寒区水库冰盖厚度数值模拟方法的改进研究
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摘要
针对寒区水库冰盖厚度的增长变化情况的数值模拟问题，改进前人关于冰面温度与气温关系的表达形式，确定了冰面温度依赖于大气温度的线性变化关系；改进前人的寒区水库冰盖热力模型，采用与温度有关的分段函数的形式代替以往一维热传导方程中经验性常数的导温系数，以气温转换后的冰面温度作为边界条件，并根据2008年、2009年冬季黑龙江省红旗泡水库地区现场观测数据，对水库冰盖厚度的增长变化情况进行了数值模拟。本文所研究的内容是国家自然科学基金项目（40806075）的一部分，本文的主要研究成果概括如下：
1根据水库地区气温、冰盖表面温度的实测数据，改进文献中关于冰面温度与气温关系的正比例表达形式，以带截距的线性方程作为冰面温度与气温关系的表达形式，应用最小二乘法进行参数辨识，确定冰面温度与大气温度的对应关系，然后以气温转换后的冰面温度作为边界条件，对水库冰盖厚度生长问题进行数值模拟。
2传统河冰热力学模型的一维热传导方程中，导温系数常常采用经验性的常数，将经验性常数的导温系数转化为依据现场观测数据辨识得到的依赖于温度变化的函数来表示，数值模拟水库冰盖厚度的增长变化情况，并将该模拟厚度与冰盖厚度实测数据、采用常系数导温系数模拟的冰盖厚度的增长变化情况进行了对比。结果显示用依赖于温度变化的导温系数模拟得到的冰盖厚度数据与实测冰盖厚度数据吻合更好，表明在河冰热力学模型中采用新的依赖温度变化的导温系数可以更准确的描述河冰热力学变化过程。
According to the numerical simulation of the growth of the thickness of ice caps in thereservoirs of cold regions, the study has improved the representation of the relationship betweenthe temperature of ice surface and air temperature, justified the linear relationship that thetemperature of ice surface is higher than atmospheric temperature, improved the previous heatmodel of ice caps in reservoirs of cold regions. According to the observed data in the Hongqipaoreservoir, Daqing, Heilongjiang Province in2008and2009, we carried out an investigation onnumerical simulation of the growth in the thickness of the ice caps with temperature-relatedpiecewise function instead of the thermal diffusivity of one-dimensional heat transfer equation.This thesis is part of the research findings of the national natural science fundsproject(40806075). The major research findings are shown as follows:
1According to the measured data of the air temperature and the surface temperature of icecaps in the reservoirs, the thesis has improved the representations of the relationship between airtemperature and the temperature of ice surface, treats linear equation as the representation of therelationship between air temperature and the temperature of ice surface, has applied theleast-square method to the identification of parameters, and identified the correspondingrelationship between the temperature of ice surface and atmospheric temperature. Then anumerical simulation was conducted of the growth of the thickness of ice caps in the reservoirswith the temperature of ice surface that is achieved after the transformation of air temperature asthe boundary condition.
2In the one-dimensional heat transfer equation of traditional heat models of river ice,empirical constants are often employed as coefficient of temperature conductivity. The presentstudy transformed the coefficient of temperature conductivity of empirical constants into thefunctions that rely on temperature change. In addition, a numerical simulation was conducted ofthe developmental change of the thickness of ice caps in the reservoirs and a contrast was madebetween this and the measured data. The findings indicate that the data of the thickness of icecaps gained from the simulation of the coefficient of temperature conductivity that rely ontemperature change correspond with the data of measured thickness of ice caps. Hence a more accurate description of the developmental process of thermodynamics of river ice with theapplication of the coefficient of temperature conductivity that rely on the change of temperature.
