Solid-liquid Flow Research Articles

Dual-modality UDV-PIV system for measurement of solid-liquid flow in sewage facilities

Population growth and global industrialization cause a dramatic increase in the amount of sewage sludge produced annually worldwide from Municipal and Industrial Wastewater treatment. The efficient measurement of sewage, which is a typical solid-liquid two-phase flow, has become an important issue that requires to be urgently addressed. In this study, an improved Ultrasonic Doppler Velocimetry (UDV) is proposed to optimize the probe design and hardware design, which reduces the influence of working frequency and echo reverberation on accuracy and improves the stability of the system. A Doppler peak extraction and superposition method is also put forward to correct the offset of Doppler peak frequency. In this paper, Particle Image Velocimetry (PIV) is used to calibrate the UDV system to modify the measurement model of ultrasonic Doppler liquid-solid two-phase flow, and dynamic experiments are carried out in a vertical steel pipe with inner diameter of 50 mm at different flow conditions. The results show that the accuracy and stability of UDV measurement system are greatly improved, with a maximum relative error of 1.49%.

Liquid–Solid Flow Characteristics in Vertical Swirling Hydraulic Transportation with Tangential Jet Inlet

In order to improve the efficiency and safety of vertical hydraulic transport systems for non-spherical particles, a new pipeline transport system with a tangential jet inlet is adopted in this study, and a modified non-spherical drag coefficient model is used to analyze the liquid–solid flow characteristics based on the CFD-DEM (Computational Fluid Dynamics-Discrete Element Method) coupling method. The focus of the study is on the influence of different tangential flow proportions in terms of the velocity distribution, the vorticity, the total pressure, the concentration and drag force of particles of various shapes. The conveying efficiency is measured according to the fluid velocity distribution and the particle concentration, and the safety of conveying is evaluated according to the flow structure and drag force of the particles. The result shows that the velocity of the swirling pipes is significantly higher than the straight pipe. With the increase of the tangential flow proportion, the swirling number and the vorticity magnitude increase, and the vortex core is broken and merged more quickly. Furthermore, the concentration gap and axial drag force gap between particles of various shapes are reduced with the effect of swirling flow, the particle concentration increases, and the particles of each component are uniformly mixed and transported.

Optimization of the centrifugal slurry pump through the splitter blades position

Optimal transfer of two-phase solid-liquid flow (slurry flow) has long been a major industrial challenge. Slurry pumps are among the most common types of centrifugal pumps used to deal with this transfer issue. The approach of improving slurry pumps and consequently increasing the efficiency of a flow transmission system requires overcoming the effects of slurry flow such as the reduction in head, efficiency, and wear. This study attempts to investigate the changes in the pump head by modifying the slip factor distribution in the impeller channel. For this purpose, the effect of splitter blades on slip factor distribution to improve the pump head was investigated using numerical simulation tools and validated based on experimental test data. Next, an optimization process was used to determine the characteristics of the splitter (i.e., length, number, and environmental position of the splitter) based on a combination of experimental design methods, surface response, and genetic algorithm. The optimization results indicate that the splitters were in a relative circumferential position of 67.2% to the suction surface of the main blade. Also, the optimal number and length of splitter blades were 6 and 62.8% of the length of the main blades, respectively. Because of adding splitter blades and the reduction in the flow passage, the best efficiency point (BEP) of the slurry pump moved toward lower flow rates. The result of splitter optimization was the increase in pump head from 29.7 m to 31.7 m and the upkeep of efficiency in the initial values.

An experimental and numerical study of slurry erosion behavior in a horizontal elbow and elbows in series

Erosion in elbows is one of the most important issues in pipeline flow assurance for the oil and gas and mining industries. In this study, slurry erosion in a horizontal elbow and elbows in series are numerically and experimentally investigated. The maximum erosion location of horizontal elbow is revealed by conducting slurry erosion painting experiment. The erosion process is then modeled by using computational fluid dynamics (CFD) techniques. The accuracy and stability of the CFD-based erosion model are carefully examined using experimental results. Using the validated numerical methods, the effects of particle concentration, geometry parameter, inlet conditions are investigated. The erosion processes under these different conditions are further analyzed by examining fluid flow development, particle trajectories and impact information. The results of this CFD study present some cautious guidelines for conducting erosion studies of liquid-solid flows and pipeline system designs.

