Measurements of two-phase mass flow rate: A comparison of different techniques

The development of practical and accurate methods to measure two-phase mass flow rates is of prime interest to applied nuclear reactor safety research. This article summarizes a comparison and evaluation of four commonly used mass flow rate devices. The particular systems investigated include (a) the true mass flow meter (TMFM), (b) the radionuclide technique, (c) the combination of a free field drag disk-turbine meter-transducer (DTT) and a gamma densitometer, and (d) the combination of a venturi nozzle and a full flow turbine meter. The experiments were performed under similar conditions in steady-state steam-water flow. The flow direction upstream of the instruments was horizontal except for the last method. The pressures varied between 3 and 9 MPa, and the highest values of the mass flow rate, the quality were 5 kg/s and 90 per cent respectively. The test matrix included wave-, slug- and annular flow. The measuring techniques are described briefly and a classification is proposed, which is based on the different ways of mass flow rate evaluation. The experimental results show that the accuracy of some methods is distinctively dependent on phase distribution (flow regime). Simple calibration correlations were developed to account for these effects.     

Mass flow rate measurements in gas–liquid flows by means of a venturi or orifice plate coupled to a void fraction sensor

Two-phase flow measurements were carried out using a resistive void fraction meter coupled to a venturi or orifice plate. The measurement system used to estimate the liquid and gas mass flow rates was evaluated using an air–water experimental facility. Experiments included upward vertical and horizontal flow, annular, bubbly, churn and slug patterns, void fraction ranging from 2% to 85%, water flow rate up to 4000 kg/h, air flow rate up to 50 kg/h, and quality up to almost 10%. The fractional root mean square (RMS) deviation of the two-phase mass flow rate in upward vertical flow through a venturi plate is 6.8% using the correlation of Chisholm (D. Chisholm, Pressure gradients during the flow of incompressible two-phase mixtures through pipes, venturis and orifice plates, British Chemical Engineering 12 (9) (1967) 454–457). For the orifice plate, the RMS deviation of the vertical flow is 5.5% using the correlation of Zhang et al. (H.J. Zhang, W.T. Yue, Z.Y. Huang, Investigation of oil–air two-phase mass flow rate measurement using venturi and void fraction sensor, Journal of Zhejiang University Science 6A (6) (2005) 601–606). The results show that the flow direction has no significant influence on the meters in relation to the pressure drop in the experimental operation range. Quality and slip ratio analyses were also performed. The results show a mean slip ratio lower than 1.1, when bubbly and slug flow patterns are encountered for mean void fractions lower than 70%.     

Slurry flow metering by pressure differential devices

A simple system for measuring slurry concentrations and flow rates by pressure difference devices has been studied. Solids concentrations have been determined by pressure measurements in vertically upwards and downwards sections of the flow, and flow rates measured by a venturi meter located alternately in horizontal, vertically upwards and vertically downwards flows. The venturi performance has been described in terms of a discharge coefficient based on mixture density, and the concentration measurements have been compared to values determined by weigh tank samples. A range of sand slurries with median particle size from 150 to 740μm and an ilmenite slurry with a median particle size of 170μm have been tested. A limited number of tests on a 17μm sand slurry have also been recorded.For fine sand slurries (150μm or below) it was found that the water value of venturi-discharge coefficient applied, so that the accuracy of flow measurements will be limited only by the accuracy of the pressure and specific weight measurements. Experimental values of specific weight from the vertical loop section were on average within 1% of the values from the weigh tank, where the majority of this scatter was caused by the limitations of the weigh tank method.For coarser slurries, the venturi-discharge coefficients depended primarily on solids concentration, with a secondary dependence on Reynolds number, and values were below the water value. An analysis of the flow based on a one-dimensional momentum balance indicated that relative velocity between the phases could account for these low values of discharge coefficient. This was verified by high-speed photography of the flow which suggested a movement of particles towards the centre of the flow at the throat.The overall indications are that the combination of a vertical loop section of flow (for concentration or specific weight measurements) and a venturi meter (for flow rates) provides a simple and accurate means of metering slurry flows. For fine slurries only water calibrations or calibrations from Standards are required.     

