阻力线性化条件下纵向离散系数的半解析解法
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摘要
纵向离散系数是水质模型的关键参数,对于污染物的影响范围具有决定性影响,一直是环境水力学的研究热点。目前纵向离散系数的确定以经验、半经验方法为主,物理机制不够明确。基于底部阻力局部线性化假定,利用幂级数求解断面流速分布,代入Fischer纵向离散系数积分公式,建立了纵向离散系数的半解析方法。利用100余条天然河流数据进行验证,结果表明计算值为实测值的0.3～3.0倍,精度符合工程要求。该方法推导严密、计算量较小,一定程度上反映了离散的物理机制,与前人计算公式的误差在同一量级,具有一定的可靠性。
The longitudinal dispersion coefficient is a key parameter in water quality model,which has a great influence to the influence area of pollutant. Thus,it has been a research focus in environmental hydraulics. At present,approaches to determine longitudinal dispersion coefficient( DL) are mainly based on empirical or semi-empirical formulas without definite physical mechanism. Based on assumption that the bottom resistance was linear with velocity,a power series form for velocity distribution was acquired. By adopting Fischer's integral formula,a semi-analytical method to compute DLwas established and generalized to natural rivers. The applications in more than 100 rivers show that the computed value of DLis about 0.3 to 3 times of the measured value,meeting the requirements of the project. With acceptable accuracy,low computational complexity,the method reflects the dispersion physical mechanism to some extent. Moreover,this formula has the same magnitude error with previous formulas and it means the formula has certain reliability.
The longitudinal dispersion coefficient is a key parameter in water quality model,which has a great influence to the influence area of pollutant. Thus,it has been a research focus in environmental hydraulics. At present,approaches to determine longitudinal dispersion coefficient( DL) are mainly based on empirical or semi-empirical formulas without definite physical mechanism. Based on assumption that the bottom resistance was linear with velocity,a power series form for velocity distribution was acquired. By adopting Fischer's integral formula,a semi-analytical method to compute DLwas established and generalized to natural rivers. The applications in more than 100 rivers show that the computed value of DLis about 0.3 to 3 times of the measured value,meeting the requirements of the project. With acceptable accuracy,low computational complexity,the method reflects the dispersion physical mechanism to some extent. Moreover,this formula has the same magnitude error with previous formulas and it means the formula has certain reliability.
引文
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[10]DISLEY T,GHARABAGHI B,MAHBOUBI A A,et al.Predictive Equation for Longitudinal Dispersion Coefficient[J].Hydrological Processes,2015,29(2):161-172.
[11]李锦秀,黄真理,吕平毓.三峡库区江段纵向离散系数研究[J].水利学报,2000,31(8):84-87.
[12]刘震,孙熙.黄河下游干流纵向离散系数估算方法[J].河海大学学报(自然科学版),2008,36(2):157-160.
[13]DENG Z Q,SINGH V P,BENGTSSON L.Longitudinal Dispersion Coefficient in Straight Rivers[J].Journal of Hydraulic Engineering,2001,127(11):919-927.
[14]陈永灿,朱德军.梯形断面明渠中纵向离散系数研究[J].水科学进展,2005,16(4):511-517.
[15]WANG Y,HUAI W.Estimating the Longitudinal Dispersion Coefficient in Straight Natural Rivers[J/OL].Journal of Hydraulic Engineering,2016,142(11):04016048[2017-05-10].http://ascelibrary.org/doi/10.1061/%28ASCE%29HY.1943-7900.0001196.
[16]张文俊,胡煜,任华堂,等.基于流速幂级数解的明渠纵向离散系数计算方法[R].北京:中央民族大学,2017:4-5.
[17]顾莉,华祖林.天然河流纵向离散系数确定方法的研究进展[J].水利水电科技进展,2007,27(2):85-89.
[18]SEO I W,BAEK K O.Estimation of the Longitudinal Dispersion Coefficient Using the Velocity Profile in Natural Streams[J].Journal of Hydraulic Engineering,2004,130(3):227-236.
