Analysis of impact pressure,rock-breaking effect,and ground vibration induced by the disposable CO_(2)fracturing tube

The technology of expansion fracturing with liquid CO_(2)(EFLCO_(2))has attracted increasing attention due to reduced vibration and damage.The disposable fracturing tube has been developed and is gradually replacing the Cardox tube.However,there is a lack of impact pressure testing of disposable tubes under real working conditions,selection of gas explosion design parameters,and systematic analysis of blasting vibration.This limitation has constrained the widespread application of disposable fracturing tubes in engineering.A joint monitoring of the pressure-time curves in the disposable tubes and boreholes was conducted.The rock-breaking effect of varying hole spacing parameters in the EFLCO_(2)design was analyzed,and a systematic study was carried out on the vibration peak value,frequency,and energy characteristics.The results show that(1)the pressure distribution characteristics,stress peak value,and duration in the disposable tubes are different from those of Cardox tubes,which show multi-peak distribution,low-pressure peak value,and short duration.The correlation between the pressure in the disposable tube,filling pressure,and liquid CO_(2)weight is established,and a theoretical calculation method for the borehole wall pressure is proposed;(2)The hole spacing in rocks of different hardness is suggested;and(3)At the same scale distance,the peak particle velocity(PPV)caused by EFLCO_(2)(PPVCO_(2))is significantly smaller than that caused by blasting(PPVexplosive).The ratio of PPVexplosive to PPVCO_(2)is a power function related to scale distance,and a distance-related zonality exist in this relationship.The frequency composition of the vibration signal caused by EFLCO_(2)is relatively simple with a narrow frequency band.Its PPV and energy are mainly concentrated in the low-frequency band.This research contributes to the optimization of disposable fracturing tubes,gas explosion design,and vibration hazard control.

A Review on Vibration Control of Multiple Cylinders Subjected to FlowInduced Vibrations

The fatigue damage caused by flow-induced vibration(FIV)is one of the major concerns for multiple cylindrical structures in many engineering applications.The FIV suppression is of great importance for the security of many cylindrical structures.Many active and passive control methods have been employed for the vibration suppression of an isolated cylinder undergoing vortex-induced vibrations(VIV).The FIV suppression methods are mainly extended to the multiple cylinders from the vibration control of the isolated cylinder.Due to the mutual interference between the multiple cylinders,the FIV mechanism is more complex than the VIV mechanism,which makes a great challenge for the FIV suppression.Some efforts have been devoted to vibration suppression of multiple cylinder systems undergoing FIV over the past two decades.The control methods,such as helical strakes,splitter plates,control rods and flexible sheets,are not always effective,depending on many influence factors,such as the spacing ratio,the arrangement geometrical shape,the flow velocity and the parameters of the vibration control devices.The FIV response,hydrodynamic features and wake patterns of the multiple cylinders equipped with vibration control devices are reviewed and summarized.The FIV suppression efficiency of the vibration control methods are analyzed and compared considering different influence factors.Further research on the FIV suppression of multiple cylinders is suggested to provide insight for the development of FIV control methods and promote engineering applications of FIV control methods.

Nonplanar flow-induced vibrations of a cantilevered PIP structure system concurrently subjected to internal and cross flows

Pipe-in-pipe(PIP)structures are widely used in offshore oil and gas pipelines to settle thermal insulation issues.A PIP structure system usually consists of two concentric pipes and one softer layer for thermal insulation consideration.The total response of the system is related to the dynamics of both pipes and the interactions between these two concentric pipes.In the current work,a theoretical model for flow-induced vibrations of a PIP structure system is proposed and analyzed in the presence of an internal axial flow and an external cross flow.The interactions between the two pipes are modeled by a linear distributed damper,a linear distributed spring and a nonlinear distributed spring along the pipe length.The unsteady hydrodynamic forces due to cross flow are modeled by two distributed van der Pol wake oscillators.The nonlinear partial differential equations for the two pipes and the wake are further discretized by the aid of Galerkin’s technique,resulting in a set of ordinary differential equations.These ordinary differential equations are further numeri cally solved by using a fourth-order Runge-Kutta integration algorithm.Phase portraits,bifurcation diagrams,an Argand diagram and oscillation shape diagrams are plotted,showing the existence of a lock-in phenomenon and figure-of-eight trajectory.The PIP system subjected to cross flow displays some interesting dynamical behaviors different from that of a single-pipe structure.

