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第49卷第3期2021年5月河海大学学报(自然科学版)Journal of Hohai University(Natural Sciences)Vol.49No.3May 2021DOI :10.3876/j.issn.10001980.2021.03.001 基金项目:国家重点研发计划(2018YFC1508102);国家自然科学基金(41775111,41875131)作者简介:包红军(1980 ),男,正高级工程师,博士,主要从事水文气象预报与气象灾害风险预警研究㊂E⁃mail:baohongjun@通信作者:曹勇,高级工程师㊂E⁃mail:caoyong@引用本文:包红军,曹勇,曹爽,等.基于短时临近降水集合预报的中小河流洪水预报研究[J].河海大学学报(自然科学版),2021,49(3):197⁃203.BAO Hongjun,CAO Yong,CAO Shuang,et al.Flood forecasting of small and medium⁃sized rivers based on short⁃term nowcasting and ensemble precipitation forecasts [J].Journal of Hohai University(Natural Sciences),2021,49(3):197⁃203.基于短时临近降水集合预报的中小河流洪水预报研究包红军1,2,曹 勇1,2,曹 爽1,2,王 蒙1,2(1.国家气象中心,北京 100081;2.中国气象局-河海大学水文气象研究联合实验室,北京 100081)摘要:为了延长中小河流洪水预报预见期,建立了基于短时临近精细化网格降水集合预报的中小河流洪水预报模型㊂模型采用百分位映射订正技术,发展数值模式降水预报场与实况场映射关系,结合Bayesian 模型,构建基于GRAPES⁃3KM 模式和Time⁃Lag⁃Ensemble 融合技术的短时临近降水集合预报(最优集成㊁最大(95%分位数)㊁最小(5%分位数))格点场,作为GMKHM (Grid⁃and⁃Mixed⁃runoff⁃generation⁃and⁃Kinematic⁃wave⁃based Hydrological Model )的降水驱动,进行中小河流洪水逐小时实时滚动预报㊂选择新安江屯溪流域作为试验流域,对2020年汛期流域大洪水进行实时预报㊂检验结果表明,基于短时临近最优降水预报的中小河流洪水预报模型提前了7h 预报出屯溪断面洪峰,洪峰误差为5.6%,峰现时差为-1h ,比不考虑预见期降水的中小河流洪水预报提前了4h ;基于短时临近最大㊁最小降水预报的中小河流洪水预报模型提前了13h 预报出洪峰区间,并且自7月7日9时起滚动预报最大与最小预报跨度呈逐渐减少趋势㊂在中小河流洪水预报中引入短时临近集合预报降水,对提升中小河流洪水风险防控能力有重要意义㊂关键词:中小河流洪水预报;短时临近降水预报;GRAPES⁃3KM 模式;Time⁃Lag⁃Ensemble ;分布式水文模型;屯溪流域中图分类号:P338 文献标志码:A 文章编号:10001980(2021)03019707Flood forecasting of small and medium⁃sized rivers based on short⁃termnowcasting and ensemble precipitation forecastsBAO Hongjun 1,2,CAO Yong 1,2,CAO Shuang 1,2,WANG Meng 1,2(1.National Meteorological Center ,Beijing 100081,China ;2.CMA⁃HHU Joint Laboratory for Hydrometeorological Studies ,Beijing 100081,China )Abstract :A flood forecasting model for small and medium⁃sized rivers,based on the short⁃term nowcasting and fine ensemble gridded precipitation forecasts,is established for increasing the flood foresight period.The model adopts the percentile correction method to develop the mapping relationship between the precipitation forecast field of numerical model and the observed field.Based on the GRAPES⁃3KM model and the Time⁃Lag⁃Ensemble fusion technique,a short⁃term ensemble precipitation forecasting that is consist of three members (the optimal,maximum (95%quantile)and minimum (5%quantile))is developed with the Bayesian model.Taking the developed ensemble precipitation forecasts as the driving force of GMKHM,the hourly real⁃time rolling forecasting of flood for small to medium⁃sized basin is performed.The Tunxi Basin of the Xin’anjiang River is selected as the experimental basin to test the real⁃time flood forecasting in 2020flood season.Results show that the developed model performed well,the peak discharge of the Tunxi hydrological station was forecasted with 7hours in advance,the relative error was 5.6%,and the peak time difference was pared with that without considering the precipitation in lead⁃time period,the flood forecast lead⁃time can be increased by 4hours with the optional precipitation forecasts and 13hours with the maximum and minimum precipitation forecasts.The developed model has certain reference significance for the flood forecast of similar basin.The span between maximum and minimum forecasts presented the trend of decreasing gradually since 9:00on July 7th.It is of great significance to improve the flood risk prevention and control ability of small and medium⁃sized rivers with introducing the ensemble nowcasting and short⁃term precipitation forecasts.Key words :flood forecasting of small and medium⁃sized rivers;short⁃term nowcasting precipitation forecasts;GRAPES⁃3KM model;Time⁃Lag⁃Ensemble;distributed hydrological model;Tunxi Basin891河海大学学报(自然科学版)第49卷我国中小河流众多,洪水频发,灾害严重,已经成为当前洪水防控的薄弱环节[1]㊂根据国务院‘全国山洪灾害防治规划“,中小流域面积在200~3000km2之间,流域面积小,灾害突发性强,基础与观测资料不全,坡陡流急㊁汇流快㊁预见期短,预报预警难度大[2]㊂目前,国内外中小河流洪水预报主要有精细化分布式水文模型预报法和致洪临界雨量阈值预警预报法两种[3⁃5]㊂为了获得更长时效的预报预见期,引入预见期内的降水预报是提升中小河流洪水防控与减灾救灾的重要途径之一[6]㊂中小河流汇流一般在12h以内,如何提升面向中小流域0~12h的短时临近降水精准性预报,成为中小河流洪水精细化预报与风险防控研究的重要前沿问题[7⁃8]㊂根据中国气象局2017年‘全国短时临近预报业务规定“,短时临近降水预报分为0~2h临近降水预报和2~12h短时降水预报,不同时效的降水预报技术不尽相同[9]㊂目前,国内外的临近降水预报主要是以观测信息或分析数据进行外推,外推方法以卢卡斯卡纳德(Lucas⁃Kanade)光流法(简称LK光流法)为主,目前在天气业务中应用广泛[10]㊂中小尺度天气系统短时降水预报能力的提升主要依赖于数值天气预报模式,特别是快速滚动更新的高分辨率中尺度模式[11]㊂在国内,中国气象局GPAPES⁃3KM模式[11]㊁华东中尺度模型(SMB⁃WARMS)[12]和北京RMAPS模式[13]是提升短时降水预报能力的主要途径之一㊂但中小尺度天气系统降水局地性㊁突发性强,确定性数值模式难以考虑其不确定性,而传统基于初始场扰动㊁多物理过程等的集合数值预报,耗时费力,时效性难以满足需求[8]㊂本文面向中小流域,构建基于短时临近精细化网格降水集合预报的中小河流洪水预报模型㊂模型以中国气象局雷达组网和GRAPES⁃3KM模式为基础,发展基于金字塔架构的LK光流技术和强度守恒约束的Semi⁃Lagrangian平流技术的雷达外推临近降水预报技术,提出基于GRAPES⁃3KM模式和Time⁃Lag融合的短时降水集成预报和集合预报方法,实现0~12h逐小时降水集成与集合预报,驱动GMKHM(Grid⁃and⁃Mixed⁃runoff⁃generation⁃and⁃Kinematic⁃wave⁃based Hydrological Model)[14⁃16],建立中小河流洪水预报模型㊂以皖南山区新安江江屯溪以上流域(简称屯溪流域)为例,将洪水预报模型应用于2020年7月汛期洪水中进行实时预报,以探讨其对中小河流洪水预报精度与预见期延长的效果㊂1 短时临近降水集合预报的中小河流洪水预报模型建立基于短时临近降水集合预报的中小河流洪水预报模型包括短时临近降水集合预报和GMKHM两部分㊂基于多雷达组网和GRAPES⁃3KM模式,结合Time⁃Lag⁃Ensemble技术,发展短时临近降水三成员(最优集成㊁最大和最小)集合预报技术,以短时临近集合降水预报作为分布式水文模型的雨量驱动场,实现中小河流洪水预报㊂1.1 短时临近降水集合预报1.1.1 最优集成预报短时临近降水最优集成预报包括改进的雷达LK临近(0~2h)降水预报和基于GRAPES⁃3KM模式的短时(2~12h)降水集成预报两部分㊂1.1.1.1 改进的LK临近降水预报技术目前,国内外主要应用LK光流技术进行雷达外推临近降水预报㊂传统的LK光流法难以解决估计无降水区域的最优风场㊁雨强衰减计算误差以及系统生效问题,这是制约降水临近预报精度提升的重要因素之一㊂本文基于金字塔架构改进传统的LK光流法,利用空间升尺度技术,构建金字塔结构物理量场,生成8种空间尺度的降水预报场,从底层到高层逐渐分辨率降低(自底层起5km×5km至最高层30km×30km),再由上至下逐层利用LK光流技术获取当层的平流背景风场,并作为下一层的平流背景风场的初始场,实现最优估计无降水区域背景平流风场和有降水区域背景平流风场的精细结构㊂用于降水临近外推的Semi⁃Lagrangian技术,往往由于降水的非网格点插值易导致计算的外推降水强度逐渐减弱㊂本文利用插值前后两时刻降水累积百分位匹配技术,保持降水强度守恒,并结合GRAPES⁃3KM 模式环境场预报,建立前两个时次的降水生消变化及热力不稳定环境场定量关系,实时构建降水强度增减幅统计经验关系模型,实现在外推过程中降水强度订正计算㊂结合实时Z鄄R关系动态反演降水技术[10],实现基于改进LK光流法的雷达外推临近降水预报㊂第3期包红军,等 基于短时临近降水集合预报的中小河流洪水预报研究1.1.1.2 基于GRAPES⁃3KM 模式和Time⁃Lag 融合的短时降水最优集成预报GRAPES⁃3KM 模式是中国气象局国家级区域数值天气预报业务模式,自应用以来,大大提升了中央气象台中小尺度天气预报能力[11]㊂目前,GRAPES⁃3KM 快速更新同化系统实现了逐3h 快速滚动更新预报,并实时同化最新观测资料,在短时降水预报中小尺度系统强降水预报中准确率高㊂将GRAPES⁃3KM 模式预报作为短时定量降水预报的基础场,采用实时频率匹配订正技术,利用待订正量以及观测量样本资料,分别计算待订正量经验累积概率分布函数以及观测量经验累积概率分布函数,并利用两者在经验累积概率分布函数之间的差异,进行待订正量的数值订正,最终使得订正后待订正量的经验累积概率分布函数与观测量经验累积概率分布函数一致,具体计算公式如下:x c =F -1o (F m (x m ))(1)式中:x m 待订正量;F m (x m ) 待订正量的经验累积概率分布函数;F -1o (F m (x m )) 观测量经验累积概率分布函数的逆函数;x c x m 对应的订正值㊂Time⁃Lag 技术是针对某个预报时效㊁不同起报时刻的短时定量降水预报;Bayesian 模型根据前期降水预报与实况对应关系,计算出对应于某个预报时效各个起报时刻的短时定量降水预报融合权重系数,进行集成得到短时降水最优集成预报㊂基于GRAPES⁃3KM 模式的预报实时偏差订正技术流程见图1㊂图1 基于GRAPES⁃3KM 模式的预报实时偏差订正技术流程Fig.1 Flow chart of forecast real⁃time error correction technique based on GRAPES⁃3KM mode1.1.2 最大、最小预报考虑到天气过程固有的混沌效应以及预报技术对初始场的敏感性,相邻时刻起报的临近降水预报往往会有差异,这种差异表现为预报不确定㊂利用该特点,构建基于多起报时刻的时间滞后集合降水预报(Time⁃Lag Ensemble Forecast)㊂时间滞后集合降水预报的核心是基于快速更新同化系统构建集合成员,每一次循环更新将产生高频次的预报场,贡献新的集合成员,这一过程并不占用额外的计算机资源,成为一种经济实用的集合预报方案㊂考虑到不同起报时刻的临近降水预报成员不多,一般使用6个成员㊂由于直接使用概率预报以及求解分位数极值存在跳跃误差,为此采用一致性排序技术以及线性插值技术,拟合集合概率分布曲线,并利用该曲线,构建最小可能降水(5%分位)和最大可能降水(95%分位),与最优集成降水预报,形成3个集合预报成员,提供短时临近降水预报的最优预报和最大㊁最小预报㊂1.2 GMKHM 分布式水文模型Bao 等[14]在新安江水文模型的基础上,结合DEM 和RS 技术,构建基于DEM 网格的分布式混合产流水文模型(GMKHM)㊂模型是将流域内的DEM 网格作为水文响应过程的基本单元,并假设单元网格内地形地貌㊁陆面植被覆盖和土壤组成类型等下垫面条件和降水强迫空间分布一致,GMKHM 中只考虑DEM 网格间水文要素的变异性㊂在网格水文单元中,植被冠层截留和蒸散发计算后得到的净雨量,经过混合产流计算与划分水源,根据河网逐网格汇流演算次序,依次将地表径流㊁壤中流与地下径流演算至流域出口断面,得到其水文过程㊂在单元网格垂直方向上分为4层:植被层㊁上层土壤㊁下层土壤㊁深层土壤㊂在植被层考虑植被截留,对3层土壤层采用新安江水文模型的3层蒸散发模型进行蒸散发计算㊂应用考虑蓄满与超渗两种产流机制的混合产流模型进行网格内产流计算;坡面汇流和河道汇流均采用逐网格的一维运动波水流演算模型㊂在逐网格分布式汇流模型中,将上游网格入流作为当前网格单元产流计算中降水量的一部分处理,当此网格为河道网格,径流量将按比例汇入河道[15]㊂2 模型应用2.1 流域介绍及主要数据选取新安江屯溪流域作为模型应用检验流域㊂屯溪流域位于新安江流域上游皖南山区,属于副热带季991002河海大学学报(自然科学版)第49卷风气候区,多年平均降水量约为1800mm,为典型的湿润中小流域㊂屯溪水文站是新安江干流上游主要控制站,流域面积2693km2,地势西高东低,坡陡流急,最大落差达1018m,极易形成洪水㊂流域内植被良好,主要包括常绿针叶林㊁落叶阔叶林㊁混合林㊁灌木林㊁牧草地与耕地,土壤类型主要为壤土㊁砂质黏壤土㊁砂壤土和壤砂土㊂新安江流域为山区型河流,雨期集中在4 7月,洪水暴涨暴落,洪峰持续时间短,汛期与降水量一致,其降水量占年降水总量的65%㊂屯溪流域面积占整个新安江流域面积的24.4%㊂屯溪水文站实测最大洪峰流量5780m3/s(1969年5月5日)㊂屯溪流域1980 2013年间共34场次洪水,其中2008年的洪水最大,洪峰流量达5250m3/s;用于中小河流实时洪水预报的2020年汛期洪水,洪峰流量为5040m3/s㊂本文使用的气象数据来自中国气象数据网,水文数据摘自‘中华人民共和国水文年鉴“[17],DEM数据来自美国地质调查局(USGS)提供的全球30″×30″分辨率的DEM数据[18]㊂流域下垫面覆盖数据采用美国地质调查局提供的全球30″×30″土地覆盖数据[19]㊂2.2 模型参数空间估计GMKHM参数呈现空间网格上的不均匀分布,如直接应用传统流域出口断面水文过程难以进行模型参数率定㊂GMKHM依据参数的物理意义,建立与流域地貌特征㊁土壤类型以及植被覆盖等之间的定量关系,减少了模型参数对流域出口断面水文资料的依赖,可以获得参数合理的空间分布[19]㊂GMKHM蒸散发参数中叶面指数㊁最大叶面指数㊁作物高度通过每个栅格单元的LADS直接获取[20];深层蒸散发系数与栅格单元的植被覆盖率有关,在植被密集地区可取0.18,因此可假定其与植被覆盖率的比值为0.18[21];蒸散发折算系数主要与测量水面蒸发所用的蒸发器有关,对于国内普遍采用的E⁃601蒸发皿而言,一般取1;地表曼宁糙率系数可由陆面地表覆盖类型得到[22]㊂产流模型(含分水源)参数包括蓄满产流与超渗产流两类参数㊂单元栅格张力水容量㊁自由水蓄水容量根据赵人俊等[23]比较新安江模型与SACRAMENTO模型后得出㊂壤中流的出流系数和地下水的出流系数根据赵人俊等[23]的研究成果,其和表示自由水出流的快慢,与土壤类型有关㊂超渗产流计算中,Green⁃Ampt下渗方法参数的有效水力传导度㊁湿润锋面土壤吸力均根据水文学手册[24]取值,饱和含水率由栅格单元的土壤类型获取[25]㊂由于新安江屯溪流域为典型湿润流域,以蓄满产流为主,模型运行时关闭超渗产流计算模块㊂汇流参数包括河道曼宁糙率系数㊁地表坡度㊁河道坡度㊂河道曼宁糙率系数和河道坡度与上游汇水面积有关,地表坡度㊁河道坡度均可通过DEM数据求得[17]㊂2.3 模型应用与分析2.3.1 对历史典型洪水的验证选取1980 2013年间34场屯溪流域历史典型洪水,时间步长取为1h,用GMKHM对其进行洪水模拟,探求模型的适用性㊂根据DEM与下垫面覆盖数据的分辨率(30″×30″),屯溪流域划分为3605个30″×30″的水文计算单元网格,流域降水资料采用反距离权重法插值到网格计算单元㊂表1为34场洪水模拟结果特征值㊂GMKHM参数直接由空间估计获取,减少了对历史资料的依赖㊂从预报结果可以看出,与新安江模型相比,GMKHM在屯溪流域洪水模拟效果评估中,根据GBT22482 2008‘水文情报预报规范“,均为甲等预报方案,应用效果良好:GMKHM与新安江模型模拟精度相当,径流量相对误差和峰现时差平均值GMKHM稍优,洪峰相对误差平均值相近㊂GMKHM是在新安江模型基础上发展的,应用于屯溪流域时,只保留蓄满产流,从1986⁃06⁃11㊁1989⁃05⁃01㊁1994⁃05⁃01㊁1999⁃05⁃21㊁2008⁃06⁃09㊁2013⁃06⁃27等模拟结果可以看出,模型对流域洪水预报精度良好,也证明了GMKHM应用的合理性和可靠性㊂2.3.2 2020年汛期洪水实时预报2020年6月23日至7月11日,屯溪流域历经13场较强降水过程,流域累计面雨量为710.4mm,持续强降水致使屯溪水文站在7月7日16时流量达5040m3/s,中小河流洪水灾害严重㊂本文以发展的短时临近降水逐小时滚动集合(最优㊁最大㊁最小)预报驱动GMKHM,对本次洪水过程进行逐小时实时滚动预报,探求对中小河流洪水预报预见期的延长效果㊂其中,洪水起报时间从7月7日2时开始,起报时间前使用实况降水,起报时间至峰现时间预见期内使用降水集合预报;以较强降水(5mm/h以上)量级进行检验评估,0~ 2h临近定量降水预报逐小时Threat Scores(TS)评分平均为0.15,高于传统LK光流法的0.07;2~12h短时定量降水预报逐小时TS评分平均为0.12;12h累计定量降水预报TS评分达0.51,高于GRAPES⁃3KM同预第3期包红军,等 基于短时临近降水集合预报的中小河流洪水预报研究表1 屯溪流域洪水模拟特征值对比Table1 Characteristic comparison of flood simulation results in Tunxi Basin序号洪水起始日期累计降水量/mm实测洪峰流量/(m3㊃s-1)径流量相对误差/%洪峰相对误差/%峰现时差/h确定性系数G X G X G X G X11982⁃05⁃01191.324280-1.33 1.99-0.2 2.8100.980.97 21983⁃05⁃1174.151300-7.137.28-10.1 2.50-10.920.96 31983⁃05⁃1474.591510 3.8612.57-15.3-1.70-10.980.95 41983⁃05⁃29125.6124908.7215.4711.118.7-2-30.950.85 51983⁃06⁃0997.352170-3.99 2.94 4.5-6.0-300.90.97 61984⁃05⁃0189.615708.2510.66-26.0-24.9-1-20.860.79 