Rough-wall layer modeling using the Brinkman equation

References

• Nikuradse , J. Stromungsgesetze in Rauhen Rohren VDI Forshungsheft Ser. B 4(361) (1933) (English Translation, NACA TM1292, 1950)
   Google Scholar
• Schlichting , H. 1960 . Boundary Layer Theory, , 4th ed. , New York : McGraw Hill Book Co. .
   Google Scholar
• Laganelli , A. L. and Sontowski , J. 1982 . Prediction of skin friction with coupled roughness and blowing based on transformation functions AIAA Paper No. 82-0033
   Google Scholar
• Dvorak , F. A. 1969 . Calculation of turbulent boundary layers on rough surfaces in pressure gradient . AIAA J. , 7 ( 9 ) : 1752 – 1759 .
   Google Scholar
• Saffman , P. G. 1971 . On the boundary condition at the surface of a porous medium . Stud. Appl. Math. , 50 : 93 – 101 .
   Web of Science ®Google Scholar
• Perry , A. E. , Schofield , W. H. and Joubert , P. N. 1969 . Rough-wall turbulent boundary layers . J. Fluid Mech. , 37 ( 2 ) : 383 – 413 .
   Web of Science ®Google Scholar
• Ligrani , P. M. and Moffat , R. J. 1986 . Structure of transitionally rough and fully rough turbulent boundary layers . J. Fluid Mech. , 162 : 69 – 98 .
   Web of Science ®Google Scholar
• Poggi , D. , Porporato , A. and Ridolfi , L. 2003 . Analysis of the small-scale structure of turbulence on smooth and rough walls . Phys. Fluids , 15 ( 1 ) : 35 – 46 .
   Google Scholar
• Fang , Y. , Liou , W. W. and Xu , S. 2004 . Skin friction prediction for high-speed turbulent boundary layers with ablation . J. Spacecraft Rockets , 41 ( 5 ) : 893 – 895 .
   Google Scholar
• Liou , W. W. and Fang , Y. 2003 . Modeling of the surface roughness effects for microchannel flows AIAA Paper No. 2003-3586
   Google Scholar
• Raupach , M. R. , Antonia , R. A. and Rajagopalan , S. 1991 . Rough-wall turbulent boundary layers . Appl. Mech. Rev. , 44 ( 2 ) : 1 – 25 .
   Google Scholar
• Patel , V. C. 1998 . Perspective: Flow at high Reynolds number and over rough surface-Achilles heel of CFD . J. Fluids Eng. , 120 : 434 – 444 .
   Web of Science ®Google Scholar
• Wilcox , D. C. 1988 . Reassessment of the scale-determining equation for advanced turbulence models . AIAA J. , 26 ( 11 ) : 1299 – 1310 .
   Google Scholar
• Durbin , P. A. 2001 . Rough wall modification of two-layer k–ϵ . J. Fluids Eng. , 123 : 16 – 21 .
   Web of Science ®Google Scholar
• Chen , H. C. and Patel , V. C. 1988 . Near-wall turbulence models for complex flows including separation . AIAA J. , 26 ( 6 ) : 641 – 648 .
   Google Scholar
• Maruyama , T. 1993 . Optimization of roughness parameters for staggered arrayed cubic blocks using experimental data . J. Wind Eng. Ind. Aerodyn. 46– , 47 : 165 – 171 .
   Web of Science ®Google Scholar
• Miyake , Y. , Tsujimoto , K. and Agata , Y. 2000 . A DNS of a turbulent flow in a rough-wall channel using roughness elements model . JSME Int. J. Ser. B , 43 : 233 – 242 .
   Web of Science ®Google Scholar
• Cui , J. , Patel , V. C. and Lin , C.-L. 2003 . Prediction of turbulent flow over rough surfaces using a force filed in large eddy simulation . J. Fluids Eng. , 125 : 2 – 9 .
   Web of Science ®Google Scholar
• Lu , M. and Liou , W. 2009 . New two-equation closure for rough-wall turbulent flows using the Brinkman equation . AIAA J. , 47 ( 2 ) : 386 – 398 .
