Jet Characteristics and Optimization of a Cavitation Nozzle for Hydraulic Fracturing Applications

Hydraulic jetting is a form of fracturing that involves using a high-pressure jet of water to create fractures in the reservoir rock with a nozzle serving as the central component of the hydraulic sandblasting perforation tool.In this study,the flow behavior of the nozzle is simulated numerically in the framework of a SST k-ωturbulence model.The results show that the nozzle structure can significantly influence the jet performance and related cavitation effect.Through orthogonal experiments,the nozzle geometric parameters are optimized,and the following configuration is found accordingly:contraction angle 20°,contraction segment length 6 mm,cylindrical segment diameter 6 mm,cylindrical segment length 12 mm,spread segment length 10 mm,and spread angle 55°.

The Optimization Design of the Nozzle Section for theWater Jet Propulsion System Applied in Jet Skis

The performance of a water jet propulsion system is related to the inlet duct,rotor,stator,and nozzle.Generally,the flow inlet design must fit the bottom line of the hull,and the design of the inlet duct is often limited by stern space.The entire section,from the rotor to the nozzle through the stator,must be designed based on system integration in that the individual performance of these three components will influence each other.Particularly,the section from the rotor to the nozzle significantly impacts the performance of a water jet propulsion system.This study focused on nozzle design and established referable analysis results to facilitate subsequent integrated studies on the design parameters regarding nozzle contour.Most existing studies concentrate on discussions on rotor design and the tip leakage flow of rotors or have replaced the existing complex computational domain with a simple flow field.However,research has yet to implement an integrated,optimal design of the section from the rotor to the nozzle.Given the above,our program conducted preliminary research on this system integration design issue,discussed the optimal nozzle for this section in-depth,and proposed design suggestions based on the findings.This program used an existing model as the design case.This study referred to the actual trial data as the design conditions for the proposed model.Unlike prior references’simple flow field form,this study added a jet ski geometry and free surface to the computational domain.After the linear hull shape was considered,the inflow in the inlet duct would be closer to the actual condition.Based on the numerical calculation result,this study recommends that the optimal nozzle outlet area should be 37%of the inlet area and that the nozzle contour should be linear.Furthermore,for the pump head,static pressure had a more significant impact than dynamic pressure.

Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows

Capturing elaborated flow structures and phenomena is required for well-solved numerical flows.The finite difference methods allow simple discretization of mesh and model equations.However,they need simpler meshes,e.g.,rectangular.The inverse Lax-Wendroff(ILW)procedure can handle complex geometries for rectangular meshes.High-resolution and high-order methods can capture elaborated flow structures and phenomena.They also have strong mathematical and physical backgrounds,such as positivity-preserving,jump conditions,and wave propagation concepts.We perceive an effort toward direct numerical simulation,for instance,regarding weighted essentially non-oscillatory(WENO)schemes.Thus,we propose to solve a challenging engineering application without turbulence models.We aim to verify and validate recent high-resolution and high-order methods.To check the solver accuracy,we solved vortex and Couette flows.Then,we solved inviscid and viscous nozzle flows for a conical profile.We employed the finite difference method,positivity-preserving Lax-Friedrichs splitting,high-resolution viscous terms discretization,fifth-order multi-resolution WENO,ILW,and third-order strong stability preserving Runge-Kutta.We showed the solver is high-order and captured elaborated flow structures and phenomena.One can see oblique shocks in both nozzle flows.In the viscous flow,we also captured a free-shock separation,recirculation,entrainment region,Mach disk,and the diamond-shaped pattern of nozzle flows.

Effect of Nozzle Inclination Angle on Fuel-Air Mixing and Combustion in a Heavy Fuel Engine

Heavy-fuel engines are widely used in UAVs(Unmanned Autonomous Vehicles)because of their reliability and high-power density.In this study,a combustion model for an in-cylinder direct injection engine has been imple-mented using the AVL FIRE software.The effects of the angle of nozzle inclination on fuel evaporation,mixture distribution,and combustion in the engine cylinder have been systematically studied at 5500 r/min and consider-ing full load cruise conditions.According to the results,as the angle of nozzle inclination increases,the maximum combustion explosion pressure in the cylinderfirst increases and then it decreases.When the angle of nozzle incli-nation is less than 45°,the quality of the mixture in the cylinder and the combustion performance can be improved by increasing the angle.When the angle of nozzle inclination is greater than 45°,however,the mixture unevenness increases slightly with the angle,leading to a deterioration of the combustion performances.When the angle of nozzle inclination is between 35°and 55°,the overall combustion performance of the engine is rela-tively good.When the angle of nozzle inclination is 45°,the combustion chamber’s geometry and the cylinder’s airflow are well matched with the fuel spray,and the mixture quality is the best.Compared with 25°,the peak heat release rate increases by 20%,and the maximum combustion burst pressure increases by 5.5%.

