Hua-lin Liao,Sheng-li Zhao,3,Yan-feng Cao,Lei Zhang,Can Yi,Ji-lei Niu,Li-hong Zhu

1.School of Petroleum Engineering,China University of Petroleum,Qingdao 266580,China

2.State Key Laboratory of Offshore Oil Exploitation, Beijing 100028,China

3. Huanghe Drilling Co., Shengli Engineering Co., SINOPEC, Dongying 257000,China

4.Orion Energy International Co., Ltd, Beijing 100101,China

Abstract:In order to study the effectsof the confining pressureon the erosion characteristicsof the self-resonating cavitating jet under wellbore and deep-water conditions,experiments are conducted on aluminum specimens impinged by the organ pipe cavitation nozzle and the conical nozzle with the confining pressure in the range 0 MPa-10.0 MPa.Meanwhile,through the numerical simulation of the collapsing process of the cavitation bubble and the noise test,the cavitation erosion mechanism is analyzed.The experimental results show that the optimal standoff distance and the confining pressure can be obtained for the maximum erosion quantities,and the optimal standoff distance is 5 to 7 times greater than the equivalent nozzle outlet diameter and the confining pressure is about 2.0 MPa.Under the same conditions, the erosion caused by the cavitation nozzle is up to 2 times larger than that caused by the conical nozzle. According to the numerical simulation and the noise test, the cavitation erosion on the aluminum specimens is mostly caused by mechanical forces due to the high-frequency pressure pulse generated during the collapse of cavitation bubbles,while just a small part is caused by micro-jets.

Key words:Cavitating jet,cavitation erosion,confining pressure,nozzle

Introduction

The key concern in the utilization of the self-oscillating cavitating jets in the oil and gas wellbore,the deep-water,and other high hydraulic pressure environments is to avoid the cavitation inception under a high confining pressure.In the petroleum engineering and the ocean resource exploitation,the cavitating jets are widely used.In the early 1980s,a self-resonating cavitating jet known as the Stratojet was proposed[1],with an enhanced erosivity from the increased cavitation activity due to the large pressure oscillations associated with the intensification of the cavitation,the resonance in the nozzle assembly,and the generation and the disappearance of large vortical structures.In addition,the jet structural features are measured for the selfresonating organ pipe cavitating nozzle,the Helmholtz oscillator nozzle and the nozzle with fixed inlet contour to determine their effects on the critical Strouhal number.It is demonstrated that the cavitating jets can be generated with a high cavitation inception number[2-3].The field tests show that the tricone bits utilizing the self-resonating cavitation effects can improve the drilling rate by 2 to 4 times as compared with the conventional nozzles.A design method was developed for the organ pipe cavitation nozzle and the Helmholtz oscillator nozzle,and applied in the drilling engineering[4].The drilling tests simulated in the laboratory demonstrate that the cavitation can be initiated in a nozzle with a high inception number and that a hydraulic confining environment may enhance the cavitation erosion effects[5].The pressure pulse characteristics and the frequency distribution of a self-excited oscillating nozzle were studied under different confining pressures[6-7].The results indicate that the self-excited oscillating cavitating jets can be used as an effective method to prolong the production period because of the minimization of the block formations.

With regard to the self-resonating cavitating jet,a lower confining pressure can improve the cavitation erosion efficiency.With the increase of the confining pressure,the cavitation erosion effect isweakened due to the increased difficulty of the cavitation inception[8-11].So far,the characteristics of the cavitating jet erosion under different confining pressures have not been made completely clear,as well as the influence of the confining pressure on the cavitating jet erosion properties.Also,due to the complexity of the jet dynamics under the confining pressure,the available theoretical models have limitations to predict the properties of the corresponding cavitation erosion and bubble collapsing process[12-15].In this study,we investigate the influence of various factors including the erosion time,the standoff distance,and the magnitude of the confining pressure on the erosion of a self-resonating cavitating jet with a self-developed autoclave,and then the results are analyzed using the numerical simulation and the noise test of the cavitation bubble collapsing process.

