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.     

Measurement of velocity profiles in multiphase flow using a multi-electrode electromagnetic flow meter

This paper describes an electromagnetic flow meter for velocity profile measurement in single phase and multiphase flows with non-uniform axial velocity profiles. A Helmholtz coil is used to produce a near-uniform magnetic field orthogonal to both the flow direction and the plane of an electrode array mounted on the internal surface of a non-conducting pipe wall. Induced voltages acquired from the electrode array are related to the flow velocity distribution via variables known as ‘weight values’ which are calculated using finite element software. Matrix inversion is used to calculate the velocity distribution in the flow cross section from the induced voltages measured at the electrode array. This paper presents simulations and experimental results including, firstly the effects of the velocity profile on the electrical potential distribution, secondly the induced voltage distribution at the electrode pair locations, and thirdly the reconstructed velocity profile calculated using the weight values and the matrix inversion method mentioned above. The flow pipe cross-section is divided into a number of pixels and, in the simulations, the mean flow velocity in each of the pixels in single phase flow is calculated from the measured induced voltages. Reference velocity profiles that have been investigated in the simulations include a uniform velocity profile and a linear velocity profile. The results show good agreement between the reconstructed and reference velocity profiles. Experimental results are also presented for the reconstructed velocity profile of the continuous water phase in an inclined solids-in-water multiphase flow for which the axial water velocity distribution is highly non-uniform. The results presented in this paper are most relevant to flows in which variations in the axial flow velocity occur principally in a single direction.     

Effect of wall roughness changes on ultrasonic gas flowmeters

A theoretical flow model has been developed to describe accurately a fully developed velocity profile of a gas flow in pipe lines with wall roughness as parameter. The model applies the Colebrook and White skin friction correlation which has been adjusted based on experimental data from Princeton SuperPipe facilities. This has resulted in a flow profile model in line with the latest views. The model has shown a significant flow profile variation for wall roughness changes. An ultrasonic ray propagation model of a single path meter has been developed to study the influence of the mentioned flow profile variations on ultrasonic meters. The model has been applied for various cases with different Reynolds number and wall roughness. The results of the study confirm field data that ultrasonic meters are affected by wall roughness changes. To quantify the effect for multipath ultrasonic meters the flow meter algorithm and path position is required.     

高压天然气田用旋风分离器内流场的数值模拟

对高压天然气田旋风分离器的内流场进行三维稳态数值模拟。将不同压力下的旋风分离器的内部流场进行对比,结果表明,压力对旋风分离器的轴向速度和径向速度的影响很小,但是对切向速度影响较大。旋风分离器的压降随着压力的增大而增大,基本成线性关系。在高压条件下,排气管的直径和入口面积对旋风分离器内流场速度的影响是比较有规律的。     

A novel approach to multi-path ultrasonic transit time flow meter based on measurement model analysis to improve accuracy

Ultrasonic transit time flow meter (UTTFM) is commonly used in a wide range of applications. It is commonly believed amongst researchers, industrialists, and standard committee members that due to nonuniform flow velocity distribution inside the pipe (flow velocity profile) the measured flow velocity using UTTFM needs to be corrected by the flow profile. Mathematical analysis of UTTFM measured quantity shows that UTTFM measures flow correctly when flow is fully developed or laminar. However, the measurement results using flow profile correction factor produces erroneous values. The UTTFM measurement model assessment shows, when flow is not fully developed, there are unknown quantities contributed by flow velocity in the axial and diametrical direction to measurement results. These unknown quantities lead to erroneous measurement results when it is simply corrected by flow profile. Assessment of the UTTFM error model shows that using multi-path UTTFM can significantly reduce the impact of the unaccounted quantities and improve accuracy. A novel approach to UTTFM design utilizing multiple acoustic paths (using different planes and transmitting angles) is proposed to reduce potential error for UTTFM. This approach is consistent with the general measurement modeling method with incomplete information recommended by JCGM GUM-6:2020.     

Unsteady magnetohydrodynamic couette flow

The effect of a uniform transverse magnetic field on the Couette flow of an electrically conducting fluid between two parallel plates for impulsive and uniformly accelerated motion of one of the plates is discussed. The magnetic lines of force are assumed to be fixed relative to the moving plate. The Laplace transform technique has been used to obtain the expressions for the velocity field and skin friction. The effect of the magnetic field is to increase the velocity field in both cases.     

