K. V. Osintsev, N. A. Pshenisnov, A. I. Pshenisnov
{"title":"Analysis of Operation of the Oil-Supply System of Steam Turbine before and after Maintenance","authors":"K. V. Osintsev, N. A. Pshenisnov, A. I. Pshenisnov","doi":"10.1134/S0040601524700319","DOIUrl":"10.1134/S0040601524700319","url":null,"abstract":"<p>Lubricants are the most important element of mating friction pairs and largely determine their reliability and service life. Components of oil systems of turbine units are susceptible to contamination of the working fluid; therefore, during equipment operation, it is necessary to take oil samples and monitor cleanliness. In many cases, when equipment is stopped for maintenance or is in standby mode, the quality of the oil is not given due attention. Ultimately, this may affect the reliability of the unit. The quality of the oil when starting a turbine is often not the same as when the unit is taken out of service. Increasing filtration efficiency plays a key role in reducing wear rates. Cleaning requirements are most important during turbine commissioning and when equipment is spinning at low speeds. To clean the working fluid during operation, effective full-flow filters are required. The research was carried out on a T-180/210 LMZ turbine unit; Tp-22S turbine oil was used as the working fluid, and the volume of the oil system was 36 m<sup>3</sup>. After modernizing the filters of the main oil tank (MOT), solid particles in the oil decreased by 5.8 times, the purity corresponds to class six to seven by GOST 17216-2001. After the turbine unit was put into operation after routine repairs, a large amount of contaminants entered the system. The amount of solid particles in the oil increased 27 times. The purity of the oil in the system increased over 14 days of operation of the turbine after routine repairs, and solid contaminants in it during this period decreased by approximately 14 times and corresponds to class eight, and that over 28 days was by approximately 25 times and corresponds to class seven according to GOST 17216-2001. This increase in oil purity is a consequence of filtering out contaminants introduced and formed in the system during routine repairs and the completion of the running-in period of the associated turbine friction pairs. The most sensitive element of the oil system is the control system. As a result of research and compilation of oil-cleanliness data, the recommended level of industrial cleanliness for the hydraulic control system is class eight (GOST 17216-2001). The most common method of reducing the risk to equipment during commissioning operation is the use of additional oil-purification equipment. Oil-purification costs can be offset by reduced maintenance costs and replacement of damaged equipment.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 9","pages":"726 - 733"},"PeriodicalIF":0.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414178","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}
{"title":"Experimental Investigation on Effect of Height and Pore Density of Porous Medium on Flame and Emission Characteristics of Inverse Diffusion Combustor","authors":"A. Dekhatawala, P. V. Bhale, R. Shah","doi":"10.1134/S0040601524700216","DOIUrl":"10.1134/S0040601524700216","url":null,"abstract":"<p>The flame structure, appearance, and emission characteristics of an inverse diffusion porous combustor (IDPC) are investigated experimentally. Unstructured ceramic foam made of silicon carbide (SIC) is used as a porous medium. At stoichiometry conditions, a reactive analysis is performed with methane as a fuel and variations in the pore distribution density (pore density) of ceramic foam SIC. Height of ceramic foam and Reynolds number of air jet (<span>({{operatorname{Re} }_{{air}}})</span>) are varied. Porous medium alters flow momentum in radial and axial directions which affects flame appearance and emissions. Increased radial momentum produces wider and shorter flame in case of IDPC. A bright blue zone is detected at the base of the flame, and a luminous orange or orange-blue zone is observed in the post-combustion zone near the flame tip. As the pore density is enhanced from 10 pores per inch (PPI) to 20 PPI, the flame is detached from the surface of the porous medium at a higher Reynolds number of the air jet. The visible flame height of IDPC is significantly reduced at 10 PPI when compared to a case without a porous medium. The Reynolds number of the air jet and the pore density of the porous medium strongly influence the emission levels of NO<sub><i>x</i></sub> and CO. The IDPC with porous media height of 28 mm, <span>({{operatorname{Re} }_{{air}}})</span> = 8122 and 10 PPI pore density performs optimum in terms of flame shapes and CO and NO<sub><i>x</i></sub> emissions.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 9","pages":"741 - 752"},"PeriodicalIF":0.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414190","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}
I. A. Ryzhii, A. V. Shtegman, D. V. Sosin, A. S. Natal’in
{"title":"Description of the Tiltable Vortex Burner Design and Modeling Its Operation during Coal and Natural Gas Combustion","authors":"I. A. Ryzhii, A. V. Shtegman, D. V. Sosin, A. S. Natal’in","doi":"10.1134/S0040601524700186","DOIUrl":"10.1134/S0040601524700186","url":null,"abstract":"<p>The computational studies carried out previously taking as an example the BKZ-210-140 boiler installed at Tomsk-2 state-owned district power plant (SDPP) have shown that, given the existing scatter in the characteristics of coals fired at the power plant, the temperature of gases at the boiler furnace outlet may vary in a wide range (more than 100°С). Such variability of the operational parameters entails a number of problems, including difficulties with keeping a stable superheated steam temperature, increased risk of heating surfaces becoming slagged, and less efficient fuel combustion. A conclusion