SAE International Journal of Engines最新文献

{"title":"Optical Study on Spark Plug Gap in Extending Methane Lean Combustion\u0000 Limits under High Ignition Energy Conditions","authors":"Xiao Zhang, Ren Zhang, Lin Chen","doi":"10.4271/03-16-08-0059","DOIUrl":"https://doi.org/10.4271/03-16-08-0059","url":null,"abstract":"Lean combustion has the potential to achieve high thermal efficiency for internal\u0000 combustion engines. However, natural gas (NG) engines often suffer from slow\u0000 burning rates and large cyclic variations when adopting lean combustion. In this\u0000 study, the effects of spark plug gaps (SPGs) on methane lean combustion are\u0000 optically investigated under high ignition energy conditions. Synchronization\u0000 measurements of in-cylinder pressure and high-speed photography are performed\u0000 for combustion analysis. The results show that large SPGs with high ignition\u0000 energy exhibit great improvement in engine combustion stability and power\u0000 capability. Under ultra-lean conditions, a large SPG with a high ignition energy\u0000 of 150–200 mJ can extend the lean limit to 1.55. Combustion images indicate that\u0000 this is contributed by the enlarged initial flame kernel, which promotes early\u0000 flame propagation. Besides, an empirical criterion is adopted to quantify the\u0000 underlying mechanism, and the results confirm that a more stable early flame\u0000 development with a faster burning rate can be obtained by a larger SPG and\u0000 higher ignition energy under lean conditions. Therefore, a large SPG is an\u0000 effective way to improve combustion stability and thermal efficiency for NG\u0000 engines.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76216011","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":"Repetitive Multi-pulses Enabling Lean CH\u00004\u0000-Air Combustion\u0000 Using Surface Discharges","authors":"R. Umstattd, C. Jiang","doi":"10.4271/03-16-08-0061","DOIUrl":"https://doi.org/10.4271/03-16-08-0061","url":null,"abstract":"The development of efficient and reliable ignition systems for lean fuel-air\u0000 mixtures is of great interest for applications associated with the use of\u0000 combustion in transportation, electricity production, and other heavy\u0000 industries. In this study, we report the use of repetitive nanosecond pulsed\u0000 surface discharges for the ignition of lean methane (CH4)-air\u0000 mixtures at pressures above 1 bar. Powered by ten 10-ns voltage pulses at 10\u0000 kHz, a commercially available non-resistive spark plug was used to generate\u0000 surface discharges, which were able to ignite CH4-air mixtures at 1.5\u0000 bar and with equivalence ratios (ϕ) ranging from 1.0 to 0.5. At the leanest\u0000 conditions, e.g., ϕ ≤ 0.6, nitric oxide (NO) and nitrogen dioxide\u0000 (NO2) emission were reduced to <10% of their values at ϕ =\u0000 1.0, demonstrating the advantage of lean burn in emission reduction. Consistent\u0000 ignition was obtained under extremely lean conditions (e.g., ϕ = 0.5) with a\u0000 minimum of five pulses and a minimum Coulomb transfer of 82 μC. Additionally,\u0000 the surface plug durability was tested for 114 hours or over 12 million pulse\u0000 trains by operating the surface plug in 3.5 bar of dry air at 30 pulse trains\u0000 per second. This study shows that the use of repetitive nanosecond pulses with\u0000 surface discharge-based plugs holds promise for a durable ignition solution.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86550357","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":"Ignition Characteristics of Dielectric Barrier Discharge Ignition\u0000 System under Elevated Pressure and Temperature in Rapid Compression and\u0000 Expansion Machine","authors":"Saurabh Agrawal, Shuya Yamamoto, N. Horibe, J. Hayashi, H. Kawanabe","doi":"10.4271/03-16-08-0060","DOIUrl":"https://doi.org/10.4271/03-16-08-0060","url":null,"abstract":"A rapid compression and expansion machine (RCEM) was used to experimentally\u0000 investigate the ignition phenomena of dielectric-barrier discharge (DBD) in\u0000 engine conditions. The effect of elevated pressure and temperature on ignition\u0000 phenomena of a methane/air premixed mixture was investigated using a DBD\u0000 igniter. The equivalence ratio was changed to elucidate the impact of DBD on\u0000 flame kernel development. High-speed imaging of natural light and OH*\u0000 chemiluminescence enabled visualization of discharges and flame kernel.\u0000 According to experimental findings, the discharges become concentrated and the\u0000 intensity increases as the pressure and temperature rise. Under different\u0000 equivalence ratios, the spark ignition (SI) system has a shorter flame\u0000 development time (FDT) as compared with the DBD ignition system.