Critical Flow Velocity Research Articles

Effect of Impact Angle on the Critical Flow Velocity for Erosion–Corrosion of 304 Stainless Steel in Simulated Sand-Containing Sea Water

Effect of Impact Angle on the Critical Flow Velocity for Erosion–Corrosion of 304 Stainless Steel in Simulated Sand-Containing Sea Water

Determination of rational process variables for multi-step centrifugal mills

This paper presents the results of experimental studies into milling under multiple impacts in multi-step centrifugal mill designed at the Chersky Institute of Mining. In order to enhance milling capacity, it is proposed to add breakers of the mill with more breaking elements. However, addition of breaking elements sometimes fails to intensify milling and can adversely affect on the milling efficiency to to higher velocity air flows generated in the working space between the top and bottom breakers. The tests have determined the rational number of additional breaking elements, conditioned by the critical air flow velocity of 10 m/s in the breaker chamber of the lab-scale multi-step centrifugal mill. Given these conditions are fulfilled, the fineness number of the multi-step centrifugal mill with additional breaking elements grows considerable as against the base case of the mill without additional elements.

FLUID-INDUCED ELECTROCHEMICAL CORROSION OF 13Cr STAINLESS STEEL IN HIGH-SPEED FLOWING LIQUID CONTAINING 1 w/% AND 2 w/% NaCl

In order to study the electrochemical corrosion law for the 13Cr stainless-steel tubing material in a high-speed Cl-containing liquid, a high-speed-flow experiment and a small three-electrode system, embedded in a small pipe, were used. The open circuit potential (OCP), polarization curve (PC) and electrochemical impedance spectroscopy (EIS) of the stainless-steel surface were tested in a medium with a flow velocity ranging from 10 to 22 m/s containing 1 w/% and 2 w/% of NaCl. By comparing it with the changes in the electrochemical-reaction parameters of the material in distilled water, the results of the experiment including the critical flow velocity, the change of corrosion rate and the electrochemical-reaction control steps were obtained. By theoretically solving the frictional force of the liquid against the wall surface and the adsorption capacity of the oxide film, and assuming that the oxide film is a macromolecular combination, the relationship between the adsorption capacity of different surface films and the critical flow velocity in the high-speed pipe flow was established. The results of this experiment and calculation can provide a preliminary prediction of the critical flow velocity corresponding to the inflection point of the wall-surface corrosion rate in an industrial pipe flow, thereby improving the process parameters and reducing the wall damage.

Correlation between depassivation and repassivation processes determined by single particle impingement: Its crucial role in the phenomenon of critical flow velocity for erosion-corrosion

The correlation between depassivation and repassivation processes, which is significant in erosion-corrosion, was quantitatively investigated by single particle impingement tests at various flow velocities and impact angles. The results show that both repassivation and depassivation processes are associated with the kinetic energy of solid particle, and demonstrate that the repassivation is retarded by depassivation. This phenomenon probably results from the depassivation-induced microstructure evolution. On this basis, the dependence of critical flow velocity (CFV) for erosion-corrosion on the solid particle concentration and diameter is further theoretically predicted and experimentally verified. Accordingly, the crucial role of depassivation-repassivation in CFV phenomenon is further highlighted.

New insight into the stability and dynamics of fluid-conveying supported pipes with small geometric imperfections

In several previous studies, it was reported that a supported pipe with small geometric imperfections would lose stability when the internal flow velocity became sufficiently high. Recently, however, it has become clear that this conclusion may be at best incomplete. A reevaluation of the problem is undertaken here by essentially considering the flow-induced static deformation of a pipe. With the aid of the absolute nodal coordinate formulation (ANCF) and the extended Lagrange equations for dynamical systems containing non-material volumes, the nonlinear governing equations of a pipe with three different geometric imperfections are introduced and formulated. Based on extensive numerical calculations, the static equilibrium configuration, the stability, and the nonlinear dynamics of the considered pipe system are determined and analyzed. The results show that for a supported pipe with the geometric imperfection of a half sinusoidal wave, the dynamical system could not lose stability even if the flow velocity reaches an extremely high value of 40. However, for a supported pipe with the geometric imperfection of one or one and a half sinusoidal waves, the first-mode buckling instability would take place at high flow velocity. Moreover, based on a further parametric analysis, the effects of the amplitude of the geometric imperfection and the aspect ratio of the pipe on the static deformation, the critical flow velocity for buckling instability, and the nonlinear responses of the supported pipes with geometric imperfections are analyzed.

