Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this cha...Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.展开更多
In studying the diffusion-controlled adsorption kinetics of aqueous surfactant solutions at the air/solution surface by means of the maximal bubble pressure method, Fick's diffusion equation for a sphere should be...In studying the diffusion-controlled adsorption kinetics of aqueous surfactant solutions at the air/solution surface by means of the maximal bubble pressure method, Fick's diffusion equation for a sphere should be used. In this paper the equation was solved by means of Laplace transformation under different initial and boundary conditions. The dynamic surface adsorption F(t) for a surfactant solution, which was used to describe the diffusion-controlled adsorption kinetics at the solution surface, was derived. Different from the planar surface adsorption, the dynamic surface adsorption F(t) for the short time consists of two terms: one is the same as Ward-Tordai equation and the other reflects the geometric effect caused by the spherical bubble surface. This effect should not be neglected for the very small radius of the capillary. The equilibrium surface tension γeq and the dynamic surface tension γ(t) of aqueous C10E6 [CH3(CH2)9(OCH2CH2)6OH] solution at temperature 25℃ were measuredby means of Wilhelmy plate method and maximal bubble pressure method respectively. As t→ 0, the theoreticalanalysis is in good agreement with experimental results and the dependence of γ(t) on is linear.展开更多
Accurately reconstructing rock structures using numerical methods is vital in rock mechanics research community,especially when obtaining rock samples is difficult and expensive.The reconstructed models must reflect t...Accurately reconstructing rock structures using numerical methods is vital in rock mechanics research community,especially when obtaining rock samples is difficult and expensive.The reconstructed models must reflect the comprehensive characteristics of natural rock,including mineral content and spatial distributions.This study employs the bubbling method to reconstruct granite containing multiple minerals in both two-(2D)and three-dimensions(3D),proposing a general procedure for granite structure reconstruction.The bubbling method utilizes numerous bubbles(hemispheres or spheres)of varying sizes and gradually changing properties,which are randomly overlapped to create a heterogeneous plane(2D)or space(3D).The properties of these overlapped areas are adjusted based on the sum of neighboring bubbles'properties,allowing specific regions with extreme properties to be selected and intercepted to form the desired mineral shapes.The results demonstrate that the reproduced granite samples can accurately exhibit the mineral distributions and sizes of real granite,quantified by fractal dimension(D)and the hourglass parameter(V_(Sum)=V_(Total)).The proposed method is also suitable for reconstructing anisotropic granite models,with anisotropy described by a fitted elliptic curve derived from ratios between directional mineral sizes and cross-sectional dimensions.Based on these findings,a series of numerical granite models with similar structures were reconstructed and tested.Results indicate that different mineral distributions significantly impact the macroscopic mechanical behaviors,but variability in numerical simulation results decreases with increasing specimen size.The compressive and tensile strength values of the reconstructed numerical models show less variation than those of natural granite specimens.This suggests that,beyond mineral distribution,other factors such as internal defects within natural granite contribute to the observed discrepancies.Additionally,the bubbling method shows great potential for modeling porous structures and offers high computational efficiency.展开更多
The falling ball method was changed to the rising ball method to determine the viscosity coefficient of liquid, study and measure the related characteristics of the oil droplets in the water, replace the traditional m...The falling ball method was changed to the rising ball method to determine the viscosity coefficient of liquid, study and measure the related characteristics of the oil droplets in the water, replace the traditional method, measure the viscosity coefficient of water. This method is innovative, simple and can effectively observe and measure the viscosity coefficient of liquid.展开更多