71984⁃08⁃26135.932513-4.48-14.68 1.4-0.7440.970.96 81986⁃06⁃1191.5722600.73-1.27 6.3 5.70-10.940.92 91987⁃06⁃1927.0394519.9329.6916.725.0450.80.78 101988⁃05⁃0777.301390-6.65-5.91-16.1-13.6-1-20.850.81 111988⁃06⁃1140.191000 6.0424.91 1.919.3-1-20.880.83 121989⁃05⁃0178.92174010.207.49 1.8-8.20-30.970.84 131989⁃06⁃12113.472274 1.71 6.59-10.8-0.40-10.970.98 141989⁃06⁃3071.451740 2.3117.36 1.413.50-20.970.93 151989⁃07⁃2289.21470-6.53-29.60 2.20.8-2-40.870.76 161990⁃05⁃0152.671700-9.41 3.3414.815.8-1-20.960.93 171990⁃06⁃11126.942500 5.327.66-12.7-6.8310.940.98 181991⁃05⁃18130.3722208.96 3.96-19.3-14.6-3-40.90.84 191991⁃06⁃3054.552060 2.7910.4622.630.7-1-20.870.84 201992⁃06⁃20114.8531509.10-12.76-2.2-6.4-1-20.960.83 211993⁃05⁃27193.614700 1.5111.49-18.0 4.70-20.950.91 221994⁃05⁃01154.6841607.660.53-0.8-19.4-1-20.970.83 231995⁃05⁃15113.244070 6.62 6.3312.7 3.4-3-20.890.95 241996⁃06⁃01180.696490 3.83-5.2814.3-3.11-30.960.87 251997⁃06⁃06116.272730-6.15-1.830.918.9-3-40.950.84 261998⁃05⁃01132.32427015.69-3.0719.18.7-1-40.930.91 271999⁃05⁃2191.262960-2.5016.26 4.3 3.61-10.980.91 281999⁃06⁃22131.2337809.7625.099.419.80-40.960.82 291999⁃08⁃24118.4128900.2411.28-19.49.0000.960.92 302001⁃05⁃0172.361410-25.7314.41-19.210.80-10.870.88 312001⁃06⁃20134.523640-9.23-15.33-1.50-3-20.890.92 322002⁃05⁃13123.812120-8.319.40-4.3-1.2010.860.94 332008⁃06⁃09154.315250-1.33 1.62-0.20.3110.980.98 342013⁃06⁃27137.213980-7.137.82-10.19.1000.920.93绝对值平均 6.9010.509.89.7 1.2 1.90.920.89 注:G代表GMKHM,X代表新安江水文模型㊂报时效评分;以洪峰误差20%㊁峰现时间误差为1h衡量洪峰预报准确性㊂从表2和图2可以看出,7月7日2 7时起报的降水预报精度相对不高,导致最优预报洪峰效果越来越差,但随着7时之后起报的降水预报精度逐步提升,洪水最优预报精度随着预见期临近越来越高;自9时起报的洪峰误差均在10%,最优预报的峰现时间误差均小于1h,而不考虑预见期降水的中小河流洪水预报直到13时才预报出洪峰,且峰现时间误差为1h,对比预见期提前了4h;且自2时起报的最大预报与最小预报很好地包含了实况流量过程线,之间的跨度(最大与最小预报之差)越来越小,接近于实况过程㊂3 结 语为了延长中小河流洪水预报的预报预见期,发展了短时临近精细化网格降水集合预报(3个成员:最优预报㊁最大预报㊁最小预报)技术,驱动GMKHM,建立基于短时临近集合预报的中小河流洪水预报模型㊂以皖南山区新安江上游屯溪流域为验证流域,对流域2020年汛期大洪水进行实时滚动预报㊂结果表明,基于短时临近最优降水预报的中小河流洪水预报模型提前了7h预报出屯溪洪峰,洪峰误差为5.6%,峰现时差为-1h,比不考虑预见期降水的中小河流洪水预报提前了4h;基于短时临近最大㊁最小降水预报的中小河流102河海大学学报(自然科学版)第49卷表2 屯溪流域2020年实时预报洪水洪峰Table 2 Flood peak of Tunxi Basin by real⁃time forecasting in 2020序号洪水起报时间预报洪峰/(m 3㊃s -1)最优最大最小跨度最优预报峰现时间/h17月7日2时5333.39040.53242.05798.5-427月7日3时5488.96169.32529.23640.1-337月7日4时4537.35893.92663.63230.3-347月7日5时3943.16400.12964.53435.6-257月7日6时3433.75694.12867.92826.2-267月7日7时2967.14721.52134.82586.7-277月7日8时4360.54647.43459.91187.5-287月7日9时4777.95586.74063.31523.4-197月7日10时4887.95281.84089.21192.6-1107月7日11时4910.05588.14414.61173.5-1117月7日12时5085.85187.14456731.10127月7日13时5017.35481.34816.2665.1雨量实况场(6月23日17时至7月7日9时)㊁雨量预报场(7月7日9 16时)图2 2020年屯溪流域基于降水最优预报的洪水预报结果Fig.2 Flood forecasting result based on optimal precipitation forecasts in Tunxi Basin in 2020洪水预报模型提前13h 预报出洪峰区间,并自7月7日9时起,最大与最小预报之间跨度逐渐减少㊂笔者认为,针对面向中小河流洪水预报的流域雨量场构建,仍需要进一步的研究㊂a.流域雨量实况场㊂中小流域水文气象监测不足,呈 东密西疏” 大密小疏”,空间代表性不够,基于天气雷达回波反演特别是在复杂地形地区的降水反演精度不够,难以准确捕捉中小河流致洪强降水的精细化分布㊂随着多源遥感技术的快速发展,基于天基㊁空基㊁地基等多源监测资料,研发复杂地形影响下不同水文气象分区基于大数据识别与融合同化技术的三维降水监测技术,是提升面向中小河流洪水预报的流域雨量场精度的重要手段之一㊂b.流域雨量预报场㊂降水是决定中小河流洪水预报精度和预见期的关键因素,目前,面向中小流域的高分辨率雨量预报场构建技术亟须加强㊂构建不同水文气象分区降水特征条件下多源信息融合的高时空分辨率雨量场,发展基于人工智能与数值模式的雷达智能外推短时临近降水预报技术,构建面向中小流域的无缝隙精细化智能网格降水预报,是中小河流洪水预报下一步要解决的关键技术㊂参考文献:[1]李致家,朱跃龙,刘志雨,等.中小河流洪水防控与应急管理关键技术的思考[J].河海大学学报(自然科学版),2021,49(1):13⁃18.(LI Zhijia,ZHU Yuelong,LIU Zhiyu,et al.Thoughts on key technologies of flood prevention and emergencymanagement in small and medium⁃sized rivers[J].Journal of Hohai University (Natural Sciences),2021,49(1):13⁃18.(in Chinese))[2]WAN Y,KONYHA K.A simple hydrologic model for rapid prediction of runoff from ungauged coastal catchments[J].Journal of Hydrology,2015,528:571⁃583.[3]REED S,SCHAAKE J,ZHANG Z.A distributed hydrologic model and threshold frequency⁃based method for flash 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《抗冻蛋白对冰-水界面体系影响的分子动力学模拟》篇一一、引言在极地环境中，生物体通过合成抗冻蛋白（AFPs）来抵御严寒环境，保持其生存环境中的水活性。
抗冻蛋白的独特性质，如对冰的抑制和稳定作用，引起了科学家的广泛关注。
近年来，随着分子动力学模拟技术的发展，我们能够更深入地理解抗冻蛋白与冰-水界面之间的相互作用。
本文将通过分子动力学模拟技术，探究抗冻蛋白对冰-水界面体系的影响。
二、理论与方法2.1 分子动力学模拟分子动力学模拟是一种用于研究原子和分子层面的系统动态的计算机实验方法。
本研究将采用这种方法来观察和分析抗冻蛋白在冰-水界面处的行为和作用机制。
2.2 模型构建我们将构建一个包含冰-水界面的模型，并在其中加入抗冻蛋白分子。
模型中的水分子将使用TIP3P模型进行描述，而抗冻蛋白的原子结构则根据其已知的三维结构进行建模。
2.3 模拟过程我们将使用合适的力场和参数进行模拟，并设定适当的温度和压力条件。
在模拟过程中，我们将观察和分析抗冻蛋白与冰-水界面的相互作用，以及这种相互作用如何影响冰的稳定性和生长。
三、结果与讨论3.1 抗冻蛋白与冰-水界面的相互作用模拟结果显示，抗冻蛋白与冰-水界面之间存在强烈的相互作用。
抗冻蛋白的某些部分会吸附在冰的表面，而其他部分则可能深入到水相中。
这种吸附作用可能会改变冰-水界面的性质，从而影响冰的稳定性和生长。
3.2 抗冻蛋白对冰稳定性的影响通过分析模拟结果，我们发现抗冻蛋白能够显著提高冰的稳定性。
这可能是由于抗冻蛋白的吸附作用减缓了冰的晶格结构重组，从而阻止了冰的生长和融化的过程。
此外，抗冻蛋白也可能通过降低冰表面的自由能来增强其稳定性。
3.3 抗冻蛋白对冰生长的影响我们的模拟结果表明，抗冻蛋白可以显著抑制冰的生长。
这可能是由于抗冻蛋白的吸附作用阻止了新的水分子在冰表面进行有序排列和结晶的过程。
此外，抗冻蛋白也可能通过改变水的物理性质（如粘度、表面张力等）来影响冰的生长。
!!!!!"氢原子由一个质子（即氢原子核）和一个电子组成。
根据经典模型，在正常状态下，电子绕核作圆周运动，轨道半径是""#$#%&!%%!"已知质子质量$"%%"’(#%&!#(#$，电子质量$%%$"%%#%&!)%#$，电荷分别为&’%&%"’&#%&!%$&，万有引力常量(%’"’(#%&!%%’·!#(#$#"（%）求电子所受质子的库仑力和引力；（#）库仑力是万有引力的多少倍？（)）求电子的速度。
解：（%）!)&%%*!!&*%*#+#%%*#)"%*#+"+"#%&!%#（%"’&#%&!%$）#（""#$#%&!%%）#’%+"#)#%&!+’，!))%($%$#+#%’"’(#%&!%%#$"%%#%&!)%#%"’(#%&!#(（""#$#%&!%%）#’%)"’)#%&!*(’"!（#）)&))%+"#)#%&!+)"’)#%&!*(%#"#(#%&)$"!（)）$%,#+%)&，,,%) & + $!%%+"#)#%&!+#""#$#%&!%%$"%%#%&!!)%!(*%#"%$#%&’!(*"!!!!""卢瑟福实验证明：当两个原子核之间的距离小到"#!"$!时，它们之间的排斥力仍遵守库仑定律。
第３９卷第３期２０２０年３月硅㊀酸㊀盐㊀通㊀报ＢＵＬＬＥＴＩＮＯＦＴＨＥＣＨＩＮＥＳＥＣＥＲＡＭＩＣＳＯＣＩＥＴＹＶｏｌ.３９㊀Ｎｏ.３Ｍａｒｃｈꎬ２０２０ＳｉＣ模具高温模压石英玻璃物相接触角的分子动力学模拟吴㊀悠１ꎬ２ꎬ３ꎬ邹㊀斌１ꎬ２ꎬ３ꎬ王俊成１ꎬ２ꎬ３ꎬ黄传真１ꎬ２ꎬ３ꎬ朱洪涛１ꎬ２ꎬ３ꎬ姚㊀鹏１ꎬ２ꎬ３(１.山东大学机械工程学院先进射流工程技术研究中心ꎬ济南㊀２５００６１ꎻ２.山东大学高效洁净机械制造教育部重点实验室ꎬ济南㊀２５００６１ꎻ３.山东大学机械工程国家级实验教学示范中心ꎬ济南㊀２５００６１)摘要:针对高温下石英玻璃纳米液滴在ＳｉＣ模具表面接触角难以测量的问题ꎬ采用分子动力学方法ꎬ模拟研究了不同温度和粗糙表面面向模压的ＳｉＯ２/ＳｉＣ高温接触角以及ＳｉＯ２熔体的界面结构ꎮ应用压力张量法发现了ＭＳ￣Ｑ势函数模拟的ＳｉＯ２熔体表面张力较接近实际值ꎬ即ＳｉＯ２高温表面特性模拟可优先采用ＭＳ￣Ｑ势函数ꎮ针对ＳｉＣ模具纳米级表面的粗糙度ꎬ发现当粗糙度因子ｒ>１.５时润湿模式由Ｗｅｎｚｅｌ变为Ｃａｓｓｉｅ￣Ｂａｘｔｅｒꎬ此时Ｒａ的变化对接触角值无明显影响ꎬＲｍｒ值减小使得接触面积分数ｆ减小ꎬ接触角值随之增大ꎮ因此ꎬ保持ｒ大于１.５的同时适当减小Ｒｍｒ值有利于减小固液摩擦ꎬ降低石英玻璃工件和ＳｉＣ模具界面上的脱模力ꎮ随着温度升高ＳｉＯ２表面结构变得松散ꎬ导致其在ＳｉＣ表面接触角减小ꎮ在超过２３００Ｋ时接触角值的变化率增大ꎬ为减小工件￣模具界面的粘附ꎬ模压温度应选择２３００Ｋ以下ꎮ关键词:石英玻璃ꎻ碳化硅ꎻ接触角ꎻ分子动力学ꎻ模压中图分类号:Ｏ６４７.１ꎻＴＳ９４３.６５㊀㊀文献标识码:Ａ㊀㊀文章编号:１００１￣１６２５(２０２０)０３￣０９２３￣０９ＭｏｌｅｃｕｌａｒＤｙｎａｍｉｃｓＳｉｍｕｌａｔｉｏｎｏｆＨｉｇｈＴｅｍｐｅｒａｔｕｒｅＣｏｎｔａｃｔＡｎｇｌｅｆｏｒＭｏｌｄｅｄＳｉｌｉｃａＧｌａｓｓｉｎＳｉＣＤｉｅＷＵＹｏｕ１ꎬ２ꎬ３ꎬＺＯＵＢｉｎ１ꎬ２ꎬ３ꎬＷＡＮＧＪｕｎｃｈｅｎｇ１ꎬ２ꎬ３ꎬＨＵＡＮＧＣｈｕａｎｚｈｅｎ１ꎬ２ꎬ３ꎬＺＨＵＨｏｎｇｔａｏ１ꎬ２ꎬ３ꎬＹＡＯＰｅｎｇ１ꎬ２ꎬ３(１.ＣｅｎｔｅｒｆｏｒＡｄｖａｎｃｅｄＪｅｔＥｎｇｉｎｅｅｒｉｎｇＴｅｃｈｎｏｌｏｇｉｅｓꎬＳｃｈｏｏｌｏｆＭｅｃｈａｎｉｃａｌＥｎｇｉｎｅｅｒｉｎｇꎬＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙꎬＪｉｎａｎ２５００６１ꎬＣｈｉｎａꎻ２.ＫｅｙＬａｂｏｒａｔｏｒｙｏｆＨｉｇｈＥｆｆｉｃｉｅｎｃｙａｎｄＣｌｅａｎＭｅｃｈａｎｉｃａｌＭａｎｕｆａｃｔｕｒｅꎬＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙꎬＭｉｎｉｓｔｒｙｏｆＥｄｕｃａｔｉｏｎꎬＪｉｎａｎ２５００６１ꎬＣｈｉｎａꎻ３.ＮａｔｉｏｎａｌＤｅｍｏｎｓｔｒａｔｉｏｎＣｅｎｔｅｒｆｏｒＥｘｐｅｒｉｍｅｎｔａｌＭｅｃｈａｎｉｃａｌＥｎｇｉｎｅｅｒｉｎｇＥｄｕｃａｔｉｏｎꎬＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙꎬＪｉｎａｎ２５００６１ꎬＣｈｉｎａ)Ａｂｓｔｒａｃｔ:Ｄｕｅｔｏｔｈｅｄｉｆｆｉｃｕｌｔｉｅｓｏｆｍｅａｓｕｒｅｍｅｎｔｏｆｃｏｎｔａｃｔａｎｇｌｅｗｈｅｎｐｒｅｓｓｉｎｇｓｉｌｉｃａｇｌａｓｓｎａｎｏ￣ｄｒｏｐｌｅｔｉｎＳｉＣｄｉｅｓｕｒｆａｃｅａｔｈｉｇｈｔｅｍｐｅｒａｔｕｒｅꎬｔｈｅＳｉＯ２/ＳｉＣｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｃｏｎｔａｃｔａｎｇｌｅａｔｄｉｆｆｅｒｅｎｔｔｅｍｐｅｒａｔｕｒｅａｎｄｒｏｕｇｈｓｕｒｆａｃｅａｓｗｅｌｌａｓｔｈｅｓｕｒｆａｃｅｓｔｒｕｃｔｕｒｅｏｆＳｉＯ２ｍｅｌｔｗｅｒｅｓｉｍｕｌａｔｅｄｂｙｍｏｌｅｃｕｌａｒｄｙｎａｍｉｃｓ.ＵｓｉｎｇｔｈｅｐｒｅｓｓｕｒｅｔｅｎｓｏｒｍｅｔｈｏｄꎬｉｔｉｓｆｏｕｎｄｔｈａｔｔｈｅｓｕｒｆａｃｅｔｅｎｓｉｏｎｏｆＳｉＯ２ｍｅｌｔｓｉｍｕｌａｔｅｄｂｙＭＳ￣Ｑｐｏｔｅｎｔｉａｌｆｕｎｃｔｉｏｎｉｓｃｌｏｓｅｔｏｔｈｅｅｘｐｅｒｉｍｅｎｔａｌｖａｌｕｅ.ＴｈｕｓｔｈｅＭＳ￣ＱｐｏｔｅｎｔｉａｌｃａｎｂｅｐｒｅｆｅｒｒｅｄｉｎｓｉｍｕｌａｔｉｏｎｏｆＳｉＯ２ｈｉｇｈ￣ｔｅｍｐｅｒａｔｕｒｅｓｕｒｆａｃｅｃｈａｒａｃｔｅｒ.ＦｏｒｔｈｅｒｏｕｇｈｎｅｓｓｏｆｎａｎｏｓｃａｌｅｓｕｒｆａｃｅｏｆＳｉＣｄｉｅ.Ｗｈｅｎｔｈｅｒｏｕｇｈｎｅｓｓｆａｃｔｏｒｒｅｘｃｅｅｄｓ１.５ꎬｔｈｅｗｅｔｔｉｎｇｍｏｄｅｃｈａｎｇｅｓｆｒｏｍＷｅｎｚｅｌｔｏＣａｓｓｉｅ￣Ｂａｘｔｅｒ.ＡｔｔｈｉｓｔｉｍｅꎬｔｈｅｃｈａｎｇｅｏｆＲａｈａｓｎｏｓｉｇｎｉｆｉｃａｎｔｉｍｐａｃｔｏｎｔｈｅｃｏｎｔａｃｔａｎｇｌｅꎬａｎｄｔｈｅｒｅｄｕｃｅｄＲｍｒｖａｌｕｅｒｅｓｕｌｔｓｉｎｔｈｅｄｅｃｒｅａｓｅｏｆｃｏｎｔａｃｔａｒｅａｆｒａｃｔｉｏｎｆａｎｄｔｈｅｉｎｃｒｅａｓｅｏｆｃｏｎｔａｃｔａｎｇｌｅ.Ｔｈｅｒｅｆｏｒｅꎬｋｅｅｐｉｎｇｒｇｒｅａｔｅｒｔｈａｎ１.５ｗｈｉｌｅａｐｐｒｏｐｒｉａｔｅｌｙｒｅｄｕｃｉｎｇＲｍｒｖａｌｕｅｉｓｃｏｎｄｕｃｉｖｅｔｏｒｅｄｕｃｉｎｇｓｏｌｉｄ￣ｌｉｑｕｉｄｆｒｉｃｔｉｏｎａｎｄｒｅｄｕｃｉｎｇｔｈｅｓｔｒｉｐｐｉｎｇｆｏｒｃｅｏｎｔｈｅｉｎｔｅｒｆａｃｅｂｅｔｗｅｅｎｆｕｓｅｄｓｉｌｉｃａｗｏｒｋｐｉｅｃｅａｎｄＳｉＣｄｉｅ.ＡｓｔｈｅｔｅｍｐｅｒａｔｕｒｅｉｎｃｒｅａｓｅｓꎬｔｈｅｓｕｒｆａｃｅｓｔｒｕｃｔｕｒｅｏｆＳｉＯ２ｂｅｃｏｍｅｌｏｏｓｅꎬｒｅｓｕｌｔｉｎｇｉｎｉｔｓｃｏｎｔａｃｔａｎｇｌｅｄｅｃｌｉｎｉｎｇｏｎｔｈｅＳｉＣｓｕｒｆａｃｅ.Ｔｈｅｃｈａｎｇｅｒａｔｅｏｆｔｈｅｃｏｎｔａｃｔａｎｇｌｅｉｎｃｒｅａｓｅｓｗｈｅｎｔｅｍｐｅｒａｔｕｒｅｅｘｃｅｅｄｓ２３００Ｋ.Ｉｎｏｒｄｅｒｔｏｒｅｄｕｃｅｔｈｅａｄｈｅｓｉｏｎｏｆｔｈｅｗｏｒｋｐｉｅｃｅｗｉｔｈｔｈｅｄｉｅꎬｔｈｅｍｏｌｄｉｎｇｔｅｍｐｅｒａｔｕｒｅｓｈｏｕｌｄｂｅｂｅｌｏｗ２３００Ｋ.Ｋｅｙｗｏｒｄｓ:ｓｉｌｉｃａｇｌａｓｓꎻｓｉｌｉｃｏｎｃａｒｂｉｄｅꎻｃｏｎｔａｃｔａｎｇｌｅꎻｍｏｌｅｃｕｌａｒｄｙｎａｍｉｃｓꎻｃｏｍｐｒｅｓｓｉｏｎｍｏｌｄｉｎｇ基金项目:山东省自然科学基金重大基础研究项目(ＺＲ２０１８ＺＢ０５２１)作者简介:吴㊀悠(１９９４￣)ꎬ男ꎬ硕士研究生ꎮ主要从事模具摩擦磨损方面的研究ꎮＥ￣ｍａｉｌ:ｊｏｌｍｕｇｉ＠１６３.ｃｏｍ通讯作者:邹㊀斌ꎬ教授ꎮＥ￣ｍａｉｌ:ｚｂ７８＠ｓｄｕ.ｅｄｕ.ｃｎ９２４㊀陶㊀瓷硅酸盐通报㊀㊀㊀㊀㊀㊀第３９卷０㊀引㊀言近年来ꎬ微结构光学元件因其在信息通信领域的广泛应用受到越来越多的关注ꎮ模压是制造光学玻璃元件常用的方法之一ꎮ模压过程中ꎬ一方面模具上精准的几何结构复印到了玻璃元件上ꎻ另一方面玻璃元件与模压模具之间的摩擦与粘附造成了模具的磨损ꎬ从而导致模具几何结构精度的丧失ꎮ这些均为模具与工件的固液界面相互接触㊁相对运动作用的结果ꎮ因此ꎬ有必要研究它们的接触特性ꎬ从而对模具结构和模压工艺的设计提供一定的指导ꎮ润湿是能够实现模压的先决条件ꎬ而接触角是表征润湿性的主要参数ꎮ对于理想光滑表面的接触角模型ꎬＹｏｕｎｇ[１]从固㊁液㊁气界面张力平衡的角度建立了经典的杨氏方程ꎮ对于粗糙表面和非均质表面ꎬＷｅｎｚｅｌ[２]和Ｃａｓｓｉｅ[３]等学者在杨氏方程的基础上分别建立了Ｗｅｎｚｅｌ和Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ模型ꎮＷｅｎｚｅｌ润湿模式中ꎬ液体始终完全浸渍粗糙结构波谷中ꎬ即出现所谓 钉扎 现象ꎮ而在模压工艺中ꎬ这一现象增大了工件液相在模具表面流动的阻力ꎬ从而增大了固液摩擦ꎬ使得模具更易磨损ꎮ而Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ润湿模式认为由于粗糙结构波谷中存在气相ꎬ液体无法浸渍其中ꎬ因此是模压比较期望的润湿模式ꎮ在光学玻璃材料中ꎬ石英玻璃的光学性能有其独特之处ꎮ它既可以透过远紫外光谱ꎬ且透射率在同类材料中最优ꎬ又可透过可见光和近红外光谱ꎮ同时ꎬ其机械性能也高于普通玻璃[４]ꎮ目前ꎬ石英玻璃光学元件的制造多采用超精密磨削或是激光刻蚀的方法ꎬ生产效率低ꎬ生产成本高ꎮ而模压方法可以提高加工效率ꎬ实现大规模生产ꎮ然而ꎬ由于石英玻璃软化点温度高达１５００~１６００ħꎬ常用的模具材料如ＷＣ等在此温度下无法正常工作ꎬ而ＳｉＣ热稳定性好ꎬ熔点达２８３０ħ[５]ꎬ故较为适合作为模压石英玻璃的模具材料ꎮ由于模压温度高ꎬ超出了目前接触角测量仪器的工作范围ꎬ并且微结构模具表面粗糙度达到纳米级ꎬ要研究粗糙度对润湿性的影响需要测量纳米尺度微液滴的接触角ꎬ因此试验测定比较困难ꎮ分子动力学方法使微纳液滴高温接触角的模拟及研究其成因机理成为可能ꎮ徐威等[６]通过改变ＬＪ势函数中的作用参数模拟了纳米水滴在不同能量表面上的铺展过程和润湿形态ꎬ模拟结果与经典润湿理论计算得到的结果呈现相似变化趋势ꎮ王龙[７]研究了铜和金液滴在石墨烯和碳纳米管等不同结构基底上的润湿和融合过程ꎬ发现金属液滴的融合受液滴形状和基底结构影响ꎮ由于势函数的限制ꎬ目前对于界面润湿的分子动力学模拟多集中于ＬＪ流体ꎬ如水和液氩等ꎬ而多元素流体较少见于报道ꎮ势函数按多体作用的复杂程度可分为对势和多体势ꎮ对于石英玻璃的模拟ꎬ多体势不能较好地计算Ｓｉ￣Ｏ键的断裂ꎬ因此不利于高温动力学性能的研究[８]ꎮＢｅｅｓｔ等[９]基于石英玻璃经典的ＢＭＨ势提出了ＢＫＳ势ꎬ并运用第一性原理方法结合实验数据拟合了参数ꎮＳｕｎｄａｒａｒａｍａｎ等[１０]使用ＢＫＳ势预测了石英玻璃的力学性能ꎬ发现当短程和长程截止半径分别为５.５Å和１０Å时模拟的石英玻璃结构更符合实际ꎮＤｅｍｉｒａｌｐ等[１１]首先将Ｍｏｒｓｅ势与电荷平衡法(ＱＥｑ)相结合ꎬ建立了ＭＳ￣Ｑ力场ꎬ并研究了石英玻璃在压力变化过程中的相变ꎮ丁元法等[１２]比较了ＢＫＳ与ＭＳ￣Ｑ模型下石英玻璃的高温扩散特性ꎬ认为计算高温下石英玻璃的扩散传输性能可优先选择ＭＳ￣Ｑ力场ꎬ但并未比较其表面特性ꎮ从以上文献可以看出ꎬＢＫＳ和ＭＳ￣Ｑ是石英玻璃分子动力学模拟中常用的对势ꎮ其中ꎬＢＫＳ势从低温到高温的较大温度范围均具有较好性能ꎬ而ＭＳ￣Ｑ势在高温下的传输性能要优于ＢＫＳ势ꎮ目前对于石英玻璃高温表面特性的模拟的报道较为少见ꎬ因此仍需要对两种势函数性能的优劣进行比较ꎮＨｏｓｓｅｉｎｉ等[１３]研究了不同形貌的疏水表面上的水滴行为ꎬ发现表面形貌㊁柱高度㊁空隙率和沉积角是影响表面疏水性的主要参数ꎮ因此ꎬ本模拟在ＳｉＣ表面构建了纳米方柱阵列ꎬ并分别使用粗糙度评定参数Ｒａ和Ｒｍｒ表示柱高和空隙率ꎬ研究了纳米级表面粗糙结构对面向高温模压的ＳｉＯ２/ＳｉＣ接触角的影响ꎮ本文使用分子动力学方法ꎬ对比了分别采用ＢＫＳ和ＭＳ￣Ｑ势函数计算的ＳｉＯ２熔体高温表面张力ꎮ模拟了不同模压温度和ＳｉＣ模具表面粗糙结构ＳｉＯ２的高温接触角ꎬ研究了微尺度下的高温界面润湿特征和ＳｉＯ２熔体表面层结构特点ꎬ本研究的结构框图如图１所示ꎮ１㊀模拟方法和模型１.