1根据水库地区气温、冰盖表面温度的实测数据，改进文献中关于冰面温度与气温关系的正比例表达形式，以带截距的线性方程作为冰面温度与气温关系的表达形式，应用最小二乘法进行参数辨识，确定冰面温度与大气温度的对应关系，然后以气温转换后的冰面温度作为边界条件，对水库冰盖厚度生长问题进行数值模拟。
2传统河冰热力学模型的一维热传导方程中，导温系数常常采用经验性的常数，将经验性常数的导温系数转化为依据现场观测数据辨识得到的依赖于温度变化的函数来表示，数值模拟水库冰盖厚度的增长变化情况，并将该模拟厚度与冰盖厚度实测数据、采用常系数导温系数模拟的冰盖厚度的增长变化情况进行了对比。结果显示用依赖于温度变化的导温系数模拟得到的冰盖厚度数据与实测冰盖厚度数据吻合更好，表明在河冰热力学模型中采用新的依赖温度变化的导温系数可以更准确的描述河冰热力学变化过程。
According to the numerical simulation of the growth of the thickness of ice caps in thereservoirs of cold regions, the study has improved the representation of the relationship betweenthe temperature of ice surface and air temperature, justified the linear relationship that thetemperature of ice surface is higher than atmospheric temperature, improved the previous heatmodel of ice caps in reservoirs of cold regions. According to the observed data in the Hongqipaoreservoir, Daqing, Heilongjiang Province in2008and2009, we carried out an investigation onnumerical simulation of the growth in the thickness of the ice caps with temperature-relatedpiecewise function instead of the thermal diffusivity of one-dimensional heat transfer equation.This thesis is part of the research findings of the national natural science fundsproject(40806075). The major research findings are shown as follows:
1According to the measured data of the air temperature and the surface temperature of icecaps in the reservoirs, the thesis has improved the representations of the relationship between airtemperature and the temperature of ice surface, treats linear equation as the representation of therelationship between air temperature and the temperature of ice surface, has applied theleast-square method to the identification of parameters, and identified the correspondingrelationship between the temperature of ice surface and atmospheric temperature. Then anumerical simulation was conducted of the growth of the thickness of ice caps in the reservoirswith the temperature of ice surface that is achieved after the transformation of air temperature asthe boundary condition.
2In the one-dimensional heat transfer equation of traditional heat models of river ice,empirical constants are often employed as coefficient of temperature conductivity. The presentstudy transformed the coefficient of temperature conductivity of empirical constants into thefunctions that rely on temperature change. In addition, a numerical simulation was conducted ofthe developmental change of the thickness of ice caps in the reservoirs and a contrast was madebetween this and the measured data. The findings indicate that the data of the thickness of icecaps gained from the simulation of the coefficient of temperature conductivity that rely ontemperature change correspond with the data of measured thickness of ice caps. Hence a more accurate description of the developmental process of thermodynamics of river ice with theapplication of the coefficient of temperature conductivity that rely on the change of temperature.
引文
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[21]李志军，曲月霞，沈照伟，王永学，李广伟，DUT-1非冻结合成模型冰的弯曲强度，冰川冻土，23(2),2001,170-175.
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[26]张丽敏，李志军，贾青，李广伟，人工淡水冰单轴压缩强度试验研究，水利学报，40(11),2009,1392-1396.
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[32]张学成，可素娟，潘启民，赵安林，黄河冰盖厚度演变数学模型，冰川冻土，24(2),2002,203-205.
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[2] L. Bengtsson, Mixing in ice-covered lakes, Hydrobiologia,322(1-3),1996,91-97.
[3]滕晖，邓云，黄奉斌，脱有才，水库静水结冰过程及冰盖热力变化的模拟实验研究，水科学进展，22(5),2011,720-726.
[4]郝红升，邓云，李嘉，李克锋，冰盖生长和消融的实验研究与数值模拟，水动力学研究与进展，24(3),2009,374-380.
[5]杨开林，刘之平，李桂芬，陈储军，刘翠杰，胡宏达，河道冰塞的数值模拟，水利水电技术，33(10),2002,40-47.
[6]王军，冰塞形成机理与冰盖下速度场和冰粒两相流模拟分析（博士学位论文），合肥：合肥工业大学，2007.
[7] G D. Ashton, Heat transfer to river ice covers, Proceedings30th Eastern Snow Conference,Amherst, MA,1973,125-135.
[8] H.T. Shen, and P.D. Yapa, Computer Simulation of Ice Cover Formation in the Upper St.Lawrence River, In proceedings of the3th Workshop on Hydraulics of River Ice, Fredericton,Canada,1984,227-246.
[9] J.E. Zufelt, R. Ettema, Fully coupled model of ice-jam dynamics, J. Cold Reg. Eng.,14,2000,24-41.
[10]孙肇初，隋觉义，江河冰塞的研究及其意义，地球科学进展，(03),1990,51-54.
