The evaporation ofmicrometer and millimeter liquid drops,involving a liquid-to-vapor phase transition accompanied by mass and energy transfer through the liquid-vapor interface,is encountered in many natural and indus...The evaporation ofmicrometer and millimeter liquid drops,involving a liquid-to-vapor phase transition accompanied by mass and energy transfer through the liquid-vapor interface,is encountered in many natural and industrial processes as well as in numerous engineering applications.Therefore,understanding and predicting the dynamics of evaporating flows have become of primary importance.Recent efforts have been addressed using the method of Smoothed Particle Hydrodynamics(SPH),which has proven to be very efficient in correctly handling the intrinsic complexity introduced by the multiscale nature of the evaporation process.This paper aims to provide an overview of published work on SPH-based simulations related to the evaporation of drops suspended in static and convective environments and impacting on heated solid surfaces.After a brief theoretical account of the main ingredients necessary for the modeling of drop evaporation,the fundamental aspects of SPH are revisited along with the various existing formulations that have been implemented to address the challenges imposed by the physics of evaporating flows.In the following sections,the paper summarizes the results of SPH-based simulations of drop evaporation and ends with a few comments on the limitations of the current state-of-the-art SPHsimulations and future lines of research.展开更多
The weakly compressible smooth particle hydrodynamics(WCSPH)model is studied to address the boundary pressure instability of the SPH method,resulting in the development of the SPH method with improved dynamic boundary...The weakly compressible smooth particle hydrodynamics(WCSPH)model is studied to address the boundary pressure instability of the SPH method,resulting in the development of the SPH method with improved dynamic boundary conditions.This method employs the‘fan’search method for free surface detection,effectively identifying cavity interface particles with diameters smaller than the support domain’s radius,thereby indirectly enhancing the algorithm’s accuracy.On this basis,an improved dynamic boundary condition is proposed by updating the boundary particle pressure calculation scheme to achieve a more stable and continuous pressure field,thereby effectively preventing particles from penetrating the boundary.The SPH method with improved dynamic boundary conditions is used to simulate typical high-speed impact problems such as wedge entry and dam break.The simulation results are in good agreement with the experimental data and other numerical results.展开更多
A discontinuous smoothed particle hydrodynamics(DSPH)method considering block contacts is originally developed to model the cracking,frictional slip and large deformation in rock masses,and is verified by theoretical,...A discontinuous smoothed particle hydrodynamics(DSPH)method considering block contacts is originally developed to model the cracking,frictional slip and large deformation in rock masses,and is verified by theoretical,numerical and/or experimental results.In the DSPH method,cracking is realized by breaking the virtual bonds via a pseudo-spring method based on Mohr–Coulomb failure criteria.The damaged particles are instantaneously replaced by discontinuous particles and the contact bond between the original and discontinuous particles is formed to simulate the frictional slip and separation/contraction between fracture surfaces based on the block contact algorithm.The motion of rock blocks and the contact force of discontinuous particles are determined following Newton's second law.The results indicate that the DSPH method precisely captures the cracking,contact formation and complete failure across six numerical benchmark tests.This single smoothed particle hydrodynamics(SPH)framework could significantly improve computational efficiency and is potentially applicable to broad multi-physical rock engineering problems of different scales.展开更多
为研究鸟撞飞机典型结构过程中鸟体姿态对鸟撞损伤的影响规律,以某型水陆两栖飞机-机翼前缘这一典型结构为研究对象,通过光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)耦合有限元法(Finite Element Method,FEM)建立鸟撞数...为研究鸟撞飞机典型结构过程中鸟体姿态对鸟撞损伤的影响规律,以某型水陆两栖飞机-机翼前缘这一典型结构为研究对象,通过光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)耦合有限元法(Finite Element Method,FEM)建立鸟撞数值模型,并通过鸟撞试验验证计算模型的准确性。最后,以试验修正后的机翼前缘数值模型为依托,研究分析鸟体俯仰和偏航12种撞击姿态下机翼前缘的损伤变形情况和冲击响应规律。结果表明,仿真分析和试验结果通过一致性验证;蒙皮凹坑和凹陷范围随鸟体姿态角增大而增大,鸟体剩余能量随之降低;俯仰角增大,前缘结构吸收的能量更多,蒙皮高应力区增大,结构更易破坏。因此对于鸟撞威胁影响更大的重要飞机结构的抗鸟撞安全评估应计入鸟体姿态的影响。研究结果可在飞机抗鸟撞设计与适航评估方面提供重要参考。展开更多
