Physics of Fluids最新文献

Systematical study on the aerodynamic control mechanisms of a 1:2 rectangular cylinder with Kirigami scales 利用桐神尺度对 1:2 矩形圆柱体的空气动力控制机制进行系统研究

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0218442

Haoqi Hu, Wenhan Yang, Hao Meng, Donglai Gao

{"title":"Systematical study on the aerodynamic control mechanisms of a 1:2 rectangular cylinder with Kirigami scales","authors":"Haoqi Hu, Wenhan Yang, Hao Meng, Donglai Gao","doi":"10.1063/5.0218442","DOIUrl":"https://doi.org/10.1063/5.0218442","url":null,"abstract":"Biomimetic flow control is being widely applied. In the present study, a biomimetic flow control method, i.e., Kirigami scales, was applied on a 1:2 rectangular cylinder. The effects of scales' shapes and pasting surfaces on the aerodynamics and circumferential flow patterns of a 1:2 rectangular cylinder were studied. Three scale shapes were investigated with different pasting methods, i.e., elliptical, circular, and triangular scales. The Reynolds number (Re) was set at 1.3–3.1 × 104. The surface pressure distributions and the integrated aerodynamic forces were further analyzed at Re = 1.3 × 104. Results show that pasting the elliptical scales on all surfaces performs best, reaching a 2.4% drag reduction and a 76.4% lift reduction. Moreover, the elliptical and triangular scales on the windward and leeward surfaces can significantly reduce the Re effect. To reveal the control mechanism, the particle image velocimetry technique was employed to obtain the circumferential and wake flow fields. The time-averaged and phase-averaged results indicate that the Kirigami scales can push the interactions of shear layers and the shedding vortices further downstream. The Proper orthogonal decomposition analysis and time-averaged turbulent kinetic energy (TKE) results indicate that the wake vortex shedding is significantly suppressed. The spanwise wake flow field was also investigated. Results show that the spanwise TKE values are significantly reduced. This study further deepened the application of Kirigami scales on the common blunt bodies.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141690145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Experimental study on the comparison of mechanical properties of different types of glutenite in the Ma'nan area 关于马南地区不同类型糯米糍力学性能比较的实验研究

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0218642

Shuiqing Hu, Zirui Yang, Yiqun Yan, Yiping Ye, Wei Zhang, Zhongchen Ba, Hui He, Daobing Wang

{"title":"Experimental study on the comparison of mechanical properties of different types of glutenite in the Ma'nan area","authors":"Shuiqing Hu, Zirui Yang, Yiqun Yan, Yiping Ye, Wei Zhang, Zhongchen Ba, Hui He, Daobing Wang","doi":"10.1063/5.0218642","DOIUrl":"https://doi.org/10.1063/5.0218642","url":null,"abstract":"This study delves into the mechanical properties of various rock types found in glutenite reservoirs in the Ma'nan area of the Xinjiang oilfield. It bridges a knowledge gap by exploring the mechanical deformation and failure patterns among different glutenite types. Employing porosity-permeability tests, ultrasonic wave velocity measurements, and triaxial compression tests, this research scrutinizes physical parameters, mechanical properties, deformation, and failure modes of dolomitic sandstone, calcareous coarse sandstone, calcareous fine siltstone, and glutenite. Results highlight a porosity increase from dolomitic sandstone to glutenite, with calcareous coarse sandstone having the lowest permeability and glutenite the highest. Shear wave velocity is greater in dolomitic sandstone and calcareous coarse sandstone compared to calcareous fine siltstone, while longitudinal wave velocity is higher in dolomitic sandstone than in glutenite. Deformation behavior varies: dolomitic sandstone is primarily elastic, and calcareous sandstone and glutenite show elastoplastic characteristics. Dolomitic sandstone boasts the highest compressive strength, elastic modulus, and Poisson's ratio. Calcareous fine siltstone's compressive strength and elastic modulus fall below dolomitic sandstone, while the Poisson's ratio of calcareous coarse sandstone is three-quarters that of dolomitic sandstone. Main failure modes observed are shear failure in dolomitic sandstone, calcareous coarse sandstone, and glutenite, and axial splitting failure in calcareous fine siltstone. Microscopic analyses, including environmental scanning electron microscopy and mineral composition, shed light on the mechanical differences among the rocks. In sum, this research yields crucial insights into the mechanical traits of glutenite reservoir rocks, essential for optimizing hydraulic fracturing strategies in such reservoirs.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141698821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Numerical study of thermocapillary and slip effects on interfacial destabilization under surface acoustic waves 表面声波作用下热毛细管效应和滑移效应对界面失稳的数值研究

