Computational Analysis of Centrifugal Pump Delivering Solid-liquid Two-phase Flow during Startup Period

The transient behavior of centrifugal pumps during transient operating periods, such as startup and stopping, has drawn more and more attention recently because of urgent needs in engineering. Up to now, almost all the existing studies on this behavior are limited to using water as working fluid. The study on the transient behavior related to solid-liquid two-phase flow has not been seen yet. In order to explore the transient characteristics of a high specific-speed centrifugal pump during startup period delivering the pure water and solid-liquid two-phase flow, the transient flows inside the pump are numerically simulated using the dynamic mesh method. The variable rotational speed and flow rate with time obtained from experiment are best fitted as the function of time, and are written into computational fluid dynamics （CFD） code-FLUENT by using a user defined function. The predicted heads are compared with experimental results when pumping pure water. The results show that the difference in the transient performance during startup period is very obvious between water and solid-liquid two-phase flow during the later stage of startup process. Moreover, the time for the solid-liquid two-phase flow to achieve a stable condition is longer than that for water. The solid-liquid two-phase flow results in a higher impeller shaft power, a larger dynamic reaction force, a more violent fluctuation in pressure and a reduced stable pressure rise comparing with water. The research may be useful to tmderstanding on the transient behavior of a centrifugal pump under a solid-liquid two-phase flow during startup period.

Numerical simulation of predicting and reducing solid particle erosion of solid-liquid two-phase flow in a choke

Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid particle movement as well as particle erosion characteristics of the solid-liquid two-phase flow in a choke. The corresponding erosion reduction approach by setting ribs on the inner wall of the choke was advanced. This mathematical model includes three parts： the flow field simulation of the continuous carrier fluid by an Eulerian approach, the particle interaction simulation using the discrete particle hard sphere model by a Lagrangian approach and calculation of erosion rate using semiempirical correlations. The results show that particles accumulated in a narrow region from inlet to outlet of the choke and the dominating factor affecting particle motion is the fluid drag force. As a result, the optimization of rib geometrical parameters indicates that good anti-erosion performance can be achieved by four ribs, each of them with a height （H） of 3 mm and a width （B） of 5 mm equaling the interval between ribs （L）.

Liquid holdup measurement with double helix capacitance sensor in horizontal oil-water two-phase flow pipes

This paper presents the characteristics of a double helix capacitance sensor for measurement of the liquid holdup in horizontal oil–water two-phase flow. The finite element method is used to calculate the sensitivity field of the sensor in a pipe with 20 mm inner diameter and the effect of sensor geometry on the distribution of sensitivity field is presented. Then, a horizontal oil–water two-phase flow experiment is carried out to measure the response of the double helix capacitance sensor, in which a novel method is proposed to calibrate the liquid holdup based on three pairs of parallel-wire capacitance probes. The performance of the sensor is analyzed in terms of the flow structures detected by mini-conductance array probes.

Parametric study of gas−liquid two-phase flow field in horizontal stirred tank

Based on Fluent software,the gas−liquid two-phase flow in the horizontal stirred tank was simulated with SST k−ωturbulence model,Eulerian−Eulerian two-fluid model,and multi-reference flame method.The mixing process in the tank was calculated by tracer method.The results show that increasing the rotating speed or gas flow is conducive to a more uniform distribution of the gas phase and accelerates the mixing of the liquid phase.When the rotating speed exceeds 93 r/min,the relative power demand remains basically constant.The change in the inclination angle of the upper impeller has minimal effect on the gas phase distribution.When the inclination angle is 50°,the relative power demand reaches the maximum.An appropriate increase in the impeller distance from the bottom improves the gas holdup and gas phase distribution but increases the liquid phase mixing time.