圆柱周围湍流和含沙多相流的SPH数值模拟

湍流和多相流是流体力学中最具挑战性的两个主题,湍流多相流的实验和数值模拟更是一项艰巨的挑战。此外,对颗粒干沉积方面的多相流、多尺度、多物理耦合特征的风沙流的综合实地观测仍然很少。因此,本文综合考虑湍流、多相流与多物理耦合等方面,采用以圆柱为干扰物产生对流涡流的强制干扰技术,以塔克拉玛干沙漠地带中和田至若羌铁路的过沙桥桥墩为研究背景。为摆脱有限元软件中由网格大变形或失真引起的各种问题,采用SPH方法的宏观界面追踪和微观单点追踪相结合的方式,初步揭示了以单相对流涡流为风场背景的含沙多相流环境下的圆柱周围复杂的流场变化以及对颗粒干沉积运动的影响。采用数值模拟与现场实验相结合的方式,着重对计算域边界壁面和圆柱壁面对空气单相流中对流涡流的成形运动及其特征分析、两相流中对流涡流在圆柱周围的夹沙运动模拟及其特性分析、两相流中对流涡流的夹沙率以及边界壁湍流对沙粒干沉积效率展开分析研究。     

Discrete particle modeling of granular Rayleigh–Taylor instability

The gravitational air–grain Rayleigh–Taylor (RT) flow instability in a Hele-Shaw cell was studied using a parallel three-dimensional discrete particle model (DPM). The onset of flow instability and the development of fingering flow structures were well captured by the model. Power spectra analysis of solid volume fraction field indicated the non-linear coarsening process of the fingering flow structures. The sensitivity of the flow patterns to the initial porosity, the Atwood number, and the ratio of particle size to the Hele-Shaw cell width was also demonstrated. The excellent agreement of DPM simulation results with the reported experimental observations proved the robustness and reliability of the numerical approach to model complex multiphase flows such as granular RT instability.     

Simulating gas–liquid multiphase flow using meshless Lagrangian method

A multiphase flow model has been established based on a moving particle semi‐implicit method. A surface tension model is introduced to the particle method to improve the numerical accuracy and stability. Several computational techniques are employed to simplify the numerical procedure and further improve the accuracy. A particle fraction multiphase flow model is developed and verified by a two‐phase Poiseuille flow. The multiphase surface tension model is discussed in detail, and an ethanol drop case is introduced to verify the surface tension model. A simple dam break is simulated to demonstrate the improvements with various modifications in particle method along with a new boundary condition. Finally, we simulate several bubble rising cases to show the capacity of this new model in simulating gas–liquid multiphase flow with large density ratio difference between phases. The comparisons among numerical results of mesh‐based model, experimental data, and the present model, indicate that the new multiphase particle method is acceptable in gas–liquid multiphase fluids simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

A Bayesian model selection analysis of equilibrium and nonequilibrium models for multiphase flow in porous media

The classical constitutive relations for multiphase flows in porous media assume instantaneous and local phase-equilibrium. Several alternative nonequilibrium/dynamic constitutive relations have been proposed in the literature including the works of Barenblatt, and Hassanizadeh and Gray. This work applies a Bayesian model selection framework in order to examine the relative efficacy of these three models to represent experimental observations. Experimental observations of multiphase displacement processes in natural porous media are often sparse and indirect, leading to considerable uncertainty in control conditions. Data from three core-scale drainage experiments are considered. Gaussian prior probability models are assumed for key multiphase flow parameters and measurements. Accurate numerical simulation approximations using the three constitutive relation models are implemented. The model selection analysis comprises a data-assimilation stage that calibrates the assumed model to the data while quantifying uncertainty. The second stage is the computation of the maximum likelihood estimate and its application to compute the Bayesian Information Criterion. It is observed that Barenblatt’s nonequilibrium model is more likely to match data from unstable displacements that involve higher viscosity ratios of the invading phase to the resident fluid. At the lowest viscosity ratio, there is no delineation between the goodness of fit obtained using the classical model and the model proposed by Hassanizadeh and Gray, and both outperform Barenblatt’s nonequilibrium model.     

Measurement of very small liquid flows

A measuring principle for the flow rate of liquid follows consists in the determination of the volume change of a liquid in a tank in relation to unit of time. The development and the realization of three measurement systems based on this principle are presented in this paper. The devices can measure liquid flows below 0.2 L/h. One flow meter uses an air bubble in the form of a stopper as tracer. A special design keeps the bubble in the measuring tube; it does not have to be replaced. Another flow meter measures the volume changes by determining the pressure at the bottom of a vertical tube. To achieve a continuous operation, a differential design with two corresponding tubes was realized. The third flow meter measures the mass of a drop at the end of a horizontal silicone tube working as a bending beam. The liquid flows through the tube and is forced to form drops at its end. Owing to their design, each of the three devices has distinctive characteristics. A theory of measurement systems that facilitates synthesis and analysis of measuring devices serves as the basis for the development of the flow meters.     

