Research And Application On Turbulent Diffusion Model Based On Fractal Theory

The simulation of the universal-existed turbulent flow of the nature water and the migration and diffusion of the pollutant in it has been a hot issue of current science research. The fractal theory and other non-linearity theory in recent years provide good rationale for explaining and describing the strongly stochastic turbulent flow phenomenon. In this paper, under the subsidy of the China-Germany international cooperation project"Water environment of three gorges reservoir pollution process control and safety control technique research"fractal theory was led into the research of turbulent flow diffusion. The mathematic model of water quality in turbulent flow diffusion based on fractal theory was explored and verified. The model expression was as follows:The turbulent flow model based on fractal theory was programmed with Visual Basic computer language. The model was calibrated and verified using the synchronous hydrology and water quality data during the high, normal and low flow period of Yangtze River in Wanzhou in 2003. The water quality situation in the year 2015 when the reservoir would be accomplished was predicted by the model.The following conclusion was achieved through the research:â‘ The body-fitted grid coordinate conversion technology, the finite difference calculus, ADI modus and TDMA modus were used to achieve the simulation and calculation hydraulics and water quality of the nature river in complicated boundary condition. These solving technologies had the characteristic of rapid convergence, short calculating time, adaptation to dynamic analogies.â‘¡The analog computation results of Yangtze River in Wanzhou during the low flow period in 2003 by fractal water quality model and traditional water quality model were analyzed and compared. The result indicated that the average relative error between the calculated value by fractal water quality model and the actual monitored value was 17.1%, while the average relative error of the calculated value by traditional water quality model and the actual monitored value was 19.4%. The precision of fractal water quality model was better than traditional water quality model.â‘¢The calibration and verification results of Yangtze River in Wanzhou during high and normal flow period in 2003 by fractal water quality model showed that the max relative error between the calculated value and the actual monitored value was 32.7%, the min relative error was 9.1%, and the average relative error was 18.5%. The results coincided, and the error was in permission range.â‘£The water quality in the year 2015 when the reservoir would be accomplished was predicted by the fractal model. The conclusions were as follows. Firstly, as the rise of the water height in the reservoir, the water flow rate would decrease notably, the turbulent fluctuation seepage ability would be weakened, the nonuniformity of water quality distribution along the cross section would be more apparent. Secondly, it could be seen from the variation chart of pollutant concentration along the cross direction that the pollutant concentration at the bank was obviously higher than the concentration at the center of the river. This was because the pollutants such as industrial, municipal wastewater and municipal solid waste were generally discharged at the bank. Thirdly, the hydrology circumstance under the design condition was applied for the prediction of water quality. Therefore, the prediction could accurately tell the variation of the water quality under the design condition, while it was hard to be compared with the water quality during high, normal and low flow periods before the reservoir was completed. Fourthly, it could be discovered from the concentration field under the two different design condition that the concentration range of the water quality was mainly controlled by the water quality of import cross section.