Measurements of wall shear stress in horizontal air–water bubbly flows

The mean and time-varying fluctuation property of local wall shear stress of horizontal air–water bubbly flows in a circular pipe of 35 mm I.D. is measured using a TSI-1268W hot film probe. Data are collected in both entrance and developed regions of the flows. The variation of wall shear stress with L/D is analyzed, and the entrance length is determined to be 52–65 D at present studies. It is found that the wall shear stress is not uniform around the pipe circumference due to the asymmetrical phase distribution in the flows. The mean shear stress tends to decrease circumferentially from the pipe bottom to top. An increase of air flow rate at a constant water flow rate would further lower the wall shear stress at the upper part of the pipe and at the same time raise the wall shear stress at lower part of the pipe in both entrance and developed regions. An increase of water flow rate at a constant air flow rate would result in an increase of wall shear stress at all circumferential positions. The statistical property of wall shear stress is also discussed.     

High-speed liquid film sensor for two-phase flows with high spatial resolution based on electrical conductance

A sensor is presented, that allows high-speed measurements of two-phase film flows. The sensor consists of electrodes flush to the wall, that measure the electrical conductance in a liquid film. This sensor has a time resolution of 10 kHz and 64×16 measuring points, with a spatial resolution of 3.12 mm² and a maximum film thickness range of 0.8 mm. The shape of the sensor electrodes is optimized by calculating the potential field of the liquid film. The calculated sensor characteristic is compared with experimental data received by imposing static liquid films of known thickness on top of the sensor. Further dynamic measurements of co-current air–water flow in a horizontal channel have been conducted. The statistical analysis concerning film thickness distribution and flow patterns is generally in agreement with literature. The high time and spatial resolution allows a wave analysis over a wide range of wavelengths and wave velocities. By using a continuous wavelet transform, a significant amount of additional information has been retrieved, particularly in regard to ripple waves. Preliminary experiments show the ability of the sensor to detect droplet deposition onto the liquid film. An autoregressive filter has been applied to separate droplet impacts from periodic wavy structures.     

滑动轴承二维流场的滑移现象研究

目前对于二维流场及复杂流场的界面滑移分析很少,根据螺旋油楔滑动轴承能使润滑剂产生周向和轴向二维流动的独特的结构特点,考虑周向和轴向两方向的滑移建立基于极限切应力的数学模型,并通过试验和理论对比验证模型的正确性。试验方面运用"目标速度跟踪法"证实了周向和轴向都存在滑移,获知随着供油压力的提高滑移速度有所提高,并且提出轴瓦和轴表面的极限切应力;理论方面运用有限差分法和试验测得的轴瓦和轴表面极限切应力,求解四种状态的广义雷诺方程,发现滑移发生在极限切应力大、间隙小和油膜的封油面区域;考虑界面滑移时,螺旋油楔滑动轴承的承载力和摩擦阻力有所降低;偏心率、螺旋角和转速的变化,影响着承载力和摩擦阻力降低的幅度。     

Backlight imaging tomography for slug flows in straight and helical tubes

Backlight imaging tomography is used to experimentally investigate interfacial structures of gas–liquid two-phase flow in circular tubes. The tomography method is based on the attenuation of visible light that causes the inside of the liquid phases to be colored with dye. Increasing the number of light projections provides accurate phase distributions to be reconstructed by a linear backward projection scheme. After the reconstruction performance is examined with numerical simulations for several test cases, the method is applied to slug flows that have complicated 3D interfaces from turbulence. Interfacial structures are compared between straight and helical tubes to determine the effect of centrifugal acceleration. The result demonstrates that centrifugal acceleration provides a liquid-clinging layer on the inner wall against gravity while a high-speed collision of liquid with the top wall happens in a straight tube.     

Laminar Flow in a Recess of a Hydrostatic Bearing

The flow in a recess of a hydrostatic journal bearing is studied in detail. The Navier-Stokes equations for the laminar flow of an incompressible liquid are solved numerically in a two-dimensional plane of a typical bearing recess. Pressure- and shear-induced flows, as well as a combination of these two flow conditions, are analyzed. Recess friction, pressure-ram effects at discontinuities in the flow region, and film entrance pressure loss effects are calculated. Entrance pressure loss coefficients over a forward-facing step are presented as functions of the mean flow Reynolds number for pure-pressure and shear-induced laminar flows.     