Dynamical response of a rotating cantilever pipe conveying fluid based on the absolute nodal coordinate formulation

Abstract A dynamical model of a rotating cantilever pipe conveying fluid is derived based on the absolute nodal coordinate formulation. The free vibration and dynamical response of the system are investigated in this paper. Based on the absolute nodal coordinate method and the extended Lagrangian equation proposed by Irschik for the nonmaterial system, the motion equation of the rotating flexible cantilever pipe conveying fluid is built. The influence of the rotational angular velocity and flow velocity on the natural frequency of the system is analyzed. The critical nondimensional circular frequency of in-plane vibration and critical nondimensional flow velocity are investigated. The static deformation is shown under different flow velocities and angular velocities. The nonlinear transient analyses of a rotating flexible cantilever pipe are completed with the variation of parameters. During the rotation, the Coriolis force of fluid acting on the pipe has a great effect on the static deformation.

Enhancing vibration performance of a spinning smart nanocomposite reinforced microstructure conveying fluid flow

In this article, critical angular velocity, critical velocity of fluid flow and vibration control analysis of a rotating multi-hybrid nanocomposite reinforced (MHCR) cylindrical microshell covered with a piezoelectric layer as sensor and actuator (PLSA) are presented. The current non-classical model is capable of capturing the size dependency in the microshells using only one material length scale parameter; moreover, the mathematical formulation of microshells based on the classical model can be recovered from the present model by neglecting the material length scale parameter. This structure is under conveying viscous fluid, and the related force is calculated by the modified formulation of Navier–Stokes. In addition, the current structure rotates around its axial direction. The Coriolis and centrifugal effects due to the rotation are considered. For semi-numerical method, the strains and stresses can be determined through via the first-order shear deformable theory (FSDT). For accessing to various mass densities, thermal expansion as well as Poisson ratio, the rule of mixture is applied, although a modified Halpin–Tsai theory is used for obtaining the module of elasticity. The external voltage is applied to the sensor layer, while a Proportional-Derivative (PD) controller has been utilized for controlling output of sensors. The boundary conditions are derived through governing equations of the MHCR cylindrical microshell using energy method known as Hamilton’s principle and finally are solved using generalized differential quadrature method (GDQM). The outcomes show that the angular velocity, velocity of fluid flow, external force, PD controller, external voltage and MHC’s weight fraction have a considerable impact on the amplitude, and vibration behavior of a spinning MHCR cylindrical shell conveying fluid flow.

Dynamics of a droplet on a polymer brush in channel flow

Using dissipative particle dynamics, we simulate an immiscible oil droplet on a polymer brush under a channel flow. Above a critical flow velocity, the droplet slides on the brush surface with contact angle hysteresis. Interestingly, we found the critical sliding velocity to be constant across droplet sizes and interphase interactions. Further increase in flow velocity results in droplet detachment and liftoff from the brush surface. Under poor solvent conditions, large droplets may deform into an airfoil shape, increasing the critical liftoff velocity. On an oleophilic brush, the droplet desorbs and spreads, instead of liftoff. Together, our results show surprisingly rich dynamics coupling three-way interactions between either soft or liquid phases. The present study has implications on the design of polymer brushes, as well as the removal of droplets from soft surfaces using hydrodynamics.

SPH-FEM simulation of concrete breaking process due to impact of high-speed water jet

The process of concrete breaking by a high-speed water jet was simulated in this study based on the coupled method of smoothed particle hydrodynamics and the finite element method. The Riedel–Hiermaier–Thoma constitutive model was adopted to describe the mechanical characteristics of the concrete material. Various impact velocities (250–800 m/s) and jet diameters (1.0–3.0 mm) were simulated to investigate the effect of incident parameters on the dynamic responses and damage behaviors of the concrete material. The simulation results were also verified by water-jet impact experiments. The results show that the model can reproduce the nonlinear behaviors of concrete due to the impact of the water jet, including crack propagation, large deformation of the crushing crater, and penetration. For the constant jet diameter, a critical velocity of water-jet flow is identified. Lateral cracks can be generated inside concrete when the impact velocity exceeds the critical velocity, which can enhance the water-jet capability significantly to damage the concrete. The evolution process of the concrete crushing crater is also obtained. The initial shape of the crushing crater is “ω-shaped” and then gradually transforms into “V-shaped” until being penetrated by the water jet. The section shape of the concrete crushing hole is trapezoidal after penetration. For impact velocity v ranging from 250 to 500 m/s, the size of the concrete crushing hole increases with the increase in v, and the section shape tends to be rectangular. If v exceeds 500 m/s, the size and section shape no longer change significantly. It was also found that the greater the diameter of the water jet, the more the sensitivity of crushing hole size on water-jet velocity.

