Solid-liquid Two-phase Flow Research Articles

Research on the erosion resistance characteristics of liquid-solid two-phase flow in high-pressure manifolds

During on-site throttling spray operations, the ground high-pressure manifold is subjected to the erosive effects of high-speed liquid-solid two-phase flow, which poses a high risk of erosive damage and eventual failure. In response to the erosive conditions caused by high-speed sand-carrying liquid-solid two-phase flow on the high-pressure manifold, an experimental apparatus for erosive testing was designed, taking into account key factors such as internal pressure loads. Microscopic erosive morphologies were observed in the experiments. Subsequently, numerical simulation methods were employed to investigate the identification of erosive danger zones and the influence of different installation angles, sand content, pipe flow velocities, and viscosity on erosive areas of the manifold.The research findings indicate that the microscopic morphological changes in erosive experiments align with the micro-cutting theory, which was successfully applied in simulation. Erosive danger zones are mainly distributed on the outer arch side, the curved arc connecting section, and the initial part of the outlet straight pipe. The erosive areas do not vary with changes in installation angles, sand content, and flow velocities. As viscosity increases, the erosive area shifts. The erosive rate is positively correlated with sand content and pipe flow velocity, and with increasing viscosity, the erosive rate on the first outer arch side shows an initial decrease followed by stabilization, while the second outer arch side exhibits an initial increase followed by stabilization. As the installation angle increases, the erosion rate on the second outer arch side first shows a stable trend and then decreases rapidly. At 75°, the erosion rate reaches the lowest.

Control effect on the divergent and convergent riblets in particle-laden turbulent boundary layer

Particle image velocimetry was employed to investigate the impact of convergent–divergent riblets on turbulent boundary layers in both clear water and liquid–solid two-phase flow fields containing 155 μm polystyrene particles. The turbulence statistics such as turbulence intensity and Reynolds stress were investigated. The spatial topology of spanwise vortex head and the development and evolution process of hairpin vortices were explored from Euler and Lagrange perspectives, respectively. Additionally, the particle distribution, concentration, and dispersion within the turbulent boundary layer were statistically analyzed. The results indicated that the boundary layer thickness, friction resistance, integrated turbulence intensity, and Reynolds stress were significantly lower on divergent riblet walls compared to convergent riblet walls. Notably, divergent riblets with a yaw angle of 30° exhibited the best drag reduction effect in both single-phase and two-phase flow fields. The addition of particles resulted in an increase in boundary layer thickness but effectively reduced turbulent fluctuations in the logarithmic region, enhancing drag reduction. This extended the drag reduction range of divergent riblets to a yaw angle of 45°, increasing the maximum drag reduction rate to 26.18%. Through spatial multi-scale local average structure function and finite-time Lyapunov exponent field analysis, it was found that the 30° divergent riblet wall significantly inhibited the development of vortex structures and reduced momentum exchange within the boundary layer. Conversely, the 30° convergent riblet wall had the opposite effect, while the particle phase inhibited the development of all wall turbulent structures. Analysis of particle concentration variations within different regions of the turbulent boundary layer revealed that as the normal height of the boundary layer increased, particle concentration gradually increased, and particle dispersion decreased accordingly. The analysis further showed that particle dispersion was mainly influenced by flow structures, whereas concentration was significantly affected by turbulence intensity. These findings elucidate the effect of the flow field on the particle phase and provide insights into the interaction mechanism between the flow field and particles.

Numerically investigation of particle distribution in industrial-scale DTB crystallizer based on CFD modelling

The suspension state of crystals in the crystallizer is one of the important indicators for evaluating the adaptability of the crystallizer. This study adopted the Euler-Eulerian two-fluid model to simulate and analyze the fluid motion of solid-liquid two-phase flow in the industrial-grade DTB crystallization kettle, as well as the phase suspension distribution of crystal particles. The main influencing factors investigated are: the heat transfer effect, the height of the bottom of the crystallizer, the number and position of the stirring paddle, crystal size and crystal volume fraction. Based on the research of Euler-Eulerian method to simulate fluids, the Euler-Lagrangian method was further used to simulate the motion state of particle phases with different particle sizes in the crystallizer. It was found that the designed DTB crystallizer has good recycle mixing effect. The particles can be mixed evenly during the operation, which can fully realize the solid-liquid mixing and suspension effect of the drug under study.

