Combustion and FlamePub Date : 2025-02-13DOI: 10.1016/j.combustflame.2025.114045
Jay Patel, Arindrajit Chowdhury, Neeraj Kumbhakarna
{"title":"Development and validation of a detailed reaction mechanism for the condensed phase decomposition of ammonium perchlorate","authors":"Jay Patel, Arindrajit Chowdhury, Neeraj Kumbhakarna","doi":"10.1016/j.combustflame.2025.114045","DOIUrl":"10.1016/j.combustflame.2025.114045","url":null,"abstract":"<div><div>The primary objective of the current research is to develop and validate a detailed reaction mechanism for the condensed-phase decomposition of ammonium perchlorate (AP), which is crucial for understanding the combustion behavior of AP-based propellants that are extensively used in solid rocket propulsion systems. Quantum mechanics calculations were performed at the B3LYP/6–311++G(d,p) level of theory to investigate the elementary reactions in the condensed phase, utilizing the Integral Equation Formalism of the Polarizable Continuum Model (IEFPCM) to simulate these reactions. Transition state theory was employed to determine the kinetic parameters, while the CBS-QB3 method was used to calculate the thermodynamic properties of the reactions. Experimental validation was achieved by comparing the computational results with data from laser pyrolysis and Fourier-transform infrared spectroscopy (FTIR) experiments, conducted at four isothermal conditions (410 °C, 430 °C, 450 °C, and 470 °C) in terms of mass loss and gas-phase mole fraction profiles. The computational model, incorporating a detailed reaction mechanism and product evaporation, closely matched experimental observations, with minor deviations attributed to experimental uncertainties. The model assumes that 40 % of AP undergoes sublimation, forming NH₃ and HClO₄ in the gas phase, while the remaining 60 % reacts in the condensed phase, producing species such as H₂O, HCl, NO₂, N₂O, ClO₂, HNO₃, and Cl₂, which evaporate into the gas phase. This validated reaction mechanism represents a significant advancement in modeling AP decomposition, providing valuable insights for safety and performance assessments in industrial applications.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114045"},"PeriodicalIF":5.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion and FlamePub Date : 2025-02-13DOI: 10.1016/j.combustflame.2025.114029
Andres Vargas, Arin Hayrapetyan, Ann R. Karagozian
{"title":"Dynamics of acoustically excited coaxial laminar jet diffusion flames","authors":"Andres Vargas, Arin Hayrapetyan, Ann R. Karagozian","doi":"10.1016/j.combustflame.2025.114029","DOIUrl":"10.1016/j.combustflame.2025.114029","url":null,"abstract":"<div><div>This experimental study explored combustion dynamics associated with coaxial laminar jet diffusion flames in the presence of acoustic excitation. The methane–air jets burned inside a closed cylindrical waveguide at atmospheric conditions, where flame behavior was captured via direct high-speed visible imaging. As the acoustic forcing increased at a fixed frequency in the vicinity of a pressure node associated with a standing wave, the flame underwent a transition from sustained oscillatory combustion (SOC) to periodic lift-off and reattachment (PLOR) and eventual flame blow-off (BO). The nature of this transition and flame–acoustic coupling was explored by varying a wide range of experimental parameters for five different coaxial jet geometries, including the jet Reynolds number, outer-to-inner jet velocity ratio, coaxial jet wall thicknesses and diameters, and amplitude of acoustic excitation. Flame–acoustic coupling processes were observed to vary significantly based on the annular-to-jet area ratios and tube wall thicknesses under similar flow conditions. Analyzing the spatiotemporal flame dynamics via proper orthogonal decomposition (POD) of high-speed imaging data revealed different signatures of the transition process, including abrupt changes in the mode energy distribution and a significant increase in the complexity of the phase portraits when flame dynamics involved additional time scales. Results from this study suggested that increased annular-to-inner area ratio and velocity ratio can greatly enhance flame stability and resistance to blow-off, with wall thickness playing a lesser role.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114029"},"PeriodicalIF":5.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion and FlamePub Date : 2025-02-13DOI: 10.1016/j.combustflame.2025.114039
Hang Xiao , Zhaohan Chu , Haodong Chen , Taichang Zhang , Jinghui Lu , Changyang Wang , Long Zhao , Bin Yang
