Approximate solution of the Navier-Stokes equation for digonal ducts - Гумен, Олена Миколаївна; Мілейковський, Віктор Олександрович; Дзюбенко, Володимир Григорович (Technology audit and production reserves, 2015)
This article presents the analysis of the pressure laminar flow in the digonal duct with the section formed by two equal arcs. Such ducts are used in soft film heat exchangers. In addition, they are formed in rocks for underground water. The first attempt was to perform the analysis similarly to flows in round pipes. This direction gives wrong parabolic velocity profile with a rib at the long axis of the digonal section. In addition, it causes pressure drop calculation results understated up to 14,3 %. Therefore, to obtain adequate results we need to solve the Navier-Stokes equation. We propose a grid with unequal steps for this kind of section and solve the equation numerically. The convergence is very quick. For most of the tasks, it is enough to use a 4×4 grid. To integrate the profile in case of very quick convergence and a sparse grid the interpolation with the highest possible order is required. We introduce a new coordinate system to map the digonal section to a rectangle. We perform polynomial interpolation of all nodes in the new coordinate system. The integration of this polynomial cause velocity field coefficient to converge on the 4×4 grid for most of the tasks (the error does not exceed 2,2 % compared to the 100×100 grid). We show possibility of pressure drop calculation with the same formula as for the round pipes with the error of no more than 2,86 %. However, we offer equations for more precise calculations of the pressure drop and velocity field coefficient.