水气两相流中稀疏气泡流动速度场的数字图像测量初探

由空压机提供的气体通过—排微小直径的喷嘴进入静止水体，形成水气两相流流场。在单相PIV和PTV技术的基础上，研究稀疏气液两相流情况下气泡的速度场分布。PIV算法采用快速傅立叶互相关分析法，而PTV算法需要获得每幅图像中每个气泡的形心，根据连续图像中的粒子对，计算速度。用PIV和PTV两种算法处理求出气泡的速度并对两种方法进行比较，其最终研究成果可应用于流体及多相流的流量测技术，提高我们进行低密度气液两相流相关研究的测量水平。同时为水气两相流的数值分析和理论研究提供流场测试的数据。     

微流控器件中的多相流动

微流控技术及微流控器件是近年来发展迅速的多学科交叉研究领域.相比于传统方法, 微流控技术能够实现对微量多相流体的精准操控, 可应用于化学分析、先进材料合成、蛋白质结晶、单细胞培育及检测、信息处理等领域. 该文回顾微流控器件中的多相流动现象, 概述其所涉及的流体力学机理,阐述实现多相微流控的各种方法, 并分析多相微流控技术的应用现状及面临的挑战, 最后总结针对多相微流动问题的数值模拟方法和实验测量技术, 展望多相微流控器件的研究方向及应用前景.      

Influence of geometry on separation efficiency in a hydrocyclone

A numerical study of the gas–liquid–solid multiphase flow in hydrocyclones is presented. Three models of turbulence, the RNG k–ε model, the Reynolds stress model and Large eddy simulation with the volume of fluid model (VOF) multiphase model for simulating air core are compared in order to predict axial and tangential velocity distributions. This presentation is mainly aimed at identifying an optimal method, used to study effective parameters, based on which, eventually, effect of inlet flow rate variations and body dimension variations such as underflow diameter, overflow diameter and cone angle on the separation performance and pressure drop are investigated. The results are then used in the simulation of particle flow described by the stochastic Lagrangian model. The results suggest that the predicted size classifications are approximately similar to those of RSM and LES methods. Predictions using the RSM model are found in agreement with experimental results with a marginal error within the range of 4 to 8%. Proceeding model validation, parametric studies have been carried out concerning the influence of velocity inlet, particle size and body dimension such as underflow and overflow diameter and cone angle. The predictions demonstrate that the flow fields in the hydrocyclones with different sizes and lengths are different, which yields different performances.     

The analysis of two-dimensional two-phase flow in horizontal heated tube bundles using drift flux model

This paper presents the experimental study and numerical simulation of two-dimensional two-phase flow in horizontal heated tube bundles. In the experiments, two advanced measuring systems with a single-fibre optical probe and a tri-fibre-optical-probe were developed to measure respectively the local void fraction and vapor bubble velocities among the heated tube bundles. In accordance with the internal circulation characteristics of two-phase flow in the tube bundles, a mathematical model of two-dimensional two-phase low Reynolds number turbulent flow based on the modified drift flux model and the numerical simulation method to analyze the two-phase flow structures have been developed. The modified drift flux model in which both the acceleration by gravity and the acceleration of the average volumetric flow are taken into account for the calculation of the drift velocities enables its application to the analysis of multi-dimensional two-phase flow. In the analysis the distributions of the vapor-phase velocity, liquid-phase velocity and void fraction were numerically obtained by using the modified drift flux model and conventional drift flux model respectively and compared with the experimental results. The numerical analysis results by using the modified drift flux model agree reasonably well with the experimental investigation. It is confirmed that the modified drift flux model has the capability of correctly simulating the two-dimensional two-phase flow. Received on 3 September 1998     

Analysis and application of solid-gas flow inside a venturi with particle interaction

A two-phase one-dimensional solid—gas flow model which describes the flow inside a variable area duct has been developed. The model includes multiparticle equations and considers particle—particle interaction. Predictions have been compared with experimental data for the pressure drop and pressure recovery through two venturis at different solid to gas loading ratios. Accurate knowledge of the particle-size distribution is extremely important for good comparison. No meaningful single particle-size diameter is found that yields predictions to agree with the measurements. The venturi may be used as a measuring device for solid—gas flow rates for systems if the particle-size distribution is accurately known. However, the venturi-diffuser section loses its effectiveness in recovering the pressure as the solid loading increases.     

Numerical simulation of streamwise fluidelastic instability of tube bundles subjected to two-phase cross flow

This work aims to develop and validate a numerical model to simulate the flow-structure interaction in tube bundles subjected to two-phase flow. The model utilizes a mixture multiphase module in which a drift flux formulation is used to account for the slip between the phases. Two methods of numerical flow-structure interaction are used to predict the onset of fluidelastic instability (FEI) in the streamwise direction for a two-phase air–water flow mixture in parallel triangular tube bundles. These models are the hybrid analytical-flow field model and the direct numerical flow/structure coupling model. This work investigates the effects of void fractions in the range of 20% to 80% and several pitch-to-diameter ratios (P/D) in the range of 1.3 to 1.7. The results of the fluidelastic forces and the stability threshold are validated against the experimental data available in the literature and show an excellent agreement. The streamwise FEI threshold shows a significant dependency on the pitch-to-diameter ratio while the void fraction exhibits a lesser effect. Generally, the stability threshold increases as the pitch-to-diameter ratio increases. The model that was developed paves the way for devising of more reliable prediction tools for FEI in steam generators.     