近年来,部分特高压换流变压器在运行中相继发生电弧短路故障并引发爆炸、起火事故,严重威胁直流系统安全稳定运行。充油设备故障冲击下的结构失效机制尚不明确,且缺乏成熟的数值计算方法,制约故障防爆技术的发展。基于此,该文提出一套...近年来,部分特高压换流变压器在运行中相继发生电弧短路故障并引发爆炸、起火事故,严重威胁直流系统安全稳定运行。充油设备故障冲击下的结构失效机制尚不明确,且缺乏成熟的数值计算方法,制约故障防爆技术的发展。基于此,该文提出一套适用于高能电弧故障冲击的结构失效仿真计算方法。首先,建立有限腔体内油中电弧能量持续注入的气泡动力学模型,准确描述故障气泡的脉动膨胀行为;其次,提出自适应有限元-光滑粒子流体动力学(finite element method-smoothed particle hydrodynamics,FEM-SPH)耦合方法,利用SPH粒子继承失效前的物理信息参与FEM计算;进行不同能量、不同位置的电弧故障仿真计算,获得换流变压器结构的薄弱区域及其破裂行为,复现了油箱结构失效行为。研究发现,油箱顶盖两侧及侧壁转角接缝位置容易发生应力集中现象。一旦结构出现裂缝,将在极短时间内沿着应力集中方向快速发展,最终导致壁面整体撕裂。可知,该方法揭示的结构失效行为可为改进变压器设计和提高设备安全性提供依据。展开更多
This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to impro...This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.展开更多
When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of...When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of wave propagation. Accompanied with this phenomenon, the pressure under water decays either and shows a big oscillation simultaneously. The reason is the natural potential tensile instability of modeling water motion with ordinary SPH which is caused by particle negative stress in the computation. I＇o deal with the problems, a new sextic kernel function is proposed to reduce this instability. An appropriate smooth length is given and its computation criterion is also suggested. At the same time, a new kind dynamic boundary condition is introduced. Based on these improvements, the new SPH method named stability improved SPH （SISPH） can simulate the wave propagation well. Both the water surface and pressure can be well expressed and the oscillation of pressure is nearly eliminated. Compared with other improved methods, SISPH can truly reveal the physical reality without bringing some new problems in a simple way.展开更多
The water mitigation effect on the propagation of shock wave was investigated numerically. The traditional smoothed particle hydrodynamics (SPH) method was modified based on Riemann solution. The comparison of numeric...The water mitigation effect on the propagation of shock wave was investigated numerically. The traditional smoothed particle hydrodynamics (SPH) method was modified based on Riemann solution. The comparison of numerical results with the analytical solution indicated that the modified SPH method has more advantages than the traditional SPH method. Using the modified SPH algorithm, a series of one-dimensional planar wave propagation problems were investigated, focusing on the influence of the air-gap between the high-pressure air and water and the thickness of water. The numerical results showed that water mitigation effect is significant. Up to 60% shock wave pressure reduction could be achieved with the existence of water, and the shape of shock wave was also changed greatly. It is seemly that the small air-gap between the high-pressure air and water has more influence on water mitigation effect.展开更多
Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. ...Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.展开更多
Since the jets and detonation gaseous products are separated by sharp interfaces, the traditional smoothed particle hydrodynamics (SPH) method is difficult to avoid the computational instability at interfaces. The mul...Since the jets and detonation gaseous products are separated by sharp interfaces, the traditional smoothed particle hydrodynamics (SPH) method is difficult to avoid the computational instability at interfaces. The multi-phase SPH (MSPH) method was applied to improving the stabil-ity, which smoothes the particle density and makes pressure continuous at interfaces. Numericalexamples of jet forming process were used to test capability of the MSPH method. The results show that the method remains algorithm stability for large density gradient between the jets and gaseous products and has potential application to both the explosion and the jet problems. The effect of initiation ways of the shaped charge was discussed as well.展开更多
A coupled method describing gas–solid two-phase flow has been proposed to numerically study the bubble formation at a single orifice in gas-fluidized beds.Solid particles are traced with smoothed particle hydrodynami...A coupled method describing gas–solid two-phase flow has been proposed to numerically study the bubble formation at a single orifice in gas-fluidized beds.Solid particles are traced with smoothed particle hydrodynamics,whereas gas phase is discretized by finite volume method.Drag force,gas pressure gradient,and volume fraction are used to couple the two methods.The effect of injection velocities,particle sizes,and particle densities on bubble growth is analyzed using the coupled method.The simulation results,obtained for two-dimensional geometries,include the shape and diameter size of a bubble as a function of time;such results are compared with experimental data,previous numerical results,and other approximate model predictions reported in the literature.Moreover,the flow profiles of gas and particle phases and the temperature distribution by the heat transfer model around the forming bubble are also discussed.All results show that the coupled method efficiently describes of the bubble formation in fluidized beds.The proposed method is applicable for solving gas–solid two-phase flow in fluidization.展开更多
Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical,automobile,aerospace including defence technology.Variety of modelling techniques have been a...Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical,automobile,aerospace including defence technology.Variety of modelling techniques have been adopted in the past to model mechanical behaviour of particulate composites.Due to their favourable properties,particle-based methods provide a convenient platform to model failure or fracture of these composites.Smooth particle hydrodynamics(SPH)is one of such methods which demonstrate excellent potential for modelling failure or fracture of particulate composites in a Lagrangian setting.One of the major challenges in using SPH method for modelling composite materials depends on accurate and efficient way to treat interface and boundary conditions.In this paper,a masterslave method based multi-freedom constraints is proposed to impose essential boundary conditions and interfacial displacement constraints in modelling mechanical behaviour of composite materials using SPH method.The proposed methodology enforces the above constraints more accurately and requires only smaller condition number for system stiffness matrix than the procedures based on typical penalty function approach.A minimum cut-off value-based error criteria is employed to improve the computational efficiency of the proposed methodology.In addition,the proposed method is further enhanced by adopting a modified numerical interpolation scheme along the boundary to increase the accuracy and computational efficiency.The numerical examples demonstrate that the proposed master-slave approach yields better accuracy in enforcing displacement constraints and requires approximately the same computational time as that of penalty method.展开更多
文摘The evaporation ofmicrometer and millimeter liquid drops,involving a liquid-to-vapor phase transition accompanied by mass and energy transfer through the liquid-vapor interface,is encountered in many natural and industrial processes as well as in numerous engineering applications.Therefore,understanding and predicting the dynamics of evaporating flows have become of primary importance.Recent efforts have been addressed using the method of Smoothed Particle Hydrodynamics(SPH),which has proven to be very efficient in correctly handling the intrinsic complexity introduced by the multiscale nature of the evaporation process.This paper aims to provide an overview of published work on SPH-based simulations related to the evaporation of drops suspended in static and convective environments and impacting on heated solid surfaces.After a brief theoretical account of the main ingredients necessary for the modeling of drop evaporation,the fundamental aspects of SPH are revisited along with the various existing formulations that have been implemented to address the challenges imposed by the physics of evaporating flows.In the following sections,the paper summarizes the results of SPH-based simulations of drop evaporation and ends with a few comments on the limitations of the current state-of-the-art SPHsimulations and future lines of research.
基金supported by the National Natural Science Foundation of China(Grant No.52071094).
文摘The weakly compressible smooth particle hydrodynamics(WCSPH)model is studied to address the boundary pressure instability of the SPH method,resulting in the development of the SPH method with improved dynamic boundary conditions.This method employs the‘fan’search method for free surface detection,effectively identifying cavity interface particles with diameters smaller than the support domain’s radius,thereby indirectly enhancing the algorithm’s accuracy.On this basis,an improved dynamic boundary condition is proposed by updating the boundary particle pressure calculation scheme to achieve a more stable and continuous pressure field,thereby effectively preventing particles from penetrating the boundary.The SPH method with improved dynamic boundary conditions is used to simulate typical high-speed impact problems such as wedge entry and dam break.The simulation results are in good agreement with the experimental data and other numerical results.