1.Experiments

The experiments are conducted in the autoclave we have developed with an inner diameter of 200 mm and a height of 600 mm,as shown in Fig.1.The autoclave mainly consists of the nozzle holder,the specimen holder,the tank body,and the components for adjusting the standoff distance and the confining pressure.The standoff distance S is measured from the nozzle outlet to the specimen,and the component for adjusting the standoff distance can steadily move the specimen holder to a desired position on the right or left side.The inlet of the nozzle is connected to the high pressure pump,which provides the pressure up to 120 MPa.As shown in Fig.2,two typesof nozzles are used in the experiments,one is an organ-pipe selfresonating cavitating nozzle designed based on the transient flow and hydroacoustics theory[16-18],and the other is a conventional conical nozzle based on the Leach and Walker nozzle model for studying the erosion capabilities of differently structured nozzles for purpose of comparison and their dimensions are listed in Table 1.The outlet diameter of both nozzles is1.0 mm.

The organ-pipe cavitating nozzle shown in Fig.2(a)contains two oscillating zones with two abrupt cross-section contractions,and a resonator with length L and diameter D as an oscillating amplifier.The inlet of the resonant chamber is connected with the flow pipe of diameterssD and D forming the entrance contraction section.The lower part of the resonant chamber has an outlet section with diameter d forming the outlet contraction section.The outlet contraction cross section serves as a self-resonating mechanism as well as a feedback mechanism.According to the Stratojet concept,the peak acoustic resonance can be achieved when a standing wave passesthrough the organ-pipe,i.e.,while a stable fluid passes,because the contraction surface can generate an initial pressure fluctuation for the fluid and feedback this fluctuation to the resonant chamber to trigger the feedback pressure oscillation.The peak resonance will be reached when the frequency of the organ pipe wave is near the critical jet-structuring frequency,as determined by the nozzle model parameter, the Strouhal number St, but the exact resonance depends on the contraction at each end of the organ pipe.When a strong resonance is produced,the basic relation that the organ pipe nozzle should satisfy can beexpressed as[16]

Fig.1 (Color online) Thecavitating jet eroding aluminum specimen under confining pressure

where L is the length of the nozzle outlet,d is the ID of the nozzle outlet,nK is the mode number,and Ma isthe Mach number.

Fig.2 Schematic diagram

Table 1 Nozzles parameters

The erosion characteristics of the cavitating jet are evaluated using a circular aluminum specimen with a diameter of 35 mm and a height of 50 mm,placed normal to the jet axis at standoff distances of 2 mm to 8 mm from the nozzle outlet.During the experiments,the confining pressure is controlled by adjusting the nozzleand the micrometer valve,and the confining pressureaP in the autoclave is adjusted in the range from 0 Mpa to10.0 MPa.

During the experiments,the driving pressure and the confining pressure of the water jet are measured by the pressure gauges in the system.The distance from the nozzle outlet to the specimen is regulated by adjust in the standoff distance.Thus,the variation of the erosion quality against the standoff distance is obtained.For a fixed standoff distance,different combinations of the confining pressure and the nozzle pressure-drop are realized by the regulation of the inlet control valve and the outlet control valve of the water jet.The pit formation by a cavitating jet is vital to understand the physics of the cavitating jet erosion.The impacting target is a cylindrical specimen made of aluminum with chemical compounds and mechanical properties as listed in Tables 2 and 3,respectively.Note that the specimen surface is polished by buffing for the purpose of observation of the erosion pit formation.The weight loss is measured at the erosion timeeT ,in the range 60 s to180 s,by a high precision weight meter with an accuracy of 0.01 mg.