Based on the Cahn-Hilliard phase field model, a three-dimensional multiple-field coupling model for simulating the motion characteristics of a rising bubble in a liquid is established in a gas-liquid two-phase flow. T...Based on the Cahn-Hilliard phase field model, a three-dimensional multiple-field coupling model for simulating the motion characteristics of a rising bubble in a liquid is established in a gas-liquid two-phase flow. The gas-liquid interface motion is simulated by using a phase-field method, and the effect of the electric field intensity on bubble dynamics is studied without electric field, or with vertical electric field or horizontal electric field. Through the coupling effect of electric field and flow field, the deformation of a single rising bubble and the formation of wake vortices under the action of gravity and electric field force are studied in detail. The correctness of the results is verified by mass conservation, and the influences of different electric field directions and different voltages on the movement of bubbles in liquid are considered. The results show that the ratio of the length to axis is proportional to the strength of the electric field when the air bubble is stretched into an ellipsoid along the electric field line under the action of electrostatic gravity and surface tension. In addition, the bubble rising speed is affected by the electric field, the vertical electric field accelerates the bubble rise, and the horizontal direction slows it down.展开更多
The flotation process is a particle-hydrophobic surface-based separation technique. To improve the essential flotation steps of collision and attachment probabilities, and reduce the step of detachment probabilities b...The flotation process is a particle-hydrophobic surface-based separation technique. To improve the essential flotation steps of collision and attachment probabilities, and reduce the step of detachment probabilities between air bubbles and hydrophobic particles, a selectively designed cavitation venturi tube combined with a static mixer can be used to generate very high numbers of pico and nano bubbles in a flotation column. Fully embraced by those high numbers of tiny bubbles, hydrophobic particles readily attract the tiny bubbles to their surfaces. The results of column flotation of Pittsburgh No. 8 seam coal are obtained in a 5.08 cm ID and 162 cm height flotation column equipped with a static mixer and cavitation venturi tube, using kerosene as collector and MIBC as frother. Design of the experimental procedure is combined with a statistical two-stepwise analysis to determine the optimal operating conditions for maximum recovery at a specified grade. The effect of independent variables on the responses has been explained. Combustible material recovery of 85–90% at clean coal product of 10–11% ash is obtained from feed of 29.6% ash, with a much-reduced amount of frother and collector than that used in conventional column flotation. The column flotation process utilizing pico and nano bubbles can also be extended to the lower limit and upper limit of particle size ranges, minus 75 lm and 300–600 lm, respectively, for better recovery.展开更多
The effects of streaks on boundary layer transition depend on the initial amplitude of T-S waves introduced to excite the transition. This problem was studied in a flat-plate boundary layer in water tunnel by using hy...The effects of streaks on boundary layer transition depend on the initial amplitude of T-S waves introduced to excite the transition. This problem was studied in a flat-plate boundary layer in water tunnel by using hydrogen bubble method. Three T-S wave initial amplitudes were tested. The results show that both narrow and wide-spacing streaks depress the transition excited by T-S waves with lower initial amplitude. However, when transition is excited by T-S waves of higher initial amplitude, the narrow-spacing streaks depress the transition, while the wide-spacing streaks promote the transition. Futrther the underlying mechanisms were also analyzed.展开更多
The bubble packing method can generate high-quality node sets in simple and complex domains.However,its efficiency remains to be improved.This study is a part of an ongoing effort to introduce several acceleration sch...The bubble packing method can generate high-quality node sets in simple and complex domains.However,its efficiency remains to be improved.This study is a part of an ongoing effort to introduce several acceleration schemes to reduce the cost of simulation.Firstly,allow the viscosity coefficient c in the bubble governing equations to change according the coordinate of the bubble which are defined separately as odd and normal bubbles,and meanwhile with the saw-shape relationship with time or iterations.Then,in order to relieve the over crowded initial bubble placement,two coefficients w1 and w2 are introduced to modify the insertion criterion.The range of those two coefficients are discussed to be w1=1,w2∈[0.5,0.8].Finally,a self-adaptive termination condition is logically set when the stable system equilibrium is achieved.Numerical examples illustrate that the computing cost can significantly decrease by roughly 80%via adopting various combination of proper schemes(except the uniform placement example),and the average qualities of corresponding Delaunay triangulation substantially exceed 0.9.It shows that those strategies are efficient and can generate a node set with high quality.展开更多