Effect of Single Particle High-Speed Impingement on the Electrochemical Step Characteristics of a Stainless-Steel Surface.

In the process of particle erosion and electrochemical corrosion interaction, the electrolyte flow state change, product film destruction, and matrix structure change caused by particle impact affect the electrochemical corrosion process. Such transient, complex physical and electrochemical changes are difficult to capture because of the short duration of action and the small collision area. The peak, step time, and recovery time in this transient step cycle can indirectly reflect the smoothness and reaction rate of the electrochemical reaction system, and thus characterize the resistance to scouring corrosion coupling damage of metals in liquid-solid two-phase flow. In this study, in order to obtain the electrochemical response at the moment of particle impact, electrochemical monitoring experiments using a specially designed miniature three-electrode system were used to test step-critical values, including step potential, current, and resistance, among others. Meanwhile, an electrochemical step model under particle impact considering boundary layer perturbation was developed. The experimental results reflect the effect law of particle impact velocity and particle size on the peak step and recovery period. Meanwhile, the effect of particle impingement on the electrochemical step of stainless steel in different electrolyte solutions was obtained by comparing the step curves in distilled water and Cl-containing water. The connection between the parameters in the electrochemical step model and in the particle impact, as well as the effect of the variation of these parameters on the surface repassivation process are discussed in this paper. By fitting and modeling the test curves, a new mathematical model of electrochemical step-decay under single-particle impact was obtained, which can be used to characterize the change pattern of electrochemical parameters on the metal surface before and after the impingement.

Numerical Simulation of Solid-Liquid Two-Phase Flow in Pump

Abstract This paper is based on EDEM-FLUENT coupling calculation, the solid-liquid two-phase flow at pump is analyzed. Three kinds of solid phase volume concentration and three solid phase particle diameters are given respectively, and the solid-liquid two-phase flow numerical simulation of the internal flow field of the pump is carried out. The position distribution of solid particles in the flow field and the change of particle average velocity with time and the distribution of particle velocity are analyzed. The results show that the inlet of the runner and the pressure surface of the blade are the concentrated distribution areas of particles. With the increase in particle concentration, the particle distribution at the outlet of the volute is more uniform. The average velocity of particles at different particle concentrations varies similarly with time, but the average velocity of particles increases with the increase of concentration. With the increase in particle size, the average velocity of particles decreases, but the velocity value with the largest proportion of particles becomes larger.

Liquid–solid two-phase flow and separation behavior in a novel cyclone separator

In response to the prevalent issue of sand presence in liquid, particularly prominent in petroleum engineering, a novel cyclone separator has been meticulously engineered for fine-particle separation. Experiments and numerical simulation methods have provided a profound understanding of the flow-field characteristics and separation efficacy of this device. The internal architecture of the swirling flow inside the separator features a distinctive central vortex core, complemented by a turbulent secondary vortex formation in the lower section of the underflow. As the axial height increases, the secondary vortex gradually dissipates. An analysis of pressure and velocity distribution within the cyclone separator confirms the establishment of a stable cyclone field in the built-in cyclone and a tendency for the flow field within the tank to exhibit uniformity with increasing height. These flow-field characteristics show that the cyclone separator has a good separation effect on fine-rust particle impurities. Furthermore, the separation efficiency of the novel cyclone separator demonstrates a positive correlation with increasing particle size. Of the parameters studied, variation of the inlet velocity is the best method for obtaining optimum separation efficiency for a cyclone desander with a fixed particle size. Specifically, when the inlet velocity reaches 3 m/s, the desander attains an impressive separation efficiency of up to 70%.

Numerical simulation of sand erosion in Venturi tube under different flow characteristics and sand content

Abstract In the solid-liquid two-phase flow, there is flow erosion of solid relative to the surrounding wall or other components, which has attracted the attention of many scholars. Wherever flows are involved, erosion tends to be a problem. Especially in rivers with large sediment content, hydraulic machinery including pumps, water turbines, reversible water pump turbines and pipelines in a long time of flow erosion, it is easy to cause the material damage of the flow parts, affect the head and efficiency to a certain extent, may also lead to the increase of the gap between the flow parts resulting in noise and other hazards. However, in different flow conditions, the location of erosion is different, which makes it difficult to prevent erosion. As a common measuring tool, Venturi tube has a certain representative geometric shape. The erosion prediction of Venturi tube by computational fluid dynamics can provide a certain reference for other structures. In this study, the solid-liquid two-phase flow analysis method based on CFD was used to analyze the flow erosion under different velocity and sediment content. Through numerical simulation, it is found that the erosion problem in Venturi tube is closely related to its flow characteristics.

