Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

Comprehensive modeling of frictional pressure drop during carbon dioxide two-phase flow inside channels using intelligent and conventional methods

Environmentally friendly nature of CO_(2),associated with its safety and high efficiency,has made it a widely used working fluid in heat exchangers.Since CO_(2)has strange thermophysical features,specific models are required to estimate its two-phase characteristics,particularly frictional pressure drop(FPD).Herein,a widespread dataset,comprising 1195 experimental samples for two-phase FPD of CO_(2)was adopted from 10 sources to fulfill this requirement.The literature correlations failed to provide satisfactory precisions and exhibited the average absolute relative errors(AAREs)between 29.29% and 67.69% from the analyzed data.By inspiring the theoretical method of Lockhart and Martinelli,three intelligent FPD models were presented,among which the Gaussian process regression approach surpassed the others with AARE and R^(2)values of 5.48% and 98.80%,respectively in the test stage.A novel simple correlation was also derived based on the least square fitting method,which yielded opportune predictions with AARE of 19.76% for all data.The truthfulness of the newly proposed models was assessed through a variety of statistical and visual analyses,and the results affirmed their high reliability over a broad range of conditions,channel sizes and flow patterns.Furthermore,the novel models performed favorably in describing the physical attitudes corresponding to two-phase FPD of CO_(2).Eventually,the importance of operating factors in controlling the FPD was discussed through a sensitivity analysis.

Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines.Friction factors play an important role in the accurate calculation of pressure drop.Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall,gas-wall and interfacial friction in two-phase pipe flow.However most of them are empirical correlations found under special experimental conditions.In this paper by modification of a friction model available in the literature,an improved semiempirical model is proposed.The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved.Pressure gradient and velocity profiles are validated against experimental data.Using the improved model,the pressure gradient deviation from experiments diminishes by about 3%;the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.

Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.

Frictional contact algorithm study on the numerical simulation of large deformations in deep soft rock tunnels

There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces （the excavation boundaries）, the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.

Two-dimensional Dynamics Simulation of Two-phase Debris Flow

To investigate the movement mechanism of debris flow, a two-dimensional, two-phase, depthintegrated model is introduced. The model uses Mohr-Coulomb plasticity for the solid rheology, and the fluid stress is modeled as a Newtonian fluid. The interaction between solid and liquid phases, which plays a major role in debris flow movement, is assumed to consist of drag and buoyancy forces. The applicability of drag force formulas is discussed. Considering the complex interaction between debris flow and the bed surface, a combined friction boundary condition is imposed on the bottom, and this is also discussed. To solve the complex model equations, a numerical method with second-order accuracy based on the finite volume method is proposed. Several numerical experiments are performed to verify the feasibilities of model and numerical schemes. Numerical results demonstrate that different solid volume fractions substantially affect debris flow movement.

Lockhart-Martinelli两相流摩擦压降模型与典型均相流模型的验证对比分析

两相流摩擦压降的计算对于两相流设备与管道的设计选型和流阻分析至关重要。在已有的两相流摩擦压降模型中,均相流模型和Lockhart-Martinelli模型(L-M模型)是比较常用的两相流摩擦阻力压降计算模型。两相流压力对两相流摩擦压降影响很大,然而,之前的模型验证分析并未分析这些模型在不同压力条件下的计算精度。L-M模型是否适用于中高压两相流,均相流模型在什么压力范围内适用,并未有相关验证分析及结论。本研究对比了均相流模型和L-M模型计算值与文献中公开发表的两相流摩擦压降数据,主要包括OuldDidi的制冷剂两相流摩擦压降数据、GASPARI的7 MPa两相流摩擦压降数据及陈听宽的高压两相流摩擦压降实验数据。通过验证对比分析发现在中高压条件下,L-M模型计算误差非常大,压力越高,模型计算误差越大。而均相流模型,对于高压两相流,特别是对高压低质量含气率两相流有比较好的预测精度。

The Relation between the Coefficient of Friction and Pressure Drop by Using the Different Reynolds Number in a Circular Tube

This study explains the relationship between friction coefficient and pressure change at a range of Reynolds (21,056 - 28,574) and (0 - 1.4) solid loading ratio of two-phase flow (gas-solid) inside a circular copper pipe by using laboratory apparatus and solving the equations mathematically. An experimentally relationship of friction coefficient and pressure change with Reynolds number and flow velocity obtained also the relationship between the Solid loading ratio with friction coefficient and pressure change has been done for a Limit range of Reynolds number. It was noticed that the increase in friction coefficient and pressure change for two-phase flow was occurred when solid loading ratio increased. Also the relationship between pressure change and Reynolds number was direct proportion while the relationship between friction coefficient and Reynolds Number was inversely related.

