THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

Multi-Parameter Influence Analysis of Interaction Between Internal Solitary Wave and Fixed Submerged Body

To obtain the interaction characteristics between Internal solitary waves(ISWs)and submerged bodies,a three-dimensional numerical model for simulating ISWs was established in the present study based on the RANS equation.The velocity entrance method was adopted to generate the ISWs.First,the reliability of this numerical model was validated by comparing it with theoretical and literature results.Then,the influence of environmental and navigation parameters on interactions between ISWs and a fixed SUBOFF-submerged body was studied.According to research,the hydrodynamic performance of the submerged body has been significantly impacted by the ISWs when the body is nearing the central region of the wave.Besides,the pitching moment(y')will predominate when the body encounters the ISWs at a certain angle between 0°and 180°,and the lateral force is larger than the horizontal force.Additionally,the magnitude of the force acting on the body is mostly affected by the wave amplitude.The variation of the vertical force is the main way that ISWs affect the hydrodynamic performance of the bodies.The investigations and findings discussed above can serve as a guide to forecast how ISWs will interact with submerged bodies.

Feedback control and quantum error correction assisted quantum multi-parameter estimation

Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement.In this paper,a combined control scheme with feedback and quantum error correction(QEC)is proposed to achieve the Heisenberg limit in the presence of spontaneous emission,where the feedback control is used to protect a stabilizer code space containing an optimal probe state and an additional control is applied to eliminate the measurement incompatibility among three parameters.Although an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be noiseless.In addition,the control scheme in this paper has a low-dimensional code space.For the three components of a magnetic field,it can achieve the highest estimation precision with only a 2-dimensional code space,while at least a4-dimensional code space is required in the common optimal error correction protocols.

Effect of fracture fluid flowback on shale microfractures using CT scanning

The field data of shale fracturing demonstrate that the flowback performance of fracturing fluid is different from that of conventional reservoirs,where the flowback rate of shale fracturing fluid is lower than that of conventional reservoirs.At the early stage of flowback,there is no single-phase flow of the liquid phase in shale,but rather a gas-water two-phase flow,such that the single-phase flow model for tight oil and gas reservoirs is not applicable.In this study,pores and microfractures are extracted based on the experimental results of computed tomography(CT)scanning,and a spatial model of microfractures is established.Then,the influence of rough microfracture surfaces on the flow is corrected using the modified cubic law,which was modified by introducing the average deviation of the microfracture height as a roughness factor to consider the influence of microfracture surface roughness.The flow in the fracture network is simulated using the modified cubic law and the lattice Boltzmann method(LBM).The results obtained demonstrate that most of the fracturing fluid is retained in the shale microfractures,which explains the low fracturing fluid flowback rate in shale hydraulic fracturing.

Synthetic polymers:A review of applications in drilling fluids

With the growth of deep drilling and the complexity of the well profile,the requirements for a more complete and efficient exploitation of productive formations increase,which increases the risk of various complications.Currently,reagents based on modified natural polymers(which are naturally occurring compounds)and synthetic polymers(SPs)which are polymeric compounds created industrially,are widely used to prevent emerging complications in the drilling process.However,compared to modified natural polymers,SPs form a family of high-molecular-weight compounds that are fully synthesized by undergoing chemical polymerization reactions.SPs provide substantial flexibility in their design.Moreover,their size and chemical composition can be adjusted to provide properties for nearly all the functional objectives of drilling fluids.They can be classified based on chemical ingredients,type of reaction,and their responses to heating.However,some of SPs,due to their structural characteristics,have a high cost,a poor temperature and salt resistance in drilling fluids,and degradation begins when the temperature reaches 130℃.These drawbacks prevent SP use in some medium and deep wells.Thus,this review addresses the historical development,the characteristics,manufacturing methods,classification,and the applications of SPs in drilling fluids.The contributions of SPs as additives to drilling fluids to enhance rheology,filtrate generation,carrying of cuttings,fluid lubricity,and clay/shale stability are explained in detail.The mechanisms,impacts,and advances achieved when SPs are added to drilling fluids are also described.The typical challenges encountered by SPs when deployed in drilling fluids and their advantages and drawbacks are also discussed.Economic issues also impact the applications of SPs in drilling fluids.Consequently,the cost of the most relevant SPs,and the monomers used in their synthesis,are assessed.Environmental impacts of SPs when deployed in drilling fluids,and their manufacturing processes are identified,together with advances in SP-treatment methods aimed at reducing those impacts.Recommendations for required future research addressing SP property and performance gaps are provided.