{"title":"An experimental and modeling study on norbornane pyrolysis aided by chemical information from neural network-assisted molecular dynamics","authors":"Hang Xiao , Zhaohan Chu , Haodong Chen , Taichang Zhang , Jinghui Lu , Changyang Wang , Long Zhao , Bin Yang","doi":"10.1016/j.combustflame.2025.114039","DOIUrl":"10.1016/j.combustflame.2025.114039","url":null,"abstract":"<div><div>Norbornane has been reported in recent years as a diesel additive that can improve soot characteristics or as the backbone of new jet fuels to increase fuel density and the net heat of combustion. However, there is still a lack of experimental and modeling studies on norbornane pyrolysis, which limits its further application. This work uses a flow tube reactor to conduct experiments at 30 torr, 923 K ∼ 1373 K, with a photoionization molecular-beam mass spectrometer to identify and quantify the pyrolysis species. At the same time, an attempt is made to apply high-precision deep potential molecular dynamics (DPMD) to assist in kinetic model construction. Species analysis on MD simulations provides additional chemical information on key pyrolysis species in the norbornane pyrolysis system, which agrees with experimental results. Therefore, the reactions appearing in MD simulations are supposed to play a nonnegligible role in the experimental system, so that high-frequency reactions of selected are added to the pyrolysis kinetic model. Further comparison of experimental and modeling results shows that the modeling results can accurately predict experimental concentrations for most species. By analyzing the rate of production of all species in the system, we highlight their primary production and consumption pathways, especially the pathways from norbornane to benzene in the system. When conducting sensitivity analysis, it is found that the initial decomposition reactions of the fuel have large sensitivity coefficients on the experimental results, especially the concentration of norbornane; it is also noteworthy that the reactions extracted in the MD results have an essential impact on the concentration of 1,3-cyclohexadiene.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114039"},"PeriodicalIF":5.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion and FlamePub Date : 2025-02-13DOI: 10.1016/j.combustflame.2025.114028
Ignacio Trueba-Monje, Jeffrey A. Sutton
{"title":"Filtered Rayleigh scattering thermometry in premixed flames, Part II: Implementation and accuracy in turbulent flames","authors":"Ignacio Trueba-Monje, Jeffrey A. Sutton","doi":"10.1016/j.combustflame.2025.114028","DOIUrl":"10.1016/j.combustflame.2025.114028","url":null,"abstract":"<div><div>An important issue for conversion of measured filtered Rayleigh scattering (FRS) signals into temperature in combustion systems is the degree to which the local chemical state needs to be known or approximated. To avoid the need for simultaneous multi-species measurements, Part I of this paper series introduced a framework based on state relationships from one-dimensional laminar flame simulations to account for composition effects. Following the demonstration of accurate and reliable FRS-based thermometry under laminar flame conditions (Part I), this paper uses both computational and experimental data to evaluate the accuracy of this methodology in turbulent premixed flames. First, synthetic results from direct numerical simulations (DNS) of CH<sub>4</sub>/air flames under varying turbulence levels are used to directly evaluate the proposed FRS approach. Results demonstrate accurate temperature determination using the proposed FRS methodology with uncertainties of less than 3%. Analysis shows that, even when the local species composition fluctuates significantly in space and time, the conditional relationship between a given species and temperature shows relatively little scatter compared to the most probable value. Furthermore, there exists an apparent stable behavior where the under-prediction of some species by the presumed state relationship is counter-balanced by an over-prediction of other species in such a manner that the composition-dependent portion of the FRS signal-temperature relationship remains relatively unchanged and well represented by the laminar flame state relationship, regardless of temperature or turbulence level. Experimental results are also presented in a series of turbulent premixed flames with variations in reactant composition, equivalence ratio, and Reynolds numbers. Simultaneous laser Rayleigh scattering (LRS) and FRS measurements converge to common temperatures, indicating accuracy of the proposed FRS methodology within turbulent premixed flames. Overall, results demonstrate that laminar flame state relationships sufficiently capture the net effect of species formation, mixing, and transport with respect to their influence on the local FRS signal. This allows accurate FRS-based temperature measurements in turbulent premixed flames without the need for additional species measurements.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114028"},"PeriodicalIF":5.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion and FlamePub Date : 2025-02-12DOI: 10.1016/j.combustflame.2025.114044
Justin Sprunger , Andrew J. La Sorsa , Rachel Hytovick , Jonathan Sosa , Kareem A. Ahmed
{"title":"Turbulent flame compressibility criterion for scramjet unstart and transition","authors":"Justin Sprunger , Andrew J. La Sorsa , Rachel Hytovick , Jonathan Sosa , Kareem A. Ahmed","doi":"10.1016/j.combustflame.2025.114044","DOIUrl":"10.1016/j.combustflame.2025.114044","url":null,"abstract":"<div><div>A new criterion predicting the onset of scramjet unstart is proposed. The source of unstart is hypothesized to stem from the turbulent compressible flame choking altering the optimal thermal choking design location or geometry of a scramjet combustor for heat release. This criterion is useful for assessing scramjet unstart and engine tuning for optimal heat release for ideal expansion and engine performance.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114044"},"PeriodicalIF":5.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion and FlamePub Date : 2025-02-12DOI: 10.1016/j.combustflame.2025.114025
