Two-phase micro- and macro-time scales in particle-laden turbulent channel flows. (English) Zbl 1345.76086
Summary: The micro- and macro-time scales in two-phase turbulent channel flows are investigated using the direct numerical simulation and the Lagrangian particle trajectory methods for the fluid- and the particle-phases, respectively. Lagrangian and Eulerian time scales of both phases are calculated using velocity correlation functions. Due to flow anisotropy, micro-time scales are not the same with the theoretical estimations in large Reynolds number (isotropic) turbulence. Lagrangian macro-time scales of particle-phase and of fluid-phase seen by particles are both dependent on particle Stokes number. The fluid-phase Lagrangian integral time scales increase with distance from the wall, longer than those time scales seen by particles. The Eulerian integral macro-time scales increase in near-wall regions but decrease in out-layer regions. The moving Eulerian time scales are also investigated and compared with Lagrangian integral time scales, and in good agreement with previous measurements and numerical
predictions. For the fluid particles the micro Eulerian time scales are longer than the Lagrangian ones in the near wall regions, while away from the walls the micro Lagrangian time scales are longer. The Lagrangian integral time scales are longer than the Eulerian ones. The results are useful for further understanding two-phase flow physics and especially for constructing accurate prediction models of inertial particle dispersion.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76F99 | Turbulence |
| 76T99 | Multiphase and multicomponent flows |
Keywords:
micro-time scale; Lagrangian integral time scale; moving Eulerian time scale; particle-laden turbulent flow; particle Stokes number; direct numerical simulation (DNS); Lagrangian trajectory methodReferences:
| [1] | Haworth, D.C., Pope, S.B.: A generalized Langevin model for turbulent flows. Physics of Fluids 29, 387–405 (1986) · Zbl 0631.76051 · doi:10.1063/1.865723 |
| [2] | Yeung, P.K., Pope, S.B.: Lagrangian statistics from direct numerical simulations of isotropic turbulence. Journal of Fluid Mechanics 207, 531–586 (1989) · doi:10.1017/S0022112089002697 |
| [3] | Bocksell, T.L.: Numerical simulation of turbulent particle diffusion. [Ph. D. Thesis], University of Illinois at Urbana-Champaign, Illinois, Urbana-Champaign (2004) |
| [4] | Wang, B.: On time scales in a particle-laden turbulent flow. AIAA paper No.2008-3840 |
| [5] | Corrsin, S.: Estimates of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence. Journal of the Atmospheric Science 20, 115–119 (1963) · doi:10.1175/1520-0469(1963)020<0115:EOTRBE>2.0.CO;2 |
| [6] | Kaneda, Y.: Lagrangian and Eulerian time correlations in turbulence. Physics of Fluids A5, 2835–2845 (1993) · Zbl 0790.76040 · doi:10.1063/1.858747 |
| [7] | Reynolds, A.M.: A Lagrangian stochastic model for heavy particle dispersion. Journal of Colloid and Interface Science 215, 85–91 (1999) · doi:10.1006/jcis.1999.6251 |
| [8] | Oesterlé, B., Zaichik, L.I.: On Lagrangian time scales and particle dispersion modeling in equilibrium turbulent shear flows. Physics of Fluids 16, 3374–3384 (2004) · Zbl 1187.76388 · doi:10.1063/1.1773844 |
| [9] | Carlier, J. Ph., Khalij, M., Oesterlé, B.: An improved model for anisotropic dispersion of small particles in turbulent shear flow. Aerosol Science and Technology 39, 196–205 (2005) · doi:10.1080/027868290921394 |
| [10] | He, G.W., Rubinstein R., Wang, L.P.: Effects of sub-gridscale modeling on time correlations in large eddy simulation. Physics of Fluids 14, 2186–2193 (2002) · Zbl 1185.76164 · doi:10.1063/1.1483877 |
| [11] | Bernard, P.S., Ashmawey, M.F., Handler, R.A.: An analysis of particle trajectories in computer-simulated turbulent channel flow. Physics of Fluids A 1, 1532–1540 (1989) · doi:10.1063/1.857330 |