１㊀界面张力的计算为了保证成形精度并减小工件与模具的粘附ꎬ光学玻璃模压温度一般选择在转变点温度到软化点温度第３期吴㊀悠:ＳｉＣ模具高温模压石英玻璃物相接触角的分子动力学模拟９２５㊀之间[１４]ꎬ故选择石英玻璃实际软化点附近温度１９００Ｋ作为模拟温度ꎮＳｉＯ２表面张力模拟系统如图２所示ꎮＳｉＯ２熔体表面模型的建立方法是在模拟盒子中随机加入８００个Ｓｉ原子和１６００个Ｏ原子ꎬ使其密度约为２.２ｇ/ｃｍ３ꎮ随后在５０００Ｋ下驰豫２００ｐｓ以消除初始构型的影响ꎬ并以１００Ｋ/２０ｐｓ的速度降温至１９００Ｋꎮ最后在ｘ轴方向模型两边各添加一厚度为２０Å的真空层ꎬ以避免周期性边界的影响ꎮ面向高温模压的ＳｉＯ２/ＳｉＣ界面张力模拟系统如图３(ｃ)所示ꎬ其中ＳｉＣ是由金刚石结构的β￣ＳｉＣ原胞排列而成ꎮ分别将ＳｉＯ２和ＳｉＣ单独在１９００Ｋ下驰豫２００ｐｓꎬ然后将它们添加进同一模拟盒子中ꎬ使ＳｉＯ２与ＳｉＣ{１００}表面接触并对整个体系进行驰豫ꎮ图１㊀基于分子动力学的ＳｉＣ模具高温模压石英玻璃的物相接触角模拟研究关系框图Ｆｉｇ.１㊀ＳｔｕｄｙｒｅｌａｔｉｏｎｓｈｉｐｏｆｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｃｏｎｔａｃｔａｎｇｌｅｏｆｍｏｌｄｅｄｏｐｔｉｃａｌｇｌａｓｓｉｎＳｉＣｄｉｅｂａｓｅｄｏｎｍｏｌｅｃｕｌａｒｄｙｎａｍｉｃｓ图２㊀ＳｉＯ２熔体表面张力模拟计算体系Ｆｉｇ.２㊀ＳｉｍｕｌａｔｉｏｎｓｙｓｔｅｍｏｆＳｉＯ２ｍｅｌｔｓｕｒｆａｃｅｔｅｎｓｉｏｎ图３㊀ＳｉＯ２/ＳｉＣ高温界面张力模拟计算体系Ｆｉｇ.３㊀ＳｉｍｕｌａｔｉｏｎｓｙｓｔｅｍｏｆＳｉＯ２/ＳｉＣｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｉｎｔｅｒｆａｃｅｔｅｎｓｉｏｎ㊀㊀表面与界面张力的计算均采用压力张量法[１５]ꎬγ＝１２ʏＬｘ２－Ｌｘ２[ＰＮ(ｘ)－ＰＴ(ｘ)]ｄｘ(１)式中ꎬγ表示表面张力ꎻＬｘ为模拟体系在ｘ方向的长度ꎻ因子１/２是由于模拟系统有两个界面ꎻＰＮ与ＰＴ分别为系统界面法向和切向压力张量分量ꎮＰＮ(ｘ)＝ρｋＢＴ－１Ｖðｉ<ｊｘ２ｉｊｒｉｊｄＵ(ｒｉｊ)ｄｒｉｊ[](２)９２６㊀陶㊀瓷硅酸盐通报㊀㊀㊀㊀㊀㊀第３９卷ＰＴ(ｘ)＝ρｋＢＴ－１Ｖðｉ<ｊｙ２ｉｊ－ｚ２ｉｊ２ｒｉｊｄＵ(ｒｉｊ)ｄｒｉｊ[](３)式中ꎬｋＢ为玻尔兹曼常数ꎻＶ为模拟盒子体积ꎻＵ表示势函数ꎻρ为液体密度ꎻＴ为温度ꎻｒ为原子间距ꎬｘ㊁ｙ㊁ｚ为其在三个坐标轴方向的分量ꎮ为了比较不同势函数模拟界面张力的可靠性ꎬ在模拟中ꎬＳｉＯ２原子间的相互作用先后用ＢＫＳ[１０]和ＭＳ￣Ｑ[１１]势函数进行表征如下ꎬ势函数参数见表１ꎮＵＢｉｊ＝ｑｉｑｊｅ２ｒｉｊ＋Ａｉｊｅ－ｒｉｊρ－Ｃｉｊｒ６ｉｊ(４)ＵＭｉｊ＝ｑｉｑｊｅ２ｒｉｊ＋Ｄ０[ｅ－２α(ｒｉｊ－ｒ０)－２ｅ－α(ｒｉｊ－ｒ０)](５)式中ꎬｑ表示电荷量ꎻＡ㊁Ｃ㊁Ｄ均为与相互作用强度有关的参数ꎻα为与平衡距离有关的参数ꎮ表１㊀ＳｉＯ２势函数参数Ｔａｂｌｅ１㊀ＰａｒａｍｅｔｅｒｓｏｆｐｏｔｅｎｔｉａｌｓｆｏｒＳｉＯ２ＰａｉｒＢＫＳＡｉｊ/(ｋｃａｌ ｍｏｌ－１)ρ/ÅＣｉｊ/(ｋｃａｌ ｍｏｌ－１ Å６)ＭＳ￣ＱＤ０/(ｋｃａｌ ｍｏｌ－１)α/Å－１ｒ０/ÅＳｉ￣Ｓｉ￣￣￣０.１７７３２.０４４３.７６０Ｏ￣Ｏ３２０２５.７９９８０.３６２３４０３５.５８７５０.５３６３１.３７３３.７９１Ｓｉ￣Ｏ４１５１７５.６４２９０.２０５２３０７９.４５５４４５.９９７０２.６５２１.６２８㊀㊀ＳｉＣ原子间的相互作用使用ｔｅｒｓｏｆｆ势函数表征ꎮ由于ＳｉＯ２/ＳｉＣ界面间为范德华作用ꎬ因此使用ＬＪ势函数表征ꎬ其参数来自于ＵＦＦ力场[１６]ꎬ如表２所示ꎮ表２㊀ＳｉＯ２/ＳｉＣ势函数参数Ｔａｂｌｅ２㊀ＰａｒａｍｅｔｅｒｓｏｆｐｏｔｅｎｔｉａｌｆｏｒＳｉＯ２/ＳｉＣｉｎｔｅｒａｃｔｉｏｎＰａｉｒε/(ｋｃａｌ ｍｏｌ－１)σ/ÅＳｉ￣Ｓｉ０.４０２３.８２６Ｏ￣Ｓｉ０.１５５３３.４７２３Ｓｉ￣Ｃ０.２０５３.６２８Ｏ￣Ｃ０.０７９３３.２７４５㊀㊀模拟过程中ꎬ模拟盒子三个方向均为周期性边界ꎮＢＫＳ势函数Ｓｉ和Ｏ原子所带电荷分别为＋２.４ｅ㊁－１.２ｅꎬ截断半径为５.５ÅꎻＭＳ￣Ｑ势函数Ｓｉ和Ｏ原子所带电荷分别为＋１.３１８ｅ㊁－０.６５９ｅꎬ截断半径为９Åꎮ静电力的计算采用ＰＰＰＭ(Ｐａｒｔｉｃｌｅ￣ＰａｒｔｉｃｌｅＰａｒｔｉｃｌｅ￣Ｍｅｓｈ)方法且精度为１０－５ꎬ截断半径为１０Åꎮ时间步长为１ｆｓꎮ模拟均在正则系综(ＮＶＴ)下进行ꎬ调温使用Ｎｏｓé￣Ｈｏｏｖｅｒ方法ꎮ１.２㊀接触角的模拟图４㊀面向高温模压的ＳｉＯ２/ＳｉＣ接触角模拟系统Ｆｉｇ.４㊀ＳｉｍｕｌａｔｉｏｎｓｙｓｔｅｍｏｆＳｉＯ２/ＳｉＣｃｏｎｔａｃｔａｎｇｌｅｆｏｒｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｍｏｌｄｉｎｇ在模拟系统中ＳｉＯ２与ＳｉＣ分别为液相和固相ꎬ其中ꎬＳｉＣ基底为ＳｉＣ单胞排列而成的超晶胞ꎬ对其作出三点假设:(１)假设ＳｉＣ表面为不存在缺陷的理想表面ꎻ(２)由于ＳｉＣ不同晶面表面能相差较小ꎬ假设其{１００}晶面为与ＳｉＯ２相接触的表面ꎻ(３)假设ＳｉＯ２熔体液滴为理想的球形ꎮ接触角的模拟系统如图４所示ꎬ首先在半径２.３４８Å的球体区域随机添加１２００个Ｓｉ原子和２４００个Ｏ原子ꎬ随后在５０００Ｋ下驰豫２００ｐｓ并以１００Ｋ/２０ｐｓ的速度降温至１９００Ｋ得到模拟所用的ＳｉＯ２液滴模型ꎮ最后将ＳｉＯ２和ＳｉＣ添加进同一模拟盒子ꎬｘ㊁ｙ方向使用周期性边界ꎬｚ方向使用固定和镜像边界ꎬ其他第３期吴㊀悠:ＳｉＣ模具高温模压石英玻璃物相接触角的分子动力学模拟９２７㊀设置与上一节相同ꎮ图５㊀微结构阵列模具表面多尺度形貌示意图Ｆｉｇ.５㊀Ｍｕｌｔｉｓｃａｌｅｓｕｒｆａｃｅｔｏｐｏｇｒａｐｈｙｏｆｍｉｃｒｏ￣ｓｔｒｕｃｔｕｒｅａｒｒａｙｄｉｅ为了研究纳米级表面粗糙结构对接触角的影响ꎬ采用文献[１３]的方法构建了方柱形阵列ＳｉＣ壁面ꎮ其结构如图５所示ꎮＷｅｎｚｅｌ[２]和Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ[３]模型可用式(６)㊁(７)表示:ｃｏｓθＷ＝ｒｃｏｓθＹ(６)ｃｏｓθＣ＝ｆｃｏｓθＹ＋ｆ－１(７)式中ꎬθＹ为本征接触角ꎻθＷ与θＣ为Ｗｅｎｚｅｌ和Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ模型接触角ꎻｒ为粗糙度因子ꎬ表示表面的实际面积与表观面积之比ꎻｆ为接触面积分数ꎬ表示液滴与基底实际接触的面积和基底表观面积之比ꎮｒ与ｆ可用粗糙度评定参数表示为ｒ＝１＋８ＲｍｒＲａＳｍ(８)ｆ＝Ｒｍｒ２(９)式中ꎬＲａ为轮廓算数平均偏差ꎬＲｍｒ为轮廓支承长度率ꎬＳｍ为轮廓微观不平度的平均间距ꎮ模拟中若Ｒｍｒ㊁Ｓｍ取恒值ꎬ则Ｒａ取０.２５㊁０.５㊁１㊁１.５倍晶格参数ꎬ分别对应ｒ值为１.５㊁２.０㊁３.０㊁４.０ꎻ若Ｒａ取恒值ꎬ改变柱间距为２㊁１.５㊁１㊁０.５倍晶格参数使Ｒｍｒ取０.３３㊁０.４０㊁０.５０㊁０.６７ꎬ分别对应ｆ值为０.１１㊁０.１６㊁０.２５㊁０.４４ꎮ２㊀模拟结果与讨论２.１㊀界面张力图６为１９００Ｋ下ＢＫＳ与ＭＳ￣Ｑ模型中ＳｉＯ２熔体表面张力随时间的演化ꎮ由于使用压力张量法时系统需要较长时间稳定ꎬ模拟连续进行了２０ｎｓꎮ为了降低模拟初期结构不稳定的影响ꎬ在计算累计平均值时采用最后１０ｎｓ数据ꎮＢＫＳ与ＭＳ￣Ｑ势函数的计算结果分别为０.４１０Ｎ/ｍ和０.３９０Ｎ/ｍꎮ由文献[１７]可知ꎬＳｉＯ２在１９００Ｋ下的实际表面张力应为０.３０２Ｎ/ｍ左右ꎮ考虑到模拟本身的准确性以及实际实验过程中ꎬ氧分子等充当表面活性剂降低了测定的表面张力值ꎬ因此模拟值高出实验值０.０７~０.１１Ｎ/ｍ左右是可接受的[１８]ꎮ可以看出ＭＳ￣Ｑ势函数的模拟结果比ＢＫＳ势函数更为接近实验值ꎮ图６㊀ＢＫＳ势函数与ＭＳ￣Ｑ势函数下ＳｉＯ２熔体表面张力演化Ｆｉｇ.６㊀ＥｖｏｌｕｔｉｏｎｏｆＳｉＯ２ｍｅｌｔｓｕｒｆａｃｅｔｅｎｓｉｏｎｕｓｉｎｇＢＫＳｐｏｔｅｎｔｉａｌａｎｄＭＳ￣Ｑｐｏｔｅｎｔｉａｌ图７为两种不同势函数模拟的面向模压的ＳｉＯ２/ＳｉＣ高温界面张力演化图ꎮ界面张力系统达到稳定时间相对较短ꎬ因此模拟时间设为１５ｎｓꎬ取最后４.５ｎｓ时间段的数据计算平均值ꎮ从图中可见ꎬＢＫＳ和ＭＳ￣Ｑ势函数的模拟结果分别为０.８４６Ｎ/ｍ和０.６８２Ｎ/ｍꎮ同时ꎬ计算了两种表面模型的一维密度分布和径向分布函数(ＲａｄｉａｌＤｉｓｔｒｉｂｕｔｉｏｎＦｕｎｃｔｉｏｎꎬＲＤＦ)ꎮ图８(ａ)为模型中心至模拟盒子边缘的密度分布ꎬＢＫＳ与ＭＳ￣Ｑ模型的表面均存在类似汽液共存界面的低密度相ꎬ其厚度分别为４Å与６ÅꎮＢＫＳ模型内部的密度约为９２８㊀陶㊀瓷硅酸盐通报㊀㊀㊀㊀㊀㊀第３９卷２.６９ｇ/ｃｍ３ꎬ大于ＭＳ￣Ｑ的２.２５ｇ/ｃｍ３ꎮ这说明ＢＫＳ表面模型的密度大于ＭＳ￣Ｑ模型ꎬ因此原子间距要小于ＭＳ￣Ｑ模型ꎬ具有更强的原子间作用力ꎬ从而具有更大的表面张力ꎮ图８(ｂ)中ＲＤＦ的计算结果也支持了这一解释ꎮＲＤＦ图中前三个峰代表Ｏ￣Ｏ㊁Ｓｉ￣Ｏ㊁Ｓｉ￣Ｓｉ原子对的第一近邻ꎬ峰值点的横坐标即原子对的键长ꎬ其数值如图８(ｂ)所示ꎬＭＳ￣Ｑ模型中数量较多且强度较大的Ｓｉ￣Ｏ㊁Ｏ￣Ｏ键长均大于ＢＫＳ模型ꎬ从而导致其表面张力小于ＢＫＳ模型ꎮ综上所述ꎬ高温模压时ＳｉＯ２表面性质的模拟可优先选择ＭＳ￣Ｑ势函数ꎮ图７㊀面向高温模压的ＳｉＯ２/ＳｉＣ界面张力演化过程Ｆｉｇ.７㊀ＥｖｏｌｕｔｉｏｎｏｆＳｉＯ２/ＳｉＣｉｎｔｅｒｆａｃｅｔｅｎｓｉｏｎｆｏｒｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｍｏｌｄｉｎｇ图８㊀使用ＢＫＳ与ＭＳ￣Ｑ势函数的ＳｉＯ２表面结构对比Ｆｉｇ.８㊀ＣｏｍｐａｒｉｓｏｎｏｆＳｉＯ２ｓｕｒｆａｃｅｓｔｒｕｃｔｕｒｅｕｓｉｎｇＢＫＳａｎｄＭＳ￣Ｑｐｏｔｅｎｔｉａｌ２.２㊀表面粗糙结构对接触角的影响液滴在理想光滑表面上的接触角称为本征接触角ꎮ由于微纳尺度下液滴表面存在一定的密度和压力涨落ꎬ为了获得具有统计学意义的接触角值ꎬ在处理数据时采用等密度拟合曲线法[１９]ꎮ最后得到面向高温模压的ＳｉＯ２/ＳｉＣ的本征接触角为１１９.２５ʎꎮ根据杨氏方程[１]ꎬ可以利用上节模拟得到的界面张力对本征接触角进行检验ꎮｃｏｓθ＝γｓｖ－γｓｌγｌｖ(１０)式中ꎬγｓｖ表示固￣气界面能ꎻγｓｌ与γｌｖ分别表示固￣液界面能和气￣液界面能ꎬ它们在数值上与固￣液界面张力和液体表面张力相等ꎮ由上节可知ꎬγｓｌ和γｌｖ的值分别为０.６８２Ｎ/ｍ和０.３９０Ｎ/ｍꎮ由于本模拟中采用的ＳｉＯ２/ＳｉＣ相互作用参数来自ＵＦＦ力场ꎬ因此选择文献[２０]中使用ＵＦＦ力场算得的ＳｉＣ{１００}晶面表面能数值０.５０２Ｎ/ｍ代入式(１０)ꎮ最终得到的本征接触角理论值为１１７.４９ʎꎬ与模拟数值差别不大ꎮ图９是ＳｉＯ２熔体在具有不同粗糙度因子的ＳｉＣ模具表面上接触角的模拟ꎬ从图中可见ꎬ接触角总体值在１３５ʎ左右波动ꎮ接触角变化不大则表明固液相互作用能较为稳定ꎬ但图９(ｂ)显示ꎬ在ｒ＝１.５时固液相互作用能较大ꎮ由图１０可以看出ꎬ当粗糙度因子ｒ＝１.５时ꎬＳｉＯ２熔体浸润了沟槽ꎬ出现 钉扎 现象ꎬ此时润湿第３期吴㊀悠:ＳｉＣ模具高温模压石英玻璃物相接触角的分子动力学模拟９２９㊀接近于Ｗｅｎｚｅｌ状态ꎮ 钉扎 现象增强了固液界面的摩擦ꎬ液滴的铺展需要克服更大的能垒ꎬ因此虽然固液相互作用能较大但并未使液滴接触角减小ꎻｒ>１.５时ꎬＳｉＯ２均处于Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ润湿状态ꎬ因此接触角不再受粗糙度因子变化的影响ꎮ从Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ状态到Ｗｅｎｚｅｌ状态的过渡称为润湿转变ꎮ润湿转变可以通过施加压力实现ꎬ但临界转变压力会随着纳米柱的高度减小而减小[２１]ꎻ当其减小到一定程度ꎬ就可能仅仅依靠系统压力实现润湿转变ꎮ本研究中ꎬ当ｒ>１.５时系统压力无法使液滴保持Ｗｅｎｚｅｌ状态ꎬ因此转变为Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ状态ꎻ而此状态下ꎬ界面的固液相互作用比Ｗｅｎｚｅｌ状态更低ꎬ液滴在固体表面的扩散系数变小[２２]ꎬ说明此时ＳｉＯ２熔体在剪切作用下更易在ＳｉＣ模具表面滑移ꎬ从而导致粘性摩擦作用较小ꎮ图９㊀ＳｉＣ模具表面粗糙度对ＳｉＯ２熔体液滴接触角和两者相互作用能的影响Ｆｉｇ.９㊀ＥｆｆｅｃｔｏｆＳｉＣｄｉｅｒｏｕｇｈｎｅｓｓｏｎｃｏｎｔａｃｔａｎｇｌｅｏｆＳｉＯ２ｍｅｌｔｄｒｏｐｌｅｔａｎｄｉｎｔｅｒａｃｔｉｏｎｅｎｅｒｇｙ图１０㊀ＳｉＣ模具表面粗糙度对ＳｉＯ２熔体液滴接触状态的影响Ｆｉｇ.１０㊀ＥｆｆｅｃｔｏｆＳｉＣｄｉｅｒｏｕｇｈｎｅｓｓｏｎｃｏｎｔａｃｔｓｔａｔｅｏｆＳｉＯ２ｍｅｌｔｄｒｏｐｌｅｔ图１１㊀接触面积分数对面向高温模压的ＳｉＯ２/ＳｉＣ接触状态的影响Ｆｉｇ.１１㊀ＥｆｆｅｃｔｏｆｃｏｎｔａｃｔａｒｅａｆｒａｃｔｉｏｎｏｎＳｉＯ２/ＳｉＣｃｏｎｔａｃｔｓｔａｔｅｆｏｒｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｍｏｌｄｉｎｇ图１２㊀接触面积分数对面向高温模压的ＳｉＯ２/ＳｉＣ接触角和相互作用能的影响Ｆｉｇ.１２㊀ＥｆｆｅｃｔｏｆｃｏｎｔａｃｔａｒｅａｆｒａｃｔｉｏｎｏｎＳｉＯ２/ＳｉＣｃｏｎｔａｃｔａｎｇｌｅａｎｄｉｎｔｅｒａｃｔｉｏｎｅｎｅｒｇｙｆｏｒｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｍｏｌｄｉｎｇ９３０㊀陶㊀瓷硅酸盐通报㊀㊀㊀㊀㊀㊀第３９卷图１１为粗糙度因子ｒ>１.５时ＳｉＣ模具表面接触面积分数对ＳｉＯ２熔体液滴接触状态的影响ꎬ此时ＳｉＯ２始终呈现Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ润湿状态ꎬ液滴随接触面积分数的增大逐渐在ＳｉＣ表面铺展ꎮ图１２(ａ)对比了模拟接触角和理论接触角ꎬ虽然两者存在一定误差ꎬ但其都随着接触面积分数的增大而减小ꎻ同时图１２(ｂ)显示接触角越小ꎬＳｉＯ２/ＳｉＣ高温模压界面具有越强的相互作用ꎮ表面粘着力和热应力是脱模力的两个组成部分[２３]ꎬ减小轮廓支承长度率即减小了ＳｉＯ２与ＳｉＣ模具界面的实际接触面积ꎬ从而能减小工件和模具之间的表面粘着力ꎮ而Ｃａｓｓｉｅ￣Ｂａｘｔｅｒ润湿模式无 钉扎 现象ꎬ减小了工件和模具的传热面积ꎬ在一定程度上减小了热应力ꎮ因此适当减小Ｒｍｒ值可以降低以及工件与模具之间的脱模力ꎬ从而减小模具磨损ꎬ提高寿命ꎮ同时也缩减了模具制造过程中抛光工序的工作量ꎮ２.３㊀温度对接触角的影响图１３㊀面向高温模压的ＳｉＯ２/ＳｉＣ接触角与温度的关系Ｆｉｇ.１３㊀ＲｅｌａｔｉｏｎｓｈｉｐｂｅｔｗｅｅｎＳｉＯ２/ＳｉＣｃｏｎｔａｃｔａｎｇｌｅａｎｄｔｅｍｐｅｒａｔｕｒｅｆｏｒｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｍｏｌｄｉｎｇ图１３为接触面积分数为０.２５时温度对面向高温模压的ＳｉＯ２/ＳｉＣ接触角的影响ꎮ从图可见ꎬ接触角值随温度的增大而减小ꎬ说明温度升高ＳｉＯ２的表面张力减小ꎻ当温度高于２３００Ｋ时ꎬ接触角的变化较大ꎬ这是因为使用ＭＳ￣Ｑ势函数模型的ＳｉＯ２自扩散激活温度约为２３００Ｋ左右[１２]ꎮ自扩散激活温度可以视作石英玻璃的软化点温度ꎬ在此温度附近ꎬ石英玻璃的结构发生较大变化ꎬ松动和新生的化学键均大大增加[２４]ꎮ图１４(ａ)是不同温度下ＳｉＯ２熔体表面的结构特点ꎬ由图可见ꎬＳｉＯ２熔体表面存在一个等密度层ꎻ在等密度层外部ꎬ密度随温度升高而增大ꎻ在等密度层内部ꎬ密度随温度升高而减小ꎻ这意味着ＳｉＯ２熔体内部的原子在高温作用下逐渐向外扩散ꎬ这种密度梯度的减小使ＳｉＯ２表面结构更加松散ꎬ减小了其表面张力ꎮ图１４(ｂ)还表明ꎬ温度对ＳｉＯ２熔体表面原子化学键的键长并未产生较大影响ꎬ但随着温度升高ꎬ各化学键对应的峰值依次减小ꎬ表明表面层原子的无序程度增加ꎮ同时ꎬ对比图８(ｂ)可以发现ꎬ表面层中Ｓｉ￣Ｓｉ对应的峰值变得较为微弱甚至消失ꎬ这说明在表面层硅原子数量较少ꎬ而氧原子大量聚集ꎬＯ￣Ｏ键的强度远小于Ｓｉ￣Ｏ键强度ꎬ这可能是ＳｉＯ２表面张力随温度减小的另一个原因ꎮ图１４㊀不同温度下ＳｉＯ２熔体表面结构特点Ｆｉｇ.１４㊀ＳｕｒｆａｃｅｓｔｒｕｃｔｕｒｅｏｆＳｉＯ２ｍｅｌｔｉｎｄｉｆｆｅｒｅｎｔｔｅｍｐｅｒａｔｕｒｅ３㊀结㊀论采用分子动力学方法模拟了ＳｉＯ２熔体的界面结构ꎬ将ＳｉＣ模具纳米级表面理想化为纳米方柱阵列ꎬ研㊀第３期吴㊀悠:ＳｉＣ模具高温模压石英玻璃物相接触角的分子动力学模拟９３１究了粗糙度和温度对面向模压的ＳｉＯ２/ＳｉＣ高温接触角的影响ꎬ得到以下结论:(１)使用ＭＳ￣Ｑ势函数模拟的ＳｉＯ２熔体表面张力比ＢＫＳ势函数计算的结果与实验值更为接近ꎬ因此模拟ＳｉＯ２高温熔体的表面性质使用ＭＳ￣Ｑ势函数更为合理ꎮ(２)在１９００Ｋ的模压温度下ꎬ当粗糙度因子ｒ>１.５时ꎬＲａ的变化对接触角值无明显影响ꎮＲｍｒ值减小使得接触面积分数ｆ减小ꎬ接触角值随之增大ꎮ此时润湿模式从Ｗｅｎｚｅｌ转变为Ｃａｓｓｉｅ￣Ｂａｘｔｅｒꎬ减小了工件￣模具之间的摩擦ꎮ由于热应力和界面粘着力的减小ꎬ石英玻璃光学元件模压后的脱模力将会降低ꎮ同时ꎬ由于降低了Ｒｍｒ值的要求ꎬＳｉＣ模具加工过程中抛光工序的工作量也相应得到了减小ꎮ(３)面向高温模压的ＳｉＯ２/ＳｉＣ的接触角随模压温度升高而减小ꎮ当模压温度超过２３００Ｋ时ꎬ接触角变化率显著增大ꎮ因此模压温度选择在２３００Ｋ以下可以降低模压时模具因玻璃熔体的粘附造成的磨损ꎮ参考文献[１]㊀ＹｏｕｎｇＴＨ.Ａｎｅｓｓａｙｏｎｔｈｅｃｏｈｅｓｉｏｎｏｆｌｉｑｕｉｄｓ[Ｊ].Ｐｈｉｌ.Ｔｒａｎｓ.Ｒｏｙ.Ｓｏｃ.Ｌｏｎｄｏｎꎬ１８０５ꎬ９５:６５￣８７.[２]㊀ＷｅｎｚｅｌＲＮ.Ｒｅｓｉｓｔａｎｃｅｏｆｓｏｌｉｄｓｕｒｆａｃｅｓｔｏｗｅｔｔｉｎｇｂｙｗａｔｅｒ[Ｊ].Ｉｎｄ.Ｅｎｇ.Ｃｈｅｍ.ꎬ１９３６ꎬ２８:９８８￣９４.[３]㊀ＣａｓｓｉｅＡＢＤꎬＢａｘｔｅｒＳ.Ｗｅｔｔａｂｉｌｉｔｙｏｆｐｏｒｏｕｓｓｕｒｆａｃｅｓ[Ｊ].Ｔｒａｎｓ.Ｆａｒａｄａｙ.Ｓｏｃ.ꎬ１９４４ꎬ４０:５４６￣５１.[４]㊀陈㊀光.新材料概论[Ｍ].北京:科学出版社ꎬ２００３:４６￣４８.[５]㊀和丽芳.纳米碳化硅材料的制备及应用[Ｄ].太原:山西大学ꎬ２０１１.[６]㊀徐㊀威ꎬ兰㊀忠ꎬ彭本利ꎬ等.微液滴在不同能量表面上润湿状态的分子动力学模拟[Ｊ].物理学报ꎬ２０１６(２１):２１６８０１.[７]㊀王㊀龙.金属液滴在碳纳米材料表面的润湿与融合[Ｄ].济南:山东大学ꎬ２０１７.[８]㊀ＤｉｎｇＹꎬＺｈａｎｇＹꎬＺｈａｎｇＦꎬｅｔａｌ.ＭｏｌｅｃｕｌａｒｄｙｎａｍｉｃｓｓｔｕｄｙｏｆｔｈｅｓｔｒｕｃｔｕｒｅｉｎｖｉｔｒｅｏｕｓｓｉｌｉｃａｗｉｔｈＣＯＭＰＡＳＳｆｏｒｃｅｆｉｅｌｄａｔｅｌｅｖａｔｅｄｔｅｍｐｅｒａｔｕｒｅｓ[Ｃ].ＭａｔｅｒｉａｌｓＳｃｉｅｎｃｅＦｏｒｕｍ.２００７.[９]㊀ＢｅｅｓｔＢＷＨＶꎬＫｒａｍｅｒＧＪꎬＳａｎｔｅｎＲＡＶ.Ｆｏｒｃｅｆｉｅｌｄｓｆｏｒｓｉｌｉｃａｓａｎｄａｌｕｍｉｎｏｐｈｏｓｐｈａｔｅｓｂａｓｅｄｏｎａｂｉｎｉｔｉｏｃａｌｃｕｌａｔｉｏｎｓ[Ｊ].ＰｈｙｓｉｃａｌＲｅｖｉｅｗＬｅｔｔｅｒｓꎬ１９９０ꎬ６４(１６):１９５５.[１０]㊀ＳｕｎｄａｒａｒａｍａｎＳꎬＣｈｉｎｇＷＹꎬＨｕａｎｇＬ.Ｍｅｃｈａｎｉｃａｌｐｒｏｐｅｒｔｉｅｓｏｆｓｉｌｉｃａｇｌａｓｓｐｒｅｄｉｃｔｅｄｂｙａｐａｉｒｗｉｓｅｐｏｔｅｎｔｉａｌｉｎｍｏｌｅｃｕｌａｒｄｙｎａｍｉｃｓｓｉｍｕｌａｔｉｏｎｓ[Ｊ].ＪｏｕｒｎａｌｏｆＮｏｎ￣ＣｒｙｓｔａｌｌｉｎｅＳｏｌｉｄｓꎬ２０１６ꎬ４４５￣４４６:１０２￣１０９.[１１]㊀ＤｅｍｉｒａｌｐＥꎬＣａｇｉｎꎬＴａｈｉｒꎬＧｏｄｄａｒｄＷＡ.Ｍｏｒｓｅｓｔｒｅｔｃｈｐｏｔｅｎｔｉａｌｃｈａｒｇｅｅｑｕｉｌｉｂｒｉｕｍｆｏｒｃｅｆｉｅｌｄｆｏｒｃｅｒａｍｉｃｓ:ａｐｐｌｉｃａｔｉｏｎｔｏｔｈｅｑｕａｒｔｚ￣ｓｔｉｓｈｏｖｉｔｅｐｈａｓｅｔｒａｎｓｉｔｉｏｎａｎｄｔｏｓｉｌｉｃａｇｌａｓｓ[Ｊ].ＰｈｙｓｉｃａｌＲｅｖｉｅｗＬｅｔｔｅｒｓꎬ１９９９ꎬ８２(８):１７０８￣１７１１.[１２]㊀丁元法ꎬ张㊀跃ꎬ张凡伟ꎬ等.石英玻璃高温分子动力学模拟中的势函数[Ｊ].物理化学学报ꎬ２００８ꎬ２４(５):７８８￣７９２.[１３]㊀ＨｏｓｓｅｉｎｉＳꎬＳａｖａｌｏｎｉＨꎬＳｈａｈｒａｋｉＭＧ.Ｉｎｆｌｕｅｎｃｅｏｆｓｕｒｆａｃｅｍｏｒｐｈｏｌｏｇｙａｎｄｎａｎｏ￣ｓｔｒｕｃｔｕｒｅｏｎｈｙｄｒｏｐｈｏｂｉｃｉｔｙ:Ａｍｏｌｅｃｕｌａｒｄｙｎａｍｉｃｓａｐｐｒｏａｃｈ[Ｊ].ＡｐｐｌｉｅｄＳｕｒｆａｃｅＳｃｉｅｎｃｅꎬ２０１９ꎬ４８５:５３６￣５４６.[１４]㊀周书强.小口径非球面玻璃透镜的模压仿真及实验研究[Ｄ].长沙:湖南大学ꎬ２０１６.[１５]㊀ＨｅｒｄｅｓＣꎬＥｒｖｉｋＡꎬＭｅｊíａꎬｅｔａｌ.Ｐｒｅｄｉｃｔｉｏｎｏｆｔｈｅｗａｔｅｒ/ｏｉｌｉｎｔｅｒｆａｃｉａｌｔｅｎｓｉｏｎｆｒｏｍｍｏｌｅｃｕｌａｒｓｉｍｕｌａｔｉｏｎｓｕｓｉｎｇｔｈｅｃｏａｒｓｅ￣ｇｒａｉｎｅｄＳＡＦＴ￣γＭｉｅｆｏｒｃｅｆｉｅｌｄ[Ｊ].ＦｌｕｉｄＰｈａｓｅＥｑｕｉｌｉｂｒｉａꎬ２０１８ꎬ４７６:９￣１５.[１６]㊀ＲａｐｐｅＡＫꎬＣａｓｅｗｉｔＣＪꎬＣｏｌｗｅｌｌＫＳꎬｅｔａｌ.ＵＦＦꎬａｆｕｌｌｐｅｒｉｏｄｉｃｔａｂｌｅｆｏｒｃｅｆｉｅｌｄｆｏｒｍｏｌｅｃｕｌａｒｍｅｃｈａｎｉｃｓａｎｄｍｏｌｅｃｕｌａｒｄｙｎａｍｉｃｓｓｉｍｕｌａｔｉｏｎｓ[Ｊ].ＪｏｕｒｎａｌｏｆｔｈｅＡｍｅｒｉｃａｎＣｈｅｍｉｃａｌＳｏｃｉｅｔｙꎬ１９９２ꎬ１１４(２５):１００２４￣１００３５.[１７]㊀ＷｕＣꎬＣｈｅｎＧ.ＣｏｍｐｕｔａｔｉｏｎａｌｍｏｄｅｌｏｎｓｕｒｆａｃｅｔｅｎｓｉｏｎｏｆＣａＯ￣ＭｎＯ￣ＳｉＯ２ｓｌａｇｓｙｓｔｅｍ[Ｊ].ＨｏｔＷｏｒｋｉｎｇＴｅｃｈｎｏｌｏｇｙꎬ２０１４ꎬ４３(１９):５８￣６２. [１８]㊀ＢｅｌａｓｈｃｈｅｎｋｏＤＫꎬＯｓｔｒｏｖｓｋｉｉＯＩ.Ｃｏｍｐｕｔｅｒｓｉｍｕｌａｔｉｏｎｏｆｓｍａｌｌｎｏｎｃｒｙｓｔａｌｌｉｎｅｓｉｌｉｃａｃｌｕｓｔｅｒｓ[Ｊ].ＩｎｏｒｇａｎｉｃＭａｔｅｒｉａｌｓꎬ２００２ꎬ３８(９):９１７￣９２１. [１９]㊀王宝和ꎬ李㊀群.接触角的研究现状及其在凝胶干燥中的作用[Ｊ].干燥技术与设备ꎬ２０１４ꎬ１２(１):３９￣４６.[２０]㊀罗晓光.ＺｒＢ２/ＳｉＣ复合材料界面结构的分子动力学模拟[Ｄ].哈尔滨:哈尔滨工业大学ꎬ２００７.[２１]㊀ＬｉｕＢꎬＬａｎｇｅＦＦ.Ｐｒｅｓｓｕｒｅｉｎｄｕｃｅｄｔｒａｎｓｉｔｉｏｎｂｅｔｗｅｅｎｓｕｐｅｒｈｙｄｒｏｐｈｏｂｉｃｓｔａｔｅｓ:ｃｏｎｆｉｇｕｒａｔｉｏｎｄｉａｇｒａｍｓａｎｄｅｆｆｅｃｔｏｆｓｕｒｆａｃｅｆｅａｔｕｒｅｓｉｚｅ[Ｊ].ＪｏｕｒｎａｌｏｆＣｏｌｌｏｉｄ＆ＩｎｔｅｒｆａｃｅＳｃｉｅｎｃｅꎬ２００６ꎬ２９８(２):８９９￣９０９.[２２]㊀ＫａｌｉｎＭꎬＰｏｌａｊｎａｒＭ.Ｔｈｅｅｆｆｅｃｔｏｆｗｅｔｔｉｎｇａｎｄｓｕｒｆａｃｅｅｎｅｒｇｙｏｎｔｈｅｆｒｉｃｔｉｏｎａｎｄｓｌｉｐｉｎｏｉｌ￣ｌｕｂｒｉｃａｔｅｄｃｏｎｔａｃｔｓ[Ｊ].ＴｒｉｂｏｌｏｇｙＬｅｔｔｅｒｓꎬ２０１３ꎬ５２(２):１８５￣１９４.[２３]㊀叶㊀伟.强流脉冲电子束处理对热模压脱模性能的影响[Ｄ].重庆:重庆理工大学ꎬ２０１３.[２４]㊀ＷａｎｇＣꎬＫｕｚｕｕＮꎬＴａｍａｉＹ.Ｍｏｌｅｃｕｌａｒｄｙｎａｍｉｃｓｓｔｕｄｙｏｎｓｕｒｆａｃｅｓｔｒｕｃｔｕｒｅｏｆｈｏｔｗｏｒｋｉｎｇｔｅｃｈｎｏｌｏｇｙα￣ＳｉＯ２ｂｙｃｈａｒｇｅｅｑｕｉｌｉｂｒａｔｉｏｎｍｅｔｈｏｄ[Ｊ].ＪｏｕｒｎａｌｏｆＮｏｎ￣ＣｒｙｓｔａｌｌｉｎｅＳｏｌｉｄｓꎬ２００３ꎬ３１８:１３１￣１４１.。
