The Numerical Simulation of Collapse Pressure and Boundary of the Cavity Cloud in Venturi

The idea that the collapse proceeds from the outer boundary of the cavity cloud towards its center for the ultrasonic cavitation proposed by Hasson and Morch in 1980s is further developed for calculating the collapse pressure and boundaries of cavity cloud at the collapse stage of bubbles for hydraulic cavitation flow in Venturi in present research. The numerical simulation is carried out based on Gilmore＇s eouations of bubble dynamics, which take account of the compressibility of fluid besides the viscosity and interfacial tension. The collapse of the cavity cloud is considered to proceed layer by layer from the outer cloud towards its inner part. The simulation results indicate that thepredicted boundaries of the cavity cloudat the collapse stage agree.well with the exPerimental ones.It is also found that the maximum collapse pressure of the cavity cloud is several times as high as the collapse pressure of outside boundary, and it is located at a point in the axis, where the cavity cloud disappears completely. This means that a cavity cloud has higher collapse pressure or strength than that of a single bubble due to the interactions of the bubbles. The effects of operation and structural parameters on the collapse pressure are also analyzed in detail.

Prediction of Collapse Pressure of Submarine Pipelines in A Wide Range of Diameter–Thickness Ratio

Submarine pipelines play an important role in offshore oil and gas development.A touchy issue in pipeline design and application is how to avoid the local collapse of pipelines under external pressure.The pipe diameter-thickness ratio D/t is one of the key factors that determine the local critical collapse pressure of the submarine pipelines.Based on the pipeline collapse experiment and finite element simulation,this paper explores the pressure-bearing capacity of the pipeline under external pressure in a wide range of diameter-thickness ratio D/t.Some interesting and important phenomena have been observed and discussed.In the range of 16<D/t<80,both DNV specification and finite element simulation can predict the collapse pressure of pipeline quite well;in the range of 10<D/t<16,the DNV specification is conservative compared with the experimental results,while the finite element simulation results are slightly larger than the experimental results.Further parameter analysis shows that compared with thin-walled pipes,improving the material grade of thick-walled pipes has higher benefits,and for thin-walled pipes,the ovality f_(0)should be controlled even more.In addition,combining the results of finite element simulation and model experiment,an empirical formula of critical collapse pressure for thick-walled pipelines is proposed,which is used to correct the error of DNV specification in the range of 10<D/t<16.

A new cable truss support system for coal roadways affected by dynamic pressure

The support of coal roadways is seriously affected by intense dynamic pressures.This can lead to problems with large deformation of the roof and the two side walls of coal roadways.Rapid convergence of the walls and roof,a high damage rate to the bolts and cables,or even abrupt roof collapse or rib spalling can occur during the service period of these coal roadways.Analyzing the main support measures used in China leads to a proposed new cable truss supporting system.Thorough study of the entire structure shows the superiority of this design for roadways suffering under dynamic pressure.A corresponding mechanical model of the rock surrounding the cable truss system is described in this paper and formulas for calculating pre-tightening forces of the truss cable,and the minimum anchoring forces,were deduced.The new support system was applied to a typical roadway affected by intensive dynamic pressure that is located in the Xinyuan Coal Mine.The results show that the largest subsidence of the roof was 97 mm,the convergence of the two sides was less than 248 mm,and the average depth of the loose,fractured layer was only 6.12 mm.This proves that the new support system is feasible and effective.

Ultimate Strength Assessment of Steel-Welded Hemispheres under External Hydrostatic Pressure

This paper focusses on steel-welded hemispherical shells subjected to external hydrostatic pressure.The experimental and numerical investigations were performed to study their failure behaviour.The model was fabricated from mild steel and made through press forming and welding.We therefore considered the effect of initial shape imperfection,variation of thickness and residual stress obtained from the actual structures.Four hemisphere models designed with R/t from 50 to 130 were tested until failure.Prior to the test,the actual geometric imperfection and shell thickness were carefully measured.The comparisons of available design codes(PD 5500,ABS,DNV-GL)in calculating the collapse pressure were also highlighted against the available published test data on steel-welded hemispheres.Furthermore,the nonlinear FE simulations were also conducted to substantiate the ultimate load capacity and plastic deformation of the models that were tested.Parametric dependence of the level of sphericity,varying thickness and residual welding stresses were also numerically considered in the benchmark studies.The structure behaviour from the experiments was used to verify the numerical analysis.In this work,both collapse pressure and failure mode in the numerical model were consistent with the experimental model.

The Spherically-Symmetric Pressure Free Collapse of the White-Black Hole

The vector model for gravitational field is a modified theory of gravitational field. In this model, the gravitational field is a vector field and its source is the gravitational mass of matter. This model predicts the existence of a new universal object after the black hole disappeared. It is named the white-black hole （or white hole） in the vector model for the gravitational field. The white- black hole has many interesting properties different from that of black hole in Einstein＇s theory of gravity. This paper presents an investigation of the spherically-symmetric pressure free collapse of a white-black hole in the vector model for gravitational field from the point of view of an observer at infinity and on its surface. The obtained results have many interesting differences compared with that in the spherically-symmetric pressure free collapse of black holes. In addition, the metric of space-time of the white-black hole in modified Eddington-Finkelstein coordinates and modified Kruskal-Szekeres coordinates are found.

