Approximate solution of the Navier-Stokes equation for digonal ducts

Authors

  • Олена Миколаївна Гумен National Technical University of Ukraine "Kyiv Polytechnic Institute", Peremohy 37, Kyiv, 03056, Ukraine https://orcid.org/0000-0003-3992-895X
  • Віктор Олександрович Мілейковський Kyiv National University of Construction and Architecture, Povitroflotskyi prosp., 31, Kyiv, 03680, Ukraine https://orcid.org/0000-0001-8543-1800
  • Володимир Григорович Дзюбенко Kyiv National University of Construction and Architecture, Povitroflotskyi prosp., 31, Kyiv, 03680, Ukraine https://orcid.org/0000-0003-2468-2555

DOI:

https://doi.org/10.15587/2312-8372.2015.41212

Keywords:

laminar flow, digonal duct, heat utilization, polymer film, polymer heat exchanger, underground water

Abstract

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.

Author Biographies

Олена Миколаївна Гумен, National Technical University of Ukraine "Kyiv Polytechnic Institute", Peremohy 37, Kyiv, 03056

Doctor of Technical Science, Professor, Member of International Society for Geometry and Graphics (ISGG)

Department of descriptive geometry, engineering and computer graphics

 

Віктор Олександрович Мілейковський, Kyiv National University of Construction and Architecture, Povitroflotskyi prosp., 31, Kyiv, 03680

Candidate of Technical Sciences, Associate Professor, Member of International Society for Geometry and Graphics (ISGG)

Department of heat gas supply and ventilation

Володимир Григорович Дзюбенко, Kyiv National University of Construction and Architecture, Povitroflotskyi prosp., 31, Kyiv, 03680

Senior Lecturer, Colonel

Department of labour and environment protection

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Published

2015-04-02

How to Cite

Гумен, О. М., Мілейковський, В. О., & Дзюбенко, В. Г. (2015). Approximate solution of the Navier-Stokes equation for digonal ducts. Technology Audit and Production Reserves, 2(5(22), 42–50. https://doi.org/10.15587/2312-8372.2015.41212

Issue

Vol. 2 No. 5(22) (2015): Mathematical modeling. Information and control systems

Section

Mathematical Modeling: Original Research

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Copyright (c) 2016 Олена Миколаївна Гумен, Віктор Олександрович Мілейковський, Володимир Григорович Дзюбенко

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