Lubricant flow in pressure pipes during wire drawing in a hydrodynamic friction mode

The process of wire drawing under hydrodynamic friction is simulated by a liquid flow whose viscosity is a linear function of pressure. Accurate analytical solutions for the velocity and pressure distribution over the clearance between the moving wire and the pressure pipe lengthwise and through depth are obtained. The pressure distribution is shown to be asymmetrical through depth and nonlinear along the channel length, the velocity profile being other than parabolic.     

Monitoring of fat crystallization process using UVP–PD technique

The dynamic response of the cocoa butter shear crystallization process to a step reduction in temperature of a two stage shear crystallizer is investigated by measuring the pulsed ultrasound Doppler based velocity profile (UVP) and pressure drop (PD) in a pipe section. In addition, the velocity of sound, attenuated amplitude of the transmitted signal and temperature are continuously recorded. The temporal variation in rheological properties such as the apparent viscosity at different shear rates and the corresponding radial position in the pipe are determined by fitting the velocity profile and pressure drop to the power law rheological model. The linear dependence of sound velocity on the solid fat content (SFC) in the cocoa butter crystal suspension previously determined using the nuclear magnetic resonance technique is used to characterize crystallization. The cocoa butter crystal suspension is found to be shear thinning, the value of the power law exponent decreasing with increase in SFC. Newly developed software is used to integrate on-line measurement of flow profiles, pressure difference, temperature, velocity of sound and the attenuated amplitude of the transmitted signal. The software also calculates velocity profiles using spectral signal analysis, determines the rheological properties, and provides a graphical user interface and tools for data visualization. It is demonstrated that the cocoa butter shear crystallization process can be monitored using the UVP–PD technique.     

旋风分离器排气管缩口半径优化的数值模拟

利用FLUENT中的RSM模型和DPM模型对不同排气管底口半径r的缩口式旋风分离器进行了内部流场的数值模拟。对结果的时均图进行分析,得到随着收缩半径r的减小,排气管入口面积在减小,轴向速度及切向速度均增加,速度的增加可使靠近中心的颗粒获得更大的离心力,因此被捕集的颗粒数增多。当半径r与排气管半径R比值为1~0.9时,分离效率提高不大,压降变化也较小,比值为0.8~0.5时,分离效率提高很多,同时能量损失也较大,在半径r逐渐减小的过程中,旋风分离器分离效率增加,压降增加。综合考虑,当r/R为0.6~0.5左右时,分离效率约为97%~98%,此时压降也较合理。     

Ion slip effect on the flow of a dusty fluid through a circular pipe

In this paper, the transient flow of a dusty viscous incompressible electrically conducting fluid through a circular pipe is studied taking the ion slip into consideration. A constant pressure gradient in the axial direction and a uniform magnetic field directed perpendicular to the flow direction are applied. The particle-phase is assumed to behave as a viscous fluid. A numerical solution for the governing equations is obtained using finite differences.     

The effect of major parameters on simulation results of gas pipelines

Predictions of the gas temperature and pressure profiles are vital to the design and operation of gas transmission lines. Available analytical methods for the calculation of these profiles are evaluated and a numerical framework for the rigorous calculation has been developed. The predictions from both the analytical and numerical procedure have been compared to field data from the Iranian Gas Trunk-lines (IGAT). These comparisons showed that all the available methods were tuned using data obtained from small to medium diameter pipes extrapolated poorly to large diameter pipelines. In order to improve the predictions for large diameter pipelines, the effect of model parameters such as soil thermal conductivity, pipe relative roughness and velocity profile correction factor has been evaluated. The results show that temperature and pressure profiles at high Reynolds number are sensitive to the Fanning friction factor; however, thermal conductivity and velocity distribution correction factor have almost no effect on the temperature and pressure profiles provided these parameters were set at an average acceptable industry value. Since the pressure profile for large diameter pipes was most sensitive to the Fanning friction factor a parameter optimization method was used to fine-tune the Fanning friction factor as a function of Reynolds number at an average accepted industry relative pipe roughness.     