Experimental and simulation study on mixing time and suspension quality of liquid-solid flow field in stirred reactor with draft tube

Abstract The solid-liquid flow field is established in the stirred reactor with baffles and draft tube. Mixing time and suspension quality of the flow field are studied. Based on the Eulerian multiphase flow model and RNG k−ε turbulence model, the CFD model is established for the simulation research. By comparing the experimental data of solid concentration distribution and mixing time with the simulated values, it is proved that the CFD model established can be used to study the flow field in the stirred reactor. The effects of stirring speed, liquid viscosity and solid particle size on mixing time and suspension quality are considered. With the increase of stirring speed, mixing time decreases, mixing uniformity is improved. Mixing time decreases first, then increases slightly with the increase of liquid viscosity, and the suspension quality is improved. When the solid particle size increases, mixing time increases rapidly, but the mixing uniformity becomes worse.

Testing and modeling of particle size effect on erosion of steel and cobalt-based alloys

Direct impingement (DI) erosion testing of steel and cobalt-based alloys is conducted with particles entrained in air and water. The tests are performed using 75- and 300-μm silica particles with three particle velocities and five impact angles. The mass loss results are used to develop an empirical equation that contains an explicit exponential term for the particle size effect. The erosion equation obtained from the gas jet experiments is implemented into a CFD solver with Lagrangian particle tracking for the liquid-submerged geometry. The CFD-based erosion predictions agree fairly with the experimental measurement for both particles. Strong effect has been observed for the exponential correction term in the erosion equation for liquid-solid flow cases; particularly with small particles at low impact velocities.

Modeling the interstitial fluid effect in turbulent disperse slurry flow in a vertical pipe

A numerical study was conducted to assess the performance of a Two-Fluid Model (TFM) developed for gas-solid flow in predicting liquid-solid flow, as well as a TFM specifically modified for liquid-solid flow, which considers the effect of the interstitial fluid. Both cases use the Kinetic Theory of Granular Flow (KTGF) for prediction of the solid phase flow features. Some of the physics involved in gas-solid and liquid-solid flows is intuitively different, and some model terms that can be neglected in a gas-solid formulation turn out to be important for liquid-solid flow. For instance, the much larger density and viscosity of the liquid compared to a gas suggest that the solid particle fluctuations and collisions are reduced. Three intermediate model formulations were developed to assess the relevance of the interstitial terms. The intermediate model formulations, together with the two base case models, were assessed based on their predictions for the case of fully developed, turbulent, steady flow of a liquid solid mixture in a vertical pipe. The main differences in the model formulations pertain to the transport equations for the streamwise liquid momentum, granular temperature and turbulence kinetic energy. The predictions considered such flow features as: the velocity profiles of both the liquid and solid phases, the solids volume fraction profile and budgets of the transport equations for the granular temperature and turbulence kinetic energy. The results obtained were used to identify the most significant model terms. These include modified formulations for the solids viscosity and granular temperature conductive coefficient to include the effects of the interstitial fluid. The single most important term was the model for the long-range particle fluctuations through the fluid, which played a dominant role in the balance of the turbulence kinetic energy and granular temperature transport equations. The present analysis demonstrates that this term should be reconfigured as a sink term in the granular temperature equation and a source term in the turbulence kinetic energy equation. With this modification, the numerical predictions were much closer to the experimental data, especially in terms of the solids volume fraction profile.

Numerical Modelling of Heat Transfer in Fine Dispersive Slurry Flow

Slurry flows commonly appear in the transport of minerals from a mine to the processing site or from the deep ocean to the surface level. The process of heat transfer in solid–liquid flow is especially important for the long pipeline distance. The paper is focused on the numerical modelling and simulation of heat transfer in a fine dispersive slurry, which exhibits yield stress and damping of turbulence. The Bingham rheological model and the apparent viscosity concept were applied. The physical model was formulated and then the mathematical model, which constitutes conservative equations based on the time average approach for mass, momentum, and internal energy. The slurry flow in a pipeline is turbulent and fully developed hydrodynamically and thermally. The closure problem was solved by taking into account the Boussinesque hypothesis and a suitable turbulence model, which includes the influence of the yield shear stress on the wall damping function. The objective of the paper is to develop a new correlation of the Nusselt number for turbulent flow of fine dispersive slurry that exhibits yield stress and damping of turbulence. Simulations were performed for turbulent slurry flow, for solid volume concentrations 10%, 20%, 30%, and for water. The mathematical model for heat transfer of the carrier liquid flow has been validated. The study confirmed that the slurry velocity profiles are substantially different from those of the carrier liquid and have a significant effect on the heat transfer process. The highest rate of decrease in the Nusselt number is for low solid concentrations, while for C > 10% the decrease in the Nusselt number is gradual. A new correlation for the Nusselt number is proposed, which includes the Reynolds and Prandtl numbers, the dimensionless yield shear stress, and solid concentration. The new Nusselt number is in good agreement with the numerical predictions and the highest relative error was obtained for C = 10% and Nu = 44.3 and is equal to −12%. Results of the simulations are discussed. Conclusions and recommendations for further research are formulated.