Experimental Study on the Movement Law of Solid-liquid Two-phase Flow in slurry Pump

Abstract The foundation for the research of two-phase flow pumps is the movement law of solid-liquid two-phase flow in the pump. Currently, research in this direction is mostly conducted through numerical simulation technology, while experimental research is less. In this paper, through the development of a transparent two-phase flow pump, a visual pump test platform with a pipe diameter of 150 mm has been built, and a large number of experimental studies have been conducted on the motion laws of solid-liquid two-phase flow in the pump. The motion laws of particles with different particle diameters in the pump under different flow rates and rotational speeds were obtained through high-speed cameras, including particle velocity and trajectory, and particle collision with the wall. Meanwhile, the wear tests on the pump were carried out with a cast steel and medium high concentration sand pump. The test results show that the location where particles collide with the wall surface more frequently is also the location where wear is more severe. Based on the above test research results, the optimization design direction for two-phase flow pumps is proposed.

Solid-liquid particle flow sealing mucus (PFSM) in enhancing coalbed methane (CBM) recovery: Multiple-perspectives analysis and mechanism insights

The paper presents an in-depth investigation of solid-liquid two-phase particle flow sealing mucus (PFSM) for enhanced coalbed methane (CBM) recovery. PFSM is composed of solid waste particles such as fly ash and rubber particles. The PFSM is assessed using multiple-perspectives analysis, which includes measurements of water retention, pressure expansion, rheological characteristics, adhesion, wettability, microscopy and field case studies. Single-factor and multi-factor studies are used to optimize slurry material ratios. The results show that PFSM has outstanding water retention characteristics, with over 80 % retention for 30 days at 30 °C, and impressive expansion performance, with 9.52 % at 0.6 MPa. The shear thinning curve conforms to the Cross model. After 30 s, the final contact angle is 75.17 °, which is about 6 ° smaller than that of cement based materials. Field experiments show that, after applying PFSM, the drainage gas concentration can be improved at least 60 % comparing to other sealing materials. This research findings could offer novel insights into enhancing CBM extraction, indicating potential for safer and more efficient coal mine production.

Flow Velocity Computation in Solid–Liquid Two-Phase Flow by a Hybrid Network CNN–RKSVM

As an advanced detection technique, electrical resistive tomography (ERT) has been applied to detect the solid–liquid two-phase flow velocity based on available ERT measurements. The flow velocity computation by ERT must depend on the relative algorithms, including both the cross-correlation (CC) principle and convolutional neural networks (CNNs). However, these two types of algorithms have poor accuracy and generalization under complex measuring conditions and various flow patterns. To address this issue, in this paper, a hybrid network is proposed that combines a CNN with a reproducing kernel-based support vector machine (RKSVM) technique. The features hidden in ERT measurements are extracted using the CNN, and then the flow velocity is computed by the RKSVM in a high-dimensional feature space. According to the ERT measurements in an actual experimental platform, the results show that the hybrid network has higher accuracy and generalization ability for flow velocity computation compared with the existing CC, RKSVM, and CNN methods.

A Review on Underwater Collection and Transportation Equipment of Polymetallic Nodules in Deep-Sea Mining

In response to the anticipated scarcity of terrestrial land resources in the coming years, the acquisition of marine mineral resources is imperative. This paper mainly summarizes the development of underwater collection and transportation equipment of polymetallic nodules in deep-sea mining. Firstly, the collection equipment is reviewed. The deep-sea mining vehicle (DSMV), as the key equipment of the collection equipment, mainly includes the collecting device and the walking device. The micro and macro properties of sediments have a great influence on the collection efficiency of mining vehicles. For the collecting device, the optimization of the jet head structure and the solid–liquid two-phase flow transport of the hose are discussed. The structure of the walking device restricts mining efficiency. The optimization of the geometric structure is studied, and the geometric passability and lightweight design of the walking device are discussed. Secondly, the core of transportation equipment is the lifting device composed of a riser and lifting pump. In order to explore the key factors affecting mineral transport, the lifting device is summarized, and the design optimization of the lifting pump and the factors affecting the stability of the riser are discussed. Then, the relationship between each device is discussed, and the overall coupling of the device is summarized. Finally, the existing problems and future research focus are summarized.