Non-trivial equilibriums and natural frequencies of a slightly curved pipe conveying supercritical fluid

Despite extensive use of curved pipes conveying high-speed fluids in many engineering fields, few researches have been conducted on the supercritical dynamics of curved pipes to explore new dynamic behavior. For the first time, this paper investigates the vibration characteristics of a slightly curved pipe conveying fluids in a supercritical range. The generalized Hamilton's principle is adopted to derive the governing equation. The non-trivial equilibriums and the critical flow velocities are then analytically obtained. The analytical predictions agree well with the numerical results obtained using the finite difference method and the differential quadrature element method. By introducing the coordinate transformation, the governing equation of the curved pipe is established for the vibration about the non-trivial equilibrium position. The natural frequencies of the pipe are obtained by the Galerkin truncation method and verified with the discrete Fourier transform. It is found that the critical velocities and the natural frequencies are highly dependent on the initial curvature. The research results show an interesting phenomenon that the natural frequency of the curved pipe may increase as the pipe length increases, but may not in monotonous manner. The obtained results provide useful information for further studies of fluid-conveying pipes with geometric imperfection.

Hygro-thermo-mechanical vibration of two vertically aligned single-walled boron nitride nanotubes conveying fluid

The nonlocal strain gradient theory, when combined with the first-order shear deformation theory, provides many capabilities in size-dependent structures. The aim of the present study is evaluation of the free vibration behavior of two vertically aligned fluid-conveying single-walled boron nitride nanotubes in hygrothermal environments considering slip boundary condition based on Knudsen number. These two adjacent nanotubes are coupled in the context of linear deformation through van der Waals interaction according to Lennard–Jones potential function. Actually, the contribution of the present work, compared with those previously reported, is investigating the simultaneous effect of hygrothermal loading and slip boundary condition on the dynamic behavior of two vertically aligned fluid-conveying single-walled boron nitride nanotubes. As an additional step to achieve a more accurate model of low-scale structures, both hardening and softening effects of materials are taken as important variables in the nonlocal strain gradient approach. To derive the motion equations and associated boundary conditions, Hamilton’s variational principle is used. The equations are then solved with the aid of differential quadrature method. Numerical studies are also performed to depict the effects of a number of parameters such as boundary conditions, size scale, aspect ratio, inter-tube distance, and temperature alteration on the variations of dimensionless eigenfrequency and critical flow velocity.

Researches of technological mode of operation of gas wells with a single-lift elevator at a critical speed of upper flow

The article discusses the modes of movement of gas-liquid flows in relation to the operating conditions of waterlogged gas wells at a late stage of field development. Algorithms have been developed for calculating gas well operation modes based on experimental work under conditions that reproduce the actual operating conditions of flooded wells of Cenomanian gas deposits. The concept of calculating the technological mode of operation of gas wells with a single-row elevator according to the critical velocity of the upward flow is considered based on the study of the equilibrium conditions of two oppositely directed forces: the gravity of water drops directed downward and the lifting force moving water drops with a gas flow directed upward. A calculation was made according to the method of the averaged physical parameters of formation water and natural gas in the conditions of flooded Cenomanian gas wells in Western Siberia. The results of a study of the dependence of the critical flow rate of Cenomanian wells on bottomhole pressure and diameter of elevator pipes are presented.

Detachment of coal fines deposited in proppant packs induced by single-phase water flow: Theoretical and experimental analyses

Hydraulic fracturing is an effective approach to improve the productivity of coalbed methane (CBM) reservoirs. However, during hydraulic fracturing and CBM production, massive coal fines are deposited on the surface of proppants, leading to a sharp reduction in fracture conductivity. Herein, the detachment of deposited coal fines, caused by single-phase water flow in proppant packs, was investigated to elucidate the release mechanism of fines, which would be applied towards their effective removal in the field. First, coal fines detachment experiments, including permeability and effluent measurements, were conducted on proppant packs under saturated conditions. The experiments were performed with different sizes of coal fines and gradual/abrupt increases in flow velocity to study the effects of fines size and the variation pattern of flow velocity on the release of coal fines. The experimental results indicated that there existed a critical flow velocity (CFV) for the release of coal fines in proppant packs. The value of CFV decreased at first, and then increased with the increase in fines size. Additionally, both the amounts of fines produced and the increases in permeability were more pronounced under a gradual increase in flow velocity than those under an abrupt increase in flow velocity. Second, based on Happel's sphere-in-cell model, the forces/torques acting on the deposited coal fines were analyzed to illustrate the mechanisms underlying the release of fines in proppant packs. The theoretical results revealed that, with the increase in flow velocity, the release of fines began at the proppant midpoint and ended at the front and rear stagnation points. Theoretical CFV, corresponding to the detachment flow velocity of fines at the midpoint, first decreased with the increase in fines size and then increased. Theoretical CFVs were consistent with the experimental data, thus validating the proposed model. Finally, the implications of this research on the removal of coal fines in proppant packs were also discussed.