Step-over of strike-slip faults and overpressure fluid favor occurrence of foreshocks:Insights from the 1975 Haicheng fore-main-aftershock sequence,China

This study analyzed and summarized in detail the spatial and temporal distributions of earthquakes,tidal responses,focal mechanisms,and stress field characteristics for the M 7.3 Haicheng earthquake sequence in February 1975.The foreshocks are related to the main fault and the conjugate faults surrounding the extension step-over in the middle.The initiation timing of the foreshock clusters and the original time of the mainshock were clearly modulated by the Earth's tidal force and coincided with the peak of dilational volumetric tidal strain.As a plausible and testable hypothesis,we proposed a fluid-driven foreshock model,by which all observed seismicity features can be more reasonably interpreted with respect to the results of existing models.Together with some other known examples,the widely existing step-over along strike-slip faults and associated conjugate faults,especially for extensional ones in the presence of deep fluids,favor the occurrence of short-term foreshocks.Although clustered seismicity with characteristics similar to those of the studied case is not a sufficient and necessary condition for large earthquakes to occur under similar tectonic conditions,it undoubtedly has a warning significance for the criticality of the main fault.Subsequent testing would require quantification of true/false positives/negatives.

Reservoir quality evaluation of the Narimba Formation in Bass Basin,Australia:Implications from petrophysical analysis,sedimentological features,capillary pressure and wetting fluid saturation

The evaluation of reservoir quality was accomplished on the Late Paleocene to Early Eocene Narimba Formation in Bass Basin,Australia.This study involved combination methods such as petrophysical analysis,petrography and sedimentological studies,reservoir quality and fluid flow units from derivative parameters,and capillary pressure and wetting fluid saturation relationship.Textural and diagenetic features are affecting the reservoir quality.Cementation,compaction,and presence of clay minerals such as kaolinite are found to reduce the quality while dissolution and secondary porosity are noticed to improve it.It is believed that the Narimba Formation is a potential reservoir with a wide range of porosity and permeability.Porosity ranges from 3.1%to 25.4%with a mean of 15.84%,while permeability ranges between 0.01 mD and 510 mD,with a mean of 31.05 mD.Based on the heterogenous lithology,the formation has been categorized into five groups based on permeability variations.Group I showed an excellent to good quality reservoir with coarse grains.The impacts of both textural and diagenetic features improve the reservoir and producing higher reservoir quality index(RQI)and flow zone indicators(FZI)as well as mostly mega pores.The non-wetting fluid migration has the higher possibility to flow in the formation while displacement pressure recorded as zero.Group II showed a fair quality reservoir with lower petrophysical properties in macro pores.The irreducible water saturation is increasing while the textural and digenetic properties are still enhancing the reservoir quality.Group III reflects lower quality reservoir with mostly macro pores and higher displacement pressure.It may indicate smaller grain size and increasing amount of cement and clay minerals.Group IV,and V are interpreted as a poor-quality reservoir that has lower RQI and FZI.The textural and digenetic features are negatively affecting the reservoir and are leading to smaller pore size and pore throat radii(r35)values to be within the range of macro,meso-,micro-,and nano pores.The capillary displacement pressure curves of the three groups show increases reaching the maximum value of 400 psia in group V.Agreement with the classification of permeability,r35 values,and pore type can be used in identifying the quality of reservoir.

Effect of bubble morphology and behavior on power consumption in non-Newtonian fluids’aeration process

Due to a prolonged operation time and low mass transfer efficiency, the primary challenge in the aeration process of non-Newtonian fluids is the high energy consumption, which is closely related to the form and rate of impeller, ventilation, rheological properties and bubble morphology in the reactor. In this perspective, through optimal computational fluid dynamics models and experiments, the relationship between power consumption, volumetric mass transfer rate(kLa) and initial bubble size(d0) was constructed to establish an efficient operation mode for the aeration process of non-Newtonian fluids. It was found that reducing the d0could significantly increase the oxygen mass transfer rate, resulting in an obvious decrease in the ventilation volume and impeller speed. When d0was regulated within 2-5 mm,an optimal kLa could be achieved, and 21% of power consumption could be saved, compared to the case of bubbles with a diameter of 10 mm.