Theoretical Prediction Method for Erosion Damage of Horizontal Pipe by Suspended Particles in Liquid-Solid Flows.

In order to study the erosion of a pipe wall via a liquid–solid suspension flow, a two-phase flow model combined with an erosion forecasting model for multiparticle impact on horizontal pipe wall surfaces was established in this work on the basis of low-cycle fatigue theory. In the model establishment process, the effects of particle motion and material damage were considered, and a simplified method for predicting horizontal wall erosion was obtained. The calculated results showed that the particles impact the wall at a small angle of most liquid flow velocities, causing cutting erosion damage of the wall. The settling velocity and fluctuating velocity of the particles together determine the radial velocity of the particles, which affects the impact angle of the particles. The cutting erosion caused by the small-angle impact of the particles in the pipe is more likely to cause rapid loss of the wall material. Therefore, the pipe wall is usually evenly thinned.

Numerical simulations of liquid-solid flows with free surface by coupling IMPS and DEM

Liquid-solid two-phase flow with free surface is a significant issue in nature and engineering fields. In present study, an in-house solver MPSDEM-SJTU based on a fully Lagrangian coupled method is developed to solve the problems of liquid-solid two-phase flows. The improved moving particle semi-implicit (IMPS) method is applied for the simulation of incompressible viscous liquid flows while the discrete element method (DEM) is used to model the interaction among the solid particles. The coupling strategy is based on the local averaging technique. Multiple time-step algorithm is adopted for those two methods to balance the stability and the efficiency. The free surface detection and the solid-fluid neighbor search are modified. A simulation of multi-balls collapse is conducted to verify the DEM program of the present solver. The distributions of solid balls at different instants are in good agreement with the experimental results. Then, this solver is applied for two typical problems of two-phase flows, including the two-phase dam-break and the liquid-solid flows in a rotating cylindrical tank. The flow front, flow patterns and the shape of solid beds all agree well with experimental observations.

CFD Simulation of Solid Suspension for a Liquid–Solid Industrial Stirred Reactor

The present study examines the possibility of using an industrial stirred chemical reactor, originally employed for liquid–liquid mixtures, for operating with two-phase liquid–solid suspensions. It is critical when obtaining a high-quality chemical product that the solid phase remains suspended in the liquid phase long enough that the chemical reaction takes place. The impeller was designed for the preparation of a chemical product with a prescribed composition. The present study aims at finding, using a numerical simulation analysis, if the performance of the original impeller is suitable for obtaining a new chemical product with a different composition. The Eulerian multiphase model was employed along with the renormalization (RNG) k-ε turbulence model to simulate liquid–solid flow with a free surface in a stirred tank. A sliding-mesh approach was used to model the impeller rotation with the commercial CFD code, FLUENT. The results obtained underline that 25% to 40% of the solid phase is sedimented on the lower part of the reactor, depending on the initial conditions. It results that the impeller does not perform as needed; hence, the suspension time of the solid phase is not long enough for the chemical reaction to be properly completed.

Improving the Homogenization of the Liquid-Solid Mixture Using a Tandem of Impellers in a Baffled Industrial Reactor

The paper explores a tandem configuration of three-blade impellers in a stirred reactor. The working fluid is a liquid-solid mixture and the stirring mechanism fitted with the two impellers must prevent the sedimentation of solid particles while homogenously dispersing them in the bulk liquid. The present numerical investigation, performed with the expert software Ansys® Fluent, Release 16, employs the Eulerian multiphase model along with the RNG k–ε turbulence model to simulate the free-surface liquid–solid flows in the baffled stirred reactor. A sliding mesh approach is used to model the impellers rotation. The tandem configuration is clearly superior to a single impeller, while the existing electrical motor that drives the stirring mechanism still provides the necessary power.

