Study on the compressible viscous flows through a straight pipe

When sonic nozzles of significantly smaller diameter are used as standard flow meters, the critical backpressure ratio is affected by the boundary layer at the nozzle throat. It is known that, as the flow pathway is complicated in actual valves, the critical pressure ratio differs from the ideal value. However, the effect of the boundary layer thickness on choking criteria is still controversial. Choking phenomenon in a sonic nozzle fitted with a straight circular pipe of variable length is investigated numerically and the results are compared with experimental and theoretical ones. The results show that the actual critical pressure ratio is less than the ideal value and it decreases with increase in pipe length. The effect of boundary layer thickness on main flow Mach number is also made clear in this work. In addition, sonic conductance and pressure loss in actual viscous flows computed are compared with the ISO 6358 standard.     

Computational study of the unsteady flow characteristics of a micro shock tube

Micro shock tubes are widely employed in many micro instruments which require high speed and high temperature flow field. The small flow dimension introduces additional flow physics such as rarefaction effects, viscous effects etc, which makes the micro shock tube different from conventional macro shock tubes. In the present study, a numerical investigation of the flow physics associated with shock propagation and reflection inside micro shock tubes was carried out using unsteady Navier Stokes equations. Maxwell’s slip boundary conditions were incorporated to simulate the rarefaction effects produced due to low pressure and very small length scale. The effect of initial pressures on the shock propagation was investigated keeping the pressure ratio constant. The dependency of the shock tube diameter on shock propagation was also investigated. The results show that shock strength attenuates drastically in a micro shock tube compared to macro shock tubes. The viscous boundary layer becomes a governing parameter in controlling micro shock tube wave propagations. The implementation of slip velocity to model rarefaction effects increases the shock strength and aids in shock wave propagation. The simulation with slip wall exhibits a wider hot zone (shock-contact distance) compared to no-slip simulation. The contact surface propagation distance reduces under the slip effects. A drastic attenuation in shock propagation distance was observed with reduction in diameter. The shock wave when reflected from the end wall inhibits the rarefaction effects, generally happening at very low pressure micro shock tubes, and the associated slip effect vanishes for the post reflected shock flow field.     

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.     

基于分子动力学的密封副润湿特性对泄漏量影响研究

在微纳尺度下的间隙密封中,流体流经不同润湿特性的界面时固液交界处会产生不同程度的边界滑移,进而影响其流动状态及泄漏量。为深入研究密封副润湿特性与泄漏量关系,基于分子动力学原理,建立间隙密封模型,模拟在不同润湿性的壁面上,以不同壁面运动速度剪切下表层水分子的边界滑移及其单向泄漏情况。研究结果:表明壁面上的最大剪应力随壁面运动速度的提高呈线性增加,在高速的剪切作用下,亲水性壁面上依然会产生轻微的边界滑移;随着剪切速率的增加,滑移长度与泄漏量趋于稳定;在实际生产中通常剪切速率较小,剪应力不足以引起边界滑移,水分子易吸附于壁面之上导致更大的泄漏量,因此在低剪切速率下,壁面润湿性对于单向剪切泄漏的影响很小;而在剪切速率较高时,润湿性较差的壁面上泄漏更小,因此可以通过在密封表面采用疏水涂层处理以达到更好的密封效果。     

Influence of slip velocity in Herschel-Bulkley fluid flow between parallel plates - A mathematical study

This theoretical study investigates three types of basic flows of viscous incompressible Herschel-Bulkley fluid such as (i) plane Couette flow, (ii) Poiseuille flow and (iii) generalized Couette flow with slip velocity at the boundary. The analytic solutions to the nonlinear boundary value problems have been obtained. The effects of various physical parameters on the velocity, flow rate, wall shear stress and frictional resistance to flow are analyzed through appropriate graphs. It is observed that in plane Poiseuille flow and generalized Couette flow, the velocity and flow rate of the fluid increase considerably with the increase of the slip parameter, power law index, pressure gradient. The fluid velocity is significantly higher in plane Poiseuille flow than in plane Couette flow. The wall shear stress and frictional resistance to flow decrease considerably with the increase of the power law index and increase significantly with the increase of the yield stress of the fluid. The wall shear stress and frictional resistance to flow are considerably higher in plane Poiseuille flow than in generalized Couette flow.

     

Prediction of pressure drop in Venturi based on drift-flux model and boundary layer theory

Venturi, as the primary flow measurement sensor, is widely used in various industrial fields of oil and natural gas. Pressure drop of the Venturi is a crucial factor in the process design of exploitation and transportation of natural gas. Based on the drift-flux model and boundary layer theory, a pressure drop prediction model is established. Except for divergent section, a uniform void fraction model is established basing on drift-flux model. The thickness of boundary layer grows rapidly due to the existence of adverse pressure gradient in the divergent section, which results in an increase of the irrecoverable pressure drop. Considering the influence of slip between gas and liquid, weight coefficient is used to adjust the proportion of displacement thickness in the cross section of the Venturi. Compared to experiment, the theoretical model is applied to stratified wavy flow and annular mist flow. For different diameter, the relative deviations of experiment points are within ±15%.     

