Abstract
The number and distribution of pollutant concentration in a trapezoidal open channel flow with a side discharge is calculated and effects of the bank gradient are investigated in this paper. A sigma-coordinate water quality numerical model is used to simulate the process of both water and pollutant transportation in the trapezoidal channel open flow. The diffusion coefficient used in the prediction is determined by two methods including constant coefficient and the depth-averaged k-epsilon turbulence closure model. The change of the concentration with the bank gradient is acquired based on the simulation of cases with different bank gradients. An analytical formula is derived by using the mirror image method and related diffusion theories, ignoring the discharge momentum and the influence of the opposite bank. The formula can predict the number and distribution of pollutant concentration with some acceptable errors. The results demonstrate that the bank gradient has great influence on the concentration distribution which will decrease with the increase of the bank gradient approximately following a hyperbolic law.
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References
Chen Y-c and Zhu D-j (2005). Study on longitudinal dispersion coefficient in open channel trapezoidal cross-section. Adv Water Sci 16(4): 511–517
Fischer HB, Imberger J, List EJ et al (1979) Mixing in inland and coastal waters. Academic press
Holley ER, Siemous J and Abraham G (1972). Some aspects of analyzing transverse diffusion in rivers. J Hydraul Res 10(1): 27–57
Li L, Li Y and Chen J (2003). Experimental study on transverse diffusion coefficients in an open trapezoidal channel. J Tsinghua Univ (Sci Technol) 43(8): 1124–1126
Liu Z-w (2005) Studies on Characteristics and Carrying Capacity of the water environment near the riverside in Three Gorges Reservoir. Ph.D. thesis, Tsinghua University
Mikhail R et al (1975) The reattachment of a two-dimensional turbulent jet in a confined cross flow. In: Progress of 16th IAHA Congress, San Paulo, Brazil, vol 3, pp 414–419
Phillips NG (1957). A coordinate system having some special advantages for numerical forecasting. J Meteorol 14: 184–185
Rannacher R and Turek S (1992). Simple nonconforming quadrilateral stokes element. Numer Meth Partial Diff Eq 8(2): 97–111
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Liu, Z., Chen, Y. & Zhu, D. Study on the concentration distribution in a trapezoidal open-channel flow with a side discharge. Environ Fluid Mech 7, 509–517 (2007). https://doi.org/10.1007/s10652-007-9042-7
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DOI: https://doi.org/10.1007/s10652-007-9042-7