Measurement of high-water-content oil-water two-phase flow by electromagnetic flowmeter and differential pressure based on phase-isolation

When the oil field has been exploited by long-term water-flooding, it will be in high water-content stage of production. However, it is a great challenge for high-water-content measurement due to oil droplets extremely dispersed in the water. In this paper, we developed a phase-isolation based method for high-water-content oil-water two-phase flow measurement. Phase-isolation was realized by axial-flow swirler to concentrate scattered and random oil droplets into the pipe center and change the inlet flow pattern into a particular annular flow before measuring. Owing to the axisymmetric velocity and phase distribution, the electromagnetic flow meter avoided the effect of random distribution of insulating phase, and then had a good measurement performance for total volume flow rate. Furthermore, we respectively studied using axial pressure drop, radial pressure drop and the ratio of the two pressure drops to measure water content. The results showed that the ratio of the two pressure drops not only improves the resolution of oil and water, but also effectively reduces the impact of error transfer. In the dual-parameter measurement experiment, the relative errors of total volume flow rate and water content were almost within ±5%.     

An investigation into the performance and diagnostics from different chordal integration schemes in asymmetric flow

The purpose of the work is firstly to explore the proposal from a previous North Sea Flow Measurement Workshop paper that increasing the number of chordal locations above 4 yields little improvement in the performance of ultrasonic flow meters. Secondly the work examines the relationship between profile factor and symmetry on theoretical velocity profiles and how that changes with an increased number of chordal locations. Finally, the benefits of more paths for the purposes of swirl cancellation are reviewed, particularly when axial asymmetry and swirl are present concurrently.It is found that in the presence of axial asymmetry there is a significant performance improvement to be had with an increased number of chordal locations.A relationship between profile factor and error is also apparent. The interpolation polynomial and weight function are used to visualise the quadrature and explain the correlation. The theory that more chordal locations will improve the correlation between error and profile factor is investigated, however initial results suggest this is not true.The theory behind swirl cancellation is explained and the velocity profile diagnostics of common designs in the presence of swirl and axial asymmetry are shown. Examples of how the user can be fooled into thinking all is well in the presence of both axial asymmetry and swirl are also shown. The sensitivity of some designs to swirl is also examined.The modelling suggests that in cases where swirl and axial asymmetry are present together and non-axial velocity components are not removed by swirl cancellation or flow conditioners, a change in traditional velocity profile diagnostics cannot be used to indicate the magnitude of the error.     

Uncertainty analysis for multiphase flow: A case study for horizontal air-water flow experiments

This work describes the procedure used to define the measurement uncertainties of horizontal two-phase air-water flow experiments conducted to determine influences due to pipe diameter on pressure gradient on such flows. These experiments were performed with 4 different pipe diameters, always using the same test section length, therefore varying the length-to-diameter (L/D) ratio. Several parameters were measured, such as volumetric/mass flow rate, pressures, temperatures and pressure drop; other parameters were calculated, such as the superficial velocities of each fluid, as well as their corresponding properties. The main parameters studied were the flow patterns for different velocity configurations and the two-phase pressure drop to be used for model improvement, thus the importance of uncertainties analysis. The sources of uncertainty were defined, detailed, systematically studied and quantified. Also, the reproducibility capacity of the experimental setups were analysed through the uncertainty analysis and proving them to be able for future similar studies. The flow maps with their uncertainties could help understand the thresholds for each defined flow pattern region, and the plots of two-phase pressure drop variation with diameter confirmed the homogeneous model as a possible approach to calculate pressure drop if the uncertainties are considered.     

Relative errors in evaluating the electromagnetic flowmeter signal using the weight function method and the finite volume method

In the signal analysis of an electromagnetic flowmeter, the weight function method (WFM) involves a numerical integration of products between the magnetic flux density vector, the weight function and the velocity profile function in two-dimensional analysis. The electromagnetic flowmeter signal can also be predicted by solving the governing flowmeter equation by the finite volume method (FVM). The present study is aimed at comparing the calculation accuracies of WFM and FVM. The test flows are fully developed laminar and turbulent flows in a straight pipe under uniformly distributed magnetic field. The calculation accuracies are also compared between different O-type grid systems. It was found that the accuracy of both methods depended strongly on the grid system. In particular, for turbulent flow whose axial velocity component changes very rapidly near the wall, the accuracy of WFM was found to depend strongly on the cell configuration near the electrodes.     

