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 and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump

Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.

Numerical Study of Solid-Liquid Two-Phase Flow in StirredTanks with Rushton Impeller(Ⅱ) Prediction of Critical Impeller Speed

Three-dimensional solid-liquid flow is mathematically formulated by means of the 'two-fluid' approach and the two-phase k-ε-AP turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved 'inner-outer'iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of the simulation with experimental data on the mean velocities and the turbulence quantities of the solid phase is made and quite reasonable agreement is obtained except for the impeller swept volume. The counterpart of liquid phase is presented as well.The predicted solid concentration distribution for three experimental cases with the average solid concentration up to 20% is also found to agree reasonably with the experimental results published in the literature.

Numerical Study of Solid-Liquid Two-Phase Flow in Stirred Tanks with Rushton Impeller (Ⅰ) Formulation and Simulation of Flow Field

The critical impeller speed, N_(JS), for complete suspension of solidparticles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standardRushton impeller is predicted using the computational procedure proposed in Part Ⅰ. Three differentnumerical criteria are tested for determining the critical solid suspension. The predicted N_(JS)is compared with those obtained from several empirical correlations. It is suggested the mostreasonable criterion for determining the complete suspension of solid particles is the positive signof simulated axial velocity of solid phase at the location where the solid particles are mostdifficult to be suspended.

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）.

A transient production prediction method for tight condensate gas wells with multiphase flow

Considering the phase behaviors in condensate gas reservoirs and the oil-gas two-phase linear flow and boundary-dominated flow in the reservoir,a method for predicting the relationship between oil saturation and pressure in the full-path of tight condensate gas well is proposed,and a model for predicting the transient production from tight condensate gas wells with multiphase flow is established.The research indicates that the relationship curve between condensate oil saturation and pressure is crucial for calculating the pseudo-pressure.In the early stage of production or in areas far from the wellbore with high reservoir pressure,the condensate oil saturation can be calculated using early-stage production dynamic data through material balance models.In the late stage of production or in areas close to the wellbore with low reservoir pressure,the condensate oil saturation can be calculated using the data of constant composition expansion test.In the middle stages of production or when reservoir pressure is at an intermediate level,the data obtained from the previous two stages can be interpolated to form a complete full-path relationship curve between oil saturation and pressure.Through simulation and field application,the new method is verified to be reliable and practical.It can be applied for prediction of middle-stage and late-stage production of tight condensate gas wells and assessment of single-well recoverable reserves.

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.

Thermophoresis effects on gas-particle phases flow behaviors in entrained flow coal gasifier using Eulerian model

A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles are thoroughly investigated. The thermophoresis is due to the gas temperature gradient caused by absorpted heat of coal char gasification. This work, firstly, calculates the gas temperature gradient and thermophoretic force at1100 °C,1200 °C,1300 °C and 1400 °C wall temperatures. Then, the changes of particle volume fraction and velocity in the gasifier are studied in the simulation with thermophoresis or not. The results indicate that considering the particle thermophoresis has some effects on the calculation of particle volume fraction in the gasifier, especially at wall temperature of 1400 °C, and the maximum particle volume fraction variance ratio reaches up to 1.38% on wall surface of the gasifier. These effects are mainly caused by large gas temperature gradient along the radial direction of the gasifier. For the particle velocity, the changes are small but can be observable along radial direction of the gasifier, which has good agreement with the distributions of radial gas temperature gradient and thermophoretic force. These changes above may have certain effects on gasification reaction rates in this Eulerian model. So the change of gasification reaction rates in the simulation with thermophoresis or not is studied finally.

IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.

Phase-Based Optical Flow Method with Optimized Parameter Settings for Enhancing Displacement Measurement Adaptability

To enhance the applicability and measurement accuracy of phase-based optical flow method using complex steerable pyramids in structural displacement measurement engineering applications, an improved method of optimizing parameter settings is proposed. The optimized parameters include the best measurement points of the Region of Interest (ROI) and the levels of pyramid filters. Additionally, to address the issue of updating reference frames in practical applications due to the difficulty in estimating the maximum effective measurement value, a mechanism for dynamically updating reference frames is introduced. Experimental results demonstrate that compared to representative image gradient-based displacement measurement methods, the proposed method exhibits higher measurement accuracy in engineering applications. This provides reliable data support for structural damage identification research based on vibration signals and is expected to broaden the engineering application prospects for structural health monitoring.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

Effect of forced lamina flow on microsegregation simulated by phase field method quantitatively

The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.