has been drawn based on the obtained computation results that the possibility of adjusting the flame’s initial section vector by ±15° will make it possible to solve the above-mentioned problems to a significant extent. A tiltable burner is the key component of the combustion system with adjusting the flame position. Based on an analysis of the current operation conditions of the Tomsk-2 SDPP BKZ-210-140 boiler, technical solutions were developed on the design of a tiltable vortex burner intended for combusting pulverized coal as well as natural gas and fuel oil. The burner’s outlet part is made so that it is possible to tilt it by ±15° in the vertical plane and by ±5° in the horizontal plane, which will make it possible to adjust the combustion mode in an efficient manner. The furnace process is simulated in the ANSYS Fluent software package under different boiler operation conditions. The simulation results show that, in the case of using the new burners, it is possible to improve the furnace process efficiency. By tilting the burner by ±15° in the vertical plane, it becomes possible to obtain the temperature adjustment range at the furnace outlet equal to 120°С. Based on the adopted technical solutions, design documentation for the burner has been developed. An experimental sample of the low-toxic tiltable vortex burner installed in the Tomsk-2 SDPP BKZ-210-140 boiler has been manufactured.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 8","pages":"700 - 711"},"PeriodicalIF":0.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206184","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}
{"title":"Analysis of the Influence of Aerosol Particle Size Distribution on the Behavior of Fission Products during Simulation of an Accident at an NPP with VVER","authors":"S. S. Savekin, Yu. B. Shmelkov","doi":"10.1134/S0040601524700198","DOIUrl":"10.1134/S0040601524700198","url":null,"abstract":"<p>Due to the potential danger of exposure to aerosol particles on the human body, maximum permissible concentrations of harmful substances are limited by current regulatory documentation. The formation of aerosol particles is possible during beyond design basis accidents at nuclear power plants. The consequences of the radioactive impact of radioactive aerosol particles formed during an accident at a nuclear power plant on the human body are significantly more severe than from the mechanical impact of such particles. An important characteristic of radioactive aerosol particles is their polydispersity (unevenness in size) since particles of different sizes during an accident at a nuclear power plant have different rates of removal from the atmosphere of the nuclear power plant’s containment. Thus, when considering the movement of particles in the containment and the release of aerosol particles into the environment, it is important to correctly model the size distribution of aerosol particles. This paper presents the results of calculating the count and mass distributions of aerosol particles by size in the TOSQAN and Phebus-FP experiments. Methods are given for describing polydisperse systems (using particle size distribution or “average” sizes characterizing the entire distribution) and their influence on processes associated with the transfer of aerosol particles in a containment, and practical recommendations for working with particle size distributions are given. A comparison is made of the use of average size distribution characteristics and the lognormal distribution of aerosol particles to estimate the release during a hypothetical accident at a nuclear power plant with VVER.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 8","pages":"689 - 699"},"PeriodicalIF":0.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206183","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}
{"title":"Phase Change Materials for Applications in Building Thermal Energy Storage (Review)","authors":"Md Ahsan Habib, Muhammad Mustafizur Rahman","doi":"10.1134/S0040601524700174","DOIUrl":"10.1134/S0040601524700174","url":null,"abstract":"<p>A unique substance or material that releases or absorbs enough energy during a phase shift is known as a phase change material (PCM). Usually, one of the first two fundamental states of matter—solid or liquid—will change into the other. Phase change materials for thermal energy storage (TES) have excellent capability for providing thermal comfort in building’s occupant by decreasing heating and cooling energy demands. Because of its latent heat property, a PCM has a high energy density. The building uses PCMs mainly for space heating or cooling, control of building material temperature and increase in building durability, solar water heating, and waste heat recovery from high heat loss locations. Phase change materials for thermal energy storage has been proven to be useful for reducing peak electricity demand or increasing energy efficiency in heating, ventilation, and air-conditioning systems. The primary grid benefit of PCM based thermal energy storage system is load shifting and shedding, which is accomplished by recharging the storage system during off-peak times and substituting heating, ventilation, and air-conditioning system operation during peak times. This study examines PCM based thermal energy storage systems in building applications and benefits, focusing on their substantial limitations, and closes with recommendations for further improvement of design for use.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 8","pages":"649 - 663"},"PeriodicalIF":0.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206181","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}
I. S. Antanenkova, Yu. A. Geller, M. M. Vinogradov, E. A. Gorbunova, D. S. Pisarev, V. I. Kuznetsov