Microscopic characteristics of tight sandstone reservoirs and their effects on the imbibition efficiency of fracturing fluids:A case study of the Linxing area,Ordos Basin

The Linxing area within the Ordos Basin exhibits pronounced reservoir heterogeneity and intricate micro-pore structures,rendering it susceptible to water-blocking damage during imbibition extraction.This study delved into the traits of tight sandstone reservoirs in the 8th member of the Shihezi Formation(also referred to as the He 8 Member)in the study area,as well as their effects on fracturing fluid imbibition.Utilizing experimental techniques such as nuclear magnetic resonance(NMR),high-pressure mercury intrusion(HPMI),and gas adsorption,this study elucidated the reservoir characteristics and examined the factors affecting the imbibition through imbibition experiments.The findings reveal that:①The reservoir,with average porosity of 8.40%and average permeability of 0.642×10^(-3)μm^(2),consists principally of quartz,feldspar,and lithic fragments,with feldspathic litharenite serving as the primary rock type and illite as the chief clay mineral;②Nano-scale micro-pores and throats dominate the reservoir,with dissolution pores and intercrystalline pores serving as predominant pore types,exhibiting relatively high pore connectivity;③Imbibition efficiency is influenced by petrophysical properties,clay mineral content,and microscopic pore structure.Due to the heterogeneity of the tight sandstone reservoir,microscopic factors have a more significant impact on the imbibition efficiency of fracturing fluids;④A comparative analysis shows that average pore size correlates most strongly with imbibition efficiency,followed by petrophysical properties and clay mineral content.In contrast,the pore type has minimal impact.Micropores are vital in the imbibition process,while meso-pores and macro-pores offer primary spaces for imbibition.This study offers theoretical insights and guidance for enhancing the post-fracturing production of tight sandstone reservoirs by examining the effects of these factors on the imbibition efficiency of fracturing fluids in tight sandstones.

Endoscopic intramural cystogastrostomy for treatment of peripancreatic fluid collection: A viewpoint from a surgeon

Percutaneous or endoscopic drainage is the initial choice for the treatment of peripancreatic fluid collection in symptomatic patients.Endoscopic transgastric fenestration(ETGF)was first reported for the management of pancreatic pseu-docysts of 20 patients in 2008.From a surgeon’s viewpoint,ETGF is a similar procedure to cystogastrostomy in that they both produce a wide outlet orifice for the drainage of fluid and necrotic debris.ETGF can be performed at least 4 wk after the initial onset of acute pancreatitis and it has a high priority over the surgical approach.However,the surgical approach usually has a better success rate because surgical cystogastrostomy has a wider outlet(>6 cm vs 2 cm)than ETGF.However,percutaneous or endoscopic drainage,ETGF,and surgical approach offer various treatment options for peripancreatic fluid collection patients based on their conditions.

An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

Application and prospect of the fluid cooling system of solar arrays for probing the Sun

The Solar Close Observations and Proximity Experiments(SCOPE)mission,which has been proposed by the Yunnan Observatories,Chinese Academy of Sciences,aiming to operate at a distance of 5 to 10 solar radii from the Sun,plans to complete the in situ detection of the solar eruption process and observation of the magnetic field structure response.The solar flux received by the satellite ranges from 10^(3) to 10^(6) Wm^(-2),which poses challenges for thermal management of the solar arrays.In this work,the solar array cooling system of the Parker Solar Probe is discussed,the developments of the fluid loop technique are reviewed,and a research plan for a next-generation solar array cooling system is proposed.This paper provides a valuable reference for novel thermal control systems in spacecraft for solar observation.

A Multi-Parameter Sensor Based on Cascaded Photonic Crystal Cavities Filled with Magnetic Fluid

A kind of photonic crystal (PC) micro-cavity sensor based on magnetic fluid (MF) filling is designed with simulation model. Generally, many sensors’ designs are based on a universal temperature in the whole structure. However, strong photothermal effect in high Q micro-cavities will lead to different temperatures between cavities and environment inevitably. In many theoretical PC sensor designs, researchers neglected the different temperature between environment and cavities. This simple hypothesis will probably lead to failure of sensor design and get wrong temperature. Moreover, few theoretical or experimental works have been done to study optical cavity’s heating process and temperature. We propose that researchers should take seriously about this point. Here, the designed cascaded micro-cavity structure has three spectral lines and a reversible sensitivity matrix, which can simultaneously detect magnetic field, ambient temperature and MF micro-cavity temperature. It can solve the magnetic field and temperature cross-sensitivity problem, and further, distinguish the different temperatures of environment and magnetic fluid cavities. The influence of hole radius and slab thickness on the depth and Q value of the resonant spectral line are also studied. Responses of three dips to magnetic field, ambient temperature and MF micro-cavity temperature are simulated, respectively, where dip 1 belongs to MF cavity 1, dip 2 and dip 3 belong to MF cavity 2. The obtained magnetic field sensitivities are 2.89 pm/Oe, 4.57 pm/Oe, and 5.14 pm/Oe, respectively;the ambient temperature sensitivities are 65.51 pm/K, 50.94 pm/K, and 58.98 pm/K, respectively;and the MF micro-cavity temperature sensitivities are −14.41 pm/K, −17.06 pm/K, and −18.81 pm/K, respectively.