[19]LIU H.Predicting Dispersion Coefficient of Streams[J].Journal of the Environmental Engineering Division,1977,103(1):59-69.
[20]BOGLE G V.Stream Velocity Profiles and Longitudinal Dispersion[J].Journal of Hydraulic Engineering,1997,123(9):816-820.
[21]ZENG Y,HUAI W.Estimation of Longitudinal Dispersion Coefficient in Rivers[J].Journal of Hydro-Environment Research,2014,8(1):2-8.
[2]ELDER J W.The Dispersion of Marked Fluid in Turbulent Shear Flow[J].Journal of Fluid Mechanics,1959,5(4):544-560.
[3]FISCHER H B,LIST E J,KOH R C Y,et al.Mixing in Land Coastal Waters[M].New York:Academic Press,1979:125-131.
[4]张江山.瞬时源示踪实验确定河流纵向离散系数[J].环境科学,1991(6):40-43.
[5]吕巍,张建军,闫莉,等.黄河潼关河段污染物示踪扩散研究[J].人民黄河,2016,38(9):59-63.
[6]黄爱珠.桂江下游梧州河段纵向离散系数的选定[J].人民珠江,1992(6):34-36.
[7]SAHAY R R,DUTTA S.Prediction of Longitudinal Dispersion Coefficients in Natural Rivers Using Genetic Algorithm[J].Hydrology Research,2009,40(6):544-552.
[8]SEO I W,CHEONG T S.Predicting Longitudinal Dispersion Coefficient in Natural Streams[J].Journal of Hydraulic Engineering,1998,124(1):25-32.
[9]KASHEFIPOUR S M,FALCONER R A.Longitudinal Dispersion Coefficients in Natural Channels[J].Water Research,2002,36(6):1596.
[10]DISLEY T,GHARABAGHI B,MAHBOUBI A A,et al.Predictive Equation for Longitudinal Dispersion Coefficient[J].Hydrological Processes,2015,29(2):161-172.
[11]李锦秀,黄真理,吕平毓.三峡库区江段纵向离散系数研究[J].水利学报,2000,31(8):84-87.
[12]刘震,孙熙.黄河下游干流纵向离散系数估算方法[J].河海大学学报(自然科学版),2008,36(2):157-160.
[13]DENG Z Q,SINGH V P,BENGTSSON L.Longitudinal Dispersion Coefficient in Straight Rivers[J].Journal of Hydraulic Engineering,2001,127(11):919-927.
[14]陈永灿,朱德军.梯形断面明渠中纵向离散系数研究[J].水科学进展,2005,16(4):511-517.
[15]WANG Y,HUAI W.Estimating the Longitudinal Dispersion Coefficient in Straight Natural Rivers[J/OL].Journal of Hydraulic Engineering,2016,142(11):04016048[2017-05-10].http://ascelibrary.org/doi/10.1061/%28ASCE%29HY.1943-7900.0001196.
[16]张文俊,胡煜,任华堂,等.基于流速幂级数解的明渠纵向离散系数计算方法[R].北京:中央民族大学,2017:4-5.
[17]顾莉,华祖林.天然河流纵向离散系数确定方法的研究进展[J].水利水电科技进展,2007,27(2):85-89.
[18]SEO I W,BAEK K O.Estimation of the Longitudinal Dispersion Coefficient Using the Velocity Profile in Natural Streams[J].Journal of Hydraulic Engineering,2004,130(3):227-236.
[19]LIU H.Predicting Dispersion Coefficient of Streams[J].Journal of the Environmental Engineering Division,1977,103(1):59-69.
[20]BOGLE G V.Stream Velocity Profiles and Longitudinal Dispersion[J].Journal of Hydraulic Engineering,1997,123(9):816-820.
[21]ZENG Y,HUAI W.Estimation of Longitudinal Dispersion Coefficient in Rivers[J].Journal of Hydro-Environment Research,2014,8(1):2-8.