In this paper, the equilibrium surface tension and the dynamic surface tension of aqueous Triton X-100 solution at temperature 25 ℃ were measured by means of Wilhelmy plate method and maximal bubble pressure method r...In this paper, the equilibrium surface tension and the dynamic surface tension of aqueous Triton X-100 solution at temperature 25 ℃ were measured by means of Wilhelmy plate method and maximal bubble pressure method respectively. The determined critical micellar concentration（cmc） of Triton X-100 at 25 ℃ is (2.2×10-4) mol/dm3. The adsorption mechanics of Triton X-100 at air/solution was determined. For the submicellar concentrations it is diffusion-controlled. The diffusion coefficient was calculated from the experimental data in the range of short limit. In the range of long time adsorption, the subsurface concentration is fitted from the measured dynamic surface tensions.展开更多
In China,marine natural gas hydrate(NGH)resources are mainly distributed in the deepwater areas of 300-3000 m deep in the coastal continental shelf,and they are characterized by weak cementation and non-diagenesis.In ...In China,marine natural gas hydrate(NGH)resources are mainly distributed in the deepwater areas of 300-3000 m deep in the coastal continental shelf,and they are characterized by weak cementation and non-diagenesis.In order to test and study this type of NGH,it is necessary to prepare samples quickly in situ in large quantities.At present,the commonly used preparation technologies(e.g.stirring method,spraying method and bubbling method)are defective with slow generation and low gas storage density.In view of this,the 1062 L rapid non-diagenetic NGH preparation kettle was designed and developed independently.Then,based on the physical properties of non-diagenetic NGH in the South China Sea,NGH preparation tests were carried out on stirring method,spraying method,bubbling method and“three-in-one”method(the combination of stirring method,spraying method and bubbling method).Temperature,pressure,resistivity and reaction time in the process of test were tested,and NGH generation situations and preparation efficiency of different preparation processes were analyzed and compared.And the following research results were obtained.First,in the process of NGH preparation by stirring method,spraying method and bubbling method,respectively,the generated NGH increases slowly and spreads the whole liquid level gradually.Second,inducing period is obvious in the preparation process by the stirring method,but not obvious by the spraying method,the bubbling method and the“three-in-one”method.Third,in the process of NGH preparation by stirring method,spraying method,bubbling method and“three-in-one”method,the resistivity increases as the reaction goes,and its change trend is basically accordant with the NGH preparation rate.Fourth,the preparation cycle of NGH by“three-in-one”method is greatly shorter than that by single preparation method.The preparation time by stirring method,spraying method and bubbling method is about 5.14 times,3.59 times and 3.16 times that of“three-in-one”method respectively.In conclusion,the 1062 L rapid NGH preparation kettle developed in this paper can prepare marine non-diagenetic NGH samples quickly in situ.And compared with single preparation method,“three-in-one”method is much higher in NGH preparation efficiency.展开更多
The boundary integral method（BIM） is used to simulate the 3-D gas bubble, generated within the two bubble pulsation periods in proximity to a free surface in an inviscid, incompressible and irrotational flow. The pr...The boundary integral method（BIM） is used to simulate the 3-D gas bubble, generated within the two bubble pulsation periods in proximity to a free surface in an inviscid, incompressible and irrotational flow. The present method is well validated by comparing the calculated shapes of the bubble and the free surface with both the experimental results and the numerical ones obtained by the Axisymmetric BIM code. The expansion, the collapse of the gas bubble and the further evolution of the rebounding non-spherical bubble are simulated. The various variation patterns of the free surface spike and the bubble centroid for different standoff distances, the buoyancy parameters and the strength parameters are obtained to reveal the nonlinear interaction between the bubble and the free surface. The amplitude of the second maximum bubble volume and the four typical patterns of the bubble jet and the free surface spike are examined in the context of the standoff distance. The large buoyancy is used to elevate the spray dome rather than the free surface spike.展开更多
基金funded by the National Key R&D Program of China(Grant No.2022YFC2903904)the National Natural Science Foundation of China(Grant Nos.51904057 and U1906208).
