Research on Critical Flow of Water under Supercritical Pressures in Nozzles

An experiment on critical flow of water was conducted in two nozzles of 1.41 mm in diameter and 4.35 mm in length with rounded-edge and sharp-edge respectively, covering the ranges of inlet pressure of 22.1-29.1 MPa and inlet temperature of 38-474 ℃. More than 200 data points were obtained and the characteristics and parametric trends were investigated. In the region of near and beyond pseudo-critical temperature the thermal-equilibrium is dominant, and the flow rate can be estimated by the modified homogeneous equilibrium model. In the below pseudo-critical region the results exhibit scattered feature as a result of hysteresis effect in the onset of vaporization, characterizing a bifurcation behavior. This effect is more significant in the nozzle with sharp-edge, especially at higher pressure. For temperature well below the pseudo-critical point, the flow is not at critical condition and the flow rate can be represented by the Bernoulli equation reasonably.

Experimental Analysis of the Flow Characteristics of an Adjustable Critical-Flow Venturi Nozzle

The response of an adjustable critical-flow Venturi nozzle is investigated through a set indoor experiments aimed to determine the related critical flow rate,critical pressure ratio,and discharge coefficient.The effect of a variation in the cone displacement and liquid content on the critical flow characteristics is examined in detail and it is shown that the former can be used to effectively adjust the critical flow rate.The critical pressure ratio of the considered nozzle is above 0.85,and the critical flow control deviation of the gas flow is within±3%.Liquid flow can reduce the gas critical mass flow rate accordingly,especially for the cases with larger liquid volume and lower inlet pressure.The set of results and conclusions provided are intended to support the optimization of steam injection techniques in the context of heavy oil recovery processes.

Incipient sediment motion in vegetated open-channel flows predicted by critical flow velocity

Incipient sediment motion plays a key role in scouring and bed load transport. However, the incipient sediment motion in the vegetated open-channel flows has yet to be fully understood. This study aims to quantify the critical conditions of the sediment particle movement in the presence of emergent and submerged vegetation. A new formula of the critical flow velocity was proposed to predict the incipient sediment motion based on the force balance equation of a sediment particle and the assumption that the velocity distribution in the bed roughness boundary layer fits the logarithmic law. Analysis of the derived formula revealed that the critical flow velocity for incipient sediment motion decreases with the increase in vegetation density. The proposed formula agrees well with the experimental data in the literature, thereby implying that the critical flow velocity can effectively quantify the incipient sediment motion in the vegetated open channel flows.

Analogy Between Hydraulic Jump in Films Formed by Impinging Liquid Jet and Critical Flow in Internal Flows

Formulated are simple models for the flow in liquid film, formed by impinging jet, and a two-phase downward flow in pipe. The models are based on simplified equations of mass, momentum and energy. The solutions of such conservation equations may have regular points belonging to one integral curve only as well as turning points can be found amongst them, which refer to extreme values in the appropriate co-ordinate system. The solutions can also have singular points belonging to none or more than one integral curve. Both the turning and singular points have a clear physical meaning. They could be linked to critical flow conditions in the pipe flow or to the so-called hydraulic jump. Analogy existing between critical conditions in the pipe and the flow of liquid films formed by the liquid jet have been shown in the paper.

Numerical modelling of supercritical flow in circular conduit bends using SPH method

The capability of 1he smoothed-particle hydrodynamics （SPH） method to model supercritical flow in circular pipe bends is considered. The standard SPH method, which makes use of dynamic boundary particles （DBP）, is supplemented with the original algorithm for the treatment of open boundaries. The method is assessed through a comparison with measured free-surface profiles in a pipe bend, and already proposed regression curves for eslimation of the flow-type in a pipe bend. The sensitivity of the model to different parameters is also evaluated. It is shown that an adequate choice of the artificial viscosity coefficient and the initial particle spacing can lead to correct presentation of the flow-type in a bend. Due to easiness of its implementation, the SPH method can he efficiently used in the design of circular conduits with supercritical flow in a bend, such as tunnel spillways, and bottom outlets of dams, or storm sewers.

