Vestnik YuUrGU. Ser. Mat. Model. Progr., 2014, Volume 7, Issue 2, Pages 74–86
This article is cited in 1 scientific paper (total in 1 paper)
Modelling Liquid Flows in Diffusers by Reduced Equations
Yu. I. Sapronov
Voronezh State University, Voronezh, Russian Federation
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 $n \le 5$.
Navier–Stokes equations; Helmholtz equations; diffuser current; Hamel substitution; Lyapunov–Schmidt variation method; velocity diagram.
PDF file (1458 kB)
MSC: 90C30, 90C90
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
\paper Modelling Liquid Flows in Diffusers by Reduced Equations
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
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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
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