Lattice Boltzmann Method for Turbulent Heat Transfer in Wavy Channel Flows
The hydrodynamic and thermal lattice Boltzmann
methods are applied to investigate the turbulent convective heat
transfer in the wavy channel flows. In this study, the turbulent
phenomena are modeling by large-eddy simulations with the
Smagorinsky model. As a benchmark, the laminar and turbulent
backward-facing step flows are simulated first. The results give good
agreement with other numerical and experimental data. For wavy
channel flows, the distribution of Nusselt number and the skin-friction
coefficients are calculated to evaluate the heat transfer effect and the
drag force. It indicates that the vortices at the trough would affect the
magnitude of drag and weaken the heat convection effects on the wavy
surface. In turbulent cases, if the amplitude of the wavy boundary is
large enough, the secondary vortices would be generated at troughs
and contribute to the heat convection. Finally, the effects of different
Re on the turbulent transport phenomena are discussed.
<p>[1] G. R. McNamara and G. Zanetti, “Use of the Boltzmann equation to
simulate lattice-gas automata,” Phys. Rev. Lett., vol. 61, pp. 2332–2335,
1988.
[2] J. Zhang, “Lattice Boltzmann method for microfluidics: models and
applications,” Microfluid. Nanofluid., vol. 10, pp. 1–28, 2011.
[3] D. Grunau, S. Chen and K. Eggert, “A lattice Boltzmann model for
multiphase fluid flows,” Phys. Fluids, vol. 5, pp. 2557–2562, 1993.
[4] C. K. Chen, S. C. Chang, and S. Y. Sun, “Lattice Boltzmann method
simulation of channel flow with square pillars inside by the field synergy
principle,” CMES-Comp. Model. Eng. Sci., vol. 22, pp. 203–215, 2007.
[5] Z. Guo and T. S. Zhao, “Lattice Boltzmann model for incompressible
flows through porous media,” Phys. Rev. E, vol. 66, p. 036304, 2002.
[6] S. C. Chang, Y. S. Hsu, and Chen CL, “Lattice Boltzmann simulation of
fluid flows with fractal geometry: An unknown-index algorithm,” J. Chin.
Soc. Mech. Eng., vol. 32, pp. 523–531, 2011.
[7] P. L. Bhatnagar, E. P. Gross, and M. Krook, “A model for collision
processes in gases. I. Small amplitude processes in charged and neutral
one-component systems,” Phys. Rev., vol. 94, pp. 511–521, 1954.
[8] S. Chen and GD Doolen, “Lattice Boltzmann model for fluid flows,”
Annu. Rev. Fluid Mech., vol. 30, pp. 329–364, 1998.
[9] H. Chen, S. Kandasamy, S. Orszag, R. Shock, S. Succi, and V. Yakhot,
“Extended Boltzmann kinetic equation for turbulent flows,” Science, vol.
301, pp. 633–636, 2003.
[10] J. W. Deardoff, “The use of subgrid transport equations in a
three-dimensional model of atmospheric turbulence,” J. Fluids
Eng.-Trans. ASME, vol. 95, pp. 429–438, 1973.
[11] W. W. Kim, S. Menon, and H. C. Mongia, “Large eddy simulation of a
gas turbine combustor flow,” Combust. Sci. Technol., vol. 143, pp. 25–62,
1999.
[12] X. Zhou, K. H. Luo, and J. J. R. Williams, “Study of density effects in
turbulent buoyant jets using large-eddy simulation,” Theor. Comput.
Fluid Dyn., vol. 15, pp. 95–120, 2001.
[13] G. Yu, E. J. Avital, and J. J. R. William, “Large eddy simulation of flow
past free surface piercing circular cylinders,” J. Fluids Eng.-Trans. ASME,
vol. 130, p. 101304, 2008.
[14] S. M. Hashemian, M. Rahnama, and M. Farhadi, “Large eddy simulation
of turbulent heat transfer in a channel with a square cylinder,” Heat
Transf. Eng., vol. 33, pp. 1052–1062, 2012.
[15] J. S. Smagorinsky, “General circulation experiments with the primitive
equations─ I. The basic experiment,” Mon. Weather Rev., vol. 91, pp.
99–164, 1963.
[16] S. Hou, J. Sterling, S. Chen, and G. D. Doolen, “A lattice Boltzmann
subgrid model for high Reynolds number flows,” In Pattern Formation
and Lattice Gas Automata, A. T. Lawniczak and R. Kapral, Ed. Fields
Institute Communications American Mathematical Society, 1996, pp.
151–166.
[17] S. Chen, “A large-eddy-based lattice Boltzmann model for turbulent flow
simulation,” Appl. Math. Comput., vol. 215, pp. 591–598, 2009.
[18] H. Guan and C. Wu, “Large-eddy simulations of turbulent flows with
lattice Boltzmann dynamics and dynamical system sub-grid models,” Sci.
China Ser. E-Technol. Sci., vol. 52, pp. 670–679, 2009.
