河冰数学模拟研究综述

随着计算机的发展和对冰情物理现象认识的加深，人们对洒冰动态发展过程的数学模型不断地进行完善。近几年来，国内外许多科学工作者根据的假设提出了许多河冰动态过程的数学模型，现有的河不流模型、热力模型和冰冻模型，以及冰盖糙率和冰期河道综合糙率的各种计算方法。水力模型用于计算河道中流场和其他不力要素；热力模型用于计算水体热交换，水温和水内冰浓度分布；冰冻模型用于模拟冰盖的产生、发展和消融过程。     

河冰演变的数值模拟

提出了一种适用于河网的精细河冰模型——ＲＩＣＥＮ模型。该模型由两大部分组成：挟冰河网非恒定水流模型；热力和冰情模拟模型。ＲＩＣＥＮ模型模拟了：包括过冷过程的水温沿河道的变化；水内冰浓度分布；底冰的增长和消融；面冰输移；冰盖的推进、稳定和消融；冰盖下冰的输移、堆积和冲蚀。该模型已应用于尼亚加拉（Ｎｉａｇａｒａ）河上游和黄河下游的冰情研究。     

雪覆盖下冰盖的热力增厚和消融

雪覆盖下冰盖的热力增厚和消融是急需研究的问题,对于冬季降雪频繁地区开河预报、冰凌洪水风险分析具有重要的实用价值。基于雪盖和冰盖的热力条件是准稳态假设,建立了冰盖热力增厚和消融速率与雪厚、冰厚、大气传递给雪面的净热通量和水体传递给冰底面净热通量的函数关系,包括：太阳辐射、反射和透射,雪面和大气的长波辐射,雪面蒸发-对流,河床地温等因素。提出了雪面温度和冰盖垂向温度分布的理论公式及冰盖热力增厚和消融发展过程的数值计算模型。最后,以黑龙江漠河段实测的冰情为例,验证了所提冰盖热力增厚和消融数学模型的实用性,并分析了一些重要参数随时间的变化特点。     

弯曲冰块在顺直河段中的输移条件

针对弯曲冰块在顺直河段中的输移条件,以春季封冻河道的冰盖破裂机理为基础,根据水动力学、热力学、固体力学及气象水文等学科理论,综合考虑水力、热力、河势及地貌特征等影响因素,引入顺直河道固体边壁的约束条件,建立力学分析模型,进而提出了弯曲冰块在顺直河道中输移所需最小流量即临界流量的判别准则,并对其适用性及相关参数进行了研究分析。应用黄河河曲段的原型观测资料对该准则及相关参数进行了率定及验证,结果表明提出的针对弯曲冰块在顺直河段输移的临界流量计算值与实测值较为接近,可以认为该输移判别准则能够较好地用于判别弯曲冰块在顺直河段中的输移情况。此外,根据实测资料提出了反映热力消融对冰盖体厚度减小、强度降低等的综合系数表达式,可用于没有开河历史观测资料河道的冰情研究。     

宁夏吴忠金积工业园区冬季供水一维结冰问题数值模拟

利用QUICK格式对一维水力热力数学模型中的对流项进行离散,通过模拟结冰点的位置和比较不同温度、水深、风力条件下对结冰点位置的影响,主要改进了冰盖厚度发展模型.利用该模型对冰盖厚度的发展进行了模拟,通过与经验公式及实测结果进行比较,表明改进后的冰盖厚度发展模型是可靠的,可以用于金积引水渠的冰盖厚度模拟.     

冰盖生长和消融的实验研究与数值模拟

为研究冰盖生长和消融的规律,在实验室内设计了水体结冰实验.通过实验得到冰盖厚度、水温和冰内温度随时间的变化过程.根据对水体结冰和融化物理过程的分析,建立水温与冰盖生长、消融相互作用的耦合模型.采用耦合模型来模拟水体结冰和融化过程,通过对模拟结果与实测结果的对比,发现冰厚和水温的计算值与实测值基本吻合.此结果为研究高海拔、高纬度地区封冻水库的结冰机制及冰盖下的水温时空分布提供重要理论基础.     

