NUMERICAL INVESTIGATION OF EFFECTED TURBULENT FLOW ON THE BASE OF PRESSURE FLUCTUATIONS FRACTAL DIMENSION ANALYSIS

Today, mathematical modeling is widely used for calculation of turbulent flows characteristics. The mathematical problem of turbulent flow with intensive effects is nonclosed. It is being closed with the help of turbulence models. At present we know a lot of turbulence models. As a rule, they have limited application areas, especially when we speak about the flow with impact. In this regard, it would be convenient to get a model with universal effects characteristics. The authors suggest to use fractal dimension of pressure fluctuations of the turbulent flow as a characteristic not related to physical, geometrical or other effects parameters, and not depending on their nature. Experimental research of turbulent pressure fluctuations was undertaken in order to determine the fractal dimension of turbulent flow pressure fluctuations. The experimental series of pressure fluctuations were analyzed. Pressure fluctuations fractal dimension of undisturbed turbulent flow and turbulent flow with various degrees of effect on the wall-adjacent turbulence was determined with the R/S method. The results show that the fractal dimension is different for different cases. The smallest pressure fluctuations fractal dimension corresponds to optimal effect on wall-adjacent turbulence, when the flow friction resistance was minimal. Further, the fractal dimension was correlated with the experimental data on friction resistance and velocity profiles, and on the basis of generalization the dependence of intensity of turbulent exchange in the boundary layer on the flow pressure fluctuations fractal dimension was obtained. This dependence was loaded into the mixing length model of Prandtl. On the base of suggested model the program was created and a numerical investigation of friction resistance and structure of turbulent flow has been conducted. Calculation error on friction resistance differs from the experimental values by 5%.