Flow Instability Induced by Viscosity Variation in High Pressure Two-Dimensional Laminar Flow Between Parallel Plates

Abstract

This paper presents the results of an analysis of fluid flow in high pressure hydrostatic bearings and seals which can be modeled as infinitely long, closely spaced, rigid parallel plates. The flow is laminar and at low Reynolds number. The fluid is Newtonian with a viscosity which is an exponential function of temperature and pressure. The effect of the temperature variation across the fluid film is found to be extremely significant, and limits the application of the integrated adiabatic energy equation to a narrow range of the parameters.

Slit die viscometry at shear rates up to 5 � 106s?1: An analytical correction for small viscous heating errors

“…× yes power-law analytical 2 isothermal Galili et al [13] x yes power-law analytical 3, r/(P) adiabatic and isothermal Hieber [14] x yes power-law analytical 3, t/(P) adiabatic and isothermal Gee and Lyon [15] x yes Ellis numerical 1 isothermal Duda et al [16] x yes Newtonian numerical 3, ~/(P) isothermal and adiabatic Winter [17] x × yes power-law numerical 1 isothermal and adiabatic Dihn and Armstrong [18] x no power-law analytical 1 arbitrary Langer and Werner [19] x yes Newtonian analytical 1 linear temperature Gould [20] × yes Newtonian numerical 1 isothermal and adiabatic Note: r/, 0, k denote viscosity, density, thermal conductivity of the liquid, respectively; T and P are temperature andpressure. 0(P) means that pressure dependent density was used in the analysis, etc.…”