管内两相流摩擦压力损失计算研究进展

管内两相流摩擦压力损失计算广泛应用于各种工业领域,一直是热流体科学的重要研究方向。本文对管内两相流摩擦压降计算的研究成果进行了全面总结与归纳,系统综述了分相摩擦倍增因子方法、全相摩擦倍增因子方法以及均相模型方法,并且对各模型进行了评价和分析,可为相关研究提供参考。

双面约束多点摩擦多体系统的建模和数值方法

提出了一种建立具有固定双面约束多点摩擦的多体系统动力学方程的方法.用笛卡尔坐标阵描述系统的位形,根据局部方法的递推关系建立系统的约束方程,应用第一类Lagrange方程建立该系统的动力学方程,使得具有摩擦的约束面的法向力与Lagrange乘子一一对应,便于摩擦力的分析与计算,并用矩阵形式给出了摩擦力的广义力的一般表达式.应用增广法将微分-代数方程组转化为常微分方程组,并用分块矩阵的形式给出,以便于方程的编程与计算.给出了一种改进的试算法,可提高计算效率.最后给出了一个算例,应用试算法和RK法对算例进行了数值仿真.

三维摩擦接触问题算法精度和收敛性研究

回顾了摩擦接触问题的现有解法,包括Lagrange乘子法、惩罚函数法、增广Lagrangian乘子法,线性互补模型及互补类非线性方程组方法等,尤其是近期关于非线性方程组方法的系列研究结果:(1)三维弹性摩擦接触问题互补类非线性方程组的光滑化解法;(2)将其推广为非光滑解法;(3)三维弹塑性摩擦接触问题增量方程和算法.非线性方程组方法解法基于严格的数学理论基础,严格地满足接触条件,并用随机数产生的接触柔度矩阵证实了算法的收敛性,由于每个接触点对的未知数只有3个,不含任何人工变量,同时,算法有局部二次收敛率且计算效率很高.为了考察以增广拉格朗日法为代表的工程中流行算法的精度和收敛性,设计了一个典型的弹性摩擦接触问题算例,证实了通用程序ANSYS的增广拉格朗日法是近似的并且不能保证收敛.

低质量流速优化内螺纹管摩擦阻力特性实验研究

在绝热及加热条件下,对低质量流速四头优化内螺纹管的摩擦压降进行了实验研究,探讨了其单相及两相摩擦阻力特性,分析了压力、质量流速和蒸汽干度变化对两相摩擦压降倍率的影响,并给出了能用于工程实际的实验关联式。实验结果表明:(1)内螺纹管的单相摩擦系数在低雷诺数区域随雷诺数的增大而显著减小,但在高雷诺数区域几乎保持不变;(2)内螺纹管的两相摩擦倍率随着蒸汽干度的增大先增大、随后增幅减小甚至略有下降,随着压力的增大而迅速减小,但受质量流速的影响较小。(3)受热管的单相摩擦系数小于绝热管,但两相摩擦倍率大于绝热管。

窄矩形通道内两相流动压降特性研究

以空气和水为实验工质,分别在40mm×1.6mm和40mm×3mm的矩形通道中对竖直向上气-液两相流动阻力特性进行了实验研究。该研究还对比了现有的两相流动阻力计算关系式,结果表明,对于窄缝为1.6mm的通道,传统的阻力计算关系式均不适用;而窄缝为3mm的通道,除Friedel模型和Tran模型外,其余模型与实验值符合较好。为此结合实验数据,以分液相雷诺数为依据将流动分为层流区、过渡区和湍流区3个区域,分别对Chisholm关系式进行修正,结果表明:C为当量直径的线性函数,当量直径越大,C越小。修正关系式与实验数据的误差较小,能很好地预测本次实验结果。

基于临界滑脱长度的短纤纱断裂强力计算

为得到一种更加合理的短纤纱断裂强力的近似计算方法,根据短纤纱结构的理想化假设和临界滑脱长度的概念,推导出短纤纱断裂过程中纤维临界滑脱长度的近似计算表达式以及发生断裂和滑脱的纤维对短纤纱断裂强力的实际贡献。鉴于短纤纱截面纤维根数的不匀,根据计算得到的临界滑脱长度采用纤维在短纤纱中随机排列的模拟对短纤纱断裂强力进行计算。通过纺制不同线密度下具有不同捻系数的粘胶纱与涤纶纱,并测试其断裂强力对该计算方法进行验证。计算和验证结果表明:临界滑脱长度的计算值随着捻系数的增加而减小,且当捻系数增加时,短纤纱断裂强力的计算值随着捻系数的增加升高至最高值而后发生下降,这与实测短纤纱强力值的变化趋势是一致的。

