Modeling of the viscous fluid flow around rotating circular cylinders with the lattice Boltzmann method at moderate Reynolds numbers
Keywords:
viscous fluid, rotating circular cylinder, lattice of cylinders, Boltzmann equation, Reynolds number
Abstract
In this work the task of the viscous fluid flow around both a circular cylinder which rotates with the constant speed in a plane channel and a lattice of rotating cylinders has been numerically solved by the lattice Boltzmann method. The method of setting the boundary conditions on the rotating cylinder boundary has been developed and tested. The comparison of obtained results with known numerical results obtained by other numerical methods has been made. Both stationary and periodic solutions have been investigated. The dependence of the computational grid resolution on the cylinder rotation speed for the predefined accuracy has been shown.Downloads
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References
Mazo A. B. Numerical Simulation Of a Viscous Separation Flow Around a Rotating Circular Cylinder / A. B. Mazo, I. V. Morenko // Journal of Engineering Physics and Thermophysics. – 2006. – Vol. 79, No. 3. – P. 496 – 502
Mittal S. Flow Past a Rotating Cylinder / S. Mittal, B. Kumar // J. Fluid Mech. – 2003. – Vol. 476. – P. 303-334
Калинин Е. И. Стационарные и периодические режими ламинарного обтекания вращающегося цилиндра / Е. И. Калинин, А. Б. Мазо // Ученые записки ЦАГИ. – 2011. – Т. 17, № 5. – С. 59 - 71
Succi S. The Lattice Boltzmann Equation: A New Tool For Computational Fluid-Dynamics / S. Succi, R. Benzi // Physica D: Nonlinear Phenomena. – 1991. – Vol. 47. – P. 219-230.
Куперштох А.Л. Трехмерное моделирование двухфазных систем типа жидкость-пар методом решеточных уравнений Больцмана на GPU / А.Л. Куперштох // Вычислительные методы и программирование. – 2012. – № 13. – С. 130-138.
Leclaire S. Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models / S. Leclaire, N. Pellerin, M. Reggio, J.-Y. Trepanier // International Journal of Multiphase Flow. – 2013. – Vol. 57. – P. 159-168.
Anderl D. Free surface lattice Boltzmann with enhanced bubble model / D. Anderl, S. Bogner, C. Rauh, U. Rude, A. Delgado // Computers and Mathematics with Applications. – 2014. – Vol.67, № 2. – P. 331-339.
Coupanec E. Boundary conditions for the lattoce Boltzmann method. Mass conserving boundary conditions for moving walls / E. Coupanec. – Trondheim: Norwegian University of Science and Technology. Department of Energy and Process Engineering, 2010. – 39 p.
Grazyna K.The numerical solution of the transient heat conduction problem using the lattice Boltzmann method / K. Grazyna // Scientific Research of the Institute of Mathematics and Computer Science. – 2006. – № 11. – P. 23-30.
Yu D. Viscous flow computations with the method of lattice Boltzmann equation / D. Yu, R. Mei, L. Luo, W. Shyy // Progress in Aerospace Sciences. – 2003. – V. 39. – P. 329-367
Zu Y. Q. Numerical method of lattice Boltzmann simulation for flow past a rotating circular cylinder with heat transfer / Y. Q. Zu, Y. Y. Yan // Int. J. of Num. Methods for Heat and Flud. – 2008. – V. 18, N. 6. – P. 766-782
Fallah K. Numerical simulation of flow around two rotating circular cylinders in straggered arrangement by multi-relaxation-time lattice Boltzmann method at low Reynolds number / K. Fallah, A. Fardad, N. Sedaghatizadeh, E. Fattahi, A. Ghaderi // World Applied Sciences Journal. – 2011. – 15 (4). – P. 544-554
Mussa M. Numerical Simulation of Lid-Driven Cavity Flow Using the Lattice Boltzmann Method / M. Mussa // Applied Mathematics. – 2008. – Vol. 13. – P. 236-240.
Wolf-Gladrow D. Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction / D. Wolf-Gladrow. – Bremerhaven: Alfred Wegener Institute for Polar and Marine, 2005. – 273 p.
Sucop M. Lattice Boltzmann Modeling. An Introduction for Geoscientists and Engineers / M.Sucop. – Miami: Springer, 2006. – 171 p.