INTERNET TRAFFIC DATA FLOW FORECAST BY RBF NEURAL NETWORK BASED ON PHASE SPACE RECONSTRUCTION

Characteristics of the Internet traffic data flow are studied based on the chaos theory. A phase space that is isometric with the network dynamic system is reconstructed by using the single variable time series of a network flow. Some parameters, such as the correlative dimension and the Lyapunov exponent are calculated, and the chaos characteristic is proved to exist in Internet traffic data flows. A neural network model is construct- ed based on radial basis function （RBF） to forecast actual Internet traffic data flow. Simulation results show that, compared with other forecasts of the forward-feedback neural network, the forecast of the RBF neural network based on the chaos theory has faster learning capacity and higher forecasting accuracy.

Review of gas-solid two phase flow rate-concentration detection technology

The indirect detection method basic principle of rate and concentration,application range and research results on gassolid two phase flow were discussed.The present development situation and the existing problems of rate and concentration detection technology were analyzed and summarized.Emphatically analyzed the existing problems in the industrial application and research status of electrostatic method in measuring phase concentration.Design criterion of electrostatic phase concentration sensor is given,the superiority and wide industrial application prospect of the sensor used for phase concentration measurement are clarified.

LOCAL NONLINEAR CHARACTERISTICS OF GAS LIQUID SOLID THREE PHASE SELF ASPIRATED REVERSED FLOW JET LOOP REACTOR

Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressure fluctuations obtained from a gas liquid solid three phase self aspirated reversed flow jet loop reactor,respectively.The results indicate that the local fractal dimensions and the local largest Lyapunov exponents in both the jet region and the tubular region inside the draft tube increase with the increase in the jet liquid flowrates and the solid loadings,the local fractal dimension profiles are similar to those of the largest Lyapunov exponent,the local largest lyapunov exponents are positive for all cases,and the flow behavior of such a reactor is chaotic.The local nonlinear characteristic parameters such as the local fractal dimension and the local largest Lyapunov exponent could be applied to further study the flow properties such as the flow regime transitions and flow structures of this three phase jet loop reactor.

Gas Condensate Two Phase Flow Performance in Porous Media Considering Capillary Number and Non-Darcy Effects

Retrograde condensation frequently occurs during the development of gas condensate reservoirs. The loss of productivity is often observed due to the reduced relative permeability to gas as condensate accumulates near the well bore region. How to describe the condensate blockage effect exactly has been a continuous research topic. However, up to now, the present methods usually over-estimate or underestimate the productivity reduction due to an incorrect understanding of the mechanism of flow in porous medium, which inevitably results in an inaccurate prediction of production performance. It has been found in recent numerous theoretical and experimental studies that capillary number and non-Darcy flow have significant influence on relative permeability in regions near the well bore. The two effects impose opposite impacts on production performance, thus leading to gas condensate flow showing characteristics different from general understanding. It is significant for prediction of performance in gas condensate wells to understand the two effects exactly. The aim of the paper is to describe and analyze the flow dynamics in porous media accurately during the production of gas condensate reservoirs. Based on the description of three-zone flow mechanism, capillary number and non-Darcy effect are incorporated in the analysis of relative permeability, making it possible to describe the effect of condensate blockage. The effect of capillary number and inertial flow on gas and condensate relative permeability is analyzed in detail. Novel Inflow Performance Relation (IPR) models considering high velocity effects are formulated and the contrast analysis of different IPR models is conducted. The result shows that the proposed method can help predict the production performance and productivity more accurately than conventional methods.

Annular multiphase flow behavior during deep water drilling and the effect of hydrate phase transition

It is very important to understand the annular multiphase flow behavior and the effect of hydrate phase transition during deep water drilling. The basic hydrodynamic models, including mass, momentum, and energy conservation equations, were established for annular flow with gas hydrate phase transition during gas kick. The behavior of annular multiphase flow with hydrate phase transition was investigated by analyzing the hydrate-forming region, the gas fraction in the fluid flowing in the annulus, pit gain, bottom hole pressure, and shut-in casing pressure. The simulation shows that it is possible to move the hydrate-forming region away from sea floor by increasing the circulation rate. The decrease in gas volume fraction in the annulus due to hydrate formation reduces pit gain, which can delay the detection of well kick and increase the risk of hydrate plugging in lines. Caution is needed when a well is monitored for gas kick at a relatively low gas production rate, because the possibility of hydrate presence is much greater than that at a relatively high production rate. The shut-in casing pressure cannot reflect the gas kick due to hydrate formation, which increases with time.

NUMERICAL SIMULATION OF CHARGED GAS-LIQUID TWO PHASE JET FLOW IN ELECTROSTATIC SPRAYING

Multi-fluid k-e-kp, two phase turbulence model is used to simulate charged gas-liquid two phase coaxial jet, which is the transorting flow field in electrostatic spraying. Compared with the results of experiment, charged gas-liquid two-phase turbulence can be well predicted by this model.