turbulent shear stress are smaller during the acceleration phase when compared with those during deceleration period. Various parametric equations within a pulsatile cycle have also been formulated through numerical experimentations with different pulsatile amplitudes. In the vicinity of constrictions, the empirical relationships were obtained for the instantaneous flow rate (Q), the pressure gradient (dp/dz), the pressure loss (P_loss), the maximum velocity (V_max), the maximum vorticity (ζ_max), the maximum wall vorticity (ζ_w,max), the maximum shear stress (τ_max) and the maximum wall shear stress (τ_w,max). Elliptic relation was observed between flow rate and pressure gradient. Quadratic relations were observed between flow rate and the pressure loss, the maximum values of shear stress, wall shear stress, turbulent kinematic energy and the turbulent viscosity. Linear relationships exist between the instantaneous flow rate and the maximum values of vorticity, wall vorticity and velocity. The time‐average axial pressure gradient and the time average pressure loss across the constriction were observed to increase linearly with the pulsatile amplitude. Copyright © 1999 John Wiley & Sons, Ltd.     

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.     

Predicting Turbulent Spectra in Drag-reduced Flows

In the present work we describe how turbulent skin-friction drag reduction obtained through near-wall turbulence manipulation modifies the spectral content of turbulent fluctuations and Reynolds shear stress with focus on the largest scales. Direct Numerical Simulations (DNS) of turbulent channels up to Re _τ = 1000 are performed in which drag reduction is achieved either via artificially removing wall-normal turbulent fluctuations in the vicinity of the wall or via streamwise-travelling waves of spanwise wall velocity. This near-wall turbulence manipulation is shown to modify turbulent spectra in a broad range of scales throughout the whole channel. Above the buffer layer, the observed changes can be predicted, exploiting the vertical shift of the logarithmic portion of the mean streamwise velocity profile, which is a classic performance measure for wall roughness or drag-reducing riblets. A simple model is developed for predicting the large-scale contribution to turbulent fluctuation and Reynolds shear stress spectra in drag-reduced turbulent channels in which a flow control acts at the wall. Any drag-reducing control that successfully interacts with large scales should deviate from the predictions of the present model, making it a useful benchmark for assessing the capability of a control to affect large scales directly.     

Dynamic response of micro-pillar sensors measuring fluctuating wall-shear-stress

We present in this paper test results of flexible micro-pillars and pillar arrays for wall shear stress measurements in flows with fluctuating wall shear stress such as unsteady separated flows or turbulent flows. Previous papers reported on the sensing principle and fabrication process. Static calibrations have shown this sensor to have a maximum nonlinearity of 1% over two orders of wall-shear-stress. For measurements in flows with fluctuating wall shear stress the dynamic response has been experimentally verified in an oscillating pipe flow and compared to a calculated response based on Stokes’ and Oseen’s solution for unsteady flow around a cylinder. The results demonstrate good agreement under the given boundary conditions of cylindrical micro-pillars and the limit of viscous Stokes-flow around the pillar. Depending on the fluid and pillar geometry, different response curves result ranging from a flat low-pass filtered response to a strong resonant behavior. Two different methods are developed to detect the frequency content and the directional wall shear stress information from image processing of large sensor films with arrays of micro-pillars of different geometry. Design rules are given to achieve the optimal conditions with respect to signal-to-noise ratio, sensitivity and bandwidth for measurements in turbulent flows.     

A method for estimating wall friction in turbulent wall-bounded flows

We describe a simple method for estimating turbulent boundary layer wall friction using the fit of measured velocity data to a boundary layer model profile that extends the logarithmic profile all the way to the wall. Two models for the boundary layer profile are examined, the power-series interpolation scheme of Spalding and the Musker profile which is based on the eddy viscosity concept. The performance of the method is quantified using recent experimental data in zero pressure gradient flat-plate turbulent boundary layers, and favorable pressure gradient turbulent boundary layers in a pipe, for which independent measurements of wall shear are also available. Between the two model profiles tested, the Musker profile performs much better than the Spalding profile. Results show that the new procedure can provide highly accurate estimates of wall shear with a mean error of about 0.5% in friction velocity, or 1% in shear stress, an accuracy that is comparable to that from independent direct measurements of wall shear stress. An important advantage of the method is its ability to provide accurate estimates of wall shear not only based on many data points in a velocity profile but also very sparse data points in the velocity profile, including only a single data point such as that originating from a near-wall probe.     

Structure of near wall turbulence downstream of a wall mounted protrusion: an interesting Reynolds stress suppression phenomena

A local suppression in the generation of near wall Reynolds stress is achieved by modifying the buffer region and sublayer (y ⁺ <30) of a turbulent pipe flow with a 16.4 wall unit high wall mounted protrusion. Multi-component, multi-point, time resolved laser Doppler velocimetry measurements are made in the undisturbed and modified ARL/PSU glycerin tunnel pipe flow at a Reynolds number of approximately 10000. A downstream converging flow field is produced by the divergence of the approaching mean flow around the protrusion. A pair of counter-rotating vortices, 15 wall units in diameter with common flow down, are generated by the protrusion and also contribute to the wall directed flow convergence. The convergence region is 15 wall units high and more than 100 wall units long and appears to decouple the near wall region from the outer turbulent wall layer. Locally, turbulent velocity fluctuations in the form of Reynolds stress producing events, sweeps and ejections, are retarded within this region. This results in a reduction in near wall uv Reynolds stress and local wall shear. Interestingly, the counter-rotating vortices act to increase turbulent diffusion in a manner which is uncorrelated with Reynolds stress generation.