Design and Study of a Sediment Erosion Test Device for a Single-Flow Channel in the Guide Apparatus of a Reaction Hydraulic Turbine

Sediment erosion damage is one of the main causes of structural failure in reaction turbine units. To study the mechanism through which sediment erosion affects the water-guiding mechanism of a reaction turbine unit, this study obtained the average concentration and particle size of sediment during the flood season based on the statistics of the measured sediment data from the power station. Additionally, the characteristics of the solid–liquid two-phase flow of the diversion components of the reaction hydraulic turbine were numerically calculated. Based on the velocity triangle change in the guide apparatus and the flow similarity principle, a flow-around wear test device for the guide apparatus of the reaction turbine was designed. Furthermore, the similarity of the sand–water flow field between the guide apparatus of the prototype unit and the test device was compared and analyzed. The results demonstrated that the sand–water flow field of the diversion components of the prototype unit was axisymmetric and exhibited a potential flow distribution. Additionally, uniform sand–water flow occurred within the guide apparatus, with a small sand–water velocity gradient near the wall of the stay vanes (SV) and the guide vanes (GV). The maximum volume fraction of sediment particles was observed in the tailing area of the spiral casing, indicating an enrichment phenomenon of sediment particles. The velocity of the sediment particles on the surface of the guide vane in the single-channel sediment wear test device and prototype unit ranged from 6.2 to 7.8 m/s, and the velocity of the sediment particles on the surface of the stay vane ranged from 5.1 to 14.6 m/s, and the difference of the sediment particles’ velocity near the wall was 1 to 3 m/s. The trailing vorticity of the guide vane reached a maximum of 120 s−1. Consequently, the single-channel sediment erosion test device can unveil the sediment erosion mechanism of the guide apparatus of a reaction turbine.

Influence of a Long Flexible Fiber on the Transport Capability of a Non-Clogging Pump

During the operation of non-clogging pumps, the flexible long fiber is prone to clogging and winding during the flow process, which can result in damage to the non-clogging pump, so a numerical simulation method of a solid–liquid two-phase flow in a non-clogging pump with a flexible long fiber is proposed in this paper. The unsteady numerical simulation of the two-phase flow of a single flexible fiber with different densities, lengths and diameters in a double-blade non-clogging pump was carried out to study the influence of fiber parameters on fiber transport capability. The results show that at a density of 920 kg/m3, 300 kg/m3 and 732 kg/m3, the transport capability of flexible fibers decreases successively, and the transport time T0 is 0.32 s, 0.36 s and 0.48 s, respectively. The transport capability of flexible fibers with a length of 150 mm, 200 mm and 250 mm decreases successively, and the transport time T0 is 0.34 s, 0.48 s and 0.96 s, respectively. The transport time T0 is 0.48 s when the fiber diameter dp is 5 mm. When the fiber diameter dp is 7.5 mm, the transport time T0 is 0.51 s. When the fiber diameter dp is 10 mm, the fiber transport capability of the non-clogging pump decreased significantly, and the transport time T0 is 0.68 s. The fiber length has the most obvious effect on fiber transport capability, followed by the fiber diameter and fiber density.

Study on the anisotropic flow characteristics of wet particles in liquid-solid fluidized beds

In liquid-solid fluidized beds, the presence of a liquid film around the surface of particles influences their collision behavior, leading in turn to the restitution coefficient no longer a constant. The present study introduces a dynamic restitution coefficient for wet particles to describe its dynamic variation during the process of particles colliding. The liquid-solid two-phase flow is simulated with Eulerian-Eulerian two-fluid method incorporating the anisotropic kinetic theory of granular flow based on second-order moment (SOM) model, in view of the anisotropy of particle fluctuations. This study aims to probe into the influence of liquid film and anisotropy of particle fluctuation on the particle-particle interactions and collision mechanisms. The predicted particle velocity and solid volume fraction are verified by the Limtrakul's et al. experiments. The simulated results show that the particle velocity fluctuations exhibit significant anisotropy, and the SOM model is superior to the KTGF model in capturing inhomogeneity and anisotropy of the flow field. The existence of a liquid film enhances energy dissipation during particle collisions and diminishes the anisotropy of particle velocity fluctuations. Also, the enhancement of particle density leads to a thicker liquid film and higher restitution coefficient, while the second-order moments are weakened and the anisotropy is remarkable. Furthermore, the effect of liquid viscosity on the liquid film thickness and restitution coefficient is more significant, where the particle fluctuations are reduced and the anisotropy is intensified by enhancing the liquid viscosity. In brief, both the liquid film and the anisotropy have impact on liquid-solid two-phase flow, by comparison, the effect of anisotropy is greater than liquid film.

