About the authors

First name, Middle name, Last name, Scientific degree, Scientific rank, Current position. Full and brief name of the organization, The organization address. | Vachagina E.K. – doctor of technical sciences E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Kazakh Scientific Center of the Russian Academy of Sciences The organization address: 420111, Russia, Kazan, Lobachevsky st., 2/3 E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Zolotonosov Ya.D. – doctor of technical sciences, professor E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Mustakimova S.A. – lead programmer E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Krutova I.A. – post-graduate student E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Kazan State University of Architecture and Civil Engineering The organization address: 420043, Russia, Kazan, Zelenaya st., 1 |

Title of the article | The definition of equivalent diameter of spring-twisted pipes |

Abstract. | The method of calculating the area of the living section, wetted perimeter and equivalent diameter of the cylindrical spring twisted channel was presented. The inner boundary of such channels is formed closely adjacent to each other coils coiled in a spiral with some constant pitch of the wire. For this the equation of the surface of wire twisted in a helical spiral was written in parametric form. Was formulated in terms of tight junction turns of wire to each other. These conditions are reduced to the dependence of one geometric parameter from the other geometric parameter. It makes sense the relationship of the step helix to the diameter of the wire, and has a sense of the relationship of the wire diameter to the diameter of the axial bending of the Central helix of wire. The required dependence is obtained from the search of the root of the nonlinear equation in the where parameter can be considered as a parameter. To search root used numerical methods to find the root of nonlinear equation, including the method of halving. The equation of the boundary of the cross section was obtained as the equation of a curve in cross-section of his plane. Thus, the equation of this curve is the border was also presented in a parametric form. To compute the area of the living section was used standard formulas to find the area of a curvilinear sector in polar coordinates. The formula for calculating the cross sectional area has been transformed considering the fact that the curve bounding the cross section is given in parametric form. To calculate the wetted perimeter was used the standard formula of mathematical analysis to determine the length of a curve given parametrically. Calculation of equivalent diameter using the proposed method allows producing engineering calculations series of heat exchangers in which heat exchange elements are spring-twisted channels. |

Keywords. | heat transfer, fluid flow, and spring-twisted channels, covariant and contravariant components of velocity, streamlines, secondary flows. |

For citations: | Vachagina E.K., Zolotonosov Ya.D., Mustakimova S.A., Krutova I.A. The definition of equivalent diameter of spring-twisted pipes // Izvestiya KGASU. 2016. №3(37) P.188-194. |