Pressure Drop of Liquid–Solid Two-Phase Flow in the Vertical Tube Bundle of a Cold-Model Circulating Fluidized Bed Evaporator

A cold-model vertical multi-tube circulating fluidized bed evaporator was designed and built to conduct a visualization study on the pressure drop of a liquid–solid two-phase flow and the corresponding particle distribution.Water and polyformaldehyde particle(POM)were used as the liquid and solid phases,respectively.The effects of operating parameters such as the amount of added particles,circulating flow rate,and particle size were systematically investigated.The results showed that the addition of the particles increased the pressure drop in the vertical tube bundle.The maximum pressure drop ratios were 18.65%,21.15%,18.00%,and 21.15%within the experimental range of the amount of added particles for POM1,POM2,POM3,and POM4,respectively.The pressure drop ratio basically decreased with the increase in the circulating flow rate but fluctuated with the increase in the amount of added particles and particle size.The difference in pressure drop ratio decreased with the increase in the circulating flow rate.As the amount of added particles increased,the difference in pressure drop ratio fluctuated at low circulating flow rate but basically decreased at high circulating flow rate.The pressure drop in the vertical tube bundle accounted for about 70%of the overall pressure drop in the up-flow heating chamber and was the main component of the overall pressure within the experimental range.Three-dimensional phase diagrams were established to display the variation ranges of the pressure drop and pressure drop ratio in the vertical tube bundle corresponding to the operating parameters.The research results can provide some reference for the application of the fluidized bed heat transfer technology in the industry.

Mechanism from particle compaction to fluidization of liquid–solid two-phase flow

A new model of particle yield stress including cohesive strength is proposed,which considers the friction and cohesive strength between particles.A calculation method for the fluidization process of liquid–solid two-phase flow in compact packing state is given,and the simulation and experimental studies of fluidization process are carried out by taking the sand–water two-phase flow in the jet dredging system as an example,and the calculation method is verified.

Experimental analysis on adjusting performance of vapor-liquid two-phase flow controller

The vapor-liquid self-adjusting controller is an innovative automatic regulating valve.In order to ensure adjusted objects run safely and economically,the controller automatically adjusts the liquid flux to keep liquid level at a required level according to physical properties of vapor-liquid two-phase fluid.The adjusting mechanics,the controller’s performance and influencing factors of its stability have been analyzed in this paper.The theoretical analysis and successful applications have demonstrated this controller can keep the liquid level steady with good performance.The actual application in industry has shown that the controller can satisfactorily meet the requirement of industrial production and has wide application areas.

SIMULATION OF GAS AND LIQUID TWO-PHASE FLOW THROUGH THE BLAST FURNACE DROPPING ZONE

A three-dimensional mathematical model,based on differential balances of mass and momentum,hasbeen developed to describe the two-phase flow of gas and liquid through the dropping zone of the blast fur-nace.Agreement between observed and calculated values verifies the validity of this model.On the basis of this model,various parameters for the surrounding of the dry zone of Blast FurnaceNo.I-BF of the Beijing Iron and Steel Company have been computed,from which a diagram for demar-cation of fluidization of coke and flooding of slag has been proposed.

Experimental Investigation of Vibration Response of A Free-Hanging Flexible Riser Induced by Internal Gas-Liquid Slug Flow

The vibration response of a free-hanging flexible riser induced by internal gas-liquid slug flow was studied experimentally in a small-diameter tube model based on Froude number criterion. The flow regime in a curved riser model and the response displacements of the riser were simultaneously recorded by high speed cameras. The gas superficial velocity ranges from 0.1 m/s to 0.6 m/s while the liquid superficial velocity from 0.06 m/s to 0.3 m/s.Severe slugging type 3, unstable oscillation flow and relatively stable slug flow were observed in the considered flow rates. Severe slugging type 3 characterized by premature gas penetration occurs at relatively low flow rates. Both the cycle time and slug length become shorter as the gas flow rate increases. The pressure at the riser base undergoes a longer period and larger amplitude of fluctuation as compared with the other two flow regimes. Additionally, severe slugging leads to the most vigorous in-plane vibration. However, the responses in the vertical and horizontal directions are not synchronized. The vertical vibration is dominated by the second mode while the horizontal vibration is dominated by the first mode. Similar to the vortex-induced vibration, three branches are identified as initial branch, build-up branch and descending branch for the response versus the mixture velocity of gas-liquid flow.