Nonlinear Contact Between Inner Walls of Deep Sea Pipelines in Buckling Process

In order to study buckling propagation mechanism in deep sea pipelines, the contact between pipeline's inner walls in buckling process was studied. A two-dimensional ring model was used to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between inner walls. Based on the elastoplastic constitutive relationship and the principle of virtual work theory, the coupling effect of pipeline's nonlinear large deformation and wall contact was included in the theoretical analysis with the aid of MATLAB, and the application scope of the theoretical model was also discussed. The calculated results show that during the loading process, the change in external pressure is closely related to the distribution of section stress, and once the walls are contacting each other, the external pressure increases and then remains stable after it reaches a specific value. Without fracture, the pipeline section will stop showing deformation. The results of theoretical calculations agree well with those of numerical simulations. Finally, in order to ensure reliability and accuracy of the theoretical results, the collapse pressure and propagation pressure were both verified by numerical simulations and experiments. Therefore, the theoretical model can be used to analyze pipeline's buckling deformation and contact between pipeline's inner walls, which forms the basis for further research on three-dimensional buckling propagation.

Energy analysis of face stability of deep rock tunnels using nonlinear Hoek-Brown failure criterion

The nonlinear Hoek-Brown failure criterion was introduced to limit analysis by applying the tangent method. Based on the failure mechanism of double-logarithmic spiral curves on the face of deep rock tunnels, the analytical solutions of collapse pressure were derived through utilizing the virtual power principle in the case of pore water, and the optimal solutions of collapse pressure were obtained by using the optimization programs of mathematical model with regard of a maximum problem. In comparison with existing research with the same parameters, the consistency of change rule shows the validity of the proposed method. Moreover, parametric study indicates that nonlinear Hoek-Brown failure criterion and pore water pressure have great influence on collapse pressure and failure shape of tunnel faces in deep rock masses, particularly when the surrounding rock is too weak or under the condition of great disturbance and abundant ground water, and in this case, supporting measures should be intensified so as to prevent the occurrence of collapse.

The Collapse Intensity of Cavities and the Concentration of Free Hydroxyl Radical Released in Cavitation Flow

Enhancing the chemical reaction processes by means of the energy released in the collapse of micro bubbles or cavities in the cavitation flow is a new research area. In the previous work, a new approach of measuring concentration of free hydroxyl radicals induced in cavitation flow by using methylene blue as the indicator was developed and used to study concentration of free radical induced in Venturi cavitation flow under various experimental conditions. In the present research, the radial evolution of a cavity bubble and the corresponding collapse pressure in sonic cavitation field are obtained by solving three different bubble dynamics equations： Rayleigh equation, Rayleigh-Plesset equation and Gilmore equation. By comparing with the experimental data on the radial evolution of a cavity bubble in the literature, it is found that the predicted results by the Gilmore equation, which takes account of the compressibility of fluid in addition to the viscosity and interfacial tension, agree with the experimental ones better than those by other two equations. Moreover, the theoretically predicted collapse pressures are consistent with the concentration of the free hydroxyl radical induced in the experimental venture. Thus, the concentration of the liberated free hydroxyl radical not only influences the reaction rate but also is used as an available parameter for measuring collapse intensity of cavities.

Experimental study on the cavity evolution and liquid spurt of hydrodynamic ram

In research of the characteristics of the cavity evolution, the pressure, and the liquid spurt in hydrodynamic ram, the experiment of the high-velocity fragment impacting the water-filled container had been conducted. The relationships between the above three characteristics have been researched. The evolution of the cavity can be divided into three processes according to its shape characteristics. The first liquid spurt occurred in Process Ⅱ and the rest of it occurred in Process Ⅲ. The duration of the second liquid spurt is longer than the first liquid spurt. When the impact velocity of the fragment is less than996 m/s, the velocity of the second liquid spurt is the highest. When the velocity of the fragment is greater than 996 m/s, the velocity of the first liquid spurt is the highest. The maximum velocities of the first and second liquid spurt are 111 m/s and 94 m/s respectively. The pressure fluctuated sharply in Processes Ⅰ and Ⅲ. The maximum peak pressures in the shock and the cavity oscillation phases are15.51 MPa and 7.96 MPa respectively. The time interval of the two adjacent pressure pulses increases with the increase of the fragment velocity.

Theoretical analysis on water-inrush mechanism of concealed collapse pillars in floor

In order to study the water-inrush mechanism of concealed collapse pillars from the mechanical view, a mechanical model for water-inrush of collapse pillars has been established based on thick plate theory of elastic mechanics in this paper.By solving this model the deformation of water-resistant rock strata under the action of water pressure and the expression of critical water pressure for collapse pillar waterinrush have been obtained The research results indicate that：the boundary conditions and strength of water-resistant strata play important roles in influencing water-inrush of collapse pillars.The critical water-inrush pressure is determined by both relative thickness and absolute thickness of water-resistant strata.

Wellbore stability analysis of layered shale based on the modified Mogi-Coulomb criterion

Borehole instability was frequently encountered during shale gas drilling.Most conventional models are not applicable to layered formation's wellbore stability analysis on account of anisotropic strength characteristic.In this study,an empirical equation for predicting anisotropic strength was implemented in the Mogi–Coulomb criterion to describe variations of cohesive strength and friction angle of shale formations.A collapse pressure model and its appropriate solution method for layered shale formations were proposed.The impact of different strength criteria and rock anisotropy type on rock strength and collapse pressure was investigated.The analysis indicated that the predicted strength of our modified criterion was usually higher than the weak plane failure criteria.The collapse pressure calculated by the modified Mogi–Coulomb criterion was lower than the weakplane failure criteria.Furthermore,it was more consistent with real mud weight.Additionally,the anisotropy type of rock notably influences wellbore stability.More significant anisotropy coefficients correspond to higher strengths,which results in smaller collapse pressure values.Improper anisotropy coefficients can over-or underpredict the collapse pressure.Reasonable estimates of collapse pressure of anisotropic rocks can be made through the modified Mogi–Coulomb criterion using limited experimental data and the anisotropy rock type.