3D Modeling of kinematic and dynamic ruptures inanisotropic mediaG. Brietzke1, H. Igel1, Y. Ben−Zion2,Ludwig−Maximilians−Universität, München, Germany1University of Southern California, Los Angeles, USA2We study the behavior of expanding sources and their radiated wave fields in the context of fault zone typical velocity structures and anisotropy(due to cracking)in the surrounding material.We solve the set of elasto−dynamic equations for the three−dimensional anisotropic case [2] using standard finite difference scheme.Fault zones are thought to consist of a narrow zone of reduced seismic velocities and considerable material anisotropy due to aligned cracks and fractures.In this study we focus on two questions:How does material anisotropy in the fault zone effect the radiated wave field of expanding directed sources,and how does dynamic rupture propagation interact with the anisotropic media and reduced seismic velocity in the fault zone.We start with a simple kinematic rupture propagation to search for robust signals in the recorded seismograms and try to classify the effects caused by anisotropy,by velocity variations and by geometry and size of the fault.The dynamic behavior of seismic rupture processes is controlled by a more complex interaction between pre−existing stress distributions,assumed friction law and the feedback of the radiated wave field.We apply simple slip and slip−rate weakening friction at the fault zone boundary using stress glut method[1].We study how the anisotropic medium effects the dynamics of the rupture and the recorded seismograms by comparison to the isotropic medium and the kinematic models.[1] D.J.Andrews,1999,Test of two methods for faulting in finite−difference calculations. BSSA, 89(4):931−937, 1999.[2]H.Igel,P.Mora,and B.Riollet.Anisotropic wave propagation through finite difference grids. Geophysics, 60(4):1203−1216, 1995.。
八年级英语物理现象单选题60题1. A lever is a simple machine. We can use it to lift heavy objects more easily. Which part of the lever is the fixed point around which the lever rotates?A. Effort armB. Resistance armC. FulcrumD. Load答案：C。
解析：“fulcrum”是杠杆的支点，是杠杆绕着转动的固定点。
“effort arm”是动力臂，是施加力的那部分杠杆；“resistance arm”是阻力臂，是承受阻力的那部分杠杆；“load”是负载，也就是要被抬起的重物，所以A、B、D选项错误。
2. A pulley can change the direction of the force. If we want to lift a box using a single fixed pulley, which statement is correct?A. The force we need to apply is equal to the weight of the box.B. The force we need to apply is half of the weight of the box.C. The force we need to apply is twice the weight of the box.D. We don't need to apply any force.答案：A。
解析：对于单个定滑轮，它不省力，只是改变力的方向，所以我们施加的力等于箱子的重量，A选项正确。
B选项，力是箱子重量一半的情况适用于动滑轮；C选项力是箱子重量两倍是错误的；D选项不施加力是不可能将箱子抬起的。
SIGRAD(2002)Mark Ollila(Editors)Animation of Water Droplet Flow on Structured SurfacesMalin JonssonUniversity of Gävle,Kungsbäcksvägen47,S-80176Gävle,Sweden.na99mjn@student.hig.seAnders HastCreative Media LabUniversity of Gävle,Kungsbäcksvägen47,S-80176Gävle,Sweden.aht@hig.seAbstractSeveral methods for rendering and modeling water have been made and a few of them address the natural phe-nomenon of water dropletsflow.As far as we know,none of those methods have used bump maps in order to simulate theflow of a droplet on structured surfaces.The normals of the bump map,that describes the geometry of the micro structured surface,are used in theflow computation of the droplets.As a result,the water droplets will meander down on the surface as if it has a micro structure.Existing models were not suitable for this purpose.Therefore,a new model is proposed in this paper.The droplet will also leave a trail,which is produced by chang-ing the background texture on the surface.This method will not present a physically correct simulation of water dropletsflow on a structured surface.However,it will produce a physically plausible real-time animation.1.IntroductionThere is an endless ever-changing kingdom of phenomenon provided by the nature that is possible to model,animate and render.These phenomenons offers,with their complex-ity and richness,a great challenge for every computer artist. Several natural phenomenons,likefire,smoke,snow,clouds, waves,trees and plants,have with different success been modeled in computer graphics through the years.Several different methods that address the problems of rendering and modeling water and other similarfluids have been developed since the1980t’s.Most of them concern animation of mo-tion in water in forms of waves and other connectedfluids and surfaces,i.e.whole bodies of water.For example have oceans waves10513and waves approaching and braking on a beach12been modeled.Realistic and practical animation of liquids23has also been made.Only a few methods that have been proposed during the1990’s address the problems of the natural phenomenon of water droplets.Methods for simulating theflow of liquids were proposed to render a tear falling down a cheek4and changes in appearances due to weathering1.Different methods for animation of theflow of water droplets running down a curved surface with7or without obstacles on it8have also been proposed.Different ways to create droplets have been used6,for example meta-balls that are affected by the gravitation were used as one solution14.It is quite difficult to simulate theflow of water droplets for the purpose of high-precision engineering,due to the complicated process that theflow and the shape of the droplet represent.This process has many unknown factors that plays a big role.The shape and the motion of a water droplet on a surface depend on the gravity force that acts on the droplet,the respective surface tensions of the surface and the water droplet,and the inter-facial tension between them6.Shape and motion is also under the sway of other things like air resistance and evaporation.These effecting factors can be divided into two different groups.As an exam-ple,gravity and wind can be placed in the group of external forces.Factors like surface tension and inter-facial tension belongs to the group of internal forces.To be able to create an accurate physical simulation of the phenomenon of water droplets,a tremendous amount of forces and factors wouldc SIGRAD2002.have to be taken into account.As mentioned above many of the dominant factors for water droplets are still unknown not only within computer graphics but also within physics.To the long list of effecting factors these ones can be added:•Motion of the water within the droplet.•The capillarity of the surface.•The interaction forces between each point on the surface of the droplet and the solid surface.1.1.Main ContributionTrying to take all of these different factors into account would create an accuracy that goes far beyond what is pos-sible to do in the scope of this paper.A method is proposed for generating an animation of theflow of water droplets on a structured surface.Instead of creating a structured surface with a huge amount of polygons,a bump mapped9flat sur-face is used.Furthermore,the bump normal is used to control the motion of the droplets.To our knowledge,this has never been investigated before.Hence,the droplet will meander down the surface and move as if it actually wasflowing on a structured surface.However,as mentioned earlier,all the different factors which have an influence on water droplets and theirflow,have not been taken to account in the method. The aim of this paper is not to make a simulation that is physically correct at every point,but to make a plausible an-imation of droplets meandering down on a bump mapped surface.2.Previous ResearchThere are at least four published papers about droplets and theirflow that address similar problems as this paper.2.1.Animation of Water Droplets on a Glass Plate Kaneda et al6propose a method for realistic animation of water droplets and their streams on a glass plate.The main purpose is to generate a realistic animation,taken into ac-count gravity of water droplets,inter-facial tensions and merging of water.Those are the dominant parameters of dy-namical systems.A high-speed rendering is also proposed, which takes reflection and refraction of light into account. Their method will reduce the calculation cost of animations that contains scenes seen through a rainy windshield or win-dowpane.The route that the water a droplet takes as it meanders down on a glass plate is determined by impurities on the surface and inside the droplet itself.To be able to animate water droplets and their stream a discrete surface model is developed and the surface of the glass plate is divided into a mesh.Figure1shows a lattice that is used on a glass plate. To every lattice point on the glass plate an affinity,0-1,for water is assigned in advance.A water droplet begins to meander down a surfacewhen Figure1:A discrete surface model,with the droplet at posi-tion(i,j)the mass exceeds a static critical weight.To simulate the me-andering the droplet at point(i,j)can move to one of three different points on the lattice,as shown in Figure1.If some water exists on any of the three points,the droplet will move to the lattice point with the direction(i,j+1)has the highest priority.In case there is no water already existing on the dif-ferent points,a value depending on for