Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-18T01:29:23.647Z Has data issue: false hasContentIssue false
  • English
  • Français

Roughness-induced flow instability: a lattice Boltzmann study

Published online by Cambridge University Press:  05 February 2007

FATHOLLAH VARNIK ,
DOROTHÉE DORNER  and
DIERK RAABE
FATHOLLAH VARNIK
Affiliation:
Max-Planck Institut für Eisenforschung, Max-Planck Straße 1, 40237 Düsseldorf, Germany
DOROTHÉE DORNER
Affiliation:
Max-Planck Institut für Eisenforschung, Max-Planck Straße 1, 40237 Düsseldorf, Germany
DIERK RAABE
Affiliation:
Max-Planck Institut für Eisenforschung, Max-Planck Straße 1, 40237 Düsseldorf, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Effects of wall roughness/topography on flows in strongly confined (micro-)channels are studied by means of lattice Boltzmann simulations. Whereas wall roughness in macroscopic channels is considered to be relevant only for high-Reynolds-number turbulent flows (where the flow is turbulent even for smooth walls), it is shown in this paper that, in micro-channels, surface roughness may even modify qualitative features of the flow. In particular, a transition from laminar to unsteady flow is observed. It is found that this roughness-induced transition is strongly enhanced as the channel width is decreased. The reliability of our results is checked by computing the viscous shear stress and the Reynolds stress across the channel, their sum following the theoretical prediction for the stress balance perfectly. Furthermore, the solutions obtained obey the transformation rules of the Navier–Stokes equation: When expressed in reduced (dimensionless) units, results for various channel dimensions, forcing term or dynamic viscosity are identical provided that the channel shape and the Reynolds number are unchanged. The time evolution of the velocity fluctuations at the initial stages of the transition to flow instability is monitored. It is found that fluctuations first occur in the vicinity of the rough wall, supporting the interpretation of wall roughness as a source of fluctuations and thus flow instability. In addition to their physical significance, our results provide further evidence for the reliability of the lattice Boltzmann method in dealing with complex unsteady flows.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 191 - 209
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahlrichs, P. & Dünweg, B. 1999 Simulation of a single polymer chain in solution by combining lattice boltzmann with molecular dynamics. J. Chem. Phys. 111, 8225.CrossRefGoogle Scholar
Benzi, R., Biferale, L., Sbragaglia, M., Succi, S. & Toschi, F. 2006 Mesoscopic modelling of heterogeneous boundary conditions for microchannel flows. J. Fluid Mech. 548, 257.CrossRefGoogle Scholar
Benzi, R., Succi, S. & Vergassola, M. 1992 The lattice-Boltzmann equation – theory and applications. Phys. Rep. 222, 145.Google Scholar
Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S. & Yakhot, V. 2003 Extended boltzmann kinetic equation for turbulent flows. Science 301, 633.Google Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329.Google Scholar
Cornubert, R., d'Hummiières, D. & Levermore, D. 1991 A knudsen layer theory for lattice gases. Physica D 47, 241.CrossRefGoogle Scholar
Dupuis, A. & Chopard, B. 2003 Theory and applications of an alternative lattice boltzmann grid refinement algorithm. Phys. Rev. E 67, 066707.CrossRefGoogle Scholar
Filippova, O. & Hänel, D. 1998 Grid refinement for lattice bgk models. J. Comput. Phys. 147, 219.Google Scholar
Filippova, O., Succi, S., Mazzocco, F., Arrighetti, C., Bella, G. & Hänel, D. 2001 Multiscale lattice boltzmann schemes with turbulent modeling. J. Comput. Phys. 170, 812.Google Scholar