{"title":"Design Solutions for the Main Heat Exchangers in the Organic Rankine Cycle Circuit (Review)","authors":"I. S. Antanenkova, Yu. A. Geller, M. M. Vinogradov, E. A. Gorbunova, D. S. Pisarev, V. I. Kuznetsov","doi":"10.1134/S0040601524700162","DOIUrl":"10.1134/S0040601524700162","url":null,"abstract":"<p>The results are presented of the search for and systematization of information on typical design solutions for the main heat exchangers of installations with low-boiling working fluids. The organic Rankine cycle (ORC) has been widely accepted as a way for converting waste (exhaust) heat into electrical energy. An increase in the installed capacity of operating commercial ORC power plants and their total capacity is noted in the world every year. At the same time, design options for the main heat exchangers (heater, evaporator-superheater, condenser, regenerative heat exchanger) are not available in open access and presented in catalogues: information about them is not disclosed by the manufacturers and information available in publications is limited and disembodied. An attempt is made in this paper to systematize the available information and, based on an analysis of world and domestic experience in industrial production, formulate an idea of potential engineering solutions for heat and mass transfer installations, which can be offered as prototypes of the considered apparatuses. At the same time, the search for such solutions was focused primarily on apparatuses used in the refrigeration industry, conventional steam turbine power units, and modern ventilation and air-conditioning systems. The advantages and disadvantages of such apparatuses are examined. The results are presented of a comparative analysis of their design, power range, operational features, and the potential effect of these factors on the operation of the overall ORC installation. Approaches to the selection of heat-exchange equipment for ORC installations given in the available publications and proven in practice have been investigated and described.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 8","pages":"631 - 648"},"PeriodicalIF":0.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206180","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}
{"title":"Water Chemistries of VVER-SCW Nuclear Power Plants: The Choice and Justification (Review)","authors":"N. L. Kharitonova, V. F. Tyapkov","doi":"10.1134/S0040601524700204","DOIUrl":"10.1134/S0040601524700204","url":null,"abstract":"<p>The article discusses the potential problems that have to be solved in the framework of development and justification of the water chemistry (WC) conditions required to ensure corrosion resistance of the structural materials used in the core and coolant circuit of the power-generating reactor used in the supercritical water cooled VVER-SCW nuclear power plant (NPP). In reactors cooled with water at supercritical temperature and pressure, the integrity of their physical barriers (fuel-rod claddings and reactor coolant circuit boundaries) depends in many respects on the possibility of maintaining the necessary water chemistry conditions that will guarantee the corrosion resistance of equipment and pipeline structural materials for the power unit’s entire service life. The most complex challenge in this regard is to inhibit corrosion and flow-accelerated corrosion processes and to minimize the formation of deposits on the surface of equipment operating in the domain of near-critical and supercritical conditions. The article formulates the limitations that are suggested to be considered in transferring the experience gained from the standardization of water chemistry in supercritical pressure (SCP) power units at thermal and nuclear power plants to the VVER-SCW NPPs. An analysis is carried out that makes it possible to estimate the effect the chemical composition of a supercritical water coolant has on the corrosion state of candidate structural materials for fuel-rod claddings with the aim to get better insight in the main processes occurring in aqueous solutions and for developing (elaborating) a WC conduction technology as applied to ensuring the integrity of the VVER-SCW NPP physical safety barriers.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 8","pages":"675 - 688"},"PeriodicalIF":0.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206182","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}
{"title":"Regularities of Bubble Formation at the Orifices of Submerged Perforated Sheets of Bubblers","authors":"V. A. Devyanin","doi":"10.1134/S0040601524700150","DOIUrl":"10.1134/S0040601524700150","url":null,"abstract":"<p>Based on literature data, an analysis of the modes of bubble formation at orifices immersed into the working environment of bubblers was carried out. The limits of applicability of calculated dependencies for determining the average bubble diameter between different areas of bubble formation on single orifices under conditions of constant gas flow into the bubble and constant gas pressure in the resulting bubble are given. When comparing calculated and experimental data on the sizes of the formed bubbles, it was found that, for the jet mode, there is no single calculation dependence that can at the same time quite accurately reflect the influence of both the orifice diameter and the physical properties of the two-phase medium on the bubble sizes. Despite the fact that a number of studies have shown experimentally and theoretically that the movement of liquid caused by bubbles floating above has a significant effect on the size of the bubbles, there are no verified calculation dependencies at present in the literature that take into account this effect over the entire range of gas flow through orifices of different diameters under different physical properties of the working environment. Based on the balance of forces acting at the moment of bubble separation, a model is proposed that also takes into account the dependence of the size of bubbles formed at the orifice by the movement of liquid caused by bubbles floating above. As a result of generalizing a large amount of experimental data available in the literature, a generalized dependence of the dimensionless average diameter of bubbles on the Bond, Froude, and Reynolds numbers was obtained for constant flow conditions for bubble and jet modes. The derived relationship is valid for orifices with different inner diameters and a wide range of physical properties of the working medium. The lower and upper limits of applicability of the formula for bubble and jet modes of bubble formation have been established.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 8","pages":"664 - 674"},"PeriodicalIF":0.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226379","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}