example the angle of inclination is used as a decision parameter.They claim that the speed of the droplet is not depending on the mass of the droplet.Instead it depends on the wetness and the angle of inclination of the glass plate.When two droplets collides and merges the speed of the new droplet is calculated by using equation law of conservation of the momentum.A meander-ing droplet that has no water ahead will decelerate and when the dynamic critical weight is larger than the mass of the droplet,it willfinally stop.2.2.Animation of Water Droplet Flow on CurvedSurfacesThe previously proposed method is not able to simulate a water droplet on a curved surface,which is an important and necessary technique for drive simulators.Therefore an ex-tended method for generating realistic animation of water droplets and their streams on curved surfaces is proposed by Kaneda et al8.The dynamics,such as gravity and inter-facial tension that acts on water droplets is also taken into account in this method.Two different rendering methods that takes refraction and reflection into account,is also proposed.One method pursues photo-reality with help of a high quality ren-dering.The other proposes a fast rendering method that uses a simple model of water droplets.A discrete surface model is used to make it possible to simulate theflow of droplets running down the curved sur-face.The curved surface is divided into small quadrilateral meshes and may be specified by Beziér patches.It is con-verted to a discrete model,using a quadrilateral mesh with a normal vector at the center.Affinity contributes to the mean-der of the streams and to the wetting phenomenon.The de-gree of affinity for water is assigned to each mesh in advance.c SIGRAD2002.Figure2:The eight directions of movementThis value describes the lack of uniformity on a surface,for example a glass plate.The uniformity can be impurities and small scratches.The droplet is affected by gravity and wind.When these forces exceed a static critical force,the water droplet starts to meander down the surface.The critical force originates from the inter-facial tension between water and a surface and is the resistance that prevents the droplet from moving. The direction of movement is classified into eight different directions as shown infigure2.The probabilities for each direction is calculated based on three different factors.The first one is the direction of movement under circumstances in which it obeys Newton’s law of motion.The second factor is the degree of affinity for water on the meshes next to the droplet.The last one is the wet or dry condition of the eight neighboring meshes.The water droplet is moved to the next mesh when the direction of movement is determined and if the accumulated time exceeds a frame time,the droplet is moved to the next mesh.A solution to the wetting phenomenon that appears when a droplet meander down a surface,as well as the problem with two droplets merging,is also addressed.Two different methods for rendering water droplets are proposed.The fast version use spheres.The more sophisticated use meta-balls.2.3.Simulating theflow of liquid dropletsFournier et al4present a model that is oriented towards an efficient and visually satisfying simulation.It focuses on the simulation of large liquid droplets as they travel down a sur-face.The aim is to simulate the visual contour and shape of water droplets when it is affected by the underlying surface and other forcefields.The surface is defined as a mesh of triangles.At the be-ginning of the simulation a"neighborhood"graph is built. In this graph each triangle is linked to the triangles adja-cent to itself.Through the entire simulation each triangle knows which droplets are over it as well as every droplet know which triangle it lies on at the moment.Adhesion and roughness is considered in this method.The adhesion is a force that works along the surface normal.A droplet will fall from a leaning surface if the adhesion force of the droplet becomes smaller than the component of the droplets accel-eration force that is normal to the surface.The roughness of the surface is assumed to only reduce the tangential force. The motion of droplets is generated by a particle sys-tem,where droplet is represented by one particle each.This representation offers many advantages for simulations that have a wide spectrum of behaviors,because of the general-ity andflexibility such systems can offer.A droplet might travel over several triangles between two time steps.To en-sure that the droplet is properly affected by the deformations on the surface it has traversed,the motion of the droplet over each individual triangle is computed.When a droplet travel from one triangle to another,the neighborhood graph is used to quickly identify which triangle the droplet moves to.The two forces gravity,and friction,which affects the water droplets,are assumed to be constant over a triangle.2.4.Animation of Water Droplets Moving Down aSurfaceKaneda at al7propose a method for generating an animation with water droplets that meander down a transparent surface.A large amount of droplets are used to generate a realis-tic and useful animation for drive simulators.There method employs a particle system in which water droplets travel on a discrete surface model.The proposed method involves ex-tensions of previously discussed papers68.One of the main achievements is modeling of obstacles that act against water droplets,like the wiper on the windshield.The curved surface is divided into small quadrilateral meshes and the droplets move from one mesh point to an-other under the influence of external forces and obstacles. The degree of affinity for water is assigned in advance to each mesh.Affinity describes the lack of uniformity on an object surface due to such things as small scratches and other impurities.The degree of affinity in most cases is assigned randomly based on a normal distribution in order render the droplets meandering and wetting phenomenon.By taking into account some dominant factors the direc-tion of movement can be determined.The dominant factors that affects the meandering of water droplets that is men-tioned the paper is:1.Direction of movement under circumstances in which itobeys Newton’s law of motion.2.Degree of affinity for water of the neighboring meshes.3.The wet or dry condition of the neighboring meshes4.Existence of obstacles on the neighboring meshesA stochastic approach is taken for determining the direc-tion of movement,because the route of the stream cannot be calculated deterministically.This is due to the many un-known factors that play a role.This means in other words that the direction of movement is classified into eight differ-ent directions,as done in an earlier mentioned paper8.Thec SIGRAD2002.probabilities of movement for every direction is calculated with the four dominate factors,described above,taken into account.The method for rendering water droplets which is pro-posed in this paper is based on a method that is published by Kaneda et al6.The method uses environment mapping to generate realistic images of water droplets.Spheres are used to approximate the water droplets.The contact angle of the water on the surface is taken into account.This method has been extended further in this paper.Such factors as defocus and blur effects are added to generate more realistic images.3.Droplet Flow Controlled by Bump mapsThe different factors that have an affect on theflow of the water droplet are almost countless.Hence,a correct anima-tion is more or less impossible to make.The goal of this pa-per is therefore to make a physically plausible animation that will produce a natural looking animation of theflow.A real wetting effect which will affect other droplets was not be im-plemented.Neither was a method for merging of droplets.A simple solid sphere was used to model the droplets.An ani-mation was implemented using C++and OpenGL.In the an-imation aflat surface is modeled using a texture and a bump map which is retrieved from the texture.An object oriented particle system was used where each droplet is a particle. This will make the animation easy to control.Furthermore, it is easy to add more droplets to the animation.3.1.External and internal forcesThere are different forces that acts on the water droplets as they meander on the surface.The different forces can be di-vided into two groups,the external forces,f ext,and the in-ternal forces,f int.Kaneda et al8set the external forces to be gravity and wind.However,we will set the external force to be gravity only,since no wind is applied in the proposed model.Nonetheless wind or any other external force could be added if applicable.Moreover,we will use the same deno-tation of vectors as used by Kaneda et al and also introduce some new vectors.The internal force is a force of resistance and its direction is opposite to the direction of movement,d p:f int=−αd p.(1) The resistance originates from the inter-facial tension that exists between the water droplet and the surface.The affinity which is denotedαis in advance experimentally set to some value,which is assumed to be constant all over the surface for simplicity.3.2.Direction of movementThe direction of movement can be computed by applying the Gram Schmidt orthogonalization algorithm11as shownNf extd psc©Figure3:The direction of movement d p for a bump with normal N and gravity f extNf extf inta psc©Figure4:Forces acting on the dropletinfigure3:d p=f ext−N·f extN.(2)The normal vector N is the unit length normal which is re-trieved at every point from the bump map.This normal will affect the water droplets as they meander down the surface. It will appear as the droplets are directed in a natural way by the visual bumps on the surface underneath the droplet. Furthermore,the whole polygon has a main direction down-wards or tangent T,computed from the external force f ext and the normal of the polygon N :T=f ext−N ·f extN .