Research on the Critical Conditions for Clay Particle Release During Saline Aquifer Freshening Process

Water sensitivity phenomenon occurs during saline aquifer freshening process in seawater intrusion area, and clay particles released in the phenomenon can damage the infiltration capacity of the aquifer. In order to find out the factors and mechanisms for clay particle release, laboratory column infiltration experiments simulating saline aquifer freshening process were designed to measure the critical conditions(critical flow velocity, critical salt concentration and critical ionic strength) and force analysis for clay particle according to DLVO electric double layer theory was employed to illustrate the mechanisms for particle release. The research results showed that critical flow velocity for clay particle release is influenced by salt concentration of injecting solution. When salt concentration of injecting solution is very high, clay particles are not released, indicating that there does not exist a critical flow velocity in this situation. As salt concentration of injecting solution decreases, particles start to be released. The critical salt concentration for clay particle release is 0.052 mol L-1 in our work, which was determined by a constant-flux experiment for stepwise displacement of high concentration Na Cl solution. The critical ionic strength for clay particle release decreases as Ca2+ molar content percentage of the mixed solution of Na Cl and Ca Cl2 increases following the first-order exponential decay equation y = 0.0391e-0.266 x + 0.0015.

A General Thermal Equilibrium Discharge Flow Model

Based on isentropic flow and thermal equilibrium assumptions, a model was derived to calculate discharge flow rate, which unified the rules of room temperature water discharge, high temperature and high pressure water discharge, two-phase critical flow, saturated steam and superheated steam critical flow, and gave a method to calculate critical condition. Because of the influence of friction, the entropy is increased in the actual discharge process, and the discharge flow rate in thermal equilibrium condition can be obtained by the original model multiplied by an appropriate correction coefficient. The model calculated results agreed well with the experiment data of long nozzle critical flow.

A New Distribution Method for Wet Steam Injection Optimization

A new approach and a new related distribution system are proposed to address the issue of uneven steam injection caused by the different suction capacities of the used wells during the application of steam“stimulation”methods for enhanced oil recovery.The new distribution system consists of a swirler,spiral dividing baffles,and critical flow nozzles.Numerical simulations are used to analyze the flow-field and degree of steam homogeneity obtained with such an approach.The results indicate that a higher inlet pressure leads to better results.Additionally,the internal flow field becomes more stable,and the deviation from an even distribution reduces to±4.0%even when the resistance of each branch is inconsistent.Furthermore,field tests have yielded satisfactory results.

Analysis of Maximum Liquid Carrying Capacity Based on Conventional Tubing Plunger Gas Lift

China’s unconventional gas fields have a large number of low-productivity and low-efficiency wells, many of whichare located in remote and environmentally harsh mountainous areas. To address the long-term stable productionof these gas wells, plunger-lift technology plays an important role. In order to fully understand and accurately graspthe drainage and gas production mechanisms of plunger-lift, a mechanical model of plunger-liquid column uplift inthe plunger-lift process was established, focusing on conventional plunger-lift systems and representative wellboreconfigurations in the Linxing region. The operating casing pressure of the plunger-lift process and the calculationmethod for the maximum daily fluid production rate based on the work regime with the highest fluid recovery ratewere determined. For the first time, the critical flow rate method was proposed as a constraint for the maximumliquid-carrying capacity of the plunger-lift, and liquid-carrying capacity charts for conventional plunger-lift withdifferent casing sizes were developed. The results showed that for 23/8 casing plunger-lift, with a well depth ofshallower than 808 m, the maximum drainage rate was 33 m3/d;for 27/8 casing plunger-lift, with a well depth ofshallower than 742 m, the maximum drainage rate was 50.15 m3/d;for 31/2 casing plunger-lift, with a well depthof shallower than 560 m, the maximum drainage rate was 75.14 m3/d. This research provides a foundation for thescientific selection of plunger-lift technology and serves as a decision-making reference for developing reasonableplunger-lift work regimes.

