A Modified Turbulence Model for Low Reynolds Numbers: Application to Hydrostatic Seals

A modification of the Elrod and Ng turbulence model is presented. The order of magnitude of the Reynolds number in thin lubricant films varies between 102 and 105. For Reynolds numbers higher than 103, the fluid flow becomes turbulent. It is well accepted in lubrication to use a zero-equation turbulence model of the type developed by Constantinescu (1962, ASME J. Basic Eng., 84(1), pp. 139–151), Ng (1964, ASLE Trans., 7, pp. 311–321), Ng and Pan (1965, ASME J. Basic Eng., 87, pp. 675–688), Elrod and Ng (1967, ASME J. Lubr. Technol., 89, pp. 346–362), or Hirs (1973, ASME J. Lubr. Technol., 95, pp. 137–146). The Elrod and Ng approach is certainly the most efficient for combined pressure and shear flows where the Reynolds number is above 104. This paper proposes a modification of the Elrod and Ng model in order to ensure a good correlation with experimental data obtained with low Reynolds number turbulent flows. The present model, coupled with a scaling factor for taking into account the transition to turbulence, is therefore accurate for all of the typical Reynolds number values recorded in lubrication. The model is then applied to hydrostatic noncontacting face seals, which usually operate at Reynolds numbers varying from 103 to 104. The accuracy of the model is shown for this particular application of radial rotating flow. A special study is made of the transition to turbulence. The results are compared with those obtained using the initial Elrod and Ng model. The axial stiffness coefficient and the stability threshold are significantly affected by the turbulence model.