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0215087

Jia Ning, Qing-Yun Huang, Chen-Hui Gai, Yi-Zhan Ding, Bing Zhang, Yu-Lin Lei, Yang Wu, Hong Hu

{"title":"Numerical study of thermocapillary and slip effects on interfacial destabilization under surface acoustic waves","authors":"Jia Ning, Qing-Yun Huang, Chen-Hui Gai, Yi-Zhan Ding, Bing Zhang, Yu-Lin Lei, Yang Wu, Hong Hu","doi":"10.1063/5.0215087","DOIUrl":"https://doi.org/10.1063/5.0215087","url":null,"abstract":"The rapid development of microfluidics has significantly highlighted the role of surface acoustic waves (SAWs) in microfluidic actuation. SAW influences droplet manipulation, inducing interface instability and processes such as droplet splitting, jetting, and atomization, which have been key research focal points. Previous studies have identified a close correlation between these instability mechanisms and three critical parameters: the Marangoni number (Ma), associated with piezoelectric substrate thermal effects; the slip coefficient (β0), related to piezoelectric substrate slip; and the acoustic capillary number (C). Given the intimate link between the aspect ratio (H/L, where H is the characteristic height, and L is the characteristic width of droplets) and atomization size, this study comprehensively investigates the combined effects of these factors on the droplet aspect ratio H/L. Specifically, increases in the acoustic capillary number C and slip coefficient β0 promote reductions in droplet height (H) and outward expansion (L), while the Marangoni number Ma counteracts this expansion, maintaining larger H/L values. This inhibitory effect is particularly pronounced when C and β0 are small but diminishes as their values increase. Additionally, higher values of C and β0 accelerate the convergence of the H/L ratio, whereas Ma decreases the rate of this convergence. Through the coordinated interplay of Ma, β0, and C, multidimensional and fine-tuned adjustments of the droplet aspect ratio H/L over a wide range can be achieved.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141716611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of interfacial effect and boundary layer for forced convection on the macroscopic hydrophilic-hydrophobic hybrid surface: A large eddy simulation 宏观亲水-疏水混合表面强制对流的界面效应和边界层分析：大涡模拟

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0215005

Haotian Cong, Minli Bai, Xuecheng Lv, Yubai Li, Yongchen Song

{"title":"Analysis of interfacial effect and boundary layer for forced convection on the macroscopic hydrophilic-hydrophobic hybrid surface: A large eddy simulation","authors":"Haotian Cong, Minli Bai, Xuecheng Lv, Yubai Li, Yongchen Song","doi":"10.1063/5.0215005","DOIUrl":"https://doi.org/10.1063/5.0215005","url":null,"abstract":"Hydrophilic-hydrophobic hybrid surfaces are developed to solve the flow and heat transfer performance contradiction. However, hybrid surfaces often have micro- or nano-scale featured sizes and are used in phase change heat transfer because hydrophilic regions contribute to droplet nucleation, and hydrophobic regions contribute to bubble nucleation. In this study, large eddy simulation is used to investigate the forced convection on macroscopic hydrophilic-hydrophobic hybrid surfaces where only the surface local wettability is changed. Three hybrid surfaces with different hydrophilic-hydrophobic ratios and two homogeneous wettability surfaces are designed, and representative flow Reynolds numbers of 4000, 6000, 10 000, and 40 000 are explored to achieve different turbulent styles. The transient parameters of kinematics, vorticity, and boundary layer are analyzed to clarify the mechanism of turbulence change and eddy generation and explain the causes of variations in flow and heat transfer performances. It proves that macroscopic hydrophilic-hydrophobic hybrid surfaces are suitable for forced convection due to the drag reduction on hydrophobic regions, backflows at hydrophilic-hydrophobic interfaces, and eddies at hydrophobic-hydrophilic interfaces, which can enhance the internal disturbance and harmonize the flow and heat transfer performances. The mechanism has a profound significance in broadening the application of hydrophilic-hydrophobic hybrid surfaces and designing the arrangement of hydrophobic regions.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141697394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mathematical modeling of creeping electromagnetohydrodynamic peristaltic propulsion in an annular gap between sinusoidally deforming permeable and impermeable curved tubes 正弦变形可渗透和不可渗透弯曲管之间环形间隙中蠕动电磁流体力学蠕动推进的数学建模