Table 2 Chemical compositions of specimen (%)

2.Analysis of experimental results

2.1 Erosion features

For the submerged jet flow,due to the entraining of the surrounding liquid,usually three sections can be identified,the initial section,the transient section,and the essential section,and the essential section in the downstream of the transient zone is the main concern.The velocity distribution of the submerged free jet shows a great velocity gradient in the submerged jets except in the potential core[18].Due to the concurrent effects of the viscous stress due to the pressure difference of the water and the reversed water,the jet boundary is full of vortices.Once the pressure at the center of the vortices decreases to the level of the water vapor pressure,the cavitation bubbles can be observed being formed inside of the jets. It is widely believed that under certain conditions a cavitation is present in the submerged jets,especially in those with high velocity.In our experiments,these phenomena are confirmed,as shown in Fig.3,where it is obvious that the specimens impacted by the nozzles show annular cavitation erosion with discrete pitting,as is consistent with the erosion features observed by other researchers in their cavitating jet experiments on aluminum alloy with a confining pressure[19-20].

Table 3 Mechanical properties of specimen

Fig.3 Cavitation erosion with erosion time of T e =180 s and standoff distance of S =4 mm

The self-resonating cavitating jets are produced by the transmission of small perturbation waves in the channels and the self-excitation of the jets themselves,with large vertices and the pressure oscillation,thus with stronger cavitation effects than the conventional cavitating jets under normal or confining pressure conditions.As indicated in Fig.4,the self-resonating cavitating jets with the same inlet pressure,confining pressure,and standoff distance as the conical jet,penetrateinto the specimen much wider and deeper.

Fig.4 Erosion comparison under the same conditions:j=P 100 MPa,a =2.0 MPaP,=6 mm S ,e=180 sT

2.2 Effect of erosion time on erosion quantity

The erosion quantityem(specimen weight loss)as a function of the erosion time ispresented in Fig.5.As can be seen in Fig.5,all erosion quantities increase with the time.The conical jets begin to level out after 3 min,while the cavitating jets still keep a steady erosion rate.Namely,as the depth of the hole increases,the resistances like the friction between the jet and the hole wall and the backflow of the jet increasingly absorbs the impact energy of the new jet,thereafter, the erosion is dominated by the cavitation effect,which is almost not affected by the resistance.The stronger the cavitation effect,the steadier the results of self-resonating cavitating jets in the erosion of the aluminum specimen will be.

2.3 Effect of standoff distance on erosion quantity

Theerosion curves of the self-resonating cavita-

Fig.5 (Color online)The relationship between erosion quantity and erosion time

The erosion curves of the conical jets under the same experimental conditions are presented in Fig.7,where it can be seen that the trendsaresimilar to those of the self-resonating cavitating jets,except when the optimal standoff distance is smaller than that in the previous case,namely it is 3 to 5 as the nondimensional standoff distance.According to the noise analysis of the cavitation nozzle and the conical nozzle[21],the cavitation inception number of the self-resonating cavitation nozzle is 1.67,while that of the conical nozzle is 0.54,suggesting that the conical nozzle has a lower cavitation inception capability,which is connected with the optimal standoff distance corresponding to the maximum erosion quantity.

Fig.6 (Color online)The relationship between standoff distance and erosion quantity of cavitation nozzle

Fig.7 (Color online)The relationship between standoff distance and erosion quantity of conical nozzle

2.4 Effect of confining pressure on erosion quantity

The erosion curves of the cavitation and conical jets under different confining pressures at the standoff distances of 4.0 mm and 6.0 mm are presented in Fig.8.As can be seen in Fig.8,the erosion quantity of the self-resonating cavitating jet increases at a relatively low confining pressure,and if the pressure further increases,the erosion quantity significantly decreases,indicating the sensitivity of the erosion to the confining pressure.Specifically,for the confining pressure of about 2.0 MPa,the erosion quantity reaches its maximum.Nonetheless,the erosion quantity of the conical jets drops significantly with the increase of the confining pressure.Specially,there is a range within which the erosion quantity dropssharply,which can be explained as a confinement of the environmental pressure which inhibits the formation of the cavitation,eliminating partly or totally the cavitation erosion mechanism.