文摘Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.
基金Supported by the Scientific Research Foundation of the State Education Ministry for the Returned Overseas Chinese Scholars (D4200111).
文摘In studying the diffusion-controlled adsorption kinetics of aqueous surfactant solutions at the air/solution surface by means of the maximal bubble pressure method, Fick's diffusion equation for a sphere should be used. In this paper the equation was solved by means of Laplace transformation under different initial and boundary conditions. The dynamic surface adsorption F(t) for a surfactant solution, which was used to describe the diffusion-controlled adsorption kinetics at the solution surface, was derived. Different from the planar surface adsorption, the dynamic surface adsorption F(t) for the short time consists of two terms: one is the same as Ward-Tordai equation and the other reflects the geometric effect caused by the spherical bubble surface. This effect should not be neglected for the very small radius of the capillary. The equilibrium surface tension γeq and the dynamic surface tension γ(t) of aqueous C10E6 [CH3(CH2)9(OCH2CH2)6OH] solution at temperature 25℃ were measuredby means of Wilhelmy plate method and maximal bubble pressure method respectively. As t→ 0, the theoreticalanalysis is in good agreement with experimental results and the dependence of γ(t) on is linear.
基金funded by the National Key Research and Development Program of China(Grant No.2022YFC2903904)National Natural Science Foundation of China(Grant Nos.U1906208 and U21A20106).
文摘Accurately reconstructing rock structures using numerical methods is vital in rock mechanics research community,especially when obtaining rock samples is difficult and expensive.The reconstructed models must reflect the comprehensive characteristics of natural rock,including mineral content and spatial distributions.This study employs the bubbling method to reconstruct granite containing multiple minerals in both two-(2D)and three-dimensions(3D),proposing a general procedure for granite structure reconstruction.The bubbling method utilizes numerous bubbles(hemispheres or spheres)of varying sizes and gradually changing properties,which are randomly overlapped to create a heterogeneous plane(2D)or space(3D).The properties of these overlapped areas are adjusted based on the sum of neighboring bubbles'properties,allowing specific regions with extreme properties to be selected and intercepted to form the desired mineral shapes.The results demonstrate that the reproduced granite samples can accurately exhibit the mineral distributions and sizes of real granite,quantified by fractal dimension(D)and the hourglass parameter(V_(Sum)=V_(Total)).The proposed method is also suitable for reconstructing anisotropic granite models,with anisotropy described by a fitted elliptic curve derived from ratios between directional mineral sizes and cross-sectional dimensions.Based on these findings,a series of numerical granite models with similar structures were reconstructed and tested.Results indicate that different mineral distributions significantly impact the macroscopic mechanical behaviors,but variability in numerical simulation results decreases with increasing specimen size.The compressive and tensile strength values of the reconstructed numerical models show less variation than those of natural granite specimens.This suggests that,beyond mineral distribution,other factors such as internal defects within natural granite contribute to the observed discrepancies.Additionally,the bubbling method shows great potential for modeling porous structures and offers high computational efficiency.
文摘The falling ball method was changed to the rising ball method to determine the viscosity coefficient of liquid, study and measure the related characteristics of the oil droplets in the water, replace the traditional method, measure the viscosity coefficient of water. This method is innovative, simple and can effectively observe and measure the viscosity coefficient of liquid.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51661020,11504149,and 11364024)the Postdoctoral Science Foundation of China(Grant No.2014M560371)the Funds for Distinguished Young Scientists of Lanzhou University of Technology,China(Grant No.J201304)
文摘Based on the Cahn-Hilliard phase field model, a three-dimensional multiple-field coupling model for simulating the motion characteristics of a rising bubble in a liquid is established in a gas-liquid two-phase flow. The gas-liquid interface motion is simulated by using a phase-field method, and the effect of the electric field intensity on bubble dynamics is studied without electric field, or with vertical electric field or horizontal electric field. Through the coupling effect of electric field and flow field, the deformation of a single rising bubble and the formation of wake vortices under the action of gravity and electric field force are studied in detail. The correctness of the results is verified by mass conservation, and the influences of different electric field directions and different voltages on the movement of bubbles in liquid are considered. The results show that the ratio of the length to axis is proportional to the strength of the electric field when the air bubble is stretched into an ellipsoid along the electric field line under the action of electrostatic gravity and surface tension. In addition, the bubble rising speed is affected by the electric field, the vertical electric field accelerates the bubble rise, and the horizontal direction slows it down.