The Conversion of Non-Dispersed Polymers into Low-Potassium Anti-Collapse Drilling Fluids

Different drillingfluid systems are designed according to mineral composition,lithology and wellbore stability of different strata.In the present study,the conversion of a non-dispersed polymer drillingfluid into a low potas-sium anti-collapsing drillingfluid is investigated.Since the two drillingfluids belong to completely different types,the key to this conversion is represented by new inhibitors,dispersants and water-loss agents by which a non-dispersed drillingfluid can be turned into a dispersed drillingfluid while ensuring wellbore stability and reason-able rheology(carrying sand—inhibiting cuttings dispersion).In particular,the(QYZ-1)inhibitors and(FSJSS-2)dispersants are used.The former can inhibit the hydration expansion capacity of clay,reduce the dynamic shear force and weaken the viscosity;the latter can improve the sealing effect and reduce thefiltrate loss.The results have shown that after adding a reasonable proportion of these substances(QYZ-1:FSJSS-2)to the non-dispersed polymer drillingfluid,while the apparent viscosity,plastic viscosity,structural viscosity andfluidity index under-went almost negligible changes,the dynamic plastic ratio increased,and thefiltration loss decreased significantly,thereby indicating good compatibility.According to the tests(conducted in the Leijia area),the density was 1.293 g/cm3,and after standing for 24 h,the SF(static settlement factor)was 0.51.Moreover,thefiltration loss was reduced to 4.0 mL,the rolling recovery rate reached 96.92%,with excellent plugging and anti-collapse performances.

Imaging the Architecture of Mineral Systems and the Pathways of Ore-forming Fluids across Mongolia with Magnetotellurics

In the framework of a mineral system approach,a combination of components is required to develop a mineral system.This includes the whole-lithosphere architecture,which controls the transport of ore-forming fluids,and favorable tectonic and geodynamic processes,occurring at various spatial and temporal scales,that influence the genesis and evolution of ore-forming fluids(Huston et al.,2016;Groves et al.,2018;Davies et al.,2020).Knowledge of the deep structural framework can advance the understanding of the development of a mineral system and the emplacement of mineral deposits.Deep geophysical exploration carried out with this aim is increasingly important for targeting new ore deposits in unexplored and underexplored regions(Dentith et al.,2018;Dentith,2019).

Averaged Dynamics of Fluids near the Oscillating Interface in a Hele-Shaw Cell

The steady flow in a Hele-Shaw cell filled with fluids with a high viscosity contrast in the presence of fluid oscillations is experimentally studied.The control of oscillatory dynamics of multiphase systems with interfaces is a challenging technological problem.We consider miscible(water and glycerol)and immiscible(water and high-viscosity silicone oil PMS-1000)fluids under subsonic oscillations perpendicular to the interface.Observations show that the interface shape depends on the amplitude and frequency of oscillations.The interface is undisturbed only in the absence of oscillations.Under small amplitudes,the interface between water and glycerol widens due to mixing.When the critical amplitude is reached,the interface becomes unstable to the fingering instability:Aqueous fingers penetrate the high-viscosity glycerol and induce intensive mixing of miscible fluids and associated decay of the instability.After the disappearance of the fingers,the interface takes a U-shape in the central part of the cell.A similar effect is observed for immiscible fluids:The oscillating interface tends to bend to the side of a high-viscosity fluid.Again,when the critical amplitude is reached,the fingering instability arises at the convex interface.This paper focuses on the causes of bending of the initially undisturbed interface between miscible or immiscible fluids.For this purpose,we measure the steady flow velocity near the interface and in the bulk of a high-viscosity fluid using Particle Image Velocimetry(PIV).

Functional thermal fluids and their applications in battery thermal management:A comprehensive review

With the increasing requirements for fast charging and discharging,higher requirements have been put forward for the thermal management of power batteries.Therefore,there is an urgent need to develop efficient heat transfer fluids.As a new type of heat transfer fluids,functional thermal fluids mainly includ-ing nanofluids(NFs)and phase change fluids(PCFs),have the advantages of high heat carrying density,high heat transfer rate,and broad operational temperature range.However,challenges that hinder their practical applications remain.In this paper,we firstly overview the classification,thermophysical prop-erties,drawbacks,and corresponding modifications of functional thermal fluids.For NFs,the high ther-mal conductivity and high convective heat transfer performance were mainly elaborated,while the stability and viscosity issues were also analyzed.And then for PCFs,the high heat carrying density was mainly elaborated,while the problems of supercooling,stability,and viscosity were also analyzed.On this basis,the composite fluids combined NFs and PCFs technology,has been summarized.Furthermore,the thermal properties of traditional fluids,NFs,PCFs,and composite fluids are compared,which proves that functional thermal fluids are a good choice to replace traditional fluids as coolants.Then,battery thermal management system(BTMS)based on functional thermal fluids is summarized in detail,and the thermal management effects and pump consumption are compared with that of water-based BTMS.Finally,the current technical challenges that parameters optimization of functional thermal fluids and structures optimization of BTMS systematically are presented.In the future,it is necessary to pay more attention to using machine learning to predict thermophysical properties of functional thermal fluids and their applications for BTMS under actual vehicle conditions.