Development of Liquid Slug Length in Gas-Liquid Slug Flow along Horizontal Pipeline: Experiment and Simulation

The liquid slug length distribution is crucial for designing the downstream processing system with mul-tiphase pipeline. Experiments were conducted in a 133m long horizontal test loop. The measurements were per-formed by conductivity probes to determine the liquid slug length distribution. The data covered both the slug and plug flow regimes. From experimental results, the mean liquid slug lengths were relatively insensitive to gas and liquid flow rates in the higher mixture velocity range. But in the lower mixture velocity range, the mean liquid slug length decreased and then increased with mixture velocity. It shows that the development length of slug flow was longer than x/D=1157. A slug tracking model was adapted to study the evolution of liquid slug length distribution in a horizontal pipeline. In the present model, the wake effect of elongated bubble and the pressure drop due to accel-eration are taken into account and random slug lengths are introduced at the entrance. The results of the model are compared with the measured slug length distributions of slug flow regime. It shows that the predicted mean and maximum slug lengths are in agreement with the experimental data at x/D=1157 and the form of the slug length distributions is also predicted well by the model.

Application of time–frequency entropy from wake oscillation to gas–liquid flow pattern identification

Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.

RESEARCH ON METHOD TO CALCULATE VELOCITIES OF SOLID PHASE AND LIQUID PHASE IN DEBRIS FLOW

Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham＇s rheology equation of liquid phase and Bagnold＇s testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.

Investigation on Liquid Holdup in Vertical Zero Net-Liquid Flow

Zero net-liquid flow (ZNLF) is a special case of upward gas-liquid two-phase flow. It is a phenomenon observed as a gas-liquid mixture flows in a conduit but the net liquid flow rate is zero. Investigation on the liquid holdup of ZNLF is conducted in a vertical ten-meter tube with diameter of 76 mm, both for Newtonian and nonNewtonian fluids. The gas phase is air. The Newtonian fluid is water and the non-Newtonian fluids are water-based guar gel solutions. The correlations developed for predicting liquid holdup on the basis of Lockhart-Martinelli parameter are not suitable to ZNLF. A constitutive correlation for the liquid holdup of vertical ZNLF was put forward by using the mass balance. It is found that the liquid holdup in ZNLF is dependent on both the gas flow rate and the flow distribution coefficient.

Effects of tube cross-sectional shapes on flow pattern, liquid film and heat transfer of n-pentane across tube bundles

The heat transfer of hydrocarbon refrigerant across tube bundles have been widely used in refrigeration.Three-dimensional simulation model using volume of fluid(VOF) was presented to study the effects of tube shapes on flow pattern, film thickness and heat transfer of n-pentane across tube bundles, including circle, ellipse-shaped, egg-shaped and cam-shaped tube bundles. Simulation results agree well with experimental data in the literature. The liquid film thickness of sheet flow and heat transfer for different tube shapes were obtained numerically. The flow pattern transition occurs lower vapor quality for ellipse-shaped tube than other tube shapes. For sheet flow, the liquid film on circle tube and ellipseshaped tube is symmetrically distributed along the circumferential direction. However, the liquid film on egg-shaped tube at circumferential angles(θ) = 15°–60° is thicker than θ = 135°–165°. The liquid film on cam tube at θ = 15°–60° is slightly thinner than θ = 135°–165°. The liquid film thickness varies from thinner to thicker for ellipse-shaped, cam-shaped, egg-shape and circle within θ = 15°–60°. The effect of tube shape is insignificant on thin liquid film thickness. Ellipse-shaped tube has largest heat transfer coefficient for sheet flow. In practical engineering, the tube shape could be designed as ellipse to promote heat transfer.

ON EQUATION OF DISCRETE SOLID PARTICLES' MOTION IN ARBITRARY FLOW FIELD AND ITS PROPERTIES

The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached.

Liquid film dryout model for predicting critical heat flux in annular two-phase flow

Gas-liquid two-phase flow and heat transfer can be encountered in numerous fields, such as chemical engineering, refrigeration, nuclear power reactor, metallurgical industry, spaceflight. Its critical heat flux (CHF) is one of the most important factors for the system security of engineering applications. Since annular flow is the most common flow pattern in gas-liquid two-phase flow, predicting CHF of annular two-phase flow is more significant. Many studies have shown that the liquid film dryout model is successful for that prediction, and determining the following parameters will exert predominant effects on the accuracy of this model: onset of annular flow, inception criterion for droplets entrainment, entrainment fraction, droplets deposition and entrainment rates. The main theoretical results achieved on the above five parameters are reviewed; also, limitations in the existing studies and problems for further research are discussed.

