Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-04T19:15:00.077Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical simulation of viscous shear effects on poroussqueeze-film using the Darcy-Brinkman model

Published online by Cambridge University Press:  24 December 2010

Mohamed Nabhani ,
Mohamed El Khlifi  and
Benyebka Bou-saïd
Mohamed Nabhani*
Affiliation:
Universitéde Lyon, CNRS INSA-Lyon, LaMCoS, UMR 5259, 69621 Villeurbanne Cedex, France
Mohamed El Khlifi
Affiliation:
University Hassan II Mohammedia – Casablanca, Faculty of Sciences and Technics, BP 146, 20650 Mohammedia, Morocco
Benyebka Bou-saïd
Affiliation:
Université de Lyon, CNRS INSA-Lyon, LaMCoS, UMR 5259, 20 avenue Albert Einstein, 69621 Villeurbanne Cedex, France
*
a Corresponding author:[email protected]
Get access

Abstract

In recent decades, problems related to the squeeze of fluid films in the presence of aporous medium draw attention of researchers and are the subject of many applied studiesfor industry and biomechanics. Our concerns in this paper are the numerical simulation ofthe viscous shear stresses effects on the fluid film characteristics between two discswith one porous. This study is based on the coupling, at the fluid film-porous discinterface, of the Darcy-Brinkman equations in the porous medium and the modified Reynoldsequation describing the flow in the fluid film. The system of equations obtained isdiscretized by the means of finite differences method and solved numerically using thetechnique of Successive Over-Relaxation (SOR). The results show that the viscous sheareffects increase the radial and the axial fluid film velocities as well as the squeezefilm velocity but decrease the response time. Moreover, these effects are enlarged forsmaller viscous shear parameter and for smaller fluid film thickness.

Keywords

Porous mediumDarcy-Brinkman modelsqueeze-filmmodified Reynolds equationnumerical simulationMilieu poreuxmodèle de Darcy-Brinkmanécrasement de filméquation de Reynolds modifiéesimulation numérique
Type
Research Article
Information
Mechanics & Industry , Volume 11 , Issue 5 , September 2010 , pp. 327 - 337
Copyright
© AFM, EDP Sciences 2010

