Thermal Engineering最新文献

{"title":"Development and Study of Operating Characteristics of a Loop Heat Pipe with Increased Heat Transfer Distance","authors":"Yu. F. Maydanik,&nbsp;V. G. Pastukhov,&nbsp;M. A. Chernysheva","doi":"10.1134/S004060152402006X","DOIUrl":"10.1134/S004060152402006X","url":null,"abstract":"<p>The task of energy-efficient heat supply and removal in thermal control, heating and cooling systems is very relevant for many branches of technology. The paper presents the results of the development and study of a 21 m long loop heat pipe (LHP) that is a passive heat-transfer device operating on a closed evaporation-condensation cycle and using capillary pressure to pump a working fluid. These devices can be used in systems where the heat source and the heat sink are removed from each other by a distance measured in meters and even tens of meters, without the use of additional energy sources. The device has a 24 mm diameter evaporator with a 188 mm long heating zone, a vapor line and a liquid line (external/internal diameters of 8/6 mm and 6/4 mm). A 310 mm long pipe-in-pipe heat exchanger equipped with a cooling jacket was used as a condenser. The tests were conducted with the LHP in a horizontal position. Heat was removed from the condenser by forced convection of a water-ethylene glycol mixture with temperatures of 20 and –20°C and a flow rate of 6 dm³/min. The heat load supplied to the evaporator from the electric heater increased from 200 to 1700 W in the first case and to 1300 W in the second. The vapor temperature at the outlet of the evaporator varied from 25 to 62°C and from 24 to 30°C, respectively. Its maximum temperature difference along the length of the vapor line did not exceed 4°C. Such devices can be used in energy-efficient systems for utilizing low-potential heat, heating or cooling remote objects, and for uniformly distributing heat over a large surface area of heat sinks.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 2","pages":"158 - 166"},"PeriodicalIF":0.9,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152086","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":"Numerical Investigation of a Developed Turbulent Flow and Heat Transfer in a Rectangular Channel with Single-Sided Internal Ribs","authors":"V. V. Ris,&nbsp;S. A. Galaev,&nbsp;A. M. Levchenya,&nbsp;I. B. Pisarevskii","doi":"10.1134/S0040601524020083","DOIUrl":"10.1134/S0040601524020083","url":null,"abstract":"<p>The problem of a fully developed turbulent flow and developed heat transfer was solved numerically at a Reynolds number ranging from 5 × 10⁴ to 2 × 10⁵ for a spatially periodic model of a one-sided ribbed channel as a prototype of the flow path of an internal convective cooling system for a gas turbine blade. The flow and heat transfer were investigated at the Prandtl number of 0.7. The channel has a rectangular cross-section with an aspect ratio of 1.5. Square ribs with a 10% rib-to-channel height ratio are installed on one of the wide channel walls at an angle of 45° to the longitudinal axis of the channel. To quantify the effect of ribs on the flow and heat transfer, the integral parameters, such as hydraulic resistance factor and Nusselt number determined from the grid-converged solutions, are compared with the integral parameters for a fully developed flow and heat transfer in a smooth channel predicted by the same numerical method. The results of numerical simulation for the ribbed channel are also compared with published experimental data obtained under partly similar conditions. The predicted hydraulic resistance factor agrees well with the experiment. The predicted heat transfer agrees with the experiment within 11%, but the trends in heat transfer with increasing Reynolds number obtained using numerical and physical simulation are different. This difference may be caused by the fact that fully developed heat transfer could not be attained in the short experimental channel. Analytical power-law dependences on the Reynolds number are obtained for the hydraulic resistance factor and the Nusselt number pertaining to all channel walls and only to the ribbed wall. It is pointed out that the hydraulic resistance factor depends weakly on the Reynolds number, which is typical for local resistances, and the dependences for Nusselt numbers corrected for the specifics of the problem are close to the dependences for near-wall layers and flows in smooth channels.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 2","pages":"167 - 175"},"PeriodicalIF":0.9,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152156","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":"Improving the PGU-450T Unit’s Maneuverability while Retaining Its Reliability and Economic Efficiency in Variable Load Modes","authors":"E. K. Arakelyan,&nbsp;A. V. Andryushin,&nbsp;F. F. Pashchenko,&nbsp;S. V. Mezin,&nbsp;K. A. Andryushin,&nbsp;A. A. Kosoi","doi":"10.1134/S0040601524020022","DOIUrl":"10.1134/S0040601524020022","url":null,"abstract":"<p>The article addresses the problem of securing reliable and economically efficient operation of cogeneration combined cycle power plants (CCPPs) taking the PGU-450 unit as an example during its operation at partial loads and performing control of the electrical loads in the condensing mode and heat and electrical loads in the cogeneration mode. The main constraints hindering wide-scale involvement of CCPPs to control of electrical and heat loads are noted. The need to switch the gas turbines, which feature limited capacities of bearing variable loads, into a mild operation mode with shifting the main load on the steam turbine is pointed out. A technology of PGU-450 operation at partial loads is suggested: CCPP unloading in accordance