{"title":"Contribution of Coal Electricity to Global CO2 Emissions: The Existing Situation and Current Trends of Their Reduction","authors":"A. N. Tugov","doi":"10.1134/S0040601524700125","DOIUrl":"10.1134/S0040601524700125","url":null,"abstract":"<p>CO<sub>2</sub> emissions into the atmosphere in the electricity sector in 2022 exceeded 12.4 billion t, which is 1.8 times more than in 2000. The reasons for this growth are analyzed. It is noted that a significant contribution to these emissions (75%) is made by electricity generation using coal as fuel. It has been shown that it cannot be expected that CO<sub>2</sub> emissions will decrease in the near future as a result of the reduction in coal capacity; there is a steady increase in the world. In the 21st century, the total capacity of coal-fired thermal power plants increased approximately 1.9 times. Alternative ways to reduce greenhouse gas emissions are being considered, primarily through the construction of new, highly efficient power units with increased steam parameters and the decommissioning of obsolete equipment. Thanks to this, the structure of coal generation in the world is changing significantly: Thermal power plants with power units for super-supercritical (SSCP) steam parameters and supercritical pressure (SCP) already account for more than 47% of the total capacity of coal-fired thermal power plants. Such changes contributed to a reduction in specific greenhouse gas emissions from 466 g CO<sub>2</sub>/(kW h) in 2000 to 436 g CO<sub>2</sub>/(kW h) in 2022. In the Russian electricity sector, CO<sub>2</sub> emissions in 2022 amounted to approximately 410 million t. Since 2000, they have grown by only 22%. The share of CO<sub>2</sub> emissions from coal thermal power plants in Russia are estimated at 35–45% of the total amount of greenhouse gases associated with electricity production and does not exceed 0.5% of the global total due to the use of fossil fuels. Due to the low contribution of CO<sub>2</sub> emissions by Russian coal-fired thermal power plants, reducing greenhouse gas emissions from coal-fired power generation is not so relevant in the global problem and are solved mainly by replacing coal with natural gas. The need to introduce highly efficient but expensive equipment (for example, SSCP power units) at coal-fired thermal power plants to reduce emissions greenhouse gases is not as obvious as abroad, and its implementation requires a detailed feasibility study.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 7","pages":"547 - 559"},"PeriodicalIF":0.9,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772439","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}
M. M. Bedretdinov, O. E. Stepanov, D. N. Moisin, M. A. Bykov
{"title":"Computational Studies of Thermal Hydraulics in a New Integral Reactor Plant VVER-I with Natural Circulation","authors":"M. M. Bedretdinov, O. E. Stepanov, D. N. Moisin, M. A. Bykov","doi":"10.1134/S0040601524700071","DOIUrl":"10.1134/S0040601524700071","url":null,"abstract":"<p>In the present-day conditions under which the nuclear power industry is developed, a need arises to diversify the designs of new nuclear power plant units, which should differ from the previously constructed ones by featuring flexibility to the customer requirements and by using safety systems based on fully passive safety assurance principles. In 2022, specialists of Experimental and Design Organization (OKB) Gidropress commenced activities on elaborating the draft design of a new integral pressurized water-cooled reactor plant VVER-I with natural circulation of coolant for a basic thermal capacity of 250 MW. The design incorporates passive safety systems able to provide reliable heat removal from the core under the conditions of a long-term NPP blackout and without the operator’s participation. The article presents the results obtained from thermal and fluid dynamic computations of the new reactor plant carried out using the KORSAR/GP code that has been certified for safety analyses. A reactor plant thermal-hydraulic model, which can be used for computations of stationary normal operation conditions and, subsequently, also for simulating the accident scenarios evolvement dynamics, has been developed and tested. Computations carried out using the system code have confirmed a correct choice of the reactor’s main geometric parameters and the steam generator’s heat-transfer surface for operation at the nominal power. Based on the computation results for optimizing the design, it is proposed to use a jacketed steam generator, which will make it possible to exclude stray coolant leaks in bypass of the heat-transfer surface. It is shown that the newly developed reactor plant has a significant potential for increasing the thermal power capacity up to 400 MW without introducing fundamental changes in the design. The study results can be used in designing new VVER reactors with natural coolant circulation, and also in the development of passive safety systems.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 7","pages":"591 - 599"},"PeriodicalIF":0.9,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772443","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}