基于离散元方法与水动力学耦合的河冰动力学模型

流凌和冰坝是我国北方冬季比较常见的河冰现象,尤其冰坝,可导致严重的凌洪灾害,是河冰研究中的重要部分。本文将离散单元方法与二维水动力学相耦合,建立河冰的动力学数值模型,以模拟河冰输移、聚集、堆积,以及冰坝形成的动力过程。针对河道中大量密集且几何形状随机的流冰现象,采用扩展多面体单元对冰块进行构造,并通过离散元接触模型表征河冰输移和冰坝形成过程中冰块间的相互作用。河流水动力部分则采用考虑河冰影响的二维非定常浅水方程进行描述,并采用有限元方法进行数值计算。冰水耦合中的计算参数由河冰离散单元与其所在水动力学有限元网格节点的位置插值计算得到。通过对冰盖封河造成水位抬高过程的数值模拟,并将计算结果与理论分析结果以及DynaRICE河冰模型的模拟结果进行对比,以验证模型的有效性。在此基础上,对规则河道中河冰输移、堆积和形成冰坝的过程进行数值模拟和结果分析。通过以上河冰离散元与水动力学的耦合方法及其对河冰动力过程的数值模拟,对河冰动力过程从细观角度进行新的认识并为河冰动力过程研究提供一种有效的数值方法。     

基于离散元方法的河冰动力过程短期预测模型及应用

秋末冬初时黄河河道平稳封河对于预防凌汛意义重大,而什四份子作为黄河内蒙古河段主要首封河段备受重视。根据寒区河道具体冰情,基于河冰离散元方法,考虑河流表面冰的动力输移和河流水动力学的相互耦合作用,建立了针对特定重点河段的短期预测模型,可根据实际水力要素、气温、现场冰情等条件进行河冰输移、封河开河等情况的模拟和预测。模型考虑了河道的岸冰边界以及上游来冰情况,包括来冰的密集度、冰块体的尺寸分布、冰块体的冻结强度等因素对河冰输移和卡冰封河过程的影响。基于该预测模型,针对什四份子弯道在不同工况下的封河情况进行研究,结合现场情况探究了流速、来冰量、冰块尺寸、岸冰尺寸等因素对卡冰封河的影响,从冰流量和河道输冰量的角度解释了各要素的影响机理,为特定河段的封河预测工作提供参考。     

河流冰塞的形成与壅水计算

我国北方河流,冬季普遍存在着冰情现象,依据成因不同,将河流冰盖分为热力冰盖和动力冰盖2种.河流冰情分为3种类型,第一种形成热力冰盖,第二种形成动力冰盖,即冰塞,第三种流冰花但不封河.冰塞可分为头部段、稳定段和尾部段3部分,其中冰塞稳定段的水流状态近似于管流,基于管流理论,依据黄河万家寨水库实测冰塞资料时形成冰塞稳定段的各种水力要素进行相关分析,推导出水库冰塞的计算方法.从验证计算和合理性检验两方面看,该方法的计算结果比较合理,可用于计算水库冰塞.     

冰波运动特性及盖移质输冰能力研究

冰下盖移质冰颗粒集体运动时易形成一种特殊的冰情现象——冰波，其运动特性与冰塞形成、堆积演变及输冰能力密切相关。为探究冰波运动特性及盖移质输冰能力，借鉴泥沙输移理论，从理论层面建立了冰波运动的基本控制方程与盖移质输冰率方程，进一步推求了无量纲盖移质输冰强度（输冰能力）与水流强度的本构关系。结果表明:冰波形成需要一定的水力条件，冰波波高与背流面波长的变化及表征水流强度的弗劳德数Fr相关，同时也受水深、冰下阻力等因素的综合影响；建立的输冰率公式体现了输冰能力与水流条件的关系，且考虑了冰盖影响，优化了输冰能力的计算结果；总体上，输冰能力与水流强度呈复杂的函数关系，但水流强度仍是体现输冰能力的主要指标与便捷指标。研究结果可为寒区河流输冰能力的计算提供理论参考，同时可辅助揭示河流冰塞的形成机理。     

