MATHEMATICAL MODEL OF TRANSFORMATIONTHE PLANE FLOW PARAMETERS TO SPATIAL ONES AND OPTIMIZATION METHOD THAT BASED ON IT
The article presented a new optimization mathematical model that based on transformation method of plane flow parameters to the spatial flow variables. This model is transforming the frequency, amplitude and phase of two-dimensional flow to equivalent parameters for three-dimensional flow. This method allows to significantly reduce the simulation time. The time costs are reduced by 36 times in the task presented in this paper. The report presents the analysis results an existing 3D model, which implemented in ANSYS software package. It is used to flow simulate in the flow part of vortex flow meter. The main properties and settings of a numerical model are presented that are performed when the problem is formulated. The control points of flow part geometry the vortex flow meter was define as an analysis results of stream simulation result in the flow part of vortex flowmeter. Mathematical modeling was carried out in these control points and collected the simulation results. In particularly, pressure fluctuations. The functional structure of a mathematical model for determining the flow parameters in the flow part of the vortex flow meter was created for the variant of two - dimensional simulation. The mathematical method of transformation the two-dimensional simulation results to a three-dimensional model was selected for flow simulation in the flow part of vortex flow meter. A computational algorithm is a mathematical model relating the three-dimensional and two-dimensional model of a vortex flow meter flow part was created. The algorithm is based on the fast Fourier transform and the minimization problem solution to determine the frequency, amplitude and phase of the signal. Functional dependencies between plane flow parameters and spatial one was determined, in particularly frequency, phase and amplitude. The new algorithm for signal processing based on the transformation method was presented. This algorithm decreased simulation point number in ten times, from ten thousand to one thousand. Next, a mathematical model is connected to the optimization algorithm based on the Rosenbrock method and test calculations were made. According to the calculation result, time of obtaining the optimal flowing part prototype is reduced by 36 times, from 18 months to 0.5 ones. Research relevance related to the choice of optimal mathematical algorithm simulation vortex shedding process from bluff body in a tube (the flow part of the vortex flowmeter), and vortices distribution of downstream. For the optimal flow part shape develop.