with the operation manual to the gas turbine permissible base load, e.g., according to the environmental constraint during its operation in the condensing mode, and further decrease of the power unit electric output at a constant base power output of the gas turbines and heat recovery steam generators through decreasing the steam turbine output by applying bypass steam admission or shifting a part of the high-pressure cylinder (HPC) or the entire HPS, or the steam turbine as a whole to operate in the generator-driven mode. The article presents the results of applying various bypass steam admission configurations during the CCPP operation in the condensing mode, including when shifting part of the HPC or the entire HPC, and the steam turbine as a whole is shifted to operate in the generator-driven mode when the CCPP is shut down in a standby mode in passing off-peak load hours. It has been shown that the use of bypass steam admission during the CCPP operation in the cogeneration mode is more economically efficient than it is in the condensing mode. The article also shows the advantage, in terms of reliability and economic efficiency, of shifting the steam turbine to operate in the generator-driven mode instead of its shutdown during the PGU-450 unit’s operation in the gas turbine unit‒combined heat and power plant (GTU‒CHPP) mode and passing the electric load curve off-peak hours.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 2","pages":"108 - 117"},"PeriodicalIF":0.9,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140151991","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":"Substantiation by Calculation of a System for Hydrogen Production from Biomass Using Chemical Looping Gasification","authors":"D. S. Litun,&nbsp;G. A. Ryabov","doi":"10.1134/S0040601524020058","DOIUrl":"10.1134/S0040601524020058","url":null,"abstract":"<p>Modern requirements for the production of hydrogen with a minimum carbon footprint, the possibility of using polygenerating systems for production of electricity, heat, or useful products, and chemical-looping technologies for producing hydrogen combined with capture of carbon dioxide are considered. A new system has been developed that integrates the use of biomass as a fuel, chemical looping, and syngas production in a polygenerating system of interconnected reactors, which is very promising in maximizing the effectiveness of hydrogen production without a carbon footprint (or with a negative carbon footprint). A procedure and results of calculations of the composition and consumption of generator gas, material balance of a chemical looping system, heat values of chemical reactions in a system of interconnected reactors, heat balance and temperatures in individual reactors, and heat and material balances in exhaust gas heat recovery units are presented. The effect of the main operating conditions of a chemical looping system on temperatures in the reactors was determined on the basis of the calculated and material balances. The calculated efficiency in terms of hydrogen production (75.93%) is given. This value fits well into the broad outline of the results obtained in simulation of similar systems for chemical looping hydrogen production from metal oxides and can be considered as a guideline when developing engineering solutions within the scope of the proposed process flow diagram. Potential directions of further studies are set.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 2","pages":"176 - 190"},"PeriodicalIF":0.9,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140151989","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":"Determining the Optimum Pressure Differential Across the Control Valve of a Hydroturbine Driven Pump","authors":"A. V. Popov,&nbsp;E. N. Kulakov,&nbsp;P. A. Kruglikov,&nbsp;F. A. Svyatkin,&nbsp;P. G. Pavlov,&nbsp;R. S. Tarasenko,&nbsp;I. B. Denisova,&nbsp;A. V. Proukhin","doi":"10.1134/S0040601524020071","DOIUrl":"10.1134/S0040601524020071","url":null,"abstract":"<p>When using lead as a primary circuit coolant, certain difficulties arise not only from the side of the reactor plant (structural materials, fuel, etc.) but also from the side of the steam turbine cycle. A feature of the second circuit of a lead-cooled NPP is noted, such as the need to maintain a high temperature of the feedwater in front of the steam generator, caused by its melting/freezing temperature. For the pilot demonstration power unit with the BREST-OD-300 reactor plant, it was decided to use a mixing feedwater heater, which entailed the appearance of a second rise in the feed pump circuit. Due to the lack of electric drive pumps for such high parameters, it was proposed to use a hydraulic turbine driven pump as a feed pump behind the mixing feedwater heater. These pumps have a significant impact on efficiency due to the multistage energy conversion, and there is no recommendation for selecting resistance on the control valve of these pumps. A computational study was carried out to determine the optimal pressure drop on the control valve of the hydraulic turbine drive of the feed pump of the power unit with the BREST-OD-300 reactor plant. Optimal is understood as the ultimate minimum differential at which the valve is able to carry out regulation with specified quality criteria and ensure the lowest energy consumption for its own needs. Recommendations are given for choosing the optimal pressure drop on the control valve of the hydraulic turbine drive of the feed pump of a turbine unit with the BREST-OD-300 reactor. A methodology has been developed for solving problems of optimizing pressure drop in units of complex hydraulic systems.