[11]隋觉义，方达宪，周亚飞，黄河河曲段冰塞水位的分析计算，水文，(02),1994,18-24.
[12]王军，冰盖前缘处冰块稳定性分析，人民黄河，(1),1997,9-12.
[13]王军，冰盖下散沙体泥沙起动流速的试验研究，水利水运科学进展，(2),1998,164-169.
[14]王军，初始冰塞厚度与水流条件及冰流量关系的试验研究，水利水运科学进展，(4),1999,385-390.
[15]王军，冰塞下冰块起动分析，水利水运科学进展，(2),1999,165-171.
[16]王军，平衡冰塞输冰的试验研究，水力发电学报，(1),2002,61-67.
[17]王军，平衡冰塞厚度与水流条件和冰流量关系的试验研究，兰州大学学报，38(1),2002,117-121.
[18]茅泽育，张磊，王永填，吴剑疆，采用适体坐标变换方法数值模拟天然河道河冰过程，冰川冻土，25,2003,214-219.
[19]黄焱，史庆增，宋安，冰温度膨胀力的有限元分析，水利学报，36(3),2005,316-317.
[20]白乙拉，李志军，冯恩民，韩明，卢鹏，静水条件下淡水冰有效导温系数的优化辨识，计算力学学报，24(2),2007,187-191.
[21]李志军，曲月霞，沈照伟，王永学，李广伟，DUT-1非冻结合成模型冰的弯曲强度，冰川冻土，23(2),2001,170-175.
[22]卢鹏，李志军，现行规范中计算桩柱冰荷载的比较，冰川冻土，25,2003,356-359.
[23]李志军，王永学，王喜文，李广伟，水泥含量和养生时间对合成模型冰物理力学性质的影响，水利学报，(6),2004,41-45.
[24]李志军，韩明，秦建敏，郗玉珠，卢鹏，冰厚变化的现场监测现状和研究进展，水科学进展，16(5),2005,753-757.
[25]白乙拉，李志军，冯恩民，水库天然冰温度场数值模拟，黑龙江大学自然科学学报，23(3),2006,331-335.
[26]张丽敏，李志军，贾青，李广伟，人工淡水冰单轴压缩强度试验研究，水利学报，40(11),2009,1392-1396.
[27]贾青，李志军，李长玉，李士森，谷欣，不同重现期水库冰厚度曲线的绘制与分析，黑龙江水专学报，36(3),2009,114-118.
[28]P. D. Yapa, H. Shen, Unsteady flow simulation for an ice-covered river, J. Hydr. Div., ASCE.112(11),1986,1036-1049.
[29]H. T. Shen, S. Lu, Dynamics of River Ice Jam Release, Cold Regions Engineering,1996,594-605.
[30]D. Iliescu, I. Baker, The structure and mechanical properties of river and lake ice, ColdRegions Science and Technology,48(3),2007,202-217.
[31]刘全录，钱希仁，谢永刚，宋世田，郑炳旭，胜利水库冰盖生消理论的试验研究，黑龙江水专学报，(1-2),1997,33-39.
[32]张学成，可素娟，潘启民，赵安林，黄河冰盖厚度演变数学模型，冰川冻土，24(2),2002,203-205.
[33]肖建民，金龙海，谢永刚,霍跃东，寒区水库冰盖形成与消融机理分析，水利学报，(6),2004,80-85.
[34]李志军，杨宇，彭旭明，王国志，卢永超，黑龙江红旗泡水库冰生长过程现场观测数据的剖析，西安理工大学学报，25(3),2009,270-274.
[35]王世瑞，王金金，冯有前，李彦民，喻方元，茹有刚，计算方法（第二版），西安：西安电子科技出版社，2004.
[36]苏金明，阮沈勇，MATLAB实用教程（第2版），北京：电子工业出版社，2008.
[37]张德丰等，MATLAB语言高级编程，北京：机械工业出版社，2010.
[38]陆金甫，关治，偏微分方程数值解法(第二版)，北京：清华大学出版社，2004.
[39]张宝琳，谷同祥，莫则尧，数值并行计算原理与方法，北京：国防工业出版社，1999.
[40]郭本瑜，偏微分方程的差分方法，北京：科学出版社，1988.
[41]李荣华，冯果忱，微分方程数值解法（第3版），北京：高等教育出版社，1996.
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