(3) The bi-normal of the plane is computed as:B=T×N .(4)In order to calculate the acceleration of the water droplet, the mass,m,and the forces that acts on the droplet,f ext and f int,are used.The acceleration a p shown infigure4is then decomposed into the component toward the direction of movement d p,by projecting it onto this vector8:a p=f ext+f int·d pmd p.(5)The velocity v of the droplet is computed by adding the acceleration a p to the velocity for each step.Similarly,the velocity is added to the position P.Furthermore,the velocityc SIGRAD2002.Figure5:One frame from the droplet animation.The trails show that the droplets are affected by the underlying bump mapped surface.must be projected down onto the plane,in order to prevent the drop from leaving the surface,which of course is mod-eled in nature by other forces.Nevertheless,this will work for our purposes.This algorithm gives us the new position of the droplet and the droplet is moved to that point during one frame of animation.Hence,the following computations are necessary besides computing the acceleration:v i+1=v i+a p,(6)v p=T(T·v i+1)+B(B·v i+1),(7)P i+1=P i+v p.(8)3.3.Speed ControlIn nature,water meandering down a surface will not accel-erate up to full speed,due to several of the forces mentioned in the introduction.Therefore,a speed controller was imple-mented,delimiting the speed in two ways.First a maximum speed was introduced.Secondly,the speed will be reduced on bumpy areas.Thus,letting the dropletflow rapidly onflat surfaces,but be slowed down considerably on bumpy areas.A bumpy area is defined as a position where:N·N <1−ε,(9) whereεis a threshold value that can be used to control how large the bumps should be in order to slow down the droplet more than usual bumpiness would.3.3.1.The trailIn order to produce a natural looking trail on the surface which the droplet has traversed,a texture map is used.A snapshot from the animation is shown infigure5In the an-imation a texture map is used and the height map is derived from it.The trail is produced by altering the glossiness of the part of the texture that the droplet has passed.It can easily be confirmed by looking on a wall,on which water have been poured on,that the thin layer of water in the trail reflects light with a higher degree of specularity than the underlying surface has.4.DiscussionThe aim is to make an animation that look as natural and re-alistic as possible.Because of that and several physical fac-tors that still are unknown for theflow of water droplets, there are lot of tampering that needs to be done with the dif-ferent parameters.The only way to get a satisfying result is to experiment with the different values and see what is going to happen.As shown earlier the velocity is projected down to the plain in order to prevent the droplet from leaving the sur-face.This is something that maybe can be controlled in a smoother way.For example,a factor that makes the droplet adhere to the surface would be one way to handle it.The wetting effects that theflow of a droplet has on the traversed surface is only implemented as a change of the specular light in the trail after the water droplet.If the wet-ting phenomenon were to be more correct implemented,the droplet would for instance leave a small amount of water behind as itflows down the surface.This would reduce the size of the droplet andfinally make it stop.The wetting phe-nomenon would also make other droplets that comes near a trail of water adhere to it.Subsequently it wouldflow almost strictly in the same trail as the droplet before.The problem with two merging droplets is not addressed in this paper. Only one normal is retrieved from the map for each droplet.Nonetheless,it is also possible to use several nor-mals for this computation.The droplet is after all covering more than one position in the height map.It turns out not to be an good idea to compute an average of the normals in-volved to use in the droplet computations,since the effect on the droplet will be diminished due to the averaging. Another way to use more than one normal would be to define the bumpiness which should slow down the droplet as described earlier.If the average deviation of the normals from the mean normal,under the droplet,is larger than some threshold value,then the area is considered being bumpy. Even though the animation is realistic,nature can some-times surprise you.This is especially true for droplets on a structured surface.Sometimes droplets will not meanderc SIGRAD2002.straight down on a totallyflat surface.Instead they will me-ander sideways.By making an experiment where two pic-tures are taken,one of the structured surface and one of a water droplet thatflow over the surface,a comparison of the simulated result and the real thing could be done.The picture taken on the surface would subsequently be used as a texture and a bump map could be retrieved from it in order to pro-duce an animation.The result would show how far from the real thing the animation is.The proposed model in will make the simulation of the flow of a water droplet on a structured surface considerable faster than if polygons were used to form the micro structure. The object itself will also be rendered faster.5.ConclusionsA method for animation of water dropletsflow on struc-tured surfaces was proposed and the droplets in this method were affected by the underlying bump mapped surface.The proposed method will save time due to the use of a bump mapped surface instead of a larger amount of different tri-angles.Several parameters where used for the animation of theflow of a water droplets,like the gravity working on the droplet,affinity of the surface,and the mass of the droplet used in the proposed method.Moreover,is the algorithm simplified in such way that adhesion to the surface on bumpy areas is modeled by slowing down the drop.A maximum speed is also used for modeling adhesion.All this will make the animation of the individual droplets fast.5.1.Future WorkThere are several improvements that can be done to the pro-posed method.Moreover,there are various of extensions that can be employed to the present method.Some examples of possible improvements are,to make a better simulation of the wetting phenomenon,so that it will affect the droplets size and shape.Hence,droplets will become smaller as they leave a trail.Another improvement would be to create the droplet with help of Beziér curves and let the control points be altered by the bump mapped normals.Different normals should affect the different parts of the droplet,making the droplet stretch and bend.The shape of the water droplet is something that overall should be improved.If the affinity of the surface would depend on the bump map,then it would probably give the meandering of the water droplet a much more realistic and natural look.The method should be extended so that the droplet adheres to the surface and when the adhesion becomes small enough the droplet will depart from the surface.Other proposals for extensions can be,to implement the enlargement effect that water droplets have on their underly-ing surface and how light are reflected in the water droplets.Another extension is implement collision and merging of water droplets.References1.Dorsey J,Pedersen H,Hanrahan P.Flow and changesin appearances.SIGGRAPH96,pp.411-420,1996. 2.Foster N,Metaxas D.Realistic Animation of Liq-uids.Graphical Models and Image Processing.58(5) pp.471-483,1996.3.Foster N,Fedkiw,R.Practical Animation of Liquids.Proceedings of the28th annual conference on Com-puter graphics and interactive techniques,2001.4.Fournier P,Habibi A,Poulin P.Simulating theflow ofliquid droplets.Proceedings of Graphics Interface98 pp.133-42,1998.5.Fournier A.A Simple Model of Ocean -puter Graphics20(4),pp.75-84,1986.6.Kaneda K,Kagawa T,Yamashita H.Animation of Wa-ter Droplets on a Glass Plate.Proceedings of Computer Animation93,pp.177-89,1993.7.Kaneda K,Shinya I,Yamashita H.Animation of Wa-ter Droplets Moving Down a Surface.The Journal of Visualization and Computer Animation101999.8.Kaneda K,Zuyama Y,Yamashita H,Nishita T.Anima-tion of Water Droplet Flow on Curved Surfaces,Pro-ceedings of Pacific Graphics96,pp.50-65,1996.9.Kilgard M.J.A Practical and Robust Bump-mappingTechnique for Today s GPUs Game Developers Con-ference,Advanced OpenGL Game Development.2000.10.Max N.Vectorized procedural models for natural ter-rain:Waves and islands in the sunset.SIGGRAPH15, pp.317-324,1981.11.Nicholson W.K.Linear Algebra With ApplicationsPWS Publishing Company,Third Edition,pp.275, 1995.12.Peachey D.Modeling Waves and puterGraphics20(4),pp.65-74,1986.13.Ts’o P,Barsky B.Modeling and Rending Waves:Wave-Tracing Using Beta-Splines and Reflective and Refrac-tive Texture Mapping.ACM Transactions on Graphics 6,pp.191-214,1987.14.Yu Y-J,Jung H-Y,Cho H-G.A new water dropletmodel using metaball in the gravitationalfi-puter&Graphics23,pp.213-222,1999.c SIGRAD2002.。
纳米结构及浸润性对液滴润湿行为的影响*李文1) 马骁婧1)† 徐进良1)2) 王艳1) 雷俊鹏1)1) (华北电力大学, 低品位能源多相流与传热北京市重点实验室, 北京 102206)2) (华北电力大学, 电站能量传递转化与系统教育部重点实验室, 北京 102206)(2020 年9 月23日收到; 2021 年2 月20日收到修改稿)
液滴在纳米结构表面的润湿模式研究(Dewetting, Cassie, Partial Wenzel及Wenzel)对强化冷凝、表面自清洁、油水分离等具有重要意义, 现有文献主要研究了液滴在微柱阵列纳米结构表面的润湿行为. 本文采用分子动力学模拟, 研究了纳米结构倾角及表面浸润性对氩液滴在铂固体壁面上润湿模式及其相互转换的影响, 采用了三种纳米结构, 其倾角分别为60° (倒梯形)、90° (长方形)及120° (正梯形); 以本征接触角qe表征表面浸润性. 研究表明, 当qe < 118°时, 液滴在纳米结构表面均呈Wenzel状态, 即液体向纳米结构缝隙完
全渗透; 当118° < qe < 145°时, 倒梯形纳米结构有助于液滴保持Cassie状态, 即液体不向纳米结构缝隙渗透,
正梯形纳米结构容易使液滴形成Partial Wenzel状态, 即液体向纳米结构缝隙部分渗透. 分析表明, 三种纳米结构倾角对液滴润湿模式的影响及转换满足自由能最小原理. 本文工作揭示出采用倒置纳米结构, 可使液滴更好维持Cassie模式.
