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Theoretical Analysis of Rolling Fluid Turbines

Published: 01 January 2022 Publication History

Abstract

The rolling fluid turbine is a bladeless hydraulic device that exhibits peculiar behavior, making it interesting from the aspect of fluid dynamics. The rotor of this turbine has an unusually symmetrical shape and can rotate in two directions---the one it “chooses" seems to be random. Explanation of the underlying hydraulic mechanism is an open problem, which we tackle here. This paper suggests that the hydraulic force on the rotor acts as positive feedback on the motion of the rotor itself. Such an effect can exist since the system is thermodynamically open. Power generation is described in an analytical computation based mostly on the arguments of symmetry. The result is then tested in a numerical simulation.

References

[1]
M. S. Aln\aes, UFL: A finite element form language, in Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.-A. Mardal, and G. N. Wells, eds., Lect. Notes Comput. Sci. Eng. 84, Springer, 2012, pp. 303--338.
[2]
M. S. Aln\aes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells, The FEniCS Project Version 1.5, Arch. Numer. Software, 3 (2015), https://doi.org/10.11588/ans.2015.100.20553.
[3]
M. S. Aln\aes, A. Logg, and K.-A. Mardal, UFC: A finite element code generation interface, in Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.-A. Mardal, and G. N. Wells, eds., Lect. Notes Comput. Sci. Eng. 84, Springer, 2012, pp. 283--302.
[4]
M. S. Aln\aes, A. Logg, K.-A. Mardal, O. Skavhaug, and H. P. Langtangen, Unified framework for finite element assembly, Internat. J. Comput. Sci. Engrg., 4 (2009), pp. 231--244, https://www.inderscience.com/info/inarticle.php?artid=29160.
[5]
M. S. Aln\aes, A. Logg, K. B. Ølgaard, M. E. Rognes, and G. N. Wells, Unified form language: A domain-specific language for weak formulations of partial differential equations, ACM Trans. Math. Software, 40 (2014), 9, https://doi.org/10.1145/2566630.
[6]
V. Beran, M. Sedl\'a\vcek, and F. Mar\vs\'ik, A new bladeless hydraulic turbine, Appl. Energy, 104 (2013), pp. 978--983.
[7]
S. Dong, G. Karniadakis, and C. Chryssostomidis, A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains, J. Comput. Phys., 261 (2014), pp. 83--105, https://doi.org/10.1016/j.jcp.2013.12.042.
[8]
S. Hostin, M. Sedláček, and J. Špidla, Small Hydroelectric Power Plant, Final Report, Bratislava, 1997.
[9]
O. Kincl, Thermodynamic Modeling of Rolling Fluid Turbine, Master's thesis, Charles University, Prague, 2020.
[10]
O. Kincl, M. Pavelka, F. Maršík, and M. Sedláček, How Sedláček bladeless turbine works?, in Proceedings Topical Problems of Fluid Mechanics 2021, Prague, T. Bodn\'ar, T. Neustupa, and D. Šimurda, eds., 2021, pp. 70--78, https://doi.org/https://doi.org/10.14311/TPFM.2021.010.
[11]
R. C. Kirby, Algorithm 839: FIAT, a new paradigm for computing finite element basis functions, ACM Trans. Math. Software, 30 (2004), pp. 502--516, https://doi.org/10.1145/1039813.1039820.
[12]
R. C. Kirby, FIAT: Numerical construction of finite element basis functions, in Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.-A. Mardal, and G. N. Wells, eds., Lect. Notes Comput. Sci. Eng. 84, Springer, 2012, pp. 247--255.
[13]
R. C. Kirby and A. Logg, A compiler for variational forms, ACM Trans. Math. Software, 32 (2006), pp. 417--444, https://doi.org/10.1145/1163641.1163644.
[14]
L. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon Press, 1987.
[15]
G. Lebon, D. Jou, and J. Casas-Vázquez, Understanding Non-Equilibrium Thermodynamics: Foundations, Applications, Frontiers, Springer-Verlag, 2008.
[16]
A. Logg, K.-A. Mardal, and G. N. Wells, eds., Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, Springer, 2012, https://doi.org/10.1007/978-3-642-23099-8.
[17]
A. Logg, K. B. Ølgaard, M. E. Rognes, and G. N. Wells, FFC: The FEniCS form compiler, in Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.-A. Mardal, and G. N. Wells, eds., Lect. Notes Comput. Sci. Eng. 84, Springer, 2012, pp. 227--238.
[18]
A. Logg and G. N. Wells, DOLFIN: Automated finite element computing, ACM Trans. Math. Software, 37 (2010), 20, https://doi.org/10.1145/1731022.1731030.
[19]
A. Logg, G. N. Wells, and J. Hake, DOLFIN: A C++/Python finite element library, in Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.-A. Mardal, and G. N. Wells, eds., Lect. Notes Comput. Sci. Eng. 84, Springer, 2012, pp. 173--225.
[20]
F. Maršík, J. Falta, and M. Sedláček, Theoretical analysis and experimental verification of the rolling turbines performance, in Proceedings of the 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Anatolia, Turkey, 2010.
[21]
F. E. McCaughan, Bifurcation analysis of axial flow compressor stability, SIAM J. Appl. Math., 50 (1990), pp. 1232--1253, https://doi.org/10.1137/0150075.
[22]
K. B. Ølgaard and G. N. Wells, Optimizations for quadrature representations of finite element tensors through automated code generation, ACM Trans. Math. Software, 37 (2010), 8, https://doi.org/10.1145/1644001.1644009.
[23]
M. Pavelka, V. Klika, P. Vágner, and F. Maršík, Generalization of exergy analysis, Appl. Energy, 137 (2015), pp. 158--172, https://doi.org/10.1016/j.apenergy.2014.09.071.
[24]
A. Sommerfeld, Mechanics of Deformable Bodies, Academic Press, 1997.

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Published In

cover image SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics  Volume 82, Issue 1
DOI:10.1137/smjmap.82.1
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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2022

Author Tags

  1. bladeless turbine
  2. fluid mechanics
  3. SETUR
  4. analytical solution
  5. numerical simulation

Author Tag

  1. 76-10

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