Immersed Boundary–Thermal Lattice Boltzmann Method with Sharp Interface: Heat Transfer of Non-Newtonian Fluid over a Cylinder

Document Type : Research Article

Authors

Abstract

In the current study, the problem of heat transfer in non-Newtonian fluid flow over a cylinder has been simulated using the Immersed Boundary – thermal lattice Boltzmann method and direct forcing algorithm. The sharp interface scheme isused to transfer the values of velocity and temperature between the fluid Eulerian and boundary Lagrangian nodes. In order to consider the effects of both discrete grid and boundary forces (thermal forces), the split-forcing lattice Boltzmann method is developed for non-Newtonian power-law fluids. A simple technique for calculating the Nusselt number based on the sharp immersed boundary method is extracted. Heat transfer of different fluid regimes consist of steady and unsteady flow in wide ranges of Reynolds numbers (20<Re<80) and power-law indices (0.6<n<1.4) has been investigated. It is found that the increment of the shear-thinning and shear-thickening behavior of the fluid leads to an increase and decrease of heat transfer rate of immersed body, respectively. In future studies, the proposed algorithm will be used as a suitable method for thermal modeling of moving bodies in non-Newtonian fluids.

Keywords

References

[1] Clift, R., Grace, J., Weber, M.E., “Bubbles, Drops and Particles”, New York: Academic Press, 1978.
[2] Coutanceau, M., Defaye, J.R., “Circular cylinder wake configuration: a flow visualization survey”, Applied Mechanics Reviews, vol. 44, pp. 255–305, 1991.
[3] Williamson, C.H.K., “Vortex dynamics in the cylinder wake”, Annual Review of Fluid
Mechanics, vol. 28, pp. 477–539, 1996.
[4] Sasmal, C., Chhabra, R.P., “Laminar natural convection from a heated square cylinder immersed in power-law liquids”, J. Non-Newtonian Fluid Mech., vol. 166, pp. 811–830, 2011.
[5] Gupta, R.K., “Polymer and Composites Rheology”, second ed., New York: Marcel Dekker, 2000.
[6] Sivakumar, P., Bharti, R.P., Chhabra, R.P., “Effect of power-lawindex on critical parameters for power-law flow across an unconfined circular cylinder”, Chem. Eng. Sci., vol. 61, pp. 6035 – 6046, 2006.
[7] Chhabra, R.P., “Bubbles, Drops and Particles in Non-Newtonian Fluids”, second ed., CRC Press, Boca Raton, FL, 2006.
[8] Patnana, V.K., Bharti, R.P., Chhabra, R.P., “Two-dimensional unsteady forced convection heat transfer in power-law fluids from a cylinder”, International Journal of Heat and Mass Transfer, vol. 53, pp. 4152–4167, 2010.
[9] Bharti, R.P., Sivakumar, P., Chhabra, R.P., “Forced convection heat transfer from an elliptical cylinder to power-law fluids”, Int. J. Heat Mass Transfer, vol. 51, pp. 1838–1853, 2008.
[10] Bharti, R.P., Chhabra, R.P., Eswaran, V., “Steady forced convection heat transfer from a heated circular cylinder to power-law fluids”, Int. J. Heat Mass Transfer, vol. 50, pp. 977–990, 2007.
[11] Soares, A.A., Ferreira, J.M., Chhabra, R.P., “Flow and forced convection heat transfer in cross flow of non-Newtonian fluids over a circular cylinder”, Ind. Eng. Chem. Res., vol. 44, pp. 5815–5827, 2005.
[12] Peskin, C.S., “Flow patterns around heart valves: a digital computermethod for solving the equations of motion”, PhD thesis, Physiol, Albert Einstein Coll. Med., Univ. Mi- crofilms. Vol. 378, 1972.
[13] Kim, J., Kim, D., Choi, H., “An immersed-boundary finite-volume method for simulations of flow in complex geometries”, J. Comput. phys., vol. 171, pp. 132–150, 2001.
[14] Artoli, A.M., Sequeira, A., “Mesoscopic simulations of unsteady shear-thinning flows”, in: Lecture Notes in Comput. Sci., Berlin: Springer,pp. 78–85, 2006.
[15] Gabbanelli, S., Drazer, G., Koplik, J., “Lattice Boltzmann method for non-Newtonian (Power-Law) fluids”, Phys. Rev. E., vol. 72, pp. 046312, 2005.
[16] Aharonov, E., Rothman, D.H., “Non-Newtonian flow (through porous-media): a lattice Boltzmann method”, Geophys. Res. Lett., vol. 20, pp. 679, 1993.
[17] Chen, Y.L., Cao, X.D., Zhu, K.Q., “A gray lattice Boltzmann model for Power-Law fluid and its application in the study of slip velocity at porous interface”, J. Non-Newtonian Fluid Mech., vol. 159, pp. 130–136, 2009.
[18] Boek, E.S., Chin, J., Coveney, P.V., “Lattice Boltzmann simulation of the flow of non-Newtonian fluids in porous media”, Int. J. Mod. Phys. B., vol. 17, pp. 99–102, 2003.
[19] Kang, S.K., Hassan, Y.A., “A comparative study of direct-forcing immersed boundary-lattice Boltzmann methods for stationary complex boundaries”, Int. J. Numer. Meth. Fluids., vol. 66, pp. 1132–1158, 2011.
[20] Wu, J., Shu, C., “Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications”, Journal of Computational Physics, vol. 228, pp. 1963–1979, 2009.
[21] Kang, S.K., Hassan, Y.A., “A direct-forcing immersed boundary method for the thermal lattice Boltzmann method”, Computers & Fluids, vol. 49, pp. 36–45, 2011.
[22] Wu, J., Shu, C., Zhao, N., “Simulation of Thermal Flow Problems via a Hybrid Immersed Boundary-Lattice Boltzmann Method”, Journal of Applied Mathematics, Article ID 161484, 2012.
[23] Guo, Z., Zheng, C., Shi, B., “Discrete lattice effects on the forcing term in the lattice Boltzmann method”, Physical Review E., vol. 65, pp. 046308, 2002.
[24] Wang, C.H., Ho, J.R., “A lattice Boltzmann approach for the non-Newtonian effect in the blood flow”, Comput. Math. Appl., vol. 62, pp. 75–86, 2011.
[25] Nejat, A., Abdollahi, V., Vahidkhah, K., “Lattice Boltzmann simulation of non-Newtonian flows past confined cylinders”, J. Non-Newtonian Fluid
Mech., vol. 166, pp. 689-697, 2011.
[26] Feng, Z.G., Michaelides, E.E., “Proteus: a direct forcing method in the simulation of particulate flows”, J. Comput. Phys., vol. 202, pp. 20–51, 2005.
[27] Sui, Y., Chew, Y.T., Roy, P., Low, H.T., “A hybrid immersed-boundary and multi-block lattice Boltzmann method for simulating fluid and moving-boundaries interactions”, Int. J. Numerical Methods in Fluids, vol. 53, pp. 1727–1754, .2007.
[28] Wang, C-H, Ho, J-R., “A lattice Boltzmann approach for the non-Newtonian effect in the blood flow”, Computers and Mathematics with Applications, vol. 62, pp. 75–86, 2011.
[29] Chandra, A., Chhabra, R.P., “Flow over and forced convection heat transfer in Newtonian fluids from a semi-circular cylinder”, International Journal of Heat and Mass Transfer, vol. 54, pp. 225–241, 2011.

Files

Share

How to cite

Statistics