John H. Kim , Andrew B. Mansfield , Miles A. Burnett , Robert S. Tranter , Margaret S. Wooldridge
{"title":"Time-resolved measurements of OH during auto-ignition of syngas with trimethylsilanol and hexamethyldisiloxane","authors":"John H. Kim , Andrew B. Mansfield , Miles A. Burnett , Robert S. Tranter , Margaret S. Wooldridge","doi":"10.1016/j.combustflame.2025.114025","DOIUrl":"10.1016/j.combustflame.2025.114025","url":null,"abstract":"<div><div>The effects of trimethylsilanol (TMSO) and hexamethyldisiloxane (HMDSO) addition on OH time histories during syngas (H<sub>2</sub> and CO) ignition were investigated using the University of Michigan rapid compression facility. Experiments spanned temperatures of 1010–1080 K, at a pressure of approximately 5 atm. Syngas mixtures of 1.2 % H<sub>2</sub>/2.8 % CO/20 % O<sub>2</sub> by volume (balance N<sub>2</sub> and Ar) provided a baseline for comparison with mixtures that included 100, 200, and 1000 ppm of the TMSO and 100 ppm of HMDSO. Narrow-line ultraviolet laser-absorption was used to measure OH mole-fraction during ignition. The addition of TMSO and HMDSO significantly shifted the OH time-histories earlier in time, by up to 51 %, compared with the baseline syngas mixture. The value of the maximum OH mole fraction was consistent between the 100 and 200 ppm TMSO mixtures and the 100 ppm HMDSO mixtures, but the maximum OH increased significantly with the 1000 ppm TMSO mixtures. The OH data indicate TMSO and HMDSO were not direct sources of OH radicals. Analysis further indicates the TMSO and HMDSO decompose rapidly followed by reactions that enhance the production of H atoms, and the increased reactivity observed is via the <em>H</em> + O<sub>2</sub> = OH + O reaction.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114025"},"PeriodicalIF":5.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion and FlamePub Date : 2025-02-12DOI: 10.1016/j.combustflame.2025.114040
Ying Qu , Zhixun Xia , Xudong Na , Likun Ma , Yunchao Feng , Binbin Chen , Jiarui Zhang
{"title":"Primary combustion and near-burning surface conglomeration characteristics of boron-containing fuel-rich propellant","authors":"Ying Qu , Zhixun Xia , Xudong Na , Likun Ma , Yunchao Feng , Binbin Chen , Jiarui Zhang","doi":"10.1016/j.combustflame.2025.114040","DOIUrl":"10.1016/j.combustflame.2025.114040","url":null,"abstract":"<div><div>The study of primary combustion and near-burning surface conglomeration characteristics of boron-containing fuel-rich propellant can assist in the comprehension of the primary combustion mechanism. Here, the macroscopic combustion process and particles conglomeration behavior in the vicinity of the burning surface were investigated using a combination of online and offline analysis methods. Concurrently, the size of the relatively large conglomerates escaping from the burning surface was measured online by image measurement methods, and the corresponding size distribution and morphological parameters were provided. The results demonstrate that the combustion of this kind of propellant exhibited an obvious layered structure, characterized by a distinctive phenomenon of a “sedimentary layer”. The presence of the sedimentary layer exerted a certain influence on the combustion process. Boron particles could participate in the reaction during the primary combustion process, but appropriate reaction conditions, such as sufficient temperature and oxidizing gas concentration, were required. The accumulation and conglomeration of metal particles were completed under the influence of adhesion and separation forces, with the particles escaping from the burning surface in the form of coral-like conglomerates. The adhesion and detachment of conglomerates on the burning surface led to consistent fluctuations in the shape and height of the combustion flame, as well as the thickness of the sedimentary layer. Furthermore, due to the uneven stress on the conglomerates in the sedimentary layer, it was possible to observe the occurrence of a secondary conglomeration process, whereby small-sized conglomerates were captured by larger conglomerates as they escaped from the burning surface. The coral-like conglomerates consist of B, Mg, and Al monomers and their combustion products. They were widely distributed in the submicron to millimeter size range, which was significantly different from the size distribution of the combustion products obtained from the nozzle outlet of the gas generator.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114040"},"PeriodicalIF":5.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion and FlamePub Date : 2025-02-12DOI: 10.1016/j.combustflame.2025.114041
Zechang Liu , Guangyuan Feng , Xu He , Chengyuan Zhao , Xiaoran Zhou , Zhi Wang , Qingchu Chen