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90706426","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":"Improved Correlations for the Unstretched Laminar Flame Properties of\u0000 Mixtures of Air with Iso-octane and Gasoline Surrogates TRF86 and\u0000 TRF70","authors":"Delong Li, Matthew J. Hall, R. Matthews","doi":"10.4271/03-16-08-0058","DOIUrl":"https://doi.org/10.4271/03-16-08-0058","url":null,"abstract":"Laminar flame properties embody the fundamental information in flame chemistry\u0000 and are key parameters to understanding flame propagation. The current study\u0000 focuses on two parameters: the unstretched laminar flame speed (LFS) and\u0000 ϕm\u0000 (the equivalence ratio at which the LFS reaches its maximum). Most\u0000 existing correlations for LFS are either only applicable within a narrow range\u0000 of conditions or built on a large number of coefficients. Few correlations are\u0000 available for ϕm\u0000 . Thus, the objectives of the current study are to provide accurate,\u0000 while concise, correlations for both properties for a wide range of working\u0000 conditions in internal combustion (IC) engines, including dilution effects. The\u0000 original results were obtained for iso-octane and gasoline surrogates from\u0000 one-dimensional (1D) simulations for a range of 300–950 K for unburned\u0000 temperature, 1–120 bar for system pressure, 0.6–1.4 for equivalence ratio, and\u0000 0–0.5 for diluent mass fraction, and then were correlated using an improved\u0000 power law method and an improved Arrhenius form method. Comparisons with the\u0000 literature show that the predicted LFSs from both methods and\u0000 ϕm\u0000 s are close to the experimental measurements for a wide range of\u0000 conditions. The predicted dilution factor has a similar trend with others, but\u0000 fewer coefficients are needed. Overall, the improved Arrhenius form is\u0000 recommended to calculate the LFS for future use, considering its lower standard\u0000 errors. The experimental measurements at very high temperatures and pressures\u0000 are limited, and thus the predictions under these conditions need further\u0000 validation.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77968920","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":"Effect of the Thermal Mean Stress Value on the Vibration Fatigue\u0000 Assessment of the Exhaust System of a Motorcycle Engine","authors":"S. G. Barbieri, V. Mangeruga, M. Giacopini, Marco Severino Callegari, Leonardo Bagnoli","doi":"10.4271/03-16-08-0057","DOIUrl":"https://doi.org/10.4271/03-16-08-0057","url":null,"abstract":"The exhaust manifold of a high-performance motorcycle engine is subjected to\u0000 combined thermal and vibrational loadings. In this research, the whole fatigue\u0000 assessment of an exhaust manifold is addressed. First, a classic low-cycle\u0000 fatigue analysis is performed. Then, a specific methodology for determining the\u0000 fatigue cycle of components subjected to thermal and vibration loadings is\u0000 developed and presented in a way that possible damages can be evaluated. The\u0000 results are post-processed and the damage caused by fatigue cycles is computed\u0000 referring to the Wöhler curve of the material using the Dirlik approach.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91268769","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":"Thin-Wire Thermocouple Design for Exhaust Gas Temperature Pulse\u0000 Measurements in Internal Combustion Engines","authors":"Varun Venkataraman, O. Stenlaas, A. Cronhjort","doi":"10.4271/03-16-07-0055","DOIUrl":"https://doi.org/10.4271/03-16-07-0055","url":null,"abstract":"Accurate exhaust gas temperature (EGT) measurements are vital in the design and\u0000 development process of internal combustion engines (ICEs). The unsteady ICE\u0000 exhaust flow and thermal inertia of commonly used sheathed thermocouples and\u0000 resistance thermometers require high bandwidth EGT pulse measurements for\u0000 accurate cycle-resolved and mean EGTs. The EGT pulse measurement challenge is\u0000 typically addressed using exposed thin-wire resistance thermometers or\u0000 thermocouples. The sensor robustness to response tradeoff limits ICE tests to\u0000 short durations over a few exhaust conditions. Larger diameter multiwire\u0000 thermocouples using response compensation potentially overcomes the tradeoff.\u0000 However, the literature commonly adopts weaker slack wire designs despite\u0000 indications of coated weld taut wires being robust. This study experimentally\u0000 evaluates the thin-wire thermocouple design placed in the exhaust of a\u0000 heavy-duty diesel engine over wide-ranging exhaust conditions for improving both\u0000 sensor robustness and accuracy of the measured EGT. The assessed design\u0000 parameters included the wire diameter (51 μm to 254 μm), the exposed wire\u0000 length, and the wires placed slack or taut with coated weld faces. All taut\u0000 wires with ceramic-coated weld faces endured over 3 h of engine operation, while\u0000 similar diameter slack wires (51 μm and 76 μm) were sensitive to the exhaust\u0000 condition and exposed wire length. Reducing the wire diameter from 76 μm to 51\u0000 μm significantly impacted response improvements as evidenced at certain test\u0000 conditions by a peak-peak EGT increase of 92 °C, a mean EGT drop of 26 °C, and a\u0000 doubling of the sensitivity of mean EGT cycle-to-cycle variations to ±12 °C.