基金provided by West Virginia State Coal and Energy Research Bureau (CERB)the Department of Mining Engineering,West Virginia University
文摘The flotation process is a particle-hydrophobic surface-based separation technique. To improve the essential flotation steps of collision and attachment probabilities, and reduce the step of detachment probabilities between air bubbles and hydrophobic particles, a selectively designed cavitation venturi tube combined with a static mixer can be used to generate very high numbers of pico and nano bubbles in a flotation column. Fully embraced by those high numbers of tiny bubbles, hydrophobic particles readily attract the tiny bubbles to their surfaces. The results of column flotation of Pittsburgh No. 8 seam coal are obtained in a 5.08 cm ID and 162 cm height flotation column equipped with a static mixer and cavitation venturi tube, using kerosene as collector and MIBC as frother. Design of the experimental procedure is combined with a statistical two-stepwise analysis to determine the optimal operating conditions for maximum recovery at a specified grade. The effect of independent variables on the responses has been explained. Combustible material recovery of 85–90% at clean coal product of 10–11% ash is obtained from feed of 29.6% ash, with a much-reduced amount of frother and collector than that used in conventional column flotation. The column flotation process utilizing pico and nano bubbles can also be extended to the lower limit and upper limit of particle size ranges, minus 75 lm and 300–600 lm, respectively, for better recovery.
基金supported by the National Natural Science Foundation of China (11072017)
文摘The effects of streaks on boundary layer transition depend on the initial amplitude of T-S waves introduced to excite the transition. This problem was studied in a flat-plate boundary layer in water tunnel by using hydrogen bubble method. Three T-S wave initial amplitudes were tested. The results show that both narrow and wide-spacing streaks depress the transition excited by T-S waves with lower initial amplitude. However, when transition is excited by T-S waves of higher initial amplitude, the narrow-spacing streaks depress the transition, while the wide-spacing streaks promote the transition. Futrther the underlying mechanisms were also analyzed.
基金National Natural Science Foundation of China(No.11071196,90916027).
文摘The bubble packing method can generate high-quality node sets in simple and complex domains.However,its efficiency remains to be improved.This study is a part of an ongoing effort to introduce several acceleration schemes to reduce the cost of simulation.Firstly,allow the viscosity coefficient c in the bubble governing equations to change according the coordinate of the bubble which are defined separately as odd and normal bubbles,and meanwhile with the saw-shape relationship with time or iterations.Then,in order to relieve the over crowded initial bubble placement,two coefficients w1 and w2 are introduced to modify the insertion criterion.The range of those two coefficients are discussed to be w1=1,w2∈[0.5,0.8].Finally,a self-adaptive termination condition is logically set when the stable system equilibrium is achieved.Numerical examples illustrate that the computing cost can significantly decrease by roughly 80%via adopting various combination of proper schemes(except the uniform placement example),and the average qualities of corresponding Delaunay triangulation substantially exceed 0.9.It shows that those strategies are efficient and can generate a node set with high quality.
文摘In this paper, the equilibrium surface tension and the dynamic surface tension of aqueous Triton X-100 solution at temperature 25 ℃ were measured by means of Wilhelmy plate method and maximal bubble pressure method respectively. The determined critical micellar concentration（cmc） of Triton X-100 at 25 ℃ is (2.2×10-4) mol/dm3. The adsorption mechanics of Triton X-100 at air/solution was determined. For the submicellar concentrations it is diffusion-controlled. The diffusion coefficient was calculated from the experimental data in the range of short limit. In the range of long time adsorption, the subsurface concentration is fitted from the measured dynamic surface tensions.