Effect of droplet characteristics on liquid-phase distribution in spray zone of internal mixing air-mist nozzle

In continuous casting production,droplet characteristics are important parameters for evaluating the nozzle atomization quality,and have a significant impact on the secondary cooling effect and the slab quality.In order to study the behavior of atomized droplets after reaching the slab surface and to optimize the spray cooling effect,the influence of droplet diameter and droplet velocity on the migration behavior of droplets in the secondary cooling zone was analyzed by FLUENT software.Results show that the droplets in the spray zone and on the slab surface are mainly concentrated in the center,thus,the liquid volume fraction in the center is higher than that of either side.As the droplet diameter increases,the region of high liquid volume fraction on the slab surface becomes wider,and the liquid phase distribution in the slab width direction becomes uneven.Although increasing the droplet velocity at the nozzle exit has little effect on droplet diffusion in the spray zone,the distribution becomes more uneven due to more liquid reaches the slab surface per unit time.A prediction formula of the maximum water flow rate on the slab surface for specific droplet characteristics was proposed based on dimensionless analysis and validated by simulated data.A nozzle spacing of 210 mm was recommended under the working conditions in this study,which ensures effective coverage of the spray water over the slab surface and enhances the distribution uniformity of water flow rate in the transverse direction.

Research on static characteristic of double redundance double nozzle flapper valve based on AMESim

The feedback spring rod of the armature assembly is cancelled in the double redundance double nozzle flapper valve(DRDNFV),and the difficulty of valve core displacement control is increased.Therefore,this paper intends to study the static characteristic of DRDNFV through the AMESet and AMESim simulation.It is explored under the circumstance of the fixed orifices being clogged and experimentally verified on the test bench.The results show that the pressure gain increases and the flow gain decreases with the increasing clogged degree of the fixed orifices on both sides.The zero bias increases synchronously with the increasing clogged degree of the unilateral fixed orifice.The experimental results are basically consistent with the theoretical curves and the theoretical correctness of the simulation model is effectively verified.The results can provide the theoretical reference for design,debugging,maintenance and fault diagnosis of DRDNFV.

Effect of gas blowing nozzle angle on multiphase flow and mass transfer during RH refining process

A three-dimensional mathematical model was developed to investigate the effect of gas blowing nozzle angles on multiphase flow,circulation flow rate,and mixing time during Ruhrstahl-Heraeus(RH) refining process.Also,a water model with a geometric scale of 1:4 from an industrial RH furnace of 260 t was built up,and measurements were carried out to validate the mathematical model.The results show that,with a conventional gas blowing nozzle and the total gas flow rate of 40 L·min^(-1),the mixing time predicted by the mathematical model agrees well with the measured values.The deviations between the model predictions and the measured values are in the range of about 1.3%–7.3% at the selected three monitoring locations,where the mixing time was defined as the required time when the dimensionless concentration is within 3% deviation from the bath averaged value.In addition,the circulation flow rate was 9 kg·s^(-1).When the gas blowing nozzle was horizontally rotated by either 30° or 45°,the circulation flow rate was found to be increased by about 15% compared to a conventional nozzle,due to the rotational flow formed in the up-snorkel.Furthermore,the mixing time at the monitoring point 1,2,and 3 was shortened by around 21.3%,28.2%,and 12.3%,respectively.With the nozzle angle of 30° and 45°,the averaged residence time of 128 bubbles in liquid was increased by around 33.3%.