基金financial support from the National Key Research and Development Program of China(Grant No.2019YFC1509702)the Fundamental Research Funds for the Central Universities in Chinathe National Natural Science Foundation of China(Grant No.42377162).
文摘A discontinuous smoothed particle hydrodynamics(DSPH)method considering block contacts is originally developed to model the cracking,frictional slip and large deformation in rock masses,and is verified by theoretical,numerical and/or experimental results.In the DSPH method,cracking is realized by breaking the virtual bonds via a pseudo-spring method based on Mohr–Coulomb failure criteria.The damaged particles are instantaneously replaced by discontinuous particles and the contact bond between the original and discontinuous particles is formed to simulate the frictional slip and separation/contraction between fracture surfaces based on the block contact algorithm.The motion of rock blocks and the contact force of discontinuous particles are determined following Newton's second law.The results indicate that the DSPH method precisely captures the cracking,contact formation and complete failure across six numerical benchmark tests.This single smoothed particle hydrodynamics(SPH)framework could significantly improve computational efficiency and is potentially applicable to broad multi-physical rock engineering problems of different scales.
文摘为研究鸟撞飞机典型结构过程中鸟体姿态对鸟撞损伤的影响规律,以某型水陆两栖飞机-机翼前缘这一典型结构为研究对象,通过光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)耦合有限元法(Finite Element Method,FEM)建立鸟撞数值模型,并通过鸟撞试验验证计算模型的准确性。最后,以试验修正后的机翼前缘数值模型为依托,研究分析鸟体俯仰和偏航12种撞击姿态下机翼前缘的损伤变形情况和冲击响应规律。结果表明,仿真分析和试验结果通过一致性验证;蒙皮凹坑和凹陷范围随鸟体姿态角增大而增大,鸟体剩余能量随之降低;俯仰角增大,前缘结构吸收的能量更多,蒙皮高应力区增大,结构更易破坏。因此对于鸟撞威胁影响更大的重要飞机结构的抗鸟撞安全评估应计入鸟体姿态的影响。研究结果可在飞机抗鸟撞设计与适航评估方面提供重要参考。
文摘近年来,部分特高压换流变压器在运行中相继发生电弧短路故障并引发爆炸、起火事故,严重威胁直流系统安全稳定运行。充油设备故障冲击下的结构失效机制尚不明确,且缺乏成熟的数值计算方法,制约故障防爆技术的发展。基于此,该文提出一套适用于高能电弧故障冲击的结构失效仿真计算方法。首先,建立有限腔体内油中电弧能量持续注入的气泡动力学模型,准确描述故障气泡的脉动膨胀行为;其次,提出自适应有限元-光滑粒子流体动力学(finite element method-smoothed particle hydrodynamics,FEM-SPH)耦合方法,利用SPH粒子继承失效前的物理信息参与FEM计算;进行不同能量、不同位置的电弧故障仿真计算,获得换流变压器结构的薄弱区域及其破裂行为,复现了油箱结构失效行为。研究发现,油箱顶盖两侧及侧壁转角接缝位置容易发生应力集中现象。一旦结构出现裂缝,将在极短时间内沿着应力集中方向快速发展,最终导致壁面整体撕裂。可知,该方法揭示的结构失效行为可为改进变压器设计和提高设备安全性提供依据。
基金supported by the National Natural Science Foundation of China(No.51379039)the Excellent Young Scientists Fund(No.51222904)
文摘This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51579038 and 51490672)the National Basic Research Program of China(Grant No.2013CB036101)
文摘When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of wave propagation. Accompanied with this phenomenon, the pressure under water decays either and shows a big oscillation simultaneously. The reason is the natural potential tensile instability of modeling water motion with ordinary SPH which is caused by particle negative stress in the computation. I＇o deal with the problems, a new sextic kernel function is proposed to reduce this instability. An appropriate smooth length is given and its computation criterion is also suggested. At the same time, a new kind dynamic boundary condition is introduced. Based on these improvements, the new SPH method named stability improved SPH （SISPH） can simulate the wave propagation well. Both the water surface and pressure can be well expressed and the oscillation of pressure is nearly eliminated. Compared with other improved methods, SISPH can truly reveal the physical reality without bringing some new problems in a simple way.