Fig.8 (Color online)The effect of confining pressure on erosion quantity

According to the test and the data analysis,two factors contribute to the decrease of the erosion intensity under the confining pressure conditions.On one hand,the confining pressure has significant effects on the jet dynamic pressure and the axial spray speed.Under the confining pressure conditions,the attenuation of the axial dynamic pressure of a jet is accelerated significantly.When the jet reaches the impact surface,the jet stagnation pressure decreases with the increase of the confining pressure[22].On the other hand,the confining pressure inhibits the cavitation inception,which can be expressed by the cavitation number σdefined as

whereaP is the ambient pressure,vP is the vaporizing pressure,jV is the jet velocity relative to the ambient flow,and ρis the density of the jet fluid.

At the beginning of the cavitation process,the cavitation incipiency number takes the value ofiσ ,and as the cavitation further develops,this number increases.According to Eq.(2),the confining pressure generally plays an important role in the cavitation inception.In the case of the conical nozzle,the jet dynamic pressure hasa greater effect on thealuminum specimen than the cavitation erosion,resulting in a sharp decrease of the erosion quantity.

3.Analysisof erosion mechanism of the self-resona- ting cavitating jet

3.1 Micro-jets generated during cavitation bubble co- llapse

According to the experimental results of the cavitation erosion,if the cavitation bubbles collapse due to the impact surface of the specimen,the erosion capacity of the jets is greatly improved.The standoff distance and the confining pressure are two dominant factors affecting the erosion;microscopically,they represent the distance to the impact surface when the cavitation collapses and the fluid pressure around the cavitation,respectively.To investigate their effects on the collapsing process,a numerical calculation model was built for the cavitation bubble collapse,as shown in Fig. 9 and it was solved with the volume of fluid (VOF)model[23-24].It was shown that the VOF model can satisfactorily simulate the cavitation collapsing process[25-26].Especially,it can accurately calculate the pressure pulse and the micro-jets velocity which are difficult to measure in experiments.Therefore,the VOF should be effective in calculating the impact of the cavitating jets on the target surface and analyzing their erosion features.

The VOF model is applied in the simulation of the cavitation bubble collapsing process,in which a volume fraction function f is introduced to characterize the grid area percentage of the fluid that occupies the grid for interface tracking and satisfies the transport equation as follows

where f is the volume fraction function,t is the erosion time,xv andrv represent the bubble velocities in x and radial directions in the 2-D symmetrical scenario.

Fig.9 (Color online)Calculation model of cavitation bubble collapse

In Eq.(3),it can be seen that f is the function of time and space,and after its discretization in the computation domain ( )F ,the ratio of the area occupied by the fluid to the total grid area can be defined by

In the numerical simulation of the bubble collapse with the VOF model,the rectangular unstructured grids are adopted in the simulation domain;moreover,a self-adaptive method is employed to make the grid finer around the cavitation.The computation domain is 15 mm×20 mm,with 216 720 grids in total,of which 3 224 are occupied with the cavitation bubble.As shown in Fig.10,the initial cavitation bubble radius is Ro=25 μm ,the water viscosity isμ= 1 ×10-3Pa ? s ,the water density is ρ= 1 ×103kg/m3,the confining pressure is Pc=2.0 MPa,and no slip boundary conditions are used.In the calculation,OC is set as a fixed boundary,AB and BC are set as a pressure boundary,and AO is set asa symmetric axis.

Fig.10 (Color online) Calculation mesh

As shown in Fig.11,during the final stage of the cavitation bubble collapsing,the micro-jet velocity is very high near the impact surface (r is the radio distance,h is the height from impact surface),but also decays very fast.In Fig.12,it can beseen that the velocity of the micro-jets decreases almost exponentially as the ratio H of the bubble distance h to its radiusoR increases.When =1.1H ,the velocity of the micro-jets impacting on the surface is 170.2 m/s,exerting an impact pressure approximately of 14.5 MPa,for =3.0H ,the velocity is reduced to 21.2 m/s,resulting in the impact pressure of only 0.2 MPa.The impact of the micro-jets generated during the cavitation bubble collapse is inconspicuous,thus it is not the main factor contributing to the cavitation erosion.