Frisch, U., Hasslacher, B. & Pomeau, Y. 1986 Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56, 1505–1508.Google Scholar
Frisch, U., d'Humiéres, D., Hasslacher, B., Lallemand, P., Pomeau, Y. & Rivet, J. P. 1987 Lattice gas hydrodynamics in two and three dimensions. Complex Systems 1, 649–707.Google Scholar
Ginzbourg, I. & d'Humières, D. 1996 Local Second-order boundary methods for lattice Boltzmann models. J. Stat. Phys. 84, 927.CrossRefGoogle Scholar
Ginzbourg, I. & d'Humières, D. 2003 Multireflection boundary conditions for lattice boltzmann models. Phys. Rev. E 68, 066614.CrossRefGoogle Scholar
Gunstensen, A. K. & Rothman, D. H. 1993 Lattice-boltzmann studies of two-phase flow through porous media. J. Geophys. Res. 98, 6431.Google Scholar
He, X. & Luo, L. S. 1997 Lattice Boltzmann model for the incompressible Navier-Stokes equation. J. Stat. Phys. 88, 927.Google Scholar
Higuera, F., Succi, S. & Benzi, R. 1989 Lattice gas dynamics with enhanced collisions. Europhys. Lett. 9, 345.Google Scholar
Krogstad, P.-A. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exps. Fluids 27, 450.Google Scholar
Ladd, A. J. C. & Verberg, R. 2001 Lattice-boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104, 1191.Google Scholar
Landau, L. D. & Lifschitz, E. M. 1991 Hydrodynamik, vol. VI. Berlin: Akademie Verlag.Google Scholar
Luo, L. S. 1997 Analytic solutions of linearized lattice boltzmann equations for simple flows. J. Stat. Phys. 88, 913.Google Scholar
Mathieu, J. & Scott, J. 2000 An Introduction to Turbulent Flow. Cambridge University Press.Google Scholar
McNamara, G. & Zanetti, G. 1988 Use of boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett. 61, 2332.Google Scholar
Mei, R., Yu, D., Shyy, W. & Luo, L.-S. 2002 Force evaluation in the lattice Boltzmann method involving curved geometry. NASA/CR-2002-211662, ICASE Rep. 2002-22.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Prandtl, L. 1925 Bericht über die entstehung der turbulenz. Z. Angew. Math. Mech. 5, 136.CrossRefGoogle Scholar
Qian, Y. H., d'Humieres, D. & Lallemand, P. 1992 Lattice bgk models for Navier-Stokes equation. Europhys. Lett. 17, 479.Google Scholar
Raabe, D. 2004 Overview of the lattice boltzmann method for nano- and microscale fluid dynamics in materials science and engineering. Modelling Simul. Mater. Sci. Engng 12, R13.Google Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1.CrossRefGoogle Scholar
Rothman, D. H. & Zaleski, S. 1997 Lattice-Gas Cellular Automata (Simple Models of Complex Hydrodynamics). Cambridge University Press.Google Scholar
Rotta, J. C. 1962 Turbulent boundary layers in incompressible flow. In Progress in Aeronautical Sciences (ed. Ferri, A., Kuchemann, D. & Sterne, L. H. G.), vol. 2, p. 1. Pergamon.Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Succi, S. 2001 The Lattice Boltzmann Equation: for Fluid Dynamics and Beyond. Series Numerical Mathematics and Scientific Computation. Oxford University Press.Google Scholar
Succi, S. 2002 Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneous catalysis. Phys. Rev. Lett. 89, 064502.Google Scholar
Succi, S., Filippova, O., Chen, H. & Orszag, S. 2002 Towards a renormalized lattice boltzmann equation for fluid turbulence. J. Stat. Phys. 107, 261.Google Scholar
Varnik, F. & Raabe, D. 2006 Scaling effects in microscale fluid flows at rough solid surfaces. Modelling Simul. Mater. Sci. Engng 14, 857.CrossRefGoogle Scholar
Wolf-Gladrow, D. A. 2000 Lattice-Gas Cellular Automata and Lattice Boltzmann Models. Springer.Google Scholar
Xi, H., Peng, G. & Chou, S.-H. 1999 Finite-volume lattice boltzmann method. Phys. Rev. E 59, 6202.Google Scholar