Prediction of atomization characteristics of pressure swirl nozzle with different structures

The structure of the pressure swirl nozzle is an important factor affecting its spray performance.This work aims to study pressure swirl nozzles with different structures by experiment and simulation.In the experiment,10 nozzles with different structures are designed to comprehensively cover various geometric factors.In terms of simulation,steady-state simulation with less computational complexity is used to study the flow inside the nozzle.The results show that the diameter of the inlet and outlet,the direction of the inlet,the diameter of the swirl chamber,and the height of the swirl chamber all affect the atomization performance,and the diameter of the inlet and outlet has a greater impact.It is found that under the same flow rate and pressure,the geometric differences do have a significant impact on the atomization characteristics,such as spray angle and SMD(Sauter mean diameter).Specific nozzle structures can be customized according to the actual needs.Data analysis shows that the spray angle is related to the swirl number,and the SMD is related to turbulent kinetic energy.Through data fitting,the equations for predicting the spray angle and the SMD are obtained.The error range of the fitting equation for the prediction of spray angle and SMD is within 15% and 10% respectively.The prediction is expected to be used in engineering to estimate the spray performance at the beginning of a real project.

Design and Fluid-Dynamic Analysis of a Flushing Nozzle for Drilling Applications

The actuator is a key component of the creaming tool in drilling applications.Its jet performances determine the effective reaming efficiency.In this work,a new selective reaming tool is proposed and the RNG k-εturbulence model is used to calculate its internal and externalflowfields.In particular,special attention is paid to the design of theflushing nozzle.The results show that the jet originating from theflushing nozzle has a significant influence on rock cutting and blade cooling effects.In turn,the jet performances depend on geometric structure of the creaming actuator.In this framework,a conical-cylindrical nozzle with a diameter of 7 mm is initially considered as a basis to implement a strategy to optimize the structural parameters of the reaming actuator,and improve the related side tracking reconstruction technology.

Optimization of a Diesel Injector Nozzle

Multiphase simulations based on the VOF(Volume of Fluid)approach,used in synergy with the cavitation Schnerr-Sauer method and the K-Epsilon turbulence model,have been conducted to study the behavior of an injector nozzle as a function of relevant structural parameters(such as the spray hole diameter and length).The related performances have been optimized in the framework of orthogonal experimental design and range analysis methods.As made evident by the results,as the spray hole diameter increases from 0.10 to 0.20 mm,the outlet massflow rate grows by 243.23%.A small diameter of the spray hole,however,has a beneficial effect in terms of cavitation suppression.Moreover,rounding the spray hole can effectively increase the outlet massflow rate and improve theflow characteristics while mitigating the cavitation phenomenon inside the spray hole.In particular,with the optimized nozzle design,the outlet massflow rate can be increased by 13.33%,while the fuel vapor volume is reduced by 33.53%,thereby,leading to significant improvements in terms offlow characteristics and cavitation control.

Investigations of the effects of two typical jet crushing methods on the atomization and dust reduction performance of nozzles

Single-fuid nozzles and dual-fuid nozzles are the two typical jet crushing methods used in spray dust reduction. To distinguish the atomization mechanism of single-fuid and dual-fuid nozzles and improve dust control efciency at the coal mining faces, the atomization characteristics and dust reduction performance of the two nozzles were quantitatively compared. Results of experiments show that, as water supply pressure increased, the atomization angle of the swirl pressure nozzle reaches a maximum of 62° at 6 MPa and then decreases, but its droplet size shows an opposite trend with a minimum of 41.7 μm. The water supply pressure helps to improve the droplet size and the atomization angle of the internal mixing air–liquid nozzle, while the air supply pressure has a suppressive efect for them. When the water supply pressure is 0.2 MPa and the air supply pressure reaches 0.4 MPa, the nozzle obtains the smallest droplet size which is 10% smaller than the swirl pressure nozzle. Combined with the dust reduction experimental results, when the water consumption at the working surface is not limited, using the swirl pressure nozzle will achieve a better dust reduction efect. However, the internal mixing air–liquid nozzle can achieve better and more economical dust reduction performance in working environments where water consumption is limited.

Effect of Intake Conditions and Nozzle Geometry on Spray Characteristics of Group-Hole Nozzle