Erosion Wear Analysis on Valve Cage of Cage-Typed Sleeve Control Valve for Coal Liquefaction

Abstract Cage-typed sleeve control valve (CSCV) is the key basic equipment in direct coal liquefaction projects. The working condition of CSCV has the characteristics of high-pressure difference, high velocity, and high solid content. There is a general issue of liquid–solid two-phase erosion wear in CSCV, which can easily lead to the failure of the internal structure in the valve cage. Therefore, it is necessary to study erosion wear characteristics of internal structures in the valve cage. Considering the real conditions of erosion wear in the valve cage, a simplified T-shaped flow path is designed, and the precision of both the liquid–solid two-phase flow model and the erosion prediction model is validated. The flow characteristics and erosion wear characteristics in the T-shaped flow path under different working conditions are studied. Based on the simulation results of different structural parameters and boundary conditions, the erosion wear of the T-shaped flow path is predicted and calculated by the response surface method. Subsequently, the prediction formula for the maximum erosion rate is derived. The formula enables the swift determination of optimal structural parameters for the flow path, aiming to mitigate damage to the valve caused by erosion wear. This work can quickly predict the erosion wear rate of the key areas in the valve cage, which can provide a certain reference value for the life prediction and structural optimization of CSCV, and it can also benefit the safety and maintenance of the coal liquefaction system.

Erosion Resistance of Casing with Resin and Metallic Coatings in Liquid–Solid Two-Phase Flow

Protective coatings are typically applied to enhance their resistance to corrosion. There is considerable research on the corrosion resistance of coated casings. However, few research studies have focused on the erosion resistance on coated casings. In this work, the erosion resistance of resin- and metallic-coated casings in liquid–solid two-phase fluids were investigated using a self-made erosion facility. The results show that the resin coating tends to peel off the material base in the form of brittle spalling or coating bulge in the high-speed sand-carrying liquid. Both resin and metallic coatings were broken through within 20 min in a liquid–solid two-phase flow environment. Compared to resin coatings, metallic coatings exhibit weaker erosion resistance in similar liquid–solid flow. Through the analysis of experimental results and fitted curves, empirical constants for materials and sand content influencing factors were determined using non-dimensional processing. The erosion prediction model of metallic coatings and resin coatings was established based on the ECRC/Zhang model with the change in flow rate, angle, and sand content. This research contributes to a better understanding of the erosion resistance performance of casings used in oil and gas fields, thereby contributing to potential improvements in their production.

Influence of the internal structure of straight microchannels on inertial transport behavior of particles

The rapid advancement of Micro-Electro-Mechanical Systems (MEMS) technology has established microfluidics as a pivotal field. This technology marks the onset of a new era in various applications, including drug testing, cell culture, and disease monitoring, underscoring its extensive practicality and potential for future exploration. This research delves into the intricate behavior of particle inertial migration within microchannels, particularly focusing on the impact of different channel structures and Reynolds numbers (Re). Our studies reveal that particles in microchannels with one-sided sharp-cornered microstructures migrate towards the sharp corner at a relative position of 0.4 under low flow rates, and towards the straight wall side at a relative position of 0.8 under high flow rates. The migration pattern of equilibrium positions varies with different arrangements of sharp-corner structures, achieving stability at the channel's center only when the sharp corners are symmetrically arranged on both sides. Our investigation into the shape of microstructures indicates that sharp-cornered structures generate a more stable secondary flow compared to rectangular and semi-circular structures, preventing particle aggregation at the outlet. To address the challenges associated with handling variable cross-section geometries and solid-wall boundaries in dissipative particle dynamics methods effectively, we have developed a dissipative particle dynamics model specifically for analyzing such microchannels. Building upon our previous research, this model introduces a conservative force coefficient for particles within the microstructured region and an interaction zone that only involves repulsive forces, aligning well with experimental outcomes. Through the study of microstructures' geometric shapes, this paper offers guidance for designing microchannels for particle enrichment. Furthermore, the dissipative particle dynamics model established for the particle flow and solid structure interaction within microstructured channels provides insights into the mesoscale dynamics of liquid-solid two-phase flow and particle motion. In conclusion, this paper aims to enhance particle motion sample preparation techniques, thereby broadening the scope of microfluidic applications in the biomedical field.