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.     

钢管内壁强化处理工艺方案

采用超高压液压自紧技术,对钢管内壁进行强化处理.设计了工艺方案,构建的系统的最高压力可达1000MPa.分析了钢管的稳定性和强度,计算了钢管内壁强化层的厚度并绘制了应力曲线图.     

Hydrodynamic plane and axisymmetric slip stagnation-point flow with thermal radiation and temperature jump

This work focuses on the steady boundary layer flow and heat transfer near the forward stagnation point of plane and axisymmetric sheet towards a stretching sheet with velocity slip and temperature jump. The resulting nonlinear partial differential equations are reduced to the system of nonlinear ordinary differential equations by means of similarity transformations. The analytical solutions for the velocity and temperature distributions are obtained for the various values of the ratio of free stream velocity and stretching velocity, velocity slip parameter, magnetic parameter, the suction parameter, temperature jump parameter, Prandtl number, the radiation parameter and dimensionality index parameter in the series forms with the help of homotopy analysis method. Convergence of the series is explicitly discussed. The flow and shear stresses depend heavily on the velocity slip parameter. The temperature gradient at the wall increases with velocity slip parameter, temperature jump factor and decreased thermal radiation.     

润滑脂管道流动阻力的测试研究

分析了存在壁滑移时的流动阻力测试原理,对测试系统和阻力计算进行了研究。为了测试润滑脂的阻力特性,去除壁滑移流动的影响,根据Mooney方法建立了扣除壁滑移后适应任一管径的流动方程;润滑脂的粘弹性、触变性等其他因素会使流动曲线不重合,研制了管流流变仪测试系统,并制定了合理的试验方法,达到使这些因素的影响降到最低和分离壁滑移流动的试验效果。通过试验验证了所建立的适应任一管径的流动方程,求解了流动方程的阻力近似解,并通过三维优化计算降低了近似解与精确解的偏差。润滑脂流动阻力的测试研究,为集中润滑系统的管路输送提供了理论和试验依据。     

A suggestion of a new method for the calculation of the coating thickness in continuous hot-dip galvanizing

It is known that the distributions of the impinging pressure gradient and the shear stress at the strip surface play a decisive key role in the decision of the coating thickness in hot-dip galvanizing. So, to predict the exact coating thickness, it is essential that the distributions of the impinging wall jet pressure and the shear stress acting between the liquid film and jet stream are measured (or calculated) exactly for each specific coating condition. So far, to obtain the impinging wall jet pressure, it was assumed that the jet issuing from an air-knife is similar to the Hiemenz plane stagnation flow, and the wall shear stress could be predicted by an equation using the assumption of a non-negative Gaussian profile in impinging wall jet pressure in general, so that it cannot be reliable for some impinging wall jet regions and nozzle systems intrinsically. Nevertheless, one cannot find a suitable method to cope with the difficulties in measuring/calculating of the shear stress and the impinging wall jet pressure. Such a difficulty which will cause an inaccuracy in the coating thickness prediction. With these connections, in the present study, we suggest a new method named as a two-step calculation method to calculate the final coating thickness, which consists of the air jet analysis and coating thickness calculation. And, from the comparison of the results one may confirm the validation of the new suggested method.     

Space-time characteristics of the wall shear-stress fluctuations in an axial turbulent boundary layer with transverse curvature

Direct numerical simulation database of an axial turbulent boundary layer is used to compute frequency and wave number spectra of the wall shear-stress fluctuations in a low-Reynolds number axial turbulent boundary layer. One-dimensional and two-dimensional power spectra of flow variables are calculated and compared. At low wave numbers and frequencies, the power of streamwise shear stress is larger than that of spanwise shear stress, while the powers of both stresses are almost the same at high wave numbers and frequencies. The frequency/streamwise wave number spectra of the wall flow variables show that large-scale fluctuations to the rms value is largest for the streamwise shear stress, while that of small-scale fluctuations to the rms value is largest for pressure. In the two-point auto-correlations, negative correlation occurs in streamwise separations for pressure, and in spanwise correlation for both shear stresses.     

Lubricating Grease Shear Flow and Boundary Layers in a Concentric Cylinder Configuration

Grease is extensively used to lubricate various machine elements such as rolling bearings, seals, and gears. Understanding the flow dynamics of grease is relevant for the prediction of grease distribution for optimum lubrication and for the migration of wear and contaminant particles. In this study, grease flow is visualized using microparticle image velocimetry (μPIV). The experimental setup includes a concentric cylinder configuration with a rotating shaft to simulate the grease flow in a double restriction seal geometry with two different grease pocket sizes. It is shown that the grease is partially yielded in the large grease pocket geometry and fully yielded in the small grease pocket. For the small grease pocket, it is shown that three distinct grease flow layers are present: a high shear rate region close to the stationary wall, a bulk flow layer, and a high shear rate boundary region near the rotating shaft. The grease shear thinning behavior and its wall slip effects have been identified. The μPIV experimental results have been compared with a numerical model for both the large and small gap size. It is shown that the flow is close to one-dimensional in the center of the small pocket. A one-dimensional analytical model based on the Herschel-Bulkley rheology model has been developed, showing good agreement with the measured velocity profiles in the small grease pocket. Furthermore, wall slip effects and shear banding are observed, where the latter imply that using the assumption of uniform shear in conventional concentric cylinder rheometers may result in erroneous rheological results.     