Erosion Characteristics of Hydraulic Turbine Guide-Vane End Clearance in Sediment Water Flow: A Simplified Model Analysis

The effect of clearance flow on the erosion characteristics of a circular cylinder with a backward facing step in sediment-laden water flow is analyzed numerically with the mixture model and the re-normalization group (RNG) k-ε turbulence model. Thirty-six monitoring points are set up on different stream surfaces to collect information on the impact erosion under different flow conditions, where the Initial Sediment Volume Fraction (ISVF) is set to 0.05, 0.075, 0.1, 0.125, and 0.15;particle diameter is set to 0.05 mm, 0.15 mm, 0.25 mm, 0.35 mm, and 0.45 mm respectively. The distribution of particle velocity and Local Solid-Phase Volume Fraction (LSVF) along different stream surfaces are calculated, based on which the trend of erosion is qualitatively evaluated. ISVF and particle diameter play different roles on the impact erosion index parameter () on the different wetted walls. Relative wear rate of numerical estimation agrees well with the practical one under the same working condition. Numerical analysis demonstrates that guide vane with a negative curvature end surface (concave surface) can decrease erosion damage effectively, which may provide a reference for optimal design and maintenance of hydraulic turbine.

PARALLEL ADAPTIVE SIMULATION OF A PLUNGING LIQUID JET

This paper is concerned with three-dimensional numerical simulation of a plunging liquid jet. The transient processes of forming an air cavity around the jet, capturing an initially large air bubble, and the break-up of this large toroidal-shaped bubble into smaller bubbles were analyzed. A stabilized finite element method （FEM） was employed under parallel numerical simulations based on adaptive, unstructured grid and coupled with a level-set method to track the interface between air and liquid. These simulations show that the inertia of the liquid jet initially depresses the pool＇s surface, forming an annular air cavity which surrounds the liquid jet. A toroidal liquid eddy which is subse- quently formed in the liquid pool results in air cavity collapse, and in turn entrains air into the liquid pool from the unstable annular air gap region around the liquid jet.

RESEARCH ON ABRASION OF DEBRIS FLOW TO HIGH-SPEED DRAINAGE STRUCTURE

As one weak topic in research of debris flow,abrasion of debris flow shortens obviously application life of control structure composed of concrete.High_speed drainage structure,one of the most effective techniques to control giant debris flow disaster,has shortened one_third application life due to abrasion by debris flow.Based on velocity calculation method founded by two_phase theory,research of abrasion mechanism of debris flow to high_speed drainage structure was made.The mechanism includes both abrasion mechanism of homogeneous sizing and shearing mechanism of particle of debris flow to high_speed drainage trough structure.Further abrasion equations of both sizing and particle were established by Newton movement theory of debris flow.And abrasion amount formula of the high_speed drainage trough structure is set up by dimensional analysis.Amount to calculating in the formula is consistent with testing data in_situ,which is valuable in design of high_speed drainage structure.

Interaction between compressibility and particulate suspension on peristaltically driven flow in planar channel

The peristaltic pumping of a viscous compressible liquid mixed with rigid spherical particles of the same size in a channel is theoretically investigated. The momentum equations for the compressible flow are solved with a perturbation analysis. The analysis is carried out by duly accounting for the nonlinear convective acceleration terms for the fluid part on the wavy wall. The zeroth-order terms yield the Poiseuille flow, and the first-order terms give the Orr-Sommerfeld equation. The explicit expression for the net axial velocity is derived. The effects of the embedded parameters on the axial fluid velocity are studied through different engineering applications. The features of the flow characteristics are analyzed and discussed in detail. The obtained results are evaluated for various parameters associated with the blood flow in the blood vessels with diameters less than 5 500 μm, whereas the particle diameter has been taken to be 8 μm. This study provides a scope to evaluate the effect of the theory of two-phase flow characteristics with compressible fluid problems, and is helpful for understanding the role of engineering applications of pumping solid-fluid mixture by peristaltically driven motion.