Flow-induced periodic snap-through dynamics

Abstract

Critical flow velocity phenomenon in erosion-corrosion of pipelines: determination methods, mechanisms and applications

The critical flow velocity phenomenon is common in erosion-corrosion of many materials. It is of great importance to develop methods to determine the critical flow velocity and understand mechanisms of the phenomenon so that it can be used for proper applications. This paper provides a critical review of the critical flow velocity phenomenon in erosion-corrosion of pipelines in terms of its determination methods, mechanisms and applications. Three types of determination methods, including mass loss, electrochemical measurements and surface roughness, are reviewed and discussed. In particular, the potentiostatic polarization method is recommended to determine the critical flow velocity. The mechanisms of the critical flow velocity phenomenon depend on the surface film, which include passive film, corrosion products film and inhibitor adsorption film, formed on the metal surface. Parametric effects on the critical flow velocity are analyzed. Finally, the applications of the critical flow velocity phenomenon are considered for material selection and surface modification for improved resistance to erosion-corrosion.

Flow measurements in the wake of an adhering and oscillating droplet using laser-Doppler velocity profile sensor

The removal of droplets on surfaces by an (air-) flow is relevant, e.g., for cleaning processes or to prevent corrosion or damage of electronic devices. Still the condition for droplet movement is not fully understood. Droplets start to move downstream at a critical (air-) flow velocity vcrit. For increasing flow velocity, this process is related to a strong oscillation of the droplet. This oscillation is supposed to be a key mechanism for the onset of droplet movement in conjunction with the flow field around the droplet. We report on measurements in the wake of the adhering droplet by means of laser-Doppler velocity profile sensor and hot wire anemometry. Thanks to the excellent spatial and temporal resolution of laser-Doppler velocity profile sensor and its capability to measure bidirectional flows, a backflow region can be detected in the wake of the droplet. Therefore, it can be concluded that this backflow structure is the driving mechanism for the strong flow movement inside the droplet against channel flow direction found in previous work. Analyzing the frequency spectra of the flow velocity, it was found that the flow is also oscillating; frequency peaks are in the same range as for the contour oscillation. Based on frequency, diameter and flow velocity, a Strouhal number can be calculated. This Strouhal number is almost constant in the investigated regime of droplet volumes and is between 0.015 and 0.03. Therefore, it can be assumed that an aeroelastic self-excitation effect may be present that eventually leads to droplet movement.Graphic abstract

In-Line and Cross-Flow Coupling Vibration Response Characteristics of a Marine Viscoelastic Riser Subjected to Two-Phase Internal Flow

This paper studies the in-line and cross-flow coupling vibration response characteristics of a marine viscoelastic riser subjected to two-phase internal flow and affected by the combined effects of several parameters including the volume fraction of gas phase, sea water flow velocity, viscoelastic coefficient of the marine riser, axial tension amplitude, and the in-line and cross-flow coupling effect taking into account both the geometric and hydrodynamic nonlinearities. On the base of extended Hamilton’s principle for open systems, the dynamic equations of the marine viscoelastic riser subjected to the axial tension and gas-liquid-structure interaction are established. Two distributed and coupled van der Pol wake oscillators are utilized to model the fluctuating lift and drag coefficients, respectively. The finite element method is adopted to directly solve the highly coupled nonlinear fluid-structure interaction equations. Model validations are firstly performed through comparisons with the published experimental data and numerical simulation results, and the characteristic curves of the in-line and cross-flow vibration pattern, the in-line and cross-flow displacement trajectories, the in-line and cross-flow space-time response of displacement, and the in-line and cross-flow space-time response of stress versus different parameters are obtained, respectively. The results show that the volume fraction of gas phase, sea water flow velocity, viscoelastic coefficient of marine riser, axial tension amplitude, the in-line and cross-flow coupling effect, and multiphase internal flow velocity have significant influences on the dynamic response characteristics of the marine viscoelastic riser. Furthermore, the maximum displacements and stresses of the marine viscoelastic riser can be increased or decreased depending on the internal flow velocity, and the critical internal flow velocities result in the increase of mode order for different cross-flow velocities. It is also demonstrated that appropriate viscoelastic coefficients are very important to effectively suppress the maximum displacements and stresses.

