Efficient numerical method for computation of thermohydrodynamics of laminar lubricating films

The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. The procedure presented here is a sequel to one presented in Leeds in 1986 that was carried out for the one-dimensional case. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. The extent of computation required makes economy in numerical processing of utmost importance. In pursuit of such economy, we here use techniques similar to those for Gaussian quadrature. We show that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes well the transverse temperature distribution

Numerical experiments with flows of elongated granules

Theory and numerical results are given for a program simulating two dimensional granular flow (1) between two infinite, counter-moving, parallel, roughened walls, and (2) for an infinitely wide slider. Each granule is simulated by a central repulsive force field ratcheted with force restitution factor to introduce dissipation. Transmission of angular momentum between particles occurs via Coulomb friction. The effect of granular hardness is explored. Gaps from 7 to 28 particle diameters are investigated, with solid fractions ranging from 0.2 to 0.9. Among features observed are: slip flow at boundaries, coagulation at high densities, and gross fluctuation in surface stress. A videotape has been prepared to demonstrate the foregoing effects

Film temperatures in the presence of cavitation

Numerical algorithms are developed and implemented for the treatment of laminar lubricating-film temperatures associated with cavitated regions. The reformation front, with its film-content discontinuity and flow reversal, is given special attention. Computational economy is achieved through the use of Lobatto-point locations for flow-property determinations

Atomic Energy Commission Report AECU-4688

The lubrication equations for an arbitrary Newtonian fluid are derived directly from the general equations for conservation of mass, momentum, and energy. From the lubrication equations an inequality is obtained for the internal film temperature rise, after which the isothermal film equations are derived. Then, for perfectly-aligned self-acting journal bearings, a conservation equation is obtained. For gas bearings this condition gives: [formula] constant along the axis of the bearing. Application of this condition to the infinitely-long gas bearing gives more accurate pressure solutions for this case. The Katto-Soda form of the differential equation for the infinitely-long bearing is solved by a series expansion in the eccentricity ratio, the first terms of which give the original, approximate Katto-Soda solution. In addition, solutions obtained numerically by digital computations are presented in graphical and tabular form for eccentricity ratios from 0 to 0.9 and compressible bearing parameter [formula]. Design charts based on these calculations are provided