CFD Assessment of the Hydrodynamic Performance of Two Impellers for a Baffled Stirred Reactor

When converting a baffled stirred reactor to work with a different fluid, usually the original impeller must be replaced with a customized one. If the original impeller was designed for mixing liquids, its performance for liquid–solid suspensions may not be satisfactory. A case study is presented, where a two-blade original impeller is replaced with a new three-blade design. The new impeller shows clear improvements in mixing a liquid–solid suspension, while keeping the shaft power practically at the same level. As a result, a practically homogenous liquid–solid mixture is obtained, thus ensuring the required quality of the final product. The present numerical investigations employ the Eulerian multiphase model with renormalization (RNG) k–ε turbulence model to simulate the three-dimensional unsteady free-surface liquid–solid flow in a stirred tank. A sliding mesh approach was used to account for the impeller rotation within the expert code, FLUENT 16. The comparative quantitative analysis of the solid phase distribution and the relevant velocity profiles show that the new design of three-blade-impeller is significantly increasing the sedimentation time of the solid phase beyond the chemical reaction specific time. The necessary power to drive the new impeller has a slightly higher value than for the original impeller but it can be sustained by the existing driving system.

Influence of solids motion on ultrasonic horn tip erosion in solid–liquid two-phase flows

Ultrasound technology is a promising technique for wastewater treatment. However, its industrial application and scale-up face numerous problems, such as ultrasonic horn tip erosion. In solid–liquid flow systems, the synergy between cavitation and solid particle erosion is unclear, and the influence of solids motion is relatively unknown. By analyzing the tribosystem near the tip surface, we hypothesize that the synergistic erosion depends on the flux of solid particles flowing past the surface, relating to the local solids concentration and velocity. This hypothesis was investigated by ultrasonic cavitation–particle erosion tests performed in an eccentrically agitated tank. To study the effect of local concentrations and velocities, we carefully controlled the total solids and impeller speeds by integrating their coupled influence. Results indicate that synergistic erosion was aggravated at higher solids concentrations and velocities, and both parameters, based on a sensitivity analysis, show similarities in their relative degree of influence on erosion. This supports our hypothesis, which unifies the two parameters into a single factor, and explains the synergism in solid–liquid flows. Understanding these influencing factors and mechanisms will contribute to erosion prediction and the optimization of ultrasound applications in wastewater treatment processes.

Solid-liquid flow in stirred tanks: “CFD-grade” experimental investigation

Computational Fluid Dynamics (CFD) simulations of solid–liquid flows in stirred tanks are feasible with appropriate closure models. However, no systematic assessment of different models has appeared yet because of lacking validation data. The present study accumulates a “CFD-grade” database on solid–liquid two-phase flow experiments in a stirred tank (diameter = 90 mm), including single-phase flows for comparison. The velocity fields of the liquid and solid phases are measured with Particle Image Velocimetry and Particle Shadow Velocimetry, respectively. The experiments cover a range of density ratios, particle diameters, solid volume fractions and impeller rotation speeds. The mean and fluctuating liquid and solid velocities are obtained by time-averaging and angle-resolved averaging, as well as the time-averaged local solid fraction. The experimental data for the single-phase flows is compared with CFD simulations which show reasonably good predictions. A systematic assessment of CFD models for solid–liquid flows will appear as a sequel.

Heat Transfer and Hydrodynamics in Stirred Tanks with Liquid-Solid Flow Studied by CFD–DEM Method

The heat transfer and hydrodynamics of particle flows in stirred tanks are investigated numerically in this paper by using a coupled CFD–DEM method combined with a standard k-e turbulence model. Particle–fluid and particle–particle interactions, and heat transfer processes are considered in this model. The numerical method is validated by comparing the calculated results of our model to experimental results of the thermal convection of gas-particle flows in a fluidized bed published in the literature. This coupling model of computational fluid dynamics and discrete element (CFD–DEM) method, which could calculate the particle behaviors and individual particle temperature clearly, has been applied for the first time to the study of liquid-solid flows in stirred tanks with convective heat transfers. This paper reports the effect of particles on the temperature field in stirred tanks. The effects on the multiphase flow convective heat transfer of stirred tanks without and with baffles as well as various heights from the bottom are investigated. Temperature range of the multiphase flow is from 340 K to 350 K. The height of the blade is varied from about one-sixth to one-third of the overall height of the stirred tank. The numerical results show that decreasing the blade height and equipping baffles could enhance the heat transfer of the stirred tank. The calculated temperature field that takes into account the effects of particles are more instructive for the actual processes involving solid phases. This paper provides an effective method and is helpful for readers who have interests in the multiphase flows involving heat transfers in complex systems.