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0217370

P. Yadav, Muhammad Roshan

{"title":"Mathematical modeling of creeping electromagnetohydrodynamic peristaltic propulsion in an annular gap between sinusoidally deforming permeable and impermeable curved tubes","authors":"P. Yadav, Muhammad Roshan","doi":"10.1063/5.0217370","DOIUrl":"https://doi.org/10.1063/5.0217370","url":null,"abstract":"The present work investigates the creeping peristaltic propulsion of viscid fluid in an annular gap between sinusoidally deforming permeable and impermeable curved tubes of similar shape under the influence of an externally imposed electric and magnetic field. In this model, the outer tube with a permeable wall surface is supposed to satisfy the Saffman slip condition. The flow equations are simplified by the estimation of a large wavelength in comparison with the radius of the external tube. An analytical solution for the axial velocity is obtained in the computational software MATHEMATICA. Graphical analyses are conducted to explore the variations in wall shear stress, velocity, pressure rise, frictional force, and stream function with respect to different emergent parameters, providing insight into the underlying physics of the flow phenomena. An investigation of the effects of the Hartmann number and electric field strength on the flow through a gap between deformable tubes with curved structures has important implications for a variety of engineering applications, including mechanical and biomedical engineering. The streamlines are plotted to discuss fluid trapping and visualize the flow pattern of the viscid fluid inside the curved annular domain. A comparative analysis of fluid transport induced by sinusoidal, triangular, trapezoidal, and square wave shapes is encountered with the help of streamlined contour diagrams. The comparison of pressure gradients in three different models is also discussed to gain insight due to fluid–structure interaction. A gap in the body of recently published literature is filled by the results discussed in this paper.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141690227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Wake-induced response of a flexible splitter plate detachedly placed downstream of a circular cylinder 圆形圆筒下游分离式柔性分流板的波浪诱导响应

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0217046

Hongjun Zhu, Quanyu Chen, Jiawen Zhong, Wenxiang Zhang, Tongming Zhou

引用次数: 0

Reynolds number effect of a vortex ring impinging on a concave hemi-cylindrical shell 撞击凹面半圆柱形壳体的涡环的雷诺数效应

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0214319

Liangquan Zhang, Guangtao Li, Wen-li Chen, Donglai Gao

{"title":"Reynolds number effect of a vortex ring impinging on a concave hemi-cylindrical shell","authors":"Liangquan Zhang, Guangtao Li, Wen-li Chen, Donglai Gao","doi":"10.1063/5.0214319","DOIUrl":"https://doi.org/10.1063/5.0214319","url":null,"abstract":"Experimental investigations were conducted on a single vortex ring impinging on a concave hemi-cylindrical shell with Dm/De = 2 at different Reynolds numbers. Vortex rings with five different Reynolds numbers were generated for experimental studies, i.e., Re = 750, 1500, 3000, 5000, and 7000. The planar laser-induced fluorescence visualizations and two-dimensional particle image velocimetry measurements were used in the experiment. The vorticity field based on the Eulerian framework and the finite-time Lyapunov exponent (FTLE) field based on the Lagrangian framework were used to identify the dynamic processes of vortex rings, respectively. The results show that as the vortex rings impinge on concave surfaces from Re = 750 to Re = 7000, the extension of the main vortex ring in the straight-edged direction is larger than that in the concave direction, and the instability of the vortex ring is promoted. While the Reynolds number is increasing, the vortex ring deformation becomes larger, and the overall vortex ring cross section becomes smaller, leading to a larger attenuation of the vortex ring rotation. Calculations performed by the FTLE field were used to derive the Lagrangian coherent structure to analyze the boundaries of the vortex ring motion process, clearly observe the shape of the secondary vortex connecting segments, and verify the speculation by the vortex ring trajectory identification results. Finally, a dynamic model of vortex rings impinging a concave surface was proposed, and the inference of the experimental process was explained by the model.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141716168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Effects of fuel/air mixing distances on combustion instabilities in non-premixed combustion 燃料/空气混合距离对非预混燃烧中燃烧不稳定性的影响