基金supported by the National Key R&D Program of China“Innovative technologies for test of marine natural gas hydrates through solid fluidization”(No.:2016YFC0304008)National Key R&D Program of China“Technologies and processes for dual-gradient drilling system with riser inflation”(No.:2018YFC0310203)+1 种基金the Medium-and Long-term Development Strategy Research Project of Chinese Academy of Engineering for Engineering Science and Technology“Research on deep-sea natural gas hydrate development strategies,2035”(No.:2017-ZCQ-5)the Fundamental Research for Application Projects of Sichuan Province“Researches on mechanisms and application technologies for the largest and fastest natural gas hydrate preparation in the world”(No.:2019YJ0351).
文摘In China,marine natural gas hydrate(NGH)resources are mainly distributed in the deepwater areas of 300-3000 m deep in the coastal continental shelf,and they are characterized by weak cementation and non-diagenesis.In order to test and study this type of NGH,it is necessary to prepare samples quickly in situ in large quantities.At present,the commonly used preparation technologies(e.g.stirring method,spraying method and bubbling method)are defective with slow generation and low gas storage density.In view of this,the 1062 L rapid non-diagenetic NGH preparation kettle was designed and developed independently.Then,based on the physical properties of non-diagenetic NGH in the South China Sea,NGH preparation tests were carried out on stirring method,spraying method,bubbling method and“three-in-one”method(the combination of stirring method,spraying method and bubbling method).Temperature,pressure,resistivity and reaction time in the process of test were tested,and NGH generation situations and preparation efficiency of different preparation processes were analyzed and compared.And the following research results were obtained.First,in the process of NGH preparation by stirring method,spraying method and bubbling method,respectively,the generated NGH increases slowly and spreads the whole liquid level gradually.Second,inducing period is obvious in the preparation process by the stirring method,but not obvious by the spraying method,the bubbling method and the“three-in-one”method.Third,in the process of NGH preparation by stirring method,spraying method,bubbling method and“three-in-one”method,the resistivity increases as the reaction goes,and its change trend is basically accordant with the NGH preparation rate.Fourth,the preparation cycle of NGH by“three-in-one”method is greatly shorter than that by single preparation method.The preparation time by stirring method,spraying method and bubbling method is about 5.14 times,3.59 times and 3.16 times that of“three-in-one”method respectively.In conclusion,the 1062 L rapid NGH preparation kettle developed in this paper can prepare marine non-diagenetic NGH samples quickly in situ.And compared with single preparation method,“three-in-one”method is much higher in NGH preparation efficiency.
基金supported by the National Natural Science Foun-dation of China(Grant Nos.51221961,51279030)the National Key Basic Research Development Program of China(973 Pro-gram,Grant Nos.2013CB036101,2010CB832704)the Fundamental Research Funds for the Central Universities(Grant No.L2012016)
文摘The boundary integral method（BIM） is used to simulate the 3-D gas bubble, generated within the two bubble pulsation periods in proximity to a free surface in an inviscid, incompressible and irrotational flow. The present method is well validated by comparing the calculated shapes of the bubble and the free surface with both the experimental results and the numerical ones obtained by the Axisymmetric BIM code. The expansion, the collapse of the gas bubble and the further evolution of the rebounding non-spherical bubble are simulated. The various variation patterns of the free surface spike and the bubble centroid for different standoff distances, the buoyancy parameters and the strength parameters are obtained to reveal the nonlinear interaction between the bubble and the free surface. The amplitude of the second maximum bubble volume and the four typical patterns of the bubble jet and the free surface spike are examined in the context of the standoff distance. The large buoyancy is used to elevate the spray dome rather than the free surface spike.