Ляпин И.И. Введение в теорию кинетических уравнений: Учебное пособие / И.И. Ляпин. – Екатеринбург: УГТУ-УПИ, 2003. – 205 с.
Rettinger C. Fluid Flow Simulation using the Lattice Boltzmann Method with multiple relaxation times / C. Rettinger. – Erlander: Friedrich-Alexander Universuty Erlander-Nuremberg, 2013. – 38 p.
Mohamad A.A. Lattice Boltzmann Method. Fundamentals and Engineering Applications with Computer Codes / A.A. Mohamad. – London: Springer, 2011. – 178 p.
He X. Lattice Boltzmann Model for the Incompressible Navier – Stokes Equation / X. He // Journal of statistical physics. – 1997. – Vol.88. – P. 927–944.
Bulanchuk G. Stability investigation of the two-dimensional nine-vectors model of the lattice Boltzmann method for fluid flows in a square cavity / G. Bulanchuk, O. Bulanchuk, A. Ostapenko // Вестник Харьковского нац. унив. им. В.Н. Каразина. Серия: Математическое моделирование. Информационные технологии. Автоматизированные системы управления. –2015. – № 28. – C. 113-125.
Aslan E. Investigation of the Lattice Boltzmann SRT and MRT Stability for Lid Driven Cavity Flow / E. Aslan, I. Taymaz, A.C. Benim // International Journal of Materials, Mechanics and Manufacturing. – 2014. – Vol.2, №4. – P. 317-324.
Succi S. The Lattice Boltzmann Equation for Fluid Dinamics and Beyond / S. Succi. – Oxford: Univercity Press, 2001. – 288 p.
Latt J. Straight velocity boundaries in the lattice Boltzmann method / J. Latt, B. Chopard, O. Malaspinas, M. Deville, A. Michler // Physical Review. – 2008. – Vol. 77. – P.1-17.
Zou Q. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model / Q. Zou, X. He // Phys. Fluids. – 1997. – Vol. 9, No. 6. – P. 1591-1598
Остапенко А. А. Исследование влияния переменной скорости звука в ячейке при моделировании течения в плоском канале и обтекания кругового цилиндра потоком вязкой жидкости при расчете методом решеточных уравнений Больцмана / А. А. Остапенко, О. Н. Буланчук, Г. Г. Буланчук // Вестник Черкаского унив. Серия физ-матем. н. – 2016. – № 1. – С. 50-64
Mittal S. Flow Past a Rotating Cylinder / S. Mittal, B. Kumar // J. Fluid Mech. – 2003. – Vol. 476. – P. 303-334
Калинин Е. И. Стационарные и периодические режими ламинарного обтекания вращающегося цилиндра / Е. И. Калинин, А. Б. Мазо // Ученые записки ЦАГИ. – 2011. – Т. 17, № 5. – С. 59 - 71
Succi S. The Lattice Boltzmann Equation: A New Tool For Computational Fluid-Dynamics / S. Succi, R. Benzi // Physica D: Nonlinear Phenomena. – 1991. – Vol. 47. – P. 219-230.
Куперштох А.Л. Трехмерное моделирование двухфазных систем типа жидкость-пар методом решеточных уравнений Больцмана на GPU / А.Л. Куперштох // Вычислительные методы и программирование. – 2012. – № 13. – С. 130-138.
Leclaire S. Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models / S. Leclaire, N. Pellerin, M. Reggio, J.-Y. Trepanier // International Journal of Multiphase Flow. – 2013. – Vol. 57. – P. 159-168.
Anderl D. Free surface lattice Boltzmann with enhanced bubble model / D. Anderl, S. Bogner, C. Rauh, U. Rude, A. Delgado // Computers and Mathematics with Applications. – 2014. – Vol.67, № 2. – P. 331-339.
Coupanec E. Boundary conditions for the lattoce Boltzmann method. Mass conserving boundary conditions for moving walls / E. Coupanec. – Trondheim: Norwegian University of Science and Technology. Department of Energy and Process Engineering, 2010. – 39 p.
Grazyna K.The numerical solution of the transient heat conduction problem using the lattice Boltzmann method / K. Grazyna // Scientific Research of the Institute of Mathematics and Computer Science. – 2006. – № 11. – P. 23-30.
