Mathematical modeling and two-dimensional analysis of thermo-fluid dynamics around heated rotating cylinders with heat transfer by forced convection to low Reynolds numbers / Modelagem Matemática e Análise Bidimensional da Termofluidodinâmica em torno de Cilindros Rotativos Aquecidos com Tranferência de Calor por Convecção Forçada para Baixos Números de Reynolds

Authors

  • Rômulo Damasclin Chaves dos Santos Brazilian Journals Publicações de Periódicos, São José dos Pinhais, Paraná

DOI:

https://doi.org/10.34117/bjdv6n10-221

Keywords:

Immersed Boundary Method, Virtual Physical Model, Stationary and Heated Rotating Cylinder.

Abstract

In this present work is employed the Immersed Boundary Method coupled to Virtual Physical Model (IBM/VPM) for the two-dimensional analysis thermo-fluid dynamic and numerical simulations of incompressible flows. The heated stationary and rotating cylinders with forced convection use the Navier-Stokes equations, to know, mass conservation, momentum and energy to modeling the physical problem. The calculation of the forces exerted on the cylinder is realized using the VPM, which is based on conservation equations of linear momentum and energy. The numerical simulation of the fluid temperature at each instant of time, determined through auxiliary points distributed in Cartesian coordinates. The motivation is contributing with the computational implementation of the methodology mentioned using code developed in C++ for an experimental and numerical analysis, imposing different rates of rotation, comparing with an experimental results. Few are the studies about the thermal effects in combination with the aerodynamic coefficients and dimensionless numbers, for example, Strouhal, Nusselt, Péclet and Reynolds. The results obtained prove the efficiency of the method.

References

L. BARANYI, Computation of unsteady momentum and heat transfer from a fixed circular cylinder in laminar flow, Journal of Computational and Applied Mechanics, (4)(1) (2003), pp. 13-25.

G. B., CARVALHO, Estudo experimental do escoamento em torno de cilindros circulares em movimento de rotação, Master’s Thesis, Universidade Estadual Paulista, Brazil, 2003.

M. W. CHANG AND B. A. FINLAYSON, Heat transfer in flow past cylinder at Relet 150 – Part I. Calculations of constant fluid properties, Numer. Heat Transfer 12 (1987), pp. 179-198.

CHUAN-CHIEH LIAO AND CHAO-AN LIN, Transitions of natural convection flows in square enclosure with a heated circular cylinder, Applied Thermal Engineering, 72 (2014), pp. 41-47.

Z.-G. FENG AND E. E. MICHAELIDES, Heat transfer in particulate flows with direct numerical simulation (DNS), Int. J. Heat Mass Tran., 52(3) (2009), pp. 777-786.

D. GOLDSTEIN, R. HANDLER AND L. SIRIVICH, Modeling and no-slip flow boundary with an external force field, J. Comput. Phys., 105(2) (1993), pp. 354-366.

S. KANG, H. CHOI AND S. LEE, Laminar flow past a rotating circular cylinder, Phys. Fluids, 11 (1999), pp. 3312-3320.

J. KIM, D. KIM AND H. CHOI, An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171(1) (2002), pp. 132-150.

M.-C. LAI AND C. S. PESKIN, A immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput., 160(2) (2000), pp. 705-719.

C. LIU, X. ZHENG AND C. H. SUNG, Preconditioned multigrid methods for unsteady incompressible flows, J. Comput. Phys., (139)(1) (1998), pp. 35-57.

A. L. F. LIMA E SIILVA, Desenvolvimento e implementação de uma nova metodologia para modelagem de escoamentos sobre geometrias complexas: método da fronteira imersa com modelo físico virtual, Ph.D. Thesis, Universidade Federal de Uberlândia, Brazil, 2002.

A. L. F. LIMA E SILVA, A. SILVEIRA-NETO AND J. J. R., DAMASCENO, Numerical simulation of two-dimensional flow over a circular cylinder using the immersed boundary method, J. Comput. Phys., 189(2) (2003), pp. 351-370.

A. L. F. LIMA E SILVA, A. R. SILVA AND A. SILVEIRA-NETO, Numerical simulation of two-dimensional complex flows around bluff bodies using the immersed boundary method, J. of the Braz. Soc. of Mech. Sci. & Eng., (29) (4) (2007), pp. 379-387.

A. L. F. LIMA E SILVA AND S. M. M. SILVA, Convection heat transfer around a bank of tubes, Proc. Of the ENCIT, 14th Brazilian Congress of Thermal Sciences and Engineering, Brazil (2012).

N. MARIR AND Z. ALTAC, Numerical investigation of convective heat transfer in unsteady flow past two cylinders in tandem arrangements, Int. J. Heat Fluid Fl., (29)(5) (2008), pp. 1309-1318.

S. B. PARAMANE AND A. SHARMA, Numerical investigation of heat and fluid flow across a rotating circular cylinder maintained at constant temperature in 2-D laminar flow regime, Int. J. Heat Mass Trans., (52)(13-24) (2009), pp. 3205-3216.

C.S. PESKIN, Flow patterns around heat valves: a numerical method, J. Comput. Phys., (10)(2) (1972), pp. 252-271.

C. S. PESKIN, Numerical analysis of blood flow in the heart, J. Comput. Phys., (25)(3) (1977), pp. 220-252.

C. S. PESKIN AND D. M. McQUEEN, A general method for the computer simulation of biological systems interacting with fluids, SEB – Symposium on Biological Fluid Dynamics, Leeds, England, (1994), pp. 5-8.

H. DING, C. SHU, K. S. YEO AND D. XU, Simulation of incompressible-viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method, Comput. Method. Appl. M. (193) (2004), pp. 727-744.

J. E. S. OLIVEIRA, A. F. L. LIMA E SILVA AND A. SILVEIRA-NETO, Influência de modelos de turbulência na simulação de escoamentos sobre aerofólios móveis usando o método de fronteira imersa, IV Congresso Nacional de Engenharia Mecânica, Brasil, 2006.

G. E. SCHNEIDER AND M. ZEDAN, A modified strongly implicit procedure for the numerical solution of field problems, Numer. Heat Transfer, (4)(1) (1981), pp. 1-19.

V. SHRIVASTAVA, P. BADAMI, N. HIREMATH, V. SARAVANAN AND K.N. SEETHARAMU, Numerical investigation of heat transfer for flow around circular cylinder with triangular and rectangular wake splitter, Word Academy of Science, Engineering and Technology, (69) (2012), pp. 406-416.

T. YE, R. MITTAL, H. S. UDAYKUMAR AND W. SHYY, An accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries, J. Comput. Phys., (156)(2) (1999), 209-240.

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Published

2020-10-09

How to Cite

Santos, R. D. C. dos. (2020). Mathematical modeling and two-dimensional analysis of thermo-fluid dynamics around heated rotating cylinders with heat transfer by forced convection to low Reynolds numbers / Modelagem Matemática e Análise Bidimensional da Termofluidodinâmica em torno de Cilindros Rotativos Aquecidos com Tranferência de Calor por Convecção Forçada para Baixos Números de Reynolds. Brazilian Journal of Development, 6(10), 77103–77121. https://doi.org/10.34117/bjdv6n10-221

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