Flow-induced Noise and Vibration Analysis of a Piping Elbow with/without a Guide Vane

The effect of a guide vane installed at the elbow on flow-induced noise and vibration is investigated in the range of Reynolds numbers from 1.70×10^5 to 6.81×10^5, and the position of guide vane is determined by publications. The turbulent flow in the piping elbow is simulated with large eddy simulation （LES）. Following this, a hybrid method of combining LES and Lighthill＇s acoustic analogy theory is used to simulate the hydrodynamic noise and sound sources are solved as volume sources in code Actran. In addition, the flow-induced vibration of the piping elbow is investigated based on a fluid-structure interaction （FSI） code. The LES results indicate that the range of vortex zone in the elbow without the guide vane is larger than the case with the guide vane, and the guide vane is effective in reducing flow-induced noise and vibration in the 90° piping elbow at different Reynolds numbers.

Numerical Study on Flow-Induced Vibration of Ejector Structure

High-speed airflow in wind tunnel tests usually causes dramatic vibration of ejector structure,which may lead to fatigue and even destruction of the wind tunnel.Therefore,analyzing and solving the flow-induced vibration problem is a tough and indispensable part of the wind tunnel security design.In this paper,taking a kind of two-stage ejector as the study object,multiple numerical simulation methods are adopted in order to carry out research on the analysis technique of the flow-induced vibration characteristics of ejector structure.Firstly,the structural dynamics characteristic is analyzed by using the ejector structural dynamics numerical model,which is built on the basis of finite element method.Secondly,the complex flow phenomenon is explored applying numerical fluid-dynamics model of the inner flow field of the ejector,which is constructed on the basis of finite volume method.Finally,based on the two numerical models above,the vibration response of the ejector structure induced by the high-speed airflow is computed via the fluid-solid coupling technique.The comparison of the simulation results with the actual vibration test indicates that these numerical simulation methods can accurately figure out the rule of flow-induced vibration of ejectors.

Prediction of Streamwise Flow-Induced Vibration of A Circular Cylinder in the First Instability Range

The streamwise flow-induced vibration of a circular cylinder with symmetric vortex shedding in the first instability range is investigated, and a wake oscillator model for the dynamic response prediction is proposed. An approach is applied to calibrate the empirical parameters in the present model; the numerical and experimental results are compared to validate the proposed model. It can be found that the present prediction model is accurate and sufficiently simple to be easily applied in practice.

Fully coupled flow-induced vibration of structures under small deformation with GMRES method

Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual （GMRES） method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GiViRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.

Passive Control of Flow-Induced Vibration(FIV)by Helical Strakes for Two Staggered Flexible Cylinders

Helical strake is a widely-used device for passive flow-induced vibration(FIV)control of cylindrical structures.It is omnidirectional and can effectively reduce FIV response amplitude.Studies on the passive FIV control for cylindrical structures are mainly concerned with a single isolated cylinder,while the influence of wake interference between multiple cylinders on FIV suppression devices is less considered up to now.In engineering applications,multiple flexible cylinders with large aspect ratios can be subjected to complex flow forces,and the effects of wake interference are obvious.The FIV suppression effect of helical strake of a common configuration(17.5D pitch and 0.25D height,where D is the cylinder diameter)in two staggered cylinders system is still unknown.This paper systematically studied the FIV response of multiple cylinders system fitted with the helical strakes by model tests.The relative spatial position of the two cylinders is fixed at S=3.0D and T=8.0D,which ensures the cylindrical structures in the flow interference region.The experimental results show that the helical strakes effectively reduce the FIV response on staggered upstream cylinder,and the suppression efficiency is barely affected by the smooth or straked downstream cylinder.The corresponding FIV suppression efficiency on the downstream cylinder is remarkably reduced by the influence of the upstream wake flow.The wake-induced vibration(WIV)phenomenon is not observed on the staggered downstream cylinder,which normally occurs on the downstream straked cylinder in a tandem arrangement.

Recent advancement of flow-induced piezoelectric vibration energy harvesting techniques:principles,structures,and nonlinear designs

Energy harvesting induced from flowing fluids(e.g.,air and water flows)is a well-known process,which can be regarded as a sustainable and renewable energy source.In addition to traditional high-efficiency devices(e.g.,turbines and watermills),the micro-power extracting technologies based on the flow-induced vibration(FIV)effect have sparked great concerns by virtue of their prospective applications as a self-power source for the microelectronic devices in recent years.This article aims to conduct a comprehensive review for the FIV working principle and their potential applications for energy harvesting.First,various classifications of the FIV effect for energy harvesting are briefly introduced,such as vortex-induced vibration(VIV),galloping,flutter,and wake-induced vibration(WIV).Next,the development of FIV energy harvesting techniques is reviewed to discuss the research works in the past three years.The application of hybrid FIV energy harvesting techniques that can enhance the harvesting performance is also presented.Furthermore,the nonlinear designs of FIV-based energy harvesters are reported in this study,e.g.,multi-stability and limit-cycle oscillation(LCO)phenomena.Moreover,advanced FIV-based energy harvesting studies for fluid engineering applications are briefly mentioned.Finally,conclusions and future outlook are summarized.