压力管道快速连接新技术

借助液压油缸的轴向运动在斜面副上产生的径向分力,使得凸台压入管子外壁面内,在凸台与凹陷面内形成足够的密封比压和连接强度,实现管道的快速连接。创建了压力管道快速连接新技术领域内的关键术语,简述了其工艺过程、技术特点、适用温度、规格尺寸和应用领域。定义了压力管道快速连接新技术机理。基于金属材料的硬度理论,建立了管接头的力学模型,通过压力试验论证了压力管道快速连接新技术的密封可靠性和连接强度的安全性。其连接机理对其他机械工程领域内的金属连接,具有启发和借鉴作用,是压力管道连接领域内的创新成果。     

Design and validation of a uniform flow microreactor

We present a design method to characterize uniform flows in a microreactor for high performance surface plasmon resonance (SPR) a general-purpose biosensor chips. The shape of the microreactor is designed based on an approximate pressure drop model. The number of micro-pillars and the slopes of the inlet and outlet linear chambers are two dominant parameters used to minimize the velocity difference in the microreactor. The flow uniformity was examined quantitatively by numerical and experimental visualization methods. A computational fluid dynamics (CFD) analysis demonstrates that the designed microreactor has a fairly uniform velocity profile in the reaction zone for a wide range of flow rates. The velocity field in the fabricated microreactor was measured using the micro-particle image velocimetry (μ-PIV) method, and the flow uniformity was confirmed experimentally. The performance of the uniform flow microreactor was verified using the fluorescence antibody technique.     

Laminar flow in the gap between two rotating parallel frictional plates in hydro-viscous drive

The velocity,pressure and temperature distributions of the flow in the gap between hydro-viscous drive friction disks are the key parameters in the design of hydro-viscous drive and angular velocity controller.In the previous works dealing with the flow in the gap between disks in hydro-viscous drive,few authors considered the effect of Coriolis force on the flow.The object of this work is to investigate the flow with consideration of the effects of centrifugal force,Coriolis force and variable viscosity.A simplified mathematical model based on steady and laminar flow is presented.An approximate solution to the simplified mathematical model is obtained by using the iteration method assuming that the fluid viscosity remains constant.Then the model considering the effect of variable viscosity is solved by means of computational fluid dynamics code FLUENT.Numerical results of the flow are obtained.It is found that radial velocity profile diverges from the ideal parabolic curve due to inertial forces and tangential velocity profile is nonlinear due to Coriolis force,and pressure has two possible solution branches.In addition,it is found that variable viscosity plays an important role on pressure profiles which are significantly different from those of fluid with constant viscosity.The experimental device designed for this work consists of two disks,and one of them is fixed.Experimental pressure and temperature of the flow within test rig are obtained.It is shown that the trend of numerical results is in agreement with that of experimental ones.The research provides a theoretical foundation for hydro-viscous drive design.     

超(超)临界疏水阀开阀水锤及管道振动

针对超(超)临界疏水阀开阀水锤及阀后管道振动问题,运用充液管道振动分析的流固耦合理论及特征线法,建立开阀水锤及管道振动的数学模型,求解得到疏水阀在不同流量特性及不同套筒层数下阀开启时水锤压力、流体流速、管道轴向内力和管道振速的时域曲线。研究结果表明:水锤压力取决于流体的流速与压力相互作用,管道内力受水锤压力影响较大,局部受管道振速影响;额定流量恒定时,线性流量特性下水锤峰值压力明显小于快开特性,流速大于等百分比特性,超(超)临界疏水阀宜选用线性流量特性;随着套筒层数增加,水锤压力峰值和管道轴向内力峰值减小,但开阀初始阶段流速波动和管道振动增加。     

Performance study based on inner flow field numerical simulation of magnetic drive pumps with different rotate speeds

Magnetic drive pump has gotten great achievement and has been widely used in some special fields.Currently,the researches on magnetic drive pump have focused on hydraulic design,bearing,axial force in China,and a new magnetic drive pump with low flow and high head have been developed overseas.However,low efficiency and large size are the common disadvantages for the magnetic drive pump.In order to study the performance of high-speed magnetic drive pump,FLUENT was used to simulate the inner flow field of magnetic drive pumps with different rotate speeds,and get velocity and pressure distributions of inner flow field.According to analysis the changes of velocity and pressure to ensure the stable operation of pump and avoid cavitation.Based on the analysis of velocity and pressure,this paper presents the pump efficiency of magnetic drive pumps with different rotated speeds by calculating the power loss in impeller and volute,hydraulic loss,volumetric loss,mechanical loss and discussing the different reasons of power loss between the magnetic drive pumps with different rotated speeds.In addition,the magnetic drive pumps were tested in a closed testing system.Pressure sensors were set in inlet and outlet of magnetic drive pumps to get the pressure and the head,while the pump efficiency could be got by calculating the power loss between the input power and the outlet power.The results of simulation and test were similar,which shows that the method of simulation is feasible.The proposed research provides the instruction to design high-speed magnetic drive pump.