黑龙江上游开江期河道特征对流冰速度的影响

为探究黑龙江上游江段开江期流冰速度沿程变化规律和运移过程，通过抛投微型冰浮标定位器进行流冰追 踪试验，分析黑龙江干流开江期流冰速度分布特征及河道形态对流冰速度的影响规律。结果表明：2019 年开江期 距黑龙江干流源头 69~692?km 河段流冰速度分布为 0.79~3.56?m/s，平均速度为 1.65?m/s，流冰速度与河道宽度、河 道弯曲系数呈负相关关系；在弯曲河段、江心岛河段和弯曲分汊型河段流冰速度降低趋势明显，且河道特征对流 冰速度的影响依次减弱。流冰速度沿程分布规律可为冰坝预测及预防凌汛灾害提供数据支持，研究成果对寒区 河流治理具有十分重要的意义。     

黄河什四份子弯道河冰生消及冰塞形成过程分析

什四份子弯道因其特殊的河道形态及地理位置而成为黄河内蒙古段易发生冰塞断面。通过对2014—2015年冬季该段野外冰情监测及水文、气象资料分析,结合Landsat8遥感影像数据解译,研究了什四份子弯道河冰生消及冰塞形成过程。结果表明,野外观测结合遥感影像解译能够准确地反映河冰的时空特性。该河段弯道凹岸处冲积岸冰及凸岸静态岸冰的生长,极大地束窄了河面宽度,降低了水流的输冰能力,而使其成为初始卡冰位置;冰盖至此向上游发展,弯道下游因来冰量减少和上下游水力坡度增大而形成清沟;受弯道径向水流方向改变及弯道螺旋流的影响,导致冰花在冰盖下主槽与滩地的交界处堆积;稳封期受气温升降变化使得冰盖表面冻融交替,冲积冰反射率增大,后期解译的遥感影像中平滑岸冰面积较初始封河期增加。     

Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method简

River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.     

Numerical simulation of mechanical breakup of river ice-cover

Ice jams and ice dams in rivers will cause significant rises of water levels. Under extreme conditions, the ice flooding during winter or early spring may occur. In this paper, by considering the fluid-solid coupling effect caused by the water and the ice cover, the mechanisms of the mechanical breakup of the river ice cover are studied. A formula is obtained for determining whether or not the mechanical breakup process would happen under the hydraulic pressure of the flow. Combined with the hydraulic model under the ice covered flow, a numerical model is built and the interaction between the discharge, the hydraulic pressure under the ice cover and the date for the mechanical breakup of the river ice cover is simulated. The simulated results of the dates for the mechanical breakup of the river ice cover agree very well with the field observations of the breakups of the river ice cover in the Hequ Reach of the Yellow River. Therefore, the numerical model might serve as a good preliminary step in studying the breakup of the river ice-cover, evidencing many important parameters that affect the ice-cover process.     

Simulation and analysis of ice processes in an artificial open channel

The Middle Route Project for South-to-North Water Transfer, which consists of a long artificial open channel and various hydraulic constructions, is a big water conveyance system. A numerical modeling of water conveyance in the ice period for such large-scale and long distance water transfer project is developed based on the integration of a river ice model and an unsteady flow model with complex inner boundaries. A simplified method to obtain the same flow discharge in the upstream and downstream of the structure by neglecting the storage effect is proposed for dealing with the inner boundaries. According to the measured and design data in winter-spring period, the whole ice process, which includes the formation of the ice cover, its development, the melting and the breaking up as well as the ice-water dynamic response during the gate operation for the middle route, is simulated. The ice characteristics and the water conveyance capacity are both analyzed and thus the hydraulic control conditions for a safety regulation are obtained. At last, the uncertainties of some parameters related to the ice model are discussed.     