Cavitating nozzle flows in micro- and minichannels under the effect of turbulence

The cavitation phenomenon inside micro- and minichannel configurations was numerically investigated. The simulations for each channel were performed at different upstream pressures varying from 1 to 15 MPa. Two microchannel configurations with inner diameters of 152 and 254 μm and two minichannel configurations with inner diameters of 504 and 762 μm were simulated. To validate the numerical approach, micro-jet impingement from a microchannel with an inner diameter of 152 μm was first simulated at different Reynolds numbers. Then, the mixture model was used to model the multiphase flow inside the channels. The results of this study present major differences in the cavitating flows between the micro- and miniscale channels and show that the pressure profile and vapor phase distribution exhibit different features. The static pressure drops to negative values (tensile stress) in microchannels, while the minimum static pressure in minichannels is found to be equal to vapor saturation pressure, and higher velocity magnitudes especially at the outlet are visible in the microchannels. It is shown that for higher upstream pressures, the cavitating flow extends over the length of the micro/minichannel, thereby increasing the possibility of collapse at the outlet. The effect of energy associated with turbulence was investigated at high Reynolds numbers for both micro/minichannels and its impact was analyzed using wall shear stress, turbulence kinetic energy and mean velocity at various locations of the micro/minichannels.     

边界滑移对柱塞偶件间油膜流动规律的影响

斜盘式轴向柱塞泵内柱塞偶件间油膜为相对运动的偶件提供润滑及密封作用。油膜流动将直接影响柱塞偶件的工作性能。深入分析偶件间油膜的流动规律对设计与优化柱塞偶件有重要意义。基于Navier-Stokes（N-S）方程,引入Navier边界滑移推导偶件间油膜流动方程,根据柱塞运动的周期性规律,分析单个周期内滑移长度和柱塞泵转速对油膜流动剪应力及流量的影响。研究发现：吸油阶段时近柱塞壁面处油膜剪应力随滑移长度增大而减小,流量随着滑移长度增大而增大,柱塞运动速度最大且滑移长度由1 μm增大到3 μm后,剪应力减小18%,流量增大13.59%;排油阶段柱塞运动速度越大,近柱塞壁面处剪应力和油膜流量与无滑移条件下的差距越小。在滑移长度为1 μm的条件下柱塞泵转速由1 500 r/min增大到4 000 r/min时,近柱塞壁面处的油膜剪应力与无滑移条件下相比降低明显,一个周期内油膜总流量与无滑移条件下相比差距减小。     

A near-wall reynolds stress model for backward-facing step flows

A near-wall Reynolds stress model has been used in numerical computations for two-dimensional, incompressible turbulent flows over backward-facing steps. Numerical results are compared with Direct Numerical Simulation data as well as experimental data for flow quantities such as the skin friction, wall pressure,U-velocity and the Reynolds stress. Budgets of the transport equations for theU-velocity, turbulence kinetic energy,k and the Reynolds shear stress,— are also calculated and compared with the Direct Numerical Simulation data. The comparison reveals that the near-wall Reynolds stress model predicts the reattachment length fairly accurately. The near-wall Reynolds stress model also predicts the development of the boundary layer downstream of the reattachment point correctly when the Reynolds number is low. However, the model generally predicts a weak separation bubble and a slowly developing boundary layer when the Reynolds number is high.     

Supersonic moist air flow with condensation in a wavy wall channel

The characteristics of Prandtl-Meyer expansion of supersonic flow with condensation along a wavy wall in a channel are investigated by means of experiments and numerical analyses. Experiments are carried out for the case of moist air flow in an intermittent indraft supersonic wind tunnel. The flow fields are visualized by a Schlieren system and the distributions of static pressure along the upper wavy wall are measured by a scanning valve system with pressure transducers. In numerical analyses, the distributions of streamlines, Mach lines, iso-pressure lines, and iso-mass fractions of liquid are obtained by the two-dimensional direct marching method of characteristics. The effects of stagnation temperature, absolute humidity, and attack angle of the upper wavy wall on the generation and the locations of generation and reflection of an oblique shock wave are clarified. Futhermore, it is confirmed that the wavy wall plays an important role in the generation of an oblique shock wave and that the effect of condensation on the flow fields is apparent.     

Liquid holdup measurement in horizontal oil–water two-phase flow by using concave capacitance sensor

Due to the complex flow structures of horizontal oil–water flows, the liquid holdup measurement is still a challenging problem. In this paper, we using the finite element analysis build a two-dimensional model of the concave capacitance sensor and investigate the effect of sensor geometry on the distribution of the sensitivity field. Through calculating the sensor static response for different horizontal oil–water flow patterns, we figure out the optimum geometry of the concave capacitance sensor. In addition, we conduct experiment to obtain the measured response of the concave capacitance sensor and achieve the oil-holdup by using quick closing valve. The results indicate that the optimized concave capacitance sensor shows good performance for liquid holdup measurement of horizontal oil–water two-phase flow.     

FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries

A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.     

Streamlined shape of endothelial cells

Flow induced shape change is important for spatial interpretation of vascular response and for understanding of mechanotransduction in a single cell. We investigated the possible shapes of endothelial cell (EC) in a mathematical model and compared these with experimental results. The linearized analytic solution from the sinusoidal wavy wall and Stokes flow was applied with the constraint of EC volume. The three dimensional structure of the human umbilical vein endothelial cell was visualized in static culture or after various durations of shear stress (20 dyne/cm² for 5, 10, 20, 40, 60, 120min). The shape ratio (width: length: height) of model agreed with that of the experimental result, which represented the drag force minimizing shape of stream-lining. EC would be streamlined in order to accommodate to the shear flow environmented by active reconstruction of cytoskeletons and membranes through a drag force the sensing mechanism.     

A lubrication equation including slip velocity for hydrodynamic porous bearings in the lower turbulent regime — a perturbation approach

A first attempt is made to analyse pressure development in the form of a new lubrication equation including slip velocity for finite self-acting hydrodynamic porous metal bearings operating in the turbulent regime (fully developed) with a single phase Newtonian incompressible lubricant. The derivation is based on the analogy of boundary layer theory wherein lubricant motion is treated as a generalized turbulent channel flow in which the impermeable wall is in motion and the porous wall is stationary. The type of flow varies from pure couette flow to shear flow coupled with codirectional and transverse pressure flow. A linearization (or perturbation) technique is used to decouple the two orthogonal flows by assuming that the shear stress in a finite bearing is a small perturbation of the shear stress valid for couette flow. Using Boussinesq's eddy viscosity formulation and the wellestablished power law as a universal law of wall, the governing pressure distribution equation is obtained from considerations of the conservation of momentum and continuity. The surfaces are considered to be hydrodynamically smooth. The whole treatment is approached from the viewpoint of fluid film design rather than from a fundamental fluid mechanics approach. No slip model has been used. The lubrication equation is fully analytical and can be applied to a number of particular bearing problems by using the simplifying restrictive conditions. The lubrication equation derived can be used to predict the bearing performance characteristics even in situations where the permeability of the bearings is anisotropic and the Poiseuille flow in the porous matrix does not obey Darcy's law.     

一种测量液膜厚度的超声相控阵实验装置

气液两相流存在于核反应堆蒸发、飞行器冷却、化工生产降膜蒸发等过程,界面波的动态测量对工业过程监控和生产优 化具有重要意义。 界面波的准确识别与特性参数测量是开展科学研究与工程实践的重要前提。 基于超声相控阵测量系统,设 计了扇扫的测量方式,可以用于气液界面清晰的流型中液膜厚度和界面波形态三维测量。 通过静态标定和圆管验证,确定了像 素点和液膜厚度之间的关系,在气相表观流速为 0. 071 9~ 0. 431 6 m/ s,液相表观流速为 0. 056 7~ 1. 416 1 m/ s 的工况下进行实 时动态实验,获得了实时流动过程中较高精度的截面气液相界面信息,并构建了管道内部界面波三维分布形态,为界面波特性 研究提供了一种实验参考方法。     

A Molecular Dynamics Study of the Transition from Ultra-Thin Film Lubrication Toward Local Film Breakdown

The transition from ultra-thin lubrication to dry friction under high pressure and shear is studied using molecular dynamics: the quantity of lubricant in the confined film is progressively reduced toward solid-body contact. A quantized layer structure is observed for n-alkanes confined between smooth, wettable walls, featuring an alternation of well-layered, low friction configurations, and disordered ones, characterized by high friction, and heat generation. The molecular structure influences the ordering of the fluid and the resulting shear stress. In fact, Lennard-Jones fluids are characterized by low friction due to the absence of interlayer bridges, opposed to the always entangled states and high shear stresses for branched molecules. Surface geometry and wettability also affect the behavior of the confined lubricant. The presence of nanometer-scale roughness frustrates the ordering of the fluid molecules, leading to high friction states. Furthermore, local film breakdown can be observed when the asperities come into contact, with strong wall–wall interactions causing the maximum in shear stress. Finally, friction is limited to a small, constant value by the presence of smooth, non-wettable surfaces in the system due to the occurrence of wall slip.     