Study on Wear Characteristics of a Guide Vane Centrifugal Pump Based on CFD–DEM

Guide vane submersible centrifugal pumps are a kind of submersible pump, and the fluid inside the pump is often mixed with gravel and other impurities during operation, affecting the pump’s operating efficiency and life expectancy. However, past studies on solid–liquid two-phase flow (STF) and wear characteristics in guided vane centrifugal pumps have been limited to the particle trajectory and wear region distribution. These studies have lacked research on the effect of particles on the fluid flow and the specific amount of wear on the overflow components. Additionally, most of them have used the DPM discrete-phase model, which does not consider the particle–particle and particle–wall interactions. This paper is based on the CFD–DEM method, combined with the Archard wear model. A solid–liquid two-phase flow simulation is carried out for pumps with different particle sizes and particle shapes to analyze the particle movement inside the pump, the wear distribution and average wear amount of the overflow components, and the effect of particles on the turbulent kinetic energy of the fluid. The results show that the particles mainly collide with the leading and trailing edges of the impeller blades and the leading edge of the guide vane blades and form a buildup at the trailing edge of the concave surface of the guide vane blades, resulting in the wear being mainly distributed in these regions. With an increase in particle size and a decrease in sphericity, the average wear on the overflow components increases. The change of particle size directly affects the resistance of the fluid and the structure of the flow field, which has a large impact on the fluid flow pattern and generates large turbulent kinetic energy fluctuations. The shape of the particles only changes the structure of the local flow field, which has a small impact on the fluid flow pattern.

Study on Proppant Transport and Placement in Shale Gas Main Fractures

In this paper, based on the background of a deep shale reservoir, a solid–liquid two-phase flow model suitable for proppant and fracturing fluid flow was established based on the Euler method, and a large-scale fracture model was established. Based on field parameters, a proppant transport experiment was conducted. Then, on the basis of the experimental fracture model, proppant transport simulation under different influencing factors was carried out. The results show that the laboratory experiment was in good agreement with the simulated results. The process of proppant accumulation in fractures can be divided into three stages according to the characteristics of sand banks. The displacement mainly affects the sedimentation distance of the proppant in the first stage, and the viscosity of the fracturing fluid represents the strength of the fluid sand carrying performance. Compared with 40/70 mesh proppant, 70/140 mesh proppant is more easily fluidizable, the fracture width has less influence on proppant migration and placement, and the perforation location only affects the accumulation pattern at the fracture entrance, but has less influence on proppant placement in the remote well zone.

Numerical analysis of coarse particle two-phase flow in deep-sea mining vertical pipe transport with forced vibration

Exploring the dynamics and flow characteristics of coarse particles within vertical lifting pipes is essential to ensure safe and efficient pipeline transportation. This study combines computational fluid dynamics (CFD) and the discrete element method (DEM) to investigate the behavior of coarse particle solid–liquid two-phase flow in a vertical pipe utilized for deep-sea mining under forced vibration and compares it with that in stationary pipes. This study examined the effects of pipe amplitude, vibration frequency, and initial internal flow velocity separately. The amplitude values tested were 0D (static), 1D, 2D, 3D, and 4D, where D represents pipe diameter. The vibration frequencies of 0 Hz (static), 0.25 Hz, 0.5 Hz, 1 Hz, and 2 Hz were tested, respectively. Finally, initial velocities of 1 m/s, 2 m/s, 3 m/s, and 4 m/s were tested. Compared with stationary pipes, particle-induced turbulence gradually disrupts the flow field, leading to a more dispersed particle volume distribution during pipe vibration. An increase in the amplitude and vibration frequency of the pipe results in an augmentation of the pressure drop within the pipe. By comparing the results of the vibrating pipe with those of the stationary pipe, the effect of the pipe vibration gradually weakened as the initial velocity increased.