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0220095

Jiaying Cheng, Bofan Liu, Tong Zhu

{"title":"Effects of fuel/air mixing distances on combustion instabilities in non-premixed combustion","authors":"Jiaying Cheng, Bofan Liu, Tong Zhu","doi":"10.1063/5.0220095","DOIUrl":"https://doi.org/10.1063/5.0220095","url":null,"abstract":"Combustion instability has been widely reported in several combustion types; however, there is limited information on different fuel/air mixing distances in non-premixed combustion. Setting different distances between air tube and fuel tubes, the fuel/air mixing distances (δ) are changed by structural variations of nozzles. Keeping the heat load and equivalence ratios constant, the present work aims to examine the effects of fuel/air mixing distances on combustion instability in non-premixed combustion. Experimental observations suggest that combustion oscillations occur in non-premixed combustion with flame ignited outside the nozzle rather than other types of non-premixed combustion. Quasiperiodic oscillations, limit cycle modes, and intermittency modes are found in three fuel/air mixing distances in non-premixed combustion. The calculation methods of convection time for non-premixed combustion are established in the present work. The convection time of the limit cycle oscillations is then calculated, which is further found to trigger the second resonance modes of the combustion system. The further analysis reveals that varying fuel/air mixing distances can cause influences on local equivalence ratio distributions, and the convection time are correspondingly varied. The changes in convection time affects the coupling characteristics between heat release rate fluctuations and the acoustic modes in the combustion chamber. When the thermoacoustic coupling occurs, combustion instabilities appear. This work establishes a link between combustion instability and fuel/air mixing distances in non-premixed combustion and highlights the influences on spatial distributions of local equivalence ratios and then convection time, which can provide technical guidance for actual applications in various fuel/air mixing types.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141703227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Angle-of-attack characteristics of opposing jet for improving drag and heat reduction 用于改善阻力和减少热量的对向射流的攻击角特性

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0219134

Haonan Xu, Xueying Li, Jing Ren

{"title":"Angle-of-attack characteristics of opposing jet for improving drag and heat reduction","authors":"Haonan Xu, Xueying Li, Jing Ren","doi":"10.1063/5.0219134","DOIUrl":"https://doi.org/10.1063/5.0219134","url":null,"abstract":"While the opposing jet technique has the potential to achieve efficient drag and heat reduction, it can be severely affected by the incoming angle of attack. To analyze the angle-of-attack characteristics of opposing jet for improving drag and heat reduction, a three-dimensional blunt model was studied under various jet stagnation pressure ratios and angles of attack using the verified numerical method. The results showed that the enhanced reattachment shock on the windward side resulted in a higher pressure and temperature rise, which led to the deterioration of drag and heat reduction. Under the influence of the incoming angle of attack, the recirculation vortex transformed into a longitudinal vortex, resulting in a slanted U-shaped distribution of the surface pressure coefficient and Stanton number. Increasing the jet stagnation pressure ratio widened the coverage of the recirculation vortex on both the windward and leeward sides, which brought an improvement in drag and heat reduction. The interaction between the incoming angle of attack and the opposing jet caused a double-peak distribution of Stanton number due to the recirculation vortex reattachment and the compression of the incoming flow. The inclined opposing jet could reduce the peak values of pressure coefficient and Stanton number when subjected to the incoming flow with an angle of attack by spreading the recirculation vortex along the windward side. There should exist an optimal inclination angle that can effectively reduce the peak caused by the compression of the incoming flow without generating an excessive peak due to the recirculation vortex reattachment.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141706286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Onset and growth of viscous fingering in miscible annular ring 可混溶环形圈中粘性指状结构的形成与发展

Physics of Fluids Pub Date : 2024-07-01 DOI: 10.1063/5.0216418

Joung-Sook Hong, L. Palodhi, Manoranjan Mishra, Min Chan Kim

{"title":"Onset and growth of viscous fingering in miscible annular ring","authors":"Joung-Sook Hong, L. Palodhi, Manoranjan Mishra, Min Chan Kim","doi":"10.1063/5.0216418","DOIUrl":"https://doi.org/10.1063/5.0216418","url":null,"abstract":"We investigate the onset and growth of viscous fingering (VF) of miscible annulus in a radial Hele-Shaw cell. Systematic numerical study on a finite annulus domain is performed by employing finite element method solver in COMSOL Multiphysics software. We justify that concentration field analysis is not a good choice for dynamic study in radial flows. Instead, velocity magnitude is a better tool to understand the dynamics. Therefore, we propose velocity field analysis to better differentiate the stable and unstable states and present a new stability criterion using the velocity field method. Most interestingly, using the velocity field analysis and the new stability criterion, we show a restabilization of the VF at a critical time when the system becomes diffusion dominant and able to provide both the onset time, τon (time at which instability develops), and the time at which the interface returns to the stable state, τd. Furthermore, the study successfully suggests the critical values for several dimensionless parameters, the Péclet number (Pe), log-viscosity ratio (R), and volumetric ratio (ra) and time (τ), to induce instability. When Pe is higher than 103, the evolution of VF instability is no longer enhanced by Pe, and Rc converges to a certain value. In particular, for the transiently unstable system of low Pe, the restabilization of VF instability is identified even though R is higher than Rc. The unstable system (τ>τon) returns to the stable state as injection time increases further. Moreover, we obtained a critical value of the volumetric ratio (rc,a).","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141694951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0