Magmatic-hydrothermal Evolution and Mineralization Mechanisms of the Wangjiazhuang Cu(-Mo)Deposit in the Zouping Volcanic Basin,Shandong Province,China:Constraints from Fluid Inclusions

The Wangjiazhuang Cu(-Mo)deposit,located within the Zouping volcanic basin in western Shandong Province,China,is unique in this area for having an economic value.In order to expound the metallogenetic characteristics of this porphyry-like hydrothermal deposit,a detailed fluid inclusion study has been conducted,employing the techniques of representative sampling,fluid inclusion petrography,microthermometry,Raman spectroscopy,LA-ICP-MS analysis of single fluid inclusions,as well as cathode fluorescence spectrometer analysis of host mineral quartz.The deposit contains mainly two types of orebodies,i.e.veinlet-dissemination-stockwork orebodies in the K-Si alteration zone and pegmatiticquartz sulfide veins above them.In addition,minor breccia ore occurs locally.Four types of fluid inclusions in the deposit and altered quartz monzonite are identified:L-type one-or two-phase aqueous inclusions,V-type vapor-rich inclusions with V/L ratios greater than 50%-90%,D-type multiphase fluid inclusions containing daughter minerals or solids and S-type silicate-bearing fluid inclusions containing mainly muscovite and biotite.Ore petrography and fluid inclusion study has revealed a three-stage mineralization process,driven by magmatic-hydrothermal fluid activity,as follows.Initially,a hydrothermal fluid,separated from the parent magma,infiltrated into the quartz monzonite,resulting in its extensive K-Si alteration,as indicated by silicate-bearing fluid inclusions trapped in altered quartz monzonite.This is followed by the early mineralization,the formation of quartz veinlets and dissemination-stockwork ores.During the main mineralization stage,due to the participation and mixing of meteoric groundwater with magmatic-sourced hydrothermal fluid,the cooling and phase separation caused deposition of metals from the hydrothermal fluids.As a result,the pegmatitic-quartz sulfide-vein ores formed.In the late mineralization stage,decreasing fluid salinity led to the formation of L-type aqueous inclusions and chalcopyrite-sulfosalt ore.Coexistence of V-type and D-type inclusions and their similar homogenization temperatures with different homogenization modes suggest that phase separation or boiling of the ore-forming fluids took place during the early and the main mineralization stages.The formation P-T conditions of S-type inclusions and the early and the main mineralization stages were estimated as ca.156-182 MPa and 450-650℃,350-450℃,18-35 MPa and 280-380℃,8-15 MPa,respectively,based on the microthermometric data of the fluid inclusions formed at the individual stages.

Application of fluid modulus inversion to complex lithology reservoirs in deep-water areas

It has been a challenge to distinguish between seismic anomalies caused by complex lithology and hydrocarbon reservoirs using conventional fluid identification techniques,leading to difficulties in accurately predicting hydrocarbon-bearing properties and determining oil-water contacts in reservoirs.In this study,we built a petrophysical model tailored to the deep-water area of the Baiyun Sag in the eastern South China Sea based on seismic data and explored the feasibility of the tri-parameter direct inversion method in the fluid identification of complex lithology reservoirs,offering a more precise alternative to conventional techniques.Our research found that the fluid modulus can successfully eliminate seismic amplitude anomalies caused by lithological variations.Furthermore,the seismic databased direct inversion for fluid modulus can remove the cumulative errors caused by indirect inversion and the influence of porosity.We discovered that traditional methods using seismic amplitude anomalies were ineffective in detecting fluids,determining gas-water contacts,or delineating high-quality reservoirs.However,the fluid factor Kf,derived from solid-liquid decoupling,proved to be sensitive to the identification of hydrocarbon-bearing properties,distinguishing between high-quality and poor-quality gas zones.Our findings confirm the value of the fluid modulus in fluid identification and demonstrate that the tri-parameter direct inversion method can significantly enhance hydrocarbon exploration in deep-water areas,reducing associated risks.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.