\u0000 Increasing the exposed wire length showed less significant response\u0000 improvements. The Type-K thin-wire thermocouples showed negligible drift,\u0000 thereby indicating the possibility of using smaller and longer wires built taut\u0000 with coated weld faces for improved accuracy of EGT measurements in ICEs.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88310678","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":"Investigation Effects of Pre-chamber Volume Variations on the\u0000 Performance of a Natural Gas Lean-Burn Engine","authors":"M. Talei, S. Jafarmadar, Seyed Reza Amini Niaki","doi":"10.4271/03-16-07-0054","DOIUrl":"https://doi.org/10.4271/03-16-07-0054","url":null,"abstract":"The pre-chamber ignition system accelerates combustion efficiently by supplying\u0000 multiple ignition points, high ignition energy, and strong turbulent\u0000 disturbance. This system expands the lean combustion limit and improves\u0000 combustion stability on natural gas engines. This work studied the effects of\u0000 pre-chamber volume variations on combustion, performance, and emission behaviors\u0000 of a natural gas lean-burn engine under experimental and numerical methods.\u0000 Results show an increase in the pre-chamber volume from 0.3% to 4.4% of\u0000 compression volume can increase the in-cylinder pressure in single-stage\u0000 combustion. The energy and exergy efficiency of the engine Model-1.3% increased\u0000 up to 43.7% and 41.9%, respectively, which are the highest values among the\u0000 prepared models. Simultaneously, the model heat loss with the maximum\u0000 pre-chamber volume was two times higher than the minimum pre-chamber volume. The\u0000 exhaust gas exergy of Model-1.3% and Model-2.1% are the lowest values,\u0000 approximately 29% of the fuel exergy. Increasing the volume of the pre-chamber\u0000 from 1.3% of compression volume led to a reduction in emissions. An increase in\u0000 the pre-chamber volume increases the exit velocity of gases from the pre-chamber\u0000 bores, and turbulence in the entrance, exit, and inside the bores, which\u0000 generates uniform and isothermal heat across the cylinder. Therefore, a\u0000 pre-chamber with a compression volume below 5% stabilizes the combustion. Under\u0000 stable working conditions, a pre-chamber volume can be defined such that the\u0000 spark ignition (SI) engine would have the highest energy and exergy efficiencies\u0000 with the lowest emission.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74701925","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 Research on Performance Development of Direct Injection\u0000 Hydrogen Internal Combustion Engine with High Injection Pressure","authors":"Zhen Hu, Wenzhong Ma, Junjie Ma, Lei Zhou, Haiqiao Wei, H. Wei, Zeyuan Huang, Yinuo Hu, Ke Hu, Shuang Yuan","doi":"10.4271/03-16-07-0053","DOIUrl":"https://doi.org/10.4271/03-16-07-0053","url":null,"abstract":"As a carbon-free power with excellent performance, the direct injection (DI)\u0000 hydrogen-fueled internal combustion engine (H2-ICE) has the potential\u0000 to contribute to carbon dioxide (CO2)-neutral on-road transport\u0000 solutions. Aiming at high thermal efficiency, the influences of key factors on\u0000 thermal efficiency over wide operating conditions of a turbocharging DI\u0000 H2-ICE were investigated under the lean-burn strategy. And the\u0000 nitrogen oxides (NOx) emission characteristics region was clarified\u0000 in the high efficiency. The results confirm the optimal ignition strategy with\u0000 the CA50 of 8–9 crank angle degrees after top dead center (°CA ATDC). The\u0000 late-injection strategy manifests a significant advantage in brake thermal\u0000 efficiency (BTE) compared with the early-injection strategy, and this advantage\u0000 can be amplified by the increased load or injection pressure. The effects of\u0000 injection (EOIs) pressure on BTE exhibit different laws at different EOIs. Under\u0000 the early-injection strategy, the lower injection pressure improves BTE due to a\u0000 more sufficient mixing. While under the late-injection strategy with strong\u0000 mixture stratification, the high injection pressure conditions exhibit a higher\u0000 BTE due to reduced compression work. In terms of air-fuel ratio, the BTE is\u0000 improved monotonically with increased λ at low and medium loads. But there is an\u0000 optimal λ value limited by the oxygen concentration at a high load. The\u0000 late-injection strategies with high BTE perform a high level of NOx\u0000 emissions, which confirms the strong trade-off relationship between the thermal\u0000 efficiency and NOx emissions of H2-ICEs. A moderate\u0000 late-injection strategy with an EOI of about 40°CA BTDC can significantly reduce\u0000 the NOx emissions with a slight loss in BTE. The injection pressure\u0000 shows different effects on NOx emissions in different EOI ranges,\u0000 depending on the mixture distribution. In addition, ultra-lean burn and lower\u0000 intake temperature are effective means to reduce NOx emissions\u0000 without losing thermal efficiency.