A coupled model for multiphase fluid flow and sedimentation deformation in oil reservoir and its numerical simulation

A mathematical model for coupled multiphase fluid flow and sedimentation deformation is developed based on fluid-solid interaction mechanism. A finite difference-finite element numerical approach is presented. The results of an example show that the fluid-solid coupled effect has great influence on multiphase fluid flow and reservoir recovery performances, and the coupled model has practical significance for oilfield development.     

Numerical study of elbow erosion due to sand particles under annular flow considering liquid entrainment

Sand particle erosion is always a challenge in natural gas production. In particular, the erosion in gas–liquid–solid annular flow is more complicated. In this study, a three-phase flow numerical model that couples the volume of fluid multiphase flow model and the discrete phase model was developed for prediction of erosion in annular flow. The ability of the numerical model to simulate the gas–liquid annular flow is validated through comparison with the experimental data. On the basis of the above numerical model, the phase distribution in the pipe was analyzed. The liquid entrainment behavior was reasonably simulated through the numerical model, which guaranteed the accuracy of predicting the particle erosion. Additionally, four erosion prediction models were used for the erosion calculation, among them, the Zhang et al. erosion model predicted the realistic results. Through the analysis of the particle trajectory and the particle impact behavior on the elbow, the cushion effect of the liquid film on the particles and the erosion morphology generation at the elbow were revealed.     

Construction of three-dimensional flow structure out of two-dimensional steady flow field velocity measurements

 Two-dimensional particle image velocimetry (PIV) is used to obtain a set of parallel vector maps in spanwise direction over the delta wing configuration ELAC. The out-of-plane velocity component is then constructed by application of continuity equation. This yields the whole three-dimensional separated flow field over the leeward side of the model. The spatial resolution of the measurements enables a detailed examination of the three-dimensional flow structure. The growth and the helical structure of primary vortex as well as smaller flow structures caused by secondary separation can be observed. Accuracy of the constructed velocity component is estimated with help of a numerically obtained three-dimensional dataset of the flow field around this configuration. The reconstruction procedure was applied to this data set taking the experimental uncertainty and the grid spacing of the PIV measurements into consideration. A comparison of reconstructed out-of-plane component and data of the numerical solution of Navier–Stokes equations results in a promising low error. A statistical analysis of different procedures allows interpretation of reconstruction capabilities. Received: 15 April 1998 / Accepted: 15 September 1998     

Benchmark PIV database for the validation of CFD simulations in a transitional cavity flow

We present an experimental benchmark database for the transitional cavity flow. The database is obtained by planar Particle Image Velocimetry measurements at the median plane of the cavity model, for Reynolds numbers between 6300 and 19,000 based on the cavity height. A detailed uncertainty analysis of the experimental results is performed via the correlation statistics method for PIV uncertainty quantification and linear error propagation.The experimental results are compared to two-dimensional Reynolds-Averaged Navier Stokes (RANS) numerical simulations with different turbulence models. It is shown that, when the standard k-ω turbulence model is employed, the discrepancy between numerical simulations and experimental results exceeds the uncertainty of the latter. Conversely, RANS simulations with the SST k-ω turbulence model agree well with the experimental data in terms of time-averaged flow properties; however, the turbulent kinetic energy results present significant discrepancies at all considered Reynolds numbers. The data presented in this paper is made available for open-access download via the 4TU.ResearchData repository with DOI: https://doi.org/10.4121/14061233.     

弹塑性变形油藏中多相渗流的数值模拟

基于流固耦合力学理论,建立了弹性变形油藏中多相渗流的数学模型,该模型考虑了渗流与变形的耦合作用,以及注采交变载荷作下油藏多孔介质的弹性变形特征,给出了耦合数值模拟方法和算例。     

Investigation of pressure drop in horizontal pipes with different diameters

The pressure drop has a significant importance in multiphase flow systems. In this paper, the effect of the volumetric quality and mixture velocity on pressure drop of gas-liquid flow in horizontal pipes of different diameters are investigated experimentally and numerically. The experimental facility was designed and built to measure the pressure drop in three pipes of 12.70, 19.05 and 25.40 mm. The water and air flow rates can be adjusted to control the mixture velocity and void fraction. The measurements are performed under constant water flow rate (CWF) by adding air to the water and constant total flow rate (CTF) in which the flow rates for both phases are changed to give same CTF. The drift-flux model is also used to predict the pressure drop for same cases. The present data is also compared with a number of empirical models from the literature. The results show that: i) the pressure drop increases with higher volumetric qualities for the cases of constant water flow rate but decreases for higher volumetric qualities of constant total flow rate due to the change in flow pattern. ii) The drift-flux model and homogenous model are the most suitable models for pressure drop prediction.