| [12] | Wang, Q., Squires, K.D., Wu, X., Lagrangian statistics in turbulent channel flow. Atmospheric Environment 29, 2417–2427 (1995) · doi:10.1016/1352-2310(95)00190-A |
| [13] | Luo, J.P., Ushijima, T., Kitoh, O.: Lagrangian and Eulerian statistics from direct numerical simulation of turbulent channel flow. China Physics Letter 23, 883–886 (2006) · doi:10.1088/0256-307X/23/4/034 |
| [14] | Choi, J., Yeo, K., Lee, C.: Lagrangian statistics in turbulent channel flow. Physics of Fluids 16, 779–793 (2004) · Zbl 1186.76106 · doi:10.1063/1.1644576 |
| [15] | Zhao, X., He, G.W.: Space time correlation of fluctuating velocities in turbulent shear flows. Physical Review E 79, 046316 (2009) · doi:10.1103/PhysRevE.79.046316 |
| [16] | Luo, J.P., Ushijima, T., Kitoh, O.: Lagrangian dispersion in turbulent channel flow and its relationship to Eulerian statistics. International Journal of Heat and Fluid Flow 28, 871–881 (2007) · doi:10.1016/j.ijheatfluidflow.2007.02.008 |
| [17] | Jin, G.D., He, G.W., Wang, L.P., et al.: Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence. International Journal of Multiphase Flow 36, 432–437 (2010) · doi:10.1016/j.ijmultiphaseflow.2009.12.005 |
| [18] | Jin, G.D., He, G.W., Wang, L.P.: Large eddy simulation of turbulent collision of heavy particles in isotropic turbulence. Physics of Fluids 22, 055106 (2010) · Zbl 1190.76056 · doi:10.1063/1.3425627 |
| [19] | Rouson, D.W.I., Eaton, J.K.: Direct numerical simulation of turbulent channel flow with immersed particles. Proceedings of Numerical Methods in Multiphase Flows, ASME FED-Vol. 185, 47–57 (1994) |
| [20] | Rouson, D.W.I, Eaton, J.K.: Direct numerical simulation of particles interacting with a turbulent channel flow. In: Sommerfeld, M. ed. Proceedings of the 7th Workshop on Two-phase Flow Predictions, Erlangen, Germany (1994) |
| [21] | Wang, Q., Squires, K.D.: Large eddy simulation of particleladen turbulent channel flow. Physics of Fluids 8, 1207–1223 (1996) · Zbl 1086.76032 · doi:10.1063/1.868911 |
| [22] | Yamamoto, Y., Potthoff, M., Tanaka, T., et al.: Large eddy simulation of turbulent gas-solid flow in a vertical channel: effect of considering inter-particle collisions. Journal of Fluid Mechanics 442, 303–334 (2001) · Zbl 1004.76513 · doi:10.1017/S0022112001005092 |
| [23] | Wu, X., Squires, K.D., Wang, Q.: Extension of the fractional step method to general curvilinear coordinate systems. Numerical Heat Transfer. B-Fundamental 27, 175–194 (1995) · doi:10.1080/10407799508914952 |
| [24] | Orlandi, P.: Fluid Flow Phenomena. Kluwer Academic Publishers, the Netherlands, 188–196 (2000) |
| [25] | Schiller, L., Nauman, A.Z.: A drag coefficient correlation. Ver. Dtsh. Ing. 77, 318–320 (1933) |
| [26] | Fukagata, K.: Numerical analyses on dispersed gas-particle two-phase turbulent flows. [Ph. D. Thesis], The University of Tokyo (2000) |
| [27] | Mito, Y., Hanratty, T.J.: Use of a modified Langevin equation to describe turbulent dispersion of fluid particle in a channel flow. Flow, Turbulence and Combustion 68, 1–26 (2002) · Zbl 1094.76527 · doi:10.1023/A:1015614823809 |
| [28] | Anfossi, D., Rizza U., Mangia, C., et al.: Estimation of the ratio between the Lagrangian and Eulerian time scales in an atmospheric boundary layer generated by large eddy simulation. Atmospheric Environment 40, 326–337 (2006) · doi:10.1016/j.atmosenv.2005.09.041 |
| [29] | Rambaud, P., Oesterlé, B., Tanière, A.: Assessment of integral time scales in a gas-solid channel flow with relevance to particle dispersion modeling. In: Sommerfeld. M. ed. Proc. 10th Workshop on Two-phase Flow Predictions, Mersburg. Germany: Martin-Luther-universitaet, 182–194 (2002) |
| [30] | Wang, L.P., Stock, D.E.: Dispersion of heavy particles by turbulent motion. Journal of Atmospheric Science 50, 1897–1913 (1993) · doi:10.1175/1520-0469(1993)050<1897:DOHPBT>2.0.CO;2 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