[19] T. A. Rush, T. A. Newell, and A. M. Jacobi, “An experimental study of
flow and heat transfer in sinusoidal wavy passages,” Int. J. Heat Mass
Transf., vol. 42, pp. 1541–1553, 1999.
[20] C. C. Wang and C. K. Chen, “Forced convection in a wavy-wall channel,”
Int. J. Heat Mass Transf., vol. 45, pp. 2587–2595, 2002.
[21] E. M. Alawadhi, “Forced convection flow in a wavy channel with a
linearly increasing waviness at the entrance region,” J. Heat
Transf.-Trans. ASME, vol. 131, p. 011703, 2009.
[22] B. F. Armaly, F. Durst, J. C. F. Pereira, and B. T. Schonung,
“Experimental and theoretical investigation of backward-facing step
flow,” J. Fluid Mech., vol. 127, pp. 473–496, 1983.
[23] E. Erturk, “Numerical solutions of 2-D steady incompressible flow over a
backward-facing step. Part I: High Reynolds number solutions,” Comput.
Fluids, vol. 37, pp. 633–655, 2008.
[24] K. Ma, W. L. Wei, L. L. Wang, X. J. Zhao, “Large eddy numerical
simulation of flows over a backward-facing step,” International
Symposium on Water Resource and Environmental Protection, vol. 4, pp.
3024–3026, 2011.
[25] L. Jongebloed, “Numerical study using FLUENT of the separation and
reattachment points for backwards-facing step flow,” Master's thesis in
mechanical engineering, Rensselaer Polytechnic Institute, 2008.
[26] Y. H. Qian, D. d’Humiéres, P. Lallemand, “Lattice BGK models for
Navier-Stokes equation,” Europhys. Lett., vol. 17, pp. 479–484, 1992.
[27] X. Shan, “Simulation of Rayleigh-Bénard convection using a lattice
Boltzmann method,” Phys. Rev. E, vol. 55, pp. 2780–2788, 1997.
[28] X. Shan and H. Chen, “Lattice Boltzmann model for simulating flows
with multiple phases and components,” Phys. Rev. E, vol. 47, pp.
1815–1819, 1993.
[29] D. P. Ziegler, “Boundary conditions for lattice Boltzmann simulation,” J.
Stat. Phys., vol. 71, pp. 1171–1177, 1993.</p>
<p>[1] G. R. McNamara and G. Zanetti, “Use of the Boltzmann equation to
simulate lattice-gas automata,” Phys. Rev. Lett., vol. 61, pp. 2332–2335,
1988.
[2] J. Zhang, “Lattice Boltzmann method for microfluidics: models and
applications,” Microfluid. Nanofluid., vol. 10, pp. 1–28, 2011.
[3] D. Grunau, S. Chen and K. Eggert, “A lattice Boltzmann model for
multiphase fluid flows,” Phys. Fluids, vol. 5, pp. 2557–2562, 1993.
[4] C. K. Chen, S. C. Chang, and S. Y. Sun, “Lattice Boltzmann method
simulation of channel flow with square pillars inside by the field synergy
principle,” CMES-Comp. Model. Eng. Sci., vol. 22, pp. 203–215, 2007.
[5] Z. Guo and T. S. Zhao, “Lattice Boltzmann model for incompressible
flows through porous media,” Phys. Rev. E, vol. 66, p. 036304, 2002.
[6] S. C. Chang, Y. S. Hsu, and Chen CL, “Lattice Boltzmann simulation of
fluid flows with fractal geometry: An unknown-index algorithm,” J. Chin.
Soc. Mech. Eng., vol. 32, pp. 523–531, 2011.
[7] P. L. Bhatnagar, E. P. Gross, and M. Krook, “A model for collision
processes in gases. I. Small amplitude processes in charged and neutral
one-component systems,” Phys. Rev., vol. 94, pp. 511–521, 1954.
[8] S. Chen and GD Doolen, “Lattice Boltzmann model for fluid flows,”
Annu. Rev. Fluid Mech., vol. 30, pp. 329–364, 1998.
[9] H. Chen, S. Kandasamy, S. Orszag, R. Shock, S. Succi, and V. Yakhot,
“Extended Boltzmann kinetic equation for turbulent flows,” Science, vol.
301, pp. 633–636, 2003.
[10] J. W. Deardoff, “The use of subgrid transport equations in a
three-dimensional model of atmospheric turbulence,” J. Fluids
Eng.-Trans. ASME, vol. 95, pp. 429–438, 1973.
[11] W. W. Kim, S. Menon, and H. C. Mongia, “Large eddy simulation of a
gas turbine combustor flow,” Combust. Sci. Technol., vol. 143, pp. 25–62,
1999.
[12] X. Zhou, K. H. Luo, and J. J. R. Williams, “Study of density effects in
turbulent buoyant jets using large-eddy simulation,” Theor. Comput.
Fluid Dyn., vol. 15, pp. 95–120, 2001.