关键词：液滴, 纳米结构, 润湿模式, 分子动力学PACS：61.30.Pq, 61.46.–w, 68.08.Bc, 71.15.Pd DOI: 10.7498/aps.70.20201584
1 引 言液滴在固体表面的润湿行为是自然界中普遍存在的物理现象, 广泛应用于印刷工艺、涂料技术、交通运输、航空航天和能源系统等领域[1]. 众所
周知, 润湿状态(Cassie, Partial Wenzel和Wenzel)是影响冷凝液滴生长和脱离的关键因素[2,3]. 受自
水利水电技术(中英文)㊀第52卷㊀2021年第1期陶明,赵光竹,陈惠明,等.城市环状水系防洪潮㊁排涝系统治理研究[J].水利水电技术(中英文),2021,52(1):41-50.TAO Ming,ZHAO Guangzhu,CHEN Huiming,et al.Research on the flood and tide control and the management of drainage system of thecity annular river system[J].Water Resources and Hydropower Engineering,2021,52(1):41-50.城市环状水系防洪潮、排涝系统治理研究陶㊀明1,赵光竹2,陈惠明1,龙章鸿1,王㊀盼2,汤维明1,黄为炜3,冯发堂1(1.中电建生态环境集团有限公司,广东深圳㊀518102;2.中国电建集团西北勘测设计研究院有限公司,陕西西安㊀710065;3.深圳市宝安区水务局,广东深圳㊀518001)摘㊀要:为探究深圳市宝安区城市环状水系防洪潮㊁排涝方案系统解决策略,在分析现存问题的基础上,打破现状 高水高排㊁低水抽排 的防洪排涝格局,确定 大片区统筹治理,小片区分散治理 为主导的治理思路㊂采用MIKE 耦合模型建立排涝河片区和沙井河片区城市水文学模型,耦合河网模型㊁管网模型及坡面模型,进行精细化水文分析计算㊂计算结果为沙井河口50a 一遇洪峰流量247m 3/s ,排涝河口50a 一遇洪峰流量357m 3/s ,设计洪水计算成果合理㊂研究成果表明,该片区最优的防洪潮㊁排涝系统解决方案为:排涝河口新建泵站规模为100m 3/s ㊁沙井河泵站扩建规模为50m 3/s ㊁排涝河片区分散泵站规模约13.74m 3/s ;排涝河泵站与沙井河泵站联合调度,降低环状水系河道水位,以上方案能够达到保障区内防洪潮安全㊁降低区域内涝风险的研究目标㊂关键词:环状水系;防洪潮㊁排涝;MIKE ;耦合模型;联合调度doi :10.13928/ki.wrahe.2021.01.004开放科学(资源服务)标志码(OSID ):中图分类号:TV87文献标志码:A文章编号:1000-0860(2021)01-0041-10收稿日期:2020-08-21基金项目:国家重点研发计划 战略性国际科技创新合作 重点专项(2018YFE0206200)作者简介:陶㊀明(1962 ),男,正高级工程师,学士,主要从事水环境治理研究㊂E-mail:1063983965@ 通信作者:王㊀盼(1989 ),女,工程师,硕士,主要从事水文㊁水动力计算工作㊂E-mail:hhu_wp@ Research on the flood and tide control and the management of drainage systemof the city annular river systemTAO Ming 1,ZHAO Guangzhu 2,CHEN Huiming 1,LONG Zhanghong 1,WANG Pan 2,TANG Weiming 1,HUANG Weiwei 3,FENG Fatang 1(1.ChinaPower Construction Ecological Environment Group Co.,Ltd.,Shenzhen㊀518102,Guangzhou,China;2.ChinaPower Construction Group Northwest Survey and Design Institute Co.,Ltd.,Xi an㊀710065,Shaanxi,China;3.Shenzhen Bao an District Water Affairs Bureau,Shenzhen㊀518001,Guangdong,China)Abstract :To investigate the solution strategy of flood control and drainage system for city annular water system in Bao an District,Shenzhen,the leading idea that the way of governance is integrated for large areas and decentralized for small areas is determined,based on the analysis of existing problems and the current situation of flood control and drainage system that high drainage for regionwith high altitude and pump drainage for region with low altitude is broken.The urban hydrology model of Pailao river area andShajing river area,with coupled model of river network,pipe network and two-dimensional model are established by MIKE,andthey are fine hydrological analyzed and calculated.The calculation results show that the flood peak discharge (once in 50years)inShajing estuary is 247m 3/s,and the flood peak discharge (once in 50years)in Pailao estuary is 357m 3/s,so the calculation re-陶㊀明,等ʊ城市环状水系防洪潮㊁排涝系统治理研究sults of designed flood are reasonable.The optimal solution of flood control and drainage system in this area by research is:The flowscales of the newly-built pumping stations of the Pailao estuary pumping station,Shajing River pumping Station,and dispersedpumping station in Drainage estuary are 100m 3/s,50m 3/s,and 13.74m 3/s respectively;and the drainage river pumping stationand Shajing river pumping station are jointly dispatched to lower the water level of circular river system.It can achieve the researchobjective that ensure the safety of flood control in the area and reduce the risk of regional waterlogging.Keywords :annular river system;flood control and drainage system;MIKE;coupled model;jointlydispatched图1㊀水系的结构Fig.1㊀Structure of river system0㊀引㊀言近年来,在气候变化和城市化发展的背景下,沿海城市暴雨频发㊁台风等极端天气频繁,造成城市内涝问题严重,如2018年台风 山竹 期间,深圳市宝安区西海岸发生超100a 一遇高潮位,区域内排涝河环状水系河口段几近漫堤,涝水短时间难以排出,防洪㊁防潮㊁排涝形势严峻㊂流域中大大小小河流交汇形成的树枝状或网状结构称为水系[1],自然形成的水系多为树状结构水系,平原地区经过人工开挖的水系多为网状结构水系;整体形状为树状结构,局部地区为网状结构,这种水系结构为环状结构水系㊂水系结构如图1所示㊂环状水系防洪排涝治理有两个特点,一是支流的水位易受干流水位(潮位)的影响,二是河口平原地区多地势平坦㊁甚至地势低洼,这两方面影响会使得支流洪涝水很难自排到干流㊂一般网状水系或环状水系防洪㊁排涝治理时,多为闸门挡水㊁泵站排水两种方式配合使用,河网密布处设有节制闸,通过控制洪水下泄方向㊁分流等措施解决特定片区防洪排涝问题㊂沿海城市环状水系治理中,要考虑潮水位顶托影响,一般的工程措施为修建干流堤防㊁且在支流汇入位置建挡潮闸,形成闭合的防潮保护圈;在落潮期开闸泄水㊁在涨潮期关闸蓄水,流域发生洪涝灾害时,干流水位(潮位)一般较高,挡潮闸一般关闸挡潮,这时需要开启排涝泵站排出支流来水㊂此外,环状水系会涉及到泵站㊁水闸联合调度,通过联合调度尽快降低河道水位,以便地势平坦处雨水管网汇水能自排入河,降低管网受水位顶托所带来的灾害风险㊂总结城市洪涝灾害[2-3]的原因,主要有暴雨发生频率和强度增加㊁城市发展在一定程度上改变了水循环的产汇流机制[4-5]㊁城市雨岛效应[6]和热岛效应日益显著㊁城市防洪排涝体系建设与城市化进程不协调等㊂目前城市防洪潮㊁排涝体系建设主要有工程措施[7-8]和非工程措施两方面,工程措施主要包括水库㊁堤防㊁水闸㊁泵站㊁排水管网等,大部分城市已初步建成 上蓄㊁中疏㊁下排 的防洪排涝格局;2014年以后,随着海绵城市建设[9]的推广,城市防洪排涝建设从传统模式逐步走向 渗㊁滞㊁蓄㊁净㊁用㊁排 为主导的生态性排水模式[10]㊂城市环状水系防洪潮㊁排涝治理的基础是城市暴雨洪涝数值模拟[11],核心是城市水文[12-13]㊁水动力学机制及其耦合模拟㊂目前大多数工程设计中,设计洪水计算方法大多数为地方水文手册[14]中推荐的综合单位线法或推理公式法,随着城市化进程的不断推进,城市蓄滞㊁入渗㊁产流㊁汇流等水文过程对洪涝特性的影响将越来越大,传统的计算方法不能很好地反映城市洪水特性[15]㊂鉴于此,城市暴雨内涝数值模拟应运而生,该模拟基于水文模型或水动力模型,Horton 产流理论㊁芝加哥流量过程线等为城市洪涝模拟提供了理论依据和关键方法㊂1971年,美国环境署提出了半分布式城市水文模型SWMM [16],该模型基本实现了地表产流㊁地表汇流和管网汇流水文过程的集成模拟,是城市水文模拟研究趋于成熟的重要标志㊂国内采用SWMM 做了一系列研究,如卢茜等[17]采用SWMM 模型研究分析了管网排水能力,对积水区域提出了相应的排涝方案;城市洪涝模拟进入综合集成模拟阶段后,DHI MIKE 等模型的应用逐渐成熟,如李品良等[18]应用MIKE URBAN 模拟排水管网陶㊀明,等ʊ城市环状水系防洪潮㊁排涝系统治理研究承压运行及管点溢流情况,周宏等[19]应用将MIKE11应用在平原水系排涝计算中,卢翔等[20]采用MIKE FLOOD[18]建立了城市排涝耦合模型,进行排涝模拟计算;在建模方法上,也集成了更多新技术,如尹占娥等[21]将GIS技术应用在暴雨灾害研究中,龚佳辉等[22]GPU加速技术应用在城市雨洪模拟中提高计算效率,王俊珲等[23]应用三维渲染展示洪涝模拟结果等㊂以上MIKE FLOOD模型的应用,侧重于城市排涝模拟,本次研究统一考虑城市洪㊁涝水模拟,采用传统水文学方法和城市洪涝模拟相结合的方法,对于水库等天然下垫面,应用水文手册中推荐的计算方法,对于城市下垫面,应用城市洪涝模拟的技术手段,构建基于MIKE FLOOD的城市水文学模型,采用管网模型模拟城市下垫面产汇流,采用一维水流数学模型模拟河道汇流,计算河道各断面设计洪水㊂在环状水系防洪潮㊁排涝治理措施研究方面,本次以深圳市宝安区排涝河㊁沙井河片区为研究对象,探索地势低洼区域环状水系防洪排涝治理策略,打破原来自排和抽排相结合的排涝方式,突出地势平坦区域抽排排水的优越性,分析环状水系水利设施联合调度的防洪排涝效益㊂以 大片区统筹治理,小片区分散治理 为主导治理思路,考虑在自排排水通道上建设排涝泵站,分析不同规模泵站及泵站联合调度组合对防洪㊁排涝效益的影响,同时也考虑小片区分散治理措施,涝水及时入河,减短区域内洪涝淹没时间,争取一切可能的综合措施,降低河道水位,减少区域内淹没面积,提高区域防洪潮㊁排涝能力㊂1㊀研究区域概况1.1㊀区位概况宝安区位于深圳市西部海岸线,处在珠江口东岸发展轴上,是穗深港黄金走廊的重要节点,也是粤港澳大湾区核心地带㊂下辖新安㊁沙井㊁松岗等10个街道,土地面积397km2,海岸线45km,海域220km2㊂本次研究区域位于沙井街道,沙井街道地处深圳市西部中心,毗邻中国特色社会主义先行示范区重点建设片区国际会展城㊁新桥智创城两大区域,研究区域与粤港澳大湾区节点位置如图2所示㊂研究区域所属流域为茅洲河流域,茅洲河为深圳第一大河,发源于深圳境内的羊台山北麓,流域范围包括深圳市宝安区㊁光明区和东莞市长安镇(2市3地)㊂茅洲河流域是原宝安县的主要产粮区,历史上就是受洪涝影响比较多的区域,改革开放以来城镇化图2㊀研究区域区位示意Fig.2㊀Location map of the study area发展迅猛,乡镇企业云集,耕地面积逐年缩减,城镇建设用地逐渐增加,一直未曾进行过全面的整治,造成河道的防洪㊁排涝㊁排污的负担日益加重㊂在近几年开展的茅洲河流域水环境综合治理中,以 水资源㊁水安全㊁水环境㊁水生态㊁水文化 五位一体的全局观念统领治水工作,全流域统筹㊁系统治理,织网成片㊁正本清源㊁理水梳岸㊁寻水溯源 四步逐级推进㊂已开展的相关工程涵盖雨污管网工程㊁河道整治工程㊁内涝整治工程㊁生态修复工程㊁活水补水工程㊁景观提升工程,通过治水与治城相结合,把茅洲河整治与环境改善㊁景观提升㊁城市更新㊁产业升级㊁土地增效相结合,实现综合效益最大化㊂茅洲河流域属南亚热带海洋性季风气候区,气候温和湿润,雨量充沛,多年平均降雨量约1600mm,降雨年内分配极不均匀,汛期(4 9月份)降雨量大而集中,约占全年降雨总量的85%左右,且降雨强度大,多以暴雨形式出现,易形成洪涝灾害,夏季常受台风侵袭,灾害性天气频发㊂宝安区作为粤港澳大湾区核心区,城市地位和重要性不断提高,在水安全建设方面,防洪排涝安全是首当其中的重要任务,是保障区域社会经济发展㊁人民生命财产安全的基石㊂1.2㊀现状防洪排涝体系及存在问题本次研究区域位于茅洲河流域,流域水系情况如图3所示,沙井片区河流有排涝河㊁沙井河㊁衙边涌㊁共和涌㊁道生围涌,均为茅洲河一级支流,排涝河和沙井河通过岗头调节池相连呈环状水系,沙井河及排涝河总流域面积为67.67km2,沙井河流域面积24.93km2,排涝河流域面积42.54km2;潭头河和潭头渠之间建设有潭头水闸,潭头水闸作陶㊀明,等ʊ城市环状水系防洪潮㊁排涝系统治理研究为节制闸,潭头河洪水下泄至排涝河,潭头渠洪水下泄至沙井河;桥头片区潭头河㊁新桥河㊁上寮河(含支流万丰河)在岗头调节池汇合后,由岗头调节池下泄至排涝河,排涝河沿程汇入石岩渠后自流排入茅洲河;沙井河沿程汇入支流潭头渠㊁东方七支渠㊁松岗河,通过沙井河口泵站(设计流量170m 