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 2","pages":"118 - 124"},"PeriodicalIF":0.9,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140151988","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":"Assessing the Effectiveness of NPP Participation in Covering Peak Electrical Loads Based on Hydrogen Technology","authors":"R. Z. Aminov,&nbsp;A. N. Egorov,&nbsp;A. N. Bayramov","doi":"10.1134/S0040601524020010","DOIUrl":"10.1134/S0040601524020010","url":null,"abstract":"<p>One of the goals of the Russian Energy Strategy until 2035 is the development of hydrogen energy, namely, achieving global leadership in the export of hydrogen obtained from the use of energy from renewable sources and nuclear power plants. Further development of nuclear energy involves its production at existing nuclear power plants. One of the real examples is the production of hydrogen by electrolysis of water at the Kola Nuclear Power Plant. Currently, active research is being conducted in the field of hydrogen energy, and effective technologies for water electrolysis and reversible fuel cells (RFC) are being developed, which are used, among other things, in decentralized energy supply systems. The achieved overall efficiency of 37.18 and 49.80% with specific capital investments in the ranges of 1595–2050 and 1828–2396 $/kW in RFCs with solid polymer and solid oxide electrolytes, respectively, allows us to consider them as a means of storage during hours of reduced generation (off-peak) electricity from nuclear power plants. A universal (generalized) scheme for the use of hydrogen technologies at nuclear power plants has been developed based on combining systems of “hot” combustion of hydrogen in an oxygen environment to produce high-parameter water vapor (temperatures up to 3600 K at a pressure of 6 MPa) and “cold” combustion of hydrogen in fuel cells, including reversible ones. A comparative assessment of the technical and economic efficiency of peak electricity production based on the proposed options for hydrogen technologies used at nuclear power plants was carried out. Capital investments in RFC have been determined, which ensure equal technical and economic efficiency of peak electricity production when implementing the considered options. Nomograms have been developed to determine the cost of production during peak hours depending on tariffs and volumes of consumption during the off-peak period as well as capital investments in RFC. As calculations have shown, the cost of its production is 1.52–2.93 rubles/(kW h). Taking into account the useful service life of RFC leads to a significant increase in cost: it varies from 3.74 to 6.53 rubles/(kW h).</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 2","pages":"125 - 141"},"PeriodicalIF":0.9,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152077","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":"A Simple Method for Increasing the Boiling Critical Heat Flux","authors":"A. V. Dedov,&nbsp;M. D. Filippov","doi":"10.1134/S0040601524010026","DOIUrl":"10.1134/S0040601524010026","url":null,"abstract":"<p>The article considers a study of the possibility to increase the boiling critical heat flux <i>q</i>_cr through the use of surfaces consisting of areas with different heat conductivity. The results of experiments on studying pool boiling heat transfer for saturated dielectric fluid methoxynonafluorobutane (Novec 7100) on bimetallic surfaces are presented. The studies were carried out for bimetallic samples and also for samples made of copper and grade 08Kh18N10T stainless steel in the pressure range 0.1–0.4 MPa. A description of the experimental setup and the procedures used is given. The boiling curves for each sample in the entire presented range of fluid pressures with a step of 0.1 MPa are obtained, and the tables of critical heat-flux values are given. The effect that the liquid pressure has on the relative increase of <i>q</i>_cr for bimetallic samples is shown. The values of <i>q</i>_cr obtained on all samples are compared with one another, and the increase of <i>q</i>_cr on bimetallic surfaces by up to 20% is shown. The previously performed studies are briefly reviewed, and the experimental data obtained by other researchers on boiling heat transfer on surfaces with modulated heat conductivity and for boiling of Novec 7100 fluid are presented, including that on samples with a modified heat-transfer surface. The obtained results are compared with rather few data of other researchers. The temperature field in a bimetallic sample is numerically simulated, and the temperature distribution over the heat-transfer surface is presented. The growth of <i>q</i>_cr is due to nonisothermal properties of the heat-transfer surface, which causes the boiling to become regularized.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 1","pages":"88 - 96"},"PeriodicalIF":0.9,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047401","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":"Towards Climate Neutrality: Will Russian Forest Stand Against Energy?","authors":"V. V. Klimenko,&nbsp;A. V. Klimenko,&nbsp;A. G. Tereshin","doi":"10.1134/S0040601524010051","DOIUrl":"10.1134/S0040601524010051","url":null,"abstract":"<p>The prospects for reducing the carbon intensity of the Russian economy and the possibility of achieving climate neutrality of the country’s national economy by 2060 are examined. Based on a historical-extrapolation approach to the study of the development of various socio-technical systems and by comparing the dynamics of carbon indicators of the economies of Russia and the leading countries of the world, it is shown that full compensation of anthropogenic greenhouse gases emissions when absorbed by the biosphere (primarily forests) is today rather only theoretically possible. The