VIBRATION AND STABILITY OF VERTICAL UPWARD-FLUID-CONVEYING PIPE IMMERSED IN RIGID CYLINDRICAL CHANNEL

A theoretical model is developed for the vibration and stability of a vertical pipe subjected concurrently to two dependent axial flows. The external fluid, after exiting the outer annular region between the pipe and a rigid cylindrical channel, is conveyed upwards inside the pipe. This configuration thus resembles of a pipe that aspirating fluid. The equation of planar mo- tion is solved by means of the differential quadrature method （DQM）. Calculations are conducted for a slender drill-string-like and a bench-top-size system, for different confinement conditions of the outer annular channel. It is shown that the vibrations of these two systems are closely related to the degree of confinement of the outer annular channel. For a drill-string-like system with narrow annuli, buckling instability may occur in the second and third modes. For a bench-top-size system, however, both buckling and flutter may occur in the lowest three modes. The form of instability depends on the annuli size.

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 Stability of Cantilevered Pipe Conveying Fluid with Inerter-Based Dynamic Vibration Absorber

Cantilevered pipe conveying fluid may become unstable and flutter instability would occur when the velocity of the fluid flow in the pipe exceeds a critical value.In the present study,the theoretical model of a cantilevered fluid-conveying pipe attached by an inerter-based dynamic vibration absorber(IDVA)is proposed and the stability of this dynamical system is explored.Based on linear governing equations of the pipe and the IDVA,the effects of damping coefficient,weight,inerter,location and spring stiffness of the IDVAon the critical flow velocities of the pipe system is examined.It is shown that the stability of the pipe may be significantly affected by the IDVA.In many cases,the stability of the cantilevered pipe can be enhanced by designing the parameter values of the IDVA.By solving nonlinear governing equations of the dynamical system,the nonlinear oscillations of the pipe with IDVA for sufficiently high flow velocity beyond the critical value are determined,showing that the oscillation amplitudes of the pipe can also be suppressed to some extent with a suitable design of the IDVA.

Two－Phase Critical Discharge of Initially Saturated or Subcooled Water Flowing in Sharp－Edged Tubes at High Pressure

The transient critical flow experiment with sharp-edged tubes as the break geometries is conducted in high pressure convective circulation test loop of Xi'an Jiaotong University. The initial steady operation pressure is up to 22.OMPa. An empirical correlation was made to obtain the critical mass flow rates, the critical pressure ratio and the thermal nonequilibrium number were correlated as the functions of the tube length to tube diameter ratio L/D. The predicted critical mass now rate gets a higher accuracy for short tubes with L/D <12, the prediction accuracy is higher than that of Henry model prediction for long tubes with L/D > 12.

The Himalayan Collisional Orogeny:A Metamorphic Perspective

This paper introduces how crustal thickening controls the growth of the Himalaya by summarizing the P-T-t evolution of the Himalayan metamorphic core.The Himalayan orogeny was divided into three stages.Stage 60–40 Ma:The Himalayan crust thickened to~40 km through Barrovian-type metamorphism(15–25°C/km),and the Himalaya rose from<0 to~1000 m.Stage 40–16 Ma:The crust gradually thickened to 60–70 km,resulting in abundant high-grade metamorphism and anatexis(peak-P,15–25°C/km;peak-T,>30°C/km).The three sub-sheets in the Himalayan metamorphic core extruded southward sequentially through imbricate thrusts of the Eo-Himalayan thrust,High Himalayan thrust,and Main Central thrust,and the Himalaya rose to≥5,000 m.Stage 16–0 Ma:the mountain roots underwent localized delamination,causing asthenospheric upwelling and overprinting of the lower crust by ultra-high-temperature metamorphism(30–50°C/km),and the Himalaya reached the present elevation of~6,000 m.Underplating and imbricate thrusting dominated the Himalaya’growth and topographic rise,conforming to the critical taper wedge model.Localized delamination of mountain roots facilitated further topographic rise.Future Himalayan metamorphic studies should focus on extreme metamorphism and major collisional events,contact metamorphism and rare metal mineralization,metamorphic decarbonation and the carbon cycle in collisional belts.

On the Development of a Model for the Prediction of Liquid Loading in Gas Wells with an Inclined Section

The ability to predict liquid loading in horizontal gas wells is of great importance for determining the time of drainage and optimizing the related production technology.In the present work,we describe the outcomes of experiments conducted using air-water mixtures in a horizontal well.The results show that the configuration with an inclined section is the most susceptible to liquid loading.Laboratory experiments in an inclined pipe were also conducted to analyze the variation of the critical gas flow rate under different angles,pressure and liquid volume(taking the equal liquid volume at inlet and outlet as the criterion for judging on the critical state).According to these results,the related angle of the inclined section ranges from 45°to 60°.Finally,a modified approach based on the Belfroid model has been used to predict the critical gas flow rate for the inclined section.After comparison with field data,this modified model shows an accuracy of 96%,indicating that it has better performances with respect to other models used in the past to predict liquid loading.