The group-hole nozzle concept is proposed to meet the requirement of nozzle hole minimization and reduce the negative impact of poor spatial spray distributions.However,there are limited researches on the effects of intake conditions and nozzle geometry on spray characteristics of the group-hole nozzle.Therefore,in this study,an accurate spray model coupled with the internal cavitating flow was established and computational fluid dynamics(CFD)simulations were done to study the effects of intake conditions and nozzle geometry on spray characteristics of the group-hole nozzle.Experimental data obtained using high-speed digital camera on the high-pressure common rail injection system was used to validate the numerical model.Effects of intake conditions(injection pressure and temperature)and nozzle geometry(orifice entrance curvature radius and nozzle length)on the flow and spray characteristics of the group-hole nozzle were studied numerically.The differences in Sauter mean diameter(SMD),penetration length and fuel evaporation mass between single-hole nozzle and group-hole nozzle under different nozzle geometry were also discussed.It was found that the atomization performance of the group-hole nozzle was better than that of the single-hole nozzle under same intake conditions,and the atomization effect of the short nozzle was better than that of the long nozzle.With increase in the orifice entrance curvature radius,the average velocity and turbulent kinetic energy of the fuel increased,which was conducive to improving the injection rate and flow coefficient of the nozzle.Meanwhile,the penetration length and SMD value rose,while evaporation mass dropped.When the ratio of the orifice entrance curvature radius(R)to the diameter of injection hole(D)was 0.12,the spray characteristics reached a constant state due to elimination of cavitation.Conclusions were made based on these.This study is expected to be a guide for the design of the group-hole nozzle.

Spray Characteristics of Non-Circular Nozzle in Air-Assisted Injection System

In order to analyze the spray characteristics of non-circular nozzle holes based on the air-assisted spray system, the spray characteristics of circular and non-circular nozzles were studied under the pressure of 0.2-0.6 MPa and the spray volume of 1000-5000 mL/h. Elliptical nozzle and triangular nozzle are classified as non-circular geometries. The spray cone angle was measured by processing the spray image captured by a CCD camera. The measured spray cone angles of the circular nozzles were analyzed, and the axis switching phenomenon of minor plane of elliptical nozzle was found during the test. Among the three shapes of nozzles, the elliptical nozzle had the largest spray cone angle, and the triangular nozzle had the smallest. The velocity field obtained depended on the PIV system. The results show that for axial velocity, elliptical orifice spray has greater kinetic energy and smaller droplet size under the same working parameters. Compared with the circular and elliptical nozzles, triangular orifice reached maximum spray velocity the fastest, but its velocity decay was the fastest. For radial velocity, away from the axis, the spray velocity of the elliptical orifice was less affected by the injection parameters, and the velocity was less than that of circular orifice and triangle orifice. Increasing air pressure will weaken radial propagation. The increase of liquid spraying rate had no remarkable effect on the increase of spraying rate. The results of particle size analysis show that the particle size of the non-circular orifice is reduced compared with that of the circular orifice, which promotes the breakup of droplets to a certain extent and enhances the atomization effect.

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.

Local Solution of Three-Dimensional Axisymmetric Supersonic Flow in a Nozzle

In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.

Clogging behavior of submerged entry nozzles for Ti-bearing IF steel

The nozzle clogging behavior of Ti-bearing IF steel was studied by metallographic analysis,scanning electron microscopy（SEM）, energy dispersive spectroscopy（EDS）,and X-ray diffraction（XRD）.According to the experimental results,nozzle clogging primarily appears three layers.There are a lot of large-sized iron particles in the inner layer and mainly slag phase in the middle and outer layers.The principal clog constituents of the inner layer are loose alumina cluster inclusions and granular shaped alumina inclusions,containing iron particles. The clog constituents of the middle layer are mainly dendrite alumina inclusions.The primary phases existing in nozzle clogging are FeO·TiO2 and FeO·Al2O3 besidesα-Al2O3 and a-Fe.The FeO·TiO2 phases among the deposits adhere the deposits together firmly enough to lead to the inferior castability of Ti-bearing ultra low carbon steel compared with that of Ti-free low carbon Al-killed steel.

Numerical Analysis of Nozzle Clearance's Effect on Turbine Performance

Variable nozzle turbine （VNT） has become a popular variable geometry turbine （VGT） technology for the diesel engine application. Nozzle clearance, which can＇t be avoided on the hub and shroud side of the VNT turbine due to the pivoting stators, can lead to turbine performance deterioration. However, its mechanism is still not clear. In this paper, numerical investigation, which is validated by experiment, is carried out to study the mechanism of the nozzle clearance＇s effect on the turbine performance. Firstly, performance of the mixed flow turbine with fixed nozzle clearances tested on flow bench. Performance of the tested turbine with the same nozzle clearance is numerically simulated. The numerical result agrees well with the test data, which proves correct of the numerical method. Then the turbine performance with different nozzle clearances is numerically analyzed. The research showed that with nozzle clearance, flow loss in the nozzle increases at first and it reaches the maximum value when the clearance ratio is 5%. Flow at the exit of the nozzle becomes less uniform with nozzle clearance. The negative incidence angle of the rotor also increases with nozzle clearance and leads to more incidence angle loss in the rotor. The low energy fluid formed in the nozzle due to the nozzle clearance migrates from hub to shroud side in the rotor, which is another main reason for the rotor＇s performance degradation. The present research exposed the mechanism of the dramatically decrease of the turbine performance with nozzle clearance： （a） The loss associated with the nozzle leakage increases with the nozzle clearance; （b） The flow loss grows up quickly in the rotor due to the incidence angle loss and migration of the low energy fluid from hub to shroud side.

