Publication detail

Methods for Simplification of the Mathematical Model for the Calculation of Flows in the Flow Path of Hydraulic Turbines

FIALOVÁ, S. POCHYLÝ, F. VOLKOV, A.V. RYZHENKOV, A.V.DRUZHININ, A.A.

Original Title

Methods for Simplification of the Mathematical Model for the Calculation of Flows in the Flow Path of Hydraulic Turbines

Type

journal article in Web of Science

Language

English

Original Abstract

The main concern of this paper is fundamental research into an acute problem arising in the operation of hydraulic turbines, namely, the formation of a vortex core downstream of the impeller. It is noted that, at present, the operating range of these machines has to be extended due to the change in power network loads in daily and seasonal cycles, thereby increasing the time of hydraulic turbines' operation under off-design or undesirable conditions, including those involving the risk of formation of a vortex of varying intensity. To describe this complex fluid flow, a mathematical model of the vortex core flow downstream of the hydraulic turbine's impeller was developed. This paper focuses on the fundamental issues encountered in developing the mathematical model. The methods are presented for simplifying the formulation of equations describing the structure of vortex rope formed in the flowpath. In this case, the equations of mathematical physics containing a dependent variable and taking the form of the Navier-Stokes equations when applied fluids flows were employed. They describe the time changes of the selected parameters in a controlled volume induced by the flow through the volume boundaries. The boundary conditions have been demonstrated to considerably affect the unsteady vortex structures. A special case is formulated for a potential force field using the stress tensor that governs the equilibrium. This makes it possible to describe complex motion in liquids without using an intricate form of the Navier-Stokes equations for vortex structures.

Keywords

unsteady flow; vortex structure; incompressible liquid; Navier-Stokes equations; unsteady term; divergence theorem; finite-volume method

Authors

FIALOVÁ, S.; POCHYLÝ, F.; VOLKOV, A.V.; RYZHENKOV, A.V.;DRUZHININ, A.A.

Released

17. 12. 2021

Publisher

PLEIADES PUBLISHING INC

Location

NEW YORK

ISBN

0040-6015

Periodical

Thermal Engineering (English translation of Teploenergetika)

Year of study

68

Number

12

State

Russian Federation

Pages from

906

Pages to

915

Pages count

10

URL

https://link.springer.com/article/10.1134/S004060152112003X

BibTex

@article{BUT175899,
  author="FIALOVÁ, S. and POCHYLÝ, F. and VOLKOV, A.V. and RYZHENKOV, A.V. and DRUZHININ, A.A.",
  title="Methods for Simplification of the Mathematical Model for the Calculation of Flows in the Flow Path of Hydraulic Turbines",
  journal="Thermal Engineering (English translation of Teploenergetika)",
  year="2021",
  volume="68",
  number="12",
  pages="906--915",
  doi="10.1134/S004060152112003X",
  issn="0040-6015",
  url="https://link.springer.com/article/10.1134/S004060152112003X"
}