RMB experimental program on the hydrodynamical behavior of fuel assemblies

The Brazilian Multipurpose Reactor - RMB is a 30 MW pool type research reactor, that uses Materials Testing Reactor - MTR type fuel assemblies. It has a 5x5 square array core with 23 fuel assemblies and two in-core irradiation positions, operating with upward flow and average velocities nearly 10 m/s in the fuel plates channels. The IEA-R1 is a 5 MW pool type research reactor, which also has a 5x5 square array core with 19 standard fuel assemblies, four control fuel assemblies and a central beryllium irradiation device. It operates with downward flow nearly 1.8 m/s in the channels. In order to verify and provide data and information about the dynamical behavior of fuel assemblies under nominal and critical conditions, the experimental circuit ORQUÍDEA is being designed. This circuit will permit upward and downward flow and dynamical behavior of the fuel assemblies and its parts will be tested and verified. Flow rate, temperature, pressure and differential pressure transducers are the instruments of the circuit. Endurance and critical flow velocity tests will be performed. The COLIBRI experimental circuit is being designed to make tests that allow the studies of the fluid-structure phenomenology of fuel plates similar to those of the RMB fuel assemblies when subjected to high flow velocities, which can induce pressure differences between the channels formed by the fuel plates. This work presents a preliminary design for the ORQUÍDEA and COLIBRI experimental circuits to be built at the Instituto de Pesquisas Energéticas e Nucleares - IPEN of the Comissão Nacional de Energia Nuclear - CNEN.

Influencing Factors of the Wellbore Cleaning Efficiency in Extended Reach Wells Based on Seawater Drilling Fluid

Under the construction of extended reach wells, cutting beds are very likely to form due to inadequate wellbore cleaning. The inorganic salts in seawater aggravate this problem by affecting the rheology of drilling fluids. By developing a cutting transport dynamic simulation platform, the reasons and laws of cutting beds formation, damage and removal were revealed. The results demonstrated that cutting beds are most likely to form at well inclination angles ranging from 30° to 45°. The larger the cuttings are, the higher the possibility of cutting bed formation. Properly increasing the viscosity and flow rate may reduce the formation probability of cutting beds. Furthermore, the novel concept of the critical flow velocity window for cutting bed migration was proposed. The velocity window narrowed with increasing cutting particle size, well inclination angle, ultimate high shear viscosity and Carson dynamic shear force. The efficiency of cutting bed removal by the drilling fluid was positively correlated with the well inclination angle, Carson dynamic shear force and ultimate high shear viscosity and negatively correlated with the cutting particle size. The migration mode varied with the particle size. Small-particle cutting beds were damaged by the drilling fluid into many blocks, which generated several failure points, and all the blocks were then separately transported. However, the migration mode of large-particle cutting beds was surface migration, which implies that the cuttings on the surface were always propelled by the drilling fluid first. Migration mode variation could be the likely reason for the change in the velocity window.

A new coal reservoir permeability model considering the influence of pulverized coal blockage and its application

In order to accurately predict the production performance of coalbed methane (CBM) wells and to formulate a reasonable production system, this paper established a coal reservoir permeability model considering the influence of pulverized coal blockage. Then, on the basis of this model, the flow velocity sensitivity (FVS) experimental data of 15 groups of coal samples taken from the Baode Block, Qinshui Basin, Liulin Block, Hancheng Block, and the Huanglong Coalfield were fitted to determine the permeability models for different coal samples. On this basis, this newly established permeability model was incorporated into a previously developed CBM well performance analysis software, and production history matching was carried out on two CBM wells. Finally, the effects of the parameters of pulverized coal blockage on the permeability of coal reservoirs and the production performance of CBM wells were studied by taking the fitting parameters of CBM Well W1 as the reference. And the following research results are obtained. First, this new model considering the influence of pulverized coal blockage can quantitatively describe the variation of coal reservoir permeability with fluid velocity. In addition, this model can be incorporated into a CBM numerical simulation software or a CBM well performance analysis software to apply it in a wide range. Second, the coal reservoir permeability is less affected by pulverized coal blockage in the Baode Block, but this effect shall not be ignored in the Qinshui Basin and the Huanglong Coalfield. Third, the greater the theoretical maximum permeability damage degree (Dmax) and the permeability damage degree index (n) are, the lower the relative flow velocity (v0.5) corresponding to the critical flow velocity of pulverized coal blockage is and the more obvious the effect of pulverized coal blockage on coal reservoir permeability is. Fourth, in order to reduce the adverse effect of pulverized coal blockage on coal reservoir permeability, it is suggested to reduce the production pressure difference appropriately in the process of production, especially in the initial stage of gas production, so as to avoid severe damage to coal reservoir permeability.