Heat transfer characteristics of gaseous slip flow in a micro-channel

Two-dimensional compressible momentum and energy equations with slip boundary conditions are solved to obtain the heat transfer characteristics of gaseous slip flow in a micro-channel with CWT (constant wall temperature) whose temperature is lower or higher than the inlet temperature (cooled case or heated case). The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The stagnation temperature is fixed at 300 K and the computations were done for the wall temperature which ranges from 250 K to 350 K. The channel height ranges from 2 to 10 μm and the channel aspect ratio is 200. The stagnation pressure is chosen in such a way that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at atmospheric condition. The bulk temperature and the total temperature of the heated case are compared with those of the cooled case and also compared with temperatures of the incompressible flow in a conventional sized channel. Heat transfer characteristics of the gaseous flow are different from those of the liquid flow. And they are also different from each cooled and heated case. A correlation for the prediction of the heat transfer rate of the gaseous slip flow in a micro-channel is proposed.     

微注塑成形中壁面滑移对熔体充模流动影响的研究

分析了微尺度下熔体壁面滑移机理，研究了微注塑成形中壁面滑移对熔体充模流动行为的影响。利用有限元方法进行数值模拟，确定了不同特征尺寸微通道中熔体的滑移系数，分析了入口剪切速率和长径比与滑移速度之间的关系。研究结果表明：壁面滑移使熔体速度曲线趋于平滑；当熔体入口速率一定时，其壁面滑移速度随微通道特征尺寸的减小而减小；入口剪切应力相同时，壁面滑移速度随微通道的长径比的增大而增大。     

Numerical Analysis of a Slider Bearing with a Heterogeneous Slip/No-Slip Surface

The behavior of a fluid-film bearing depends on the boundary conditions at the interfaces between the liquid and the solid bearing surfaces. For almost all solid surfaces, the no-slip boundary condition applies. However, a number of researchers have recently found that slip can occur with specially engineered surfaces. These include molecularly smooth surfaces and surfaces with micron-scale patterns. By constructing an engineered heterogeneous surface on which slip occurs in certain regions and is absent in others, the flow in the liquid film of a bearing can be altered, and such characteristics as load support and friction can be improved. In the present study, a numerical analysis of a slider bearing with such an engineered slip/no-slip surface is analyzed. Slip is assumed to occur when a critical shear stress is exceeded and follows the Navier relation. The results show that with a critical shear stress of zero, a significant increase in load support and decrease in friction can be achieved with an appropriate surface pattern. With nonzero values of critical shear stress, an instability occurs over a range of speeds. At speeds above this range, the bearing behaves similar to the case with zero critical shear stress, while below this range it behaves like a conventional bearing.     

空分用板翅式换热器失效分析

在某空分系统发生的一次设备故障中，由德国某公司设计并制造的高压板翅式主换热器及其附属空气管道发生了开裂、磨蚀、穿孔等失效现象，导致多种低温介质泄漏。通过宏观检查、无损检测、取样分析和故障过程逻辑推理等分析，结果表明：主换热器隔板与封条间钎焊质量的不可靠是造成换热器开裂的主要原因；而主换热器开裂后所形成的携带着珠光砂的低温喷射气流则进一步导致了管道的磨蚀穿孔。     

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。     

Occurrence of Wall Slip in Elastohydrodynamic Lubrication Contacts

Preliminary experimental work has been carried out to identify some of the boundary slip phenomena of highly pressurised polybutenes in an elastohydrodynamic lubrication (EHL) conjunction. The movement of the oil is signified using an entrapment that can be readily formed by the impact of a steel ball against a layer of oil on a glass block in an optical EHL test apparatus. The post-impact lateral movement of the entrapment was investigated under the conditions: (i) pure rolling, (ii) pure glass block sliding (steel ball stationary) and (iii) pure ball sliding (glass block stationary). It was observed that under pure rolling the entrapped oil travels within the contact region at the entrainment speed, which is correlated with EHL theory. Under pure glass block sliding conditions, the speed of the entrapped oil core is less than the entrainment speed, and in the extreme cases, this core can be nearly stationary. Under pure ball sliding conditions, the oil core moves at a speed greater than the entrainment speed. The observation indicates that the oil/steel ball interface can sustain higher shear stress than the oil/glass (chromium coated) interface and there is a boundary slip in terms of relative sliding at the latter interface under the experimental conditions. Furthermore, the amount of slip increases with an increase in the pressure. These experiments provide evidence of the existence of wall slippage, which leads to the abnormal EHL film profile characterised with an inlet dimple as reported earlier.