Proof for part of the Sttla flow experimental conclusion and the improvement of Flügel formula

Based on steam turbine’s basic working principle, we draw the conclusion that at the critical state, critical pressure is proportional to its critical flow and square root of initial temperature. Part of the Sttla flow experimental curve is verified theoretically and an improved Flügel formula with a higher accuracy is proposed. As a result, not only the calculation is simplified, but also the theory of steam turbine’s varying operation conditions is enriched.

Simulation of the effect of hydrate adhesion properties on flow safety in solid fluidization exploitation

During the solid fluidization exploitation of marine natural gas hydrates,the hydrate particles and cuttings produced via excavation and crushing are transported by the drilling mud.The potential flow safety issues arising during the transport process,such as the blockage of pipelines and equipment,have attracted considerable attention.This study aims to investigate the impact of hydrate adhesion features,including agglomeration,cohesion,and deposition,on the flow transport processes in solid fluidization exploitation and to provide a reference for the design and application of multiphase hydrate slurry transport in solid fluidization exploitation.We established a numerical simulation model that considers the hydrate adhesion properties using the coupled computational fluid dynamics and discrete element method(CFD-DEM)for the multiphase mixed transport in solid fluidization exploitation.An appropriate model to simulate the adhesion force of the hydrate particles and the corresponding parameter values were obtained.The conclusions obtained are as follows.Under the same operating conditions,a stationary bed is more likely to form in the transport process due to the hydrate adhesion forces;adhesion forces can increase the critical deposition velocity of the mixture of hydrate particles and cuttings.Hydrate adhesion lowers the height of the solid-phase moving bed,while the agglomeration and cohesion of particles can intensify the aggregation and deposition of hydrate debris and cuttings at the bottom of the pipe.These particles tend to form a deposit bed rather than a moving bed,which reduces the effective flow area of the pipeline and increases the risk of blockage.

Self-organized Criticality Behavior in Bulk Metallic Glasses

Serrated flows are known as repeated yielding of bulk metallic glasses（BMGs）during plastic deformation under different loading conditions,which are associated with the operation of shear banding.According to the statistics of some parameters,the shear avalanches can display a self-organized critical state,suggesting a large ductility of BMGs.The emergence of the self-organized criticality（SOC）behavior in different BMGs is due to the temperature,strain rate,and chemical compositions.The SOC behavior is accompanied with the following phenomena：the interactions occur in the shear bands;the incubation time is longer than the relaxation time;the time interval is lacking of typical time scale;and the spatial or temporal parameters should display apower-law distribution.

FREE VIBRATION ANALYSIS OF FLUID-CONVEYING CARBON NANOTUBE VIA WAVE METHOD

The wave method is introduced to vibration analysis of the fluid-conveying carbon nanotube. The constitutive relation of carbon nanotube on micro-scale is founded using the non- local elastic theory. The governing equation on micro-scale is obtained. And the first five orders of the natural frequency of the carbon nanotube conveying fluid with various speeds are calculated through the wave method. Besides, the critical flow velocity when the carbon nanotube loses stability is obtained. Meanwhile, a contrast is made between the result obtained through tile wave method and that in previous researches.

A NEW CALCULATION METHOD FOR GAS-WELL LIQUID LOADING CAPACITY

This article proposes a new model for calculating the gas-well liquid loading capacity, which is critical to an accurate prediction of gas well production. Based on analysis of flow regime during the gas well production with water, which is regarded as many single particles in the model, with the shape of particles being assumed as disk-like ellipsoid instead of traditional sphere and changing according to the forces exerted on them, the influences of non-Darcy flow, compressibility, and non-sphere shape on friction factor are analyzed. The differences between the new model and other models are discussed and a new formula for calculating the critical flow rate is obtained. The calculation results and a comparison with other two models show that the new model is more consistent with the actual situation and is practical.