THEORY AND EXPERIMENTAL STUDY OF THE SELF-EXCITED OSCILLATION PULSED JET NOZZLE

Comparing with usual continuous jet nozzle, the self-excited oscillationpulsed jet nozzle SEOPJN) can make jet generate a higher peak of pressure and larger scouringvolume. And it can make jet increase the effective standoff distance, too. The basic theories of theSEOPJN are introduced. Some experimental results are shown. According to the results, using tricornbits assembled the SEOPJN to drill oil well, the ROP increases by 8 percent approx 77 percent, andthe rates of the footage for tricorn bit increases by 6.7 percent approx 44.0 percent.

Experimental Investigation on Noise of Cavitation Nozzle and Its Chaotic Behaviour

The researches of cavitation noise mainly focus on the incipiency and developing of cavitation to prevent the cavititation erosion in the hydraulic machinery, while there is few report about the collapse strength of cavitation bubbles produced by water jet through the cavitation nozzle to utilize efficiently the collapse energy of cavitation bubbles. The cavitation noise signals are collected with hydrophones for the cavitation nozzle and general nozzle at the target position and the nozzle exit separately in the conditions of different standoff distance. The features of signal’s frequency spectrum and power spectrum are analyzed for various nozzles by way of classical methods. Meanwhile, based on chaotic theory, phase space reconstruction is processed and the maximum Lyapunov index is calculated separately for each cavitation signal’s time series. The results of chaotic analysis are compared with the one of conventional analysis. The analyzed data show that there are the marked differences at the spectrum between the cavitation nozzle and general nozzle at the target position while the standoff distance is 35 mm, which mainly displays at the high frequency segment (60-120 kHz). The maximum Lyapunov index calculated appear at standoff distance 35 mm, which is an optimum standoff distance for the most bubbles to collapse at the target. At the nozzle exit, the noise signal of cavitation nozzle is different from the general nozzle, which also displays at the high frequency segment. The results demonstrate that the water jet modulated by the cavitation nozzle can produce effectually cavitation, and at the target position the amplitude and energy of noise spectrum in high frequency segment for cavitation nozzle are higher than conventional nozzle and the Lyapunov index of cavitation nozzle is larger than conventional nozzle as the standoff distance is less than 55 mm. The proposed research reveals that the cavitation noise produced by collapse of cavitation bubbles attributes mainly to the high frequency segment of the spectrum, which provides references for the research on cavitation noise.

Supersonic swirling characteristics of natural gas in convergent-divergent nozzles

The supersonic nozzle is a new apparatus which can be used to condense and separate water and heavy hydrocarbons from natural gas.The swirling separation of natural gas in the convergent-divergent nozzle was numerically simulated based on a new design which incorporates a central body. Axial distribution of the main parameters of gas flow was investigated,while the basic parameters of gas flow were obtained as functions of radius at the nozzle exit.The effect of the nozzle geometry on the swirling separation was analyzed.The numerical results show that water and heavy hydrocarbons can be condensed and separated from natural gas under the combined effect of the low temperature（-80℃） and the centrifugal field（482,400g,g is the acceleration of gravity）.The gas dynamic parameters are uniformly distributed correspondingly in the radial central region of the channel,for example the distribution range of the static temperature and the centrifugal acceleration are from -80 to -55℃and 220,000g to 500,000g,respectively,which would create good conditions for the cyclone separation of the liquids.However,high gradients of gas dynamic parameters near the channel walls may impair the process of separation.The geometry of the nozzle has a great influence on the separation performance. Increasing the nozzle convergent angle can improve the separation efficiency.The swirling natural gas can be well separated when the divergent angle takes values from 4°to 12°in the convergent-divergent nozzle.