   Google Scholar
• Lu , M. and Liou , W. 2008 . Numerical study of roughness effects on a NACA0012 airfoil using a new two-equation closure of the rough wall layer modeling AIAA Paper No. 2008-4404
   Google Scholar
• Lu , M. 2008 . A new rough wall layer modeling for turbulent flows using the Brinkman equation , Ph.D. diss. MAE, Western Michigan University .
   Google Scholar
• Jiménez , J. 2004 . Turbulent flows over rough walls . Annu. Rev. Fluid Mech. , 36 : 173 – 196 .
   Web of Science ®Google Scholar
• Whitaker , S. 1999 . The Method of Volume Averaging , Dordrecht : Kluwer .
   Google Scholar
• Shukla , J. B. 1978 . A new theory of lubrication for roughness . Wear , 49 ( 1 ) : 33 – 42 .
   Google Scholar
• Tichy , J. A. 1995 . Porous media model for thin film lubrication . J. Tribol. , 117 ( 1 ) : 16 – 21 .
   Google Scholar
• Brinkman , H. C. 1948 . A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles . Appl. Sci. Res. , A1 : 27
   Google Scholar
• Koplik , J. , Levine , H. and Zee , A. 1983 . Viscosity renormalization in the Brinkman equation . Phys. Fluids , 26 ( 10 ) : 2864 – 2870 .
   Google Scholar
• Kaviany , M. 1985 . Laminar flow through a porous channel bounded by isothermal parallel plates . Int. J. Heat Mass Transf. , 28 : 851 – 858 .
   Web of Science ®Google Scholar
• Durlofsky , L. and Brady , J. F. 1987 . Analysis of the Brinkman equation as a model for flow in porous media . Phys. Fluids , 30 ( 11 ) : 3329 – 3341 .
   Google Scholar
• Renken , K. J. and Carneiro , M. J. 1992 . Effect of forced convection on enhanced film condensation within thin porous coatings . Heat Mass Transf. Porous Media , 216 : 27 – 34 .
   Google Scholar
• Goyeau , B. , Songbe , J.-P. and Gobin , D. 1996 . Numerical study of double-diffusive natural convection in a porous cavity using the Darcy-Brinkman formulation . Int. J. Heat Mass Transf. , 39 ( 7 ) : 1363 – 1378 .
   Google Scholar
• Kuznetsov , A. V. and Xiong , M. 2000 . Numerical simulation of the effect of thermal dispersion on forced convection in a circular duct partly filled with a Brinkman-Forchheimer porous medium . Int. J. Numer. Meth. Heat Fluid Flow , 10 ( 5 ) : 488 – 501 .
   Google Scholar
• Martys , N. S. 2002 . Improved approximation of the Brinkman equation using a lattice Boltzmann method . Phys. Fluids , 13 ( 6 ) : 1807 – 1810 .
   Google Scholar
• Parvazinia , M. 2006 . Finite element modelling of flow through a porous medium between two parallel plates using the Brinkman equation . Transp. Porous Media , 63 ( 1 ) : 71 – 90 .
   Google Scholar
• Beavers , G. S. and Joseph , D. D. 1967 . Boundary conditions at a naturally permeable wall . J. Fluid Mech. , 30 : 197 – 207 .
   Web of Science ®Google Scholar
• Chellaiah , S. and Viskanta , R. 1989 . Freezing of water-saturated porous media in the presence of natural convection: Experiments and analysis . J. Heat Transf. , 111 ( 2 ) : 425 – 432 .
   Google Scholar
• Kladias , N. and Prasad , V. 1991 . Experimental verification of Darcy-Brinkman-Forchheimer flow model for natural convection in porous media . J. Thermophys. Heat Transf. , 5 ( 4 ) : 560 – 576 .
   Google Scholar
• Zhong , W. H. , Currie , I. G. and James , D. F. 2006 . Creeping flow through a model fibrous porous medium . Exp. Fluids , 40 ( 1 ) : 119 – 126 .