Investigation on two-phase flow-induced vibrations of a piping structure with an elbow

The dynamic behaviors of a horizontal piping structure with an elbow due to the two-phase flow excitation are experimentally investigated.The effects of flow patterns and superficial velocities on the pressure pulsations and vibration responses are evaluated in detail.A strong partition coupling algorithm is used to calculate the flow-induced vibration(FIV)responses of the pipe,and the theoretical values agree well with the experimental results.It is found that the lateral and axial vibration responses of the bend pipe are related to the momentum flux of the two-phase flow,and the vibration amplitudes of the pipe increase with an increase in the liquid mass flux.The vertical vibration responses are strongly affected by the flow pattern,and the maximum response occurs in the transition region from the slug flow to the bubbly flow.Moreover,the standard deviation(STD)amplitudes of the pipe vibration in three directions increase with an increase in the gas flux for both the slug and bubbly flows.The blockage of liquid slugs at the elbow section is found to strengthen the vibration amplitude of the bend pipe,and the water-blocking phenomenon disappears as the superficial gas velocity increases.

Prediction Model of Kinetic Energy Conversion of Tandem Dual-Oscillator Based on Flow-Induced Vibration Experiment

Flow-induced vibration energy harvesting devices typically use an elastically supported body immersed in an oncoming flow to convert the sea and river current's hydrokinetic energy into electrical energy.The proportion of energy the device collects is greatly influenced by parameters such as the water flow velocity,spacing between device components,structure size,and damping coefficient.For parameter optimization and performance predictions of flow-induced vibration energy harvesting devices,we train a model of the power harvesting efficiency under different damping ratios,stiffnesses,spacing ratios,and reduced velocities based on experimental data.To improve the prediction accuracy,a feedforward network structure is optimized by using the topological evolutionary algorithm and a radial basis function network.Comparative analysis reveals that the radial basis function network model provides the best agreement with the experimental results and realizes accurate predictions of the power harvested by a dual-oscillator system in the vortex-induced vibration,transition region,and galloping.The prediction results show that the model's maximum power harvesting efficiency occurs in the vortex-induced vibration.The efficiency increases and then decreases with increasing stiffness and reduced velocity in this phase;an increase in the spacing ratio causes the effi-ciency to decrease and then increase;finally,increasing the damping ratio enhances the efficiency.The device achieves maximum power harvesting efficiency at a reduced velocity of U_(r)=4.11.The proposed model effectively predicts the maximum efficiency and the corresponding damping ratio and stiffness of the vortex-induced vibration and galloping,providing a new method for predicting tandem dual-oscillator hydrodynamic power conversion in flow-induced vibration.

Flow-Induced Vibration Fatigue Damage of A Pair of Flexible Cylinders in A Staggered Array

Flow-induced vibration(FIV)of a group of long,flexible cylinders involves a complex interaction between fluid and structures.Although a substantial number of studies have been devoted to assessing FIV response behaviours,fatigue damage features of staggered flexible cylinders are not fully understood.Moreover,the wake-induced flutter constitutes an intricate hydrodynamic behaviour that frequently occurs when one cylinder is in the vicinity of another one.Unfortunately,existing studies on the fatigue damage caused by wake-induced flutter are incapable of achieving better results.This paper,therefore,estimates the FIV fatigue damage of two staggered flexible cylinders with an aspect ratio of 350 and a mass ratio of 1.90 based on normal S−N curves according to Det Norske Veritas(DNV)regulations.Twelve staggered cases(cross-flow spacing ratios of 2.0,3.0,4.0,and 6.0 and in-line spacing ratios of 4.0,6.0,and 8.0)are discussed for comparison,and fatigue damage caused by wake-induced flutter is thoroughly considered.Fatigue damage results indicate that the variation of the cross-flow(CF)spacing ratio has a greater influence than that of the in-line(IL)spacing ratio on the CF fatigue damage of the upstream cylinder.Lower IL fatigue damages of the upstream cylinder are observed when reduced velocity V_(r)≥15.03 due to the wake flow patterns with different IL spacing ratios.Moreover,wake interference,especially wake-induced flutter,predominates the fatigue damage characteristics of the downstream cylinder.When V_(r)=8.77−11.27,wake-induced flutter enhances the IL fatigue damage of the downstream cylinder and slightly affects that of the upstream body.Furthermore,wake-induced flutter causes considerable IL fatigue damage disparity between the two staggered cylinders by suppressing the IL fatigue damage of the upstream cylinder when V_(r)≥20.04.