Fig.11 (Color online)Velocity vector graph of micro-jet,=T 0.250 ms,=1.1H

3.2 High pressure pulse generated by cavitation bu- bble collapse

Fig.12 The dependency of micro-jet velocity on H

The pressure distribution during the cavitation collapsefor T =0.242 ms and H =1.5 is presented in Fig.13.The instantaneous value of the pressure pulse generated by the bubble collapse can reach the maximum of 493.0 MPa.The collapse pressure has a close relation with the characteristic distance H ,namely as H increases,the high pressure pulse reduces almost exponentially.

Fig.13 (Color online) Pressure distribution when the cavitation bubblecollapses,T =0.242 ms ,H =1.5

The larger the initial distance between the cavitation bubble and the impact surface is,the lower the pulse pressure generated by the cavitation bubble collapse will be,as shown in Fig.14.However,the pulse pressure is still much higher than the impact pressure caused by micro-jets,thus dominating the cavitation erosion on the aluminum specimen.The experiments show the existence of an optimal standoff distance corresponding to the maximal erosion in the microscopic view,which embodies the high pressure pulse generated by the cavitation bubble collapsing on the target surface when the cavitation erosion reaches its maximum.When the standoff distance is larger than a certain value,the bubble reaches its maximum and then collapses before reaching the surface,impacting slightly the target,for a very short standoff distance,the bubble actually collapses before being developed to its maximum size or collapses during the rebounding phase,producing a very weak impact on the target.

Fig.14 (Color online)The maximal pulse pressure acting on the rigid surface when the bubble collapses,a =P 2.0 MPa

3.3 The inhibition of cavitation pulse by confining pre- ssure

Besides the inhibition of the jets by the impact pressure,the confining pressure also suppresses the cavitation pulse effect.During the cavitation,the bubble collapse noises are generated,which can be measured by a hydrophone,to evaluatethe sound pressure magnitudes.The schematic diagram of the device for measuring the cavitation noises is given in Fig.15.The cavitation nozzle with the high pressure water is installed inside the autoclave,through which the confining pressure can be adjusted by the valve at the water exit and the hydrophone near the nozzle can receive noises produced by the cavitation water jets and record them in a noise acquisition system.Using the sound pressure of the noises,we can judge the cavitation intensity.

Figure 16 shows the oscillograms of the cavitation noises at confining pressures of 0.5 MPa and 6.0 MPa,respectively,for the inlet pressure of 80.0 MPa.At the pressure of Pa=0.5 MPa ,the oscillogram demonstrates a great pulsation created by the self-resonating nozzle,which transforms the continuous jet into the pulsing jet.When the confining pressure increases to 6.0 MPa,the pulsing features diminish significantly,indicating a strong suppression of the pulsing magnitude by the confining pressure.

Therefore,the confining pressure has a restraining effect on the pressure fluctuation and the cavitation inception of the jet.When the confining pressure exceeds a certain value,the cavitating erosion effect disappears while the specimen erosion ismainly due to the jet dynamic pressure.

4.Conclusions

According to the erosion experiment on aluminum specimenswith the self-resonating nozzle and the conical nozzle,and thenumerical simulation of the collapsing process of the cavitation bubble and the noise test,the following conclusions could be made:

Fig.15 Diagram of the device for measuring cavitation noises under confining pressure

Fig.16 The oscillogram of the self-oscillating cavitating jet under the confining pressure

(1)The confining pressure and the standoff distance are two key factors affecting the erosion of a self-resonating cavitating jet.In the experiment,the optimum standoff distance corresponding to the maximal erosion is 5 to 7 times of the equivalent nozzle diameter and the confining pressure is about 2.0 MPa. Moreover, the specimen weight loss oftheself-resonating cavitating jet is 1-2 times larger than that of the conical jet under the same experimental conditions.

(2)The enhanced erosion of the self-resonating cavitating jet comes mainly from the mechanical damage caused by a high-frequency pressure pulse generated during the cavitation bubble collapsing process,while the contribution of the micro-jets is quitesmall.

(3)The VOF model is very effective in the simulation of the cavitation bubble collapsing process,particularly in obtaining the pressure pulse and the micro-jet velocity,which are difficult to measure.