[13] G. Yu, E. J. Avital, and J. J. R. William, “Large eddy simulation of flow
past free surface piercing circular cylinders,” J. Fluids Eng.-Trans. ASME,
vol. 130, p. 101304, 2008.
[14] S. M. Hashemian, M. Rahnama, and M. Farhadi, “Large eddy simulation
of turbulent heat transfer in a channel with a square cylinder,” Heat
Transf. Eng., vol. 33, pp. 1052–1062, 2012.
[15] J. S. Smagorinsky, “General circulation experiments with the primitive
equations─ I. The basic experiment,” Mon. Weather Rev., vol. 91, pp.
99–164, 1963.
[16] S. Hou, J. Sterling, S. Chen, and G. D. Doolen, “A lattice Boltzmann
subgrid model for high Reynolds number flows,” In Pattern Formation
and Lattice Gas Automata, A. T. Lawniczak and R. Kapral, Ed. Fields
Institute Communications American Mathematical Society, 1996, pp.
151–166.
[17] S. Chen, “A large-eddy-based lattice Boltzmann model for turbulent flow
simulation,” Appl. Math. Comput., vol. 215, pp. 591–598, 2009.
[18] H. Guan and C. Wu, “Large-eddy simulations of turbulent flows with
lattice Boltzmann dynamics and dynamical system sub-grid models,” Sci.
China Ser. E-Technol. Sci., vol. 52, pp. 670–679, 2009.
[19] T. A. Rush, T. A. Newell, and A. M. Jacobi, “An experimental study of
flow and heat transfer in sinusoidal wavy passages,” Int. J. Heat Mass
Transf., vol. 42, pp. 1541–1553, 1999.
[20] C. C. Wang and C. K. Chen, “Forced convection in a wavy-wall channel,”
Int. J. Heat Mass Transf., vol. 45, pp. 2587–2595, 2002.
[21] E. M. Alawadhi, “Forced convection flow in a wavy channel with a
linearly increasing waviness at the entrance region,” J. Heat
Transf.-Trans. ASME, vol. 131, p. 011703, 2009.
[22] B. F. Armaly, F. Durst, J. C. F. Pereira, and B. T. Schonung,
“Experimental and theoretical investigation of backward-facing step
flow,” J. Fluid Mech., vol. 127, pp. 473–496, 1983.
[23] E. Erturk, “Numerical solutions of 2-D steady incompressible flow over a
backward-facing step. Part I: High Reynolds number solutions,” Comput.
Fluids, vol. 37, pp. 633–655, 2008.
[24] K. Ma, W. L. Wei, L. L. Wang, X. J. Zhao, “Large eddy numerical
simulation of flows over a backward-facing step,” International
Symposium on Water Resource and Environmental Protection, vol. 4, pp.
3024–3026, 2011.
[25] L. Jongebloed, “Numerical study using FLUENT of the separation and
reattachment points for backwards-facing step flow,” Master's thesis in
mechanical engineering, Rensselaer Polytechnic Institute, 2008.
[26] Y. H. Qian, D. d’Humiéres, P. Lallemand, “Lattice BGK models for
Navier-Stokes equation,” Europhys. Lett., vol. 17, pp. 479–484, 1992.
[27] X. Shan, “Simulation of Rayleigh-Bénard convection using a lattice
Boltzmann method,” Phys. Rev. E, vol. 55, pp. 2780–2788, 1997.
[28] X. Shan and H. Chen, “Lattice Boltzmann model for simulating flows
with multiple phases and components,” Phys. Rev. E, vol. 47, pp.
1815–1819, 1993.
[29] D. P. Ziegler, “Boundary conditions for lattice Boltzmann simulation,” J.
Stat. Phys., vol. 71, pp. 1171–1177, 1993.</p>
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:55124", author = "H.Y. Lai and S. C. Chang and W. L. Chen", title = "Lattice Boltzmann Method for Turbulent Heat Transfer in Wavy Channel Flows", abstract = "The hydrodynamic and thermal lattice Boltzmann
methods are applied to investigate the turbulent convective heat
transfer in the wavy channel flows. In this study, the turbulent
phenomena are modeling by large-eddy simulations with the
Smagorinsky model. As a benchmark, the laminar and turbulent
backward-facing step flows are simulated first. The results give good
agreement with other numerical and experimental data. For wavy
channel flows, the distribution of Nusselt number and the skin-friction
coefficients are calculated to evaluate the heat transfer effect and the
drag force. It indicates that the vortices at the trough would affect the
magnitude of drag and weaken the heat convection effects on the wavy
surface. In turbulent cases, if the amplitude of the wavy boundary is
large enough, the secondary vortices would be generated at troughs
and contribute to the heat convection. Finally, the effects of different
Re on the turbulent transport phenomena are discussed.
", keywords = "Heat transfer, lattice Boltzmann method, turbulence,
wavy channel.", volume = "7", number = "7", pages = "1492-7", }