Flow-Induced Vibration of Four Cantilever Cylinders Arranged in A Square Configuration

Flow-induced vibration(FIV)of four separately mounted cantilever cylinders are experimentally investigated in a water flume.The four cylinders with top ends screwed vertically into a turntable platform are subjected to uniform flows with Reynolds number ranging from 3840 to 16520.A non-intrusive measurement with high-speed cameras is employed to simultaneously capture the time-varying in-line and cross-flow vibrations in the reduced velocity range of 3.0-12.9.Experimental results highlight the continuous adjustment of flow regime caused by the spatial-temporal alteration of cylinders.Consequently,the space-time varying flow interference contributes to the occurrence of multiple response frequencies.The transition from a dominant frequency to a broad-band response illustrates the enhancement of wake interference.The combination of wake flow interactions results in the irregular oscillation trajectories and the appearance of a response trough with the associated switching in vortex shedding mode.The dual-resonance phenomenon is observed in the four cylinders due to the complicated wake-structure interaction.The greatest mechanical energy possessed by the four cylinders in an in-line square arrangement is mainly resulted from the downstream cylinders,signifying the positive role of wake excitation in extracting hydrokinetic energy from ambient flow.

Noninvasive Flow Regime Identification for Wet Gas Flow Based on Flow-induced Vibration

A novel noninvasive approach, based on flow-induced vibration, to the online flow regime identification for wet gas flow in a horizontal pipeline is proposed. Research into the flow-induced vibration response for the wet gas flow was conducted under the conditions of pipe diameter 50 mm, pressure from 0.25 MPa to 0.35 MPa, Lockhart-Martinelli parameter from 0.02 to 0.6, and gas Froude Number from 0.5 to 2.7. The flow-induced vibration signals were measured by a transducer installed on outside wall of pipe, and then the normalized energy features from different frequency bands in the vibration signals were extracted through 4-scale wavelet package transform. A "binary tree" multi-class support vector machine(MCSVM) classifier, with the normalized feature vector as inputs, and Gaussian radial basis function as kernel function, was developed to identify the three typical flow regimes including stratified wavy flow, annular mist flow, and slug flow for wet gas flow. The results show that the method can identify effectively flow regimes and its identification accuracy is about 93.3%. Comparing with the other classifiers, the MCSVM classifier has higher accuracy, especially under the case of small samples. The noninvasive measurement approach has great application prospect in online flow regime identification.

Flow-Induced Stream-Wise Vibration of Circular Cylinders

Results from a series of studies on the stream-wise vibration of a circular cylinder verifying Japan Society of Mechanical Engineers Standard S012-1998, Guideline for Evaluation of Flow-induced Vibration of a Cylindrical Structure in a Pipe, are summarized and discussed in this paper. Experiments were carried out in a water tunnel and in a wind tunnel using a two-dimensional cylinder model elastically supported at both ends of the cylinder and a cantilevered cylinder model with a finite span length that was elastically supported at one end. These cylinder models were allowed to vibrate with one degree of freedom in the stream-wise direction. In addition, we adopted a cantilevered cylinder model that vibrated with two degrees of freedom in both the stream-wise and cross-flow directions under the same vibration conditions as an actual thermocouple well. The value of the Scruton number (structural damping parameter) was changed over a wide range, so as to evaluate the value of the critical Scruton number that suppressed vibration of the cylinder. For the two-dimensional cylinder, two different types of stream-wise excitations appeared in the reduced velocity range of approximately half of the resonance-reduced velocity. For the stream-wise vibration in the first excitation region, due to a symmetric vortex flow, the response amplitudes were sensitive to the Scruton number, while the shedding frequency of alternating vortex flow was locked-in to half of the Strouhal number of vibrating frequency of a cylinder in the second excitation region. In addition, the effects of the aspect ratio of a cantilevered cylinder on the flow-induced vibration characteristics were clarified and compared with the results of a two-dimensional cylinder. When a cantilevered circular cylinder with a finite length vibrates with one degree of freedom in the stream-wise di-rection, it is found that acylinder with a small aspect ratio has a single excitation region, whereas a cylinder with a large aspect ratio has two excitation regions. Furthermore, the vibration mechanism of a symmetric vortex flow was investigated by installing a splitter plate in the wake to prevent shedding of alternating vortices. The vibration amplitude of acylinder with a splitter plate increased surprisingly more than the amplitude of a cylinder without a splitter plate. For a cantilevered cylinder vibrating with two degrees of freedom, the Lissajous figure of vibration of the first excitation region shows the trajectories of elongated elliptical shapes, and in the second excitation region, the Lissajous trajectories draw a figure “8”. The results and information from these experimental studies proved that Standard S012-1998 provides sufficient design methods for suppressing hazardous vibrations of cylinders in liquid flows.