Intermittent flow parameters from void fraction analysis

Two-phase horizontal intermittent flow in straight pipes is experimentally investigated. A new procedure is proposed to characterize the flow through the statistical analysis of the instantaneous cross-sectional averaged void fraction obtained by means of ring impedance probes. The algorithm, based on the statistical analysis of the void fraction records, allows the main intermittent flow parameters, such as slug frequency and length, time average void fraction, minimum and average liquid film height to be evaluated. The procedure is validated through flow visualizations, as obtained from a fast digital video camera.Experiments on air-water horizontal flows in 40 and 60 mm inner diameter pipes are performed. The operating conditions cover the 0.3–4.0 and 0.6-3.0 m/s gas and liquid superficial velocity ranges, respectively.An extensive comparison with literature data shows a general agreement with present measurement. The reliability of both the instrumentation and the signal analysis procedures allows new correlations for minimum and average liquid film height in stratified regions to be proposed. Finally proper dimensionless numbers were applied to correlate frequency data in a wide range of superficial velocity values.     

Dynamic analysis of free-surface thin film flows driven by gravity over undulated substrate

This paper studies thin film flows with free surfaces driven by gravity through two types of undulated planes: periodically sinusoidal plane and triangle. The substrate plane is fixed and inclined to a certain angle and the flow with a free surface. Through finite element method (FEM), commenced from Navier-Stokes equations and continuity equation, the exact numerical results of free-surface film flows are obtained through discretization solution to finite equations in flowing areas. Based on the numerical calculations, the streamlines and wall shearing stress during the flowing process are visualized via post-proceeding, and the streamlines separation, the onset and evolution of vortex near the substrate boundary during the flow are also analyzed. The influences from the waviness of the substrate planes profile, height of the triangle plane, and change of the film height on film flow dynamics properties are shown.     

Dynamic analysis of free-surface thin film flows driven by gravity over undulated substrate

This paper studies thin film flows with free surfaces driven by gravity through two types of undulated planes: periodically sinusoidal plane and triangle. The substrate plane is fixed and inclined to a certain angle and the flow with a free surface. Through finite element method (FEM), commenced from Navier-Stokes equations and continuity equation, the exact numerical results of free-surface film flows are obtained through discretization solution to finite equations in flowing areas. Based on the numerical calculations, the streamlines and wall shearing stress during the flowing process are visualized via post-proceeding, and the streamlines separation, the onset and evolution of vortex near the substrate boundary during the flow are also analyzed. The influences from the waviness of the substrate planes profile, height of the triangle plane, and change of the film height on film flow dynamics properties are shown.     

Squeeze fluid film of spherical hydrophobic surfaces with wall slip

Isothermal squeeze film flow of Newtonian fluid between spherical hydrophobic surfaces with wall slip is investigated using a limiting shear stress model and complementary algorithm. Wall slip velocity is controlled by the liquid–solid interface limiting shear stress. It is found that the wall slip dramatically decreases the hydrodynamic support force of the squeeze fluid film. In the case of large wall slip the hydrodynamic support force increases only slightly with the decrease in the film thickness. We find that wall slip decreases with increasing film thickness and limiting shear stress, but increases with increasing fluid viscosity and approaching velocity. An empirical equation is given for prediction of the fluid load support capacity. The possible effect of pressure on wall slip is also discussed. It is found that fluid pressure suppresses wall slip after the proportionality coefficient of limiting shear stress reaches a critical threshold. However, almost no effect is found when it is below this critical threshold. Good agreements exist between the present theoretical predictions and some existing experimental observations.     

端面形貌和流体剪切稀化对螺旋槽液膜密封稳态特性的影响

为研究密封端面形貌变化和润滑流体的剪切稀化特性对螺旋槽液膜密封稳态特性的影响基于幂律模型,建立考虑润滑流体的剪切稀化特性、密封端面径向锥度和周向波度的螺旋槽液膜密封稳态特性数学模型,利用有限差分法求解稳态雷诺方程,分析径向锥度和周向波度对剪切稀化流体液膜密封稳态特性的影响规律。结果表明:当锥度增大时,液膜密封开启力减小、泄漏量增大、摩擦扭矩减小,润滑流体的剪切稀化特性可以明显地减小密封端面开启力和泄漏量,稍微增大摩擦扭矩;当波数增大时,液膜密封开启力增大、泄漏量小幅减小、摩擦扭矩增大;当波幅增大时,液膜密封开启力增大、泄漏量小幅增大、摩擦扭矩明显减小;波度对剪切稀化流体液膜密封稳态特性的影响程度要稍弱于对牛顿流体的影响,但整体趋势保持一致。