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

Références

Bujurke, N.M., Patil, H.P., An analysis of squeeze film action in porous layered bearings, Wear 145 (1991) 385–397 CrossRefGoogle Scholar
Bujurke, N.M., Kudenatti, R.B., Surface roughness effects on squeeze film poroelastic bearings, Appl. Math. Comput. 174 (2006) 1181–1195 Google Scholar
Bujurke, N.M., Salimath, C.S., Kudenatti, R.B., Shiralashetti, S.C., Wavelet-multigrid analysis of squeeze film characteristics of poroelastic bearings, J. Comput. Appl. Math. 203 (2007) 237–248 CrossRefGoogle Scholar
Bujurke, N.M., Kudenatti, R.B., Awati, V.B., Effects of roughness on squeeze film poroelastic bearings with special reference to synovial joints, Math. Biosc. 209 (2007) 76–89 CrossRefGoogle ScholarPubMed
Tandon, P.N., Misra, J.K., Gupta, R.S., Satyanand, Role of ultrafiltration of synovial fluid in lubrication of human joints, Int. J. Mech. Sci. 27 (1985) 29–37 CrossRefGoogle Scholar
Hlavacek, M., The role of synovial fluid filtration by cartilage in lubrication of synovial joints – II, Squeeze-film lubrication: homogeneous filtration, J. Biomech. 26 (1993) 1151–1160 CrossRefGoogle ScholarPubMed
Hlavacek, M., The role of synovial fluid filtration by cartilage in lubrication of synovial joints – III, Squeeze-film lubrication: axial symmetry under low loading conditions, J. Biomech. 28 (1995) 1193–1195 CrossRefGoogle ScholarPubMed
Hlavacek, M., The role of synovial fluid filtration by cartilage in lubrication of synovial joints – IV, Squeeze-film lubrication: the central film thickness for normal and inflammatory synovial fluids for axial symmetry under high loading conditions, J. Biomech. 28 (1995) 1199–1205 CrossRefGoogle ScholarPubMed
Hlavacek, M., Squeeze-film lubrication of the human ankle joint with synovial fluid filtrated by articular cartilage with the superficial zone worn out, J. Biomech. 33 (2000) 1415–1422 CrossRefGoogle ScholarPubMed
Hlavacek, M., The influence of the acetabular labrum seal intact articular superficial zone and synovial fluid thixotropy on squeeze-film lubrication of spherical synovial joint, J. Biomech. 35 (2002) 1325–1335 CrossRefGoogle ScholarPubMed
Hou, J.S., Mow, V.C., Lai, W.M., Holmes, M.H., An analysis of the squeeze-film lubrication mechanics for articular cartilage, J. Biomech. 25 (1992) 247–259 CrossRefGoogle Scholar
A.E. Scheidigger, The physics of flow through porous media, The MacMillan Co., New York, 1957
Bujurke, N.M., Jagadeeswar, M., Hiremath, P.S., Analysis of normal stress effects in a squeeze film porous bearings, Wear 116 (1987) 237–248 CrossRefGoogle Scholar
Bujurke, N.M., Jagadeeswar, M., Hiremath, P.S., Analysis of squeeze film lubrication between two rectangular porous plates with a second-order fluid, Wear 132 (1989) 303–320 CrossRefGoogle Scholar
Bujurke, N.M., Naduvinamani, N.B., A note on squeeze film between rough anisotropic porous rectangular plates, Wear 217 (1998) 225–230 CrossRefGoogle Scholar
Naduvinamani, N.B., Fathima, S.T., Hiremath, P.S., Effect of surface roughness on characteristics of couple stress squeeze film between anisotropic porous rectangular plates, Fluid Dyn. Res. 32 (2003) 217–231 CrossRefGoogle Scholar
Sinha, P., Singh, C., Prasad, K.R., Lubrication of human joints – a microcontinum approach, Wear 80 (1982) 159–181 CrossRefGoogle Scholar
Jurczak, P., Pressure distribution in a squeeze film biobearing lubrication by a synovial fluid, Int. J. Appl. Mech. Eng. 11 (2006) 857–864 Google Scholar
Zaheerduddin, K.H., Isa, M., Characteristics of a micropolar lubricant in a squeeze film porous spherical bearing, Wear 52 (1978) 1–10 CrossRefGoogle Scholar
Zaheerduddin, K.H., The dynamic behaviour of squeeze films in one-dimensional porous journal bearing lubricated by a micropolar fluid, Wear 71 (1981) 139–152 CrossRefGoogle Scholar
Naduvinamani, N.B., Hiremath, P.S., Gurubasavaraj, G., Squeeze film lubrication of short porous journal bearing with couple stress fluids, Tribol. Int. 34 (2001) 739–747 CrossRefGoogle Scholar
Naduvinamani, N.B., Patil, S.B., Numerical solution of finite modified Reynolds equation for couple stress squeeze film lubrication of porous journal bearings, Comput. Struct. 87 (2009) 1287–1295 CrossRefGoogle Scholar
Murti, P.R.K., Squeeze films in porous circular disks, Wear 23 (1973) 283–289 CrossRefGoogle Scholar
Murti, P.R.K., Squeeze-film behaviour in porous circular disks, ASME J. Lubr. Techno 96 (1974) 206–209 CrossRefGoogle Scholar
Megat Ahmad, M.M.H., Gethin, D.T., Claypole, T.C., Roylance, B.J., Numerical and experimental investigation into porous squeeze films, Tribol. Int. 31 (1998) 189–199 CrossRefGoogle Scholar
Srinvasan, U., Load capacity and time-height relationships for squeeze films between double-layered porous plates, Wear 43 (1977) 211–225 CrossRefGoogle Scholar
Beavers, G.S., Joseph, D.D., Boundary conditions on a naturally permeable wall, J. Fluid Mech. 30 (1967) 197–207 CrossRefGoogle Scholar
Brinkman, H.C., A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Appl. Sci. Res. A1 (1947) 27–34 Google Scholar
Lin, J.R., Hwang, C.C., Lubrication of short porous journal bearing – use of the Brinkman-extended Darcy model, Wear 161 (1993) 93–104 CrossRefGoogle Scholar
Lin, J.R., Optimal design of one-dimensional porous slider bearing using the Brinkman model, Trib. Int. 34 (2001) 57–64 CrossRefGoogle Scholar
Ming-Da, Chen, Kuo-Ming, Chang, Lin, J.R., Li, W.L., Lubrication of journal bearings – influence of stress jump condition at porous media/fluid film interface, Trib. Int. 35 (2002) 287–295 Google Scholar
Elsharkawy, A., Guedouar, L.H., Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model, Trib. Int. 34 (2001) 767–777 CrossRefGoogle Scholar
Lin, R.J., Viscous shear effects on the squeeze-film behaviour in porous circular disks, Int. J. Mech. Sci. 38 (1996) 373–384 CrossRefGoogle Scholar
A. Cameron, Basic Lubrication Theory, Wiley Eastern Ltd, New York, 1987
Pearson, J.R.A., Tardy, P.M.J., Models for flow of non Newtonian and complex fluids through porous media, J. Non Newtonian Fluid Mech. 102 (2002) 447–473 CrossRefGoogle Scholar
D.A. Nield, A. Bejan, Convection in porous media 2nd edition, Spring-verlag: New York, 1999
S. Liu, J.H. Masliyah, Dispersion in porous media. Handbook of Porous Media, K. Vafai (ed.), 2nd edition, Taylor and Francis, Boca, Raton, FL, 81–140, 2005
Valdes-Parada, F.J., Ochoa-Tapia, J.A., Alvarez-Ramirez, J., On the effective viscosity for the Darcy-Brinkman equation, Phys. A 385 (2007) 69–79 CrossRefGoogle Scholar
S. Whitaker, The Method of Volume Averaging, Kluwer, Dordrecht, 1999, p. 173
Liu, H., Patil, P.R., Narusawa, U., On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders, Entropy 9 (2007) 118–131 CrossRefGoogle Scholar