## THERMAL SCIENCE

International Scientific Journal

### MULTI-RELAXATION-TIME LATTICE BOLTZMAN MODEL FOR UNIFORM-SHEAR FLOW OVER A ROTATING CIRCULAR CYLINDER

**ABSTRACT**

A numerical investigation of the two-dimensional laminar flow and heat transfer a rotating circular cylinder with uniform planar shear, where the free-stream velocity varies linearly across the cylinder using Multi-Relaxation-Time Lattice Boltzmann method is conducted. The effects of variation of Reynolds number, rotational speed ratio at shear rate 0.1, blockage ratio 0.1 and Prandtl number 0.71 are studied. The Reynolds number changing from 50 to 160 for three rotational speed ratios of 0, 0.5, 1 is investigated. Results show that flow and heat transfer depends significantly on the rotational speed ratio as well as the Reynolds number. The effect of Reynolds number on the vortex-shedding frequency and period-surface Nusselt numbers is overall very strong compared with rotational speed ratio. Flow and heat conditions characteristics such as lift and drag coefficients, Strouhal number and Nusselt numbers are studied.

**KEYWORDS**

PAPER SUBMITTED: 2010-08-27

PAPER REVISED: 2010-11-18

PAPER ACCEPTED: 2010-10-27

**THERMAL SCIENCE** YEAR

**2011**, VOLUME

**15**, ISSUE

**Issue 3**, PAGES [859 - 878]

- Bearman, P. W., Wadcock A. J., The interaction between a pair of circular cylinder normal to a stream, J. Fluid Mech., 61 (1973), pp. 499-511
- Triyogi, Y., Suprayogi, D., Spirda, E., Reducing the drag on a circular cylinder by upstream installation of an I-type bluff body as passive control, Proc. IMechE, Part C: J. Mechanical Engineering Science, 223 (2009), 10, pp. 2291-2296
- Nair, M. T., Sengupta, T. K., Chauhan, U. S., Flow past rotating cylinders at high Reynolds numbers using higher order upwind scheme, Comput. Fluids, 27 (1998), 1, pp. 47-70
- Marchesse, Y., Changenet, C., Forced convective heat transfer over a non-circular slender cylinder, Proc. IMechE, Part C: J. Mechanical Engineering Science , 223 (2009), 2, pp. 427-437
- Kim, H. J., Durbin, P. A., Investigation of the flow between a pair of circular cylinders in the flopping regime, J. Fluid Mech., 196 (1988), pp. 431-48
- Coutanceau, M., Menard, C., Influence of rotation on the near-wake development behind an impulsively started circular cylinder, J. Fluid Mech., 158 (1985), pp. 399-466
- Sumner, D., Wong, S. S.T., Price, S. J., Paidoussis, M. P., Fluid behavior of side-by-side circular cylinders in steady cross-flow, J. Fluids Struct., 13 (1999), pp. 309-338
- Adachi, T., Kato, E., Study on the flow about a circular cylinder in shear flow, Trans. Jpn. Soc. Aeronaut. Space., 256 (1975), pp. 45-53
- Kiya, M., Tamura, H., Arie, M., Vortex shedding from a circular cylinder in moderate-Reynoldsnumber shear flow, J. Fluid Mech., 141 (1980), pp. 721-735
- Hayashi, T., Yoshino, F., On the evaluation of the aerodynamic forces acting on a circular cylinder in a uniform shear flow, Trans. Jpn. Soc. Mech. Eng., 56 (1990), 552, pp. 31-36
- Kwon, T. S., Sung, H. J., Hyun, J. M., Experimental investigation of uniform shear flow past a circular cylinder, ASME J. Fluids Eng., 114 (1992), pp. 457-460
- Sumner, D., Akosile, O. O., On uniform planar shear flow around a circular cylinder at subcritical Reynolds number, J. Fluids Struct., 13 (2003), pp. 309-338
- Tamura, H., Kiya, M., Arie, M., Numerical simulation of the shear flow past a circular cylinder, Trans. Jpn. Soc. Mech. Eng., 46 (1980), 404, pp. 555-564
- Lei, C., Cheng, L., Kavanagh, K., A finite difference solution of the shear flow over a circular cylinder, Ocean Eng., 27 (2000), pp. 271-290
- Sohankar, A., Norberg, C., Davidson, L., Simulation of three-dimensional flow around a square cylinder at moderate Reynolds number, Phys. Fluids, 11 (1999), pp. 288-306
- Jordan, S. K., Fromm, J. E., Laminar flow past a circle in a shear flow, Phys. Fluids, 15 (1972), pp. 972-976
- Delavar, M. A., Farhadi, M., Sedighi, K., Effect of the Heater Location on Heat Transfer and Entropy Generation in the Cavity Using the Lattice Boltzmann Method, Heat Trans Res., 40 (2009), pp. 505-519
- Djebali, R., Ganaoui, M. E., Sammouda, H., Bennacer, R., Some benchmarks of a side wall heated cavity using lattice Boltzmann approach, FDMP, 5 (2009), 3, pp. 261-282
- Ganaoui, M. E., Semma, E. A., A lattice Boltzmann coupled to finite volumes method for solving phase change problems, Thermal science, 13 (2009), 2, pp. 205-216
- Semma,E. A, Ganaoui, M. E., Bennacer, R., Mohamad, A.A., Investigation of flows in solidification by using the lattice Boltzmann method, Int. J. of Thermal Sciences, 47 (2008), 3, pp. 201-208
- Semma,E. A, Ganaoui, M. E., Bennacer, Lattice Boltzmann method for melting/solidification problems, Comptes Rendus M