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75209916","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":"Flame Front Vector and Turbulence Analysis for Varied Equivalence\u0000 Ratios in an Optical Direct-Injection Spark-Ignition Engine","authors":"Yuwei Lu, Chenghua Zhang, S. Kook","doi":"10.4271/03-16-07-0052","DOIUrl":"https://doi.org/10.4271/03-16-07-0052","url":null,"abstract":"Homogenous lean combustion in a direct-injection spark-ignition (DISI) engine is\u0000 a promising pathway to achieve significantly improved fuel economy, making\u0000 already competitive petrol engines even more attractive as a future powertrain\u0000 option. This study aims to enhance the fundamental understanding of flame growth\u0000 occurring in a DISI engine with varied charge equivalence ratios of 1.0 to 0.6\u0000 while keeping a low compression ratio of 10.5, a typical side-mounted injector,\u0000 and early injected homogenous charge conditions. A new flame front vector\u0000 analysis is performed using the flame image velocimetry (FIV) method applied to\u0000 100 cycles of high-speed flame movies with trackable contrast variations and\u0000 pattern changes in the flame boundary. A spatial filtering method is used to\u0000 decompose the bulk flow component and high-frequency flow component with the\u0000 latter being interpreted as turbulence. The flame front FIV analysis shows that\u0000 excess air leads to slower flame front growth and lower turbulence causing an\u0000 exponential decrease in the burning rate. Compared to the stochiometric charge\u0000 condition, a leaner mixture with 0.6 equivalence ratio results in an up to 5 m/s\u0000 decrease in the flame front growth and 3 m/s decrease in the flame front\u0000 turbulence. Spatial variations increase up to 2.8 times in the flame front\u0000 vector magnitude and up to 2.25 times in the turbulence, particularly in the\u0000 early phase of the flame growth. The results suggest a new engine design for\u0000 higher turbulence generation is required to extend the lean limit, and thus\u0000 higher fuel economy is achieved in a DISI engine.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75380251","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 Evaluation of Pilot and Main Injection Strategies on\u0000 Gasoline Compression Ignition Engine—Part 1: Combustion\u0000 Characteristics","authors":"A. Agarwal, Vishnu Singh Solanki, M. Krishnamoorthi","doi":"10.4271/03-16-06-0046","DOIUrl":"https://doi.org/10.4271/03-16-06-0046","url":null,"abstract":"Climate change and stringent emission regulations have become major challenges\u0000 for the automotive sector, prompting researchers to investigate advanced\u0000 combustion technologies. Gasoline compression ignition (GCI) technology has\u0000 emerged as a potential solution, delivering higher brake thermal efficiency with\u0000 ultra-low nitrogen oxides (NOx) and particulate emissions. Combustion stability\u0000 and controls are some of the significant challenges associated with GCI. This\u0000 study investigates the combustion characteristics of a two-cylinder diesel\u0000 engine in GCI mode. GCI experiments were performed using a low-octane fuel\u0000 prepared by blending 80% (v/v) gasoline and 20% (v/v) diesel (G80). Baseline\u0000 experiments were conducted in conventional diesel combustion (CDC) mode. These\u0000 experiments investigated the effects of double pilot injection, first pilot fuel\u0000 ratio, and the start of main fuel injection timing (10–8°CA before top dead\u0000 center, bTDC). The results indicated that the GCI mode produced significantly\u0000 lower (~10%) in-cylinder pressure than the CDC mode. Higher pilot fuel\u0000 proportions exhibited a lower heat release rate (HRR) at low loads. Retarded\u0000 main injection showed a lower heat release in the premixed combustion phase than\u0000 the advanced main injection case at all loads. In addition, retarded main\u0000 injection timing showed retarded start of combustion (SoC) and end of combustion\u0000 (EoC). GCI mode exhibited higher cyclic variations than baseline CDC mode, which\u0000 need to be addressed.","PeriodicalId":47948,"journal":{"name":"SAE International Journal of Engines","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78313587","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}