   Google Scholar
• Scheidegger , A. E. 1974 . The Physics of Flow Through Porous Media , Toronto : University of Toronto Press .
   Google Scholar
• Pedras , M. H. J. and de Lemos , M. J. S. 2001 . Macroscopic turbulence modeling for incompressible flow through undefromable porous media . Int. J. Heat Mass Transf. , 44 ( 6 ) : 1081 – 1093 .
   Web of Science ®Google Scholar
• Breugem , W. P. 2004 . The influence of wall permeability on laminar and turbulent flows , Ph.D. diss. Technische Universiteit Delft .
   Google Scholar
• Wang , H. and Takle , E. S. 1995 . Boundary-layer flow and turbulence near porous obstacles. I. Derivation of a general equation set for a porous medium . Boundary Layer Meteorol. , 74 ( 1–2 ) : 73 – 88 .
   Google Scholar
• Antohe , B. V. and Lage , J. L. 1997 . A general two-equation macroscopic turbulence model for incompressible flow in porous media . Int. J. Heat Mass Transf. , 40 ( 3 ) : 3013 – 3024 .
   Google Scholar
• Getachew , D. , Minkowycz , W. J. and Lage , J. L. 2000 . Modified form of the k–ϵ model for turbulent flows of an incompressible fluid in porous media . Int. J. Heat Mass Transf. , 43 ( 16 ) : 2909 – 2915 .
   Web of Science ®Google Scholar
• Silva , R. A. and de Lemos , M. J. S. 2003 . Turbulent flow in a channel occupied by a porous layer considering the stress jump at the interface . Int. J. Heat Mass Transf. , 46 ( 26 ) : 5113 – 5121 .
   Google Scholar
• Pedras , M. H. J. and de Lemos , M. J. S. 2000 . On the definition of turbulent kinetic energy for flow in porous media . Int. Commun. Heat Mass Transf. , 27 ( 2 ) : 211 – 220 .
   Web of Science ®Google Scholar
• Whitaker , S. 1996 . Forchheimer equation: A theoretical development . Transp. Porous Media , 25 ( 1 ) : 27 – 61 .
   Web of Science ®Google Scholar
• Sahraoui , M. and Kavinay , M. 1992 . Slip and no-slip velocity boundary conditions at interface of porous plain media . Int. J. Heat Mass Transf. , 35 ( 4 ) : 927 – 943 .
   Web of Science ®Google Scholar
• Launder , B. E. and Sharma , B. I. 1974 . Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc . Lett. Heat Mass Transf. , 1 : 131 – 138 .
   Google Scholar
• Ochoa-Tapia , J. A. and Whitaker , S. 1995 . Momentum transfer at the boundary between a porous medium and a homogeneous fluid – I. Theoretical development . Int. J. Heat Mass Transf. , 38 ( 14 ) : 2635 – 2646 .
   Web of Science ®Google Scholar
• de Lemos , M. J. S. and Silva , R. A. 2006 . Turbulent flow over a layer of a highly permeable medium simulated with a diffusion-jump model for the interface . Int. J. Heat Mass Transf. , 49 ( 3–4 ) : 546 – 556 .
   Web of Science ®Google Scholar
• Chakroun , W. , Al-Mesri , I. and Al-Fahad , S. 2004 . Effect of surface roughness on the aerodynamic characteristics of a symmetrical airfoil . Wind Eng. , 28 ( 5 ) : 547 – 564 .
   Google Scholar
• Lu , M. and Liou , W. W. 2007 . Assessment of two low-Reynolds-number k–ϵ models in turbulent boundary layers with surface roughness . J. Spacecraft Rockets , 44 ( 6 ) : 1307 – 1316 .
   Google Scholar
• Hegna , H. A. 1981 . The numerical solution of incompressible turbulent flow over airfoils AIAA Paper No. 81-0047
   Google Scholar
• Jacobs , E. and Sherman , A. 1937 . Airfoil section characteristics as affected by variations of the Reynolds Number NACA Rep. 536
   Google Scholar