Towards optimal machine learning model for terminal settling velocity

Terminal Settling velocity (Vts) is a significant phenomenon for two-phase solid-liquid flows in various process units, such as slurry pipeline, annular drillpipe, fluidized bed reactor, drier, and gasifier. A two-phase system operated below Vts encounters several technical issues, such as solid accumulation, surface wear, erosion, flow irregularity, increased energy requirement, and backflow or, even, bursting. Measuring and predicting the Vts of spherical and non-spherical particles in rheologically different fluids are of interest to the concerned research community. Although many empirical models with limited boundary conditions were proposed earlier, the application of artificial intelligence (AI) for such modeling is still in infancy. In the current study, we attempt to address the shortcomings of the previous methods of predicting Vts by using a generalized machine learning (ML) approach. The training and testing of the ML models were conducted using an extensive dataset including various particle shapes and fluid rheologies. The current dataset is substantially larger compared to the similar datasets used for previous studies. We investigated several state-of-the-art ML algorithms, including ensemble learning and multi-stage regression models to find out the most optimum model for predicting Vts. The proposed model is applicable to spherical and non-spherical particles in both Newtonian and non-Newtonian fluids. This new application of AI-based modeling in the field of engineering can be used for industrial-scale design and operation with much needed reliability in a cost-effective manner.

Review on the effect of heat exchanger tubes on flow behavior and heat/mass transfer of the bubble/slurry reactors

Bubble/Slurry bubble column reactors (BCR/SBCR) are intensively used as multiphase reactors for a wide range of application in the chemical, biochemical and petrochemical industries. Most of these applications involve complicate gas–liquid/gas–liquid–solid flow behavior and exothermic process, thus it is necessary to equip the BCR/SBCR with heat exchanger tubes to remove the heat and govern the performance of the reactor. Amounts of experimental and numerical studies have been carried out to describe the phenomena taking place in BCR/SBCRs with heat exchanger tubes. Unfortunately, little effort has been put on reviewing the experiments and simulations for examining the effect of internals on the performance and hydrodynamics of BCR/SBCR. The objective of this work is to give a state-of-the-art review of the literature on the effects of heat exchanger tubes with different types and configurations on flow behavior and heat/mass transfer, then provide adequate information and scientific basis for the design and the development of heat exchanger tubes in BCR/SBCR, ultimately provide reasonable suggestions for better comprehend the performance of different heat exchanger tubes on hydrodynamics.

Erosion evaluation of elbows in series with different configurations

Erosion of elbows in series has received more attention recently as many facilities have elbows in series with various orientations and installations. It has been observed from experiments that, for liquid-dominated flows when two elbows are placed in series and with a small distance between them, the maximum erosion takes place in the second elbow. However, it is also necessary to study the effect of the orientation of the elbows because in the oil and gas industry, for example, there are all types of combinations of elbows in series in the field. In this work, experiments were conducted in a 50.8 mm diameter experimental facility considering liquid-solid and liquid-gas-solid flows and one configuration of elbows in series: where the first elbow for both configurations is upward vertical-horizontal and the second elbow orientation is horizontal-vertical downward. Also, the distance between elbows was kept constant (being three diameters). Additionally, Computational Fluid Dynamics (CFD) studies were performed and compared with experiments. After validation and sensitivity studies concerning numerical solutions, a comprehensive numerical study was conducted, taking into account different scenarios regarding the orientation of elbows using three configurations of two elbows in series. The results show that the normal and the 180° configuration of two elbows in series are less sensitive to the gravity orientation for liquid-solid flows than the other two configurations investigated. On the other hand, for liquid-gas-solid flows, erosion changes with gravity orientation. The worst-case scenario for liquid-solid flow is suggested to be the 180° configuration, while for the liquid-gas-solid flow, the 90° configuration. Thus, it is important to understand the erosion behavior with the orientation of the elbows, because erosion can be reduced by changing the orientation or the configuration of elbows in series.

Numerical Investigation of Erosive Wear of a Centrifugal Slurry Pump Due to Solid–Liquid Flow

Abstract Centrifugal slurry pump designed for handling solid–liquid flow experiences performance reduction and shorter service life due to uneven localized erosive wear of the wetted parts. In this work, three-dimensional (3D) unsteady numerical modeling of a centrifugal slurry pump with Eulerian–Lagrangian approach coupled to the erosion model has been performed to predict the erosive wear of the pump components namely, casing and impeller. The erosion model developed to predict the erosion of the pump components of high chromium white cast iron (HCWCI) is employed, and the erosion rate distribution along the complete length and width of the casing and impeller blade surfaces namely, pressure side, suction side, front shroud, and back shroud, is determined. The numerical results showed good agreement with the experimentally measured erosion of the pump casing. It has been found that the erosion of the casing and impeller is non-uniform along the length and width. The zone of higher erosion is at the centerline and the back side of the casing, whereas, for the impeller, it is on the pressure side near the leading edge. The variation in the operating flowrate and particle size greatly influenced the material removal rate and the zone of higher erosion for the casing and impeller blade surfaces.