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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2014, Volume 7, Issue 2, Pages 74–86 (Mi vyuru132)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical Modelling

Modelling Liquid Flows in Diffusers by Reduced Equations

Yu. I. Sapronov

Voronezh State University, Voronezh, Russian Federation

Abstract: To know the dynamic characteristics of liquid in hydrocyclones and diffusers is important for optimizing the technical parameters of the liquid ends of turbine pumps on long-distance oil pipelines. It is possible to describe these characteristics by using the available analytic expressions for the solutions to the model equations of hydrodynamics or their simplified versions used in these problems.
It is known that the simplified systems of hydrodynamic type derived from the Navier–Stokes equation allow us to model quite precisely liquid flows in regions of arbitrary geometric shape. In this article we reduce the Helmholtz equation in the case of a flat diffuser flow to a boundary value problem for the Jeffrey–Hamel ODE by means of the Hamel substitution. At finite values of the Reynolds number we establish the possibility of constructing approximate solutions to the reduced equation via nonlinear Ritz–Galerkin approximation using a variational version of the Lyapunov–Schmidt method. With this approximation, we can determine the liquid velocity field to arbitrary precision. The article includes examples of approximately computed velocity diagrams for the flows close to $n$-modal with $n \le 5$.

Keywords: Navier–Stokes equations; Helmholtz equations; diffuser current; Hamel substitution; Lyapunov–Schmidt variation method; velocity diagram.

DOI: https://doi.org/10.14529/mmp140207

Full text: PDF file (1458 kB)
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Document Type: Article
UDC: 517.9
MSC: 90C30, 90C90
Received: 03.01.2014

Citation: Yu. I. Sapronov, “Modelling Liquid Flows in Diffusers by Reduced Equations”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:2 (2014), 74–86

Citation in format AMSBIB
\Bibitem{Sap14}
\by Yu.~I.~Sapronov
\paper Modelling Liquid Flows in Diffusers by Reduced Equations
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2014
\vol 7
\issue 2
\pages 74--86
\mathnet{http://mi.mathnet.ru/vyuru132}
\crossref{https://doi.org/10.14529/mmp140207}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Korotkikh, “Statsionarnye tochki uravneniya «reaktsiya-diffuziya» i perekhody v stabilnye sostoyaniya”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:1 (2017), 125–137  mathnet  crossref  elib
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