3/s)抽排至茅洲河㊂图3㊀流域水系示意Fig.3㊀River network map of the watershed近年防洪排涝治理中,该片区采用 分区设防㊁高水高排㊁低水抽排 的防洪排涝总体布局方案,其中排涝河为高水自排通道,承担并下泄潭头水闸东南片区洪水,包括桥头片区㊁石岩渠片区及排涝河区间洪水,沙井河为低水抽排通道,承担并下泄潭头水闸西北片区潭头渠㊁东方七支渠㊁松岗河洪水㊂排涝河㊁共和涌两岸地势低洼,可谓 沙井片区低点 ㊂排涝河两岸高程大部分低于河道设计水面线,导致雨水缺乏重力流排放条件㊁易受排涝河水位倒灌影响,排涝河 高水通道 未能发挥最大作用;排涝河防洪设计中,洪潮遭遇方式为50a 一遇潮位,当遭遇茅洲河50a 一遇以上潮位,排涝河关闸挡潮㊁河道洪涝水缺少下泄通道,将危及整个片区防洪安全㊂此外,排涝河河床高程高于沙井河,符合方案中分区设防㊁高水高排㊁低水抽排 的思路,但沙井河河道过流能力远大于设计洪峰流量220m 3/s(设计标准为20a 一遇),导致沙井河过流能力和河道槽蓄量富余,排涝河高水位运行将增大两岸保护区内涝风险㊂1.3㊀区域高程分析整理区域高程信息进行DEM 分析,综合分析排涝河㊁沙井河流域高程分布情况,高程如图4所示㊂从图中可以看出,区域高程最低点位于共和涌两岸,平均高程为1.0~2.0m 之间;共和涌右岸㊁排涝河右岸㊁衙边涌左岸㊁沙井河口右岸㊁沙井河上游(东方七支渠河口处)㊁松岗河中游等多处平均高程为2.0~2.7m 之间;该片区大部分区域高程在2.7~3.43m 之间(3.43m 为排涝河岗头调节池断面20a一遇设计洪水位)㊂图4㊀排涝河㊁沙井河流域高程分析示意Fig.4㊀Elevation analysis diagram of the Pailao riverand the Shajing river watershed分析排涝河下游周边高程分布情况,高程如图5所示㊂高程在2~2.5m 的流域面积占比为25.9%,高程在2.5~3.43m 占比为60.5%,高程在3.43~4.11m 占比为60.5%㊂排涝河下游约86.4%区域的高程低于排涝河岗头调节池20a 一遇防洪水位3.43m,约96.1%区域的高程低于排涝河岗头调节池50a 一遇设计洪水位4.11m㊂由此可见,排涝河下游大部分区域雨水缺乏自排条件㊂图5㊀排涝河流域高程分析示意Fig.5㊀Elevation analysis diagram of the Pailao riverwatershed陶㊀明,等ʊ城市环状水系防洪潮㊁排涝系统治理研究图7㊀耦合模型概化示意Fig.7㊀Generalized schematic diagram of the coupled model㊀㊀分析沙井河流域高程分布情况,高程如图6所示㊂高程在2.0~2.5m 的流域面积占比为2.6%,高程在2.0~2.8m 占比为14.5%,高程在2.0~3.0m占比为25.6%㊂根据‘宝安区沙井河片区排涝工程初步设计报告“,沙井河河口-潭头渠河口的20a 一遇设计洪水位为1.88~2.00m,沙井河两岸大部分基本都高于2.0m㊂图6㊀沙井河流域高程分析示意Fig.6㊀Elevation analysis diagram of the Shajing riverwatershed2㊀城市水文学模型模拟考虑到流域城市化后洪水过程较天然洪水会出现峰高量大㊁峰现提前的特点,本次研究中设计洪水计算分为水库和城市两类下垫面考虑,水库设计洪水计算采用水文手册中推荐方法计算并进行调洪演算,城市下垫面采用管网模型进行计算,河道汇流采用一维水流数学模型进行模拟,耦合管网模型和一维河道模型,最终得到河道各断面设计洪水㊂2.1㊀模型构建在城区防洪排涝模拟中,要综合考虑排水管网㊁城市河流水系㊁城市地面等要素,水流可以在降雨(洪水)过程中不断流入或溢出排水系统,要精确而有效地模拟这样复杂的水流情况,需要使用耦合模型计算㊂本次研究中一维河网数学模型应用MIKE 11构建,一维管网数学模型应用MIKE URBAN 构建,二维坡面汇流模型应用MIKE 21矩形网格计算,耦合模型应用MIKEFLOOD 模型构建,耦合模型概化示意如图7所示㊂2.2㊀模型率定和验证2018年台风 山竹 期间,茅洲河流域降雨约5a 一遇,赤湾站潮位约100a 一遇㊂本次研究采用山竹 期间降雨㊁潮位边界条件,模拟5a 一遇2h降雨条件下该区域的内涝淹没最大深度与范围,结合 山竹 期间现场实际调查涝点情况,与模型模拟的涝点进行对比,结果如图8所示㊂对比分析现场调查和模型模拟结果,内涝位置和淹没水深基本吻合,内涝点原因大多为地势低洼㊁排水能力不足㊁河水倒灌等,模型可用于方案计算㊂2.3㊀计算边界条件2.3.1㊀上边界条件MIKE URBAN 边界条件为20a 一遇㊁50a 一遇降雨过程;MIKE11上边界为五指耙水库㊁长流陂水库下泄洪水过程㊂2.3.1.1㊀降雨边界条件本次研究中设计暴雨采用石岩水库雨量站实测雨量系列,通过P-III 型频率曲线适线和‘广东省暴雨参数等值线图“(2003年)查算两种方法计算,从偏工程安全角度得出发,选取采用‘广东省暴雨参数等值线图“查图成果㊂2014年华北水利水电大学开展‘深圳市城市设计暴雨雨型分析研究“专题,根据深圳市连续51年陶㊀明,等ʊ城市环状水系防洪潮㊁排涝系统治理研究㊀㊀㊀㊀㊀图8㊀模型计算内涝点与 山竹 内涝点对比Fig.8㊀Comparison diagram of the waterlogging point calculated bymodel and measured(1962 2013年)实测降雨资料,采用 众值定位原则,确定雨峰位置;分析多场实测降雨雨型,统计各时段平均降雨量,综合确定各时段降雨占24h 降雨量的比例(最小时间间隔5min)㊂最终建立了深圳市 珠江三角洲㊁东江中下游㊁粤东沿海 三种地区类型的雨型,24h 历时的设计暴雨雨型,为水利防洪㊁市政治涝提供了统一的降雨雨型,其成果如图9所示㊂本研究区域位于珠江口,故采用珠江三角洲雨型进行水文计算㊂图9㊀深圳2015雨型分配示意Fig.9㊀Rain distribution diagram of 2015of Shenzhen采用上述计算设计暴雨成果和雨型分配过程,点面折算系数按照0.896考虑,计算用于MIKE URBAN 水文模型计算的降雨过程边界,计算得到的设计暴雨过程线如图10所示㊂2.3.1.2㊀水工建筑物边界现状方案考虑现状水工建筑物,沙井河口闸门及泵站㊁共和涌河口闸门及泵站㊁衙边涌河口闸门及泵站以及排涝河闸门㊂遵守水闸及泵站调度方案,其中,与茅洲河联通的闸门,内河水位高于茅洲河水位则开闸泄洪,反之关闸挡潮㊂沙井河泵站最高运行水位1.88m,设计水位1.0m,最低运行水位0.5m,启泵水位为0.8m;共和涌泵站最高运行水位1m,设计水位0.7m,最低运行水位-0.9m,启泵水位为0.5m;衙边涌泵站最高运行水位1.7m,设计水位0.9m,最低运图10㊀设计暴雨过程线Fig.10㊀Designed rainstorm hydrograph行水位0.6m,启泵水位为0.7m㊂系统治理方案在现状方案的基础上,根据方案设定要添加边界条件㊂2.3.2㊀下边界条件2.3.2.1㊀设计潮位茅洲河流域内无实测潮位观测资料,位于流域南㊁北海岸线附近分别设有赤湾站㊁舢舨洲潮位站,可作为本次研究设计潮位的依据站㊂本次研究中设计潮位复核并采用‘茅洲河界河整治工程(深圳部分)初步设计报告)“中设计潮位成果㊂陶㊀明,等ʊ城市环状水系防洪潮㊁排涝系统治理研究表1㊀茅洲河河口设计高潮位成果Table 1㊀Table of results of design high tide level ofMaozhou River Estuary成㊀果设计潮位/m均㊀值0.5%1%2%10%本次计算成果 2.44 3.45 3.31 3.16 2.81界河初设成果(采用)2.443.453.313.172.812.3.2.2㊀雨潮遭遇组合‘深圳市防洪潮(排涝)规划(2021 2035)“中根据赤湾站实测风暴潮资料,按照与设计高潮位接近的原则,选取赤湾站2008年6月23日08:00 25日20:00 黑格比 ㊁2017年8月22日00:00 25日00:55 天鸽 ㊁2018年9月5日00:00 19日00:00 山竹 三场典型台风潮位过程,选取其中最不利的潮位过程作为典型潮位过程线用于缩放得到挡潮工况下设计潮位过程㊂综合来看, 山竹 潮型对挡潮期间的排涝偏不利,因此选取 山竹 潮位过程作为设计潮型的典型潮位过程(见图11),按照变比例放大(主潮峰按同倍比放大,低潮位不变),得到设计潮位过程㊂图11㊀典型暴雨过程线Fig.11㊀Typical designed rainstorm hydrograph2.4㊀设计洪水成果近年来在河道综合整治工程中,调整了一些水库洪水下泄的去向,河道流域特性发生变化,沙井河流域面积由原来的27.2km 2减少为24.93km 2,排涝河流域面积由原来的44.5km 2调整为42.54km 2㊂如五指耙水库原来经松岗河水库下泄,在潭头河综合整治中,建设了五指耙分洪隧洞,五指耙水库50a 一遇洪水经分洪隧洞下泄至潭头河㊁经潭头河滞洪区调节以后下泄洪水;万丰水库原来经由万丰河下泄,在沙福河整治工程中,万丰水库洪水经石岩渠上游,下泄至沙福河㊂根据一维河网模型中沙井河口和排涝河口设计洪峰成果,本次研究设计洪水成果如表2所列㊂‘宝安区沙井河片区排涝工程初步设计报告“和‘茅洲河流域水环境综合整治工程桥头片区排涝整治工程初步设计报告“中详细计算了沙井河片区㊁排涝河片区河涌设计洪水,对比本次计算结果和已有成果如表2所列㊂从表中可以看出,洪峰流量模数随着流域面积增大而减小,且同一断面的洪峰流量模数随着频率的增加而降低,符合一般洪水的变化特性㊂由于河道整治引起的河道流域面积调整,雨水管道过流能力不足㊁雨水并未完全排放至河道等原因,引起设计洪水计算成果变动㊂本研究计算的设计洪水成果基本合理,可以用于系统治理方案研究㊂3㊀防洪潮、排涝系统治理方案研究2008年以来,排涝河㊁沙井河环状水系防洪排涝设施不断完善,目前已建设挡潮闸抵御潮水及干流高水位,采用自排和抽排结合的方式排出涝水,洪㊁涝水排出的时候存在以下难点:一是自排通道两岸低洼,河道高水位运行不利于两岸涝水自排入河;二是区域已建水利设施尚未联合调度,未能发挥已建设施最大防洪㊁排涝效益㊂㊀㊀㊀㊀㊀㊀表2㊀设计洪水成果Table 2㊀Design flood results table河流名称断面位置本次计算成果洪峰流量/m 3㊃s-1洪峰模数/m 3㊃s -1㊃km -2流域面积/km 2P =2%P =5%P =2%P =5%沙井河河㊀口24.932472149.918.58排涝河河㊀口42.543572608.396.12河流名称断面位置已有成果洪峰流量/m 3㊃s -1洪峰模数/m 3㊃s -1㊃km -2流域面积/km 2P =2%P =5%P =2%P =5%沙井河河㊀口27.22672209.828.09排涝河河㊀口44.53262677.336.00陶㊀明,等ʊ城市环状水系防洪潮㊁排涝系统治理研究㊀㊀在现状区域防洪排涝体系中,在潭头河和潭头渠间建设有潭头水闸,潭头水闸作为节制闸控制沙井河和排涝河洪水下泄去向㊂考虑到沙井河河道槽蓄量远大于排涝河,为充分利用河道槽蓄能力,本研究考虑打开潭头水闸自由泄洪,打破岗头调节池以上洪水仅从排涝河下泄的防洪格局,从排涝河和沙井河两条通道下泄洪水,在不增加沙井河防洪压力的基础上,尽可能减少排涝河两岸防洪内涝压力㊂本研究确定防洪㊁排涝标准为50a一遇,以 大片区统筹治理,小片区分散治理 为主导治理思路,既考虑骨干排涝设施的建设,也考虑小片区分散治理措施,争取一切可能的综合措施,降低河道水位,减少区域内淹没面积㊂防洪标准确定为1000a 一遇,在河口闸门改造中实施㊂3.1㊀计算方案设置本研究中计算了50a一遇设防标准下的河道设计洪水及设计水位,分别计算各方案条件下排涝河新建泵站规模及排涝河水位降低情况,降雨边界和潮位边界同频遭遇㊂设置了三个方案,方案一采用自排和抽排结合的方式排出涝水,考虑现状水工建筑物,沙井河口闸门泵站㊁共和涌河口闸门泵站㊁衙边涌河口闸门泵站㊁排涝河闸门;设置两个系统治理方案,方案二在考虑现状河口水工建筑物基础上,在排涝河口新建泵站,排涝河㊁沙井河均以抽排方式排出涝水,解决方案一中河道高水位运行时带来的问题;方案三在方案二的基础上,打开潭头水闸泄洪,排涝河㊁沙井河联合调度,通过联合调度充分利用河道槽蓄容量,进一步降低河道水位,使已建防洪排涝设施发挥最大效益㊂计算方案设置情况如表3所列㊂3.2㊀系统治理方案分析按照本次研究确定的治理原则和治理目标,计算㊀㊀㊀㊀㊀50a一遇工况下各方案下河道水位的降低情况㊁区域内涝风险情况,通过方案比选㊁最终确定最优系统治理方案㊂首先,方案一(现状方案)条件下,水工建筑物考虑了沙井闸泵㊁共和涌闸泵㊁衙边涌闸泵㊁潭头水闸㊁排涝闸门,模拟沙井河50a一遇水位为1.78~ 1.89m,排涝河水位为3.21~4.11m㊂第二,方案二(系统治理方案㊁排涝河片区方案)条件下,在考虑现状水工建筑物的基础上,排涝河口设置泵站抽排,泵站规模为100m3/s时,河道水位变化甚微,泵站规模为200m3/s时,排涝河河道水位变化约0.02~0.34m,泵站规模为300m3/s 时,排涝河河道水位变化约0.02~0.93m㊂考虑到抽排效果和经济效益,选择泵站规模为100m3/s作为系统解决方案三边界条件㊂第三,方案三(系统治理方案排涝河㊁沙井河联合调度方案)条件下,排涝河泵站流量为100m3/s㊁沙井泵站扩建50m3/s㊁两个河口泵站联合调度的情况下,排涝河水位降低0.55~1.25m,同时沙井河水位为2.37~2.85m,排涝河水位降低,区内内涝风险减小;沙井河水位上涨0.59m,增加沙井河两岸内涝风险㊁增加内涝面积约0.45km2㊂第四,方案三(系统治理方案排涝河㊁沙井河联合调度方案)条件下,排涝河泵站流量为100m3/s㊁沙井泵站扩建80m3/s㊁两个河口泵站联合调度的情况下,排涝河水位降低0.85~1.28m,同时沙井河水位为2.16~2.85m,排涝河水位降低,区内内涝风险减小;沙井河水位上涨0.8m,增加沙井河两岸内涝风险㊁增加内涝面积约0.36km2㊂50a一遇设防标准下排涝河㊁沙井河水位变化分别如图12㊁图13所示㊂从上面分析可以看出,在排涝河口设置100m3/s 泵站后,相比于沙井泵站扩建50m3/s,扩建80m3/s ㊀㊀㊀㊀㊀㊀表3㊀计算方案设置Table3㊀Calculation plan setting list table情㊀景方案一(现状方案)方案二(系统治理方案㊁排涝河片区方案)方案三(系统治理方案排涝河㊁沙井河联合调度方案)降雨边界50a一遇50a一遇50a一遇潮位边界50a一遇50a一遇50a一遇水工建筑物边界沙井河口闸泵㊁共和涌河口闸泵㊁衙边涌河口闸泵㊁排涝河闸门同方案一,新增排涝河泵站排涝河泵站100m3㊃s-1排涝河泵站200m3㊃s-1排涝河泵站300m3㊃s-1同方案一,潭头水闸打开,排涝河㊁沙井河水闸泵站联合调度潭头水闸泄洪排涝河泵站100m3㊃s-1,沙井河泵站170m3㊃s-1排涝河泵站100m3㊃s-1,沙井河泵站220m3㊃s-1排涝河泵站100m3㊃s-1,沙井河泵站250m3㊃s-1。