基金Supported by National Natural Science Foundation of China(No.50638030 and 50525825)National Science and Technology Support Program(No.2006BAJ13B02)
文摘The water mitigation effect on the propagation of shock wave was investigated numerically. The traditional smoothed particle hydrodynamics (SPH) method was modified based on Riemann solution. The comparison of numerical results with the analytical solution indicated that the modified SPH method has more advantages than the traditional SPH method. Using the modified SPH algorithm, a series of one-dimensional planar wave propagation problems were investigated, focusing on the influence of the air-gap between the high-pressure air and water and the thickness of water. The numerical results showed that water mitigation effect is significant. Up to 60% shock wave pressure reduction could be achieved with the existence of water, and the shape of shock wave was also changed greatly. It is seemly that the small air-gap between the high-pressure air and water has more influence on water mitigation effect.
基金supported by Department of Energy and Process Engineering,Norwegian University of Science and TechnologyInstitute for Energy Technology and SINTEF through the FACE(Multiphase Flow Assurance Innovation Center) Project
文摘Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.
基金Supported by New Century Exellent Talents in University(NCET) in China for National "973"Program in China (No.61338)Innvoative Research Project of Xi’an Hi-Tech Institute(No.EPXY0806)
文摘Since the jets and detonation gaseous products are separated by sharp interfaces, the traditional smoothed particle hydrodynamics (SPH) method is difficult to avoid the computational instability at interfaces. The multi-phase SPH (MSPH) method was applied to improving the stabil-ity, which smoothes the particle density and makes pressure continuous at interfaces. Numericalexamples of jet forming process were used to test capability of the MSPH method. The results show that the method remains algorithm stability for large density gradient between the jets and gaseous products and has potential application to both the explosion and the jet problems. The effect of initiation ways of the shaped charge was discussed as well.
基金The support of National Nature Science Foundation of China(No.51276192)No.61338 for the National Basic Research Program of Chinathe Innovative Research Project of Xi’an Hi-tech Institute(EPXY0806)are gratefully acknowledged.
文摘A coupled method describing gas–solid two-phase flow has been proposed to numerically study the bubble formation at a single orifice in gas-fluidized beds.Solid particles are traced with smoothed particle hydrodynamics,whereas gas phase is discretized by finite volume method.Drag force,gas pressure gradient,and volume fraction are used to couple the two methods.The effect of injection velocities,particle sizes,and particle densities on bubble growth is analyzed using the coupled method.The simulation results,obtained for two-dimensional geometries,include the shape and diameter size of a bubble as a function of time;such results are compared with experimental data,previous numerical results,and other approximate model predictions reported in the literature.Moreover,the flow profiles of gas and particle phases and the temperature distribution by the heat transfer model around the forming bubble are also discussed.All results show that the coupled method efficiently describes of the bubble formation in fluidized beds.The proposed method is applicable for solving gas–solid two-phase flow in fluidization.
基金National Key R&D Program of China(No.2018YFC0809700,No.2017YFC0803300)National Natural Science Foundation of China(No.71673158,No.11702046).
文摘Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical,automobile,aerospace including defence technology.Variety of modelling techniques have been adopted in the past to model mechanical behaviour of particulate composites.Due to their favourable properties,particle-based methods provide a convenient platform to model failure or fracture of these composites.Smooth particle hydrodynamics(SPH)is one of such methods which demonstrate excellent potential for modelling failure or fracture of particulate composites in a Lagrangian setting.One of the major challenges in using SPH method for modelling composite materials depends on accurate and efficient way to treat interface and boundary conditions.In this paper,a masterslave method based multi-freedom constraints is proposed to impose essential boundary conditions and interfacial displacement constraints in modelling mechanical behaviour of composite materials using SPH method.The proposed methodology enforces the above constraints more accurately and requires only smaller condition number for system stiffness matrix than the procedures based on typical penalty function approach.A minimum cut-off value-based error criteria is employed to improve the computational efficiency of the proposed methodology.In addition,the proposed method is further enhanced by adopting a modified numerical interpolation scheme along the boundary to increase the accuracy and computational efficiency.The numerical examples demonstrate that the proposed master-slave approach yields better accuracy in enforcing displacement constraints and requires approximately the same computational time as that of penalty method.