黄河头道拐段冰输移及堆积过程数值模拟

头道拐河段因其特殊的河道形态及地理位置而成为黄河内蒙古段最易形成冰坝的河段,研究该河段河冰输移及堆积过程是理解内蒙古段河冰过程及卡冰结坝作用机理的关键。本文基于耦合的二维有限元水动力学模型和DPM(Discrete Parcel Method)河冰动力学模型,模拟了黄河头道拐河段2020—2021年冬季封河过程并进行了验证,讨论了不同水力条件、上游流凌密集度及河道形态对封河过程的影响。结果表明：相比于官牛犋弯道,河道弯曲率大、束窄程度高的什四份子弯道更易形成卡冰,且流量越小,卡冰作用越明显,冰盖向上游发展速度越快。河道流凌密集度小于0.4时,各种流量下研究河段未发生卡冰;流凌密集度增大至0.4,表面流冰首先在弯曲率系数较大的什四份子弯道处形成卡冰,随着流凌密集度和流量的进一步增大,下潜并输移到下游的流凌也会在官牛犋弯道形成卡冰,因此,头道拐河段形成卡冰的流凌密集度临界条件为0.4。应用冰水耦合二维动力学模型可以很好地模拟天然河道河冰输移、堆积过程中河道的水力特性、冰厚增长及封河形态,揭示了影响河冰过程的相关因素及作用机理,为黄河内蒙古段防凌减灾工作提供技术支撑。     

黄河宁蒙河段冰期洪水波运动过程中的变形分析

河道中冰盖的存在会影响到洪水波的演进变形。以黄河宁蒙河段为研究对象,将马斯京根法尝试应用于冰期洪水计算,分析了马斯京根法参数与糙率的关系,比较了冰盖冻结增厚和融化减薄过程对洪水波变形的影响差异。研究结果表明,将马斯京根法应用于冰期洪水计算是可行的;断面的糙率越大,洪水波传播时间越久,变形越大;冰盖冻结增厚过程中,洪水波的变形存在先增加再减少而后又增加的现象;冰盖融化减薄过程中,洪水波随冰厚的减薄而变形增大。相同冰厚下,两种过程的变形程度存在交点。交点之前的冰厚范围,冰盖融化减薄时的洪水波变形更大;交点之后的冰厚范围,冰盖冻结增厚时的洪水波变形更大。     

A Modified Muskingum Flow Routing Model for Flood Wave Propagation during River Ice Thawing-Breakup Period

During the period of river ice thawing and breakup process (termed as “ice cover thawing-breakup”), vast amount of water stored in ice-covered river reach will be released comparing to that under open flow condition. The flow routing process during river ice thawing-breakup period will be different from that under open flow condition, since water stored in and channel from ice thawing-breakup process and flow routing process are very complicated. If the flow routing process during river ice thawing-breakup period can be predicted, it will very important for flood protection in the downstream river reach. In present study, water released from ice cover thawing process is considered as the lateral inflow to the channel flow during propagation process of flood wave from upstream to downstream. A model for the flood routing process during river ice thawing-breakup period has been developed based on the Muskingum hydrologic method. Using the modified Muskingum model, the routed outflow hydrograph has been determined along the Baotou Reach of the Yellow River during river ice thawing-breakup period. Results showed that the simulated hydrographs using developed model agree well with those of field measurements.

     

旁多坝址冰水堆积层可灌性分析

旁多水利枢纽工程是西藏自治区＂十一五＂期间重点水利工程项目,为拉萨河中段梯级开发之首。大坝基础采用全封闭防渗方案,即上墙下幕,防渗墙深入至冰水堆积层一定深度,墙下帷幕进入基岩,因此对坝基冰水堆积层可灌性分析评价是很必要的。通过对旁多坝址冰水堆积层可灌性的分析评价,结果表明坝基冰水堆积层属可灌地层。