含摩擦滑移铰平面多刚体动力学的HLCP方法

给出了一种基于水平线性互补问题(HLCP)的双边约束滑移铰含摩擦平面多刚体系统动力学的数值计算方法.首先从系统的约束方程出发建立了每个双边约束中两个约束面的法向约束力的互补关系;并利用摩擦余量的概念给出了库仑摩擦定律的互补表达式.然后针对事件驱动算法将该类非光滑多体系统动力学方程中双边约束中法向约束力切换和系统"stick-slip"运动状态切换的判断统一成HLCP的求解,通过定义一组变维数矩阵给出了HLCP形式的一般表达式,便于编程计算.最后通过一个两自由度多体系统的算例验证了该方法的有效性.

细观参数对类砂岩材料宏观参数影响规律的颗粒流分析

为快速、准确地确定颗粒流模型中的细观参数,采用单因素分析法,用平行黏结模型对类砂岩材料各宏观力学参数的影响规律进行模拟分析。结果表明,峰值强度同摩擦系数之间符合幂函数增长关系,而同平行黏结半径乘子之间符合线性增长函数关系,与平行黏结刚度比之间未有明显的函数关系;弹性模量同摩擦系数之间符合幂函数增长关系,与平行黏结半径乘子之间符合线性增长函数关系,与平行黏结刚度比之间符合指数函数衰减关系;泊松比同平行黏结刚度比之间符合幂函数增长关系,泊松比与摩擦系数、平行黏结半径乘子之间均符合指数函数衰减关系;峰值应变同平行黏结刚度比、平行黏结半径乘子之间均符合幂函数增长关系,峰值应变与摩擦系数之间未有明显的函数关系。

摩擦约束广义变分不等原理的临界变分现象及分析

对于具有摩擦约束的弹塑性接触问题,由于边界接触面上的摩擦力由不等式表示,导致得到包含摩擦约束的广义变分原理为广义变分不等原理。广义变分不等原理通过将摩擦力纳入问题的能量泛涵,可避免考虑摩擦力变化的具体过程,便于数值方法如有限元等在弹性接触问题上的应用。但是,通过对广义变分不等原理的研究,发现在弹性力学广义变分不等原理中,势能型和余能型广义变分不等原理,均存在临界变分现象,即变分时拉格朗日乘子为零,变分失败;或者得到的能量泛函变分后得不到问题的欧拉方程。在对弹性力学广义变分不等原理临界变分现象进行分析后,提出了避免发生临界变分现象的方法。实际应用证明了方法的有效性。通过避免临界变分现象的发生,可以保证拉格朗日乘子方法的有效使用。

金融摩擦与财政支出的非线性乘数效应研究

金融摩擦存在可能非线性地传播冲击,导致财政支出的非线性乘数效应。基于考虑金融摩擦的理论模型,分析了财政支出冲击对家庭部门最优投资决策行为的影响,提出关于财政支出非线性乘数效应及其可能原因的理论假设;通过构建包含金融摩擦综合测度指标的非线性实证模型,检验了财政支出的非线性乘数效应。研究结果表明,在高金融摩擦环境中,财政支出对于总产出的乘数效应更大,这主要归因于财政支出对金融摩擦的缓解作用以及对私人投资的"挤入"效应。财政政策的调控方式需要根据金融摩擦的状态变化而适时调整。

环形通道内液态金属钠沸腾两相流动特性实验研究

对环形通道内液态金属钠沸腾两相流动特性进行了实验研究。实验中质量流速G≤2 000kg·m-2·s-1,系统压力p≤0.1 MPa,热流密度q≤550kW·m-2。两相流动摩擦压降通过在相同质量流量的单相流动摩擦阻力系数的基础上引入两相摩擦倍增因子来考虑两相的影响。实验结果表明:环形通道内液态金属钠两相摩擦倍增因子随Martinelli参数的增大有减小趋势。综合本文实验数据、Lurie等的实验数据以及Kaiser等的棒束实验数据,拟合得到了计算液态金属钠沸腾两相流动摩擦倍增因子的关系式。计算了本文拟合得到的关系式与各组实验数据间的相对标准偏差(RSD),表明本文关系式适用于计算环形通道内液态金属钠沸腾两相流动特性。