condition for this is the implementation of extremely ambitious large-scale reform programs in all sectors of the Russian economy, from energy to forestry. Thus, in an optimistic scenario, the decline rate of specific indicators of greenhouse gas emissions per capita should have the maximum values achieved in the world over the last 50 years, i.e. 1%/year. Forest management must include full compensation for increasing deforestation and a 50% reduction in forest losses from fires, which are currently the second (after energy) source of greenhouse gas emissions into the atmosphere. The most likely scenario is one in which the decline rate of specific greenhouse gas emissions per capita is 0.5%/year and a moderate increase in the absorption capacity of forests is ensured, mainly due to the implementation of forest climate projects and a reduction in wildfire emissions. If the latter scenario is implemented, net greenhouse gas emissions could amount to approximately 700 Mt CO₂ (equiv.) by 2060, which will require the nation’s carbon capture and storage industry on an unprecedented scale to achieve climate neutrality.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 1","pages":"3 - 17"},"PeriodicalIF":0.9,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047439","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":"Low-Emission Combustion Chambers of GTU: Modern Trends, Diagnostics, and Optimization (Review)","authors":"L. M. Chikishev,&nbsp;D. M. Markovich","doi":"10.1134/S0040601524010014","DOIUrl":"10.1134/S0040601524010014","url":null,"abstract":"<p>A brief overview of the designs of low-emission gas turbine-type combustion chambers is given using the example of aircraft propulsion systems. The most promising technology that helps reduce emissions of harmful substances is the combustion of a lean premixed fuel-air mixture, but its use is limited by nonstationary phenomena that have a significant impact on flame stabilization and lead to the occurrence of thermoacoustic resonance. Currently, this technology is implemented for high-power engines by only two companies: General Electric and Rolls-Royce. Work on creating a high-thrust engine in Russia is being carried out at AO UEC-Aviadvigatel within the framework of the PD-35 program. The problems of developing low-emission combustion chambers for gas pumping units are successfully solved at AO UEC-Aviadvigatel together with the Baranov Central Institute of Aviation Motor Development (GTU-16P). One of the key areas of energy development is also the development of high-power gas turbines of the classes GTE-65, GTE-170 (PAO Power Machines), GTD-110M (ODK Saturn), and here it is necessary to solve the same problems as for gas turbine engines. The most pressing problems are predicting the occurrence of thermoacoustic self-oscillations of gas in combustion chambers and controlling them using feedback both in nominal modes and in low-power modes. A review of technologies using low-emission combustion chambers is presented, and the current state of experimental studies of the flow structure and transfer processes in model combustion chambers is considered. Examples of advanced experimental stands that simulate flow and combustion in gas turbine-type combustion chambers are given and the necessary operating parameters and the technical solutions used are indicated that allow efficient measurements using modern optical diagnostic methods.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 1","pages":"44 - 64"},"PeriodicalIF":0.9,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047402","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":"Heat Price Field Calculation Based on the Extreme Problem of Searching the Optimal Load Flow in Heat-Supply Systems","authors":"V. A. Stennikov,&nbsp;O. V. Khamisov,&nbsp;A. V. Pen’kovskii,&nbsp;A. A. Kravets","doi":"10.1134/S0040601524010075","DOIUrl":"10.1134/S0040601524010075","url":null,"abstract":"<p>The article proposes a method for calculating differentiated prices for heat at the nodes of a heat-supply system (HSS) based on the extreme economic formulation of the problem of searching for the optimal load flow in heat networks containing several heat sources. The problem boils down to finding the minimal total costs associated with heat generation and transportation, maintaining of material balances at heat network nodes (Kirchhoff’s first law), and constraints imposed on the heat source capacities. The problem is solved on the basis of Lagrange’s method of undetermined multipliers. An analysis of the initial optimization problem duality has shown that the dual variables (Lagrange’s multipliers) in balance constraints are nothing but nodal prices for heat, and the optimal load flow in a heat network obtained in the calculation process makes it possible to form the price field for the system as a whole. It is also shown that the prices for heat from the heat sources to end consumers increase in the direction of the steady-state optimal load flow in the heat network. With such an approach to solving the problem, it is also possible to determine the optimal action zones and levels of loading the heat sources taking into account their cost characteristics and the specified heat network’s physical, technical, and economic indicators. The nodal prices obtained from the calculations are in their economic essence marginal ones, i.e., prices based on calculating the limit low and limit high costs for generation and transportation of an additional unit of heat.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"71 1","pages":"36 - 43"},"PeriodicalIF":0.9,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047654","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}