Yu D. Viscous flow computations with the method of lattice Boltzmann equation / D. Yu, R. Mei, L. Luo, W. Shyy // Progress in Aerospace Sciences. – 2003. – V. 39. – P. 329-367
Zu Y. Q. Numerical method of lattice Boltzmann simulation for flow past a rotating circular cylinder with heat transfer / Y. Q. Zu, Y. Y. Yan // Int. J. of Num. Methods for Heat and Flud. – 2008. – V. 18, N. 6. – P. 766-782
Fallah K. Numerical simulation of flow around two rotating circular cylinders in straggered arrangement by multi-relaxation-time lattice Boltzmann method at low Reynolds number / K. Fallah, A. Fardad, N. Sedaghatizadeh, E. Fattahi, A. Ghaderi // World Applied Sciences Journal. – 2011. – 15 (4). – P. 544-554
Mussa M. Numerical Simulation of Lid-Driven Cavity Flow Using the Lattice Boltzmann Method / M. Mussa // Applied Mathematics. – 2008. – Vol. 13. – P. 236-240.
Wolf-Gladrow D. Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction / D. Wolf-Gladrow. – Bremerhaven: Alfred Wegener Institute for Polar and Marine, 2005. – 273 p.
Sucop M. Lattice Boltzmann Modeling. An Introduction for Geoscientists and Engineers / M.Sucop. – Miami: Springer, 2006. – 171 p.
Ляпин И.И. Введение в теорию кинетических уравнений: Учебное пособие / И.И. Ляпин. – Екатеринбург: УГТУ-УПИ, 2003. – 205 с.
Rettinger C. Fluid Flow Simulation using the Lattice Boltzmann Method with multiple relaxation times / C. Rettinger. – Erlander: Friedrich-Alexander Universuty Erlander-Nuremberg, 2013. – 38 p.
Mohamad A.A. Lattice Boltzmann Method. Fundamentals and Engineering Applications with Computer Codes / A.A. Mohamad. – London: Springer, 2011. – 178 p.
He X. Lattice Boltzmann Model for the Incompressible Navier – Stokes Equation / X. He // Journal of statistical physics. – 1997. – Vol.88. – P. 927–944.
Bulanchuk G. Stability investigation of the two-dimensional nine-vectors model of the lattice Boltzmann method for fluid flows in a square cavity / G. Bulanchuk, O. Bulanchuk, A. Ostapenko // Вестник Харьковского нац. унив. им. В.Н. Каразина. Серия: Математическое моделирование. Информационные технологии. Автоматизированные системы управления. –2015. – № 28. – C. 113-125.
Aslan E. Investigation of the Lattice Boltzmann SRT and MRT Stability for Lid Driven Cavity Flow / E. Aslan, I. Taymaz, A.C. Benim // International Journal of Materials, Mechanics and Manufacturing. – 2014. – Vol.2, №4. – P. 317-324.
Succi S. The Lattice Boltzmann Equation for Fluid Dinamics and Beyond / S. Succi. – Oxford: Univercity Press, 2001. – 288 p.
Latt J. Straight velocity boundaries in the lattice Boltzmann method / J. Latt, B. Chopard, O. Malaspinas, M. Deville, A. Michler // Physical Review. – 2008. – Vol. 77. – P.1-17.
Zou Q. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model / Q. Zou, X. He // Phys. Fluids. – 1997. – Vol. 9, No. 6. – P. 1591-1598
Остапенко А. А. Исследование влияния переменной скорости звука в ячейке при моделировании течения в плоском канале и обтекания кругового цилиндра потоком вязкой жидкости при расчете методом решеточных уравнений Больцмана / А. А. Остапенко, О. Н. Буланчук, Г. Г. Буланчук // Вестник Черкаского унив. Серия физ-матем. н. – 2016. – № 1. – С. 50-64
Published
2017-12-22
How to Cite
Bulanchuk, G., & Ostapenko, A. (2017). Modeling of the viscous fluid flow around rotating circular cylinders with the lattice Boltzmann method at moderate Reynolds numbers. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 36, 27-37. Retrieved from https://periodicals.karazin.ua/mia/article/view/10086
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