THE PIPELINES WARPING PROCESS UNDER THE INFLUENCE OF AERODYNAMICAL LOAD MATHEMATICAL MODELLING
Keywords:
mathematical model, wind load, aerodynamical characteristics, variational problems, pipeline deformation, Fredholm equation, numerical methods.Abstract
The steady flow around the pipeline section profile mathematical model taking into account the section configuration changing is designed together with the model of axis deformation process under the aerodynamical load action in two directions. The integral correlation method and the second Green formula for two functions – the velocity potential and the value are inverse to the distance between two points of the space. The problem dimension lowering has been solved, which allows to reduce the problem of aerodynamics to the problem of Fredholm second type integral equation solution taking to account the profile geometry, the approach flow velocity and the angle of attack. The formulas to calculate the coefficients of carrying capacity, the inductive resistance and the angular momentum have been used. To realize the models the methods of second type Fredholm integral equation solution for the tangential component of velocity vector have been used both with the full energy functional problem solution methods. The integral equation has been presented to the linear equations system, which can be solved by the Gauss method, the formulas to calculate the system matrix components taking to account the profile geometry features. The variational problems can be solved by the solution of the boundary problem for the ordinary differential equations of the fourth order using the shooting method. The test calculations have been made and confirmed the co-ordination between the results of presented calculations with the well-known theoretical and experimental results. The relation between the aerodynamical coefficients data and the angle of attack, the profile ellipse half-axle, the different ellipse half-axle on the back and lower surface have been presented. The directions of future investigations have been defined, they are connected with the investigation of more difficult configurations of pipeline sections and their mathematical formalization.
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