{"title":"Experimental investigation and kinetic analysis of ammonia addition on the laminar flame speed of toluene and α-methylnaphthalene","authors":"Zechang Liu , Guangyuan Feng , Xu He , Chengyuan Zhao , Xiaoran Zhou , Zhi Wang , Qingchu Chen","doi":"10.1016/j.combustflame.2025.114041","DOIUrl":"10.1016/j.combustflame.2025.114041","url":null,"abstract":"<div><div>This study explores the effects of ammonia (NH<sub>3</sub>) on the laminar flame speed (<span><math><msub><mi>S</mi><mi>L</mi></msub></math></span>) and kinetic interactions with toluene (C<sub>7</sub>H<sub>8</sub>) and α-methylnaphthalene (AMN), two predominant aromatic hydrocarbons in transportation fuels. Utilizing the spherical flame technique, we measured the <span><math><msub><mi>S</mi><mi>L</mi></msub></math></span> of both C<sub>7</sub>H<sub>8</sub>/NH<sub>3</sub> and AMN/NH<sub>3</sub> mixtures at an initial temperature (T<sub>i</sub>) of 484 K, NH<sub>3</sub> concentrations (X<sub>NH3</sub>) up to 70%, and equivalence ratios (<span><math><mi>ϕ</mi></math></span>) ranging from 0.8 to 1.3 under atmospheric pressure and elevated pressures. A chemical kinetic model was developed to integrate NH<sub>3</sub> with these hydrocarbons, based on the advanced CRECK model, and includes cross C-N reaction pathways involving amine (NH<sub>2</sub>) with C<sub>7</sub>H<sub>8</sub>, AMN, and benzene (C<sub>6</sub>H<sub>6</sub>). The model effectively replicated the experimental <span><math><msub><mi>S</mi><mi>L</mi></msub></math></span> and ignition delay time data for AMN/NH<sub>3</sub> mixtures. Through sensitivity and reaction pathway analyses, the study identified critical reaction types: such as small molecule chain branching reactions (e.g., H+O<sub>2</sub>=O+OH and CO+OH=CO<sub>2</sub>+H) and H-abstraction from both the methyl and ring sides, as pivotal in influencing <em>S<sub>L</sub></em>. Furthermore, the study examines the formation of NOx and soot, revealing that NH<sub>3</sub> addition both increased the mole fraction of NO in C<sub>7</sub>H<sub>8</sub>/NH<sub>3</sub> and AMN/NH<sub>3</sub> mixtures, but the mole fraction of NO in C<sub>7</sub>H<sub>8</sub>/NH<sub>3</sub> mixture is higher than AMN/NH<sub>3</sub> mixture, attributed to the higher HNO/NH<sub>2</sub>/N radicals in C<sub>7</sub>H<sub>8</sub>/NH<sub>3</sub> mixture, and finally leading to the promoted effect on the reaction pathways of NO production. The addition of NH<sub>3</sub> also inhibits soot formation by reducing the production of soot precursors and C<sub>2</sub>H<sub>2</sub>, while increasing the production of HCN and blocking the formation of larger PAHs.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114041"},"PeriodicalIF":5.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion and FlamePub Date : 2025-02-12DOI: 10.1016/j.combustflame.2025.114027
Ignacio Trueba-Monje, Jeffrey A. Sutton
{"title":"Filtered Rayleigh scattering thermometry in premixed flames—Part I: Laminar flames and the effects of mixture composition approximation","authors":"Ignacio Trueba-Monje, Jeffrey A. Sutton","doi":"10.1016/j.combustflame.2025.114027","DOIUrl":"10.1016/j.combustflame.2025.114027","url":null,"abstract":"<div><div>Filtered Rayleigh scattering (FRS) is a proven laser-based measurement technique that can be used to determine gas-phase properties in the presence of interference from unwanted surface or particulate scattering. In combustion environments, an important issue for conversion of measured FRS signals into temperature is the strong dependence on the local gas mixture composition. Previously, the importance of accurately characterizing the local chemical state has not been systematically evaluated in terms of FRS-based thermometry. Simultaneous quantitative measurements of all pertinent species are quite challenging and involve complex and expensive experimental setups. Thus, there have been previous FRS-specific approaches developed to approximate species composition that circumvent additional multi-scalar measurements. This paper is one of a two-part series that first seeks to evaluate the sensitivity of derived temperature estimates to the local composition and assess existing simplifying assumptions for approximating the unknown composition in laminar premixed flames. This paper uses a combination of simulations and experiments in laminar premixed flames of various fuels and equivalence ratios to understand the importance of composition knowledge/approximation for accurate FRS thermometry results. In general, results show that there is a need to reliably represent the most abundant species and their associated Rayleigh–Brillouin scattering spectral contributions. Approximations of the local composition by a single species lead to significant error (up to 50%) and non-physical results over a broad range of flame conditions. Finally, a simple but robust framework based on state relations from laminar flame calculations is recommended for accounting for composition effects. This approach leads to accurate (<span><math><mo><</mo></math></span>2% error) and reliable FRS-based temperature results in laminar premixed flames without the need for simultaneous species concentration measurements.</div></div>","PeriodicalId":280,"journal":{"name":"Combustion and Flame","volume":"274 ","pages":"Article 114027"},"PeriodicalIF":5.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}