Chapter 5
Numerical Simulation of Taylor Vortex
Flows Under the Periodicity Conditions
Fedor A. Maksimov
Abstract It is known from the experimental researches regarding the Taylor vortex
flows between the rotating cylinders that a different number of pairs of the Taylor
vortices can be formed within the one geometry. It means that different variants of
the problem’s solution are allowable. The simulation method with periodic boundary
conditions on the edges of the cylinder’s part was developed for the numerical
research into the Taylor vortex flows. The results of the simulation of the flow for
the various values of the periodicity sizes and different initial data are given.
5.1 Introduction
The theoretical research into the flows between the rotating cylinders assumes that
they are endlessly long [1–3]. The experimental researches into the flows deal with
the cylinders of the maximum length to reduce the edge effects. The simulation of a
rather long cylinder requires the use of greater computational resources that inevitably
lead to longer computational periods and relatively rough grid for the description of
each vortex structure. The periodic structures with the scale of the distance order
between the external cylinder and internal cylinder are formed along the axis of
the cylinders in the Taylor vortex flow. To eliminate edge effects, it is possible to
consider only a part of the cylinder, setting periodicity conditions on borders of
the computational domain throughout the length. It requires the introduction of an
additional dimension—the length L of the considered section of the cylinder. The
dimension L that is artificially assigned in the research into the Taylor vortex flows
determines their scale.
There are some experimental examples [4–6] when a different number of the
Taylor vortices are formed in the same conditions, and, accordingly, the vortex pairs
have a different size. In fact, the problem allows different stationary solutions while
F. A. Maksimov (B)
Institute for Computer Aided Design of the RAS, 19/18, Vtoraya Brestskaya ul., Moscow 123056,
Russian Federation
e-mail: f_a_maximov@mail.ru
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_5
47
Numerical Simulation of Taylor Vortex
Flows Under the Periodicity Conditions
Fedor A. Maksimov
Abstract It is known from the experimental researches regarding the Taylor vortex
flows between the rotating cylinders that a different number of pairs of the Taylor
vortices can be formed within the one geometry. It means that different variants of
the problem’s solution are allowable. The simulation method with periodic boundary
conditions on the edges of the cylinder’s part was developed for the numerical
research into the Taylor vortex flows. The results of the simulation of the flow for
the various values of the periodicity sizes and different initial data are given.
5.1 Introduction
The theoretical research into the flows between the rotating cylinders assumes that
they are endlessly long [1–3]. The experimental researches into the flows deal with
the cylinders of the maximum length to reduce the edge effects. The simulation of a
rather long cylinder requires the use of greater computational resources that inevitably
lead to longer computational periods and relatively rough grid for the description of
each vortex structure. The periodic structures with the scale of the distance order
between the external cylinder and internal cylinder are formed along the axis of
the cylinders in the Taylor vortex flow. To eliminate edge effects, it is possible to
consider only a part of the cylinder, setting periodicity conditions on borders of
the computational domain throughout the length. It requires the introduction of an
additional dimension—the length L of the considered section of the cylinder. The
dimension L that is artificially assigned in the research into the Taylor vortex flows
determines their scale.
There are some experimental examples [4–6] when a different number of the
Taylor vortices are formed in the same conditions, and, accordingly, the vortex pairs
have a different size. In fact, the problem allows different stationary solutions while
F. A. Maksimov (B)
Institute for Computer Aided Design of the RAS, 19/18, Vtoraya Brestskaya ul., Moscow 123056,
Russian Federation
e-mail: f_a_maximov@mail.ru
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_5
47