Effects of Span Length and Additional Structure on Flow-Induced Transverse Vibration Characteristic of a Cantilevered Rectangular Prism

We consider the effects of the aspect ratio L/H (where L is the length of a prism, and H is the height of a prism normal to the flow direction) and the size of additional structures (which are a plate and a fin on the surface of a prism) on a vibration characteristic of a cantilevered rectangular prism. The present research is intended to support the analysis of energy harvesting research on the flow-induced vibration in water flow using a magnetostrictive phenomenon. The prisms are constructed from stainless steel and mounted elastically to a plate spring attached to the ceiling wall of the water tunnel. The prisms with aspect ratios of L/H ≥ 5 have reasonably identical vibration characteristics. However, the difference in the vibration characteristic appears distinctly on a rectangular prism with an aspect ratio of L/H = 2.5. The rectangular prism with an aspect ratio of L/H = 10 and a side ratio of D/H = 0.2 has a stable and large response amplitude and oscillates with a lower velocity. The length of the added plate and the size of the added fin influence the velocity of vibration onset. If the length of the added plate and fin size on the rectangular prism with D/H = 0.2 becomes large, the curve of the response amplitude shifts to that of the rectangular prism with D/H= 0.5. The response amplitude of the rectangular prism with/without plate or fin is found to be related to the second moment of area of the prism.

Investigation of the Vibration Behavior of Fluidelastic Instability in Closely Packed Square Tube Arrays

Flow-induced vibrations in heat exchanger tubes have led to numerous accidents and economic losses in the past. Fluidelastic instability is the most critical flow-induced vibration mechanism in heat exchangers. Both experimental and computational studies conducted to determine fluidelastic instability were presented in this paper. In the experiment, a water channel was built, and a closely packed normal square tube array with a pitch-to-diameter ratio of 1.28 was tested, and significant fluidelastic instability was observed. A numerical model adopting large-eddy simulation and moving mesh was established using ANSYS CFX, and results showed good agreement with the experimental findings. The vibration behaviors of fluidelastic instability were discussed, and results showed that the dominant vibration direction of the tubes changed from streamwise to transverse beyond a critical velocity. A 180° phase lag between adjacent tubes was observed in both the experiment and simulations. Normal and rotated square array cases with pitch-to-diameter ratios of 1.28 and 1.5 were also simulated. The results of this study provide better insights into the vibration characteristics of a square tube array and will help improve the fundamental research and safety design of heat exchangers.

Design Optimization of Shell and Tube Heat Exchanger by Vibration Analysis

In this paper a simplified approach to optimize the design of Shell Tube Heat Exchanger [STHE] by flow induced vibration analysis [FVA] is presented. The vibration analysis of STHE helps in achieving optimization in design by prevention of tube failure caused due to flow induced vibration. The main reason for tube failure due to flow induced vibration is increased size of STHE. It is found that in case of increased size of STHE, the surface area and number of tubes increases, thus the understanding and analysis of vibration becomes a very difficult task. Again it is found that flow induced vibration analysis is considered as an integral part of mechanical & thermal design of STHE. The detailed design, fabrication, testing and analysis work was carried out at Alfa Laval (India), Ltd., Pune-10.

Flow-Induced Acoustic Resonances in Exhaust Gas Economizer Tube Banks

To investigate the conditions under which acoustic resonances occur, staggered arrays of closely spaced rigid tubes were tested in a wind tunnel under various flow velocities. The author investigated the Strouhal numbers at which flow periodicities occur, the relation between these Strouhal numbers and those at which acoustic resonances occur, and the effects of Reynolds number and longitudinal tube spacings on the occurrence of acoustic resonance. This investigation showed the following： （1） Acoustic resonance can be produced at a frequency well removed from that of vortex shedding. The results also show evidence of vortex shedding and acoustic resonance existing simultaneously but at different frequencies. （2） Acoustic resonance behavior is consistent with that of a self-excited system. （3） A new model of this phenomenon provides an improved procedure for avoiding acoustic resonances in closely spaced tube banks.

Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory

The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.